ii
ABOUT THE EDITOR IN CHIEF
Merrill Skolnik was Superintendent of the Radar Division at the U.S. Naval Research Laboratory for over 30
years. Before that he was involved in advances in radar while at the MIT Lincoln Laboratory, the Institute for
Defense Analyses, and the Research Division of Electronic Communications, Inc. He is the author of the
popular McGraw-Hill textbook Introduction to Radar Systems, now in its third edition, the editor of Radar
Applications, as well as being a former editor of the Proceedings of the IEEE. He earned the Doctor of
Engineering Degree from The Johns Hopkins University, where he also received the B.E and M.S.E degrees in
electrical engineering. He is a member of the U.S. National Academy of Engineering, a Fellow of the IEEE,
and the first recipient of the IEEE Dennis J. Picard Medal for Radar Technologies and Applications.
iii
RADAR HANDBOOK
Merrill I. Skolnik
Editor in Chief
Third Edition
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Singapore Sydney Toronto
iv
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Radar Handbook, Third Edition
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v
CONTENTS
Contributors
xiii
Preface
xv
Chapter 1 An Introduction and Overview of Radar
Merrill Skolnik
1.1 Radar in Brief /
1.1
1.2 Types of Radars /
1.5
1.3 Information Available from a Radar /
1.7
1.4 The Radar Equation /
1.10
1.5 Radar Frequency Letter-band Nomenclature /
1.13
1.6 Effect of Operating Frequency on Radar /
1.14
1.7 Radar Nomenclature /
1.18
1.8 Some Past Advances in Radar /
1.19
1.9 Applications of Radar /
1.20
1.10 Conceptual Radar System Design /
1.22
1.1
Chapter 2 MTI Radar
William W. Shrader and Vilhelm Gregers-Hansen
2.1 Preface /
2.1
2.2 Introduction to MTI Radar /
2.2
2.3 Clutter Filter Response to Moving Targets /
2.9
2.4 Clutter Characteristics /
2.10
2.5 Definitions /
2.19
2.6 Improvement Factor Calculations /
2.23
2.7 Optimum Design of Clutter Filters /
2.25
2.8 MTI Clutter Filter Design /
2.33
2.9 MTI Filter Design for Weather Radars /
2.46
2.10 Clutter Filter Bank Design /
2.52
2.11 Performance Degradation Caused by Receiver Limiting /
2.59
2.12 Radar System Stability Requirements /
2.65
2.13 Dynamic Range and A/D Conversion Considerations /
2.78
2.14 Adaptive MTI /
2.80
2.15 Radar Clutter Maps /
2.83
2.1
2.16 Sensitivity-velocity Control (SVC) /
2.87
2.17 Considerations Applicable to MTI Radar Systems /
2.91
vi
Chapter 3 Airborne MTI
James K. Day and Fred M. Staudaher
3.1 Systems Using Airborne MTI Techniques /
3.1
3.2 Coverage Considerations /
3.2
3.3 Airborne MTI Performance Drivers /
3.3
3.4 Platform Motion and Altitude Effects on MTI Performance /
3.3
3.5 Platform-motion Compensation Abeam /
3.10
3.6 Scanning-motion Compensation /
3.14
3.7 Simultaneous Platform Motion and Scan Compensation /
3.18
3.8 Platform-motion Compensation, Forward Direction /
3.21
3.9 Space-time Adaptive Motion Compensation /
3.23
3.10 Effect of Multiple Spectra /
3.31
3.11 Example AMTI Radar System /
3.32
3.1
Chapter 4 Pulse Doppler Radar
John P. Stralka and William G. Fedarko
4.1 Characteristics and Applications /
4.1
4.2 Pulse Doppler Clutter /
4.14
4.3 Dynamic-range and Stability Requirements /
4.24
4.4 Range and Doppler Ambiguity Resoluton /
4.31
4.5 Mode and Waveform Design /
4.35
4.6 Range Performance /
4.39
List of Abbreviations /
4.48
4.1
Chapter 5 Multifunctional Radar Systems for Fighter Aircraft
David Lynch, Jr. and Carlo Kopp
5.1 Introduction /
5.1
5.2 Typical Missions and Modes /
5.10
5.3 A-A Mode Descriptions & Waveforms /
5.16
5.4 A-S Mode Descriptions & Waveforms /
5.28
Chapter 6 Radar Receivers
Michael E. Yeomans
6.1 The Configuration of a Radar Receiver /
6.1
5.1
6.1
6.2 Noise and Dynamic-range Considerations /
6.4
6.3 Bandwidth Considerations /
6.9
6.4 Receiver Front End /
6.10
6.5 Local Oscillators /
6.14
6.6 Gain Control /
6.22
6.7 Filtering /
6.24
6.8 Limiters /
6.29
6.9 I/Q Demodulators /
6.31
6.10 Analog-to-Digital Converters /
6.35
6.11 Digital Receivers /
6.40
6.12 Diplex Operation /
6.46
6.13 Waveform Generation and Upconversion /
6.47
vii
Chapter 7 Automatic Detection, Tracking, and Sensor Integration
W. G. Bath and G. V.Trunk
7.1 Introduction /
7.1
7.1
7.2 Automatic Detection /
7.1
7.3 Automatic Tracking /
7.22
7.4 Networked Radars /
7.46
7.5 Unlike-sensor Integration /
7.49
Chapter 8 Pulse Compression Radar
Michael R. Ducoff and Byron W. Tietjen
8.1 Introduction /
8.1
8.1
8.2 Pulse Compression Waveform Types /
8.2
8.3 Factors Affecting Choice of Pulse Compression Systems /
8.26
8.4 Pulse Compression Implementation and Radar System Examples /
8.28
Appendix /
8.36
Chapter 9 Tracking Radar
Dean D. Howard
9.1 Introduction /
9.1
9.1
9.2 Monopulse (Simultaneous Lobing) /
9.3
9.3 Scanning and Lobing /
9.16
9.4 Servosystems for Tracking Radar /
9.17
9.5 Target Acquisition and Range Tracking /
9.20
9.6 Special Monopulse Techniques /
9.24
9.7 Sources of Error /
9.26
9.8 Target-caused Errors (Target Noise) /
9.26
9.9 Other External Causes of Error /
9.37
9.10 Internal Sources of Error /
9.42
9.11 Summary of Sources of Error /
9.43
9.12 Error Reduction Techniques /
9.46
Chapter 10 The Radar Transmitter
Thomas A. Weil and Merrill Skolnik
10.1 Introduction /
10.1
10.1
10.2 Linear-beam Amplifiers /
10.4
10.3 Magnetron /
10.14
10.4 Crossed-field Amplifiers /
10.16
10.5 Gyrotrons /
10.17
10.6 Transmitter Spectrum Control /
10.19
10.7 Grid-controlled Tubes /
10.21
10.8 Modulators /
10.23
10.9 Which RF Power Source to Use? /
10.25
viii
Chapter 11 Solid id-State Transmitters
Michael T. Borkowski
11.1 Introduction /
11.1
11.1
11.2 Advantages of Solid State /
11.1
11.3 Solid-state Devices /
11.5
11.4 Designing for the Solid-state Bottle Transmitter /
11.17
11.5 Designing for the Solid-state Phased Array Transmitter /
11.24
11.6 Solid-state System Examples /
11.37
Chapter 12 Reflector Antennas
Michael E. Cooley and Daniel Davis
12.1 Introduction /
12.1
12.7
12.2 Basic Principles and Parameters /
12.3
12.3 Reflector Antenna Architectures /
12.16
12.4 Reflector Feeds /
12.25
12.5 Reflector Antenna Analysis /
12.37
12.6 Mechanical Design Considerations /
12.35
Acknowledgments /
12.47
Chapter 13 Phased Array Radar Antennas
Joe Frank and John D. Richards
13.1 Introduction /
13.1
13.7
13.2 Array Theory /
13.9
13.3 Planar Arrays and Beam Steering /
13.15
13.4 Aperture Matching and Mutual Coupling /
13.20
13.5 Low-sidelobe Phased Arrays /
13.28
13.6 Quantization Effects /
13.34
13.7 Bandwidth of Phased Arrays /
13.38
13.8 Feed Networks (Beamformers) /
13.46
13.9 Phase Shifters /
13.57
13.10 Solid-state Modules /
13.53
13.11 Multiple Simultaneous Receive Beams /
13.54
13.12 Digital Beamforming /
13.56
13.13 Radiation Pattern Nulling /
13.57
13.14 Calibration of Active Phased Array Antennas /
13.60
13.15 Phased Array Systems /
13.62
Chapter 14 Radar Cross Section
Eugene F. Knott
14.1 Introduction /
14.1
14.1
14.2 The Concept of Echo Power /
14.4
14.3 RCS Prediction Techniques /
14.16
14.4 RCS Measurement Techniques /
14.27
14.5 Radar Echo Suppression /
14.36
ix
Chapter 15 Sea Clutter
Lewis B. Wetzel
15.1 Introduction /
15.1
15.1
15.2 The Sea Surface /
15.3
15.3 Empirical Behavior of Sea Clutter /
15.7
15.4 Theories and Models of Sea Clutter /
15.27
15.5 Summary and Conclusions /
15.37
Chapter 16 Ground Echo
Richard K. Moore
16.1 Introduction /
16.1
16.1
16.2 Parameters Affecting Ground Return /
16.4
16.3 Theoretical Models and Their Limitations /
16.7
16.4 Fading of Ground Echoes /
16.12
16.5 Measurement Techniques for Ground Return /
16.19
16.6 General Models for Scattering Coefficient (Clutter Models) /
16.29
16.7 Scattering Coefficient Data /
16.35
16.8 Polarimetry /
16.46
16.9 Scattering Coefficient Data Near Grazing /
16.52
16.10 Imaging Radar Interpretation /
16.55
Chapter 17 Synthetic Aperture Radar
Roger Sullivan
17.1 Basic Principle of SAR /
17.1
17.2 Early History of SAR /
17.2
17.3 Types of SAR /
17.2
17.4 SAR Resolution /
17.6
17.5 Key Aspects of SAR /
17.10
17.6 SAR Image Quality /
17.16
17.7 Summary of Key SAR Equations /
17.21
17.8 Special SAR Applications /
17.22
Chapter 18 Space-Based Remote Sensing Radars
R. Keith Raney
18.1 Perspective /
17.1
18.1
18.1
18.2 Synthetic Aperture Radar (SAR) /
18.5
18.3 Altimeters /
18.29
18.4 Planetary Radars /
18.43
18.5 Scatterometers /
18.53
18.6 Radar Sounders /
18.59
x
Chapter 19 Meteorological Radar
R. Jeffrey Keeler and Robert J. Serafin
19.1 Introduction /
19.1
19.1
19.2 The Radar Equation for Meteorological Targets /
19.3
19.3 Design Considerations /
19.6
19.4 Signal Processing /
19.19
19.5 Operational Applications /
19.25
19.6 Research Applications /
19.33
Chapter 20 HF Over-the-Horizon Radar
James M. Headrick and Stuart J. Anderson
20.1 Introduction /
20.1
20.2 The Radar Equation /
20.5
20.3 Factors Influencing Skywave Radar Design /
20.7
20.4 The Ionosphere and Radiowave Propagation /
20.13
20.5 Waveforms for HF Radar /
20.21
20.6 The Transmitting System /
20.23
20.7 Radar Cross Section /
20.26
20.8 Clutter: Echoes from the Environment /
20.29
20.9 Noise, Interference, and Spectrum Occupancy /
20.40
20.10 The Receiving System /
20.45
20.11 Signal Processing and Tracking /
20.49
20.12 Radar Resource Management /
20.54
20.13 Radar Performance Modeling /
20.55
Appendix: HF Surface Wave Radar /
20.70
Chapter 21 Ground Penetrating Radar
David Daniels
21.1 Introduction /
20.1
21.1
21.1
21.2 Physics of Propagation in Materials /
21.6
21.3 Modeling /
21.13
21.4 Properties of Materials /
21.18
21.5 GPR Systems /
21.20
21.6 Modulation Techniques /
21.21
21.7 Antennas /
21.24
21.8 Signal and Image Processing /
21.30
21.9 Applications /
21.35
21.10 Licensing /
21.39
Chapter 22 Civil Marine Radar
Andy Norris
22.1 Introduction /
22.1
22.1
22.2 The Challenges /
22.3
22.3 International Standards /
22.7
22.4 Technology /
22.10
22.5 Target Tracking /
22.17
xi
22.6 User Interface /
22.19
22.7 Integration with AIS /
22.23
22.8 Radar Beacons /
22.25
22.9 Validation Testing /
22.28
22.10 Vessel Tracking Services /
22.29
Appendix The Early Days of CMR /
22.31
List of Maritime Radar-related Abbreviations /
22.33
Acknowledgments /
22.34
Chapter 23 Bistatic Radar
Nicholas J. Willis
23.1 Concept and Definitions /
23.1
23.1
23.2 Coordinate Systems /
23.3
23.3 Bistatic Radar Equation /
23.4
23.4 Applications /
23.9
23.5 Bistatic Doppler /
23.14
23.6 Target Location /
23.17
23.7 Target Cross Section /
23.19
23.8 Surface Clutter /
23.22
23.9 Unique Problems and Requirements /
23.26
Chapter 24 Electronic Counter-Countermeasures
Alfonso Farina
24.1 Introduction /
24.1
24.2 Terminology /
24.2
24.3 Electronic Warfare Support Measures /
24.2
24.4 Electronic Countermeasures /
24.5
24.5 Objectives and Taxonomy of ECCM Techniques /
24.8
24.6 Antenna-related ECCM /
24.10
24.7 Transmitter-related ECCM /
24.31
24.8 Receiver-related ECCM /
24.32
24.9 Signal-processing-related ECCM /
24.33
24.10 Operational-deployment Techniques /
24.36
24.11 Application of ECCM Techniques /
24.37
24.12 ECCM and ECM Efficacy /
24.54
Acronym List /
24.56
Acknowledgments /
24.58
24.1
Chapter 25 Radar Digital Signal Processing
James J. Alter and Jeffrey O. Coleman
25.1 Introduction /
25.1
25.1
25.2 Receive Channel Processing /
25.2
25.3 Transmit Channel Processing /
25.20
25.4 DSP Tools /
25.22
25.5 Design Considerations /
25.34
25.6 Summary /
25.37
Acknowledgments /
25.38
xii
Chapter 26 The Propagation Factor, Fp, in the Radar Equation
Wayne L. Patterson
26.1 Introduction /
26.1
26.1
26.2 The Earth’s Atmosphere /
26.2
26.3 Refraction /
26.3
26.4 Standard Propagation /
26.4
26.5 Anomalous Propagation /
26.6
26.6 Propagation Modeling /
26.13
26.7 EM System Assessment Programs /
26.18
26.8 AREPS Radar System Assessment Model /
26.23
26.9 AREPS Radar Displays /
26.25
Index
1.1
xiii
CONTRIBUTORS
James J. Alter Naval Research Laboratory (CHAPTER 25)
Stuart J. Anderson Australian Defense Science and Technology Organisation (CHAPTER 20)
W. G. Bath The Johns Hopkins University Applied Physics Laboratory (CHAPTER 7)
Michael T. Borkowski Raytheon Company (CHAPTER 11)
Jeffrey O. Coleman Naval Research Laboratory (CHAPTER 25)
Michael E. Cooley Northrop Grumman, Electronic Systems (CHAPTER 12)
David Daniels ERA Technology (CHAPTER 21)
Daniel Davis Northrop Grumman Corporation (CHAPTER 12)
James K. Day Lockheed Martin Corporation (CHAPTER 3)
Michael R. Ducoff Lockheed Martin Corporation (CHAPTER 8)
Alfonso Farina SELEX Sistemi Integrati (CHAPTER 24)
William G. Fedarko Northrop Grumman Corporation (CHAPTER 4)
Joe Frank The Johns Hopkins University Applied Physics Laboratory (CHAPTER 13)
Vilhelm Gregers-Hansen Naval Research Laboratory (CHAPTER 2)
James M. Headrick Naval Research Laboratory, retired (CHAPTER 20)
Dean D. Howard Consultant to ITT Industries, Inc. (CHAPTER 9)
R. Jeffrey Keeler National Center for Atmospheric Research (CHAPTER 19)
Eugene F. Knott Tomorrow’s Research (CHAPTER 14)
Carlo Kopp Monash University (CHAPTER 5)
David Lynch, Jr. DL Sciences, Inc. (CHAPTER 5)
Richard K. Moore The University of Kansas (CHAPTER 16)
Andy Norris Consultant in Navigation Systems (CHAPTER 22)
Wayne L. Patterson Space and Naval Warfare Systems Center (CHAPTER 26)
Keith Raney The Johns Hopkins University Applied Physics Laboratory (CHAPTER 18)
John D. Richards The Johns Hopkins University Applied Physics Laboratory (CHAPTER 13)
Robert J. Serafin National Center for Atmospheric Research (CHAPTER 19)
William W. Shrader Shrader Associates (CHAPTER 2)
Merrill Skolnik (CHAPTERS 1 and 10)
Fred M. Staudaher Naval Research Laboratory, retired (CHAPTER 3)
xiv
John P. Stralka Northrop Grumman Corporation (CHAPTER 4)
Roger Sullivan Institute for Defense Analyses (CHAPTER 17)
Byron W. Tietjen Lockheed Martin Corporation (CHAPTER 8)
G. V. Trunk The Johns Hopkins University Applied Physics Laboratory (CHAPTER 7)
Thomas A. Weil (CHAPTER 10)
Lewis B. Wetzel Naval Research Laboratory, retired (CHAPTER 15)
Nicholas J. Willis Technology Service Corporation, retired (CHAPTER 23)
Michael E. Yeomans Raytheon Company (CHAPTER 6)
xv
PREFACE
Radar is an important example of an electrical engineering system. In university engineering courses, the
emphasis usually is on the basic tools of the electrical engineer such as circuit design, signals, solid state,
digital processing, electronic devices, electromagnetics, automatic control, microwaves, and so forth. But in
the real world of electrical engineering practice, these are only the techniques, piece parts, or subsystems that
make up some type of system employed for a useful purpose. In addition to radar and other sensor systems,
electrical engineering systems include communications, control, energy, information, industrial, military,
navigation, entertainment, medical, and others. These are what the practice of electrical engineering is all
about. Without them there would be little need for electrical engineers. However, the practicing engineer who
is involved in producing a new type of electrical engineering system often has to depend on acquiring
knowledge that was not usually covered in his or her engineering courses. The radar engineer, for example,
has to understand the major components and subsystems that make up a radar, as well as how they fit
together. The Radar Handbook attempts to help in this task. In addition to the radar system designer, it is
hoped that those who are responsible for procuring new radar systems, those who utilize radars, those who
maintain radar systems, and those who manage the engineers who do the above, also will find the Radar
Handbook to be of help in fulfilling such tasks.
The third edition of the Radar Handbook is evidence that the development and application of radar for both
civilian and military purposes continue to grow in both utility and in improved technology. Some of the many
advances in radar since the previous edition include the following:
- The extensive use of digital methods for improved signal processing, data processing, decision making,
flexible radar control, and multifunction radar
- Doppler weather radar
- Ground moving target indication, or GMTI
- An extensive experimental database describing low-angle land clutter, as obtained by MIT Lincoln
Laboratory, that replaced the previously widely used clutter model that dated back to World War II
- The realization that microwave sea echo at low grazing angles is due chiefly to what are called “sea spikes”
- The active-aperture phased array radar system using solid-state modules, also called active electronically
scanned arrays (AESA), which is attractive for some multifunction radar applications that need to manage
both power and spatial coverage
- Planetary exploration with radar
- Computer-based methods for predicting radar propagation performance in realistic environments
xvi
- Operational use of HF over-the-horizon radar
- Improved methods for detecting moving targets in clutter, including space-time adaptive processing
- Operational use of inverse synthetic aperture radar for target recognition
- Interferometric synthetic aperture radar, or InSAR, to obtain the height of a resolved scatterer or to detect
moving ground targets as well as provide a SAR image of a scene
- High precision space-based altimeters, with accuracy of a few centimeters, to measure the Earth’s geoid
- Ultrawideband radar for ground penetrating and similar applications
- Improved high power, wide bandwidth klystron power sources based on clustered cavity resonators, as well
as the multiple-beam klystron
- The appearance of wide bandgap semiconductors that allow better performance because of high power and
high operating temperatures
- The availability of high-power millimeter-wave generators based on the gyroklystron
- Nonlinear FM pulse compression with low sidelobe levels
- The replacement, by the computer, of the operator as information extractor and decision maker
The above are not listed in any particular order, nor should they be considered a complete enumeration of
radar developments since the appearance of the previous edition. There were also some radar topics in
previous editions of the Radar Handbook that are of lesser interest and so were not included in this edition.
The chapter authors, who are experts in their particular field, were told to consider the reader of their
chapter as being knowledgeable in the general subject of radar and even an expert in some other particular
area of radar, but not necessarily knowledgeable about the subject of the particular chapter the author was
writing.
It should be expected that with a book in print as long as the Radar Handbook has been, not all chapter
authors from the previous editions would be available to do the third edition. Many of the previous authors
have retired or are no longer with us. Sixteen of the twenty-six chapters in this edition have authors or
coauthors who were not involved in the previous editions.
The hard work of preparing these chapters was done by the individual expert authors of the various
chapters. Thus the value of the Radar Handbook is the result of the diligence and expertise of the authors who
contributed their time, knowledge, and experience to make this handbook a useful addition to the desk of radar
system engineers and all those people vital to the development, production, and employment of radar systems.
I am deeply grateful to all the contributing authors for their fine work and the long hours they had to apply to
their task. It is the chapter authors who make any handbook a success. My sincere thanks to them all.
As stated in the Preface of the previous edition, readers who wish to reference or quote material from the
Radar Handbook are asked to mention the names of the individual chapter authors who produced the material.
MERRILL SKOLNIK
Baltimore, Maryland
#HAPTER ˜Ê˜ÌÀœ`ÕV̈œ˜Ê>˜`Ê
"ÛiÀۈiÜʜvÊ,>`>À
iÀÀˆÊ-Žœ˜ˆŽ
£°£Ê , ,Ê Ê , 2ADAR IS AN ELECTROMAGNETIC SENSOR FOR THE DETECTION AND LOCATION OF REFLECTING
OBJECTS )TS OPERATION CAN BE SUMMARIZED AS FOLLOWS
L
L
L
L
L
4HE RADAR RADIATES ELECTROMAGNETIC ENERGY FROM AN ANTENNA TO PROPAGATE IN SPACE
3OME OF THE RADIATED ENERGY IS INTERCEPTED BY A REFLECTING OBJECT USUALLY CALLED
A TARGET LOCATED AT A DISTANCE FROM THE RADAR
4HE ENERGY INTERCEPTED BY THE TARGET IS RERADIATED IN MANY DIRECTIONS
3OME OF THE RERADIATED ECHO ENERGY IS RETURNED TO AND RECEIVED BY THE RADAR ANTENNA
!FTER AMPLIFICATION BY A RECEIVER AND WITH THE AID OF PROPER SIGNAL PROCESSING A
DECISION IS MADE AT THE OUTPUT OF THE RECEIVER AS TO WHETHER OR NOT A TARGET ECHO
SIGNAL IS PRESENT !T THAT TIME THE TARGET LOCATION AND POSSIBLY OTHER INFORMATION
ABOUT THE TARGET IS ACQUIRED
! COMMON WAVEFORM RADIATED BY A RADAR IS A SERIES OF RELATIVELY NARROW RECTAN
GULAR LIKE PULSES !N EXAMPLE OF A WAVEFORM FOR A MEDIUM RANGE RADAR THAT DETECTS
AIRCRAFT MIGHT BE DESCRIBED AS A SHORT PULSE ONE MILLIONTH OF A SECOND IN DURATION
ONE MICROSECOND THE TIME BETWEEN PULSES MIGHT BE ONE MILLISECOND SO THAT THE
PULSE REPETITION FREQUENCY IS ONE KILOHERTZ THE PEAK POWER FROM THE RADAR TRANSMIT
TER MIGHT BE ONE MILLION WATTS ONE MEGAWATT AND WITH THESE NUMBERS THE AVERAGE
POWER FROM THE TRANSMITTER IS ONE KILOWATT !N AVERAGE POWER OF ONE KILOWATT MIGHT
BE LESS THAN THE POWER OF THE ELECTRIC LIGHTING USUALLY FOUND IN A hTYPICALv CLASSROOM
7E ASSUME THIS EXAMPLE RADAR MIGHT OPERATE IN THE MIDDLE OF THE MICROWAVEo FRE
QUENCY RANGE SUCH AS FROM TO '(Z WHICH IS A TYPICAL FREQUENCY BAND FOR CIVIL
4HIS CHAPTER IS A BRIEF OVERVIEW OF RADAR FOR THOSE NOT TOO FAMILIAR WITH THE SUBJECT &OR THOSE WHO ARE FAMILIAR WITH
RADAR IT CAN BE CONSIDERED A REFRESHER
o -ICROWAVES ARE LOOSELY DEFINED AS THOSE FREQUENCIES WHERE WAVEGUIDES ARE USED FOR TRANSMISSION LINES AND WHERE
CAVITIES OR DISTRIBUTED CIRCUITS ARE USED FOR RESONANT CIRCUITS RATHER THAN LUMPED CONSTANT COMPONENTS -ICROWAVE
RADARS MIGHT BE FROM ABOUT -(Z TO ABOUT '(Z BUT THESE LIMITS ARE NOT RIGID
£°£
£°Ó
2!$!2 (!.$"//+
AIRPORT SURVEILLANCE RADARS )TS WAVELENGTH MIGHT BE ABOUT CM ROUNDING OFF FOR
SIMPLICITY 7ITH THE PROPER ANTENNA SUCH A RADAR MIGHT DETECT AIRCRAFT OUT TO RANGESp
OF TO NMI MORE OR LESS 4HE ECHO POWER RECEIVED BY A RADAR FROM A TARGET CAN
VARY OVER A WIDE RANGE OF VALUES BUT WE ARBITRARILY ASSUME A hTYPICALv ECHO SIGNAL
FOR ILLUSTRATIVE PURPOSES MIGHT HAVE A POWER OF PERHAPS WATTS )F THE RADIATED
POWER IS WATTS ONE MEGAWATT THE RATIO OF ECHO SIGNAL POWER FROM A TARGET TO THE
RADAR TRANSMITTER POWER IN THIS EXAMPLE IS n OR THE RECEIVED ECHO IS D" LESS
THAN THE TRANSMITTED SIGNAL 4HAT IS QUITE A DIFFERENCE BETWEEN THE MAGNITUDE OF THE
TRANSMITTED SIGNAL AND A DETECTABLE RECEIVED ECHO SIGNAL
3OME RADARS HAVE TO DETECT TARGETS AT RANGES AS SHORT AS THE DISTANCE FROM BEHIND
HOME PLATE TO THE PITCHERS MOUND IN A BASEBALL PARK TO MEASURE THE SPEED OF A PITCHED
BALL WHILE OTHER RADARS HAVE TO OPERATE OVER DISTANCES AS GREAT AS THE DISTANCES TO THE
NEAREST PLANETS 4HUS A RADAR MIGHT BE SMALL ENOUGH TO HOLD IN THE PALM OF ONE HAND
OR LARGE ENOUGH TO OCCUPY THE SPACE OF MANY FOOTBALL FIELDS
2ADAR TARGETS MIGHT BE AIRCRAFT SHIPS OR MISSILES BUT RADAR TARGETS CAN ALSO BE
PEOPLE BIRDS INSECTS PRECIPITATION CLEAR AIR TURBULENCE IONIZED MEDIA LAND FEATURES
VEGETATION MOUNTAINS ROADS RIVERS AIRFIELDS BUILDINGS FENCES AND POWER LINE
POLES SEA ICE ICEBERGS BUOYS UNDERGROUND FEATURES METEORS AURORA SPACECRAFT
AND PLANETS )N ADDITION TO MEASURING THE RANGE TO A TARGET AS WELL AS ITS ANGULAR DIREC
TION A RADAR CAN ALSO FIND THE RELATIVE VELOCITY OF A TARGET EITHER BY DETERMINING THE
RATE OF CHANGE OF THE RANGE MEASUREMENT WITH TIME OR BY EXTRACTING THE RADIAL VELOCITY
FROM THE DOPPLER FREQUENCY SHIFT OF THE ECHO SIGNAL )F THE LOCATION OF A MOVING TARGET IS
MEASURED OVER A PERIOD OF TIME THE TRACK OR TRAJECTORY OF THE TARGET CAN BE FOUND FROM
WHICH THE ABSOLUTE VELOCITY OF THE TARGET AND ITS DIRECTION OF TRAVEL CAN BE DETERMINED
AND A PREDICTION CAN BE MADE AS TO ITS FUTURE LOCATION 0ROPERLY DESIGNED RADARS CAN
DETERMINE THE SIZE AND SHAPE OF A TARGET AND MIGHT EVEN BE ABLE TO RECOGNIZE ONE TYPE
OR CLASS OF TARGET FROM ANOTHER
"ASIC 0ARTS OF A 2ADAR &IGURE IS A VERY ELEMENTARY BASIC BLOCK DIAGRAM
SHOWING THE SUBSYSTEMS USUALLY FOUND IN A RADAR 4HE TRANSMITTER WHICH IS SHOWN HERE
AS A POWER AMPLIFIER GENERATES A SUITABLE WAVEFORM FOR THE PARTICULAR JOB THE RADAR IS
TO PERFORM )T MIGHT HAVE AN AVERAGE POWER AS SMALL AS MILLIWATTS OR AS LARGE AS MEGA
WATTS 4HE AVERAGE POWER IS A FAR BETTER INDICATION OF THE CAPABILITY OF A RADARS PERFOR
MANCE THAN IS ITS PEAK POWER -OST RADARS USE A SHORT PULSE WAVEFORM SO THAT A SINGLE
ANTENNA CAN BE USED ON A TIME SHARED BASIS FOR BOTH TRANSMITTING AND RECEIVING
4HE FUNCTION OF THE DUPLEXER IS TO ALLOW A SINGLE ANTENNA TO BE USED BY PROTECTING
THE SENSITIVE RECEIVER FROM BURNING OUT WHILE THE TRANSMITTER IS ON AND BY DIRECTING THE
RECEIVED ECHO SIGNAL TO THE RECEIVER RATHER THAN TO THE TRANSMITTER
4HE ANTENNA IS THE DEVICE THAT ALLOWS THE TRANSMITTED ENERGY TO BE PROPAGATED INTO
SPACE AND THEN COLLECTS THE ECHO ENERGY ON RECEIVE )T IS ALMOST ALWAYS A DIRECTIVE
ANTENNA ONE THAT DIRECTS THE RADIATED ENERGY INTO A NARROW BEAM TO CONCENTRATE THE
POWER AS WELL AS TO ALLOW THE DETERMINATION OF THE DIRECTION TO THE TARGET !N ANTENNA
THAT PRODUCES A NARROW DIRECTIVE BEAM ON TRANSMIT USUALLY HAS A LARGE AREA ON RECEIVE
TO ALLOW THE COLLECTION OF WEAK ECHO SIGNALS FROM THE TARGET 4HE ANTENNA NOT ONLY
CONCENTRATES THE ENERGY ON TRANSMIT AND COLLECTS THE ECHO ENERGY ON RECEIVE BUT IT ALSO
ACTS AS A SPATIAL FILTER TO PROVIDE ANGLE RESOLUTION AND OTHER CAPABILITIES
p )N RADAR RANGE IS THE TERM GENERALLY USED TO MEAN DISTANCE FROM THE RADAR TO THE TARGET 2ANGE IS ALSO USED HERE IN
SOME OF ITS OTHER DICTIONARY DEFINITIONS
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&)'52% "LOCK DIAGRAM OF A SIMPLE RADAR EMPLOYING A POWER AMPLIFIER AS THE TRANSMITTER IN THE UPPER
PORTION OF THE FIGURE AND A SUPERHETERODYNE RECEIVER IN THE LOWER PORTION OF THE FIGURE
4HE RECEIVER AMPLIFIES THE WEAK RECEIVED SIGNAL TO A LEVEL WHERE ITS PRESENCE CAN
BE DETECTED "ECAUSE NOISE IS THE ULTIMATE LIMITATION ON THE ABILITY OF A RADAR TO MAKE
A RELIABLE DETECTION DECISION AND EXTRACT INFORMATION ABOUT THE TARGET CARE IS TAKEN
TO INSURE THAT THE RECEIVER PRODUCES VERY LITTLE NOISE OF ITS OWN !T THE MICROWAVE
FREQUENCIES WHERE MOST RADARS ARE FOUND THE NOISE THAT AFFECTS RADAR PERFORMANCE
IS USUALLY FROM THE FIRST STAGE OF THE RECEIVER SHOWN HERE IN &IGURE AS A LOW
NOISE AMPLIFIER &OR MANY RADAR APPLICATIONS WHERE THE LIMITATION TO DETECTION IS THE
UNWANTED RADAR ECHOES FROM THE ENVIRONMENT CALLED CLUTTER THE RECEIVER NEEDS TO
HAVE A LARGE ENOUGH DYNAMIC RANGE SO AS TO AVOID HAVING THE CLUTTER ECHOES ADVERSELY
AFFECT DETECTION OF WANTED MOVING TARGETS BY CAUSING THE RECEIVER TO SATURATE 4HE
DYNAMIC RANGE OF A RECEIVER USUALLY EXPRESSED IN DECIBELS IS DEFINED AS THE RATIO OF
THE MAXIMUM TO THE MINIMUM SIGNAL INPUT POWER LEVELS OVER WHICH THE RECEIVER CAN
OPERATE WITH SOME SPECIFIED PERFORMANCE 4HE MAXIMUM SIGNAL LEVEL MIGHT BE SET
BY THE NONLINEAR EFFECTS OF THE RECEIVER RESPONSE THAT CAN BE TOLERATED FOR EXAMPLE
THE SIGNAL POWER AT WHICH THE RECEIVER BEGINS TO SATURATE AND THE MINIMUM SIGNAL
MIGHT BE THE MINIMUM DETECTABLE SIGNAL 4HE SIGNAL PROCESSOR WHICH IS OFTEN IN THE
)& PORTION OF THE RECEIVER MIGHT BE DESCRIBED AS BEING THE PART OF THE RECEIVER THAT
SEPARATES THE DESIRED SIGNAL FROM THE UNDESIRED SIGNALS THAT CAN DEGRADE THE DETEC
TION PROCESS 3IGNAL PROCESSING INCLUDES THE MATCHED FILTER THAT MAXIMIZES THE OUT
PUT SIGNAL TO NOISE RATIO 3IGNAL PROCESSING ALSO INCLUDES THE DOPPLER PROCESSING THAT
MAXIMIZES THE SIGNAL TO CLUTTER RATIO OF A MOVING TARGET WHEN CLUTTER IS LARGER THAN
RECEIVER NOISE AND IT SEPARATES ONE MOVING TARGET FROM OTHER MOVING TARGETS OR FROM
CLUTTER ECHOES 4HE DETECTION DECISION IS MADE AT THE OUTPUT OF THE RECEIVER SO A TARGET
IS DECLARED TO BE PRESENT WHEN THE RECEIVER OUTPUT EXCEEDS A PREDETERMINED THRESHOLD
)F THE THRESHOLD IS SET TOO LOW THE RECEIVER NOISE CAN CAUSE EXCESSIVE FALSE ALARMS )F
THE THRESHOLD IS SET TOO HIGH DETECTIONS OF SOME TARGETS MIGHT BE MISSED THAT WOULD
OTHERWISE HAVE BEEN DETECTED 4HE CRITERION FOR DETERMINING THE LEVEL OF THE DECISION
THRESHOLD IS TO SET THE THRESHOLD SO IT PRODUCES AN ACCEPTABLE PREDETERMINED AVERAGE
RATE OF FALSE ALARMS DUE TO RECEIVER NOISE
!FTER THE DETECTION DECISION IS MADE THE TRACK OF A TARGET CAN BE DETERMINED WHERE
A TRACK IS THE LOCUS OF TARGET LOCATIONS MEASURED OVER TIME 4HIS IS AN EXAMPLE OF DATA
PROCESSING 4HE PROCESSED TARGET DETECTION INFORMATION OR ITS TRACK MIGHT BE DISPLAYED
TO AN OPERATOR OR THE DETECTION INFORMATION MIGHT BE USED TO AUTOMATICALLY GUIDE A
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MISSILE TO A TARGET OR THE RADAR OUTPUT MIGHT BE FURTHER PROCESSED TO PROVIDE OTHER
INFORMATION ABOUT THE NATURE OF THE TARGET 4HE RADAR CONTROL INSURES THAT THE VARIOUS
PARTS OF A RADAR OPERATE IN A COORDINATED AND COOPERATIVE MANNER AS FOR EXAMPLE
PROVIDING TIMING SIGNALS TO VARIOUS PARTS OF THE RADAR AS REQUIRED
4HE RADAR ENGINEER HAS AS RESOURCES TIME THAT ALLOWS GOOD DOPPLER PROCESSING
BANDWIDTH FOR GOOD RANGE RESOLUTION SPACE THAT ALLOWS A LARGE ANTENNA AND ENERGY FOR
LONG RANGE PERFORMANCE AND ACCURATE MEASUREMENTS %XTERNAL FACTORS AFFECTING RADAR
PERFORMANCE INCLUDE THE TARGET CHARACTERISTICS EXTERNAL NOISE THAT MIGHT ENTER VIA THE
ANTENNA UNWANTED CLUTTER ECHOES FROM LAND SEA BIRDS OR RAIN INTERFERENCE FROM OTHER
ELECTROMAGNETIC RADIATORS AND PROPAGATION EFFECTS DUE TO THE EARTHS SURFACE AND ATMO
SPHERE 4HESE FACTORS ARE MENTIONED TO EMPHASIZE THAT THEY CAN BE HIGHLY IMPORTANT IN
THE DESIGN AND APPLICATION OF A RADAR
2ADAR 4RANSMITTERS 4HE RADAR TRANSMITTER MUST NOT ONLY BE ABLE TO GENERATE THE
PEAK AND AVERAGE POWERS REQUIRED TO DETECT THE DESIRED TARGETS AT THE MAXIMUM RANGE
BUT ALSO HAS TO GENERATE A SIGNAL WITH THE PROPER WAVEFORM AND THE STABILITY NEEDED FOR
THE PARTICULAR APPLICATION 4RANSMITTERS MAY BE OSCILLATORS OR AMPLIFIERS BUT THE LATTER
USUALLY OFFER MORE ADVANTAGES
4HERE HAVE BEEN MANY TYPES OF RADAR POWER SOURCES USED IN RADAR #HAPTER 4HE MAGNETRON POWER OSCILLATOR WAS AT ONE TIME VERY POPULAR BUT IT IS SELDOM USED
EXCEPT FOR CIVIL MARINE RADAR #HAPTER "ECAUSE OF THE MAGNETRONS RELATIVELY
LOW AVERAGE POWER ONE OR TWO KILOWATTS AND POOR STABILITY OTHER POWER SOURCES
ARE USUALLY MORE APPROPRIATE FOR APPLICATIONS REQUIRING LONG RANGE DETECTION OF SMALL
MOVING TARGETS IN THE PRESENCE OF LARGE CLUTTER ECHOES 4HE MAGNETRON POWER OSCIL
LATOR IS AN EXAMPLE OF WHAT IS CALLED A CROSSED FIELD TUBE 4HERE IS ALSO A RELATED
CROSSED FIELD AMPLIFIER #&! THAT HAS BEEN USED IN SOME RADARS IN THE PAST BUT IT
ALSO SUFFERS LIMITATIONS FOR IMPORTANT RADAR APPLICATIONS ESPECIALLY FOR THOSE REQUIR
ING DETECTION OF MOVING TARGETS IN CLUTTER 4HE HIGH POWER KLYSTRON AND THE TRAVELING
WAVE TUBE 474 ARE EXAMPLES OF WHAT ARE CALLED LINEAR BEAM TUBES !T THE HIGH
POWERS OFTEN EMPLOYED BY RADARS BOTH TUBES HAVE SUITABLY WIDE BANDWIDTHS AS WELL
AS GOOD STABILITY AS NEEDED FOR DOPPLER PROCESSING AND BOTH HAVE BEEN POPULAR
4HE SOLID STATE AMPLIFIER SUCH AS THE TRANSISTOR HAS ALSO BEEN USED IN RADAR ESPE
CIALLY IN PHASED ARRAYS !LTHOUGH AN INDIVIDUAL TRANSISTOR HAS RELATIVELY LOW POWER
EACH OF THE MANY RADIATING ELEMENTS OF AN ARRAY ANTENNA CAN UTILIZE MULTIPLE TRANSISTORS
TO ACHIEVE THE HIGH POWER NEEDED FOR MANY RADAR APPLICATIONS 7HEN SOLID STATE TRAN
SISTOR AMPLIFIERS ARE USED THE RADAR DESIGNER HAS TO BE ABLE TO ACCOMMODATE THE HIGH
DUTY CYCLE AT WHICH THESE DEVICES HAVE TO OPERATE THE LONG PULSES THEY MUST USE THAT
REQUIRE PULSE COMPRESSION AND THE MULTIPLE PULSES OF DIFFERENT WIDTHS TO ALLOW DETEC
TION AT SHORT AS WELL AS LONG RANGE 4HUS THE USE OF SOLID STATE TRANSMITTERS CAN HAVE AN
EFFECT ON OTHER PARTS OF THE RADAR SYSTEM !T MILLIMETER WAVELENGTHS VERY HIGH POWER
CAN BE OBTAINED WITH THE GYROTRON EITHER AS AN AMPLIFIER OR AS AN OSCILLATOR 4HE GRID
CONTROL VACUUM TUBE WAS USED TO GOOD ADVANTAGE FOR A LONG TIME IN 5(& AND LOWER
FREQUENCY RADARS BUT THERE HAS BEEN LESS INTEREST IN THE LOWER FREQUENCIES FOR RADAR
!LTHOUGH NOT EVERYONE MIGHT AGREE SOME RADAR SYSTEM ENGINEERSˆIF GIVEN A
CHOICEˆWOULD CONSIDER THE KLYSTRON AMPLIFIER AS THE PRIME CANDIDATE FOR A HIGH
POWER MODERN RADAR IF THE APPLICATION WERE SUITABLE FOR ITS USE
2ADAR !NTENNAS 4HE ANTENNA IS WHAT CONNECTS THE RADAR TO THE OUTSIDE WORLD
#HAPTERS AND )T PERFORMS SEVERAL PURPOSES CONCENTRATES THE RADIATED ENERGY
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ON TRANSMIT THAT IS IT IS DIRECTIVE AND HAS A NARROW BEAMWIDTH COLLECTS THE RECEIVED
ECHO ENERGY FROM THE TARGET PROVIDES A MEASUREMENT OF THE ANGULAR DIRECTION TO THE
TARGET PROVIDES SPATIAL RESOLUTION TO RESOLVE OR SEPARATE TARGETS IN ANGLE AND ALLOWS
THE DESIRED VOLUME OF SPACE TO BE OBSERVED 4HE ANTENNA CAN BE A MECHANICALLY SCANNED
PARABOLIC REFLECTOR A MECHANICALLY SCANNED PLANAR PHASED ARRAY OR A MECHANICALLY SCANNED
END FIRE ANTENNA )T CAN BE AN ELECTRONICALLY SCANNED PHASED ARRAY USING A SINGLE TRANSMIT
TER WITH EITHER A CORPORATE FEED OR A SPACE FEED CONFIGURATION TO DISTRIBUTE THE POWER TO
EACH ANTENNA ELEMENT OR AN ELECTRONICALLY SCANNED PHASED ARRAY EMPLOYING AT EACH ANTENNA
ELEMENT A SMALL SOLID STATE hMINIATUREv RADAR ALSO CALLED AN ACTIVE APERTURE PHASED ARRAY %ACH TYPE OF ANTENNA HAS ITS PARTICULAR ADVANTAGES AND LIMITATIONS 'ENERALLY THE LARGER THE
ANTENNA THE BETTER BUT THERE CAN BE PRACTICAL CONSTRAINTS THAT LIMIT ITS SIZE
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WHAT MIGHT BE THE MAJOR FEATURE THAT DISTINGUISHES ONE TYPE OF RADAR FROM ANOTHER
0ULSE RADAR 4HIS IS A RADAR THAT RADIATES A REPETITIVE SERIES OF ALMOST RECTANGULAR
PULSES )T MIGHT BE CALLED THE CANONICAL FORM OF A RADAR THE ONE USUALLY THOUGHT OF
AS A RADAR WHEN NOTHING ELSE IS SAID TO DEFINE A RADAR
(IGH RESOLUTION RADAR (IGH RESOLUTION CAN BE OBTAINED IN THE RANGE ANGLE OR DOP
PLER VELOCITY COORDINATES BUT HIGH RESOLUTION USUALLY IMPLIES THAT THE RADAR HAS HIGH
RANGE RESOLUTION 3OME HIGH RESOLUTION RADARS HAVE RANGE RESOLUTIONS IN TERMS OF
FRACTIONS OF A METER BUT IT CAN BE AS SMALL AS A FEW CENTIMETERS
0ULSE COMPRESSION RADAR 4HIS IS A RADAR THAT USES A LONG PULSE WITH INTERNAL MODU
LATION USUALLY FREQUENCY OR PHASE MODULATION TO OBTAIN THE ENERGY OF A LONG PULSE
WITH THE RESOLUTION OF A SHORT PULSE
#ONTINUOUS WAVE #7 RADAR 4HIS RADAR EMPLOYS A CONTINUOUS SINE WAVE )T ALMOST
ALWAYS USES THE DOPPLER FREQUENCY SHIFT FOR DETECTING MOVING TARGETS OR FOR MEASUR
ING THE RELATIVE VELOCITY OF A TARGET
&- #7 RADAR 4HIS #7 RADAR USES FREQUENCY MODULATION OF THE WAVEFORM TO ALLOW
A RANGE MEASUREMENT
3URVEILLANCE RADAR !LTHOUGH A DICTIONARY MIGHT NOT DEFINE SURVEILLANCE THIS WAY A
SURVEILLANCE RADAR IS ONE THAT DETECTS THE PRESENCE OF A TARGET SUCH AS AN AIRCRAFT OR
A SHIP AND DETERMINES ITS LOCATION IN RANGE AND ANGLE )T CAN ALSO OBSERVE THE TARGET
OVER A PERIOD OF TIME SO AS TO OBTAIN ITS TRACK
-OVING TARGET INDICATION -4) 4HIS IS A PULSE RADAR THAT DETECTS MOVING TARGETS
IN CLUTTER BY USING A LOW PULSE REPETITION FREQUENCY 02& THAT USUALLY HAS NO
RANGE AMBIGUITIES )T DOES HAVE AMBIGUITIES IN THE DOPPLER DOMAIN THAT RESULT IN
SO CALLED BLIND SPEEDS
0ULSE DOPPLER RADAR 4HERE ARE TWO TYPES OF PULSE DOPPLER RADARS THAT EMPLOY EITHER
A HIGH OR MEDIUM 02& PULSE RADAR 4HEY BOTH USE THE DOPPLER FREQUENCY SHIFT TO
EXTRACT MOVING TARGETS IN CLUTTER ! HIGH 02& PULSE DOPPLER RADAR HAS NO AMBIGUI
TIES BLIND SPEEDS IN DOPPLER BUT IT DOES HAVE RANGE AMBIGUITIES ! MEDIUM 02&
PULSE DOPPLER RADAR HAS AMBIGUITIES IN BOTH RANGE AND DOPPLER
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4RACKING RADAR 4HIS IS A RADAR THAT PROVIDES THE TRACK OR TRAJECTORY OF A TARGET
4RACKING RADARS CAN BE FURTHER DELINEATED AS 344 !$4 473 AND PHASED ARRAY
TRACKERS AS DESCRIBED BELOW
3INGLE 4ARGET 4RACKER 344 4RACKS A SINGLE TARGET AT A DATA RATE HIGH ENOUGH
TO PROVIDE ACCURATE TRACKING OF A MANEUVERING TARGET ! REVISIT TIME OF S
DATA RATE OF MEASUREMENTS PER SECOND MIGHT BE hTYPICALv )T MIGHT
EMPLOY THE MONOPULSE TRACKING METHOD FOR ACCURATE TRACKING INFORMATION IN
THE ANGLE COORDINATE
!UTOMATIC DETECTION AND TRACKING !$4 4HIS IS TRACKING PERFORMED BY A SUR
VEILLANCE RADAR )T CAN HAVE A VERY LARGE NUMBER OF TARGETS IN TRACK BY USING THE
MEASUREMENTS OF TARGET LOCATIONS OBTAINED OVER MULTIPLE SCANS OF THE ANTENNA
)TS DATA RATE IS NOT AS HIGH AS THE 344 2EVISIT TIMES MIGHT RANGE FROM ONE TO
SECONDS DEPENDING ON THE APPLICATION
4RACK WHILE SCAN 473 5SUALLY A RADAR THAT PROVIDES SURVEILLANCE OVER A NAR
ROW REGION OF ANGLE IN ONE OR TWO DIMENSIONS SO AS TO PROVIDE AT A RAPID
UPDATE RATE LOCATION INFORMATION ON ALL TARGETS WITHIN A LIMITED ANGULAR REGION
OF OBSERVATION )T HAS BEEN USED IN THE PAST FOR GROUND BASED RADARS THAT GUIDE
AIRCRAFT TO A LANDING IN SOME TYPES OF WEAPON CONTROL RADARS AND IN SOME
MILITARY AIRBORNE RADARS
0HASED ARRAY TRACKER !N ELECTRONICALLY SCANNED PHASED ARRAY CAN ALMOST hCON
TINUOUSLYv TRACK MORE THAN ONE TARGET AT A HIGH DATA RATE )T CAN ALSO SIMULTA
NEOUSLY PROVIDE THE LOWER DATA RATE TRACKING OF MULTIPLE TARGETS SIMILAR TO THAT
PERFORMED BY !$4
)MAGING RADAR 4HIS RADAR PRODUCES A TWO DIMENSIONAL IMAGE OF A TARGET OR A SCENE
SUCH AS A PORTION OF THE SURFACE OF THE EARTH AND WHAT IS ON IT 4HESE RADARS USUALLY
ARE ON MOVING PLATFORMS
3IDELOOKING AIRBORNE RADAR 3,!2 4HIS AIRBORNE SIDELOOKING IMAGING RADAR PRO
VIDES HIGH RESOLUTION IN RANGE AND OBTAINS SUITABLE RESOLUTION IN ANGLE BY USING A
NARROW BEAMWIDTH ANTENNA
3YNTHETIC APERTURE RADAR 3!2 3!2 IS A COHERENT IMAGING RADAR ON A MOVING
VEHICLE THAT USES THE PHASE INFORMATION OF THE ECHO SIGNAL TO OBTAIN AN IMAGE OF A
SCENE WITH HIGH RESOLUTION IN BOTH RANGE AND CROSS RANGE (IGH RANGE RESOLUTION IS
OFTEN OBTAINED USING PULSE COMPRESSION
)NVERSE SYNTHETIC APERTURE RADAR )3!2 )3!2 IS A COHERENT IMAGING RADAR THAT USES
HIGH RESOLUTION IN RANGE AND THE RELATIVE MOTION OF THE TARGET TO OBTAIN HIGH RESOLU
TION IN THE DOPPLER DOMAIN THAT ALLOWS RESOLUTION IN THE CROSS RANGE DIMENSION TO
BE OBTAINED )T CAN BE ON A MOVING VEHICLE OR IT CAN BE STATIONARY
7EAPON CONTROL RADAR 4HIS NAME IS USUALLY APPLIED TO A SINGLE TARGET TRACKER USED
FOR DEFENDING AGAINST AIR ATTACK
'UIDANCE RADAR 4HIS IS USUALLY A RADAR ON A MISSILE THAT ALLOWS THE MISSILE TO
hHOME IN v OR GUIDE ITSELF TO A TARGET
7EATHER METEOROLOGICAL OBSERVATION 3UCH RADARS DETECT RECOGNIZE AND MEASURE
PRECIPITATION RATE WIND SPEED AND DIRECTION AND OBSERVE OTHER WEATHER EFFECTS
#OHERENT IMPLIES THAT THE PHASE OF THE RADAR SIGNAL IS USED AS AN IMPORTANT PART OF THE RADAR PROCESS
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IMPORTANT FOR METEOROLOGICAL PURPOSES 4HESE MAY BE SPECIAL RADARS OR ANOTHER
FUNCTION OF SURVEILLANCE RADARS
$OPPLER WEATHER RADAR 4HIS IS A WEATHER OBSERVATION RADAR THAT EMPLOYS THE DOP
PLER FREQUENCY SHIFT CAUSED BY MOVING WEATHER EFFECTS TO DETERMINE THE WIND THE
WIND SHEAR WHEN THE WIND BLOWS IN DIFFERENT DIRECTIONS WHICH CAN INDICATE A
DANGEROUS WEATHER CONDITION SUCH AS A TORNADO OR A DOWNBURST OF WIND AS WELL AS
OTHER METEOROLOGICAL EFFECTS
4ARGET RECOGNITION )N SOME CASES IT MIGHT BE IMPORTANT TO RECOGNIZE THE TYPE OF TARGET
BEING OBSERVED BY RADAR EG AN AUTOMOBILE RATHER THAN A BIRD OR TO RECOGNIZE THE PAR
TICULAR TYPE OF TARGET AN AUTOMOBILE RATHER THAN A TRUCK OR A STARLING RATHER THAN A SPAR
ROW OR TO RECOGNIZE ONE CLASS OF TARGET FROM ANOTHER A CRUISE SHIP RATHER THAN A TANKER 7HEN USED FOR MILITARY PURPOSES IT IS USUALLY CALLED A NONCOOPERATIVE TARGET RECOG
NITION .#42 RADAR AS COMPARED TO A COOPERATIVE RECOGNITION SYSTEM SUCH AS )&&
IDENTIFICATION FRIEND OR FOE WHICH IS NOT A RADAR 7HEN TARGET RECOGNITION INVOLVES
SOME PART OF THE NATURAL ENVIRONMENT THE RADAR IS USUALLY KNOWN AS A REMOTE SENS
ING OF THE ENVIRONMENT RADAR
-ULTIFUNCTION RADAR )F EACH OF THE ABOVE RADARS WERE THOUGHT OF AS PROVIDING SOME
RADAR FUNCTION THEN A MULTIFUNCTION RADAR IS ONE DESIGNED TO PERFORM MORE THAN ONE
SUCH FUNCTIONˆUSUALLY PERFORMING ONE FUNCTION AT A TIME ON A TIME SHARED BASIS
4HERE ARE MANY OTHER WAYS TO DESCRIBE RADARS INCLUDING LAND SEA AIRBORNE SPACE
BORNE MOBILE TRANSPORTABLE AIR TRAFFIC CONTROL MILITARY GROUND PENETRATING ULTRA
WIDEBAND OVER THE HORIZON INSTRUMENTATION LASER OR LIDAR BY THE FREQUENCY BAND AT
WHICH THEY OPERATE 5(& , 3 AND SO ON BY THEIR APPLICATION AND SO FORTH
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$ETECTION OF TARGETS IS OF LITTLE VALUE UNLESS SOME INFORMATION ABOUT THE TARGET IS OBTAINED
AS WELL ,IKEWISE TARGET INFORMATION WITHOUT TARGET DETECTION IS MEANINGLESS
2ANGE 0ROBABLY THE MOST DISTINGUISHING FEATURE OF A CONVENTIONAL RADAR IS ITS ABILITY
TO DETERMINE THE RANGE TO A TARGET BY MEASURING THE TIME IT TAKES FOR THE RADAR SIGNAL TO
PROPAGATE AT THE SPEED OF LIGHT OUT TO THE TARGET AND BACK TO THE RADAR .O OTHER SENSOR CAN
MEASURE THE DISTANCE TO A REMOTE TARGET AT LONG RANGE WITH THE ACCURACY OF RADAR BASICALLY
LIMITED AT LONG RANGES BY THE ACCURACY OF THE KNOWLEDGE OF THE VELOCITY OF PROPAGATION !T MODEST RANGES THE PRECISION CAN BE A FEW CENTIMETERS 4O MEASURE RANGE SOME SORT
OF TIMING MARK MUST BE INTRODUCED ON THE TRANSMITTED WAVEFORM ! TIMING MARK CAN
BE A SHORT PULSE AN AMPLITUDE MODULATION OF THE SIGNAL BUT IT CAN ALSO BE A DISTINCTIVE
MODULATION OF THE FREQUENCY OR PHASE 4HE ACCURACY OF A RANGE MEASUREMENT DEPENDS
ON THE RADAR SIGNAL BANDWIDTH THE WIDER THE BANDWIDTH THE GREATER THE ACCURACY 4HUS
BANDWIDTH IS THE BASIC MEASURE OF RANGE ACCURACY
2ADIAL 6ELOCITY 4HE RADIAL VELOCITY OF A TARGET IS OBTAINED FROM THE RATE OF CHANGE
OF RANGE OVER A PERIOD OF TIME )T CAN ALSO BE OBTAINED FROM THE MEASUREMENT OF THE DOP
PLER FREQUENCY SHIFT !N ACCURATE MEASUREMENT OF RADIAL VELOCITY REQUIRES TIME (ENCE
TIME IS THE BASIC PARAMETER DESCRIBING THE QUALITY OF A RADIAL VELOCITY MEASUREMENT 4HE
SPEED OF A MOVING TARGET AND ITS DIRECTION OF TRAVEL CAN BE OBTAINED FROM ITS TRACK WHICH
CAN BE FOUND FROM THE RADAR MEASUREMENTS OF THE TARGET LOCATION OVER A PERIOD OF TIME
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!NGULAR $IRECTION /NE METHOD FOR DETERMINING THE DIRECTION TO A TARGET IS BY
DETERMINING THE ANGLE WHERE THE MAGNITUDE OF THE ECHO SIGNAL FROM A SCANNING ANTENNA
IS MAXIMUM 4HIS USUALLY REQUIRES AN ANTENNA WITH A NARROW BEAMWIDTH A HIGH GAIN
ANTENNA !N AIR SURVEILLANCE RADAR WITH A ROTATING ANTENNA BEAM DETERMINES ANGLE IN
THIS MANNER 4HE ANGLE TO A TARGET IN ONE ANGULAR DIMENSION CAN ALSO BE DETERMINED BY
USING TWO ANTENNA BEAMS SLIGHTLY DISPLACED IN ANGLE AND COMPARING THE ECHO AMPLI
TUDE RECEIVED IN EACH BEAM &OUR BEAMS ARE NEEDED TO OBTAIN THE ANGLE MEASUREMENT
IN BOTH AZIMUTH AND ELEVATION 4HE MONOPULSE TRACKING RADAR DISCUSSED IN #HAPTER IS
A GOOD EXAMPLE 4HE ACCURACY OF AN ANGLE MEASUREMENT DEPENDS ON THE ELECTRICAL SIZE
OF THE ANTENNA IE THE SIZE OF THE ANTENNA GIVEN IN WAVELENGTHS
3IZE AND 3HAPE )F THE RADAR HAS SUFFICIENT RESOLUTION CAPABILITY IN RANGE OR ANGLE
IT CAN PROVIDE A MEASUREMENT OF THE TARGET EXTENT IN THE DIMENSION OF HIGH RESOLU
TION 2ANGE IS USUALLY THE COORDINATE WHERE RESOLUTION IS OBTAINED 2ESOLUTION IN CROSS
RANGE GIVEN BY THE RANGE MULTIPLIED BY THE ANTENNA BEAMWIDTH CAN BE OBTAINED WITH
VERY NARROW BEAMWIDTH ANTENNAS (OWEVER THE ANGULAR WIDTH OF AN ANTENNA BEAM IS
LIMITED SO THE CROSS RANGE RESOLUTION OBTAINED BY THIS METHOD IS NOT AS GOOD AS THE
RANGE RESOLUTION 6ERY GOOD RESOLUTION IN THE CROSS RANGE DIMENSION CAN BE OBTAINED
BY EMPLOYING THE DOPPLER FREQUENCY DOMAIN BASED ON 3!2 SYNTHETIC APERTURE RADAR
OR )3!2 INVERSE SYNTHETIC APERTURE RADAR SYSTEMS AS DISCUSSED IN #HAPTER 4HERE
NEEDS TO BE RELATIVE MOTION BETWEEN THE TARGET AND THE RADAR IN ORDER TO OBTAIN THE
CROSS RANGE RESOLUTION BY 3!2 OR )3!2 7ITH SUFFICIENT RESOLUTION IN BOTH RANGE AND
CROSS RANGE NOT ONLY CAN THE SIZE BE OBTAINED IN TWO ORTHOGONAL COORDINATES BUT THE
TARGET SHAPE CAN SOMETIMES BE DISCERNED
4HE )MPORTANCE OF "ANDWIDTH IN 2ADAR "ANDWIDTH BASICALLY REPRESENTS INFOR
MATION HENCE IT IS VERY IMPORTANT IN MANY RADAR APPLICATIONS 4HERE ARE TWO TYPES OF
BANDWIDTH ENCOUNTERED IN RADAR /NE IS THE SIGNAL BANDWIDTH WHICH IS THE BANDWIDTH
DETERMINED BY THE SIGNAL PULSE WIDTH OR BY ANY INTERNAL MODULATION OF THE SIGNAL 4HE
OTHER IS TUNABLE BANDWIDTH 'ENERALLY THE SIGNAL BANDWIDTH OF A SIMPLE PULSE OF SINE
WAVE OF DURATION S IS S 0ULSE COMPRESSION WAVEFORMS DISCUSSED IN #HAPTER CAN
HAVE MUCH GREATER BANDWIDTH THAN THE RECIPROCAL OF THEIR PULSE WIDTH ,ARGE BAND
WIDTH IS NEEDED FOR RESOLVING TARGETS IN RANGE FOR ACCURATE MEASUREMENT OF RANGE TO
A TARGET AND FOR PROVIDING A LIMITED CAPABILITY TO RECOGNIZE ONE TYPE OF TARGET FROM
ANOTHER (IGH RANGE RESOLUTION ALSO CAN BE USEFUL FOR REDUCING THE DEGRADING EFFECTS
OF WHAT IS KNOWN AS GLINT IN A TRACKING RADAR FOR MEASURING THE ALTITUDE OF AN AIRCRAFT
BASED ON THE DIFFERENCE IN TIME DELAY RANGE BETWEEN THE TWO WAY DIRECT SIGNAL FROM
RADAR TO TARGET AND THE TWO WAY SURFACE SCATTERED SIGNAL FROM RADAR TO SURFACE TO TARGET
ALSO CALLED MULTIPATH HEIGHT FINDING AND IN INCREASING THE TARGET SIGNAL TO CLUTTER
RATIO )N MILITARY SYSTEMS HIGH RANGE RESOLUTION MAY BE EMPLOYED FOR COUNTING THE
NUMBER OF AIRCRAFT FLYING IN CLOSE FORMATION AND FOR RECOGNIZING AND THWARTING SOME
TYPES OF DECEPTION COUNTERMEASURES
4UNABLE BANDWIDTH OFFERS THE ABILITY TO CHANGE TUNE THE RADAR SIGNAL FREQUENCY
OVER A WIDE RANGE OF THE AVAILABLE SPECTRUM 4HIS CAN BE USED FOR REDUCING MUTUAL INTER
FERENCE AMONG RADARS THAT OPERATE IN THE SAME FREQUENCY BAND AS WELL AS IN ATTEMPTING
TO MAKE HOSTILE ELECTRONIC COUNTERMEASURES LESS EFFECTIVE 4HE HIGHER THE OPERATING
FREQUENCY THE EASIER IT IS TO OBTAIN WIDE SIGNAL AND WIDE TUNABLE BANDWIDTH
! LIMITATION ON THE AVAILABILITY OF BANDWIDTH IN A RADAR IS THE CONTROL OF THE SPECTRUM
BY GOVERNMENT REGULATING AGENCIES IN THE 5NITED 3TATES THE &EDERAL #OMMUNICATION
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#OMMISSION AND INTERNATIONALLY THE )NTERNATIONAL 4ELECOMMUNICATIONS 5NION !FTER
THE SUCCESS OF RADAR IN 7ORLD 7AR )) RADAR WAS ALLOWED TO OPERATE OVER ABOUT ONE
THIRD OF THE MICROWAVE SPECTRUM 4HIS SPECTRUM SPACE HAS BEEN REDUCED CONSIDERABLY
OVER THE YEARS WITH THE ADVENT OF MANY COMMERCIAL USERS OF THE SPECTRUM IN THE AGE OF
hWIRELESSv AND OTHER SERVICES REQUIRING THE ELECTROMAGNETIC SPECTRUM 4HUS THE RADAR
ENGINEER IS INCREASINGLY EXPERIENCING SMALLER AVAILABLE SPECTRUM SPACE AND BANDWIDTH
ALLOCATIONS THAT CAN BE VITAL FOR THE SUCCESS OF MANY RADAR APPLICATIONS
3IGNAL TO .OISE 2ATIO 4HE ACCURACY OF ALL RADAR MEASUREMENTS AS WELL AS THE
RELIABLE DETECTION OF TARGETS DEPENDS ON THE RATIO %.O WHERE % IS THE TOTAL ENERGY
OF THE RECEIVED SIGNAL THAT IS PROCESSED BY THE RADAR AND .O IS THE NOISE POWER PER
UNIT BANDWIDTH OF THE RECEIVER 4HUS %.O IS AN IMPORTANT MEASURE OF THE CAPABILITY
OF A RADAR
/PERATION WITH -ORE 4HAN /NE &REQUENCY 4HERE MAY BE IMPORTANT BENEFITS
WHEN A RADAR IS ABLE TO OPERATE AT MORE THAN ONE FREQUENCY &REQUENCY AGILITY USUALLY
REFERS TO THE USE OF MULTIPLE FREQUENCIES ON A PULSE TO PULSE BASIS &REQUENCY DIVERSITY
USUALLY RELATES TO THE USE OF MULTIPLE FREQUENCIES THAT ARE WIDELY SEPARATED SOMETIMES IN
MORE THAN ONE RADAR BAND &REQUENCY DIVERSITY MIGHT OPERATE AT EACH FREQUENCY SIMUL
TANEOUSLY OR ALMOST SIMULTANEOUSLY )T HAS BEEN USED IN ALMOST ALL CIVILIAN AIR TRAFFIC
CONTROL RADARS 0ULSE TO PULSE FREQUENCY AGILITY HOWEVER IS NOT COMPATIBLE WITH THE USE
OF DOPPLER PROCESSING TO DETECT MOVING TARGETS IN CLUTTER BUT FREQUENCY DIVERSITY CAN
BE COMPATIBLE 4HE FREQUENCY RANGE IN BOTH AGILITY AND IN DIVERSITY OPERATIONS IS MUCH
GREATER THAN THE INHERENT BANDWIDTH OF A PULSE OF WIDTH S
%LEVATION .ULL &ILLING /PERATION OF A RADAR AT A SINGLE FREQUENCY CAN RESULT IN A
LOBED STRUCTURE TO THE ELEVATION PATTERN OF AN ANTENNA DUE TO THE INTERFERENCE BETWEEN
THE DIRECT SIGNAL RADAR TO TARGET AND THE SURFACE SCATTERED SIGNAL RADAR TO EARTHS SUR
FACE TO TARGET "Y A LOBED STRUCTURE WE MEAN THAT THERE WILL BE REDUCED COVERAGE AT
SOME ELEVATION ANGLES NULLS AND INCREASED SIGNAL STRENGTH AT OTHER ANGLES LOBES !
CHANGE IN FREQUENCY WILL CHANGE THE LOCATION OF THE NULLS AND LOBES SO THAT BY OPERATING
OVER A WIDE FREQUENCY RANGE THE NULLS IN ELEVATION CAN BE FILLED IN AND THE RADAR WILL
BE LESS LIKELY TO LOSE A TARGET ECHO SIGNAL &OR EXAMPLE MEASUREMENTS WITH A WIDEBAND
EXPERIMENTAL RADAR KNOWN AS 3ENRAD WHICH COULD OPERATE FROM TO -(Z
SHOWED THAT WHEN ONLY A SINGLE FREQUENCY WAS USED THE BLIP SCAN RATIO THE EXPERI
MENTALLY MEASURED SINGLE SCAN PROBABILITY OF DETECTION WAS FOUND TO BE UNDER A
PARTICULAR SET OF OBSERVATIONS 7HEN THE RADAR OPERATED AT FOUR DIFFERENT WIDELY SEPA
RATED FREQUENCIES THE BLIP SCAN RATIO WAS ˆA HIGHLY SIGNIFICANT INCREASE DUE TO
FREQUENCY DIVERSITY
)NCREASED 4ARGET $ETECTABILITY 4HE RADAR CROSS SECTION OF A COMPLEX TARGET SUCH
AS AN AIRCRAFT CAN VARY GREATLY WITH A CHANGE IN FREQUENCY !T SOME FREQUENCIES THE
RADAR CROSS SECTION WILL BE SMALL AND AT OTHERS IT WILL BE LARGE )F A RADAR OPERATES AT A
SINGLE FREQUENCY IT MIGHT RESULT IN A SMALL TARGET ECHO AND THEREFORE A MISSED DETEC
TION "Y OPERATING AT A NUMBER OF DIFFERENT FREQUENCIES THE CROSS SECTION WILL VARY AND
CAN BE SMALL OR LARGE BUT A SUCCESSFUL DETECTION BECOMES MORE LIKELY THAN IF ONLY A
SINGLE FREQUENCY WERE USED 4HIS IS ONE REASON THAT ALMOST ALL AIR TRAFFIC CONTROL RADARS
OPERATE WITH TWO FREQUENCIES SPACED WIDE ENOUGH APART IN FREQUENCY TO INSURE THAT
TARGET ECHOES ARE DECORRELATED AND THEREFORE INCREASE THE LIKELIHOOD OF DETECTION
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2EDUCED %FFECTIVENESS OF (OSTILE #OUNTERMEASURES !NY MILITARY RADAR THAT IS SUC
CESSFUL CAN EXPECT A HOSTILE ADVERSARY TO EMPLOY COUNTERMEASURES TO REDUCE ITS EFFEC
TIVENESS /PERATING OVER A WIDE RANGE OF FREQUENCIES MAKES COUNTERMEASURES MORE
DIFFICULT THAN IF OPERATION IS AT ONLY ONE FREQUENCY !GAINST NOISE JAMMING CHANGING
FREQUENCY IN AN UNPREDICTABLE MANNER OVER A WIDE RANGE OF FREQUENCIES CAUSES THE JAM
MER TO HAVE TO SPREAD ITS POWER OVER A WIDE FREQUENCY RANGE AND WILL THEREFORE REDUCE
THE HOSTILE JAMMING SIGNAL STRENGTH OVER THE BANDWIDTH OF THE RADAR SIGNAL &REQUENCY
DIVERSITY OVER A WIDE BAND ALSO MAKES IT MORE DIFFICULT BUT NOT IMPOSSIBLE FOR A HOSTILE
INTERCEPT RECEIVER OR AN ANTIRADIATION MISSILE TO DETECT AND LOCATE A RADAR SIGNAL
4HE $OPPLER 3HIFT IN 2ADAR 4HE IMPORTANCE OF THE DOPPLER FREQUENCY SHIFT
BEGAN TO BE APPRECIATED FOR PULSE RADAR SHORTLY AFTER 7ORLD 7AR )) AND BECAME AN
INCREASINGLY IMPORTANT FACTOR IN MANY RADAR APPLICATIONS -ODERN RADAR WOULD BE
MUCH LESS INTERESTING OR USEFUL IF THE DOPPLER EFFECT DIDNT EXIST 4HE DOPPLER FREQUENCY
SHIFT FD CAN BE WRITTEN AS
FD VR L V COS Q L
WHERE VR V COS P IS THE RELATIVE VELOCITY OF THE TARGET RELATIVE TO THE RADAR IN MS V IS
THE ABSOLUTE VELOCITY OF THE TARGET IN MS K IS THE RADAR WAVELENGTH IN M AND P IS THE
ANGLE BETWEEN THE TARGETS DIRECTION AND THE RADAR BEAM 4O AN ACCURACY OF ABOUT PER
CENT THE DOPPLER FREQUENCY IN HERTZ IS APPROXIMATELY EQUAL TO VR KT DIVIDED BY K M 4HE DOPPLER FREQUENCY SHIFT IS WIDELY USED TO SEPARATE MOVING TARGETS FROM
STATIONARY CLUTTER AS DISCUSSED IN #HAPTERS THROUGH 3UCH RADARS ARE KNOWN AS -4)
MOVING TARGET INDICATION !-4) AIRBORNE -4) AND PULSE DOPPLER !LL MODERN AIR
TRAFFIC CONTROL RADARS ALL IMPORTANT MILITARY GROUND BASED AND AIRBORNE AIR SURVEILLANCE
RADARS AND ALL MILITARY AIRBORNE FIGHTER RADARS TAKE ADVANTAGE OF THE DOPPLER EFFECT 9ET IN
77)) NONE OF THESE PULSE RADAR APPLICATIONS USED DOPPLER 4HE #7 CONTINUOUS WAVE
RADAR ALSO EMPLOYS THE DOPPLER EFFECT FOR DETECTING MOVING TARGETS BUT #7 RADAR FOR
THIS PURPOSE IS NOT AS POPULAR AS IT ONCE WAS 4HE (& /4( RADAR #HAPTER COULD NOT
DO ITS JOB OF DETECTING MOVING TARGETS IN THE PRESENCE OF LARGE CLUTTER ECHOES FROM THE
EARTHS SURFACE WITHOUT THE USE OF DOPPLER
!NOTHER SIGNIFICANT APPLICATION OF RADAR THAT DEPENDS ON THE DOPPLER SHIFT IS OBSER
VATION OF THE WEATHER AS IN THE .EXRAD RADARS OF THE 53 .ATIONAL 7EATHER 3ERVICE
#HAPTER MENTIONED EARLIER IN THIS CHAPTER
"OTH THE 3!2 AND )3!2 CAN BE DESCRIBED IN TERMS OF THEIR USE OF THE DOPPLER FRE
QUENCY SHIFT #HAPTER 4HE AIRBORNE DOPPLER NAVIGATOR RADAR IS ALSO BASED ON THE
DOPPLER SHIFT 4HE USE OF DOPPLER IN A RADAR GENERALLY PLACES GREATER DEMANDS ON THE
STABILITY OF THE RADAR TRANSMITTER AND IT INCREASES THE COMPLEXITY OF THE SIGNAL PROCESS
ING YET THESE REQUIREMENTS ARE WILLINGLY ACCEPTED IN ORDER TO ACHIEVE THE SIGNIFICANT
BENEFITS OFFERED BY DOPPLER )T SHOULD ALSO BE MENTIONED THAT THE DOPPLER SHIFT IS THE KEY
CAPABILITY OF A RADAR THAT CAN MEASURE SPEED AS BY ITS DILIGENT USE BY TRAFFIC POLICE FOR
MAINTAINING VEHICLE SPEED LIMITS AND IN OTHER VELOCITY MEASURING APPLICATIONS
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4HE RADAR RANGE EQUATION OR RADAR EQUATION FOR SHORT NOT ONLY SERVES THE VERY USEFUL
PURPOSE OF ESTIMATING THE RANGE OF A RADAR AS A FUNCTION OF THE RADAR CHARACTERISTICS
!. ).42/$5#4)/. !.$ /6%26)%7 /& 2!$!2
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BUT ALSO IS QUITE USEFUL AS A GUIDE FOR DESIGNING A RADAR SYSTEM 4HE SIMPLE FORM OF THE
RADAR EQUATION MAY BE WRITTEN AS
0R 0T 'T
S
r
r !E
P 2 P 2 4HE RIGHT HAND SIDE HAS BEEN WRITTEN AS THE PRODUCT OF THREE FACTORS TO REPRESENT THE
PHYSICAL PROCESSES THAT TAKE PLACE 4HE FIRST FACTOR ON THE RIGHT IS THE POWER DENSITY
AT A DISTANCE 2 FROM A RADAR THAT RADIATES A POWER 0T FROM AN ANTENNA OF GAIN 'T 4HE
NUMERATOR R OF THE SECOND FACTOR IS THE RADAR CROSS SECTION OF THE TARGET )T HAS THE UNIT
OF AREA FOR EXAMPLE SQUARE METERS AND IS A MEASURE OF THE ENERGY REDIRECTED BY THE
TARGET BACK IN THE DIRECTION OF THE RADAR 4HE DENOMINATOR OF THE SECOND FACTOR ACCOUNTS
FOR THE DIVERGENCE OF THE ECHO SIGNAL ON ITS RETURN PATH BACK TO THE RADAR 4HE PRODUCT
OF THE FIRST TWO FACTORS REPRESENTS THE POWER PER UNIT AREA RETURNED TO THE RADAR ANTENNA
.OTE THAT THE RADAR CROSS SECTION OF A TARGET R IS DEFINED BY THIS EQUATION 4HE RECEIVING
ANTENNA OF EFFECTIVE AREA !E COLLECTS A PORTION 0R OF THE ECHO POWER RETURNED TO THE RADAR
)F THE MAXIMUM RADAR RANGE 2MAX IS DEFINED AS OCCURRING WHEN THE RECEIVED SIGNAL IS
EQUAL TO THE MINIMUM DETECTABLE SIGNAL OF THE RADAR 3MIN THE SIMPLE FORM OF THE RADAR
EQUATION BECOMES
2MAX
0T 'T !E S
P 3MIN
'ENERALLY MOST RADARS USE THE SAME ANTENNA FOR BOTH TRANSMITTING AND RECEIVING &ROM
ANTENNA THEORY THERE IS A RELATION BETWEEN THE GAIN 'T OF THE ANTENNA ON TRANSMIT AND
ITS EFFECTIVE AREA !E ON RECEIVE WHICH IS 'T P !E L WHERE K IS THE WAVELENGTH OF
THE RADAR SIGNAL 3UBSTITUTING THIS INTO %Q PROVIDES TWO OTHER USEFUL FORMS OF THE
RADAR EQUATION NOT SHOWN HERE ONE THAT REPRESENTS THE ANTENNA ONLY BY ITS GAIN AND
THE OTHER THAT REPRESENTS THE ANTENNA ONLY BY ITS EFFECTIVE AREA
4HE SIMPLE FORM OF THE RADAR EQUATION IS INSTRUCTIVE BUT NOT VERY USEFUL SINCE IT
LEAVES OUT MANY THINGS 4HE MINIMUM DETECTABLE SIGNAL 3MIN IS LIMITED BY RECEIVER
NOISE AND CAN BE EXPRESSED AS
3MIN K4O "&N 3 . )N THIS EXPRESSION K4O " IS THE SO CALLED THERMAL NOISE FROM AN IDEAL OHMIC CONDUC
TOR WHERE K "OLTZMANNS CONSTANT 4O IS THE STANDARD TEMPERATURE OF + AND " RECEIVER BANDWIDTH USUALLY THAT OF THE )& STAGE OF THE SUPERHETERODYNE RECEIVER 4HE
PRODUCT K4O IS EQUAL TO r 7(Z 4O ACCOUNT FOR THE ADDITIONAL NOISE INTRODUCED
BY A PRACTICAL NONIDEAL RECEIVER THE THERMAL NOISE EXPRESSION IS MULTIPLIED BY THE
NOISE FIGURE &N OF THE RECEIVER DEFINED AS THE NOISE OUT OF A PRACTICAL RECEIVER TO THE
NOISE OUT OF AN IDEAL RECEIVER &OR A RECEIVED SIGNAL TO BE DETECTABLE IT HAS TO BE LARGER
THAN THE RECEIVER NOISE BY A FACTOR DENOTED HERE AS 3. 4HIS VALUE OF SIGNAL TO
NOISE RATIO 3. IS THAT REQUIRED IF ONLY ONE PULSE IS PRESENT )T HAS TO BE LARGE ENOUGH
TO OBTAIN THE REQUIRED PROBABILITY OF FALSE ALARM DUE TO NOISE CROSSING THE RECEIVER
THRESHOLD AND THE REQUIRED PROBABILITY OF DETECTION AS CAN BE FOUND IN VARIOUS RADAR
TEXTS 2ADARS HOWEVER GENERALLY PROCESS MORE THAN ONE PULSE BEFORE MAKING A
DETECTION DECISION 7E ASSUME THE RADAR WAVEFORM IS A REPETITIVE SERIES OF RECTANGULAR
LIKE PULSES 4HESE PULSES ARE INTEGRATED ADDED TOGETHER BEFORE A DETECTION DECISION
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IS MADE 4O ACCOUNT FOR THESE ADDED SIGNALS THE NUMERATOR OF THE RADAR EQUATION IS
MULTIPLIED BY A FACTOR N%IN WHERE %IN IS THE EFFICIENCY IN ADDING TOGETHER N PULSES
4HIS VALUE CAN ALSO BE FOUND IN STANDARD TEXTS
4HE POWER 0T IS THE PEAK POWER OF A RADAR PULSE 4HE AVERAGE POWER 0AV IS A BETTER
MEASURE OF THE ABILITY OF A RADAR TO DETECT TARGETS SO IT IS SOMETIMES INSERTED INTO THE
RADAR EQUATION USING 0T 0AV FPS WHERE FP IS THE PULSE REPETITION FREQUENCY OF THE PULSE
RADAR AND S IS THE PULSE DURATION 4HE SURFACE OF THE EARTH AND THE EARTHS ATMOSPHERE CAN
DRASTICALLY AFFECT THE PROPAGATION OF ELECTROMAGNETIC WAVES AND CHANGE THE COVERAGE AND
CAPABILITIES OF A RADAR )N THE RADAR EQUATION THESE PROPAGATION EFFECTS ARE ACCOUNTED FOR
BY A FACTOR & IN THE NUMERATOR OF THE RADAR EQUATION AS DISCUSSED IN #HAPTER 7ITH
THE ABOVE SUBSTITUTED INTO THE SIMPLE FORM OF THE RADAR EQUATION WE GET
2MAX
0AV '!ES N%I N & P K4O &N F P 3 . ,S
)N THE ABOVE EQUATION IT WAS ASSUMED IN ITS DERIVATION THAT "S y WHICH IS GENERALLY
APPLICABLE IN RADAR ! FACTOR ,S GREATER THAN UNITY CALLED THE SYSTEM LOSSES HAS BEEN
INSERTED TO ACCOUNT FOR THE MANY WAYS THAT LOSS CAN OCCUR IN A RADAR 4HIS LOSS FACTOR
CAN BE QUITE LARGE )F THE SYSTEM LOSS IS IGNORED IT MIGHT RESULT IN A VERY LARGE ERROR IN
THE ESTIMATED RANGE PREDICTED BY THE RADAR EQUATION ! LOSS OF FROM D" TO MAY BE
D" IS NOT UNUSUAL WHEN ALL RADAR SYSTEM LOSS FACTORS ARE TAKEN INTO ACCOUNT
%QUATION APPLIES FOR A RADAR THAT OBSERVES A TARGET LONG ENOUGH TO RECEIVE N
PULSES -ORE FUNDAMENTALLY IT APPLIES FOR A RADAR WHERE THE TIME ON TARGET TO IS EQUAL
TO NFP !N EXAMPLE IS A TRACKING RADAR THAT CONTINUOUSLY OBSERVES A SINGLE TARGET FOR
A TIME TO 4HIS EQUATION HOWEVER NEEDS TO BE MODIFIED FOR A SURVEILLANCE RADAR THAT
OBSERVES AN ANGULAR VOLUME 7 WITH A REVISIT TIME TS !IR TRAFFIC CONTROL RADARS MIGHT
HAVE A REVISIT TIME OF FROM TO S 4HUS A SURVEILLANCE RADAR HAS THE ADDITIONAL
CONSTRAINT THAT IT MUST COVER AN ANGULAR VOLUME 7 IN A GIVEN TIME TS 4HE REVISIT
TIME TS IS EQUAL TO TO77O WHERE TO NFP AND 7O THE SOLID BEAMWIDTH OF THE ANTENNA
STERADIANS IS APPROXIMATELY RELATED TO THE ANTENNA GAIN ' BY ' O 7O 4HEREFORE
WHEN NFP IN %Q IS REPLACED WITH ITS EQUAL O TS '7 THE RADAR EQUATION FOR A
SURVEILLANCE RADAR IS OBTAINED AS
2MAX
0AV !ES %I N & T
r S
P K4O &N 3 . ,S 7
4HE RADAR DESIGNER HAS LITTLE CONTROL OVER THE REVISIT TIME TS OR THE ANGULAR COVERAGE
7 WHICH ARE DETERMINED MAINLY BY THE JOB THE RADAR HAS TO PERFORM 4HE RADAR CROSS
SECTION ALSO IS DETERMINED BY THE RADAR APPLICATION )F A LARGE RANGE IS REQUIRED OF
A SURVEILLANCE RADAR THE RADAR MUST HAVE THE NECESSARY VALUE OF THE PRODUCT 0AV !E
&OR THIS REASON A COMMON MEASURE OF THE CAPABILITY OF A SURVEILLANCE RADAR IS ITS
POWER APERTURE PRODUCT .OTE THAT THE RADAR FREQUENCY DOES NOT APPEAR EXPLICITLY
IN THE SURVEILLANCE RADAR EQUATION 4HE CHOICE OF FREQUENCY HOWEVER WILL ENTER
IMPLICITLY IN OTHER WAYS
*UST AS THE RADAR EQUATION FOR A SURVEILLANCE RADAR IS DIFFERENT FROM THE CONVENTIONAL
RADAR EQUATION OF %Q OR THE SIMPLE RADAR EQUATION OF %Q EACH PARTICULAR APPLICA
TION OF A RADAR GENERALLY HAS TO EMPLOY A RADAR EQUATION TAILORED TO THAT SPECIFIC APPLICA
TION 7HEN THE RADAR ECHOES FROM LAND SEA OR WEATHER CLUTTER ARE GREATER THAN THE RECEIVER
NOISE THE RADAR EQUATION HAS TO BE MODIFIED TO ACCOUNT FOR CLUTTER BEING THE LIMITATION TO
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DETECTION RATHER THAN RECEIVER NOISE )T CAN HAPPEN THAT THE DETECTION CAPABILITY OF A RADAR
MIGHT BE LIMITED BY CLUTTER IN SOME REGIONS OF ITS COVERAGE AND BE LIMITED BY RECEIVER
NOISE IN OTHER REGIONS 4HIS CAN RESULT IN TWO DIFFERENT SETS OF RADAR CHARACTERISTICS ONE
OPTIMIZED FOR NOISE AND THE OTHER OPTIMIZED FOR CLUTTER AND COMPROMISES USUALLY HAVE TO
BE MADE IN RADAR DESIGN ! DIFFERENT TYPE OF RADAR EQUATION IS ALSO REQUIRED WHEN THE RADAR
CAPABILITY IS LIMITED BY HOSTILE NOISE JAMMING
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"
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9Ê // ,‡ Ê
)T IS NOT ALWAYS CONVENIENT TO USE THE EXACT NUMERICAL FREQUENCY RANGE OVER WHICH A
PARTICULAR TYPE OF RADAR OPERATES 7ITH MANY MILITARY RADARS THE EXACT OPERATING FRE
QUENCY RANGE OF A RADAR IS USUALLY NOT DISCLOSED 4HUS THE USE OF LETTERS TO DESIGNATE
RADAR OPERATING BANDS HAS BEEN VERY HELPFUL 4HE )%%% )NSTITUTE OF %LECTRICAL AND
%LECTRONIC %NGINEERS HAS OFFICIALLY STANDARDIZED THE RADAR LETTER BAND NOMENCLATURE
AS SUMMARIZED IN 4ABLE #OMMENTS ON THE TABLE 4HE )NTERNATIONAL 4ELECOMMUNICATIONS 5NION )45
ASSIGNS SPECIFIC PORTIONS OF THE ELECTROMAGNETIC SPECTRUM FOR RADIOLOCATION RADAR
USE AS SHOWN IN THE THIRD COLUMN WHICH APPLIES TO )45 2EGION THAT INCLUDES .ORTH
AND 3OUTH !MERICA 3LIGHT DIFFERENCES OCCUR IN THE OTHER TWO )45 2EGIONS 4HUS AN
, BAND RADAR CAN ONLY OPERATE WITHIN THE FREQUENCY RANGE FROM -(Z TO -(Z
AND EVEN WITHIN THIS RANGE THERE MAY BE RESTRICTIONS 3OME OF THE INDICATED )45 BANDS
ARE RESTRICTED IN THEIR USAGE FOR EXAMPLE THE BAND BETWEEN AND '(Z IS RESERVED
4!",% )%%% 3TANDARD ,ETTER $ESIGNATIONS FOR 2ADAR &REQUENCY "ANDS
"AND $ESIGNATION
.OMINAL &REQUENCY 2ANGE
(&
6(&
-(Zn -(Z
n -(Z
5(&
n -(Z
,
3
n '(Z
n '(Z
#
n '(Z
8
+U
n '(Z
n '(Z
+
n '(Z
+A
6
7
n '(Z
n '(Z
n '(Z
3PECIFIC &REQUENCY 2ANGES FOR 2ADAR "ASED
ON )45 &REQUENCY !SSIGNMENTS
FOR 2EGION n -(Z
n -(Z
n -(Z
n -(Z
n -(Z
n '(Z
n '(Z
n '(Z
n '(Z
n '(Z
n '(Z
n '(Z
n '(Z
n '(Z
n '(Z
n '(Z
n '(Z
n '(Z
£°£{
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WITH FEW EXCEPTIONS FOR AIRBORNE RADAR ALTIMETERS 4HERE ARE NO OFFICIAL )45 ALLOCATIONS
FOR RADAR IN THE (& BAND BUT MOST (& RADARS SHARE FREQUENCIES WITH OTHER ELECTROMAG
NETIC SERVICES 4HE LETTER BAND DESIGNATION FOR MILLIMETER WAVE RADARS IS MM AND THERE
ARE SEVERAL FREQUENCY BANDS ALLOCATED TO RADAR IN THIS REGION BUT THEY HAVE NOT BEEN
LISTED HERE !LTHOUGH THE OFFICIAL )45 DESCRIPTION OF MILLIMETER WAVES IS FROM TO '(Z IN REALITY THE TECHNOLOGY OF RADARS AT +A BAND IS MUCH CLOSER TO THE TECHNOLOGY
OF MICROWAVE FREQUENCIES THAN TO THE TECHNOLOGY OF 7 BAND 4HE MILLIMETER WAVE RADAR
FREQUENCIES ARE OFTEN CONSIDERED BY THOSE WHO WORK IN THIS FIELD TO HAVE A LOWER BOUND
OF '(Z RATHER THAN THE hLEGALv LOWER BOUND OF '(Z IN RECOGNITION OF THE SIGNIFICANT
DIFFERENCE IN TECHNOLOGY AND APPLICATIONS THAT IS CHARACTERISTIC OF MILLIMETER WAVE RADAR
-ICROWAVES HAVE NOT BEEN DEFINED IN THIS STANDARD BUT THIS TERM GENERALLY APPLIES TO
RADARS THAT OPERATE FROM 5(& TO +A BAND 4HE REASON THAT THESE LETTER DESIGNATIONS MIGHT
NOT BE EASY FOR THE NON RADAR ENGINEER TO RECOGNIZE IS THAT THEY WERE ORIGINALLY SELECTED
TO DESCRIBE THE RADAR BANDS USED IN 7ORLD 7AR )) 3ECRECY WAS IMPORTANT AT THAT TIME SO
THE LETTERS SELECTED TO DESIGNATE THE VARIOUS BANDS MADE IT HARD TO GUESS THE FREQUENCIES
TO WHICH THEY APPLY 4HOSE WHO WORK AROUND RADAR HOWEVER SELDOM HAVE A PROBLEM
WITH THE USAGE OF THE RADAR LETTER BANDS
/THER LETTER BANDS HAVE BEEN USED FOR DESCRIBING THE ELECTROMAGNETIC SPECTRUM BUT
THEY ARE NOT SUITABLE FOR RADAR AND SHOULD NEVER BE USED FOR RADAR /NE SUCH DESIGNATION
USES THE LETTERS ! " # ETC ORIGINALLY DEVISED FOR CONDUCTING ELECTRONIC COUNTERMEASURE
EXERCISES 4HE )%%% 3TANDARD MENTIONED PREVIOUSLY STATES THAT THESE hARE NOT CONSISTENT
WITH RADAR PRACTICE AND SHALL NOT BE USED TO DESCRIBE RADAR FREQUENCY BANDSv 4HUS THERE
MAY BE $ BAND JAMMERS BUT NEVER $ BAND RADARS
£°ÈÊ , +1
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2ADARS HAVE BEEN OPERATED AT FREQUENCIES AS LOW AS -(Z JUST ABOVE THE !- BROAD
CAST BAND AND AS HIGH AS SEVERAL HUNDRED '(Z MILLIMETER WAVE REGION -ORE USU
ALLY RADAR FREQUENCIES MIGHT BE FROM ABOUT -(Z TO OVER '(Z 4HIS IS A VERY LARGE
EXTENT OF FREQUENCIES SO IT SHOULD BE EXPECTED THAT RADAR TECHNOLOGY CAPABILITIES AND
APPLICATIONS WILL VARY CONSIDERABLY DEPENDING ON THE FREQUENCY RANGE AT WHICH A
RADAR OPERATES 2ADARS AT A PARTICULAR FREQUENCY BAND USUALLY HAVE DIFFERENT CAPABILI
TIES AND CHARACTERISTICS THAN RADARS IN OTHER FREQUENCY BANDS 'ENERALLY LONG RANGE
IS EASIER TO ACHIEVE AT THE LOWER FREQUENCIES BECAUSE IT IS EASIER TO OBTAIN HIGH POWER
TRANSMITTERS AND PHYSICALLY LARGE ANTENNAS AT THE LOWER FREQUENCIES /N THE OTHER
HAND AT THE HIGHER RADAR FREQUENCIES IT IS EASIER TO ACHIEVE ACCURATE MEASUREMENTS OF
RANGE AND LOCATION BECAUSE THE HIGHER FREQUENCIES PROVIDE WIDER BANDWIDTH WHICH
DETERMINES RANGE ACCURACY AND RANGE RESOLUTION AS WELL AS NARROWER BEAM ANTENNAS
FOR A GIVEN PHYSICAL SIZE ANTENNA WHICH DETERMINES ANGLE ACCURACY AND ANGLE RESOLU
TION )N THE FOLLOWING THE APPLICATIONS USUALLY FOUND IN THE VARIOUS RADAR BANDS ARE
BRIEFLY INDICATED 4HE DIFFERENCES BETWEEN ADJACENT BANDS HOWEVER ARE SELDOM SHARP
IN PRACTICE AND OVERLAP IN CHARACTERISTICS BETWEEN ADJACENT BANDS IS LIKELY
4HE WAVELENGTHS OF +A BAND RANGE FROM MM TO MM WHICH QUALIFIES THEM UNDER THE hLEGALv DEFINITION OF
MILLIMETERS BUT JUST BARELY
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(& TO -(Z 4HE MAJOR USE OF THE (& BAND FOR RADAR #HAPTER IS TO
DETECT TARGETS AT LONG RANGES NOMINALLY OUT TO NMI BY TAKING ADVANTAGE OF THE
REFRACTION OF (& ENERGY BY THE IONOSPHERE THAT LIES HIGH ABOVE THE SURFACE OF THE EARTH
2ADIO AMATEURS REFER TO THIS AS SHORT WAVE PROPAGATION AND USE IT TO COMMUNICATE OVER
LONG DISTANCES 4HE TARGETS FOR SUCH (& RADARS MIGHT BE AIRCRAFT SHIPS AND BALLISTIC
MISSILES AS WELL AS THE ECHO FROM THE SEA SURFACE ITSELF THAT PROVIDES INFORMATION ABOUT
THE DIRECTION AND SPEED OF THE WINDS THAT DRIVE THE SEA
6(& TO -(Z !T THE BEGINNING OF RADAR DEVELOPMENT IN THE S
RADARS WERE IN THIS FREQUENCY BAND BECAUSE THESE FREQUENCIES REPRESENTED THE FRONTIER
OF RADIO TECHNOLOGY AT THAT TIME )T IS A GOOD FREQUENCY FOR LONG RANGE AIR SURVEILLANCE
OR DETECTION OF BALLISTIC MISSILES !T THESE FREQUENCIES THE REFLECTION COEFFICIENT ON
SCATTERING FROM THE EARTHS SURFACE CAN BE VERY LARGE ESPECIALLY OVER WATER SO THE
CONSTRUCTIVE INTERFERENCE BETWEEN THE DIRECT SIGNAL AND THE SURFACE REFLECTED SIGNAL CAN
INCREASE SIGNIFICANTLY THE RANGE OF A 6(& RADAR 3OMETIMES THIS EFFECT CAN ALMOST DOU
BLE THE RADARS RANGE (OWEVER WHEN THERE IS CONSTRUCTIVE INTERFERENCE THAT INCREASES
THE RANGE THERE CAN BE DESTRUCTIVE INTERFERENCE THAT DECREASES THE RANGE DUE TO THE DEEP
NULLS IN THE ANTENNA PATTERN IN THE ELEVATION PLANE ,IKEWISE THE DESTRUCTIVE INTERFER
ENCE CAN RESULT IN POOR LOW ALTITUDE COVERAGE $ETECTION OF MOVING TARGETS IN CLUTTER
IS OFTEN BETTER AT THE LOWER FREQUENCIES WHEN THE RADAR TAKES ADVANTAGE OF THE DOPPLER
FREQUENCY SHIFT BECAUSE DOPPLER AMBIGUITIES THAT CAUSE BLIND SPEEDS ARE FAR FEWER
AT LOW FREQUENCIES 6(& RADARS ARE NOT BOTHERED BY ECHOES FROM RAIN BUT THEY CAN BE
AFFECTED BY MULTIPLE TIME AROUND ECHOES FROM METEOR IONIZATION AND AURORA 4HE RADAR
CROSS SECTION OF AIRCRAFT AT 6(& IS GENERALLY LARGER THAN THE RADAR CROSS SECTION AT HIGHER
FREQUENCIES 6(& RADARS FREQUENTLY COST LESS COMPARED TO RADARS WITH THE SAME RANGE
PERFORMANCE THAT OPERATE AT HIGHER FREQUENCIES
!LTHOUGH THERE ARE MANY ATTRACTIVE ADVANTAGES OF 6(& RADARS FOR LONG RANGE SUR
VEILLANCE THEY ALSO HAVE SOME SERIOUS LIMITATIONS $EEP NULLS IN ELEVATION AND POOR
LOW ALTITUDE COVERAGE HAVE BEEN MENTIONED 4HE AVAILABLE SPECTRAL WIDTHS ASSIGNED TO
RADAR AT 6(& ARE SMALL SO RANGE RESOLUTION IS OFTEN POOR 4HE ANTENNA BEAMWIDTHS ARE
USUALLY WIDER THAN AT MICROWAVE FREQUENCIES SO THERE IS POOR RESOLUTION AND ACCURACY
IN ANGLE 4HE 6(& BAND IS CROWDED WITH IMPORTANT CIVILIAN SERVICES SUCH AS 46 AND &BROADCAST FURTHER REDUCING THE AVAILABILITY OF SPECTRUM SPACE FOR RADAR %XTERNAL NOISE
LEVELS THAT CAN ENTER THE RADAR VIA THE ANTENNA ARE HIGHER AT 6(& THAN AT MICROWAVE
FREQUENCIES 0ERHAPS THE CHIEF LIMITATION OF OPERATING RADARS AT 6(& IS THE DIFFICULTY OF
OBTAINING SUITABLE SPECTRUM SPACE AT THESE CROWDED FREQUENCIES
)N SPITE OF ITS LIMITATIONS THE 6(& AIR SURVEILLANCE RADAR WAS WIDELY USED BY THE
3OVIET 5NION BECAUSE IT WAS A LARGE COUNTRY AND THE LOWER COST OF 6(& RADARS MADE
THEM ATTRACTIVE FOR PROVIDING AIR SURVEILLANCE OVER THE LARGE EXPANSE OF THAT COUNTRY
4HEY HAVE SAID THEY PRODUCED A LARGE NUMBER OF 6(& AIR SURVEILLANCE RADARSˆ
SOME WERE OF VERY LARGE SIZE AND LONG RANGE AND MOST WERE READILY TRANSPORTABLE
)T IS INTERESTING TO NOTE THAT 6(& AIRBORNE INTERCEPT RADARS WERE WIDELY USED BY THE
'ERMANS IN 7ORLD 7AR )) &OR EXAMPLE THE ,ICHTENSTEIN 3. AIRBORNE RADAR OPER
ATED FROM ABOUT TO OVER -(Z IN VARIOUS MODELS 2ADARS AT SUCH FREQUENCIES
WERE NOT AFFECTED BY THE COUNTERMEASURE CALLED CHAFF ALSO KNOWN AS WINDOW 5(& TO -(Z -ANY OF THE CHARACTERISTICS OF RADAR OPERATING IN THE
6(& REGION ALSO APPLY TO SOME EXTENT AT 5(& 5(& IS A GOOD FREQUENCY FOR !IRBORNE
-OVING 4ARGET )NDICATION !-4) RADAR IN AN !IRBORNE %ARLY 7ARNING 2ADAR !%7
AS DISCUSSED IN #HAPTER )T IS ALSO A GOOD FREQUENCY FOR THE OPERATION OF LONG RANGE
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RADARS FOR THE DETECTION AND TRACKING OF SATELLITES AND BALLISTIC MISSILES !T THE UPPER
PORTION OF THIS BAND THERE CAN BE FOUND LONG RANGE SHIPBOARD AIR SURVEILLANCE RADARS
AND RADARS CALLED WIND PROFILERS THAT MEASURE THE SPEED AND DIRECTION OF THE WIND
'ROUND 0ENETRATING 2ADAR '02 DISCUSSED IN #HAPTER IS AN EXAMPLE OF WHAT
IS CALLED AN ULTRAWIDEBAND 57" RADAR )TS WIDE SIGNAL BANDWIDTH SOMETIMES COV
ERS BOTH THE 6(& AND 5(& BANDS 3UCH A RADARS SIGNAL BANDWIDTH MIGHT EXTEND
FOR INSTANCE FROM TO -(Z ! WIDE BANDWIDTH IS NEEDED IN ORDER TO OBTAIN
GOOD RANGE RESOLUTION 4HE LOWER FREQUENCIES ARE NEEDED TO ALLOW THE PROPAGATION OF
RADAR ENERGY INTO THE GROUND %VEN SO THE LOSS IN PROPAGATING THROUGH TYPICAL SOIL
IS SO HIGH THAT THE RANGES OF A SIMPLE MOBILE '02 MIGHT BE ONLY A FEW METERS 3UCH
RANGES ARE SUITABLE FOR LOCATING BURIED POWER LINES AND PIPE LINES AS WELL AS BURIED
OBJECTS )F A RADAR IS TO SEE TARGETS LOCATED ON THE SURFACE BUT WITHIN FOLIAGE SIMILAR
FREQUENCIES ARE NEEDED AS FOR THE '02
, BAND TO '(Z 4HIS IS THE PREFERRED FREQUENCY BAND FOR THE OPERATION
OF LONG RANGE OUT TO NMI AIR SURVEILLANCE RADARS 4HE !IR 2OUTE 3URVEILLANCE
2ADAR !232 USED FOR LONG RANGE AIR TRAFFIC CONTROL IS A GOOD EXAMPLE !S ONE GOES
UP IN FREQUENCY THE EFFECT OF RAIN ON PERFORMANCE BEGINS TO BECOME SIGNIFICANT SO THE
RADAR DESIGNER MIGHT HAVE TO WORRY ABOUT REDUCING THE EFFECT OF RAIN AT , BAND AND
HIGHER FREQUENCIES 4HIS FREQUENCY BAND HAS ALSO BEEN ATTRACTIVE FOR THE LONG RANGE
DETECTION OF SATELLITES AND DEFENSE AGAINST INTERCONTINENTAL BALLISTIC MISSILES
3 BAND TO '(Z 4HE !IRPORT 3URVEILLANCE 2ADAR !32 THAT MONITORS
AIR TRAFFIC WITHIN THE REGION OF AN AIRPORT IS AT 3 BAND )TS RANGE IS TYPICALLY TO NMI )F A $ RADAR IS WANTED ONE THAT DETERMINES RANGE AZIMUTH ANGLE AND ELEVATION
ANGLE IT CAN BE ACHIEVED AT 3 BAND
)T WAS SAID PREVIOUSLY THAT LONG RANGE SURVEILLANCE IS BETTER PERFORMED AT LOW FRE
QUENCIES AND THE ACCURATE MEASUREMENT OF TARGET LOCATION IS BETTER PERFORMED AT HIGH
FREQUENCIES )F ONLY A SINGLE RADAR OPERATING WITHIN A SINGLE FREQUENCY BAND CAN BE USED
THEN 3 BAND IS A GOOD COMPROMISE )T IS ALSO SOMETIMES ACCEPTABLE TO USE # BAND AS THE
CHOICE FOR A RADAR THAT PERFORMS BOTH FUNCTIONS 4HE !7!#3 AIRBORNE AIR SURVEILLANCE
RADAR ALSO OPERATES AT 3 BAND 5SUALLY MOST RADAR APPLICATIONS ARE BEST OPERATED IN A
PARTICULAR FREQUENCY BAND AT WHICH THE RADARS PERFORMANCE IS OPTIMUM (OWEVER IN
THE EXAMPLE OF AIRBORNE AIR SURVEILLANCE RADARS !7!#3 IS FOUND AT 3 BAND AND THE 53
.AVYS % !%7 RADAR AT 5(& )N SPITE OF SUCH A DIFFERENCE IN FREQUENCY IT HAS BEEN SAID
THAT BOTH RADARS HAVE COMPARABLE PERFORMANCE 4HIS IS AN EXCEPTION TO THE OBSERVATION
ABOUT THERE BEING AN OPTIMUM FREQUENCY BAND FOR EACH APPLICATION
4HE .EXRAD WEATHER RADAR OPERATES AT 3 BAND )T IS A GOOD FREQUENCY FOR THE OBSER
VATION OF WEATHER BECAUSE A LOWER FREQUENCY WOULD PRODUCE A MUCH WEAKER RADAR
ECHO SIGNAL FROM RAIN SINCE THE RADAR ECHO FROM RAIN VARIES AS THE FOURTH POWER OF
THE FREQUENCY AND A HIGHER FREQUENCY WOULD PRODUCE ATTENUATION OF THE SIGNAL AS IT
PROPAGATES THROUGH THE RAIN AND WOULD NOT ALLOW AN ACCURATE MEASUREMENT OF RAINFALL
RATE 4HERE ARE WEATHER RADARS AT HIGHER FREQUENCIES BUT THESE ARE USUALLY OF SHORTER
RANGE THAN .EXRAD AND MIGHT BE USED FOR A MORE SPECIFIC WEATHER RADAR APPLICATION
THAN THE ACCURATE METEOROLOGICAL MEASUREMENTS PROVIDED BY .EXRAD
# BAND TO '(Z 4HIS BAND LIES BETWEEN 3 AND 8 BANDS AND HAS PROPERTIES
IN BETWEEN THE TWO /FTEN EITHER 3 OR 8 BAND MIGHT BE PREFERRED TO THE USE OF # BAND
ALTHOUGH THERE HAVE BEEN IMPORTANT APPLICATIONS IN THE PAST FOR # BAND
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8 BAND TO '(Z 4HIS IS A RELATIVELY POPULAR RADAR BAND FOR MILITARY
APPLICATIONS )T IS WIDELY USED IN MILITARY AIRBORNE RADARS FOR PERFORMING THE ROLES OF
INTERCEPTOR FIGHTER AND ATTACK OF GROUND TARGETS AS DISCUSSED IN #HAPTER )T IS ALSO
POPULAR FOR IMAGING RADARS BASED ON 3!2 AND )3!2 8 BAND IS A SUITABLE FREQUENCY
FOR CIVIL MARINE RADARS AIRBORNE WEATHER AVOIDANCE RADAR AIRBORNE DOPPLER NAVIGATION
RADARS AND THE POLICE SPEED METER -ISSILE GUIDANCE SYSTEMS ARE SOMETIMES AT 8 BAND
2ADARS AT 8 BAND ARE GENERALLY OF A CONVENIENT SIZE AND ARE THEREFORE OF INTEREST FOR
APPLICATIONS WHERE MOBILITY AND LIGHT WEIGHT ARE IMPORTANT AND VERY LONG RANGE IS NOT
A MAJOR REQUIREMENT 4HE RELATIVELY WIDE RANGE OF FREQUENCIES AVAILABLE AT 8 BAND AND
THE ABILITY TO OBTAIN NARROW BEAMWIDTHS WITH RELATIVELY SMALL ANTENNAS IN THIS BAND
ARE IMPORTANT CONSIDERATIONS FOR HIGH RESOLUTION APPLICATIONS "ECAUSE OF THE HIGH FRE
QUENCY OF 8 BAND RAIN CAN SOMETIMES BE A SERIOUS FACTOR IN REDUCING THE PERFORMANCE
OF 8 BAND SYSTEMS
+U + AND +A "ANDS TO '(Z !S ONE GOES TO HIGHER RADAR FREQUENCY
THE PHYSICAL SIZE OF ANTENNAS DECREASE AND IN GENERAL IT IS MORE DIFFICULT TO GENERATE
LARGE TRANSMITTER POWER 4HUS THE RANGE PERFORMANCE OF RADARS AT FREQUENCIES ABOVE
8 BAND IS GENERALLY LESS THAN THAT OF 8 BAND -ILITARY AIRBORNE RADARS ARE FOUND AT +U
BAND AS WELL AS AT 8 BAND 4HESE FREQUENCY BANDS ARE ATTRACTIVE WHEN A RADAR OF SMALLER
SIZE HAS TO BE USED FOR AN APPLICATION NOT REQUIRING LONG RANGE 4HE !IRPORT 3URFACE
$ETECTION %QUIPMENT !3$% GENERALLY FOUND ON TOP OF THE CONTROL TOWER AT MAJOR
AIRPORTS HAS BEEN AT +U BAND PRIMARILY BECAUSE OF ITS BETTER RESOLUTION THAN 8 BAND )N
THE ORIGINAL + BAND THERE IS A WATER VAPOR ABSORPTION LINE AT '(Z WHICH CAUSES
ATTENUATION THAT CAN BE A SERIOUS PROBLEM IN SOME APPLICATIONS 4HIS WAS DISCOVERED
AFTER THE DEVELOPMENT OF + BAND RADARS BEGAN DURING 7ORLD 7AR )) WHICH IS WHY BOTH
+U AND +A BANDS WERE LATER INTRODUCED 4HE RADAR ECHO FROM RAIN CAN LIMIT THE CAPABIL
ITY OF RADARS AT THESE FREQUENCIES
-ILLIMETER 7AVE 2ADAR !LTHOUGH THIS FREQUENCY REGION IS OF LARGE EXTENT
MOST OF THE INTEREST IN MILLIMETER WAVE RADAR HAS BEEN IN THE VICINITY OF '(Z
WHERE THERE IS A MINIMUM CALLED A WINDOW IN THE ATMOSPHERIC ATTENUATION
! WINDOW IS A REGION OF LOW ATTENUATION RELATIVE TO ADJACENT FREQUENCIES 4HE WIN
DOW AT '(Z IS ABOUT AS WIDE AS THE ENTIRE MICROWAVE SPECTRUM !S MENTIONED
PREVIOUSLY FOR RADAR PURPOSES THE MILLIMETER WAVE REGION IN PRACTICE GENERALLY
STARTS AT '(Z OR EVEN AT HIGHER FREQUENCIES 4HE TECHNOLOGY OF MILLIMETER WAVE
RADARS AND THE PROPAGATION EFFECTS OF THE ENVIRONMENT ARE NOT ONLY DIFFERENT FROM
MICROWAVE RADARS BUT THEY ARE USUALLY MUCH MORE RESTRICTING 5NLIKE WHAT IS EXPERI
ENCED AT MICROWAVES THE MILLIMETER RADAR SIGNAL CAN BE HIGHLY ATTENUATED EVEN WHEN
PROPAGATING IN THE CLEAR ATMOSPHERE !TTENUATION VARIES OVER THE MILLIMETER WAVE
REGION 4HE ATTENUATION IN THE '(Z WINDOW IS ACTUALLY HIGHER THAN THE ATTENU
ATION OF THE ATMOSPHERIC WATER VAPOR ABSORPTION LINE AT '(Z 4HE ONE WAY
ATTENUATION IN THE OXYGEN ABSORPTION LINE AT '(Z IS ABOUT D" PER KM WHICH
ESSENTIALLY PRECLUDES ITS APPLICATION !TTENUATION IN RAIN CAN ALSO BE A LIMITATION IN
THE MILLIMETER WAVE REGION
)NTEREST IN MILLIMETER RADAR HAS BEEN MAINLY BECAUSE OF ITS CHALLENGES AS A FRONTIER
TO BE EXPLORED AND PUT TO PRODUCTIVE USE )TS GOOD FEATURES ARE THAT IT IS A GREAT PLACE FOR
EMPLOYING WIDE BANDWIDTH SIGNALS THERE IS PLENTY OF SPECTRUM SPACE RADARS CAN HAVE
HIGH RANGE RESOLUTION AND NARROW BEAMWIDTHS WITH SMALL ANTENNAS HOSTILE ELECTRONIC
COUNTERMEASURES TO MILITARY RADARS ARE DIFFICULT TO EMPLOY AND IT IS EASIER TO HAVE
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A MILITARY RADAR WITH LOW PROBABILITY OF INTERCEPT AT THESE FREQUENCIES THAN AT LOWER
FREQUENCIES )N THE PAST MILLIMETER WAVE TRANSMITTERS WERE NOT CAPABLE OF AN AVERAGE
POWER MORE THAN A FEW HUNDRED WATTSˆAND WERE USUALLY MUCH LESS !DVANCES IN
GYROTRONS #HAPTER CAN PRODUCE AVERAGE POWER MANY ORDERS OF MAGNITUDE GREATER
THAN MORE CONVENTIONAL MILLIMETER WAVE POWER SOURCES 4HUS AVAILABILITY OF HIGH
POWER IS NOT A LIMITATION AS IT ONCE WAS
,ASER 2ADAR ,ASERS CAN PRODUCE USABLE POWER AT OPTICAL FREQUENCIES AND IN THE
INFRARED REGION OF THE SPECTRUM 4HEY CAN UTILIZE WIDE BANDWIDTH VERY SHORT PULSES
AND CAN HAVE VERY NARROW BEAMWIDTHS !NTENNA APERTURES HOWEVER ARE MUCH SMALLER
THAN AT MICROWAVES !TTENUATION IN THE ATMOSPHERE AND RAIN IS VERY HIGH AND PER
FORMANCE IN BAD WEATHER IS QUITE LIMITED 2ECEIVER NOISE IS DETERMINED BY QUANTUM
EFFECTS RATHER THAN THERMAL NOISE &OR SEVERAL REASONS LASER RADAR HAS HAD ONLY LIMITED
APPLICATION
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-ILITARY ELECTRONIC EQUIPMENT INCLUDING RADAR IS IDENTIFIED BY THE *OINT %LECTRONICS
4YPE $ESIGNATION 3YSTEM *%4$3 AS DESCRIBED IN 53 -ILITARY 3TANDARD -), 34$
$ 4HE LETTER PORTION OF THE DESIGNATION CONSISTS OF THE LETTERS !. A SLANT BAR
AND THREE ADDITIONAL LETTERS APPROPRIATELY SELECTED TO INDICATE WHERE THE EQUIPMENT IS
INSTALLED THE TYPE OF EQUIPMENT AND ITS PURPOSE &OLLOWING THE THREE LETTERS ARE A DASH
AND A NUMERAL 4HE NUMERAL IS ASSIGNED IN SEQUENCE FOR THAT PARTICULAR COMBINATION OF
LETTERS 4ABLE SHOWS THE LETTERS THAT HAVE BEEN USED FOR RADAR DESIGNATIONS
! SUFFIX LETTER ! " # x FOLLOWS THE ORIGINAL DESIGNATION FOR EACH MODIFICATION
OF THE EQUIPMENT WHERE INTERCHANGEABILITY HAS BEEN MAINTAINED 4HE LETTER 6 IN PAREN
THESES ADDED TO THE DESIGNATION INDICATES VARIABLE SYSTEMS THOSE WHOSE FUNCTIONS
MAY BE VARIED THROUGH THE ADDITION OR DELETION OF SETS GROUPS UNITS OR COMBINATIONS
THEREOF 7HEN THE DESIGNATION IS FOLLOWED BY A DASH THE LETTER 4 AND A NUMBER THE
EQUIPMENT IS DESIGNED FOR TRAINING )N ADDITION TO THE 5NITED 3TATES THESE DESIGNA
TIONS CAN ALSO BE USED BY #ANADA !USTRALIA .EW :EALAND AND THE 5NITED +INGDOM
3PECIAL BLOCKS OF NUMBERS ARE RESERVED FOR THESE COUNTRIES &URTHER INFORMATION CAN
BE FOUND ON THE )NTERNET UNDER -), 34$ $
4HE 53 &EDERAL !VIATION !GENCY &!! USES THE FOLLOWING TO DESIGNATE THEIR AIR
TRAFFIC CONTROL RADARS
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!232
!3$%
4$72
!IRPORT 3URVEILLANCE 2ADAR
!IR 2OUTE 3URVEILLANCE 2ADAR
!IRPORT 3URFACE $ETECTION %QUIPMENT
4ERMINAL $OPPLER 7EATHER 2ADAR
4HE NUMERAL FOLLOWING THE LETTER DESIGNATION INDICATES THE PARTICULAR RADAR MODEL
IN SEQUENCE 7EATHER RADARS DEVELOPED BY THE 5 3 7EATHER 3ERVICE ./!! EMPLOY THE DES
IGNATION 732 4HE NUMBER FOLLOWING THE DESIGNATION IS THE YEAR THE RADAR WENT INTO
SERVICE 4HUS 732 $ IS THE .EXRAD DOPPLER RADAR THAT FIRST ENTERED SERVICE IN 4HE LETTER $ INDICATES IT IS A DOPPLER WEATHER RADAR
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*%4$3 ,ETTER $ESIGNATIONS THAT 0ERTAIN TO 2ADAR
)NSTALLATION FIRST LETTER
! 0ILOTED AIRCRAFT
" 5NDERWATER MOBILE
SUBMARINE
$ 0ILOTLESS CARRIER
& &IXED GROUND
4YPE OF %QUIPMENT
SECOND LETTER
, #OUNTERMEASURES
0 2ADAR
3 3PECIAL OR
COMBINATION
7 !RMAMENT
PECULIAR TO ARMAMENT
NOT OTHERWISE COVERED
' 'ENERAL GROUND USE
+ !MPHIBIOUS
- -OBILE GROUND
0URPOSE THIRD LETTER
" "OMBING
$ $IRECTION FINDER RECONNAISSANCE
AND SURVEILLANCE
' &IRE CONTROL
. .AVIGATION
1 3PECIAL OR COMBINATION
2 2ECEIVING
3 $ETECTINGRANGE AND
BEARING SEARCH
4 4RANSMITTING
7 !UTOMATIC FLIGHT OR REMOTE
CONTROL
8 )DENTIFICATION AND RECOGNITION
9 3URVEILLANCE AND CONTROL
BOTH FIRE CONTROL AND AIR CONTROL
0 0ORTABLE
3 7ATER SHIP
4 4RANSPORTABLE GROUND
5 'ENERAL UTILITY
6 6EHICULAR GROUND
7 7ATER SURFACE AND
UNDERWATER COMBINED
: 0ILOTED PILOTLESS AIRBORNE
VEHICLES COMBINED
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! BRIEF LISTING OF SOME OF THE MAJOR ADVANCES IN TECHNOLOGY AND CAPABILITY OF RADAR
IN THE TWENTIETH CENTURY IS GIVEN IN SOMEWHAT CHRONOLOGICAL BUT NOT EXACT ORDER
AS FOLLOWS
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4HE DEVELOPMENT OF 6(& RADAR FOR DEPLOYMENT ON SURFACE SHIP AND AIRCRAFT FOR
MILITARY AIR DEFENSE PRIOR TO AND DURING 7ORLD 7AR ))
4HE INVENTION OF THE MICROWAVE MAGNETRON AND THE APPLICATION OF WAVEGUIDE TECH
NOLOGY EARLY IN 77)) TO OBTAIN RADARS THAT COULD OPERATE AT MICROWAVE FREQUENCIES
SO THAT SMALLER AND MORE MOBILE RADARS COULD BE EMPLOYED
4HE MORE THAN DIFFERENT RADAR MODELS DEVELOPED AT THE -)4 2ADIATION
,ABORATORY IN ITS FIVE YEARS OF EXISTENCE DURING 77)) THAT PROVIDED THE FOUNDATION
FOR MICROWAVE RADAR
-ARCUMS THEORY OF RADAR DETECTION
4HE INVENTION AND DEVELOPMENT OF THE KLYSTRON AND 474 AMPLIFIER TUBES THAT PRO
VIDED HIGH POWER WITH GOOD STABILITY
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4HE USE OF THE DOPPLER FREQUENCY SHIFT TO DETECT MOVING TARGETS IN THE PRESENCE OF
MUCH LARGER ECHOES FROM CLUTTER
4HE DEVELOPMENT OF RADARS SUITABLE FOR AIR TRAFFIC CONTROL
0ULSE COMPRESSION
-ONOPULSE TRACKING RADAR WITH GOOD TRACKING ACCURACY AND BETTER RESISTANCE TO ELEC
TRONIC COUNTERMEASURES THAN PRIOR TRACKING RADARS
3YNTHETIC APERTURE RADAR WHICH PROVIDED IMAGES OF THE GROUND AND WHAT IS ON IT
!IRBORNE -4) !-4) FOR LONG RANGE AIRBORNE AIR SURVEILLANCE IN THE PRESENCE
OF CLUTTER
3TABLE COMPONENTS AND SUBSYSTEMS AND ULTRALOW SIDELOBE ANTENNAS THAT ALLOWED
HIGH 02& PULSE DOPPLER RADAR !7!#3 WITH LARGE REJECTION OF UNWANTED CLUTTER
(& OVER THE HORIZON RADAR THAT EXTENDED THE RANGE OF DETECTION OF AIRCRAFT AND SHIPS
BY AN ORDER OF MAGNITUDE
$IGITAL PROCESSING WHICH HAS HAD A VERY MAJOR EFFECT ON IMPROVING RADAR CAPABILI
TIES EVER SINCE THE EARLY S
!UTOMATIC DETECTION AND TRACKING FOR SURVEILLANCE RADARS
3ERIAL PRODUCTION OF ELECTRONICALLY SCANNED PHASED ARRAY RADARS
)NVERSE SYNTHETIC APERTURE RADAR )3!2 THAT PROVIDED AN IMAGE OF A TARGET AS NEEDED
FOR NONCOOPERATIVE TARGET RECOGNITION OF SHIPS
$OPPLER WEATHER RADAR
3PACE RADARS SUITABLE FOR THE OBSERVATION OF PLANETS SUCH AS 6ENUS
!CCURATE COMPUTER CALCULATION OF THE RADAR CROSS SECTION OF COMPLEX TARGETS
-ULTIFUNCTION AIRBORNE MILITARY RADAR THAT ARE RELATIVELY SMALL AND LIGHTWEIGHT THAT FIT
IN THE NOSE OF A FIGHTER AIRCRAFT AND CAN PERFORM A LARGE NUMBER OF DIFFERENT AIR TO AIR
AND AIR TO GROUND FUNCTIONS
)T IS ALWAYS A MATTER OF OPINION WHAT THE MAJOR ADVANCES IN RADAR HAVE BEEN /THERS
MIGHT HAVE A DIFFERENT LIST .OT EVERY MAJOR RADAR ACCOMPLISHMENT HAS BEEN INCLUDED
IN THIS LISTING )T COULD HAVE BEEN MUCH LONGER AND COULD HAVE INCLUDED MULTIPLE EXAM
PLES FROM EACH OF THE OTHER CHAPTERS IN THIS BOOK BUT THIS LISTING IS SUFFICIENT TO INDICATE
THE TYPE OF ADVANCES THAT HAVE BEEN IMPORTANT FOR IMPROVED RADAR CAPABILITIES
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-ILITARY !PPLICATIONS 2ADAR WAS INVENTED IN THE S BECAUSE OF THE NEED
FOR DEFENSE AGAINST HEAVY MILITARY BOMBER AIRCRAFT 4HE MILITARY NEED FOR RADAR HAS
PROBABLY BEEN ITS MOST IMPORTANT APPLICATION AND THE SOURCE OF MOST OF ITS MAJOR
DEVELOPMENTS INCLUDING THOSE FOR CIVILIAN PURPOSES
4HE CHIEF USE OF MILITARY RADAR HAS BEEN FOR AIR DEFENSE OPERATING FROM LAND SEA
OR AIR )T HAS NOT BEEN PRACTICAL TO PERFORM SUCCESSFUL AIR DEFENSE WITHOUT RADAR )N AIR
DEFENSE RADAR IS USED FOR LONG RANGE AIR SURVEILLANCE SHORT RANGE DETECTION OF LOW
ALTITUDE hPOP UPv TARGETS WEAPON CONTROL MISSILE GUIDANCE NONCOOPERATIVE TARGET
RECOGNITION AND BATTLE DAMAGE ASSESSMENT 4HE PROXIMITY FUZE IN MANY WEAPONS IS
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ALSO AN EXAMPLE OF A RADAR !N EXCELLENT MEASURE OF THE SUCCESS OF RADAR FOR MILITARY
AIR DEFENSE IS THE LARGE AMOUNTS OF MONEY THAT HAVE BEEN SPENT ON METHODS TO COUNTER
ITS EFFECTIVENESS 4HESE INCLUDE ELECTRONIC COUNTERMEASURES AND OTHER ASPECTS OF ELEC
TRONIC WARFARE ANTIRADIATION MISSILES TO HOME ON RADAR SIGNALS AND LOW CROSS SECTION
AIRCRAFT AND SHIPS 2ADAR IS ALSO USED BY THE MILITARY FOR RECONNAISSANCE TARGETING
OVER LAND OR SEA AS WELL AS SURVEILLANCE OVER THE SEA
/N THE BATTLEFIELD RADAR IS ASKED TO PERFORM THE FUNCTIONS OF AIR SURVEILLANCE INCLUD
ING SURVEILLANCE OF AIRCRAFT HELICOPTERS MISSILES AND UNMANNED AIRBORNE VEHICLES
CONTROL OF WEAPONS TO AN AIR INTERCEPT HOSTILE WEAPONS LOCATION MORTARS ARTILLERY AND
ROCKETS DETECTION OF INTRUDING PERSONNEL AND CONTROL OF AIR TRAFFIC
4HE USE OF RADAR FOR BALLISTIC MISSILE DEFENSE HAS BEEN OF INTEREST EVER SINCE THE
THREAT OF BALLISTIC MISSILES AROSE IN THE LATE S 4HE LONGER RANGES HIGH SUPERSONIC
SPEEDS AND THE SMALLER TARGET SIZE OF BALLISTIC MISSILES MAKE THE PROBLEM CHALLENGING
4HERE IS NO NATURAL CLUTTER PROBLEM IN SPACE AS THERE IS FOR DEFENSE AGAINST AIRCRAFT
BUT BALLISTIC MISSILES CAN APPEAR IN THE PRESENCE OF A LARGE NUMBER OF EXTRANEOUS CON
FUSION TARGETS AND OTHER COUNTERMEASURES THAT AN ATTACKER CAN LAUNCH TO ACCOMPANY
THE REENTRY VEHICLE CARRYING A WARHEAD 4HE BASIC BALLISTIC MISSILE DEFENSE PROBLEM
BECOMES MORE OF A TARGET RECOGNITION PROBLEM RATHER THAN DETECTION AND TRACKING
4HE NEED FOR WARNING OF THE APPROACH OF BALLISTIC MISSILES HAS RESULTED IN A NUMBER OF
DIFFERENT TYPES OF RADARS FOR PERFORMING SUCH A FUNCTION 3IMILARLY RADARS HAVE BEEN
DEPLOYED THAT ARE CAPABLE OF DETECTING AND TRACKING SATELLITES
! RELATED TASK FOR RADAR THAT IS NOT MILITARY IS THE DETECTION AND INTERCEPTION OF DRUG
TRAFFIC 4HERE ARE SEVERAL TYPES OF RADARS THAT CAN CONTRIBUTE TO THIS NEED INCLUDING THE
LONG RANGE (& OVER THE HORIZON RADAR
2EMOTE 3ENSING OF THE %NVIRONMENT 4HE MAJOR APPLICATION IN THIS CATEGORY
HAS BEEN WEATHER OBSERVATION RADAR SUCH AS THE .EXRAD SYSTEM WHOSE OUTPUT IS OFTEN
SEEN ON THE TELEVISION WEATHER REPORT 4HERE ALSO EXIST VERTICAL LOOKING WIND PROFILER
RADARS THAT DETERMINE WIND SPEED AND DIRECTION AS A FUNCTION OF ALTITUDE BY DETECTING
THE VERY WEAK RADAR ECHO FROM THE CLEAR AIR ,OCATED AROUND AIRPORTS ARE THE 4ERMINAL
$OPPLER 7EATHER 2ADAR 4$72 SYSTEMS THAT WARN OF DANGEROUS WIND SHEAR PRODUCED
BY THE WEATHER EFFECT KNOWN AS THE DOWNBURST WHICH CAN ACCOMPANY SEVERE STORMS
4HERE IS USUALLY A SPECIALLY DESIGNED WEATHER AVOIDANCE RADAR IN THE NOSE OF SMALL AS
WELL AS LARGE AIRCRAFT TO WARN OF DANGEROUS OR UNCOMFORTABLE WEATHER IN FLIGHT
!NOTHER SUCCESSFUL REMOTE SENSING RADAR WAS THE DOWNWARD LOOKING SPACEBORNE
ALTIMETER RADAR THAT MEASURED WORLDWIDE THE GEOID THE MEAN SEA LEVEL WHICH IS NOT
THE SAME ALL OVER THE WORLD WITH EXCEPTIONALLY HIGH ACCURACY 4HERE HAVE BEEN
ATTEMPTS IN THE PAST TO USE RADAR FOR DETERMINING SOIL MOISTURE AND FOR ASSESSING THE
STATUS OF AGRICULTURE CROPS BUT THESE HAVE NOT PROVIDED SUFFICIENT ACCURACY )MAGING
RADARS IN SATELLITES OR AIRCRAFT HAVE BEEN USED TO HELP SHIPS EFFICIENTLY NAVIGATE NORTH
ERN SEAS COATED WITH ICE BECAUSE RADAR CAN TELL WHICH TYPES OF ICE ARE EASIER FOR A SHIP
TO PENETRATE
!IR 4RAFFIC #ONTROL 4HE HIGH DEGREE OF SAFETY IN MODERN AIR TRAVEL IS DUE IN PART
TO THE SUCCESSFUL APPLICATIONS OF RADAR FOR THE EFFECTIVE EFFICIENT AND SAFE CONTROL OF
AIR TRAFFIC -AJOR AIRPORTS EMPLOY AN !IRPORT 3URVEILLANCE 2ADAR !32 FOR OBSERVING
THE AIR TRAFFIC IN THE VICINITY OF THE AIRPORT 3UCH RADARS ALSO PROVIDE INFORMATION ABOUT
NEARBY WEATHER SO AIRCRAFT CAN BE ROUTED AROUND UNCOMFORTABLE WEATHER -AJOR AIRPORTS
ALSO HAVE A RADAR CALLED !IRPORT 3URFACE $ETECTION %QUIPMENT !3$% FOR OBSERVING
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AND SAFELY CONTROLLING AIRCRAFT AND AIRPORT VEHICLE TRAFFIC ON THE GROUND &OR CONTROL OF
AIR TRAFFIC EN ROUTE FROM ONE TERMINAL TO ANOTHER LONG RANGE !IR 2OUTE 3URVEILLANCE
2ADARS !232 ARE FOUND WORLDWIDE 4HE !IR 4RAFFIC #ONTROL 2ADAR "EACON 3YSTEM
!4#2"3 IS NOT A RADAR BUT IS A COOPERATIVE SYSTEM USED TO IDENTIFY AIRCRAFT IN FLIGHT )T
USES RADAR LIKE TECHNOLOGY AND WAS ORIGINALLY BASED ON THE MILITARY )&& )DENTIFICATION
&RIEND OR &OE SYSTEM
/THER !PPLICATIONS ! HIGHLY SIGNIFICANT APPLICATION OF RADAR THAT PROVIDED
INFORMATION NOT AVAILABLE BY ANY OTHER METHOD WAS THE EXPLORATION OF THE SURFACE
OF THE PLANET 6ENUS BY AN IMAGING RADAR THAT COULD SEE UNDER THE EVER PRESENT CLOUDS
THAT MASK THE PLANET /NE OF THE WIDEST USED AND LEAST EXPENSIVE OF RADARS HAS BEEN
THE CIVIL MARINE RADAR FOUND THROUGHOUT THE WORLD FOR THE SAFE NAVIGATION OF BOATS AND
SHIPS 3OME READERS HAVE UNDOUBTEDLY BEEN CONFRONTED BY THE HIGHWAY POLICE USING
THE #7 DOPPLER RADAR TO MEASURE THE SPEED OF A VEHICLE 'ROUND PENETRATING RADAR
HAS BEEN USED TO FIND BURIED UTILITY LINES AS WELL AS BY THE POLICE FOR LOCATING BURIED
OBJECTS AND BODIES !RCHEOLOGISTS HAVE USED IT TO DETERMINE WHERE TO BEGIN TO LOOK
FOR BURIED ARTIFACTS 2ADAR HAS BEEN HELPFUL TO BOTH THE ORNITHOLOGIST AND ENTOMOLOGIST
FOR BETTER UNDERSTANDING THE MOVEMENTS OF BIRDS AND INSECTS )T HAS ALSO BEEN DEM
ONSTRATED THAT RADAR CAN DETECT THE GAS SEEPAGE THAT IS OFTEN FOUND OVER UNDERGROUND
OIL AND GAS DEPOSITS
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4HERE ARE VARIOUS ASPECTS TO RADAR SYSTEM DESIGN "UT BEFORE A NEW RADAR THAT HAS NOT
EXISTED PREVIOUSLY CAN BE MANUFACTURED A CONCEPTUAL DESIGN HAS TO BE PERFORMED TO
GUIDE THE ACTUAL DEVELOPMENT ! CONCEPTUAL DESIGN IS BASED ON THE REQUIREMENTS FOR
THE RADAR THAT WILL SATISFY THE CUSTOMER OR USER OF THE RADAR 4HE RESULT OF A CONCEPTUAL
DESIGN EFFORT IS TO PROVIDE A LIST OF THE RADAR CHARACTERISTICS AS FOUND IN THE RADAR EQUA
TION AND RELATED EQUATIONS AND THE GENERAL CHARACTERISTICS OF THE SUBSYSTEMS TRANSMIT
TER ANTENNA RECEIVER SIGNAL PROCESSING AND SO FORTH THAT MIGHT BE EMPLOYED 4HE
RADAR EQUATION IS USED AS AN IMPORTANT GUIDE FOR DETERMINING THE VARIOUS TRADEOFFS AND
OPTIONS AVAILABLE TO THE RADAR SYSTEM DESIGNER SO AS TO DETERMINE A SUITABLE CONCEPT TO
MEET THE DESIRED NEED 4HIS SECTION BRIEFLY SUMMARIZES HOW A RADAR SYSTEMS ENGINEER
MIGHT BEGIN TO APPROACH THE CONCEPTUAL DESIGN OF A NEW RADAR 4HERE ARE NO FIRMLY
ESTABLISHED PROCEDURES TO CARRY OUT A CONCEPTUAL DESIGN %VERY RADAR COMPANY AND
EVERY RADAR DESIGN ENGINEER DEVELOPS HIS OR HER OWN STYLE 7HAT IS DESCRIBED HERE IS A
BRIEF SUMMARY OF ONE APPROACH TO CONCEPTUAL RADAR DESIGN
'ENERAL 'UIDELINE )T SHOULD BE MENTIONED THAT THERE ARE AT LEAST TWO WAYS BY
WHICH A NEW RADAR SYSTEM MIGHT BE PRODUCED FOR SOME PARTICULAR RADAR APPLICATION /NE
METHOD IS BASED ON EXPLOITING THE ADVANTAGES OF SOME NEW INVENTION NEW TECHNIQUE
NEW DEVICE OR NEW KNOWLEDGE 4HE INVENTION OF THE MICROWAVE MAGNETRON EARLY IN
7ORLD 7AR )) IS AN EXAMPLE !FTER THE MAGNETRON APPEARED RADAR DESIGN WAS DIFFERENT
FROM WHAT IT HAD BEEN BEFORE 4HE OTHER AND PROBABLY MORE COMMON METHOD FOR CON
CEPTUAL RADAR SYSTEM DESIGN IS TO START WITH WHAT THE NEW RADAR HAS TO DO EXAMINE THE
VARIOUS APPROACHES AVAILABLE TO ACHIEVE THE DESIRED CAPABILITY CAREFULLY EVALUATE EACH
APPROACH AND THEN SELECT THE ONE THAT BEST MEETS THE NEEDS WITHIN THE OPERATIONAL AND
FISCAL CONSTRAINTS IMPOSED )N BRIEF IT MIGHT CONSIST OF THE FOLLOWING STEPS
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$ESCRIPTION OF THE NEED OR PROBLEM TO BE SOLVED
4HIS IS FROM THE VIEWPOINT OF THE CUSTOMER OR THE USER OF THE RADAR
)NTERACTION BETWEEN THE CUSTOMER AND THE SYSTEMS ENGINEER
4HIS IS FOR THE PURPOSE OF EXPLORING THE TRADEOFFS WHICH THE CUSTOMER MIGHT NOT
BE AWARE OF THAT MIGHT ALLOW THE CUSTOMER TO BETTER OBTAIN WHAT IS WANTED WITH
OUT EXCESSIVE COST OR RISK 5NFORTUNATELY INTERACTION BETWEEN THE POTENTIAL USER
OF THE RADAR AND THE RADAR SYSTEMS ENGINEER IS NOT ALWAYS DONE IN COMPETITIVE
PROCUREMENTS
)DENTIFICATION AND EXPLORATION OF POSSIBLE SOLUTIONS
4HIS INCLUDES UNDERSTANDING THE ADVANTAGES AND LIMITATIONS OF THE VARIOUS POS
SIBLE SOLUTIONS
3ELECTION OF THE OPTIMUM OR NEAR OPTIMUM SOLUTION
)N MANY ENGINEERING ENDEAVORS OPTIMUM DOES NOT MEAN THE BEST SINCE THE BEST
MIGHT NOT BE AFFORDABLE OR ACHIEVABLE IN THE REQUIRED TIME /PTIMUM AS USED HERE
MEANS THE BEST UNDER A GIVEN SET OF ASSUMPTIONS %NGINEERING OFTEN INVOLVES ACHIEV
ING A NEAR OPTIMUM NOT THE OPTIMUM 3ELECTING THE PREFERRED SOLUTION SHOULD BE
BASED ON A WELL DEFINED CRITERION
$ETAILED DESCRIPTION OF THE SELECTED APPROACH
4HIS IS IN TERMS OF THE CHARACTERISTICS OF THE RADAR AND THE TYPE OF SUBSYSTEMS TO
BE EMPLOYED
!NALYSIS AND EVALUATION OF THE PROPOSED DESIGN
4HIS IS TO VERIFY THE CORRECTNESS OF THE SELECTED APPROACH
!S ONE PROCEEDS THROUGH THIS PROCESS ONE MIGHT REACH A hDEAD ENDv AND HAVE TO
START OVERˆSOMETIMES MORE THAN ONCE (AVING TO START OVER IS NOT UNUSUAL DURING A
NEW DESIGN EFFORT
/NE CANNOT DEVISE A UNIQUE SET OF GUIDELINES FOR PERFORMING THE DESIGN OF A RADAR
)F THAT WERE POSSIBLE RADAR DESIGN COULD BE DONE ENTIRELY BY COMPUTER "ECAUSE OF THE
USUAL LACK OF COMPLETE INFORMATION MOST ENGINEERING DESIGN REQUIRES AT SOME POINT
THE JUDGMENT AND EXPERIENCE OF THE DESIGN ENGINEER IN ORDER TO SUCCEED
4HE 2ADAR %QUATION IN #ONCEPTUAL $ESIGN 4HE RADAR EQUATION IS THE BASIS
FOR CONCEPTUAL RADAR SYSTEM DESIGN 3OME PARAMETERS OF THE RADAR EQUATION ARE DETER
MINED BY WHAT THE RADAR IS REQUIRED TO DO /THERS MAY BE DECIDED UPON UNILATERALLY BY
THE CUSTOMERˆBUT THAT SHOULD BE DONE WITH CAUTION 4HE CUSTOMER USUALLY SHOULD BE
THE ONE WHO STATES THE NATURE OF THE RADAR TARGET THE ENVIRONMENT IN WHICH THE RADAR
IS TO OPERATE RESTRICTIONS ON SIZE AND WEIGHT THE USE TO WHICH THE RADAR INFORMATION
IS TO BE PUT AND ANY OTHER CONSTRAINTS THAT HAVE TO BE IMPOSED &ROM THIS INFORMATION
THE RADAR SYSTEMS ENGINEER DETERMINES WHAT IS THE RADAR CROSS SECTION OF THE TARGET
THE RANGE AND ANGLE ACCURACIES NEEDED TO MEET THE RADAR USERS NEEDS AS WELL AS THE
ANTENNA REVISIT TIME 3OME PARAMETERS SUCH AS ANTENNA GAIN MIGHT BE AFFECTED BY
MORE THAN ONE NEED OR REQUIREMENT &OR INSTANCE A PARTICULAR ANTENNA BEAMWIDTH
MIGHT BE INFLUENCED BY THE TRACKING ACCURACY RESOLUTION OF NEARBY TARGETS THE MAXI
MUM SIZE THE ANTENNA CAN BE FOR A PARTICULAR APPLICATION THE NEED FOR A DESIRED RADAR
RANGE AND THE CHOICE OF RADAR FREQUENCY 4HE RADAR FREQUENCY IS USUALLY AFFECTED BY
MANY THINGS INCLUDING THE AVAILABILITY OF ALLOWED FREQUENCIES AT WHICH TO OPERATE
4HE RADAR FREQUENCY MIGHT BE THE LAST PARAMETER OF THE RADAR TO BE SELECTEDˆAFTER
MANY OTHER COMPROMISES HAVE BEEN MADE
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)%%% 4RANS VOL !%3 PP n /CTOBER - ) 3KOLNIK )NTRODUCTION TO 2ADAR 3YSTEMS .EW 9ORK -C'RAW (ILL &IG & % .ATHANSON 2ADAR $ESIGN 0RINCIPLES .EW 9ORK -C'RAW (ILL &IG 4HIS TABLE HAS BEEN DERIVED FROM )%%% 3TANDARD ,ETTER $ESIGNATIONS FOR 2ADAR &REQUENCY "ANDS
)%%% 3TD 3PECIFIC RADIOLOCATION FREQUENCY RANGES MAY BE FOUND IN THE h&## /NLINE 4ABLE OF &REQUENCY
!LLOCATIONS v #&2 e h0ERFORMING ELECTRONIC COUNTERMEASURES IN THE 5NITED 3TATES AND #ANADA v 53 .AVY
/0.!6).34 " /CTOBER 3IMILAR VERSIONS ISSUED BY THE 53 !IR &ORCE
!&2 53 !RMY !2 AND 53 -ARINE #ORPS -#/ ! :ACHEPITSKY h6(& METRIC BAND RADARS FROM .IZHNY .OVGOROD 2ESEARCH 2ADIOTECHNICAL
)NSTITUTE v )%%% !%3 3YSTEMS -AGAZINE VOL PP n *UNE !NONYMOUS h!7!#3 VS %# BATTLE A STANDOFF v %7 -AGAZINE P -AY*UNE - 3KOLNIK $ (EMENWAY AND * 0 (ANSEN h2ADAR DETECTION OF GAS SEEPAGE ASSOCIATED WITH OIL
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Ó°£Ê *, 4HIS CHAPTER ADDRESSES SURFACE BASED RADARS EG RADARS SITED ON LAND OR INSTALLED
ONBOARD SHIPS &OR AIRBORNE RADAR RAPID PLATFORM MOTION HAS A SIGNIFICANT EFFECT ON
DESIGN AND PERFORMANCE AS DISCUSSED IN #HAPTERS AND OF THIS (ANDBOOK
4HE FUNDAMENTAL THEORY OF MOVING TARGET INDICATION -4) RADAR AS PRESENTED IN THE
PREVIOUS EDITIONS OF THE 2ADAR (ANDBOOK HAS NOT MATERIALLY CHANGED 4HE PERFORMANCE
OF -4) RADAR HOWEVER HAS BEEN GREATLY IMPROVED DUE PRIMARILY TO FOUR ADVANCES
INCREASED STABILITY OF RADAR SUBSYSTEMS SUCH AS TRANSMITTERS OSCILLATORS AND RECEIVERS
INCREASED DYNAMIC RANGE OF RECEIVERS AND ANALOG TO DIGITAL CONVERTERS !$ FASTER AND MORE POWERFUL DIGITAL PROCESSING AND BETTER AWARENESS OF THE LIMITA
TIONS AND THEREFORE REQUISITE SOLUTIONS OF ADAPTING -4) SYSTEMS TO THE ENVIRONMENT 4HESE
FOUR ADVANCES HAVE MADE IT PRACTICAL TO USE SOPHISTICATED TECHNIQUES THAT WERE CONSIDERED
AND SOMETIMES TRIED MANY YEARS AGO BUT WERE IMPRACTICAL TO IMPLEMENT %XAMPLES OF
EARLY CONCEPTS THAT WERE WELL AHEAD OF THE AVAILABLE TECHNOLOGY WERE THE VELOCITY INDICAT
ING COHERENT INTEGRATOR 6)#) AND THE COHERENT MEMORY FILTER #-& !LTHOUGH THESE IMPROVEMENTS HAVE ENABLED MUCH IMPROVED -4) CAPABILITIES
THERE ARE STILL NO PERFECT SOLUTIONS TO ALL -4) RADAR PROBLEMS AND THE DESIGN OF AN -4)
SYSTEM IS STILL AS MUCH OF AN ART AS IT IS A SCIENCE %XAMPLES OF CURRENT PROBLEMS INCLUDE
THE FACT THAT WHEN RECEIVERS ARE BUILT WITH INCREASED DYNAMIC RANGE SYSTEM INSTABILITY
LIMITATIONS WILL CAUSE INCREASED CLUTTER RESIDUE RELATIVE TO SYSTEM NOISE THAT CAN CAUSE
FALSE DETECTIONS #LUTTER MAPS WHICH ARE USED TO PREVENT FALSE DETECTIONS FROM CLUTTER
RESIDUE WORK QUITE WELL ON FIXED RADAR SYSTEMS BUT ARE DIFFICULT TO IMPLEMENT ON FOR
EXAMPLE SHIPBOARD RADARS BECAUSE AS THE SHIP MOVES THE ASPECT AND RANGE TO EACH
CLUTTER PATCH CHANGES CREATING INCREASED RESIDUES AFTER THE CLUTTER MAP ! DECREASE IN
THE RESOLUTION OF THE CLUTTER MAP TO COUNTER THE RAPIDLY CHANGING CLUTTER RESIDUE WILL
PRECLUDE MUCH OF THE INTERCLUTTER VISIBILITY SEE LATER IN THIS CHAPTER WHICH IS ONE OF
THE LEAST APPRECIATED SECRETS OF SUCCESSFUL -4) OPERATION
-4) RADAR MUST WORK IN THE ENVIRONMENT THAT CONTAINS STRONG FIXED CLUTTER BIRDS BATS
AND INSECTS WEATHER AUTOMOBILES AND DUCTING 4HE DUCTING ALSO REFERRED TO AS ANOMA
LOUS PROPAGATION CAUSES RADAR RETURNS FROM CLUTTER ON THE SURFACE OF THE %ARTH TO APPEAR
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AT GREATLY EXTENDED RANGES WHICH EXACERBATES THE PROBLEMS WITH BIRDS AND AUTOMOBILES
AND CAN ALSO CAUSE THE DETECTION OF FIXED CLUTTER HUNDREDS OF KILOMETERS AWAY
4HE CLUTTER MODELS CONTAINED IN THIS CHAPTER ARE APPROXIMATIONS OF THE TYPES OF
CLUTTER THAT MUST BE ADDRESSED 4HE EXACT QUANTITATIVE DATA SUCH AS PRECISE SPECTRUM
AND AMPLITUDE OF EACH TYPE OF CLUTTER OR THE EXACT NUMBER OF BIRDS OR POINT REFLECTORS
EG WATER TOWERS OR OIL WELL DERRICKS PER UNIT AREA IS NOT IMPORTANT BECAUSE THE -4)
RADAR DESIGNER MUST CREATE A ROBUST SYSTEM THAT WILL FUNCTION WELL NO MATTER THE ACTUAL
DEVIATION FROM THE CLUTTER MODELS OF REAL CLUTTER ENCOUNTERED
-4) RADARS MAY USE ROTATING ANTENNAS OR FIXED APERTURES WITH ELECTRONIC BEAM SCAN
NING PHASED ARRAYS 4HE ROTATING ANTENNA MAY USE A CONTINUOUS WAVEFORM PROCESSED
THROUGH EITHER A FINITE IMPULSE RESPONSE &)2 FILTER OR AN INFINITE IMPULSE RESPONSE
))2 FILTER OR MAY USE A BATCH WAVEFORM CONSISTING OF COHERENT PROCESSING INTERVALS
#0)S THAT ARE PROCESSED IN &)2 FILTERS IN GROUPS OF . PULSES 4HE TERM -4) FILTER
USED OFTEN IN THIS CHAPTER IS A GENERIC NOMENCLATURE THAT INCLUDES BOTH &)2 AND ))2
FILTERS 4HE FINITE TIME ON TARGET DICTATES THE NEED FOR A BATCH PROCESSING APPROACH
4HERE ARE MANY DIFFERENT COMBINATIONS OF SUCCESSFUL -4) TECHNIQUES BUT ANY SPE
CIFIC -4) RADAR SYSTEM MUST BE A TOTAL CONCEPT BASED ON THE PARAMETERS OF THE ANTENNA
TRANSMITTER WAVEFORM SIGNAL PROCESSING AND THE OPERATIONAL ENVIRONMENT
! NUMBER OF PLAN POSITION INDICATOR 00) PHOTOGRAPHS TAKEN YEARS AGO ARE
INCLUDED IN THIS CHAPTER TO PROVIDE A BETTER UNDERSTANDING OF THE ENVIRONMENT THAT IS
DIFFICULT TO APPRECIATE WITH MANY MODERN RADARS 4HESE PHOTOGRAPHS SHOW -4) OPERA
TION BIRDS INSECTS AND DUCTING BETTER THAN CAN BE DESCRIBED IN WORDS
!TTENTION IS ESPECIALLY DIRECTED TO THE FINAL SECTION IN THIS CHAPTER h#ONSIDERATIONS
!PPLICABLE TO -4) 2ADAR 3YSTEMS v WHICH PROVIDES INSIGHT INTO BOTH HARDWARE AND
ENVIRONMENTAL LESSONS LEARNED DURING MANY DECADES OF -4) SYSTEM DEVELOPMENT
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4HE PURPOSE OF -4) RADAR IS TO REJECT RETURNS FROM FIXED OR SLOW MOVING UNWANTED
TARGETS SUCH AS BUILDINGS HILLS TREES SEA AND RAIN AND RETAIN FOR DETECTION OR DISPLAY
SIGNALS FROM MOVING TARGETS SUCH AS AIRCRAFT &IGURE SHOWS A PAIR OF PHOTOGRAPHS
OF A 00) WHICH ILLUSTRATES THE EFFECTIVENESS OF SUCH AN -4) SYSTEM 4HE DISTANCE FROM
THE CENTER TO THE EDGE OF THE 00) IS NMI 4HE RANGE MARKS ARE AT NMI INTERVALS
4HE PICTURE ON THE LEFT IS THE NORMAL VIDEO DISPLAY SHOWING MAINLY THE FIXED TARGET
RETURNS 4HE PICTURE ON THE RIGHT SHOWS THE EFFECTIVENESS OF THE -4) CLUTTER REJECTION
4HE CAMERA SHUTTER WAS LEFT OPEN FOR THREE SCANS OF THE ANTENNA THUS AIRCRAFT SHOW UP
AS A SUCCESSION OF THREE RETURNS -4) RADAR UTILIZES THE DOPPLER SHIFT IMPARTED ON THE
REFLECTED SIGNAL BY A MOVING TARGET TO DISTINGUISH MOVING TARGETS FROM FIXED TARGETS )N
A PULSE RADAR SYSTEM THIS DOPPLER SHIFT APPEARS AS A CHANGE OF PHASE OF RECEIVED SIG
NALS BETWEEN CONSECUTIVE RADAR PULSES #ONSIDER A RADAR THAT TRANSMITS A PULSE OF RADIO
FREQUENCY 2& ENERGY THAT IS REFLECTED BY BOTH A BUILDING FIXED TARGET AND AN AIRPLANE
MOVING TARGET APPROACHING THE RADAR 4HE REFLECTED PULSES RETURN TO THE RADAR A CERTAIN
TIME LATER 4HE RADAR THEN TRANSMITS A SECOND PULSE 4HE REFLECTION FROM THE BUILDING
OCCURS IN EXACTLY THE SAME AMOUNT OF TIME BUT THE REFLECTION FROM THE MOVING AIRCRAFT
OCCURS IN LESS TIME BECAUSE THE AIRCRAFT HAS MOVED CLOSER TO THE RADAR IN THE INTERVAL
BETWEEN TRANSMITTED PULSES 4HE PRECISE TIME THAT IT TAKES THE REFLECTED SIGNAL TO REACH
THE RADAR IS NOT OF FUNDAMENTAL IMPORTANCE 7HAT IS SIGNIFICANT IS WHETHER THE TIME
CHANGES BETWEEN PULSES 4HE TIME CHANGE WHICH IS OF THE ORDER OF A FEW NANOSECONDS
FOR AN AIRCRAFT TARGET IS DETERMINED BY COMPARING THE PHASE OF THE RECEIVED SIGNAL WITH
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&)'52% A .ORMAL VIDEO AND B -4) VIDEO 4HESE 00) PHOTOGRAPHS SHOW HOW EFFECTIVE AN -4)
SYSTEM CAN BE !IRCRAFT APPEAR AS THREE CONSECUTIVE BLIPS IN THE RIGHT HAND PICTURE BECAUSE THE CAMERA SHUTTER
WAS OPEN FOR THREE REVOLUTIONS OF THE ANTENNA 4HE 00) RANGE IS NMI
THE PHASE OF A REFERENCE OSCILLATOR IN THE RADAR )F THE TARGET MOVES BETWEEN PULSES THE
PHASE OF THE RECEIVED PULSE CHANGES
&IGURE SHOWS A SIMPLIFIED BLOCK DIAGRAM OF A COHERENT -4) SYSTEM 4HE 2&
OSCILLATOR FEEDS THE PULSED AMPLIFIER WHICH TRANSMITS THE PULSES 4HE 2& OSCILLATOR
&)'52% 3IMPLIFIED BLOCK DIAGRAM OF A COHERENT -4) SYSTEM
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IS ALSO USED AS A PHASE REFERENCE FOR DETERMINING THE PHASE OF REFLECTED SIGNALS 4HE
PHASE INFORMATION IS STORED IN A PULSE REPETITION INTERVAL 02) MEMORY FOR THE PERIOD
4 BETWEEN TRANSMITTED PULSES AND IS SUBTRACTED FROM THE PHASE INFORMATION FROM THE
CURRENT RECEIVED PULSE 4HERE IS AN OUTPUT FROM THE SUBTRACTOR ONLY WHEN A REFLECTION
HAS OCCURRED FROM A MOVING TARGET
-OVING 4ARGET )NDICATOR -4) "LOCK $IAGRAM ! MORE COMPLETE BLOCK DIA
GRAM OF AN -4) RADAR IS SHOWN IN &IGURE 4HIS BLOCK DIAGRAM IS REPRESENTATIVE OF A
MODERN AIR TRAFFIC CONTROL RADAR OPERATING AT , OR 3 BAND WITH A TYPICAL INTERPULSE PERIOD
OF n MS AND A #7 PULSE LENGTH OF A FEW MS WHEN THE TRANSMITTER EMPLOYS A VACUUM
TUBE AMPLIFIER SUCH AS FOR EXAMPLE A KLYSTRON OR TENS OF MS FOR A PULSE COMPRESSION
WAVEFORM WHEN A SOLID STATE TRANSMITTER IS USED 4HE RECEIVED SIGNALS ARE AMPLIFIED IN
A LOW NOISE AMPLIFIER ,.! AND SUBSEQUENTLY DOWNCONVERTED THROUGH ONE OR MORE
INTERMEDIATE FREQUENCIES )& BY MIXING WITH STABLE LOCAL OSCILLATORS ! BANDPASS )&
LIMITER AT THE RECEIVER OUTPUT PROTECTS THE !$ CONVERTER FROM DAMAGE BUT ALSO PREVENTS
LIMITING FROM TAKING PLACE IN THE !$ CONVERTER )N EARLY -4) SYSTEMS THE )& LIM
ITER SERVED THE PURPOSE OF DELIBERATELY RESTRICTING THE DYNAMIC RANGE TO REDUCE CLUTTER
RESIDUES AT THE -4) OUTPUT 4HE RECEIVED SIGNALS ARE THEN CONVERTED INTO IN PHASE AND
QUADRATURE COMPONENTS ) 1 THROUGH THE !$ CONVERTER EITHER USING A PAIR OF PHASE
DETECTORS OR THROUGH DIRECT SAMPLING AS DISCUSSED IN 3ECTION 4HE IN PHASE ) AND
QUADRATURE 1 OUTPUTS ARE A FUNCTION OF THE AMPLITUDE AND PHASE OF THE )& SIGNAL AND
&)'52% -4) SYSTEM BLOCK DIAGRAM
-4) 2!$!2
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&)'52% "IPOLAR VIDEO RETURN FROM SINGLE TRANSMITTER PULSE
HAVE IN THE PAST BEEN REFERRED TO AS BIPOLAR VIDEOS BUT A MORE CORRECT TERMINOLOGY IS
THAT OF THE COMPLEX ENVELOPE OF THE RECEIVED SIGNALS !N EXAMPLE OF SUCH A BIPOLAR
VIDEO EITHER ) OR 1 RECEIVED FROM A SINGLE TRANSMITTED PULSE AND INCLUDING BOTH CLUT
TER AND POINT TARGETS IS SKETCHED IN &IGURE )F THE POINT TARGETS ARE MOVING THE SUPER
IMPOSED BIPOLAR VIDEO FROM SEVERAL TRANSMITTED PULSES WOULD APPEAR AS IN &IGURE 4HE REMAINDER OF THE BLOCK DIAGRAM IN &IGURE SHOWS THE REMAINING PROCESS
ING REQUIRED SO THAT THE MOVING TARGETS CAN BE DISPLAYED ON A 00) OR SENT TO AN AUTO
MATIC TARGET EXTRACTOR 4HE IN PHASE AND QUADRATURE OUTPUTS FROM THE !$ CONVERTER ARE
STORED IN A 02) MEMORY AND ALSO SUBTRACTED FROM THE OUTPUT FROM THE PREVIOUS TRANS
MITTED PULSE 4HIS IMPLEMENTATION REPRESENTS THE MOST BASIC TWO PULSE -4) CANCELER
IMPLEMENTED AS A FINITE IMPULSE RESPONSE &)2 FILTER !S DISCUSSED IN 3ECTION -4)
CANCELERS USED IN PRACTICAL RADARS USE HIGHER ORDER FILTERS AND THESE ARE SOMETIMES
IMPLEMENTED AS INFINITE IMPULSE RESPONSE ))2 FILTERS
4HE OUTPUT OF THE SUBTRACTORS IS AGAIN A BIPOLAR SIGNAL THAT CONTAINS MOVING TAR
GETS SYSTEM NOISE AND A SMALL AMOUNT OF CLUTTER RESIDUE IF THE CLUTTER CANCELLATION
IS NOT PERFECT 4HE MAGNITUDES OF THE IN PHASE AND QUADRATURE SIGNALS ARE THEN COM
PUTED ) 1 AND CONVERTED TO ANALOG VIDEO IN A DIGITAL TO ANALOG $! CON
VERTER FOR DISPLAY ON A 00) 4HE DIGITAL SIGNAL MAY ALSO BE SENT TO AUTOMATIC TARGET
DETECTION CIRCUITRY 4HE DYNAMIC RANGE PEAK SIGNAL TO RMS NOISE IS LIMITED TO ABOUT
D" FOR A 00) DISPLAY
! KEY DISTINCTION SOMETIMES LOST IN THE COMPLEXITIES OF THE SYSTEMS THAT FOLLOW IS
THAT AN -4) RADAR SYSTEM ELIMINATES FIXED CLUTTER BECAUSE THE PHASE OF SIGNALS RETURNED
FROM CONSECUTIVE TRANSMITTED PULSES DO NOT APPRECIABLY CHANGE 4HE FIXED CLUTTER IS
REMOVED AFTER AS FEW AS TWO TRANSMITTED PULSES BY THE SUBTRACTION PROCESS DESCRIBED
&)'52% "IPOLAR VIDEO FROM CONSECUTIVE TRANSMITTED PULSES
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ABOVE EVEN IF EACH TRANSMITTED PULSE HAS FREQUENCY MODULATION OR OTHER ARTIFACTS AS
LONG AS THE ARTIFACTS ARE IDENTICAL PULSE TO PULSE 4HE POINT BEING MADE HERE IS THAT -4)
SYSTEM OPERATION DOES NOT DEPEND ON THE FREQUENCY RESOLUTION OF TARGETS FROM CLUTTER
4O PROVIDE FREQUENCY RESOLUTION WOULD REQUIRE MUCH LONGER DWELL TIMES ON TARGET THAN
TWO PULSES SEPARATED BY A SINGLE 02) 3UCH EXTENDED DWELL TIMES IS ONE OF THE FUNDA
MENTAL CHARACTERISTICS OF THE MOVING TARGET DETECTOR
-OVING 4ARGET $ETECTOR -4$ "LOCK $IAGRAM 0ROGRESS IN DIGITAL SIGNAL
PROCESSING TECHNOLOGY BY THE MID S MADE IT PRACTICAL FOR THE FIRST TIME TO IMPROVE
THE PERFORMANCE OF THE CLASSICAL -4) BY IMPLEMENTING A PARALLEL BANK OF &)2 FILTERS
TO INCREASE THE OUTPUT SIGNAL TO CLUTTER RATIO AND REPLACING THE )& LIMITER USED IN
THE PAST WITH A HIGH RESOLUTION CLUTTER MAP FOR EFFECTIVE FALSE ALARM CONTROL !LTHOUGH
THESE CONCEPTS HAD BEEN EXPLORED MANY YEARS EARLIER USING THE 6ELOCITY )NDICATING
#OHERENT )NTEGRATOR 6)#) OR THE #OHERENT -EMORY &ILTER #-& TO IMPLEMENT A
DOPPLER FILTER BANK AND STORAGE TUBES OR MAGNETIC DRUM MEMORY TO IMPLEMENT CLUT
TER MAPS IT WAS THE WORK AT THE -)4 ,INCOLN ,ABORATORY TO IMPROVE THE PERFORMANCE
OF AIRPORT SURVEILLANCE RADARS THAT RESULTED IN ONE OF THE FIRST WORKING EXAMPLES OF
WHAT HAS BECOME KNOWN AS THE -OVING 4ARGET $ETECTION -4$ RADAR 4HE THEORY
AND EXPECTED BENEFITS OF THIS APPROACH WERE DESCRIBED IN TWO REPORTS IN WHICH
PROVIDED THE MATHEMATICAL FOUNDATION FOR THE UNDERSTANDING AND THE PRACTICAL IMPLE
MENTATION OF THE -4$ CONCEPT
4HE PREDICTED SUBCLUTTER VISIBILITY IMPROVEMENT FOR THE !32 AIRPORT SURVEILLANCE
RADAR WHEN THE THREE PULSE -4) PROCESSOR WAS REPLACED BY THE SECOND GENERATION
-4$ )) PROCESSOR IS SHOWN IN &IGURE ! "
# # &)'52% 3UBCLUTTER VISIBILITY COMPARISON BETWEEN THREE PULSE -4) AND -4$ ))
-4) 2!$!2
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0ART OF THIS IMPROVEMENT WAS DUE TO THE USE OF DOPPLER FILTER DESIGNS UTILIZING
EIGHT PULSES INSTEAD OF JUST THREE FOR THE -4) AND PART WAS THE RESULT OF ALLOWING A
LARGER DYNAMIC RANGE INTO THE -4$ PROCESSOR AND RELYING ON A CLUTTER MAP TO SUPPRESS
RESIDUES IN REGIONS WHERE THE CLUTTER LEVEL EXCEEDS THE MAXIMUM CLUTTER SUPPRESSION
OF THE RADAR
4HE BLOCK DIAGRAM OF THE -4$ )) SIGNAL PROCESSOR IS SHOWN IN &IGURE 0ARALLEL
PROCESSING CHANNELS ARE PROVIDED FOR MOVING TARGETS THROUGH THE TWO PULSE -4) CAN
CELER AND THE SEVEN PULSE DOPPLER FILTER BANK AND FOR NONMOVING hZERO DOPPLERv
TARGETS THROUGH THE 6ELOCITY &ILTER ! HIGH RESOLUTION CLUTTER MAP IS BUILT FROM THE
h 6ELOCITY &ILTERv OUTPUT AND THE CLUTTER MAP CONTENT IS USED FOR THRESHOLDING IN THE
TWO PROCESSING CHANNELS )N THE MOVING TARGET CHANNEL THE THRESHOLD OBTAINED FROM
THE CLUTTER MAP CONTENT IS SCALED DOWN BY THE EXPECTED CLUTTER ATTENUATION )N ADDITION
TO THE CLUTTER MAP THRESHOLDING CONVENTIONAL CONSTANT FALSE ALARM RATE THRESHOLDING
IS UTILIZED AGAINST MOVING CLUTTER RAIN AND INTERFERENCE $ETECTION OUTPUTS NAMED
0RIMITIVE 4ARGET /UTPUTS ARE OBTAINED THROUGH THIS PROCESSING FOR EACH INDIVIDUAL PRO
CESSED #0) &IGURE SHOWS THE ADDITIONAL PROCESSING REQUIRED TO GENERATE CENTROIDED
4ARGET 2EPORTS AND THE PROCESSING OF THESE 4ARGET 2EPORTS TO OBTAIN TRACK OUTPUTS FOR
DISPLAY TO THE AIR TRAFFIC CONTROL SYSTEM
4HE -4$ RADAR TRANSMITS A GROUP OF . PULSES AT A CONSTANT PULSE REPETITION FRE
QUENCY 02& AND AT A FIXED RADAR FREQUENCY 4HIS SET OF PULSES IS USUALLY REFERRED
TO AS THE COHERENT PROCESSING INTERVAL #0) OR PULSE BATCH 3OMETIMES ONE OR TWO
ADDITIONAL FILL PULSES ARE ADDED TO THE #0) IN ORDER TO SUPPRESS RANGE AMBIGUOUS CLUTTER
RETURNS AS MIGHT OCCUR DURING PERIODS OF ANOMALOUS PROPAGATION 4HE RETURNS RECEIVED
DURING ONE #0) ARE PROCESSED IN THE BANK OF . PULSE FINITE IMPULSE RESPONSE &)2
FILTERS 4HEN THE RADAR MAY CHANGE ITS 02& ANDOR 2& FREQUENCY AND TRANSMIT ANOTHER
#0) OF . PULSES 3INCE MOST SEARCH RADARS ARE AMBIGUOUS IN DOPPLER THE USE OF DIFFERENT
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02&S ON SUCCESSIVE COHERENT DWELLS WILL CAUSE THE TARGET RESPONSE TO FALL AT DIFFERENT
FREQUENCIES OF THE FILTER PASSBAND ON THE SUCCESSIVE OPPORTUNITIES DURING THE TIME ON
TARGET THUS ELIMINATING BLIND SPEEDS
%ACH DOPPLER FILTER IS DESIGNED TO RESPOND TO TARGETS IN NONOVERLAPPING PORTIONS
OF THE DOPPLER FREQUENCY BAND AND TO SUPPRESS SOURCES OF CLUTTER AT ALL OTHER DOPPLER
FREQUENCIES 4HIS APPROACH MAXIMIZES THE COHERENT SIGNAL INTEGRATION IN EACH DOPPLER
FILTER AND PROVIDES CLUTTER ATTENUATION OVER A LARGER RANGE OF DOPPLER FREQUENCIES THAN
ACHIEVABLE WITH A SINGLE -4) FILTER 4HUS ONE OR MORE CLUTTER FILTERS MAY SUPPRESS
MULTIPLE CLUTTER SOURCES LOCATED AT DIFFERENT DOPPLER FREQUENCIES !N EXAMPLE OF THE
USE OF AN -4$ DOPPLER FILTER BANK AGAINST SIMULTANEOUS LAND AND WEATHER CLUTTER 7X
IS ILLUSTRATED IN &IGURE )T CAN BE SEEN THAT FILTERS AND WILL PROVIDE SIGNIFICANT
SUPPRESSION OF BOTH CLUTTER SOURCES
4HE OUTPUT OF EACH DOPPLER FILTER IS ENVELOPE DETECTED AND PROCESSED THROUGH A CELL
AVERAGING CONSTANT FALSE ALARM RATE #! #&!2 PROCESSOR TO SUPPRESS RESIDUES DUE TO
RANGE EXTENDED CLUTTER THAT MAY NOT HAVE BEEN FULLY SUPPRESSED BY THE FILTER
!S WILL BE DISCUSSED LATER IN THIS CHAPTER THE CONVENTIONAL -4) DETECTION SYSTEM
OFTEN RELIES ON A CAREFULLY CONTROLLED DYNAMIC RANGE IN THE )& SECTION OF THE RADAR
RECEIVER TO ENSURE THAT CLUTTER RESIDUES AT THE -4) OUTPUT ARE SUPPRESSED TO THE LEVEL OF
THE RECEIVER NOISE OR BELOW 4HIS LIMITED DYNAMIC RANGE HOWEVER HAS THE UNDESIRABLE
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PRESSION IS CONSEQUENTLY REDUCED
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RAISE THE DETECTION THRESHOLD ABOVE THE LEVEL OF THE RESIDUES 4HIS IN TURN ELIMINATES
THE NEED TO RESTRICT THE )& DYNAMIC RANGE WHICH CAN THEN BE SET TO THE MAXIMUM VALUE
SUPPORTED BY THE !$ CONVERTERS 4HUS A SYSTEM CONCEPT IS OBTAINED THAT PROVIDES
A CLUTTER SUPPRESSION CAPABILITY THAT IS LIMITED ONLY BY THE RADAR SYSTEM STABILITY THE
DYNAMIC RANGE OF THE RECEIVER PROCESSOR AND THE SPECTRUM WIDTH OF THE RETURNS FROM
CLUTTER 4HE CONCEPT OF A HIGH RESOLUTION DIGITAL CLUTTER MAP TO SUPPRESS CLUTTER RESIDUES
IS RELATED TO EARLIER EFFORTS TO CONSTRUCT ANALOG AREA -4) SYSTEMS USING FOR EXAMPLE
STORAGE TUBES
!LSO INCLUDED IN THE -4$ IMPLEMENTATION ARE hxAREA THRESHOLDS MAINTAINED
TO CONTROL EXCESSIVE FALSE ALARMS PARTICULARLY FROM BIRD FLOCKS %ACH AREA OF ABOUT
SQUARE NAUTICAL MILES IS DIVIDED INTO SEVERAL VELOCITY REGIONS 4HE THRESHOLD IN EACH
REGION IS ADJUSTED ON EACH SCAN TO ACHIEVE THE DESIRED LIMIT ON FALSE ALARMS WITHOUT
RAISING THE THRESHOLD SO HIGH THAT SMALL AIRCRAFT ARE PREVENTED FROM BEING PLACED IN
TRACK STATUSv
)N SUBSEQUENT SECTIONS SPECIFIC ASPECTS OF THE DESIGN OF AN -4$ SYSTEM WILL BE
DISCUSSED 4HUS 3ECTION WILL DISCUSS THE DESIGN AND PERFORMANCE OF DOPPLER
FILTER BANKS AND A DETAILED DISCUSSION OF CLUTTER MAPS WILL FOLLOW IN 3ECTION 3INCE THE ORIGINAL WORK AT ,INCOLN ,ABORATORY TO DEVELOP THE -4$ CONCEPT A NUMBER
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LING CLUTTER RESIDUE WITH INTENTIONALLY RESTRICTED DYNAMIC RANGE HAS BEEN ADOPTED IN
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UNITY NOISE POWER GAIN IS SHOWN IN &IGURE .OTE THAT THERE IS ZERO RESPONSE
TO STATIONARY TARGETS AND ALSO TO TARGETS AT o o o KNOTS 4HESE SPEEDS
KNOWN AS BLIND SPEEDS ARE WHERE THE TARGETS MOVE WAVELENGTHS
BETWEEN CONSECUTIVE TRANSMITTED PULSES 4HIS RESULTS IN THE RECEIVED SIGNAL BEING
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6" K •
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TARGETS AT VELOCITIES MIDWAY BETWEEN THE BLIND SPEEDS IS GREATER THAN THE RESPONSE FOR
A NORMAL RECEIVER
4HE ABSCISSA OF THE VELOCITY RESPONSE CURVE CAN ALSO BE LABELED IN TERMS OF DOPPLER
FREQUENCY 4HE DOPPLER FREQUENCY OF THE TARGET CAN BE CALCULATED FROM
FD • 62
L
WHERE FD IS THE DOPPLER FREQUENCY IN HERTZ 62 IS THE TARGET RADIAL VELOCITY IN METERS
PER SECOND AND K IS THE TRANSMITTED WAVELENGTH IN METERS )T CAN BE SEEN FROM
&IGURE THAT THE DOPPLER FREQUENCIES FOR WHICH THE SYSTEM IS BLIND OCCUR AT MUL
TIPLES OF THE PULSE REPETITION FREQUENCY
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THE MAJOR RADAR DESIGN CHARACTERISTICS SUCH AS RANGE AND ANGLE RESOLUTION AS WELL AS
OPERATING FREQUENCY 4HE ABILITY OF A RADAR TO SUPPRESS CLUTTER IS DETERMINED BY RADAR
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3PECTRAL #HARACTERISTICS 4HE SPECTRAL CHARACTERISTICS OF CLUTTER AS DISCUSSED IN
MOST REFERENCES IMPLICITLY ASSUMES THAT THE RADAR TRANSMITS A CONTINUOUS CONSTANT 02&
WAVEFORM 4HE SPECTRUM OF THE OUTPUT OF A PULSED TRANSMITTER USING A SIMPLE RECTANGULAR
PULSE OF LENGTH S IS SHOWN IN &IGURE 4HE SPECTRAL WIDTH OF THE SIN 5 5 ENVELOPE
IS DETERMINED BY THE TRANSMITTED PULSE WIDTH THE FIRST NULLS OCCURRING AT A FREQUENCY OF
F o S 4HE INDIVIDUAL SPECTRAL LINES ARE SEPARATED BY A FREQUENCY EQUAL TO THE 02&
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RESPONSE SHOWN IN &IGURE 4HUS A CANCELER WILL IN THEORY FULLY REJECT CLUTTER WITH
THIS IDEAL LINE SPECTRUM )N PRACTICE HOWEVER THE SPECTRAL LINES OF THE CLUTTER RETURNS ARE
BROADENED BY MOTION OF THE CLUTTER SUCH AS WINDBLOWN TREES OR WAVES ON THE SEA SURFACE
AS WELL AS BY THE MOTION OF THE ANTENNA IN A SCANNING RADAR OR DUE TO PLATFORM MOTION
4HIS SPECTRAL SPREAD PREVENTS PERFECT CANCELLATION OF CLUTTER IN AN -4) SYSTEM
/FTEN IN THE PAST THE ASSUMPTION HAS BEEN MADE THAT THE RETURNS FROM CLUTTER HAVE A
GAUSSIAN POWER SPECTRAL DENSITY WHICH MAY BE CHARACTERIZED BY ITS STANDARD DEVIATION
RV AND MEAN VELOCITY MV BOTH IN UNITS OF MS 5SING THIS GAUSSIAN MODEL EACH OF THE
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3' F ¤ F MF ³
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SOMETIMES DERIVED FROM VIDEO SPECTRA COMPUTED USING SQUARE LAW DETECTED RETURNS
"Y THE MID S NEW EXPERIMENTAL RESULTS WERE OBTAINED WHICH SHOWED THAT
THE SPECTRUM FALL OFF WAS SLOWER THAN PREDICTED BY THE GAUSSIAN MODEL 4HIS LED TO
NEW MODELS BASED ON POLYNOMIAL REPRESENTATIONS OF THE SPECTRUM USING AN EQUATION
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4HE RELATIONSHIP BETWEEN THE STANDARD DEVIATION OF THIS SPECTRUM AND ITS D" WIDTH
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VERY LARGE RADIAL VELOCITY COMPONENTS OF THE CLUTTER INTERNAL MOTION
$URING THE S AN EXTENSIVE MEASUREMENT PROGRAM CONDUCTED AT THE -)4 ,INCOLN
,ABORATORY OBTAINED MORE ACCURATE DATA ON LAND CLUTTER SPECTRA USING A VERY STABLE
RADAR EQUIPMENT AND DATA WAS COLLECTED UNDER WELL CONTROLLED CONDITIONS 4HESE NEW
RESULTS LED TO THE FOLLOWING EXPONENTIAL MODEL FOR LAND CLUTTER SPECTRA
3%80 F LN ¤ • LN ³
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WIDTH IN MS THESE PARAMETERS CAN BE DEFINED AS FOLLOWS
G
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GAUSSIAN SPECTRRUM
POLYNOMIAL SPECTRUM WITH N EXPONENTIAL SPECTRUM
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RMS SPECTRAL SPREAD IN MS !N EXAMPLE OF A MEASURED LAND CLUTTER SPECTRUM IS SHOWN
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BE USED IN -4) AND -4$ PERFORMANCE ANALYSIS )N CASE OF DOUBT THE SPECTRAL SPREAD
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#%
%
&)'52% 4YPICAL DENSITIES OF POINT CLUTTER SCATTERERS AFTER *" "ILLINGSLEY
‘ 7ILLIAM !NDREW 0UBLISHING )NC .OTE THAT THE CLUTTER IN &IGURE B IS VERY SPOTTY IN CHARACTER INCLUDING THE
STRONG FIXED POINT TARGETS AND RETURNS FROM EXTENDED TARGETS )T IS SIGNIFICANT THAT THE
EXTENDED TARGETS ARE NO LONGER VERY EXTENDED 4HE FACE OF A MOUNTAIN AT MI FROM
TO OCLOCK IS ONLY A LINE )F THE -4) SYSTEM WERE INCAPABLE OF DISPLAYING AN AIR
CRAFT WHILE IT WAS OVER THE MOUNTAIN FACE IT WOULD DISPLAY THE AIRCRAFT ON THE NEXT SCAN
OF THE ANTENNA BECAUSE THE AIRCRAFT WOULD HAVE MOVED EITHER FARTHER OR NEARER 4HE
00) DOES NOT HAVE A RESOLUTION THAT APPROACHES THE RESOLUTION OF THE SIGNAL PROCESSING
CIRCUITS OF THIS RADAR 4HUS THE APPARENT EXTENDED CLUTTER HAS MANY WEAK AREAS NOT
VISIBLE IN THESE PHOTOGRAPHS WHERE TARGETS COULD BE DETECTED BY VIRTUE OF AN -4)
RADARS INTERCLUTTER VISIBILITY DEFINED IN 3ECTION Ó°xÊ
/" -
4HE )%%% 3TANDARD 2ADAR $EFINITIONS PROVIDE USEFUL DEFINITIONS FOR MANY OF THE
QUANTITIES NEEDED TO QUANTIFY -4) AND -4$ PERFORMANCE BUT IN SOME CASES THE
VAGUENESS OF THE ORIGINAL DEFINITION AND THE LACK OF DISTINCTION BETWEEN PERFORMANCE
AGAINST DISTRIBUTED CLUTTER VERSUS POINT CLUTTER RETURNS HAVE LED TO AMBIGUOUS INTERPRE
TATIONS OF SEVERAL TERMS )N THIS SECTION THE MAJOR DEFINITIONS WILL BE REVIEWED AND
ANNOTATED TO ATTEMPT TO CLARIFY SOME OF THESE POTENTIAL AMBIGUITIES &OR EACH TERM THE
)%%% DEFINITION WHEN AVAILABLE WILL BE QUOTED ALONG WITH A SUBSEQUENT DISCUSSION
)MPROVEMENT &ACTOR
4HE )%%% DEFINITION OF )MPROVEMENT &ACTOR READS
MOVING TARGET INDICATION -4) IMPROVEMENT FACTOR 4HE SIGNAL TO CLUTTER POWER RATIO AT
THE OUTPUT OF THE CLUTTER FILTER DIVIDED BY THE SIGNAL TO CLUTTER POWER RATIO AT THE INPUT TO THE
CLUTTER FILTER AVERAGED UNIFORMLY OVER ALL TARGET RADIAL VELOCITIES OF INTEREST 3YNONYM CLUTTER
IMPROVEMENT FACTOR
Ó°Óä
2!$!2 (!.$"//+
4HIS DEFINITION ASSUMES THAT CLUTTER IS DISTRIBUTED HOMOGENEOUSLY ACROSS MANY
RANGE CELLS )N THIS CASE THE ABOVE DEFINITION IS EQUALLY VALID BEFORE AND AFTER PULSE
COMPRESSION !GAINST POINT CLUTTER THIS DEFINITION ONLY APPLIES AFTER PULSE COMPRESSION
AND MAY RESULT IN A DIFFERENT VALUE OF THE IMPROVEMENT FACTOR 4HE REAL DIFFICULTY WITH
THIS DEFINITION IS HOWEVER THE LACK OF A PRECISE DEFINITION OF THE DOPPLER VELOCITY INTER
VAL WHICH IS TO BE USED FOR THE REQUIRED hUNIFORMv AVERAGING /RIGINALLY THIS AVERAG
ING WAS ASSUMED TO INVOLVE MULTIPLE 02& INTERVALS BASED ON CLASSICAL LOW 02& RADARS
USING A SINGLE -4) FILTER )T WAS FOR THIS REASON THAT THE -4) )MPROVEMENT &ACTOR DEFI
NITION ) PROVIDED IN THE ND EDITION OF THIS 2ADAR (ANDBOOK USED THE NOISE GAIN OF
THE DOPPLER -4) FILTER AS THE NORMALIZING FACTOR 4HE INCREASED USE OF PULSE DOPPLER
FILTER BANKS IN MODERN RADAR HAS HOWEVER LED TO A USE OF THE )%%% DEFINITION WHERE
THE AVERAGING OF THE SIGNAL TO CLUTTER RATIO IMPROVEMENT IS PERFORMED ONLY ACROSS A
NARROW REGION AROUND THE PEAK OF THE DOPPLER FILTER RESPONSE )N THIS CASE THE COHERENT
INTEGRATION GAIN OF THE DOPPLER FILTER IS AUTOMATICALLY ADDED TO THE CONVENTIONAL -4)
IMPROVEMENT FACTOR VALUE AND MUCH BETTER RADAR PERFORMANCE IS INDICATED
3INCE A DEFINITION OF CLUTTER SUPPRESSION IS OFTEN NEEDED WHICH QUANTIFIES THE INHER
ENT RADAR STABILITY LIMITATIONS APART FROM ANY ADDITIONAL COHERENT GAIN IT IS SOMETIMES
PREFERABLE TO USE THE )%%% DEFINITION OF CLUTTER ATTENUATION )N THIS CHAPTER IMPROVEMENT
FACTOR AND CLUTTER ATTENUATION WILL BE USED SYNONYMOUSLY 7HEN THE COHERENT GAIN OF THE
DOPPLER FILTER IS INCLUDED THE TERM SIGNAL TO CLUTTER RATIO IMPROVEMENT WILL BE USED
#LUTTER !TTENUATION 4HE )%%% DEFINITION READS
CLUTTER ATTENUATION #! )N MOVING TARGET INDICATION -4) OR DOPPLER RADAR THE RATIO OF
THE CLUTTER TO NOISE RATIO AT THE INPUT TO THE PROCESSOR TO THE CLUTTER TO NOISE RATIO AT THE OUT
PUT .OTE )N -4) A SINGLE VALUE OF #! WILL BE OBTAINED WHILE IN DOPPLER RADAR THE VALUE
WILL GENERALLY VARY OVER THE DIFFERENT TARGET DOPPLER FILTERS )N -4) #! WILL BE EQUAL TO -4)
IMPROVEMENT FACTOR IF THE TARGETS ARE ASSUMED UNIFORMLY DISTRIBUTED IN VELOCITY 3EE ALSO -4)
IMPROVEMENT FACTOR
(ERE IT WILL BE ASSUMED THAT hPROCESSORv REFERS TO THE -4) FILTER OR A SINGLE DOPPLER
FILTER IN A PULSE DOPPLER FILTER BANK "ASED ON THIS DEFINITION THE CLUTTER ATTENUATION IS
GIVEN BY
#! 0#). 0./54
•
0#/54 0.).
WHERE 0#). AND 0#/54 ARE THE CLUTTER POWER AT THE INPUT AND OUTPUT OF THE -4) FILTER
RESPECTIVELY AND 0.). AND 0./54 ARE THE CORRESPONDING NOISE POWERS !S NOTED IN THE
)%%% DEFINITION THE VALUE OF #! WILL MOST LIKELY DIFFER FROM FILTER TO FILTER IN A DOPPLER
FILTER BANK DUE TO SPECIFIC CLUTTER AND FILTER RESPONSE CHARACTERISTICS
)N THE DISCUSSION ABOVE THE ASSUMPTION WAS IMPLICITLY MADE THAT CLUTTER RETURNS ARE
STATIONARY AND DISTRIBUTED IN RANGE 4HE ABOVE DEFINITIONS WILL BE EQUALLY VALID BEFORE
AND AFTER PULSE COMPRESSION &OR A SINGLE PIECE OF POINT CLUTTER AS OFTEN USED IN ACTUAL
RADAR STABILITY MEASUREMENTS THE DEFINITION OF CLUTTER ATTENUATION WOULD HAVE TO BE
CHANGED AS FOLLOWS TO PROVIDE IDENTICAL RESULTS
CLUTTER ATTENUATION #! POINT CLUTTER )N MOVING TARGET INDICATION -4) OR $OPPLER RADAR
THE RATIO OF THE TOTAL ENERGY IN THE RECEIVED POINT CLUTTER RETURN AT THE INPUT TO THE PROCESSOR
TO THE TOTAL ENERGY IN THE POINT CLUTTER RESIDUE AT THE OUTPUT OF THE PROCESSOR MULTIPLIED BY THE
NOISE GAIN OF PROCESSOR
-4) 2!$!2
Ó°Ó£
4HE CLUTTER ATTENUATION AGAINST POINT CLUTTER BASED ON THIS DEFINITION WILL BE THE SAME
BEFORE OR AFTER PULSE COMPRESSION AND WILL ALSO BE IDENTICAL TO THE VALUE OF #! OBTAINED
AGAINST DISTRIBUTED CLUTTER WITH IDENTICAL SPECTRAL CHARACTERISTICS
&OR THE PRACTICAL MEASUREMENT OF #! AGAINST A SINGLE PIECE OF POINT CLUTTER IE
CORNER REFLECTOR THE TOTAL ENERGY MUST BE INTEGRATED PER THE ABOVE DEFINITION AT THE
INPUT AND OUTPUT OF EACH DOPPLER FILTER 4HE CALCULATION OF THE ENERGY IS BEST PERFORMED
PRIOR TO PULSE COMPRESSION SINCE THE PRECISE DURATION OF THE UNCOMPRESSED PULSE AND
THEREFORE THE INTEGRATION WINDOW IS ACCURATELY KNOWN )F DONE AFTER PULSE COMPRES
SION UNCERTAINTIES IN THE INTEGRATION OF ENERGY MAY ARISE DUE TO THE TRANSIENT RESPONSE
OF THE PULSE COMPRESSION FILTER
3IGNAL TO #LUTTER 2ATIO )MPROVEMENT )3#2 &OR A SYSTEM EMPLOYING MUL
TIPLE DOPPLER FILTERS SUCH AS THE -4$ EACH DOPPLER FILTER WILL ALSO HAVE A COHER
ENT GAIN '# F WHICH AT THE FILTER PEAK HAS A VALUE '# MAX 4HE COHERENT GAIN OF
A DOPPLER FILTER IS EQUAL TO THE INCREASE IN SIGNAL TO THERMAL NOISE RATIO BETWEEN
THE INPUT AND THE OUTPUT OF THE FILTER DUE TO THE COHERENT SUMMATION OF INDIVIDUAL
TARGET RETURNS !GAIN THESE COHERENT GAIN VALUES WOULD USUALLY DIFFER FROM FILTER TO
FILTER DUE TO POTENTIALLY DIFFERENT DOPPLER FILTER CHARACTERISTICS 4HESE COHERENT GAIN
VALUES WILL INCLUDE THE FILTER MISMATCH LOSS BUT NOT THE STRADDLING LOSSES BETWEEN
ADJACENT FILTERS 4HE PRODUCT OF THE CLUTTER ATTENUATION #!I AND THE COHERENT GAIN
'#MAX I FOR THE ITH DOPPLER FILTER BECOMES THE DEFINITION OF THE SIGNAL TO CLUTTER RATIO
3#2 IMPROVEMENT
)3#2 I #!I • '# MAX I
4HIS QUANTITY WAS NOT INCLUDED IN THE )%%% $ICTIONARY BUT THE FOLLOWING DEFINI
TION IS COMMONLY USED
SIGNAL TO CLUTTER RATIO IMPROVEMENT )3#2 4HE RATIO OF THE SIGNAL TO CLUTTER RATIO OBTAINED
AT THE OUTPUT OF THE DOPPLER FILTER BANK TO THE SIGNAL TO CLUTTER RATIO AT THE INPUT TO THE FILTER BANK
COMPUTED AS A FUNCTION OF TARGET DOPPLER FREQUENCY
4HIS DEFINITION DOES NOT INCLUDE ANY DOPPLER AVERAGING ACROSS THE INDIVIDUAL
FILTERS AND THE DEFINITION DOES NOT PROVIDE A SINGLE FIGURE OF MERIT FOR A RADAR DOP
PLER PROCESSOR BECAUSE EACH FILTER MAY HAVE DIFFERENT VALUES OF CLUTTER ATTENUATION
AND COHERENT GAIN
3INCE EACH DOPPLER FILTER HAS A COHERENT GAIN THAT IS A FUNCTION OF TARGET DOPPLER AN
AVERAGE VALUE OF SIGNAL TO CLUTTER IMPROVEMENT CAN BE DEFINED BY AVERAGING ALL FILTERS
OVER ITS RESPECTIVE RANGE OF TARGET DOPPLERS
F
§ F
¶
¨¯ #! • '# F • DF ¯ #! • '# F • DF ·
·
F
¨¨ F
·
)3#2 F . F ¨
F.
·
¨ #!. • '# . F • DF ·
¯
¨
·
F. ©
¸
4HE SPECIFIC FREQUENCIES COULD LOGICALLY BE CHOSEN AS THE CROSSOVER BETWEEN INDI
VIDUAL DOPPLER FILTERS 4HIS CALCULATION WILL NOW INCLUDE THE EFFECT OF A TARGET DOPPLER
Ó°ÓÓ
2!$!2 (!.$"//+
STRADDLING LOSS AND WOULD REPRESENT A SINGLE FIGURE OF MERIT FOR A DOPPLER PROCESSOR
4O SIMPLIFY THIS CALCULATION THE AVERAGE SIGNAL TO CLUTTER IMPROVEMENT MAY BE DEFINED
AS THE FINITE SUM
)3#2 . #!I • '# MAX I
.£
I
TO WHICH THE DOPPLER STRADDLING LOSS WOULD HAVE TO BE ADDED
3UBCLUTTER 6ISIBILITY 3#6
4HE )%%% DEFINITION OF SUBCLUTTER VISIBILITY IS
3UBCLUTTER VISIBILITY 4HE RATIO BY WHICH THE TARGET ECHO POWER MAY BE WEAKER THAN COINCIDENT
CLUTTER ECHO POWER AND STILL BE DETECTED WITH SPECIFIED DETECTION AND FALSE ALARM PROBABILITIES
.OTE 4ARGET AND CLUTTER POWERS ARE MEASURED ON A SINGLE PULSE RETURN AND ALL TARGET VELOCITIES
ARE ASSUMED EQUALLY LIKELY
4HE SUBCLUTTER VISIBILITY 3#6 OF A RADAR SYSTEM IS A MEASURE OF ITS ABILITY TO DETECT
MOVING TARGET SIGNALS SUPERIMPOSED ON CLUTTER SIGNALS ! RADAR WITH D" 3#6 CAN
DETECT AN AIRCRAFT FLYING OVER CLUTTER WHOSE SIGNAL RETURN IS TIMES STRONGER .OTE THAT
IT IS IMPLICITLY ASSUMED IN THE ABOVE DEFINITION THAT SIGNAL AND CLUTTER ARE BOTH OBSERVED
AFTER PULSE COMPRESSION 4HE 3#6 OF TWO RADARS CANNOT NECESSARILY BE USED TO COMPARE
THEIR PERFORMANCE WHILE OPERATING IN THE SAME ENVIRONMENT BECAUSE THE TARGET TO CLUTTER
RATIO SEEN BY EACH RADAR IS PROPORTIONAL TO THE SIZE OF THE RADAR RESOLUTION CELL AND MAY
BE A FUNCTION OF FREQUENCY 4HUS A RADAR WITH A MS PULSE LENGTH AND A — BEAMWIDTH
WOULD NEED D" MORE SUBCLUTTER VISIBILITY THAN A RADAR WITH A MS PULSE AND A —
BEAMWIDTH FOR EQUAL PERFORMANCE IN A DISTRIBUTED CLUTTER ENVIRONMENT
4HE SUBCLUTTER VISIBILITY OF A RADAR WHEN EXPRESSED IN DECIBELS IS LESS THAN THE
IMPROVEMENT FACTOR BY THE CLUTTER VISIBILITY FACTOR 6OC SEE DEFINITION BELOW )NTERCLUTTER 6ISIBILITY )#6
4HE )%%% DEFINITION IS
INTERCLUTTER VISIBILITY 4HE ABILITY OF A RADAR TO DETECT MOVING TARGETS THAT OCCUR IN RESOLUTION
CELLS AMONG PATCHES OF STRONG CLUTTER USUALLY APPLIED TO MOVING TARGET INDICATION -4) OR
PULSED $OPPLER RADARS .OTE 4HE HIGHER THE RADAR RANGE ANDOR ANGLE RESOLUTION THE BETTER THE
INTERCLUTTER VISIBILITY
4HE INTERCLUTTER VISIBILITY )#6 OF A RADAR IS A MEASURE OF ITS CAPABILITY TO DETECT
TARGETS BETWEEN POINTS OF STRONG CLUTTER BY VIRTUE OF THE ABILITY OF THE RADAR TO RESOLVE
THE AREAS OF STRONG AND WEAK CLUTTER ! RADAR WITH HIGH RESOLUTION MAKES AVAILABLE
REGIONS BETWEEN POINTS OF STRONG CLUTTER WHERE THE TARGET TO CLUTTER RATIO WILL BE SUF
FICIENT FOR TARGET DETECTION EVEN THOUGH THE 3#6 OF THE RADAR BASED ON AVERAGE CLUTTER
MAY BE RELATIVELY LOW 4O ACHIEVE )#6 A MECHANISM MUST BE FURNISHED TO PROVIDE
#&!2 OPERATION AGAINST THE RESIDUE FROM STRONG CLUTTER 4HIS #&!2 IS PROVIDED IN
OLDER -4) SYSTEM BY )& LIMITING AND IN THE -4$ IMPLEMENTATION THROUGH THE USE OF
HIGH RESOLUTION CLUTTER MAPS ! QUANTITATIVE DEFINITION OF INTERCLUTTER VISIBILITY HAS NOT
YET BEEN FORMULATED
&ILTER -ISMATCH ,OSS 4HE )%%% DEFINITION IS
FILTER MISMATCH LOSS 4HE LOSS IN OUTPUT SIGNAL TO NOISE RATIO OF A FILTER RELATIVE TO THE SIGNAL
TO NOISE RATIO FROM A MATCHED FILTER
Ó°ÓÎ
-4) 2!$!2
4HE MAXIMUM SIGNAL TO NOISE RATIO AVAILABLE FROM AN . PULSE FILTER IS . TIMES
THE SIGNAL TO NOISE RATIO OF A SINGLE PULSE ASSUMING ALL PULSES HAVE EQUAL AMPLI
TUDE 7HEN WEIGHTING IS APPLIED TO REJECT CLUTTER AND CONTROL THE FILTER SIDELOBES THE
PEAK OUTPUT SIGNAL TO NOISE RATIO IS REDUCED 4HE FILTER MISMATCH LOSS IS THE AMOUNT
BY WHICH THE PEAK OUTPUT SIGNAL TO NOISE RATIO IS REDUCED BY THE USE OF WEIGHTING
! THREE PULSE -4) FILTER USING BINOMIAL WEIGHTS HAS A FILTER MISMATCH LOSS OF D"
4HE MISMATCH LOSS FOR THE BINOMIAL WEIGHTED FOUR PULSE CANCELER IS D"
#LUTTER 6ISIBILITY &ACTOR 6OC
4HE )%%% DEFINITION IS
CLUTTER DETECTABILITY FACTOR 4HE PREDETECTION SIGNAL TO CLUTTER RATIO THAT PROVIDES STATED
PROBABILITY OF DETECTION FOR A GIVEN FALSE ALARM PROBABILITY IN AN AUTOMATIC DETECTION CIRCUIT
.OTE )N -4) SYSTEMS IT IS THE RATIO AFTER CANCELLATION OR DOPPLER FILTERING
4HE CLUTTER VISIBILITY FACTOR IS THE RATIO BY WHICH THE TARGET SIGNAL MUST EXCEED THE
CLUTTER RESIDUE SO THAT TARGET DETECTION CAN OCCUR WITHOUT HAVING THE CLUTTER RESIDUE
RESULT IN FALSE TARGET DETECTIONS 4HE SYSTEM MUST PROVIDE A THRESHOLD THAT THE TARGETS
WILL CROSS AND THE CLUTTER RESIDUE WILL NOT CROSS
Ó°ÈÊ *,"6 /Ê /",Ê 1/" -
5SING "ARTONS APPROACH THE MAXIMUM IMPROVEMENT FACTOR ) AGAINST ZERO MEAN
CLUTTER WITH A GAUSSIAN SHAPED SPECTRUM FOR DIFFERENT IMPLEMENTATIONS OF THE FINITE
IMPULSE RESPONSE BINOMIAL WEIGHT -4) CANCELER SEE 3ECTION IS
¤ F ³
) y ¥ R ´
¦ PS F µ
¤ F ³
) y ¥ R ´
¦ PS F µ
) y
¤ FR ³
¥¦ PS F ´µ
WHERE ) IS THE -4) IMPROVEMENT FACTOR FOR THE SINGLE DELAY COHERENT CANCELER ) IS THE
-4) IMPROVEMENT FACTOR FOR THE DUAL DELAY COHERENT CANCELER ) IS THE -4) IMPROVE
MENT FACTOR FOR THE TRIPLE DELAY COHERENT CANCELER RF IS THE RMS FREQUENCY SPREAD OF
THE GAUSSIAN CLUTTER POWER SPECTRUM IN HERTZ AND FR IS THE RADAR REPETITION FREQUENCY
IN HERTZ 7HEN THE VALUES OF RF FOR SCANNING MODULATION IN %Q ARE SUBSTITUTED IN
THE ABOVE EQUATIONS FOR ) THE LIMITATION ON ) DUE TO SCANNING IS
N
N
) y
N
) y
) y
Ó°Ó{
2!$!2 (!.$"//+
&)'52% 4HEORETICAL -4) IMPROVEMENT FACTOR DUE TO SCAN MODULATION GAUSSIAN ANTENNA PATTERN N NUMBER OF PULSES WITHIN THE ONE WAY HALF POWER BEAMWIDTH
4HESE RELATIONSHIPS ARE SHOWN GRAPHICALLY IN &IGURE 4HIS DERIVATION ASSUMES A
LINEAR SYSTEM 4HAT IS IT IS ASSUMED THAT THE VOLTAGE ENVELOPE OF THE ECHO SIGNALS AS THE
ANTENNA SCANS PAST A POINT TARGET IS IDENTICAL TO THE TWO WAY ANTENNA VOLTAGE PATTERN
4HIS ASSUMPTION OF A LINEAR SYSTEM MAY BE UNREALISTIC FOR SOME PRACTICAL -4) SYSTEMS
WITH RELATIVELY FEW HITS PER BEAMWIDTH HOWEVER AS DISCUSSED IN 3ECTION 4HE SCANNING LIMITATION DOES NOT APPLY TO A SYSTEM THAT CAN STEP SCAN SUCH AS
A PHASED ARRAY .OTE HOWEVER THAT SUFFICIENT PULSES MUST BE TRANSMITTED TO INITIAL
IZE THE FILTER BEFORE USEFUL OUTPUTS MAY BE OBTAINED &OR EXAMPLE WITH A THREE PULSE
BINOMIAL WEIGHT CANCELER THE FIRST TWO TRANSMITTED PULSES INITIALIZE THE CANCELER AND A
USEFUL OUTPUT IS NOT AVAILABLE UNTIL AFTER THE THIRD PULSE HAS BEEN TRANSMITTED &EEDBACK
OR INFINITE IMPULSE RESPONSE ))2 FILTERS WOULD NOT BE USED WITH A STEP SCAN SYSTEM
BECAUSE OF THE LONG TRANSIENT SETTLING TIME OF THE FILTERS
4HE LIMITATION ON ) DUE TO INTERNAL CLUTTER FLUCTUATIONS CAN BE DETERMINED BY SUB
STITUTING THE APPROPRIATE VALUE OF RF INTO %QS TO "Y LETTING RF RVK
WHERE RV IS THE RMS VELOCITY SPREAD OF THE CLUTTER THE LIMITATION ON ) CAN BE PLOTTED
FOR DIFFERENT TYPES OF CLUTTER AS A FUNCTION OF THE WAVELENGTH K AND THE PULSE REPETITION
FREQUENCY FR 4HIS IS DONE FOR ONE TWO AND THREE DELAY BINOMIAL WEIGHT CANCELERS
IN &IGURE &IGURE AND &IGURE 4HE VALUES OF 6" GIVEN ARE THE FIRST BLIND
SPEED OF THE RADAR OR WHERE THE FIRST BLIND SPEED 6" WOULD BE FOR A STAGGERED 02&
SYSTEM IF STAGGERING WERE NOT USED 4HE IMPROVEMENT FACTOR SHOWN IN THESE FIGURES
FOR RAIN AND CHAFF IS BASED ON THE ASSUMPTION THAT THE AVERAGE VELOCITY OF THE RAIN
AND CHAFF HAS BEEN COMPENSATED FOR SO THAT THE RETURNS ARE CENTERED IN THE CANCELER
REJECTION NOTCH 5NLESS SUCH COMPENSATION IS PROVIDED THE -4) OFFERS LITTLE OR NO
IMPROVEMENT FOR RAIN AND CHAFF
4WO FURTHER LIMITATIONS ON ) ARE THE EFFECT OF PULSE TO PULSE REPETITION PERIOD STAG
GERING COMBINED WITH CLUTTER SPECTRAL SPREAD FROM SCANNING AND INTERNAL CLUTTER MOTION
-4) 2!$!2
Ó°Óx
&)'52% -4) IMPROVEMENT FACTOR AS A FUNCTION OF THE RMS VELOCITY SPREAD OF CLUTTER FOR
A TWO PULSE BINOMIAL WEIGHT CANCELER
4HESE LIMITATIONS PLOTTED IN &IGURE AND &IGURE APPLY TO ALL CANCELERS WHETHER
SINGLE OR MULTIPLE 4HE DERIVATION OF THESE LIMITATIONS AND A MEANS OF AVOIDING THEM
BY THE USE OF TIME VARYING WEIGHTS ARE GIVEN IN h3TAGGER $ESIGN 0ROCEDURESv IN
3ECTION Ó°ÇÊ "*/1Ê
- Ê"Ê 1// ,Ê/ ,-
4HE STATISTICAL THEORY OF DETECTION OF SIGNALS IN GAUSSIAN NOISE PROVIDES THE REQUIRED
FRAMEWORK FOR THE OPTIMUM DESIGN OF RADAR CLUTTER FILTERS 3UCH THEORETICAL RESULTS
ARE IMPORTANT TO THE DESIGNER OF A PRACTICAL -4) OR -4$ SYSTEM IN THAT THEY ESTAB
LISH UPPER BOUNDS ON THE ACHIEVABLE PERFORMANCE IN A PRECISELY SPECIFIED CLUTTER
ENVIRONMENT )T SHOULD BE NOTED HOWEVER THAT OWING TO THE EXTREME VARIABILITY OF
THE CHARACTERISTICS OF REAL CLUTTER RETURNS POWER LEVEL DOPPLER SHIFT SPECTRUM SHAPE
SPECTRAL WIDTH ETC ANY ATTEMPT TO ACTUALLY APPROXIMATE THE PERFORMANCE OF SUCH
OPTIMUM FILTERS FOR THE DETECTION OF TARGETS IN CLUTTER REQUIRES THE USE OF ADAPTIVE
METHODS 4HE ADAPTIVE METHODS MUST ESTIMATE THE UNKNOWN CLUTTER STATISTICS AND
Ó°ÓÈ
2!$!2 (!.$"//+
&)'52% -4) IMPROVEMENT FACTOR AS A FUNCTION OF THE RMS VELOCITY SPREAD OF CLUTTER FOR
A THREE PULSE BINOMIAL WEIGHT CANCELER
SUBSEQUENTLY IMPLEMENT THE CORRESPONDING OPTIMUM FILTER !N EXAMPLE OF SUCH AN
ADAPTIVE -4) SYSTEM IS DISCUSSED IN 3ECTION &OR A SINGLE RADAR PULSE WITH A DURATION OF A FEW MICROSECONDS THE DOPPLER SHIFT
DUE TO AIRCRAFT TARGET MOTION IS A SMALL FRACTION OF THE SIGNAL BANDWIDTH AND CONVEN
TIONAL -4) AND PULSE DOPPLER PROCESSING ARE NOT APPLICABLE )T IS WELL KNOWN THAT THE
CLASSICAL SINGLE PULSE hMATCHEDv FILTER PROVIDES OPTIMUM RADAR DETECTION PERFORMANCE
WHEN USED IN A WHITE NOISE BACKGROUND !GAINST CLUTTER RETURNS THAT HAVE THE SAME
SPECTRUM AS THE TRANSMITTED RADAR PULSE THE MATCHED FILTER IS NO LONGER OPTIMUM BUT
THE POTENTIAL IMPROVEMENT IN THE OUTPUT SIGNAL TO CLUTTER RATIO BY DESIGNING A MODIFIED
OPTIMIZED FILTER IS USUALLY INSIGNIFICANT
7HEN THE DURATION OF THE TRANSMITTED RADAR SIGNAL WHETHER #7 OR A REPETITIVE TRAIN
OF . IDENTICAL PULSES IS COMPARABLE WITH OR GREATER THAN THE RECIPROCAL OF ANTICIPATED
TARGET DOPPLER SHIFTS THE DIFFERENCE BETWEEN A CONVENTIONAL WHITE NOISE MATCHED FIL
TER OR COHERENT INTEGRATOR AND A FILTER OPTIMIZED TO REJECT THE ACCOMPANYING CLUTTER
BECOMES SIGNIFICANT 4HE CHARACTERISTICS OF THE CLUTTER ARE CHARACTERIZED BY THE COVARI
ANCE MATRIX &# OF THE . CLUTTER RETURNS )F THE POWER SPECTRUM OF THE CLUTTER IS DENOTED
Ó°ÓÇ
-4) 2!$!2
&)'52% -4) IMPROVEMENT FACTOR AS A FUNCTION OF THE RMS VELOCITY SPREAD OF CLUTTER FOR
A FOUR PULSE BINOMIAL WEIGHT CANCELER
3# F AND THE CORRESPONDING AUTOCORRELATION FUNCTION IS 2# TI n TJ THEN THE ELEMENTS
OF &# ARE GIVEN BY
& IJ 2# TI
TJ
WHERE TI IS THE TRANSMISSION TIME OF THE ITH PULSE &OR EXAMPLE FOR A GAUSSIAN SHAPED
CLUTTER SPECTRUM WE HAVE
3# F 0# •
§ F FD ¶
• EXP ¨
·
P • S F
¨© • S F ·¸
WHERE 0# IS THE TOTAL CLUTTER POWER RF IS THE STANDARD DEVIATION OF THE CLUTTER SPECTRAL
WIDTH AND FD IS THE AVERAGE DOPPLER SHIFT OF THE CLUTTER 4HE CORRESPONDING AUTOCOR
RELATION FUNCTION IS
2# T 0# EXP PS F T EXP J P FDT
WHERE S IS THE SEPARATION IN TIME OF TWO CONSECUTIVE CLUTTER RETURNS
Ó°Ón
2!$!2 (!.$"//+
&)'52% !PPROXIMATE -4) IMPROVEMENT FACTOR LIMITATION DUE TO PULSE TO PULSE REPETITION PERIOD
STAGGERING AND SCANNING ALL CANCELER FIGURATIONS )D" LOG ;N F = F MAXIMUM PERIOD
MINIMUM PERIOD
&OR TWO PULSES SEPARATED IN TIME BY THE INTERPULSE PERIOD 4 THE COMPLEX CORRELATION
COEFFICIENT BETWEEN TWO CLUTTER RETURNS IS
R4 EXP
PS 4 • EXP JP F 4
F
D
4HE SECOND FACTOR IN THIS EXPRESSION REPRESENTS THE PHASE SHIFT CAUSED BY THE DOPPLER
SHIFT OF THE CLUTTER RETURNS
&OR A KNOWN TARGET DOPPLER SHIFT THE RECEIVED TARGET RETURN CAN BE REPRESENTED BY
AN . DIMENSIONAL VECTOR
S !3 • F
WHERE !3 IS THE SIGNAL AMPLITUDE AND THE ELEMENTS OF THE VECTOR F ARE FI EXP ;JOFSTI=
/N THE BASIS OF THIS DESCRIPTION OF SIGNAL AND CLUTTER IT HAS BEEN SHOWN THAT THE OPTI
MUM DOPPLER FILTER WILL HAVE WEIGHTS GIVEN BY
W /04 & # • S
-4) 2!$!2
Ӱә
&)'52% !PPROXIMATE -4) IMPROVEMENT FACTOR LIMITATION DUE TO PULSE TO PULSE STAGGERING
AND INTERNAL CLUTTER MOTION ALL CANCELER CONFIGURATIONS )D" LOG ;K F FR RV =
F MAXIMUM PERIODMINIMUM PERIOD
AND THE CORRESPONDING SIGNAL TO CLUTTER IMPROVEMENT IS
)3#2 W4OPT S • S4 W OPT
W4OPT & # W OPT
WHERE THE ASTERISK DENOTES COMPLEX CONJUGATION AND SUPERSCRIPT 4 IS THE TRANSPOSITION
OPERATOR !N EXAMPLE WHERE THE OPTIMUM PERFORMANCE IS DETERMINED FOR THE CASE OF
CLUTTER AT ZERO DOPPLER HAVING A GAUSSIAN SHAPED SPECTRUM WITH A NORMALIZED WIDTH
OF RF4 IS SHOWN IN &IGURE )N THIS CASE A COHERENT PROCESSING INTERVAL OF
#0) NINE PULSES WAS ASSUMED AND THE LIMITATION DUE TO THERMAL NOISE WAS IGNORED
BY SETTING THE CLUTTER LEVEL AT D" ABOVE NOISE
)T SHOULD BE KEPT IN MIND THAT %Q FOR THE OPTIMUM WEIGHTS WILL YIELD A DIF
FERENT RESULT FOR EACH DIFFERENT TARGET DOPPLER SHIFT SO THAT A LARGE NUMBER OF PARALLEL
FILTERS WOULD BE NEEDED TO APPROXIMATE THE OPTIMUM PERFORMANCE EVEN WHEN THE CLUTTER
CHARACTERISTICS ARE KNOWN EXACTLY !S AN EXAMPLE THE RESPONSE OF THE OPTIMUM FILTER
DESIGNED FOR ONE PARTICULAR TARGET DOPPLER FREQUENCY LABELED AS POINT ! IN &IGURE IS SHOWN IN A BROKEN LINE !T APPROXIMATELY o FROM THE DESIGN DOPPLER THE PERFOR
MANCE STARTS TO FALL SIGNIFICANTLY BELOW THE OPTIMUM
Ó°Îä
2!$!2 (!.$"//+
&)'52% /PTIMUM SIGNAL TO CLUTTER RATIO IMPROVEMENT )3#2 FOR GAUSSIAN SHAPED CLUTTER
SPECTRUM AND A #0) OF NINE PULSES CLUTTER TO NOISE RATIO D"
!LSO SHOWN IN &IGURE IS A HORIZONTAL LINE LABELED hAVERAGE 3#2 IMPROVE
MENTv 4HIS INDICATES THE LEVEL CORRESPONDING TO THE AVERAGE OF THE OPTIMUM 3#2
CURVE ACROSS ONE DOPPLER INTERVAL AND MAY BE CONSIDERED AS A FIGURE OF MERIT FOR A
MULTIPLE FILTER DOPPLER PROCESSOR SOMEWHAT ANALOGOUS TO THE -4) IMPROVEMENT FAC
TOR DEFINED FOR A SINGLE DOPPLER FILTER )N &IGURE THE OPTIMUM AVERAGE )3#2 HAS
BEEN COMPUTED FOR SEVERAL DIFFERENT VALUES OF THE #0) AS A FUNCTION OF THE NORMALIZED
SPECTRUM WIDTH 4HESE RESULTS MAY BE USED AS A POINT OF REFERENCE FOR PRACTICAL DOPPLER
&)'52% 2EFERENCE CURVE OF OPTIMUM AVERAGE 3#2 IMPROVEMENT FOR
A GAUSSIAN SHAPED CLUTTER SPECTRUM
-4) 2!$!2
ӰΣ
PROCESSOR DESIGNS AS DISCUSSED IN 3ECTION .OTE THAT FOR RF4 y THE AVERAGE 3#2
IMPROVEMENT IS DUE ONLY TO THE COHERENT INTEGRATION OF ALL THE PULSES IN THE #0)
!N -4) FILTER CAN ALSO BE DESIGNED BASED ON THE CRITERION OF MAXIMIZING THE SIGNAL
TO CLUTTER IMPROVEMENT AT A SPECIFIC TARGET DOPPLER (OWEVER SUCH A DESIGN WILL USUALLY
PROVIDE SUBOPTIMUM PERFORMANCE AT ALL OTHER TARGET DOPPLERS 4HE SINGLE EXCEPTION IS THE
TWO PULSE -4) CANCELER WHICH PROVIDES OPTIMUM PERFORMANCE FOR ALL TARGET DOPPLERS
! MORE ATTRACTIVE APPROACH FOR DESIGNING AN OPTIMUM -4) FILTER IS TO MAXIMIZE
ITS IMPROVEMENT FACTOR OR CLUTTER ATTENUATION 4O DESIGN AN OPTIMUM -4) FILTER USING
IMPROVEMENT FACTOR AS THE CRITERION THE COVARIANCE MATRIX OF THE CLUTTER RETURNS AS GIVEN
BY %Q IS AGAIN THE STARTING POINT !S SHOWN BY #APON THE WEIGHTS OF THE OPTI
MUM -4) FILTER ARE FOUND AS THE EIGENVECTOR CORRESPONDING TO THE SMALLEST EIGENVALUE
OF THE CLUTTER COVARIANCE MATRIX AND THE -4) IMPROVEMENT FACTOR IS EQUAL TO THE INVERSE
OF THE SMALLEST EIGENVALUE 4HE OPTIMUM IMPROVEMENT FACTOR FOR THE THREE MODELS FOR
THE SPECTRUM OF LAND CLUTTER INTRODUCED IN 3ECTION HAVE BEEN COMPUTED BASED ON THIS
ABOVE APPROACH
&OR THE GAUSSIAN CLUTTER SPECTRUM THE OPTIMUM IMPROVEMENT FACTOR IS SHOWN IN
&IGURE AS A FUNCTION OF THE RMS RELATIVE SPECTRUM WIDTH ASSUMING ZERO MEAN FOR
THE SPECTRUM #ALCULATIONS ARE SHOWN FOR -4) CANCELERS OF ORDER . THROUGH &OR THE POLYNOMIAL CLUTTER SPECTRUM THE OPTIMUM IMPROVEMENT FACTOR IS SHOWN IN
&IGURE AGAIN AS A FUNCTION OF THE 2-3 RELATIVE SPECTRUM WIDTH ASSUMING ZERO
MEAN FOR THE SPECTRUM
&INALLY FOR THE EXPONENTIAL CLUTTER SPECTRUM MODEL THE OPTIMUM IMPROVEMENT FAC
TOR IS SHOWN IN &IGURE AGAIN AS A FUNCTION OF THE 2-3 RELATIVE SPECTRUM WIDTH
ASSUMING ZERO MEAN FOR THE SPECTRUM
&)'52% /PTIMUM IMPROVEMENT FACTOR FOR GAUSSIAN SPECTRUM MODEL
Ó°ÎÓ
2!$!2 (!.$"//+
&)'52% /PTIMUM IMPROVEMENT FACTOR FOR POLYNOMIAL CLUTTER SPECTRUM MODEL
&)'52% /PTIMUM IMPROVEMENT FACTOR FOR "ILLINGSLEYS EXPONENTIAL SPECTRUM MODEL
-4) 2!$!2
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&)'52% #OMPARISON OF -4) IMPROVEMENT FACTOR OF BINOMIAL WEIGHT
-4) AND OPTIMUM -4) AGAINST A GAUSSIAN SHAPED CLUTTER SPECTRUM
)N &IGURE THE IMPROVEMENT FACTOR OF AN -4) USING THE OPTIMUM WEIGHTS
IS COMPARED WITH THE BINOMIAL COEFFICIENT -4) FOR DIFFERENT VALUES OF THE RELATIVE
CLUTTER SPECTRAL SPREAD AND SHOWN AS A FUNCTION OF THE NUMBER OF PULSES IN THE #0)
4HESE RESULTS AGAIN ASSUME A GAUSSIAN SHAPED CLUTTER SPECTRUM &OR TYPICAL NUMBERS
OF PULSES IN THE -4) THREE TO FIVE THE BINOMIAL COEFFICIENTS ARE REMARKABLY ROBUST
AND PROVIDE A PERFORMANCE WHICH IS WITHIN A FEW DECIBELS OF THE OPTIMUM !GAIN IT
SHOULD BE NOTED THAT ANY ATTEMPT TO IMPLEMENT AN -4) CANCELER WHICH PERFORMS CLOSE
TO THE OPTIMUM WOULD REQUIRE THE USE OF ADAPTIVE TECHNIQUES THAT ESTIMATE THE CLUTTER
CHARACTERISTICS IN REAL TIME )F THE ESTIMATE IS IN ERROR THE ACTUAL PERFORMANCE MAY FALL
BELOW THAT OF THE BINOMIAL WEIGHT -4) CANCELER
Ó°nÊ /Ê 1// ,Ê/ ,Ê
-
4HE -4) BLOCK DIAGRAMS INTRODUCED BY &IGURES AND AND WHOSE RESPONSE WAS
DISCUSSED IN DETAIL IN 3ECTION CONSIDERED A SINGLE DELAY CANCELER )T IS POSSIBLE
TO UTILIZE MORE THAN ONE DELAY AND TO INTRODUCE FEEDBACK ANDOR FEEDFORWARD PATHS
AROUND THE DELAYS TO CHANGE THE -4) SYSTEM RESPONSE TO TARGETS OF DIFFERENT VELOCITIES
&ILTERS WITH ONLY FEEDFORWARD PATHS ARE CALLED FINITE IMPULSE RESPONSE &)2 FILTERS
AND FILTERS THAT INCORPORATE FEEDBACK ARE CALLED INFINITE IMPULSE RESPONSE ))2 FILTERS
OR RECURSIVE FILTERS -ULTIPLE DELAY CANCELERS HAVE WIDER CLUTTER REJECTION NOTCHES THAN
SINGLE DELAY CANCELERS 4HE WIDER REJECTION NOTCH ENCOMPASSES MORE OF THE CLUTTER
SPECTRUM AND THUS INCREASES THE -4) IMPROVEMENT FACTOR ATTAINABLE WITH A GIVEN
CLUTTER SPECTRAL DISTRIBUTION
$ELAY IS USED HERE TO REPRESENT AN INTERPULSE MEMORY FOR AN -4) FILTER !N &)2 FILTER WITH ONE DELAY IS A TWO PULSE
FILTER &OR FEEDBACK ))2 FILTERS IT IS INAPPROPRIATE TO CALL THEM TWO PULSE OR THREE PULSE ETC FILTERS BECAUSE THEY
REQUIRE A NUMBER OF PULSES TO REACH STEADY STATE
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2!$!2 (!.$"//+
&)'52% $IRECT &ORM OR CANONICAL FORM OF ANY -4) FILTER DESIGN
! GENERAL BLOCK DIAGRAM MODEL APPLICABLE TO ANY -4) FILTER IS SHOWN IN &IGURE 4HIS MODEL HAS BEEN DENOTED THE h$IRECT &ORM v OR THE CANONICAL FORM IN THE TERMINOL
OGY SURVEY PRESENTED IN 2ABINER ET AL
)T CAN BE SHOWN THAT AN -4) FILTER AS SHOWN IN &IGURE CAN BE DIVIDED INTO A
CASCADE OF SECOND ORDER SECTIONS AS SHOWN IN &IGURE 7HEN A NUMBER OF SINGLE DELAY FEEDFORWARD CANCELERS ARE CASCADED IN SERIES
THE OVERALL FILTER VOLTAGE RESPONSE IS KN SINN O FD4 WHERE K IS THE TARGET AMPLITUDE
N IS THE NUMBER OF DELAYS FD IS THE DOPPLER FREQUENCY AND 4 IS THE INTERPULSE PERIOD
4HE CASCADED SINGLE DELAY CANCELERS CAN BE REARRANGED AS A TRANSVERSAL FILTER AND THE
WEIGHTS FOR EACH PULSE ARE THE BINOMIAL COEFFICIENTS WITH ALTERNATING SIGN FOR
TWO PULSES FOR THREE PULSES FOR FOUR PULSES AND SO ON #HANGES
OF THE BINOMIAL FEEDFORWARD COEFFICIENTS ANDOR THE ADDITION OF FEEDBACK MODIFY THE
&)'52% -4) SHOWN AS CASCADED FORM OF SECOND ORDER SECTION A IS FOR EVEN ORDER AND B IS FOR
ODD ORDER WITH FIRST ORDER SECTION AT END
Ó°Îx
-4) 2!$!2
&)'52% .TH ORDER &)2 -4) CANCELER BLOCK DIAGRAM
FILTER CHARACTERISTICS 7ITHIN THIS CHAPTER REFERENCE TO BINOMIAL WEIGHT CANCELERS REFERS
TO CANCELERS WITH THE N SINN O FD4 TRANSFER FUNCTION 4HE BLOCK DIAGRAM OF THIS TYPE OF
-4) CANCELER IS SHOWN IN &IGURE &IGURE TO &IGURE REPRESENT TYPICAL VELOCITY RESPONSE CURVES OBTAINABLE FROM
ONE TWO AND THREE DELAY CANCELERS 3HOWN ALSO ARE THE CANCELER CONFIGURATIONS ASSUMED
WITH CORRESPONDING : PLANE POLE ZERO DIAGRAMS 4HE : PLANE IS THE COMB FILTER EQUIVALENT
OF THE 3 PLANE WITH THE LEFT HAND SIDE OF THE 3 PLANE TRANSFORMED TO THE INSIDE OF THE UNIT
CIRCLE CENTERED AT : :ERO FREQUENCY IS AT : J 4HE STABILITY REQUIREMENT IS THAT
THE POLES OF THE : TRANSFER FUNCTION LIE WITHIN THE UNIT CIRCLE :EROS MAY BE ANYWHERE
&)'52% /NE DELAY CANCELER
Ó°ÎÈ
2!$!2 (!.$"//+
&)'52% 4WO DELAY CANCELER
4HESE VELOCITY RESPONSE CURVES ARE CALCULATED FOR A SCANNING RADAR SYSTEM WITH
HITS PER ONE WAY D" BEAMWIDTH !N ANTENNA BEAM SHAPE OF SIN 5 5 TERMI
NATED AT THE FIRST NULLS WAS ASSUMED 4HE SHAPE OF THESE CURVES EXCEPT VERY NEAR THE
BLIND SPEEDS IS ESSENTIALLY INDEPENDENT OF THE NUMBER OF HITS PER BEAMWIDTH OR THE
ASSUMED BEAM SHAPE
4HE ORDINATE LABELED hRESPONSEv REPRESENTS THE SINGLE PULSE SIGNAL TO NOISE OUTPUT
OF THE -4) RECEIVER RELATIVE TO THE SIGNAL TO NOISE RESPONSE OF A NORMAL LINEAR RECEIVER
FOR THE SAME TARGET 4HUS ALL THE RESPONSE CURVES ARE NORMALIZED WITH RESPECT TO THE
NOISE POWER GAIN FOR THE GIVEN CANCELER CONFIGURATION 4HE INTERSECTION AT THE ORDINATE
REPRESENTS THE NEGATIVE DECIBEL VALUE OF ) THE -4) IMPROVEMENT FACTOR FOR A POINT
CLUTTER TARGET PROCESSED IN A LINEAR SYSTEM
-4) 2!$!2
&)'52% Ó°ÎÇ
4HREE DELAY CANCELER
"ECAUSE THESE CURVES SHOW THE SIGNAL TO NOISE RESPONSE FOR EACH OUTPUT PULSE FROM
THE -4) CANCELER THE INHERENT LOSS INCURRED IN A SCANNING RADAR WITH -4) PROCESSING
DUE TO THE REDUCTION OF THE EFFECTIVE NUMBER OF INDEPENDENT PULSES INTEGRATED IS NOT
APPARENT 4HIS LOSS IS D" FOR A PULSE CANCELER AND D" FOR A PULSE CANCELER
ASSUMING A LARGE NUMBER OF PULSES )F QUADRATURE -4) CHANNELS SEE 3ECTION ARE
NOT EMPLOYED THERE IS AN ADDITIONAL LOSS OF TO D"
4HE ABSCISSA OF THESE CURVES 66" REPRESENTS THE RATIO OF TARGET VELOCITY 6 TO THE
BLIND SPEED 6" K FR WHERE K IS THE RADAR WAVELENGTH AND FR IS THE AVERAGE 02& OF
THE RADAR 4HE ABSCISSA CAN ALSO BE INTERPRETED AS THE RATIO OF THE TARGET DOPPLER FRE
QUENCY TO THE AVERAGE 02& OF THE RADAR
4HE CANCELER CONFIGURATIONS SHOWN ARE NOT THE MOST GENERAL FEEDFORWARD FEEDBACK
NETWORKS POSSIBLE 0AIRS OF DELAYS ARE REQUIRED TO LOCATE ZEROS AND POLES ELSEWHERE
Ó°În
2!$!2 (!.$"//+
THAN ON THE REAL AXIS OF THE : PLANE )N THE CONFIGURATIONS SHOWN THE ZEROS ARE CON
STRAINED TO THE UNIT CIRCLE 4O MOVE THE ZEROS OFF OF THE UNIT CIRCLE WHICH MAY BE DONE
TO CONTROL THE FLATNESS OF THE FILTER PASSBAND RESPONSE REQUIRES A CONFIGURATION SIMILAR
TO THE ELLIPTIC FILTER CONFIGURATION SHOWN IN &IGURE LATER IN THIS CHAPTER 4HE TRIPLE
CANCELER CONFIGURATION SHOWN IS SUCH THAT TWO OF THE ZEROS CAN BE MOVED AROUND THE
UNIT CIRCLE IN THE : PLANE -OVING THE ZEROS CAN PROVIDE A OR D" INCREASE IN THE -4)
IMPROVEMENT FACTOR FOR SPECIFIC CLUTTER SPECTRAL SPREADS AS COMPARED WITH KEEPING ALL
THREE ZEROS AT THE ORIGIN
.OTE THE WIDTH OF THE REJECTION NOTCHES FOR THE DIFFERENT BINOMIAL WEIGHT CANCELER
CONFIGURATIONS )F THE D" RESPONSE RELATIVE TO AVERAGE RESPONSE IS USED AS THE MEA
SURING POINT THE REJECTION IS OF ALL TARGET DOPPLERS FOR THE SINGLE CANCELER FOR THE DUAL CANCELER AND FOR THE TRIPLE CANCELER #ONSIDER THE DUAL CANCELER
%LIMINATING OF THE DOPPLERS MEANS LIMITING THE SYSTEM TO A LONG TERM AVERAGE OF
SINGLE SCAN PROBABILITY OF DETECTION &EEDBACK CAN BE USED TO NARROW THE REJECTION
NOTCH WITHOUT MUCH DEGRADATION OF ) )F FEEDBACK IS USED TO INCREASE THE IMPROVEMENT
FACTOR THE SINGLE SCAN PROBABILITY OF DETECTION BECOMES WORSE
&IGURE SHOWS THE IMPROVEMENT FACTOR LIMITATION DUE TO SCANNING FOR CANCELERS
WITH FEEDBACK 4HESE CURVES WERE CALCULATED ASSUMING A SIN 5 5 ANTENNA PATTERN
TERMINATED AT THE FIRST NULLS
4HE NO FEEDBACK CURVES SHOWN IN &IGURE ARE ALMOST INDISTINGUISHABLE FROM
THE THEORETICAL CURVES DERIVED FOR A GAUSSIAN PATTERN SHOWN IN &IGURE /NE OF THE
CURVES SHOWING THE EFFECT OF FEEDBACK ON THE TRIPLE CANCELER IS NOT STRAIGHT BECAUSE TWO
OF THE THREE ZEROS ARE NOT AT THE ORIGIN BUT HAVE BEEN MOVED ALONG THE UNIT CIRCLE THE
OPTIMUM AMOUNT FOR HITS PER BEAMWIDTH 4HUS AT HITS PER BEAMWIDTH THESE TWO
ZEROS ARE TOO FAR REMOVED FROM THE ORIGIN TO BE VERY EFFECTIVE
&)'52% )MPROVEMENT FACTOR LIMITATION DUE TO SCANNING FOR CANCELERS WITH FEEDBACK
-4) 2!$!2
ӰΙ
)N THEORY IT IS POSSIBLE TO SYNTHESIZE ALMOST ANY VELOCITY RESPONSE CURVE WITH DIGI
TAL FILTERS !S MENTIONED EARLIER FOR EACH PAIR OF POLES AND PAIR OF ZEROS ON THE :
PLANE TWO DELAY SECTIONS ARE REQUIRED 4HE ZEROS ARE CONTROLLED BY THE FEEDFORWARD
PATHS AND THE POLES BY THE FEEDBACK PATHS
6ELOCITY RESPONSE SHAPING CAN BE ACCOMPLISHED BY THE USE OF FEEDFORWARD ONLY
WITHOUT THE USE OF FEEDBACK 4HE PRINCIPAL ADVANTAGE OF NOT USING FEEDBACK IS THE
EXCELLENT TRANSIENT RESPONSE OF THE CANCELER AN IMPORTANT CONSIDERATION IN A PHASED
ARRAY OR WHEN PULSE INTERFERENCE NOISE IS PRESENT )F A PHASED ARRAY RADAR SHOULD USE A
FEEDBACK CANCELER MANY PULSES WOULD HAVE TO BE GATED OUT AFTER THE BEAM HAS BEEN
REPOSITIONED BEFORE THE CANCELER TRANSIENT RESPONSE HAS SETTLED TO A TOLERABLE LEVEL
!N INITIALIZATION TECHNIQUE HAS BEEN PROPOSED TO ALLEVIATE THIS PROBLEM BUT IT PRO
VIDES ONLY PARTIAL REDUCTION IN THE TRANSIENT SETTLING TIME )F FEEDFORWARD ONLY IS USED
ONLY THREE OR FOUR PULSES HAVE TO BE GATED OUT AFTER MOVING THE BEAM 4HE DISADVAN
TAGE OF USING FEEDFORWARD FOR VELOCITY RESPONSE SHAPING IS THAT AN ADDITIONAL DELAY
AND THEREFORE AN ADDITIONAL TRANSMIT PULSE MUST BE PROVIDED FOR EACH ZERO USED TO
SHAPE THE RESPONSE &IGURE SHOWS THE VELOCITY RESPONSE AND : PLANE DIAGRAM OF A
FEEDFORWARD ONLY SHAPED RESPONSE FOUR PULSE CANCELER !LSO SHOWN ARE THE VELOCITY
RESPONSES OF A FIVE PULSE FEEDFORWARD CANCELER AND A THREE PULSE FEEDBACK CANCELER
&OR THE CANCELERS SHOWN THE IMPROVEMENT FACTOR CAPABILITY OF THE THREE PULSE CANCELER
IS ABOUT D" BETTER THAN THE SHAPED RESPONSE FOUR PULSE FEEDFORWARD CANCELER INDE
PENDENT OF CLUTTER SPECTRAL SPREAD
4HE FIVE PULSE CANCELER RESPONSE SHOWN IS A LINEAR PHASE -4) FILTER DESCRIBED BY
:VEREV 4HE FOUR ZEROS ARE LOCATED ON THE : PLANE REAL AXIS AT AND -UCH OF THE LITERATURE ON FILTER SYNTHESIS DESCRIBES LINEAR PHASE FILTERS
BUT FOR -4) APPLICATIONS LINEAR PHASE IS OF NO IMPORTANCE !LMOST IDENTICAL FILTER
RESPONSES CAN BE OBTAINED WITH NONLINEAR PHASE FILTERS THAT REQUIRE FEWER PULSES AS
SHOWN IN &IGURE "ECAUSE ONLY A FIXED NUMBER OF PULSES IS AVAILABLE DURING THE
TIME ON TARGET NONE SHOULD BE WASTED 4HUS ONE SHOULD CHOOSE THE NONLINEAR PHASE
FILTER THAT USES FEWER PULSES
3TAGGER $ESIGN 0ROCEDURES 4HE INTERVAL BETWEEN RADAR PULSES MAY BE CHANGED
TO MODIFY THE TARGET VELOCITIES TO WHICH THE -4) SYSTEM IS BLIND 4HE INTERVAL MAY
BE CHANGED ON A PULSE TO PULSE DWELL TO DWELL EACH DWELL BEING A FRACTION OF THE
BEAMWIDTH OR SCAN TO SCAN BASIS %ACH APPROACH HAS ADVANTAGES 4HE ADVANTAGES
OF THE SCAN TO SCAN METHOD ARE THAT IT IS EASIER TO BUILD A STABLE TRANSMITTER AND MUL
TIPLE TIME AROUND CLUTTER IS CANCELED IN A POWER AMPLIFIER -4) SYSTEM 4HE TRANSMIT
TER STABILIZATION NECESSARY FOR GOOD OPERATION OF AN UNSTAGGERED -4) IS A SIGNIFICANT
CHALLENGE 4O STABILIZE THE TRANSMITTER SUFFICIENTLY FOR PULSE TO PULSE OR DWELL TO DWELL
STAGGER OPERATION IS CONSIDERABLY MORE DIFFICULT 4YPICALLY PULSE TO PULSE STAGGERING
IS USED WITH -4) PROCESSING WHEREAS DWELL TO DWELL STAGGERING IS USED WITH -4$
FILTER BANK PROCESSING
&OR MANY -4) APPLICATIONS PULSE TO PULSE OR DWELL TO DWELL STAGGERING IS PREF
ERABLE TO SCAN TO SCAN STAGGERINGo &OR EXAMPLE IF A BINOMIAL WEIGHTED THREE PULSE
CANCELER THAT HAS WIDE REJECTION NOTCHES IS EMPLOYED AND IF SCAN TO SCAN PULSE
STAGGERING IS USED OF THE DESIRED TARGETS WOULD BE MISSING ON EACH SCAN OWING
TO DOPPLER CONSIDERATION ALONE 4HIS MIGHT BE INTOLERABLE FOR SOME APPLICATIONS
o 4HE CHOICE BETWEEN PULSE TO PULSE STAGGERING AND DWELL TO DWELL -4$ OPERATION IS A SYSTEM CONCEPT DECISIONˆ
BOTH APPROACHES HAVE THEIR ADVANTAGES &OR EXAMPLE PULSE TO PULSE STAGGERING WILL NOT PROVIDE CANCELING OF CLUTTER IN
THE AMBIGUOUS RANGE INTERVALS 7ITH DWELL TO DWELL STAGGERING AN EXTRA TRANSMITTER PULSE ALSO KNOWN AS A FILL PULSE
WILL ENABLE CANCELING OF SECOND RANGE INTERVAL CLUTTER
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2!$!2 (!.$"//+
&)'52% 3HAPED VELOCITY RESPONSE FEEDFORWARD CANCELERS COMPARED WITH THREE PULSE
FEEDBACK CANCELER 3EE TEXT FOR FIVE PULSE CANCELER PARAMETERS
7ITH PULSE TO PULSE STAGGERING GOOD RESPONSE CAN BE OBTAINED ON ALL DOPPLERS OF
INTEREST ON EACH SCAN )N ADDITION BETTER VELOCITY RESPONSE CAN BE OBTAINED AT SOME
DOPPLERS THAN EITHER PULSE INTERVAL WILL GIVE ON A SCAN TO SCAN BASIS 4HIS IS SO
BECAUSE PULSE TO PULSE STAGGERING PRODUCES DOPPLER COMPONENTS IN THE PASSBAND
OF THE -4) FILTER 0ULSE TO PULSE STAGGERING MAY DEGRADE THE IMPROVEMENT FACTOR
ATTAINABLE AS SHOWN IN &IGURE AND &IGURE BUT THIS DEGRADATION MAY NOT BE
SIGNIFICANT OR IT CAN BE ELIMINATED BY THE USE OF TIME VARYING WEIGHTS AS DESCRIBED
BELOW /NE FURTHER ADVANTAGE OF PULSE TO PULSE STAGGERING IS THAT IT MAY PERMIT
ELIMINATING THE USE OF FEEDBACK IN THE CANCELERS USED TO NARROW THE BLIND SPEED
NOTCHES WHICH ELIMINATES THE TRANSIENT SETTLING PROBLEM OF THE FEEDBACK FILTERS
4HE OPTIMUM CHOICE OF THE STAGGER RATIO DEPENDS ON THE VELOCITY RANGE OVER
WHICH THERE MUST BE NO BLIND SPEEDS AND ON THE PERMISSIBLE DEPTH OF THE FIRST NULL
-4) 2!$!2
Ó°{£
&)'52% 6ELOCITY RESPONSE CURVE DUAL CANCELER NO FEEDBACK PULSE INTERVAL RATIO
IN THE VELOCITY RESPONSE CURVE &OR MANY APPLICATIONS A FOUR PERIOD STAGGER RATIO IS
BEST AND A GOOD SET OF STAGGER RATIOS CAN BE OBTAINED BY ADDING THE FIRST BLIND SPEED
IN 66" TO THE NUMBERS OR 4HUS IN &IGURE p WHERE
THE FIRST BLIND SPEED OCCURS AT ABOUT 66" THE STAGGER RATIO IS e
ALTERNATING THE LONG AND SHORT PERIODS KEEPS THE TRANSMITTER DUTY CYCLE AS NEARLY
CONSTANT AS POSSIBLE AS WELL AS ENSURING GOOD RESPONSE AT THE FIRST NULL WHERE
6 6" &IGURES AND SHOW TWO OTHER PERIOD VELOCITY RESPONSE CURVES )F
USING FOUR INTERPULSE PERIODS MAKES THE FIRST NULL TO BE TOO DEEP THEN FIVE INTERPULSE
PERIODS MAY BE USED WITH THE STAGGER RATIO OBTAINED BY ADDING THE FIRST BLIND SPEED
TO THE NUMBER &IGURE SHOWS A VELOCITY RESPONSE CURVE FOR
FIVE PULSE INTERVALS 4HE DEPTH OF THE FIRST NULL CAN BE PREDICTED FROM &IGURE WHICH IS DISCUSSED LATER
&OR A RADAR SYSTEM WITH RELATIVELY FEW HITS PER BEAMWIDTH IT IS NOT ADVANTAGEOUS TO
USE MORE THAN FOUR OR FIVE DIFFERENT INTERVALS BECAUSE THEN THE RESPONSE TO AN INDIVIDUAL
TARGET WILL DEPEND ON WHICH PART OF THE PULSE SEQUENCE OCCURS AS THE PEAK OF THE BEAM
PASSES THE TARGET 2ANDOM VARIATION OF THE PULSE INTERVALS IS NOT DESIRABLE UNLESS USED
AS AN ELECTRONIC COUNTER COUNTERMEASURE FEATURE BECAUSE IT PERMITS THE NULLS TO BE
DEEPER THAN THE OPTIMUM CHOICE OF FOUR OR FIVE PULSE INTERVALS
7HEN THE RATIO OF PULSE INTERVALS IS EXPRESSED AS A SET OF RELATIVELY PRIME INTEGERS
IE A SET OF INTEGERS WITH NO COMMON DIVISOR OTHER THAN THE FIRST TRUE BLIND SPEED
OCCURS AT
2
6
6"
2
2 ! 2.
.
p !LL VELOCITY RESPONSE CURVES PLOTTED HEREIN PRESENT THE AVERAGE POWER RESPONSE OF THE OUTPUT PULSES OF THE CANCELER
FOR THE DURATION OF THE TIME ON TARGET FOR A SCANNING RADAR )F STAGGERING WERE USED WITH BATCH PROCESSING SUCH AS IN A
PHASED ARRAY THESE CURVES WOULD NOT APPLY FOR A SINGLE OUTPUT &OR EXAMPLE IF THE STAGGER RATIO WAS AND A
THREE PULSE &)2 FILTER IS USED IT WOULD BE NECESSARY TO TRANSMIT SIX PULSES WITH INTERPULSE SPACINGS OF AND SUM THE POWER OUTPUT FROM THE FILTER AFTER THE LAST FOUR PULSES WERE TRANSMITTED TO GET THE EQUIVALENT RESPONSE
SHOWN IN THESE CURVES
e .OTE THAT THE FIRST DIFFERENCES BETWEEN ALL COMBINATIONS OF THE INTEGERS AND ARE 4HIS hPERFECT
DIFFERENCE SETv FOR THE STAGGER SEQUENCE IS THE KEY TO THE RELATIVE FLATNESS OF THE RESPONSE CURVES
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&)'52% INTERVAL RATIO
&)'52% INTERVAL RATIO
6ELOCITY RESPONSE CURVE THREE PULSE BINOMIAL CANCELER PULSE
6ELOCITY RESPONSE CURVE THREE PULSE BINOMIAL CANCELER PULSE
&)'52% 6ELOCITY RESPONSE CURVE THREE PULSE BINOMIAL CANCELER PULSE
INTERVAL RATIO 4HIS RESPONSE CURVE CONTINUES TO 66" WITH NO DIPS BELOW D" 4HE FIRST
BLIND SPEED IS AT 66" -4) 2!$!2
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WHERE 2 2 2 2. ARE THE SET OF INTEGERS AND 6" IS THE BLIND SPEED CORRESPOND
ING TO THE AVERAGE INTERPULSE PERIOD 4HE VELOCITY RESPONSE CURVE IS SYMMETRICAL ABOUT
ONE HALF OF THE VALUE FROM %Q &EEDBACK AND 0ULSE TO 0ULSE 3TAGGERING 7HEN PULSE TO PULSE STAGGERING
IS EMPLOYED THE EFFECT OF FEEDBACK IS REDUCED 3TAGGERING CAUSES A MODULATION OF
THE SIGNAL DOPPLER AT OR NEAR THE MAXIMUM RESPONSE FREQUENCY OF THE CANCELER 4HE
AMOUNT OF THIS MODULATION IS PROPORTIONAL TO THE ABSOLUTE TARGET DOPPLER SO THAT FOR AN
AIRCRAFT FLYING AT 6" THE CANCELER RESPONSE IS ESSENTIALLY INDEPENDENT OF THE FEEDBACK
EMPLOYED &IGURE SHOWS A PLOT OF THE EFFECTS OF FEEDBACK ON A DUAL CANCELER SYS
TEM WITH HITS PER BEAMWIDTH AND A RATIO OF STAGGER INTERVALS OF 4HE FEED
BACK VALUES EMPLOYED ARE SEVERAL OF THOSE USED FOR THE UNSTAGGERED VELOCITY RESPONSE
PLOT IN &IGURE )F SCAN TO SCAN PULSE INTERVAL STAGGERING HAD BEEN USED INSTEAD OF
PULSE TO PULSE THE NO FEEDBACK RMS RESPONSE FOR THREE SCANS AT A TARGET VELOCITY OF 6"
WOULD BE D" 4HE COMPOSITE RESPONSE FOR PULSE TO PULSE STAGGERING HOWEVER IS
ONLY D" AT 6" THUS ILLUSTRATING THE ADVANTAGE OF PULSE TO PULSE STAGGERING
)MPROVEMENT &ACTOR ,IMITATIONS #AUSED BY 3TAGGERING 7HEN PULSE TO PULSE
STAGGERING IS USED IT LIMITS THE ATTAINABLE IMPROVEMENT FACTOR OWING TO THE UNEQUAL
TIME SPACING OF THE RECEIVED CLUTTER SAMPLES 4HE CURVES IN &IGURE AND &IGURE WHICH HAVE BEEN REFERRED TO SEVERAL TIMES GIVE THE APPROXIMATE LIMITATION ON ) CAUSED
BY PULSE TO PULSE STAGGERING AND EITHER ANTENNA SCANNING OR INTERNAL CLUTTER MOTION
4HEY HAVE BEEN DERIVED AS EXPLAINED BELOW
! TWO DELAY CANCELER WILL PERFECTLY CANCEL A LINEAR WAVEFORM 6T C AT IF
IT IS SAMPLED AT EQUAL TIME INTERVALS INDEPENDENT OF THE CONSTANT C OR THE SLOPE A
!DDITIONAL DELAY CANCELERS PERFECTLY CANCEL ADDITIONAL WAVEFORM DERIVATIVES EG A
THREE DELAY CANCELER WILL PERFECTLY CANCEL 6T C AT BT ! STAGGER SYSTEM WITH
TWO PULSE INTERVALS SAMPLES THE LINEAR WAVEFORM AT UNEQUAL INTERVALS AND THEREFORE
&)'52% INTERVAL RATIO
%FFECT OF FEEDBACK ON THE VELOCITY RESPONSE CURVE DUAL CANCELER PULSE
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THERE WILL BE A VOLTAGE RESIDUE FROM THE CANCELERS THAT IS PROPORTIONAL TO THE SLOPE
A AND INVERSELY PROPORTIONAL TO F WHERE F IS THE RATIO OF THE INTERVALS 4HE APPAR
ENT DOPPLER FREQUENCY OF THE RESIDUE WILL BE AT ONE HALF THE AVERAGE REPETITION RATE
OF THE SYSTEM AND THUS WILL BE AT THE FREQUENCY OF MAXIMUM RESPONSE OF A BINOMIAL
WEIGHT CANCELER
4HE RATE OF CHANGE OF PHASE OR AMPLITUDE OF CLUTTER SIGNALS IN A SCANNING RADAR IS
INVERSELY PROPORTIONAL TO THE HITS PER BEAMWIDTH N 4HUS WITH THE USE OF A COMPUTER
SIMULATION TO DETERMINE THE PROPORTIONALITY CONSTANT THE LIMITATION ON ) DUE TO STAG
GERING IS APPROXIMATELY
¤ N ³
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WHICH IS PLOTTED IN &IGURE 4HESE CURVES WHICH APPLY TO ALL MULTIPLE DELAY CANCELERS GIVE ANSWERS THAT ARE
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RATIOS !N EXAMPLE OF THE ACCURACY IS AS FOLLOWS ! SYSTEM WITH HITS PER BEAM
WIDTH A FOUR PULSE BINOMIAL WEIGHT CANCELER AND A PULSE INTERVAL RATIO HAS AN
IMPROVEMENT FACTOR LIMITATION OF D" DUE TO STAGGERING 4HE CURVE GIVES A LIMITA
TION OF D" FOR THIS CASE "UT IF THE SEQUENCE OF PULSE INTERVALS WERE TO BE CHANGED
FROM TO THE ACTUAL LIMITATION WOULD BE D" WHICH IS D" LESS
THAN THAT INDICATED BY THE CURVE 4HIS OCCURS BECAUSE THE PRIMARY MODULATION WITH A
PULSE INTERVAL RATIO LOOKS LIKE A TARGET AT MAXIMUM RESPONSE SPEED WHEREAS
THE PRIMARY MODULATION WITH A PULSE INTERVAL RATIO LOOKS LIKE A TARGET AT ONE
HALF THE SPEED OF MAXIMUM RESPONSE "ECAUSE IT IS DESIRABLE TO AVERAGE THE TRANSMITTER
DUTY CYCLE OVER AS SHORT A PERIOD AS POSSIBLE THE PULSE INTERVAL RATIO WOULD
PROBABLY BE CHOSEN FOR A PRACTICAL SYSTEM
/NCE %Q FOR THE LIMITATION ON ) DUE TO SCANNING AND STAGGERING IS OBTAINED
IT IS POSSIBLE TO DETERMINE THE LIMITATION ON ) DUE TO INTERNAL CLUTTER MOTION AND STAG
GERING )F
N
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FROM %QS AND IS SUBSTITUTED INTO %Q ¤ L FR ³
¤ L FR ³
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WHERE K IS THE WAVELENGTH FR IS THE AVERAGE PULSE REPETITION FREQUENCY AND RV IS THE
RMS VELOCITY SPREAD OF SCATTERING ELEMENTS 4HIS IS PLOTTED IN &IGURE FOR RAIN AND
FOR WOODED HILLS WITH A KNOT WIND 4HIS LIMITATION ON THE -4) IMPROVEMENT FACTOR
IS INDEPENDENT OF THE TYPE OF CANCELER EMPLOYED
4IME 6ARYING 7EIGHTS 4HE IMPROVEMENT FACTOR LIMITATION CAUSED BY PULSE TO
PULSE STAGGERING CAN BE AVOIDED BY THE USE OF TIME VARYING WEIGHTS IN THE CANCELER
FORWARD PATHS INSTEAD OF BINOMIAL WEIGHTS 4HE USE OF TIME VARYING WEIGHTS HAS NO
APPRECIABLE EFFECT ON THE -4) VELOCITY RESPONSE CURVE 7HETHER THE ADDED COMPLEX
ITY OF UTILIZING TIME VARYING WEIGHTS IS DESIRABLE DEPENDS ON WHETHER THE STAGGER
-4) 2!$!2
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LIMITATION IS PREDOMINANT &OR TWO DELAY CANCELERS THE STAGGER LIMITATION IS OFTEN
COMPARABLE WITH THE BASIC CANCELER CAPABILITY WITHOUT STAGGERING &OR THREE DELAY
CANCELERS THE STAGGER LIMITATION USUALLY PREDOMINATES
#ONSIDER THE TRANSMITTER PULSE TRAIN AND THE CANCELER CONFIGURATIONS SHOWN IN
&IGURE $URING THE INTERVAL 4. WHEN THE RETURNS FROM TRANSMITTED PULSE 0. ARE
BEING RECEIVED THE TWO DELAY CANCELER WEIGHTS SHOULD BE
!
#
4. 4. " #
AND THE THREE DELAY CANCELER WEIGHTS SHOULD BE
!
# 4. 4. 4. " #
$ 4HESE WEIGHTS HAVE BEEN DERIVED BY ASSUMING THAT THE CANCELERS SHOULD PERFECTLY
CANCEL A LINEAR WAVEFORM 6T C AT SAMPLED AT THE STAGGER RATE INDEPENDENT OF THE
VALUES OF THE CONSTANT C OR THE SLOPE A !S MENTIONED AT THE BEGINNING OF THIS SECTION A
MULTIPLE DELAY CANCELER WITH BINOMIAL WEIGHTS IN AN UNSTAGGERED SYSTEM WILL PERFECTLY
CANCEL 6T C AT
4HE CHOICE OF ! IN BOTH CASES IS ARBITRARY )N THE THREE DELAY CANCELER SETTING
$ ELIMINATES THE OPPORTUNITY FOR A SECOND ORDER CORRECTION TO CANCEL THE QUADRATIC
TERM BT WHICH COULD BE OBTAINED IF $ WERE ALSO TIME VARYING #OMPUTER CALCULATIONS
HAVE SHOWN THAT IT IS UNNECESSARY TO VARY $ IN MOST PRACTICAL SYSTEMS
&)'52% 5SE OF TIME VARYING WEIGHTS A PULSE TRAIN B TWO DELAY CANCELER
AND C THREE DELAY CANCELER
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&)'52% !PPROXIMATE DEPTH OF NULLS IN THE VELOCITY RESPONSE CURVE FOR PULSE TO PULSE
STAGGERED -4)
$EPTH OF &IRST .ULL IN 6ELOCITY 2ESPONSE 7HEN SELECTING SYSTEM PARAMETERS
IT IS USEFUL TO KNOW THE DEPTH OF THE FIRST FEW NULLS TO BE EXPECTED IN THE VELOCITY
RESPONSE CURVE !S DISCUSSED EARLIER THE NULL DEPTHS ARE ESSENTIALLY UNAFFECTED BY
FEEDBACK 4HEY ARE ALSO ESSENTIALLY INDEPENDENT OF THE TYPE OF CANCELER EMPLOYED
WHETHER SINGLE DUAL OR TRIPLE OR OF THE NUMBER OF HITS PER BEAMWIDTH &IGURE SHOWS APPROXIMATELY WHAT NULL DEPTHS CAN BE EXPECTED VERSUS THE RATIO OF MAXIMUM
TO MINIMUM INTERPULSE PERIOD
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-4) FILTERS ARE USED AT THE LOWER ELEVATION ANGLES IN WEATHER RADARS TO PREVENT WEATHER
ESTIMATES FROM BEING CONTAMINATED WITH GROUND CLUTTER RETURNS )T IS HOWEVER ALSO
VERY IMPORTANT TO PRESERVE AN ACCURATE MEASUREMENT OF WEATHER INTENSITY AND PRECIPI
TATION RATE 4O MEET THIS DUAL OBJECTIVE -4) FILTERS WITH NARROW FIXED CLUTTER REJECTION
NOTCHES AND FLAT PASSBANDS ARE NEEDED 5SE OF A VERY NARROW CLUTTER NOTCH EVEN PERMITS
MEASURING WEATHER PRECIPITATION RATES WITH A MEAN RADIAL VELOCITY OF ZERO ALBEIT WITH
SOME BIAS 3UCH MEASUREMENT IS POSSIBLE BECAUSE WEATHER USUALLY HAS A WIDE SPEC
TRAL SPREADˆTYPICALLY TO MSˆWHEREAS FIXED CLUTTER HAS A MUCH NARROWER SPECTRAL
SPREADˆTYPICALLY LESS THAN MS
"IAS AS USED HEREIN REFERS TO THE ERROR IN MEASURING RADAR REFLECTIVITY DUE TO THE CLUTTER NOTCH AND LACK OF FLATNESS
OF THE -4) FILTERS 7HEN WEATHER HAS A WIDE SPECTRAL SPREAD AND THE CLUTTER NOTCH OF THE FILTERS IS NARROW THERE IS
MINIMAL MEASUREMENT ERROR INDUCED BY THE -4) FILTERS #ONVERSELY WHEN THE WEATHER SPECTRAL WIDTH IS NARROW AND
THE RADIAL VELOCITY OF THE WEATHER IS NEAR ZERO SIGNIFICANT ERROR IN THE WEATHER REFLECTIVITY MEASUREMENT WILL EXIST
4HERE ARE OTHER CAUSES OF ERROR BETWEEN RADAR ESTIMATES OF PRECIPITATION RATES AND RAIN GAUGE MEASUREMENTS THAT ARE
NOT ADDRESSED HEREIN SUCH AS THE SPATIAL AND TEMPORAL DISTRIBUTION OF RAIN
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%XAMPLES OF WEATHER RADAR APPLICATIONS FOR WHICH -4) FILTERS ARE USED
7EATHER $OPPLER 2ADARS .%82!$732 2ADARS WITH ROTATING ANTENNAS THAT
MEASURE PRECIPITATION RATE DOPPLER VELOCITY AND TURBULENCE -EASURES TOTAL RAINFALL
AND PROVIDES TORNADO WARNINGS
4ERMINAL $OPPLER 7EATHER 2ADARS 4$72 2ADARS WITH ROTATING ANTENNAS
DESIGNED TO DETECT SEVERE WIND SHEAR IN AIRCRAFT APPROACH AND DEPARTURE PATHS CLOSE
TO AIRPORTS
!IRPORT 3URVEILLANCE 2ADARS 2ADARS WITH ROTATING ANTENNAS DESIGNED FOR AIR
TRAFFIC CONTROL FUNCTIONS IN THE TERMINAL AREA BUT WITH A SECONDARY FUNCTION OF
DETECTING AND MONITORING SEVERE WEATHER AND WIND SHEAR IN AIRCRAFT APPROACH AND
DEPARTURE PATHS
0HASED !RRAY 2ADARS 2ADARS WITH FIXED ELECTRONICALLY SCANNED ANTENNAS DESIGNED
FOR MANY FUNCTIONS SUCH AS MISSILE DETECTION AND AIR TRAFFIC CONTROL AND USED CON
CURRENTLY FOR MEASURING PRECIPITATION RATES
!S AN EXAMPLE THE DESIGN OF ELLIPTIC -4) FILTERS AS USED IN THE 4$72 WILL BE
DESCRIBED 4$72 IS A # BAND RADAR USED AT AIRPORTS FOR DETECTION OF DOWNBURSTS
MICROBURSTS AND PREDICTION OF WIND DIRECTION %LLIPTIC FILTERS ARE INFINITE IMPULSE
RESPONSE ))2 FILTERS THAT HAVE THE SHARPEST POSSIBLE TRANSITION FROM REJECTION NOTCH TO
PASSBAND FOR A SPECIFIED LEVEL OF THE CLUTTER REJECTION NOTCH WIDTH AND DEPTH RIPPLE IN
THE PASSBAND AND NUMBER OF DELAY SECTIONS SEE /PPENHEIM AND 3CHAFER 4HE ELLIP
TIC FILTERS CAN BE FOLLOWED WITH PULSE PAIR PROCESSING FOR ESTIMATION OF WEATHER MEAN
VELOCITY AND SPECTRAL WIDTH TURBULENCE 4HERE ARE TWO DRAWBACKS OF ELLIPTIC FILTERS
&IRST THE LONG TRANSIENT SETTLING TIME &OR A SCANNING WEATHER RADAR IT TAKES ABOUT FOUR
BEAMWIDTHS OF SCANNING AFTER THE TRANSMITTER STARTS PULSING BEFORE CLUTTER ATTENUATION
REACHES TO D" 3ECOND IF THE INPUT CLUTTER SIGNAL REACHES THE LIMIT LEVEL IN THE
)& RECEIVER THERE WILL BE A SIGNIFICANT TRANSIENT INCREASE OF CLUTTER RESIDUE /NE OF THE
ELLIPTIC FILTERS EMPLOYED IN THE ORIGINAL 4$72 RADAR IS USED AS AN EXAMPLE
4$72 OPERATES AT # BAND '(Z 4HE ANTENNA ROTATES AT RPM AND
HAS A — ONE WAY BEAMWIDTH 4HE 02& IS (Z 4HE ELLIPTIC FILTER DESIGNED FOR
THESE PARAMETERS HAS AN IMPROVEMENT FACTOR OF D" ("7 HITS PER ONE WAY D"
BEAMWIDTH ARE 4HE SPECIFICATIONS FOR THE ELLIPTIC FILTER FOR THE ABOVE PARAMETERS
ARE NORMALIZED STOPBAND EDGE RF4 PASSBAND EDGE RF4 STOP
BAND ATTENUATION D" BELOW PEAK FILTER RESPONSE AND PASSBAND RIPPLE D"
4O MEET THESE REQUIREMENTS THE FILTER REQUIRES DELAY SECTIONS WHICH CAN BE IMPLE
MENTED AS TWO CASCADED DELAY SECTIONS AS SHOWN IN &IGURE &)'52% &OUR DELAY ELLIPTIC FILTER USED IN 4$72
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4HE FILTER COEFFICIENTS ARE
A A B B A A B B 4HE CALCULATED IMPROVEMENT FACTOR FOR THIS FILTER AGAINST LAND CLUTTER WITH ("7 IS
D" AND THE BIAS FOR WEATHER RETURNS WITH SPECTRAL SPREADS OF AND MSEC IS n D"
AND n D" RESPECTIVELY WHEN THE RADIAL VELOCITY OF THE WEATHER RETURNS IS V MS
&IGURE SHOWS THE ELLIPTIC FILTER #7 RESPONSE AND ITS RESPONSE FOR WEATHER WITH
MS AND MS RMS SPECTRAL SPREAD 4HE UNAMBIGUOUS DOPPLER INTERVAL CORRESPONDING
TO FD4 IS MS FOR THE PARAMETERS USED TO CALCULATE THIS RESPONSE
&IGURE SHOWS THE TIME DOMAIN RESPONSES FOR THIS FILTER AS THE ANTENNA SCANS
PAST A POINT OF CLUTTER SUCH AS A WATER TOWER 4HIS FIGURE SHOWS THE INPUT TO THE ELLIPTIC
FILTER AND THE RESIDUE OUTPUT ! GAUSSIAN ANTENNA PATTERN IS ASSUMED IN THIS FIGURE 4HE
CALCULATED IMPROVEMENT FACTOR FOR THE SEQUENCE SHOWN TOTAL CLUTTER POWER INTO THE
FILTER DIVIDED BY TOTAL RESIDUE POWER OUT OF THE FILTER NORMALIZED BY THE NOISE GAIN OF
THE FILTER IS D"
! SINX X ANTENNA PATTERN IS ASSUMED FOR THE FOLLOWING THREE FIGURES BUT THE LESSONS
TO BE GAINED FROM THESE FIGURES IS ESSENTIALLY INDEPENDENT OF THE ASSUMED BEAM SHAPE
&IGURE SHOWS THE FILTER RESPONSE IF THE TRANSMITTER STARTS RADIATING JUST AS A NULL OF
THE ANTENNA PATTERN PASSES THE POINT OF CLUTTER 4HE INDIVIDUAL SAMPLES OF RESIDUE ARE
OR MORE D" BELOW THE PEAK CLUTTER RETURN 4HE IMPROVEMENT FACTOR FOR THIS SEQUENCE
IS D"
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4IME DOMAIN CLUTTER INPUT AND OUTPUT RESIDUE AS ANTENNA SCANS PAST
&IGURE SHOWS THE RESIDUE IF THE TRANSMITTER STARTS RADIATING AS THE PEAK OF THE
BEAM PASSES THE POINT CLUTTER &ORTY NINE PULSES AFTER THE TRANSMITTER STARTS RADIATING
THE RESIDUE HAS DECAYED ONLY D" )T WOULD TAKE AT LEAST ANOTHER PULSES FOR THE
RESIDUE TO DECAY TO D" &OR THIS REASON WHEN THE TRANSMITTER STARTS PULSING A SET
TLING TIME OF AT LEAST PULSES MUST BE ALLOWED BEFORE USEFUL DATA IS COLLECTED
&)'52% NUMBER #LUTTER INPUT AND RESIDUE FROM ELLIPTIC FILTER 2ADAR STARTS RADIATING AT PULSE
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&)'52% NUMBER #LUTTER INPUT AND RESIDUE FROM ELLIPTIC FILTER 2ADAR STARTS RADIATING AT PULSE
&IGURE SHOWS THE EFFECT OF THE RETURNED SIGNAL IF THE POINT CLUTTER EXCEEDS THE
)& LIMIT LEVEL BY D" 7HEN THE SIGNAL REACHES THE LIMIT LEVEL THERE IS A STEP INCREASE
OF RESIDUE OF ABOUT D" 4$72 USES CLUTTER MAPS TO NORMALIZE THE RESIDUE FROM THE
STRONG POINTS OF CLUTTER THAT EXCEED THE LIMIT LEVEL
4HE WEATHER MODE OF !IRPORT 3URVEILLANCE 2ADARS IS DEMONSTRATED BY FIVE PULSE
FINITE IMPULSE RESPONSE &)2 FILTERS USED IN THE !32 AN 3 BAND RADAR USED FOR
AIR TRAFFIC CONTROL AT AIRPORTS 4HE DESIGN OF THE FILTERS IS PRIMARILY FOR -OVING 4ARGET
$ETECTOR -4$ DETECTION OF AIRCRAFT BUT SPECIAL ATTENTION IS GIVEN TO PROVIDING FLAT
PASSBAND RESPONSE FOR ACCURATE WEATHER REFLECTIVITY ESTIMATION 4HE FILTER BANK FOR
("7 IS PICTURED IN &IGURE AND THE COEFFICIENTS ARE SHOWN IN 4ABLE &)'52% %FFECT OF LIMITING ON ELLIPTIC FILTER RESPONSE
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4!",% !32 #OEFFICIENTS OF !32 0ULSE ,OW 02& &IR &ILTERS
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#OEFFICIENT #OEFFICIENT #OEFFICIENT #OEFFICIENT #OEFFICIENT D"
D"
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D"
D"
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3ELECTION OF FILTERS IS BASED ON CLUTTER AMPLITUDE INFORMATION STORED IN A CLUTTER MAP
4HE FILTERS ARE SELECTED ON A RANGE CELL BY #0) BASIS
4HESE &)2 CLUTTER FILTERS HAVE THE NARROWEST REJECTION NOTCHES THAT CAN BE OBTAINED
WITH FIVE PULSES AND THE INDICATED LEVEL OF FIXED CLUTTER REJECTION (OWEVER THE
NOTCHES ARE SIGNIFICANTLY WIDER THAN THOSE OF THE ELLIPTIC FILTERS THUS THEY WILL
HAVE GREATER BIAS FOR MEASUREMENT OF WEATHER INTENSITY WHEN THE WEATHER RADIAL
VELOCITY IS ZERO
&OR PHASED ARRAY RADARS &)2 FILTERS SIMILAR TO THOSE DESCRIBED FOR THE !32 ARE
APPLICABLE 4HE FILTERS CAN BE DESIGNED IF THE TIME BUDGET OF THE PHASED ARRAY RADAR
ALLOWS TO UTILIZE MORE THAN THE FIVE PULSES PER COHERENT PROCESSING INTERVAL #0) USED
BY THE !32 RADAR 5SING MORE PULSES MAKES POSSIBLE NARROWER REJECTION NOTCHES
AND THUS LESS BIAS FOR ESTIMATES OF PRECIPITATION WITH ZERO RADIAL VELOCITY
&)'52% 2ESPONSE OF !32 &)2 FILTERS LOW 02& FR PPS FILTERS OPERATING AGAINST FIXED CLUTTER
WITH ("7 4HE UNAMBIGUOUS DOPPLER INTERVAL F 4 IS MS FOR THE PARAMETERS USED TO CALCULATE
THIS RESPONSE
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!S DISCUSSED IN 3ECTION THE -4$ USES A WAVEFORM CONSISTING OF COHERENT PRO
CESSING INTERVALS #0)S OF . PULSES ALL AT THE SAME 02& AND 2& FREQUENCY 4HE 02&
AND POSSIBLY THE 2& ARE CHANGED FROM ONE #0) TO THE NEXT 7ITH THIS CONSTRAINT ONLY
FINITE IMPULSE RESPONSE &)2 FILTER DESIGNS ARE REALISTIC CANDIDATES FOR THE FILTER BANK
DESIGN &EEDBACK FILTERS REQUIRE A NUMBER OF PULSES TO SETTLE AFTER EITHER THE 02& OR
THE 2& IS CHANGED AND THUS WOULD NOT BE PRACTICAL
4HE NUMBER OF PULSES AVAILABLE DURING THE TIME WHEN A SURVEILLANCE RADAR BEAM
ILLUMINATES A POTENTIAL TARGET POSITION IS DETERMINED BY SYSTEM PARAMETERS AND REQUIRE
MENTS SUCH AS BEAMWIDTH 02& VOLUME TO BE SCANNED AND THE REQUIRED DATA UPDATE
RATE 'IVEN THE CONSTRAINT ON THE NUMBER OF PULSES ON TARGET ONE MUST DECIDE HOW
MANY #0)S SHOULD OCCUR DURING THE TIME ON TARGET AND HOW MANY PULSES PER #0) 4HE
COMPROMISE IS USUALLY DIFFICULT /NE WISHES TO USE MORE PULSES PER #0) TO ENABLE THE
USE OF BETTER FILTERS BUT ONE ALSO WISHES TO HAVE AS MANY #0)S AS POSSIBLE -ULTIPLE
#0)S AT DIFFERENT 02&S AND PERHAPS AT DIFFERENT 2& FREQUENCIES IMPROVE DETECTION
AND CAN PROVIDE INFORMATION FOR TRUE RADIAL VELOCITY DETERMINATION
4HE DESIGN OF THE INDIVIDUAL FILTERS IN THE DOPPLER FILTER BANK IS A COMPROMISE BETWEEN
THE FREQUENCY SIDELOBE REQUIREMENT AND THE DEGRADATION IN THE COHERENT INTEGRATION GAIN
OF THE FILTER 4HE NUMBER OF DOPPLER FILTERS REQUIRED FOR A GIVEN LENGTH OF THE #0) MUST BE
BALANCED BETWEEN HARDWARE COMPLEXITY AND THE STRADDLING LOSS AT THE CROSSOVER BETWEEN
FILTERS &INALLY THE REQUIREMENT OF PROVIDING A HIGH DEGREE OF CLUTTER SUPPRESSION AT ZERO
DOPPLER LAND CLUTTER SOMETIMES INTRODUCES SPECIAL DESIGN CONSTRAINTS
7HEN THE NUMBER OF PULSES IN A #0) IS LARGE q THE SYSTEMATIC DESIGN PRO
CEDURE AND EFFICIENT IMPLEMENTATION OF THE FAST &OURIER TRANSFORM &&4 ALGORITHM
IS PARTICULARLY ATTRACTIVE 4HROUGH THE USE OF APPROPRIATE WEIGHTING FUNCTIONS OF THE
TIME DOMAIN RETURNS IN A SINGLE #0) THE RESULTING FREQUENCY SIDELOBES CAN BE READILY
CONTROLLED &URTHER THE NUMBER OF FILTERS EQUAL TO THE ORDER OF THE TRANSFORM NEEDED
TO COVER THE TOTAL DOPPLER SPACE EQUAL TO THE RADAR 02& CAN BE CHOSEN INDEPENDENTLY
OF THE #0) AS DISCUSSED BELOW
!S THE #0) BECOMES SMALLER a IT BECOMES IMPORTANT TO CONSIDER SPECIAL
DESIGNS OF THE INDIVIDUAL FILTERS TO MATCH THE SPECIFIC CLUTTER SUPPRESSION REQUIREMENTS
AT DIFFERENT DOPPLER FREQUENCIES IN ORDER TO ACHIEVE BETTER OVERALL PERFORMANCE 7HILE
SOME SYSTEMATIC PROCEDURES ARE AVAILABLE FOR DESIGNING &)2 FILTERS SUBJECT TO SPECIFIC
PASSBAND AND STOPBAND CONSTRAINTS THE STRAIGHTFORWARD APPROACH FOR SMALL #0)S IS
TO USE AN EMPIRICAL APPROACH IN WHICH THE ZEROS OF EACH FILTER ARE ADJUSTED UNTIL THE
DESIRED RESPONSE IS OBTAINED !N EXAMPLE OF SUCH FILTER DESIGNS IS PRESENTED NEXT
%MPIRICAL &ILTER $ESIGN !N EXAMPLE OF AN EMPIRICAL FILTER DESIGN FOR A SIX PULSE
#0) FOLLOWS 4HE SIX PULSES PER #0) MAY BE DRIVEN BY SYSTEM CONSIDERATIONS SUCH AS
TIME ON TARGET "ECAUSE THE FILTER WILL USE SIX PULSES ONLY FIVE ZEROS ARE AVAILABLE FOR
THE FILTER DESIGN THE NUMBER OF ZEROS AVAILABLE IS THE NUMBER OF PULSES MINUS ONE 4HE
FILTER DESIGN PROCESS CONSISTS OF PLACING THE ZEROS TO OBTAIN A FILTER BANK RESPONSE THAT
CONFORMS TO THE SPECIFIED CONSTRAINTS 4HE EXAMPLE THAT FOLLOWS WAS PRODUCED WITH AN
INTERACTIVE COMPUTER PROGRAM WITH WHICH THE ZEROS COULD BE MOVED UNTIL THE DESIRED
RESPONSE WAS OBTAINED 4HE ASSUMED FILTER REQUIREMENTS ARE AS FOLLOWS
L
0ROVIDE A RESPONSE OF D" IN THE CLUTTER REJECTION NOTCH RELATIVE TO THE PEAK TARGET
RESPONSE OF THE MOVING TARGET FILTERS
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0ROVIDE A RESPONSE OF D" FOR CHAFF REJECTION AT VELOCITIES BETWEEN o OF THE
AMBIGUOUS DOPPLER FREQUENCY RANGE
)N THIS DESIGN ONLY FIVE FILTERS WILL BE IMPLEMENTED
4HREE OF THE FIVE FILTERS WILL REJECT FIXED CLUTTER AND RESPOND TO MOVING TARGETS 4WO
FILTERS WILL RESPOND TO TARGETS AT ZERO DOPPLER AND ITS AMBIGUITIES 7ITH GOOD FIXED
CLUTTER REJECTION FILTERS IT TAKES TWO OR MORE COHERENT FILTERS TO COVER THE GAP IN
RESPONSE AT ZERO VELOCITY
7ITH THE ABOVE CONSIDERATIONS A FILTER BANK CAN BE CONSTRUCTED
&IGURE A SHOWS THE FILTER DESIGNED TO RESPOND TO TARGETS IN THE MIDDLE OF THE
DOPPLER PASSBAND 4HE SIDELOBES NEAR ZERO VELOCITY ARE D" DOWN FROM THE PEAK
THUS PROVIDING GOOD CLUTTER REJECTION FOR CLUTTER WITHIN OF ZERO DOPPLER 4HE D"
SIDELOBE PROVIDES CHAFF REJECTION TO o "ECAUSE OF THE CONSTRAINT OF HAVING ONLY FIVE
ZEROS AVAILABLE THIS FILTER COULD NOT PROVIDE D" REJECTION TO o
&IGURE B SHOWS THE FILTER THAT RESPONDS TO TARGETS AS NEAR AS POSSIBLE TO ZERO
DOPPLER WHILE HAVING A ZERO DOPPLER RESPONSE OF D" 4WO ZEROS ARE PLACED NEAR
PROVIDING D" RESPONSE TO CLUTTER AT 4HE FILTER SIDELOBES BETWEEN AND DOPPLER PROVIDE THE SPECIFIED CHAFF REJECTION OF D" ! MIRROR IMAGE OF THIS FILTER IS
USED FOR THE THIRD MOVING DOPPLER FILTER 4HE MIRROR IMAGE FILTER HAS COEFFICIENTS THAT
ARE COMPLEX CONJUGATES OF THE ORIGINAL FILTER COEFFICIENTS
&IGURE C SHOWS THE FIRST FILTER DESIGNED FOR RESPONSE AT ZERO DOPPLER
#ONSIDERATIONS HERE ARE THAT THE DOPPLER STRADDLING LOSS OF THE FILTER BANK BE MINIMIZED
&)'52% 3IX PULSE FILTERS FOR TARGETS AT A F 4 B &T F 4 AND C COMBINED RESPONSE
OF COMPLETE BANK OF FIVE SIX PULSE FILTERS
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THIS DICTATES THE LOCATION OF THE PEAK THAT THE RESPONSE TO CHAFF AT DOPPLER BE
DOWN D" AND THAT THE MISMATCH LOSS BE MINIMIZED -INIMIZING THE MISMATCH LOSS
IS ACCOMPLISHED BY PERMITTING THE FILTER SIDELOBES BETWEEN AND TO RISE AS HIGH
AS NEEDED LOWER SIDELOBES IN THIS RANGE INCREASE THE MISMATCH LOSS 4HE SECOND ZERO
DOPPLER FILTER IS THE MIRROR IMAGE OF THIS ONE
&IGURE D SHOWS THE COMPOSITE RESPONSE OF THE FILTER BANK .OTE THAT THE FILTER
PEAKS ARE FAIRLY EVENLY DISTRIBUTED 4HE DIP BETWEEN THE FIRST ZERO DOPPLER FILTER AND
THE FIRST MOVING DOPPLER FILTER IS LARGER THAN THE OTHERS PRIMARILY BECAUSE UNDER THE
CONSTRAINTS IT IS IMPOSSIBLE TO MOVE THE FIRST DOPPLER FILTER NEARER TO ZERO VELOCITY
#HEBYSHEV &ILTER "ANK &OR A LARGER NUMBER OF PULSES IN THE #0) A MORE SYSTEM
ATIC APPROACH TO FILTER DESIGN IS DESIRABLE )F A DOPPLER FILTER DESIGN CRITERION IS CHOSEN
THAT REQUIRES THE FILTER SIDELOBES OUTSIDE THE MAIN RESPONSE TO BE BELOW A SPECIFIED LEVEL
IE PROVIDING A CONSTANT LEVEL OF CLUTTER SUPPRESSION WHILE SIMULTANEOUSLY MINIMIZ
ING THE WIDTH OF THE FILTER RESPONSE A FILTER DESIGN BASED ON THE $OLPH #HEBYSHEV DIS
TRIBUTION PROVIDES THE OPTIMUM SOLUTION 0ROPERTIES AND DESIGN PROCEDURES BASED ON
THE $OLPH #HEBYSHEV DISTRIBUTION CAN BE FOUND IN THE ANTENNA LITERATURE !N EXAMPLE
OF A FILTER DESIGN FOR A #0) OF PULSES AND A SIDELOBE REQUIREMENT OF D" IS SHOWN IN
&IGURE 4HE PEAK FILTER RESPONSE CAN BE LOCATED ARBITRARILY IN FREQUENCY BY ADDING
A LINEAR PHASE TERM TO THE FILTER COEFFICIENTS
4HE TOTAL NUMBER OF FILTERS IMPLEMENTED TO COVER ALL DOPPLER FREQUENCIES IS A DESIGN
OPTION TRADING STRADDLING LOSS AT THE FILTER CROSSOVER FREQUENCIES AGAINST IMPLEMENTA
TION COMPLEXITY !N EXAMPLE OF A COMPLETE DOPPLER FILTER BANK IMPLEMENTED WITH NINE
UNIFORMLY SPACED FILTERS IS SHOWN IN &IGURE 4HE PERFORMANCE OF THIS DOPPLER FILTER
BANK AGAINST THE CLUTTER MODEL CONSIDERED IN &IGURE IS SHOWN IN &IGURE 4HIS
GRAPH SHOWS THE SIGNAL TO CLUTTER RATIO IMPROVEMENT AGAINST CLUTTER AT ZERO DOPPLER AS
A FUNCTION OF TARGET DOPPLER FREQUENCY /NLY THE RESPONSE OF THE FILTER PROVIDING THE
GREATEST IMPROVEMENT IS PLOTTED AT EACH TARGET DOPPLER
&OR COMPARISON THE OPTIMUM CURVE FROM &IGURE IS SHOWN BY A BROKEN LINE AND
THUS PROVIDES A DIRECT ASSESSMENT OF HOW WELL THE #HEBYSHEV FILTER DESIGN PERFORMS
AGAINST A GIVEN CLUTTER MODEL !LSO SHOWN IS THE AVERAGE 3#2 IMPROVEMENT FOR BOTH
THE OPTIMUM AND THE #HEBYSHEV FILTER BANK
&)'52% #HEBYSHEV &)2 FILTER DESIGN WITH D" DOPPLER SIDELOBES
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$OPPLER FILTER BANK OF D" #HEBYSHEV FILTERS #0) PULSES
&INALLY &IGURE SHOWS THE AVERAGE 3#2 IMPROVEMENT OF THE D" #HEBYSHEV
DOPPLER FILTER BANK AS WELL AS THE OPTIMUM CURVE FROM &IGURE AS A FUNCTION
OF THE RELATIVE SPECTRUM SPREAD OF THE CLUTTER /WING TO THE FINITE NUMBER OF FILTERS
IMPLEMENTED IN THE FILTER BANK THE AVERAGE 3#2 IMPROVEMENT WILL CHANGE BY A SMALL
AMOUNT IF A DOPPLER SHIFT IS INTRODUCED INTO THE CLUTTER RETURNS 4HIS EFFECT IS ILLUSTRATED
BY THE CROSS HATCHED REGION WHICH SHOWS UPPER AND LOWER LIMITS ON THE AVERAGE 3#2
IMPROVEMENT FOR ALL POSSIBLE CLUTTER DOPPLER SHIFTS &OR A SMALLER NUMBER OF FILTERS IN
THE DOPPLER FILTER BANK THIS VARIATION WOULD BE GREATER
&AST &OURIER 4RANSFORM &ILTER "ANK &OR A LARGE NUMBER OF PARALLEL DOPPLER
FILTERS HARDWARE IMPLEMENTATION CAN BE SIMPLIFIED SIGNIFICANTLY THROUGH THE USE OF
THE &&4 ALGORITHM 4HE USE OF THIS ALGORITHM CONSTRAINS ALL FILTERS IN THE FILTER BANK TO
&)'52% THE OPTIMUM
3#2 IMPROVEMENT OF D" #HEBYSHEV DOPPLER FILTER BANK COMPARED WITH
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2!$!2 (!.$"//+
&)'52% !VERAGE 3#2 IMPROVEMENT FOR THE D" #HEBYSHEV FILTER BANK SHOWN
IN &IGURE #0) PULSES /PTIMUM IS FROM &IGURE HAVE IDENTICAL RESPONSES AND THE FILTERS WILL BE UNIFORMLY SPACED ALONG THE DOPPLER
AXIS 4HE NUMBER OF FILTERS IMPLEMENTED FOR A GIVEN SIZE OF THE #0) CAN HOWEVER
BE VARIED &OR EXAMPLE A GREATER NUMBER OF FILTERS CAN BE REALIZED BY EXTENDING THE
RECEIVED DATA WITH EXTRA ZERO VALUES ALSO KNOWN AS ZERO PADDING AFTER THE RECEIVED
RETURNS HAVE BEEN APPROPRIATELY WEIGHTED IN ACCORDANCE WITH THE DESIRED FILTER
RESPONSE EG #HEBYSHEV &ILTER "ANK $ESIGNS 5SING #ONSTRAINED /PTIMIZATION 4ECHNIQUES &OR A
GREATER NUMBERS OF PULSES IN THE #0) AND WHEN THE ECONOMY OF THE &&4 IMPLEMENTA
TION OF A DOPPLER FILTER BANK CAN BE REPLACED BY A &)2 IMPLEMENTATION MORE DESIRABLE
&)2 FILTER RESPONSES CAN BE REALIZED THROUGH THE USE OF APPROPRIATE NUMERICAL DIGITAL
FILTER DESIGN TECHNIQUES 4HE GOAL IS SIMILAR TO THAT PURSUED WITH THE EMPIRICAL FILTER
DESIGNS DISCUSSED EARLIER BUT FILTERS WITH A LARGE NUMBER OF TAPS CAN BE DESIGNED TO
EXACTING SPECIFICATIONS
!S AN EXAMPLE CONSIDER THE DESIGN OF A DOPPLER FILTER BANK FOR AN 3 BAND '(Z
RADAR USING A #0) OF . PULSES USING A 02& OF K(Z !SSUME THAT THE RADAR REQUIRE
MENTS CALL FOR A SUPPRESSION OF STATIONARY LAND CLUTTER BY D" AND A SUPPRESSION OF
MOVING CLUTTER RAIN BY D" &OR THE FILTER DESIGN A CLUTTER ATTENUATION D" BELOW
THESE REQUIREMENTS WILL BE NEEDED TO KEEP THE SENSITIVITY LOSS DUE TO THE CLUTTER RESIDUE
BELOW D" AND ALSO BECAUSE EACH DOPPLER FILTER WILL HAVE A COHERENT GAIN OF AROUND
• LOG D" THIS MUST BE ADDED TO THE FILTER DESIGN SPECIFICATION AS WELL 4HE
TOTAL 3 BAND DOPPLER SPACE FOR THE ABOVE RADAR PARAMETERS IS MS AND ASSUMING THAT
THE LAND CLUTTER SUPPRESSION REGION HAS TO BE o MS AND THAT THE MOVING CLUTTER SUPPRES
SION REGION HAS TO BE o MS THE CONSTRAINT FOR ALL DOPPLER FILTER DESIGNS NORMALIZED TO
THEIR PEAK IS AS SHOWN IN &IGURE 5SING A SIGNAL PROCESSING TOOLBOX DEVELOPED BY $R $AN 0 3CHOLNIK OF THE .AVAL
2ESEARCH ,ABORATORY A DOPPLER FILTER BANK MEETING THE ABOVE CONSTRAINTS WAS DESIGNED
4HE FIRST FILTER WHICH HAS ITS PEAK LOCATED AS CLOSE AS POSSIBLE TO THE LEFT EDGE OF THE
CONSTRAINT BOX IS SHOWN IN &IGURE WITH THE ABSCISSA NORMALIZED TO THE TOTAL AVAIL
ABLE DOPPLER SPACE
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-4) 2!$!2
" $
#$!
&)'52% $OPPLER FILTER DESIGN CONSTRAINTS
4HE MISMATCH LOSS OF THIS FILTER IS ,M D" WHICH IS WELL BELOW THAT OF A D"
$OLPH #HEBYSHEV FILTER BANK ,M D" &OR THE REMAINING FILTERS A RELATIVE SPAC
ING OF $ WAS USED BUT THIS COULD BE REDUCED IN ORDER TO MINIMIZE
DOPPLER STRADDLING LOSSES 4HE THIRD FILTER IN THE FILTER BANK IS SHOWN IN &IGURE '%#! #(
#$ ##
$& !!"(
&)'52% ,EFTMOST &)2 FILTER IN DOPPLER FILTER BANK DESIGN
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2!$!2 (!.$"//+
'%#! #(
#$ ## $& !!"(
&)'52% 4HIRD &)2 FILTER IN DOPPLER FILTER BANK DESIGN
4HE MISMATCH LOSS HAS NOW BEEN REDUCED TO D" &INALLY THE COMPLETE DOPPLER
FILTER BANK IS SHOWN IN &IGURE 4HIS FILTER BANK COULD BE AUGMENTED WITH ADDI
TIONAL FILTERS AROUND ZERO DOPPLER BUT THESE WOULD NOT MEET THE DESIGN CONSTRAINTS
DISCUSSED ABOVE 4HE MAIN BENEFIT OF A CUSTOMIZED DOPPLER FILTER BANK DESIGN AS
$" %
!#%
&)'52% #OMPLETE DOPPLER FILTER BANK DESIGN
-4) 2!$!2
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DESCRIBED HERE IS ITS REDUCED MISMATCH LOSS &OR THE FILTERS IN THE ABOVE DESIGN
THE AVERAGE MISMATCH LOSS IS ,M D" A SAVINGS OF D" AS COMPARED TO THE
ALTERNATIVE OF A D" WEIGHTED $OLPH #HEBYSHEV FILTER BANK
Ó°££Ê * ,",
Ê , /" ÊÊ
1- Ê 9Ê,
6 ,Ê/ %LSEWHERE IN THIS CHAPTER 3ECTIONS AND PARTICULARLY )& BANDPASS LIMITERS
HAVE BEEN DISCUSSED AS A MEANS OF PREVENTING RECEIVED CLUTTER SIGNALS FROM EXCEED
ING THE RANGE OF THE !$ CONVERTERS NORMALIZING -4) CLUTTER RESIDUE CAUSED BY
SYSTEM INSTABILITIES AND NORMALIZING RESIDUE DUE TO THE SPECTRAL SPREAD OF hFIXED
CLUTTERv CAUSED BY EITHER SCANNING OR WIND BLOWN MOTION 4HERE ARE OCCASIONAL CLUTTER
RESIDUE SPIKES WHEN CLUTTER EXCEEDS THE LIMIT LEVEL AND IN THE PAST THE ENERGY FROM
THESE SPIKES OF RESIDUE HAS BEEN SUPPRESSED BY FURTHER REDUCTION OF THE LIMIT LEVEL
7HEN LIMITERS HAVE BEEN USED TO NORMALIZE THE ENERGY OF CLUTTER RESIDUE SPIKES THE
AVERAGE IMPROVEMENT FACTOR OF THE -4) SYSTEMS DRASTICALLY DETERIORATES 4HE EQUA
TIONS FOR ) IMPROVEMENT FACTOR OF A SCANNING RADAR IN 3ECTION ARE BASED ON LINEAR
THEORY &IELD MEASUREMENTS HOWEVER HAVE SHOWN THAT MANY SCANNING MULTIPLE DELAY
-4) RADAR SYSTEMS FALL CONSIDERABLY SHORT OF THE PREDICTED PERFORMANCE 4HIS OCCURS
BECAUSE THE )& BANDPASS LIMITERS HAVE BEEN USED TO SUPPRESS THE ENERGY OF THE RESIDUE
SPIKES THAT ARE CAUSED BY THE LIMITING ACTION ,ATER IN THIS SECTION IT IS SHOWN THAT THE
USE OF A BINARY DETECTION SCHEME INSTEAD OF A DRASTIC REDUCTION OF THE LIMIT LEVEL CAN
BE USED TO MAINTAIN A CLUTTER REJECTION PERFORMANCE CLOSE TO LINEAR THEORY PREDICTION IN
THE RESOLUTION CELLS WHERE CLUTTER LIMITING OCCUR
!N EXAMPLE OF HOW LIMITING THE DYNAMIC RANGE ADJUSTS THE RESIDUE IS SHOWN IN THE
-4) 00) PHOTOGRAPHS SHOWN IN &IGURE 4HE RANGE RINGS ARE AT MI INTERVALS
&)'52% %FFECT OF LIMITERS A D" IMPROVEMENT FACTOR D" INPUT DYNAMIC RANGE AND
B D" IMPROVEMENT FACTOR D" INPUT DYNAMIC RANGE
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2!$!2 (!.$"//+
! NUMBER OF BIRDS ARE SHOWN ON THE DISPLAY 4HE RESIDUE FROM CLUTTER IN THE LEFT PHOTO
GRAPH IS SOLID OUT TO NMI AND THEN DECREASES UNTIL IT IS ALMOST ENTIRELY GONE AT NMI
4HE -4) IMPROVEMENT FACTOR IN BOTH PICTURES IS D" BUT THE INPUT DYNAMIC RANGE
PEAK SIGNAL TO RMS NOISE TO THE CANCELER WAS CHANGED FROM TO D" BETWEEN THE
TWO PICTURES !N AIRCRAFT FLYING OVER THE CLUTTER IN THE FIRST MI IN THE LEFT HAND PICTURE
COULD NOT BE DETECTED NO MATTER HOW LARGE ITS RADAR CROSS SECTION )N THE RIGHT HAND PIC
TURE THE AIRCRAFT COULD BE DETECTED IF THE TARGET TO CLUTTER CROSS SECTION RATIO WERE SUF
FICIENT !LTHOUGH THIS EXAMPLE IS FROM MANY YEARS AGO THE PRINCIPLE IS STILL THE SAME
EVEN THOUGH CURRENT -4) IMPROVEMENT FACTORS ARE BETTER BY TENS OF D"S 2ESTRICTION
OF THE )& DYNAMIC RANGE IS STILL A VERY EFFICIENT WAY OF NORMALIZING CLUTTER RESIDUE DUE
TO SYSTEM INSTABILITIES OR CLUTTER SPECTRAL SPREAD TO SYSTEM NOISE 4HIS IS TRUE WHETHER
OR NOT THE RADAR USES PULSE COMPRESSION
0RIOR TO THE DEVELOPMENT OF MODERN CLUTTER MAPS FOR CONTROLLING FALSE ALARMS
CAUSED BY CLUTTER RESIDUE OR THE MORE RECENT SUGGESTION THAT BINARY INTEGRATION CAN
MITIGATE IMPULSE LIKE RESIDUE THE USE OF )& LIMITING WAS ESSENTIAL FOR FALSE ALARM
CONTROL IN AN -4) RADAR 3UCH LIMITING HOWEVER SERIOUSLY AFFECTS THE MEAN IMPROVE
MENT FACTOR OBTAINABLE WITH A SCANNING LIMITED MULTIPLE DELAY CANCELER BECAUSE OF
THE INCREASED SPECTRAL SPREAD OF THE CLUTTER THAT EXCEEDS THE LIMIT LEVEL 0ART OF THE
ADDITIONAL CLUTTER SPECTRAL COMPONENTS COMES FROM THE SHARP DISCONTINUITY IN THE
ENVELOPE OF RETURNS AS THE CLUTTER REACHES THE LIMIT LEVEL ! TIME DOMAIN EXAMPLE
OF THIS PHENOMENON IS SHOWN IN &IGURE FOR A RADAR WITH . HITS PER BEAM
WIDTH /N THE LEFT IS A POINT TARGET THAT DOES NOT EXCEED THE LIMIT LEVEL ON THE RIGHT
IS A POINT TARGET THAT EXCEEDS THE LIMIT LEVEL BY D" .OTE THAT FOR THIS EXAMPLE
) DEGRADES BY D" FOR THE DUAL CANCELER AND BY D" FOR THE TRIPLE CANCELER
4HE EXACT RESULT OF THIS CALCULATION DEPENDS ON THE ASSUMED SHAPE OF THE ANTENNA
PATTERN FOR THIS EXAMPLE A SINU PATTERN TERMINATED AT THE FIRST NULLS WAS ASSUMED
U
4HERE IS A COMPARABLE IMPROVEMENT FACTOR DEGRADATION DUE TO SPECTRAL SPREADING OF
LIMITED DISTRIBUTED CLUTTER &IGURES AND SHOW THE EXPECTED MEAN
IMPROVEMENT FACTOR FOR TWO THREE AND FOUR PULSE CANCELERS AS A FUNCTION OF R,
THE RATIO OF THE RMS CLUTTER AMPLITUDE TO THE LIMIT LEVEL (ITS PER ONE WAY HALF POWER
BEAMWIDTH ARE INDICATED BY .
!N EXAMPLE OF CLUTTER RESIDUE FROM SIMULATED HARD LIMITED DISTRIBUTED CLUTTER IS
TAKEN FROM (ALL AND 3HRADER &IGURE SHOWS A POLAR PLOT OF PART OF A LINEAR CLUT
TER SEQUENCE FOR A SCANNING RADAR WITH . HITS PER BEAMWIDTH 4HIS LINEAR CLUTTER
SEQUENCE IS CONSECUTIVE COMPLEX VOLTAGE RETURNS FROM ONE RANGE CELL OF DISTRIBUTED
CLUTTER &IGURE SHOWS THE PHASE AND AMPLITUDE OF THIS SEQUENCE
)F THIS CLUTTER SEQUENCE WERE D" STRONGER AND PASSED THROUGH A 6 )& LIMITER
ONLY THE PHASE INFORMATION WOULD REMAIN %ACH PULSE WOULD HAVE A 6 AMPLITUDE
7HEN THE RESULTING LIMITED CLUTTER SEQUENCE IS PASSED THROUGH A THREE PULSE CANCELER
COEFFICIENTS n THE OUTPUT RESIDUE APPEARS AS IN &IGURE A 4HE CORRESPOND
ING PULSE TO PULSE IMPROVEMENT FACTOR IS SHOWN &IGURE B
4HE EXPECTED THREE PULSE CANCELER IMPROVEMENT FACTOR FROM EQUATION FOR
A LINEAR SYSTEM WITH . IS ) N D" )N &IGURE B IT IS SEEN THAT
THIS LEVEL OF ) IS ACHIEVED FOR MOST OF THE PULSES WITH ONLY TWO PULSES HAVING VERY
LOW VALUES OF ) 4HE STATISTICS FOR THE DISTRIBUTION OF ) FOR THE THREE PULSE CANCELER FOR
HARD LIMITED DISTRIBUTED CLUTTER ARE SHOWN IN &IGURE .OTE THAT FOR . LESS THAT OF THE HARD LIMITED SAMPLES HAVE AN IMPROVEMENT
FACTOR LESS THAN D" WHEREAS ALMOST OF THE SAMPLES EXCEED THE ) EXPECTED FOR
A LINEAR SYSTEM
-4) 2!$!2
&)'52% Ó°È£
)MPROVEMENT FACTOR RESTRICTION CAUSED BY A LIMITER
4HE TIME DOMAIN ILLUSTRATION SHOWN PREVIOUSLY IN &IGURE LEADS TO THE CONCLU
SION OF (ALL AND 3HRADER THAT USING AN - OUT OF . BINARY DETECTOR AT THE OUTPUT OF AN
-4) FILTER WILL PRECLUDE FALSE ALARMS FROM THE CLUTTER RESIDUES CAUSED BY LIMITING
&IGURE SHOWS IN ADDITION TO CLUTTER RESIDUE THE RETURNS FROM A TARGET THAT WAS
SUPERIMPOSED ON THE DISTRIBUTED CLUTTER PRIOR TO THE CLUTTER PLUS TARGET SEQUENCE PASS
ING THROUGH THE )& LIMITING PROCESS /NE CAN SEE THAT MANY OF THE INDIVIDUAL PULSE
RETURNS FROM THE TARGET EXCEED THE DETECTION THRESHOLD WHEREAS ONLY FOUR OF THE CLUTTER
RESIDUE PULSES EXCEED THE THRESHOLD
4O SUMMARIZE 4HE -4) IMPROVEMENT FACTOR IN A MAJORITY OF LIMITING CLUTTER
CELLS EXCEEDS THE AVERAGE IMPROVEMENT FACTOR OBTAINED WITH LINEAR PROCESSING CELLS
WITH POOR -4) IMPROVEMENT FACTOR CAN BE REJECTED WITH BINARY DETECTION PROCESSING
AND THEREFORE EXCELLENT -4) PERFORMANCE CAN BE OBTAINED EVEN IN REGIONS OF CLUTTER
THAT EXCEED THE )& DYNAMIC RANGE
Ó°ÈÓ
2!$!2 (!.$"//+
&)'52% -EAN IMPROVEMENT FACTOR RESTRICTION VERSUS AMOUNT OF LIMITING AND CLUTTER
SPECTRAL SPREAD FOR A TWO PULSE CANCELER AFTER 4 - (ALL AND 7 7 3HRADER Ú )%%% AND
( 2 7ARD AND 7 7 3HRADER Ú )%%% &)'52% -EAN IMPROVEMENT FACTOR RESTRICTION VERSUS AMOUNT OF LIMITING AND CLUTTER
SPECTRAL SPREAD FOR A THREE PULSE CANCELER AFTER 4 - (ALL AND 7 7 3HRADER Ú )%%% AND ( 2 7ARD AND 7 7 3HRADER Ú )%%% Ó°ÈÎ
-4) 2!$!2
'
$&
$*
) $&$*
!%*$,!%+**!)(!*)%$ *# "
&)'52% -EAN IMPROVEMENT FACTOR RESTRICTION VERSUS AMOUNT OF LIMITING AND
CLUTTER SPECTRAL SPREAD FOR A FOUR PULSE CANCELER AFTER 4 - (ALL AND 7 7 3HRADER
Ú )%%% AND ( 2 7ARD AND 7 7 3HRADER Ú )%%% .OTE THAT THIS DISCUSSION OF BINARY DETECTION IS ADDRESSED TO THE SPECTRAL DISTRIBUTION
OF REAL CLUTTER THAT WHEN VIEWED IN THE TIME DOMAIN BEFORE LIMITING HAS A SMOOTHLY
VARYING CHANGE OF THE AMPLITUDE AND PHASE OF THE CLUTTER VECTOR 4HIS IS DISTINCT FROM
CLUTTER VARIATIONS DUE TO SYSTEM INSTABILITIES THAT ARE NOISE LIKE WHEREIN THE SYSTEM
DYNAMIC RANGE SHOULD BE LIMITED TO PREVENT THE INSTABILITY RESIDUE FROM EXCEEDING THE
SYSTEM NOISE LEVEL
&)'52% 0OLAR REPRESENTATION OF A LINEAR CLUTTER SEQUENCE
FOR HITS PER BEAMWIDTH AFTER 4 - (ALL AND 7 7 3HRADER
Ú )%%% Ó°È{
2!$!2 (!.$"//+
&)'52% ,INEAR CLUTTER SEQUENCE AMPLITUDE AND PHASE FOR HITS
PER BEAMWIDTH AFTER 4 - (ALL AND 7 7 3HRADER Ú )%%% &)'52% A 4HREE PULSE CANCELER RESIDUE AND B IMPROVEMENT FACTOR FOR HARD
LIMITED CLUTTER SEQUENCE FOR . HITS PER BEAMWIDTH AFTER 4 - (ALL AND 7 7 3HRADER
Ú )%%% Ó°Èx
-4) 2!$!2
$"&)&%' #%
$%%!(!'" ! !
!
!
&!')#& )*
!
&!'))#%#+
&)'52% $ISTRIBUTION OF ) AND MEAN OF ) FOR HARD LIMITED CLUTTER FOR DIFFERENT NUMERS OF SCAN
NING HITS PER BEAMWIDTH &OR REFERENCE THE MEAN OF ) IS ALSO SHOWN FOR LINEAR PROCESSING ) REFERS TO THE
IMPROVEMENT FACTOR OF A THREE PULSE -4) CANCELER AFTER 4 - (ALL AND 7 7 3HRADER Ú )%%% # "#! "!! "
&)'52% !FTER -4) PROCESSING OF THE HARD LIMITED DISTRIBUTED CLUTTER
SEQUENCE . AND A TARGET SUPERIMPOSED ON THE CLUTTER SEQUENCE THE RESIDUE
SPIKES ARE DISTINCTLY DIFFERENT FROM THE TARGET RETURNS ! BINARY - OF . DETECTOR
WILL REJECT THE RESIDUE AND KEEP THE TARGET AFTER 4 - (ALL AND 7 7 3HRADER
Ú )%%% Ó°£ÓÊ , ,Ê-9-/ Ê-/ /9Ê
, +1, /3YSTEM )NSTABILITIES .OT ONLY DO THE ANTENNA MOTION AND CLUTTER SPECTRUM AFFECT
THE IMPROVEMENT FACTOR THAT IS ATTAINABLE BUT SYSTEM INSTABILITIES ALSO PLACE A LIMIT ON
-4) PERFORMANCE 4HESE INSTABILITIES COME FROM THE STALO AND COHO FROM THE TRANS
MITTER PULSE TO PULSE FREQUENCY CHANGE IF A PULSED OSCILLATOR AND FROM PULSE TO PULSE
Ó°ÈÈ
2!$!2 (!.$"//+
PHASE CHANGE IF A POWER AMPLIFIER FROM THE INABILITY TO LOCK THE COHO PERFECTLY TO THE
PHASE OF THE REFERENCE PULSE FROM TIME JITTER AND AMPLITUDE JITTER ON THE PULSES AND
FROM QUANTIZATION NOISE OF THE !$ CONVERTER 0HASE INSTABILITIES WILL BE CONSIDERED FIRST )F THE PHASES OF CONSECUTIVE RECEIVED
PULSES RELATIVE TO THE PHASE OF THE COHO DIFFER BY SAY RAD A LIMITATION OF D"
IS IMPOSED ON ) 4HE RAD CLUTTER VECTOR CHANGE WOULD BE EQUIVALENT TO A TARGET
VECTOR D" WEAKER THAN THE CLUTTER BEING SUPERIMPOSED ON THE CLUTTER AS SHOWN
IN &IGURE )N THE POWER AMPLIFIER -4) SYSTEM SHOWN IN &IGURE PULSE TO PULSE PHASE
CHANGES IN THE TRANSMITTED PULSE CAN BE INTRODUCED BY THE PULSED AMPLIFIER 4HE
MOST COMMON CAUSE OF A POWER AMPLIFIER INTRODUCING PHASE CHANGES IS RIPPLE ON THE
HIGH VOLTAGE POWER SUPPLY /THER CAUSES OF PHASE INSTABILITY INCLUDE AC VOLTAGE ON A
TRANSMITTER TUBE FILAMENT AND UNEVEN POWER SUPPLY LOADING SUCH AS THAT CAUSED BY
PULSE TO PULSE STAGGER
)N THE PULSED OSCILLATOR SYSTEM SHOWN IN &IGURE PULSE TO PULSE FREQUENCY
CHANGES RESULT IN PHASE RUN OUT DURING THE TRANSMITTED PULSE 0HASE RUN OUT IS THE
CHANGE OF THE TRANSMITTED PULSE PHASE DURING THE PULSE DURATION WITH RESPECT TO THE
PHASE OF THE REFERENCE OSCILLATOR )F THE COHO LOCKED PERFECTLY TO THE END OF THE TRANS
MITTED PULSE A TOTAL PHASE RUN OUT OF RAD DURING THE TRANSMITTED PULSE WOULD THEN
PLACE AN AVERAGE LIMITATION OF D" ON THE IMPROVEMENT FACTOR ATTAINABLE 0ULSE TO
PULSE FREQUENCY CHANGE IN MICROWAVE OSCILLATORS IS PRIMARILY CAUSED BY HIGH VOLTAGE
POWER SUPPLY RIPPLE )N THE PULSED OSCILLATOR SYSTEM A PULSE TO PULSE PHASE DIFFERENCE
OF RAD IN LOCKING THE COHO RESULTS IN ) LIMITATION OF D" !S NOTED ELSEWHERE
FREQUENCY CHANGE DURING A PULSE FROM A PULSED OSCILLATOR DOES NOT LIMIT ) IF IT REPEATS
PRECISELY PULSE TO PULSE
4HE LIMITATIONS ON THE IMPROVEMENT FACTOR THAT ARE DUE TO EQUIPMENT INSTABILITIES IN
THE FORM OF FREQUENCY CHANGES OF THE STALO AND COHO BETWEEN CONSECUTIVE TRANSMITTED
PULSES ARE A FUNCTION OF THE RANGE OF THE CLUTTER 4HESE CHANGES ARE CHARACTERIZED IN
TWO WAYS !LL OSCILLATORS HAVE A NOISE SPECTRUM )N ADDITION CAVITY OSCILLATORS USED
BECAUSE THEY ARE READILY TUNABLE ARE MICROPHONIC AND THUS THEIR FREQUENCY MAY VARY
AT AN AUDIO RATE 4HE LIMITATION ON THE IMPROVEMENT FACTOR DUE TO FREQUENCY CHANGES
IS THE DIFFERENCE IN THE NUMBER OF RADIANS THAT THE OSCILLATOR RUNS THROUGH BETWEEN
THE TIME OF TRANSMISSION AND THE TIME OF RECEPTION OF CONSECUTIVE PULSES 4HUS THE
IMPROVEMENT FACTOR WILL BE LIMITED TO D" IF O$F 4 RAD WHERE $ F IS THE
OSCILLATOR FREQUENCY CHANGE BETWEEN TRANSMITTED PULSES AND 4 IS THE TRANSIT TIME OF
THE PULSE TO AND FROM THE TARGET
&)'52% 0HASE INSTABILITY
-4) 2!$!2
&)'52% Ó°ÈÇ
0OWER AMPLIFIER SIMPLIFIED BLOCK DIAGRAM
4O EVALUATE THE EFFECTS OF OSCILLATOR PHASE NOISE ON -4) PERFORMANCE THERE ARE FOUR
STEPS &IRST DETERMINE THE SINGLE SIDEBAND POWER SPECTRAL DENSITY OF THE PHASE NOISE AS
A FUNCTION OF FREQUENCY FROM THE CARRIER 3ECOND INCREASE THIS SPECTRAL DENSITY BY
D" 4HIS ACCOUNTS FOR A D" INCREASE BECAUSE BOTH SIDEBANDS OF NOISE AFFECT CLUT
TER RESIDUE AND A D" INCREASE BECAUSE THE OSCILLATOR CONTRIBUTES NOISE DURING BOTH
TRANSMITTING AND RECEIVING 4HIRD ADJUST THE OSCILLATOR PHASE NOISE SPECTRAL DENSITY
DETERMINED ABOVE DUE TO THE FOLLOWING THREE EFFECTS A THE SELF CANCELLATION OF PHASE
NOISE BASED ON CORRELATION RESULTING FROM THE TWO WAY RANGE DELAY OF THE CLUTTER OF
INTEREST B NOISE REJECTION DUE TO THE FREQUENCY RESPONSE OF THE CLUTTER FILTERS AND
C NOISE REJECTION DUE TO THE FREQUENCY RESPONSE OF THE RECEIVER PASSBAND &INALLY AS
THE FOURTH STEP INTEGRATE THE ADJUSTED SPECTRAL DENSITY OF THE PHASE NOISE ACROSS THE
ENTIRE PASSBAND 4HE RESULT IS THE LIMITATION ON ) DUE TO THE OSCILLATOR NOISE
2ATHER THAN PERFORMING THIS INTEGRATION OF THE RESIDUAL NOISE NUMERICALLY A MUCH
SIMPLER ANALYSIS CAN BE CARRIED OUT IF BOTH THE OSCILLATOR PHASE NOISE CHARACTERISTIC AND
ALL OF THE ADJUSTMENTS TO PHASE NOISE ARE APPROXIMATED BY STRAIGHT LINES ON A DECIBEL
VERSUS LOG FREQUENCY PLOT 4HIS PROCEDURE BECOMES PARTICULARLY SIMPLE WHEN A -4)
&)2 FILTER USING BINOMIAL COEFFICIENTS IS ASSUMED 4HE LOCATIONS ALONG THE FREQUENCY
AXIS WHERE THE STRAIGHT LINES INTERSECT ARE CALLED BREAK FREQUENCIES 4HIS SIMPLIFIED
PROCEDURE WHICH IS SIMILAR TO THAT PRESENTED IN 6IGNERI ET AL IS DESCRIBED IN THE
FOLLOWING PARAGRAPHS
4HE FIRST OF THE THREE ADJUSTMENTSˆOSCILLATOR NOISE SELF CANCELLATION DUE TO THE
RANGE OF THE CLUTTER OF INTERESTˆREDUCES NOISE AT THE LOW FREQUENCIES BY D" PER
DECADE BELOW THE BREAK FREQUENCY OF F • 42 • P (ERE 42 • 2 C IS THE TIME
&)'52% 0ULSED OSCILLATOR SIMPLIFIED BLOCK DIAGRAM
Ó°Èn
2!$!2 (!.$"//+
&)'52% 3TRAIGHT LINE APPROXIMATION TO TWO DELAY BINOMIAL -4)
DELAY OF THE CLUTTER RETURN 2 IS THE CLUTTER RANGE AND C IS THE SPEED OF LIGHT &OR THE
SECOND ADJUSTMENT DUE TO THE FREQUENCY RESPONSE OF THE CLUTTER FILTERS WHICH AS STATED
PREVIOUSLY ARE ASSUMED TO BE &)2 CANCELERS WITH BINOMIAL WEIGHTS IT IS NOTED THAT
THE RESPONSE AT VERY LOW FREQUENCIES FALL OFF AT D" PER DECADE FOR ONE DELAY D"
PER DECADE FOR TWO DELAYS D" PER DECADE FOR THREE DELAYS ETC !S AN EXAMPLE
THE APPROXIMATION USED FOR A TWO DELAY -4) FILTER IS SHOWN IN &IGURE 4HE -4)
RESPONSE HAS A PEAK VALUE OF y D" RESULTING IN AN AVERAGE NOISE GAIN OF
UNITY AND THE STRAIGHT LINE APPROXIMATION FOLLOWS THE LOW FREQUENCY ASYMPTOTE UP TO
THE D" LEVEL WHICH OCCURS AT F 4 AND STAYS CONSTANT AT THE D" LEVEL AT ALL
HIGHER FREQUENCIES 4HE JUSTIFICATION FOR THE D" APPROXIMATION AT THE HIGHER FREQUEN
CIES IS THAT THE OSCILLATOR SPECTRAL DENSITY IS MORE NEARLY CONSTANT AND THE AVERAGE OVER
ONE PERIOD OF THE -4) RESPONSE IS UNITY &OR OTHER BINOMIAL COEFFICIENT -4) CANCELERS
THE BREAK FREQUENCIES FOR THE START OF THE RESPONSE FALLOFF ARE F 4 FOR ONE DELAY
FOR TWO DELAYS FOR THREE DELAYS AND FOR FOUR DELAYS
&OR EXAMPLE CONSIDER AN OSCILLATOR WITH SINGLE SIDEBAND PHASE NOISE SPECTRAL
DENSITY AS SHOWN IN &IGURE !LL OSCILLATOR NOISE CONTRIBUTIONS ARE ASSUMED TO BE
COMBINED INTO THIS ONE CURVE 4HE SINGLE SIDEBAND NOISE IS INCREASED BY D" BECAUSE
BOTH SIDEBANDS AFFECT SYSTEM STABILITY AND THE POWER INTEGRATION IS ONLY CARRIED OUT
FOR POSITIVE FREQUENCIES AND BY AN ADDITIONAL D" BECAUSE THE OSCILLATOR INTRODUCES
NOISE IN BOTH THE UPCONVERSION TO THE TRANSMITTED SIGNAL AND IN THE RECEIVER DOWNCON
VERSION PROCESS
&IGURE SHOWS THE SPECTRAL MODIFICATIONS DUE TO THE SYSTEM RESPONSES A 4HE
FIRST MODIFICATION ACCOUNTS FOR CORRELATION DUE TO THE RANGE TO THE CLUTTER OF INTEREST
;ASSUMED CLUTTER RANGE IS y NMI KM THUS THE BREAK FREQUENCY IS (Z=
B 3ECOND A THREE PULSE BINOMIAL WEIGHTED CANCELER IS ASSUMED WITH THE RADAR OPERAT
ING AT A 02& OF (Z 4HUS THE BREAK FREQUENCY IS r (Z C 4HIRD
THE RECEIVER PASSBAND IS ASSUMED TO EXTEND FROM K(Z TO K(Z WITH RESPECT
TO THE )& CENTER FREQUENCY -(: TOTAL PASSBAND AT THE D" POINTS AND DETERMINED
BY A TWO POLE FILTER 4HUS THE RECEIVER PASSBAND RESPONSE FALLS OFF AT D" PER DECADE
FROM THE BREAK FREQUENCY AT K(Z AS SHOWN
-4) 2!$!2
&)'52% NOISE DENSITY
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3INGLE SIDEBAND PHASE NOISE SPECTRAL DENSITY OF A MICROWAVE OSCILLATOR AND THE EFFECTIVE
4HE ADJUSTED PHASE NOISE SPECTRAL DENSITY IS SHOWN IN &IGURE 4HE TOTAL NOISE
POWER WITH RESPECT TO THE CARRIER IS DETERMINED BY INTEGRATION OF THE NOISE POWER UNDER
THE CURVE 4HE EQUATION FOR THE POWER SPECTRAL DENSITY OF ANY ONE SEGMENT AS A FUNC
TION OF FREQUENCY IS
¤ F³
3 F 3 • ¥ ´
¦ F µ
A
F a F a F
(ERE F AND F ARE THE START AND END FREQUENCIES OF THE SEGMENT RESPECTIVELY
3 (Zn IS THE PHASE NOISE SPECTRAL DENSITY RELATIVE TO THE CARRIER AT THE BEGINNING OF
THE SEGMENT AND @ IS THE SLOPE OF THE SEGMENT IN LOG UNITS PER DECADE .OTE THAT THE
&)'52% OSCILLATOR
!DJUSTMENTS BASED ON SYSTEM PARAMETERS SEE TEXT TO THE PHASE NOISE OF A MICROWAVE
Ó°Çä
2!$!2 (!.$"//+
&)'52% #OMPOSITE ADJUSTMENTS AND ADJUSTED PHASE NOISE SPECTRAL DENSITY
D"C(Z VALUES IN &IGURE CORRESPOND TO • LOG 3 &URTHER DENOTING THE PHASE
NOISE SPECTRAL DENSITY RELATIVE TO THE CARRIER AT THE END OF THE SEGMENT AS 3 (Zn THE
SLOPE IS DEFINED BY
A
LOG 3 3
LOG F F
4HE SLOPE IN D"DECADE IS EQUAL TO • A 4HE NOISE POWER CONTRIBUTION CORRESPOND
ING TO THIS SEGMENT IS FOUND AS
ª 3
A FA ¶¸
ALL A w ­ F A • A • §© F
­ 0«
­ 3 • ;LNN F
LN F =
A ­¬ FA
4ABLE GIVES THE INTEGRATION FOR THE EXAMPLE 7HEN THE INTEGRATED POWERS FOR ALL
SEGMENTS HAVE BEEN CALCULATED THEY ARE SUMMED AND THEN CONVERTED BACK TO D"C 4HE
FINAL ANSWER D"C IS THE LIMIT ON ) THAT RESULTS FROM OSCILLATOR NOISE 4HE LIMIT
ON )3#2 D" IS ) D" PLUS TARGET INTEGRATION GAIN D" )NTEGRATION OF THE 0HASE .OISE 3PECTRAL $ENSITY OF &IGURE WITH !DJUSTMENTS OF
&IGURE AS 3HOWN IN &IGURE 4!",% 3EGMENT F (Z
E
E
E
F (Z
3LOPE 3LOPE
D"DEK
@
3 D"C(Z
3 D"C(Z
)NTEGRATED
POWER
)NTEGRATED
POWER D"C
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4OTAL INTEGRATED NOISE POWER
-4) 2!$!2
Ó°Ç£
4IME JITTER OF THE TRANSMITTED PULSES RESULTS IN DEGRADATION OF -4) SYSTEMS 4IME
JITTER RESULTS IN FAILURE OF THE LEADING AND TRAILING EDGES OF THE PULSES TO CANCEL THE
AMPLITUDE OF EACH UNCANCELLED PART BEING $TS WHERE $T IS THE TIME JITTER AND S IS THE
TRANSMITTED PULSE LENGTH 4HE TOTAL RESIDUE POWER IS $TS AND THEREFORE THE LIMITA
TION ON THE IMPROVEMENT FACTOR DUE TO TIME JITTER IS ) • LOG;T $ T = D" 4HIS
LIMIT ON THE IMPROVEMENT FACTOR IS BASED ON A #7 TRANSMITTER PULSE AND ON THE ASSUMP
TION THAT THE RECEIVER BANDWIDTH IS MATCHED TO THE DURATION OF THE TRANSMITTED PULSE )N
A PULSE COMPRESSION SYSTEM THE RECEIVER BANDWIDTH IS WIDER BY THE TIME BANDWIDTH
"S PRODUCT THUS THE CLUTTER RESIDUE POWER AT EACH END OF THE PULSE INCREASES IN
PROPORTION TO THE "S PRODUCT 4HE LIMIT ON ) FOR A CHIRP PULSE COMPRESSION SYSTEM IS
THEN ) • LOG;T •$ T • " • T = &OR PULSE COMPRESSION SYSTEMS EMPLOYING PHASE
CODED WAVEFORMS THE FACTOR IN THE PRECEDING EQUATION SHOULD BE MULTIPLIED BY THE
NUMBER OF SUBPULSES IN THE WAVEFORM 4HUS FOR EXAMPLE THE LIMIT ON ) FOR A PULSE
"ARKER CODE IS
) LOG ;T r $ T = D"
0ULSE WIDTH JITTER RESULTS IN ONE HALF THE RESIDUE OF TIME JITTER AND
) LOG
T
D"
$07 "T
WHERE $07 IS PULSE WIDTH JITTER
!MPLITUDE JITTER IN THE TRANSMITTED PULSE ALSO CAUSES A LIMITATION OF
) LOG
!
D"
$!
WHERE ! IS THE PULSE AMPLITUDE AND $! IS THE PULSE TO PULSE CHANGE IN AMPLITUDE 4HIS
LIMITATION APPLIES EVEN THOUGH THE SYSTEM USES LIMITING BEFORE THE CANCELER BECAUSE
THERE IS ALWAYS MUCH CLUTTER PRESENT THAT DOES NOT REACH THE LIMIT LEVEL 7ITH MOST
TRANSMITTERS HOWEVER THE AMPLITUDE JITTER IS INSIGNIFICANT AFTER THE FREQUENCY STABILITY
OR PHASE STABILITY REQUIREMENTS HAVE BEEN MET
*ITTER IN THE SAMPLING TIME IN THE !$ CONVERTER ALSO LIMITS -4) PERFORMANCE
)F PULSE COMPRESSION IS DONE PRIOR TO THE !$ OR IF THERE IS NO PULSE COMPRESSION
THIS LIMIT IS
) LOG
T
D"
* "T
WHERE * IS THE TIMING JITTER S IS TRANSMITTED PULSE LENGTH AND "S IS THE TIME
BANDWIDTH PRODUCT )F PULSE COMPRESSION IS DONE SUBSEQUENT TO THE !$ CONVERTER
THEN THE LIMITATION IS
) LOG
T
D"
*"T
4HE LIMITATIONS ON THE ATTAINABLE -4) IMPROVEMENT FACTOR ARE SUMMARIZED IN
4ABLE 4HIS DISCUSSION HAS ASSUMED THAT THE PEAK TO PEAK VALUES OF THESE INSTA
BILITIES OCCUR ON A PULSE TO PULSE BASIS WHICH IS OFTEN THE CASE IN PULSE TO PULSE
STAGGERED -4) OPERATION )F IT IS KNOWN THAT THE INSTABILITIES ARE RANDOM THE PEAK
Ó°ÇÓ
4!",% 2!$!2 (!.$"//+
)NSTABILITY ,IMITATIONS
0ULSE TO 0ULSE )NSTABILITY
,IMIT ON )MPROVEMENT &ACTOR
/SCILLATOR PHASE NOISE
3EE DISCUSSION IN TEXT
4RANSMITTER FREQUENCY
) LOG ;O $F S =
3TALO OR COHO FREQUENCY
) LOG ;O $F 4 =
4RANSMITTER PHASE SHIFT
) LOG $E
#OHO LOCKING
) LOG $E
0ULSE TIMING
) LOG ;T $T "T =
0ULSE WIDTH
) LOG ;T $07 "T =
0ULSE AMPLITUDE
) LOG !$!
!$ JITTER
) LOG ;T * "T =
!$ JITTER WITH PULSE COMPRESSION FOLLOWING !$
) LOG ;T *"T =
WHERE $F
INTERPULSE FREQUENCY CHANGE
S
TRANSMITTED PULSE LENGTH
4
TRANSMISSION TIME TO AND FROM TARGET
$E
INTERPULSE PHASE CHANGE
$T
TIME JITTER
*
!$ SAMPLING TIME JITTER
"S
TIME BANDWIDTH PRODUCT OF PULSE COMPRESSION
SYSTEM "S UNITY FOR #7 PULSES
$07 PULSE WIDTH JITTER
!
PULSE AMPLITUDE 6
$!
INTERPULSE AMPLITUDE CHANGE
VALUES SHOWN IN THESE EQUATIONS CAN BE REPLACED BY THE RMS PULSE TO PULSE VALUES
WHICH GIVES RESULTS ESSENTIALLY IDENTICAL TO 3TEINBERGS RESULTS
)F THE INSTABILITIES OCCUR AT SOME KNOWN FREQUENCY EG HIGH VOLTAGE POWER SUP
PLY RIPPLE THE RELATIVE EFFECT OF THE INSTABILITY CAN BE DETERMINED BY LOCATING THE
RESPONSE ON THE VELOCITY RESPONSE CURVE FOR THE -4) SYSTEM FOR A TARGET AT AN EQUIVA
LENT DOPPLER FREQUENCY )F FOR INSTANCE THE RESPONSE IS D" DOWN FROM THE MAXIMUM
RESPONSE THE LIMITATION ON ) IS ABOUT D" LESS SEVERE THAN INDICATED IN THE EQUATIONS
IN 4ABLE )F ALL SOURCES OF INSTABILITY ARE INDEPENDENT AS WOULD USUALLY BE THE
CASE THEIR INDIVIDUAL POWER RESIDUES CAN BE ADDED TO DETERMINE THE TOTAL LIMITATION
ON -4) PERFORMANCE
)NTRAPULSE FREQUENCY OR PHASE VARIATIONS DO NOT INTERFERE WITH GOOD -4) OPERATION
PROVIDED THEY REPEAT PRECISELY FROM PULSE TO PULSE 4HE ONLY CONCERN IS A LOSS OF SEN
SITIVITY IF PHASE RUN OUT DURING THE TRANSMITTED PULSE OR MISTUNING OF THE COHO OR STALO
PERMITS THE RECEIVED PULSES TO BE SIGNIFICANTLY DETUNED FROM THE INTENDED )& FREQUENCY
)F A RAD PHASE RUN OUT DURING THE PULSE IS PERMITTED THE SYSTEM DETUNING MAY BE AS
LARGE AS OS (Z WITH NO DEGRADATION OF -4) PERFORMANCE
4O GIVE AN EXAMPLE OF INTERPULSE STABILITY REQUIREMENTS CONSIDER A -(Z
RADAR TRANSMITTING A #7 PULSE OF DURATION S MS AND THE REQUIREMENT THAT NO
SINGLE SYSTEM INSTABILITY WILL LIMIT THE -4) IMPROVEMENT FACTOR ATTAINABLE AT A RANGE
OF NMI TO LESS THAN D" A VOLTAGE RATIO OF 4HE RMS PULSE TO PULSE
TRANSMITTER FREQUENCY CHANGE IF A PULSED OSCILLATOR MUST BE LESS THAN
$F (Z
PT
WHICH IS A STABILITY OF ABOUT PARTS IN Ó°ÇÎ
-4) 2!$!2
4HE RMS PULSE TO PULSE TRANSMITTER PHASE SHIFT CHANGE IF A POWER AMPLIFIER MUST
BE LESS THAN
$F RAD 4HE STALO OR COHO FREQUENCY CHANGE IN THE INTERPULSE PERIOD MUST BE LESS THAN
$F (Z
P r r WHICH IS A STABILITY OF PART IN FOR THE STALO AT ABOUT '(Z AND PART IN FOR
THE COHO ASSUMING A -(Z )& FREQUENCY 4HE COHO LOCKING IF A PULSED OSCILLATOR SYSTEM MUST BE WITHIN
$F RAD 4HE PULSE TIMING JITTER MUST BE LESS THAN
$T T
r r S
4HE PULSE WIDTH JITTER MUST BE LESS THAN
$07 r T
r S
4HE PULSE AMPLITUDE CHANGE MUST BE LESS THAN
$!
PERCENT
! 4HE !$ SAMPLING TIME JITTER MUST BE LESS THAN
*
r T
r S
/F THE ABOVE REQUIREMENTS OSCILLATOR PHASE NOISE MAY DOMINATE (OWEVER IN
SYSTEMS WITH LARGE BANDWIDTHS SHORT COMPRESSED PULSES THE TIMING JITTER REQUIRE
MENTS BECOME SIGNIFICANT AND MAY REQUIRE SPECIAL CLOCK REGENERATION CIRCUITRY AT KEY
SYSTEM LOCATIONS
%FFECT OF 1UANTIZATION .OISE ON )MPROVEMENT &ACTOR 1UANTIZATION NOISE
INTRODUCED IN THE !$ CONVERTER LIMITS THE ATTAINABLE -4) IMPROVEMENT FACTOR
#ONSIDER A CONVENTIONAL VIDEO -4) SYSTEM AS SHOWN IN &IGURE "ECAUSE THE
PEAK SIGNAL LEVEL IS CONTROLLED BY THE LINEAR LIMITING AMPLIFIER THE PEAK EXCURSION OF
THE PHASE DETECTOR OUTPUT IS KNOWN AND THE !$ CONVERTER IS DESIGNED TO COVER THIS
EXCURSION )F THE !$ CONVERTER USES . BITS AND THE PHASE DETECTOR OUTPUT IS FROM TO
THE QUANTIZATION INTERVAL IS . 4HE RMS VALUE OF THE SIGNAL LEVEL DEVIATION
Ó°Ç{
2!$!2 (!.$"//+
&)'52% $IGITAL -4) CONSIDERATION
INTRODUCED BY THE !$ CONVERTER IS ; . = 4HE LIMIT ON THE -4) IMPROVE
MENT FACTOR THAT THIS IMPOSES ON A SIGNAL REACHING THE FULL EXCURSION OF THE PHASE DETEC
TOR IS FOUND BY SUBSTITUTING IN THE FOLLOWING EQUATION FROM 4ABLE ) LOG
ª
!
LOG « .
$!
¬; ¹
LOG ; .
º
= »
=
"ECAUSE TWO QUADRATURE CHANNELS CONTRIBUTE INDEPENDENT !$ NOISE THE AVERAGE
LIMIT ON THE IMPROVEMENT FACTOR OF A FULL RANGE SIGNAL IS
§
) LOG ¨ .
©
¶
LOG ; .
·
¸
=
)F THE SIGNAL DOES NOT REACH THE FULL EXCURSION OF THE !$ CONVERTER WHICH IS NORMALLY
THE CASE THEN THE QUANTIZATION LIMIT ON ) IS PROPORTIONATELY MORE SEVERE &OR EXAMPLE
IF THE SYSTEM IS DESIGNED SO THAT THE MEAN LEVEL OF THE STRONGEST CLUTTER OF INTEREST IS
D" BELOW THE !$ CONVERTER PEAK THE LIMIT ON ) WOULD BE • LOG ; . • =
4HIS IS TABULATED IN 4ABLE 4HIS DISCUSSION OF !$ QUANTIZATION NOISE HAS ASSUMED PERFECT !$ CONVERTERS
-ANY !$ CONVERTERS PARTICULARLY UNDER HIGH SLEW RATE CONDITIONS ARE LESS THAN PER
FECT 4HIS IN TURN LEADS TO SYSTEM LIMITATIONS MORE SEVERE THAN PREDICTED HERE SEE
3ECTION 4!",% 4YPICAL ,IMITATION ON ) $UE TO !$ 1UANTIZATION
.UMBER OF "ITS .
,IMIT ON -4) )MPROVEMENT &ACTOR ) D"
-4) 2!$!2
Ó°Çx
0ULSE #OMPRESSION #ONSIDERATIONSo 7HEN AN -4) SYSTEM IS USED WITH PULSE
COMPRESSION THE SYSTEM TARGET DETECTION CAPABILITY IN CLUTTER MAY BE AS GOOD AS A
SYSTEM TRANSMITTING THE EQUIVALENT SHORT PULSE OR THE PERFORMANCE MAY BE NO BETTER
THAN A SYSTEM TRANSMITTING THE SAME LENGTH #7 PULSE 4HE KIND OF CLUTTER ENVIRONMENT
THE SYSTEM INSTABILITIES AND THE SIGNAL PROCESSING UTILIZED DETERMINE WHERE THE SYSTEM
PERFORMANCE WILL FALL BETWEEN THE ABOVE TWO EXTREMES 5NLESS PROVISION IS INCORPO
RATED FOR COPING WITH SYSTEM INSTABILITIES AND CLUTTER SPECTRAL SPREAD THE -4) PULSE
COMPRESSION SYSTEM MAY FAIL TO WORK AT ALL IN A CLUTTER ENVIRONMENT
)DEALLY A PULSE COMPRESSION RECEIVER COUPLED WITH AN -4) WOULD APPEAR AS IN
&IGURE Ap )F THE PULSE COMPRESSION SYSTEM WAS PERFECT THE COMPRESSED PULSE
WOULD LOOK AS IF THE RADAR HAD TRANSMITTED AND RECEIVED A SHORT PULSE AND -4) PRO
CESSING COULD PROCEED AS IF THE PULSE COMPRESSION HAD NOT EXISTED )N PRACTICE THE
COMPRESSED PULSE WILL HAVE TIME SIDELOBES FROM THREE BASIC CAUSES 4HE FIRST IS WAVE
FORM AND SYSTEM DESIGN WHICH INCLUDES COMPONENTS THAT MAY BE NONLINEAR WITH
FREQUENCY ETC 4HESE SIDELOBES WILL BE STABLE 4HAT IS THEY SHOULD REPEAT PRECISELY ON
A PULSE TO PULSE BASIS AND THUS WILL CANCEL IN THE -4) CANCELER )T IS ASSUMED THAT THE
RADAR SYSTEM IS FULLY COHERENT AS REQUIRED BY RULE IN 3ECTION 4HE SECOND CAUSE
OF PULSE COMPRESSION SIDELOBES IS SYSTEM INSTABILITIES SUCH AS NOISE ON LOCAL OSCIL
LATORS TRANSMITTER TIME JITTER TRANSMITTER TUBE NOISE AND !$ CONVERTER JITTER 4HESE
SIDELOBES ARE NOISE LIKE AND ARE PROPORTIONAL TO THE CLUTTER AMPLITUDE 4HEY WILL NOT
CANCEL IN THE -4) CANCELER 4HE THIRD SOURCE OF SIDELOBES IS HIGH FREQUENCY RIPPLE IN
THE TRANSMITTER POWER SUPPLY
)F THE TRANSMITTER POWER SUPPLY INCORPORATES HIGH FREQUENCY AC DC ANDOR DC DC
CONVERTERS AND IF THE CONVERTER FREQUENCY COMPONENTS ARE NOT SUFFICIENTLY FILTERED
THERE WILL BE DISCRETE TIME SIDELOBES OFFSET FROM THE CLUTTER IN RANGE AS PREDICTED BY
PAIRED ECHO THEORY 4HE PAIRED ECHO SIDELOBES WILL ALSO HAVE A DOPPLER FREQUENCY
EQUAL TO THE CONVERTER FREQUENCY 4HIS FREQUENCY FCONV WILL ALIAS INTO THE 02& FR
DOPPLER INTERVAL AT THE FREQUENCY FDOP ; FDOP MODULO FCONV FR = 4HESE SIDELOBES WILL
NOT CANCEL UNLESS THE HIGH FREQUENCY CONVERTERS ARE SYNCHRONIZED TO A MULTIPLE OF THE
02& IN WHICH CASE FDOP !SSUME THAT THE NOISE LIKE COMPONENT OF THE SIDELOBES IS DOWN D" FROM THE
PEAK TRANSMITTED SIGNALS 4HIS NOISE LIKE COMPONENT WILL NOT CANCEL IN THE -4) SYS
TEM AND THEREFORE FOR EACH CLUTTER AREA THAT EXCEEDS THE SYSTEM THRESHOLD BY D"
OR MORE THE RESIDUE WILL EXCEED THE DETECTION THRESHOLD )F THE CLUTTER EXCEEDS THE
THRESHOLD BY D" THE RESIDUE FROM THE -4) SYSTEM WILL EXCEED THE DETECTION
THRESHOLD BY D" ELIMINATING THE EFFECTIVENESS OF THE -4) &IGURE B SHOWS A
SKETCH OF THIS EFFECT
4O ENSURE THAT THE NOISE LIKE PULSE COMPRESSION SIDELOBES WILL NOT EXCEED THE SYSTEM
NOISE AFTER THE -4) CANCELER THE SYSTEM STABILITY BUDGET MUST ENSURE THAT THE INSTABILITY
SIDELOBE LEVEL IS LOWER THAN THE DYNAMIC RANGE OF THE RECEIVING SYSTEM 4HE RECEIVING
SYSTEM DYNAMIC RANGE IS ULTIMATELY DETERMINED IN A WELL DESIGNED SYSTEM BY THE )&
o !LL SIGNAL PROCESSING FOLLOWING THE !$ DETECTOR IS DONE DIGITALLY )T IS MORE MEANINGFUL HOWEVER TO DESCRIBE AND
DEPICT THE PROCESSING IN AN ANALOG MANNER
p 4HE )& BANDPASS LIMITER ;2ADAR (ANDBOOK ND %D PP n= SHOWN IN THIS AND SUBSEQUENT DIAGRAMS HAS AN
AMPLITUDE OUTPUT CHARACTERISTIC THAT IS LINEAR FOR INPUT SIGNAL VOLTAGES FROM NOISE LEVEL TO WITHIN D" OF THE LIMITER
OUTPUT MAXIMUM VOLTAGE AND THEN TRANSITIONS SMOOTHLY TO THE MAXIMUM OUTPUT VOLTAGE 4HE PHASE OF THE INPUT
SIGNAL IS PRECISELY PRESERVED 4HESE LIMITER CHARACTERISTICS EXIST WHETHER THE FILTER IS IMPLEMENTED IN ANALOG CIRCUITRY
OR A DIGITAL ALGORITHM
Ó°ÇÈ
2!$!2 (!.$"//+
&)'52% 0ULSE COMPRESSION WITH -4) A IDEAL BUT DIFFICULT TO ACHIEVE COMBINATION
AND B EFFECT OF OSCILLATOR ON TRANSMITTER INSTABILITIES
BANDPASS LIMITER THAT PRECEDES THE !$ CONVERTER )F SYSTEM INSTABILITIES CANNOT BE CON
TROLLED TO BE LESS THAN THE SYSTEM DYNAMIC RANGE THEN THE SYSTEM DYNAMIC RANGE SHOULD
BE DECREASED !N ALTERNATIVE TO DECREASING THE DYNAMIC RANGE IS TO DEPEND ON A CELL
AVERAGING CONSTANT FALSE ALARM RATE #! #&!2 PROCESSOR AFTER THE SIGNAL PROCESSING
TO PROVIDE A THRESHOLD THAT RIDES OVER THE RESIDUE NOISE BUT THE EFFICACY OF THIS METHOD
DEPENDS ON THE RESIDUE NOISE BEING COMPLETELY NOISE LIKE WHICH IS UNLIKELY
!FTER ADDRESSING THE UNSTABLE PULSE COMPRESSION SIDELOBES IT IS STILL NECESSARY TO
CONTROL DETECTIONS FROM RESIDUE CAUSED BY THE SPECTRAL SPREAD OF THE CLUTTER OR BY LOW
FREQUENCY TRANSMITTER POWER SUPPLY RIPPLE 4HIS CAN BE ACCOMPLISHED BY LIMITING THE
MAXIMUM SIGNAL AMPLITUDE AT THE INPUT TO THE CANCELER 4HE PROCESS DESCRIBED ABOVE
IS DEPICTED IN &IGURE /NE APPROACH THAT HAS BEEN SUCCESSFUL IN ACHIEVING THE MAXIMUM -4) SYSTEM
PERFORMANCE ATTAINABLE WITHIN THE LIMITS IMPOSED BY SYSTEM AND CLUTTER INSTABILITIES
&)'52% 0RACTICAL -4) PULSE COMPRESSION COMBINATION
-4) 2!$!2
Ó°ÇÇ
IS SHOWN IN &IGURE 4RANSMITTER NOISE WILL BE USED IN THE FOLLOWING DISCUSSION
TO REPRESENT ALL POSSIBLE SYSTEM INSTABILITIES THAT CREATE NOISE LIKE PULSE COMPRESSION
TIME SIDELOBES
,IMITER IS SET TO LIMIT THE SYSTEM DYNAMIC RANGE TO THE RANGE BETWEEN PEAK CLUTTER
AND CLUTTER INSTABILITY NOISE ,IMITER IS SET SO THAT THE DYNAMIC RANGE AT ITS OUTPUT IS
EQUAL TO THE EXPECTED -4) IMPROVEMENT FACTOR AS LIMITED BY CLUTTER SPECTRAL SPREAD
OR LOW FREQUENCY TRANSMITTER POWER SUPPLY RIPPLE 4HESE LIMITER SETTINGS CAUSE THE
RESIDUE DUE TO TRANSMITTER NOISE AND THE RESIDUE DUE TO OTHER INSTABILITIES SUCH AS QUAN
TIZATION NOISE AND INTERNAL CLUTTER MOTION EACH TO BE EQUAL TO FRONT END THERMAL NOISE
AT THE CANCELER OUTPUT 4HIS ALLOWS MAXIMUM SENSITIVITY WITHOUT AN EXCESSIVE FALSE
ALARM RATE ,IMITER IS A VERY EFFICIENT CONSTANT FALSE ALARM RATE DEVICE AGAINST SYSTEM
INSTABILITIES BECAUSE IT SUPPRESSES THE INSTABILITY NOISE IN DIRECT PROPORTION TO THE CLUTTER
SIGNAL STRENGTH BUT DOES NOT SUPPRESS AT ANY TIME WHEN THE CLUTTER SIGNAL IS NOT STRONG
!LTHOUGH THE LIMITERS CAUSE PARTIAL OR COMPLETE SUPPRESSION OF SOME DESIRED TARGETS IN
THE CLUTTER AREAS NO TARGETS ARE SUPPRESSED THAT COULD OTHERWISE HAVE BEEN DETECTED IN
THE PRESENCE OF CLUTTER RESIDUE AT THE SYSTEM OUTPUT IF THE LIMITERS HAD NOT BEEN USED
!S A SPECIFIC EXAMPLE CONSIDER A SYSTEM WITH A PULSE COMPRESSION RATIO OF ABOUT
D" AND SYSTEM INSTABILITY NOISE APPROXIMATELY D" BELOW THE CARRIER POWER
!SSUME THAT THE -4) CANCELER IMPROVEMENT FACTOR IS D" LIMITED BY CLUTTER SPEC
TRAL SPREAD 7ITH THE ABOVE SYSTEM PARAMETERS A RECEIVER SYSTEM THAT WILL PROVIDE
THE MAXIMUM OBTAINABLE PERFORMANCE IS SHOWN IN &IGURE !T THE OUTPUT OF THE
PULSE COMPRESSION NETWORK THE SYSTEM INSTABILITY NOISE WILL BE EQUAL TO OR LESS THAN
THERMAL NOISE FOR EITHER DISTRIBUTED CLUTTER OR POINT CLUTTER AND THE PEAK CLUTTER SIGNALS
WILL VARY FROM ABOUT D" ABOVE THERMAL NOISE FOR EVENLY DISTRIBUTED CLUTTER TO D"
ABOVE THERMAL NOISE FOR STRONG POINT CLUTTER
"ECAUSE THE -4) CANCELER IS EXPECTED TO ATTENUATE CLUTTER BY D" THE SECOND LIM
ITER IS PROVIDED TO PREVENT THE RESIDUE FROM STRONG CLUTTER FROM EXCEEDING THE THRESHOLD
7ITHOUT THE SECOND LIMITER A STRONG POINT REFLECTOR THAT WAS D" ABOVE NOISE AT THE
CANCELER INPUT WOULD HAVE A RESIDUE D" ABOVE NOISE AT THE CANCELER OUTPUT 4HIS
WOULD BE INDISTINGUISHABLE FROM AN AIRCRAFT TARGET
)T THE TRANSMITTER NOISE WERE D" LESS THAN ASSUMED ABOVE THE FIRST LIMITER WOULD
BE SET D" ABOVE THERMAL NOISE AND MUCH LESS TARGET SUPPRESSION WOULD OCCUR 4HUS
TARGET DETECTABILITY WOULD IMPROVE IN AND NEAR THE STRONG CLUTTER AREAS EVEN THOUGH THE
-4) IMPROVEMENT FACTOR WAS STILL LIMITED TO D" BY INTERNAL CLUTTER MOTION
)N SUMMARY THE NOISE LIKE PULSE COMPRESSION SIDELOBES AND THE DURATION OF THE
UNCOMPRESSED PULSE DICTATE HOW EFFECTIVE A PULSE COMPRESSION -4) SYSTEM CAN BE
3YSTEMS HAVE BEEN BUILT IN WHICH TRANSMITTER NOISE AND LONG UNCOMPRESSED PULSES
COMBINED TO MAKE THE SYSTEMS INCAPABLE OF DETECTING AIRCRAFT TARGETS IN OR NEAR LAND
CLUTTER 3OME EXISTING PULSE COMPRESSION SYSTEMS HAVE NOT DELIBERATELY PROVIDED THE
&)'52% -4) WITH PULSE COMPRESSION
Ó°Çn
2!$!2 (!.$"//+
TWO SEPARATE LIMITERS DESCRIBED ABOVE BUT THE SYSTEMS WORK BECAUSE DYNAMIC RANGE IS
SUFFICIENTLY RESTRICTED BY CIRCUIT COMPONENTS /THER SYSTEMS SUCH AS THOSE THAT DELIB
ERATELY HARD LIMIT BEFORE PULSE COMPRESSION FOR #&!2 REASONS DO NOT HAVE CLUTTER
RESIDUE PROBLEMS BUT SUFFER FROM SIGNIFICANT TARGET SUPPRESSION IN THE CLUTTER AREAS
!N ALTERNATIVE TO THE USE OF LIMITERS IS THE USE OF CLUTTER MAPS IN CONJUNCTION
WITH THE #! #&!2 #LUTTER MAPS WORK WELL FOR STATIONARY RADARS OPERATING AT FIXED
FREQUENCIES BUT ARE LESS EFFECTIVE FOR OTHER RADARS 4HE #! #&!2 IS USEFUL EVEN
FOR A SYSTEM WITH )& LIMITERS BECAUSE THERE WILL BE SMALL VARIATIONS ON THE ORDER OF
A FEW D" IN THE COMBINATION OF CLUTTER RESIDUE AND SYSTEM NOISE 4O REEMPHASIZE
HOWEVER WITHOUT THE LIMITERS THERE MAY BE TENS OF D"S DIFFERENCE BETWEEN CLUTTER
RESIDUE AND SYSTEM NOISE
Ó°£ÎÊ 9 Ê, Ê
" - ,/" -
ÊÉ Ê " 6 ,-" Ê
4HE ACCURATE CONVERSION OF THE RADAR )& SIGNAL INTO A DIGITAL REPRESENTATION OF THE
COMPLEX ENVELOPE IS AN IMPORTANT STEP IN THE IMPLEMENTATION OF A MODERN DIGITAL SIG
NAL PROCESSOR 4HIS ANALOG TO DIGITAL !$ CONVERSION MUST PRESERVE THE LINEARITY OF
AMPLITUDE AND PHASE OVER THE REQUIRED DYNAMIC RANGE HAVE A SMALL EFFECT ON OVERALL
RADAR SYSTEM NOISE TEMPERATURE AND BE FREE FROM UNDESIRED SPURIOUS RESPONSES
!DVANCES IN !$ CONVERTER TECHNOLOGY IS NOW MAKING IT POSSIBLE TO DIRECTLY CON
VERT AN ANALOG )& SIGNAL INTO A CORRESPONDING DIGITAL COMPLEX REPRESENTATION RATHER
THAN GOING THROUGH THE INTERMEDIATE STEP OF FIRST DOWNCONVERTING THE )& SIGNAL INTO
BASEBAND IN PHASE ) AND QUADRATURE 1 COMPONENTS AND SUBSEQUENTLY USING A SEPA
RATE !$ CONVERTER IN EACH OF THESE TWO CHANNELS
! FLOW CHART OF A DIRECT )& !$ CONVERTER IS ILLUSTRATED IN &IGURE ALONG WITH
SPECTRAL REPRESENTATIONS OF THE SIGNAL THROUGHOUT THE CONVERSION PROCESS 4HE )& INPUT
CENTERED AT THE FREQUENCY F)& IS FIRST PASSED THROUGH A BANDPASS FILTER TO ENSURE THAT
NEGLIGIBLE ALIASING WILL OCCUR DURING THE SUBSEQUENT !$ CONVERSION PROCESS /N THE
RIGHT IN &IGURE THE TOP GRAPH SHOWS THE POSITIVE AND NEGATIVE PARTS OF THE SIGNAL
SPECTRUM AT THE )& FILTER OUTPUT 4HE POSITIVE PART OF THIS SPECTRUM CORRESPONDS TO THE
COMPLEX ENVELOPE WHICH NEEDS TO BE TRANSLATED INTO THE DIGITAL ) AND 1 REPRESENTATION
4HIS FILTER OUTPUT BECOMES THE INPUT TO THE !$ CONVERTER OPERATING AT A SAMPLING RATE
OF F!$ 4HE SPECTRUM OF THE !$ CONVERTER OUTPUT IS AGAIN SHOWN AND IT IS OBTAINED
SIMPLY BY REPLICATING THE ORIGINAL )& SPECTRUM FROM MINUS INFINITY TO PLUS INFINITY WITH
A PERIOD OF F!$ )N THIS EXAMPLE AN !$ CONVERSION RATE OF F!$ • F)& IS ASSUMED 4HE
OPTIMUM CHOICE OF THE !$ CONVERTER SAMPLING RATE ENSURES THAT THE NEGATIVE PART OF
THE SPECTRUM HAS THE SMALLEST POSSIBLE OVERLAP WITH THE POSITIVE PART OF THE SPECTRUM
4HE SMALLEST POSSIBLE OVERLAP OCCURS WHEN THE !$ SAMPLING RATE IS RELATED TO THE
RADAR )& FREQUENCY AS FOLLOWS
F!$ • F)&
•- WHERE - IS AN INTEGER GREATER THAN 4HUS OPTIMUM SAMPLING RATES ARE F)& F)&
F)& F)& x ETC 4HE CORRESPONDING MAXIMUM UNALIASED OR .YQUIST BANDWIDTH
IS ".1 F!$ 4HIS VALUE IS THEREFORE THE MAXIMUM ALLOWABLE CUTOFF BANDWIDTH OF
THE )& BANDPASS FILTER AT THE INPUT TO THE !$ CONVERTER )T IS NOT STRICTLY NECESSARY TO USE
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)MPLEMENTATION OF !$ CONVERSION USING DIRECT SAMPLING OF THE )& SIGNAL
AN !$ CONVERTER SAMPLING RATE AS GIVEN BY %Q BUT OTHER VALUES WILL RESULT IN AN
AVAILABLE .YQUIST BANDWIDTH LESS THAN F!$ 4HIS IS SHOWN IN &IGURE WHERE
THE NORMALIZED .YQUIST BANDWIDTH IS SHOWN AS A FUNCTION OF THE RELATIVE !$ CONVERTER
SAMPLING RATE &ROM THIS FIGURE IT IS SEEN THAT THE DIRECT CONVERSION APPROACH WILL FAIL
WHENEVER A VALUE OF - WHICH IS LOCATED HALFWAY BETWEEN THE OPTIMUM VALUES IS USED
!T THE !$ CONVERTER OUTPUT THE SIGNAL SAMPLES ARE STILL REAL VALUED 4O BE ABLE
TO EXTRACT THE COMPLEX ENVELOPE CORRESPONDING TO THE POSITIVE PART OF THE SPECTRUM
• ! F F)& IT IS NECESSARY TO SHIFT THE SPECTRUM AT THE !$ CONVERTER OUTPUT
DOWN IN FREQUENCY BY•PTHE AMOUNT F)& 4HIS CORRESPONDS TO A MULTIPLICATION BY THE
TIME SERIES UI E J•I• %QUIVALENTLY THE COMPLEX ENVELOPE SPECTRUM BELOW ZERO
FREQUENCYP CAN BE SHIFTED UP TO ZERO FREQUENCY BY MULTIPLICATION WITH THE TIME SERIES
UI E J•I• 4HIS RESULTS IN THE SPECTRUM SHOWN WHERE THE DESIRED SPECTRUM CORRE
SPONDING TO THE COMPLEX ENVELOPE IS CENTERED AT ZERO FREQUENCY BUT THE SIGNAL STILL
CONTAINS THE UNWANTED NEGATIVE SPECTRAL COMPONENTS LIGHT SHADING !S A RESULT OF
THIS FREQUENCY TRANSLATION THE SIGNAL HAS NOW BECOME COMPLEX ! DIGITAL &)2 BAND
PASS FILTER WITH A NEARLY RECTANGULAR RESPONSE IS THEN APPLIED TO REJECT THE NEGATIVE
FREQUENCY COMPONENTS AS SHOWN IN THE FINAL GRAPH ON THE RIGHT 4HE DESIRED SAMPLED
COMPLEX ENVELOPE REPRESENTATION HAS NOW BEEN REALIZED BUT AT THE ORIGINAL SAMPLING
RATE OF F!$ )F DESIRED THE OVERSAMPLING CAN FINALLY BE REMOVED THROUGH DECIMATION
BY A FACTOR OF AS SHOWN IN THE LAST STEP IN THE FIGURE
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&)'52% !VAILABLE .YQUIST BANDWIDTH VS !$ CONVERTER SAMPLING RATE
!$ CONVERTERS ARE TYPICALLY CHARACTERIZED BY THEIR SIGNAL TO NOISE RATIO 3.2
PERFORMANCE REFERRED TO A BANDWIDTH EQUAL TO THE !$ SAMPLING RATE /FTEN THIS 3.2
IS NOT AS HIGH AS ONE WOULD EXPECT BASED ON THE NUMBER OF BITS USED BY THE !$
CONVERTER 3OMETIMES THE ACTUAL PERFORMANCE OF AN !$ CONVERTER IS CHARACTERIZED BY
AN EFFECTIVE NUMBER OF BITS SMALLER THAN THE ACTUAL NUMBER OF BITS AND CORRESPOND
ING TO THE ACHIEVABLE 3.2 4HE 3.2 OF AN !$ CONVERTER SETS AN UPPER LIMIT ON THE
ACHIEVABLE IMPROVEMENT FACTOR
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7HEN THE DOPPLER FREQUENCY OF THE RETURNS FROM CLUTTER IS UNKNOWN AT THE RADAR INPUT
SPECIAL TECHNIQUES ARE REQUIRED TO GUARANTEE SATISFACTORY CLUTTER SUPPRESSION !S DIS
CUSSED IN 3ECTION THE DOPPLER FILTER BANK WILL USUALLY BE EFFECTIVE AGAINST MOVING
CLUTTER 4HIS REQUIRES THAT THE INDIVIDUAL FILTERS BE DESIGNED WITH A LOW SIDELOBE LEVEL
IN THE REGIONS WHERE CLUTTER MAY APPEAR AND THAT EACH FILTER BE FOLLOWED BY APPROPRI
ATE #&!2 PROCESSING CIRCUITS TO REJECT UNWANTED CLUTTER RESIDUE 7HEN CLUTTER SUP
PRESSION IS TO BE IMPLEMENTED WITH A SINGLE -4) FILTER IT IS NECESSARY TO USE ADAPTIVE
TECHNIQUES TO ENSURE THAT THE CLUTTER FALLS IN THE -4) REJECTION NOTCH !N EXAMPLE OF
SUCH AN ADAPTIVE -4) IS 4!##!2 ORIGINALLY DEVELOPED FOR AIRBORNE RADARS )N MANY
APPLICATIONS THE ADAPTIVE -4) WILL FURTHER HAVE TO TAKE INTO ACCOUNT THE SITUATION
WHERE MULTIPLE CLUTTER SOURCES WITH DIFFERENT RADIAL VELOCITIES ARE PRESENT AT THE SAME
RANGE AND BEARING
5SUALLY THE DOPPLER SHIFT OF CLUTTER RETURNS IS CAUSED BY THE WIND FIELD AND EARLY
ATTEMPTS OF COMPENSATING IN THE -4) HAVE VARIED THE COHO FREQUENCY SINUSOIDALLY AS A
FUNCTION OF AZIMUTH BASED ON THE AVERAGE WIND SPEED AND DIRECTION 4HIS APPROACH IS
-4) 2!$!2
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UNSATISFACTORY BECAUSE THE WIND FIELD RARELY IS HOMOGENEOUS OVER A LARGE GEOGRAPHICAL
AREA AND BECAUSE THE WIND VELOCITY USUALLY IS A FUNCTION OF ALTITUDE DUE TO WIND SHEAR
IMPORTANT FOR RAIN CLUTTER AND CHAFF !GAINST A SINGLE CLUTTER SOURCE AN IMPLEMENTA
TION IS REQUIRED THAT PERMITS THE -4) CLUTTER NOTCH TO BE SHIFTED AS A FUNCTION OF RANGE
!N EXAMPLE OF SUCH AN ADAPTIVE -4) IMPLEMENTATION IS SHOWN IN &IGURE 4HE
PHASE ERROR CIRCUIT COMPARES THE CLUTTER RETURN FROM ONE SWEEP TO THE NEXT 4HROUGH
A CLOSED LOOP WHICH INCLUDES A SMOOTHING TIME CONSTANT THE ERROR SIGNAL CONTROLS
A PHASE SHIFTER AT THE COHO OUTPUT SUCH THAT THE DOPPLER SHIFT FROM PULSE TO PULSE IS
REMOVED )T SHOULD BE NOTED THAT SINCE THE FIRST SWEEP ENTERING THE -4) IS TAKEN AS A
REFERENCE ANY PHASE SHIFT RUN OUT AS A FUNCTION OF RANGE WILL INCREASE PROPORTIONALLY
TO THE NUMBER OF SWEEPS 5LTIMATELY THIS RUN OUT WILL EXCEED THE SPEED OF RESPONSE
OF THE CLOSED LOOP AND THE -4) MUST BE RESET 4HIS TYPE OF CLOSED LOOP ADAPTIVE -4)
MUST THEREFORE BE OPERATED FOR A FINITE SET BATCH OF PULSES TO ENSURE THAT THIS WILL NOT
HAPPEN 3UCH BATCH MODE OPERATION IS ALSO REQUIRED IF A COMBINATION OF -4) OPERATION
AND FREQUENCY AGILITY IS DESIRED
)F A BIMODAL CLUTTER SITUATION IS CAUSED BY THE SIMULTANEOUS PRESENCE OF RETURNS FROM
LAND CLUTTER AND WEATHER OR CHAFF AN ADAPTIVE -4) CAN BE IMPLEMENTED FOLLOWING A
FIXED CLUTTER NOTCH -4) SECTION AS ILLUSTRATED IN &IGURE 4HE NUMBER OF ZEROS
USED IN THE FIXED ZERO DOPPLER CLUTTER NOTCH SECTION OF THE -4) IS DETERMINED BY THE
REQUIRED IMPROVEMENT FACTOR AND THE SPECTRAL SPREAD OF THE LAND CLUTTER 4YPICALLY THE
FIXED NOTCH -4) WOULD USE TWO OR THREE ZEROS &OR THE ADAPTIVE PORTION OF THE -4)
A FULLY DIGITAL IMPLEMENTATION IS SHOWN IN WHICH THE PULSE TO PULSE PHASE SHIFT OF THE
CLUTTER OUTPUT FROM THE FIRST CANCELER IS MEASURED AND AVERAGED OVER A GIVEN NUMBER OF
RANGE CELLS 4HIS ESTIMATED PHASE SHIFT IS ADDED TO THE PHASE SHIFT WHICH IS APPLIED TO THE
DATA ON THE PREVIOUS SWEEP AND THIS NEW PHASE SHIFT IS APPLIED TO THE CURRENT DATA
4HE RANGE AVERAGING MUST BE PERFORMED SEPARATELY ON THE ) AND 1 COMPONENTS OF
THE MEASURED PHASE IN EACH RANGE CELL DUE TO THE O AMBIGUITY OF THE PHASE REPRESENTA
TION ITSELF 4HE ACCUMULATION OF THE APPLIED PHASE SHIFT FROM SWEEP TO SWEEP HOWEVER
MUST BE PERFORMED DIRECTLY ON THE PHASE AND IS COMPUTED MODULO O 4HE NUMBER OF
ZEROS OF THE ADAPTIVE -4) SECTION IS AGAIN DETERMINED BY THE REQUIRED IMPROVEMENT
FACTOR AND THE EXPECTED SPECTRAL SPREAD OF THE CLUTTER 4HE PHASE SHIFT IS APPLIED TO THE
INPUT DATA IN THE FORM OF A COMPLEX MULTIPLY WHICH AGAIN REQUIRES THE TRANSFORMATION
OF THE PHASE ANGLE INTO RECTANGULAR COORDINATES 4HIS TRANSFORMATION CAN EASILY BE
PERFORMED BY A TABLE LOOKUP OPERATION IN A READ ONLY MEMORY
&)'52% "LOCK DIAGRAM OF CLOSED LOOP ADAPTIVE DIGITAL -4)
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/PEN LOOP ADAPTIVE -4) FOR CANCELLATION OF SIMULTANEOUS FIXED AND MOVING CLUTTER
7HEN DOPPLER SHIFTS ARE INTRODUCED BY DIGITAL MEANS AS DESCRIBED ABOVE THE ACCU
RACY OF THE ) AND 1 REPRESENTATION OF THE ORIGINAL INPUT DATA BECOMES AN IMPORTANT
CONSIDERATION !NY DC OFFSET AMPLITUDE IMBALANCE QUADRATURE PHASE ERROR OR NONLIN
EARITY WILL RESULT IN THE GENERATION OF UNDESIRED SIDEBANDS THAT WILL APPEAR AS RESIDUE
AT THE CANCELER OUTPUT ! DISCUSSION OF !$ CONVERSION CONSIDERATIONS WAS PRESENTED
IN 3ECTION )N THE ADAPTIVE -4) IMPLEMENTATION DESCRIBED ABOVE THE NUMBER OF ZEROS ALLO
CATED TO EACH OF THE TWO CANCELERS WAS FIXED BASED ON AN A PRIORI ASSESSMENT OF THE
CLUTTER SUPPRESSION REQUIREMENT 4HE ONLY VARIATION POSSIBLE WOULD BE TO COMPLETELY
BYPASS ONE OR BOTH OF THE -4) CANCELERS IF NO LAND CLUTTER OR WEATHER OR CHAFF RETURNS
ARE RECEIVED ON A GIVEN RADIAL ! MORE CAPABLE SYSTEM CAN BE IMPLEMENTED IF THE NUM
BER OF ZEROS CAN BE ALLOCATED DYNAMICALLY TO EITHER CLUTTER SOURCE AS A FUNCTION OF RANGE
4HIS LEADS TO A FULLY ADAPTIVE -4) IMPLEMENTATION USING A MORE COMPLEX ADAPTATION
ALGORITHM AS DISCUSSED BELOW 3UCH AN ADAPTIVE -4) MAY PROVIDE A PERFORMANCE
CLOSE TO THE OPTIMUM DISCUSSED IN 3ECTION )N ORDER TO ILLUSTRATE THE DIFFERENCE IN PERFORMANCE BETWEEN SUCH CANDIDATE -4)
IMPLEMENTATIONS A SPECIFIC EXAMPLE IS CONSIDERED NEXT &OR THIS EXAMPLE LAND CLUTTER
RETURNS ARE PRESENT AT ZERO DOPPLER WITH A NORMALIZED SPECTRAL SPREAD OF RF4 AND
CHAFF RETURNS ARE PRESENT AT A NORMALIZED DOPPLER OFFSET OF FD4 WITH A NORMALIZED
SPECTRAL SPREAD OF RF4 4HE POWER RATIO OF THE LAND CLUTTER TO THAT OF THE CHAFF IS
DENOTED 1 D" 4HERMAL NOISE IS NOT CONSIDERED IN THIS EXAMPLE )N BOTH CASES THE
TOTAL NUMBER OF FILTER ZEROS IS ASSUMED TO BE EQUAL TO &OR THE ADAPTIVE -4) WITH A
FIXED ALLOCATION OF ZEROS TWO ZEROS ARE LOCATED AT ZERO DOPPLER AND THE REMAINING ZERO
IS CENTERED ON THE CHAFF RETURNS )N THE OPTIMUM -4) THE ZERO LOCATIONS ARE CHOSEN
SO THAT THAT OVERALL IMPROVEMENT FACTOR IS MAXIMIZED 4HE RESULTS OF THIS COMPARISON
ARE PRESENTED IN &IGURE WHICH SHOWS THE IMPROVEMENT FACTOR FOR THE OPTIMUM
AND THE ADAPTIVE -4) AS A FUNCTION OF THE POWER RATIO 1 D" 7HEN 1 IS SMALL SO THAT
CHAFF RETURNS DOMINATE A SIGNIFICANT PERFORMANCE IMPROVEMENT CAN BE REALIZED BY
USING ALL -4) FILTER ZEROS TO CANCEL THE CHAFF RETURNS 4HE PERFORMANCE DIFFERENCE FOR
LARGE VALUES OF 1 IS A RESULT OF AN ASSUMPTION MADE THAT THE LOCATION OF THE THIRD ZERO
REMAINS FIXED AT THE CHAFF DOPPLER FREQUENCY )N REALITY THE ADAPTIVE -4) WOULD MOVE
-4) 2!$!2
&)'52% )MPROVEMENT FACTOR COMPARISON OF
OPTIMUM AND ADAPTIVE -4) AGAINST FIXED AND MOVING
CLUTTER OF RATIO 1
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&)'52% ,OCATION OF THE THREE FILTER ZEROS
FOR AN OPTIMUM -4) USED AGAINST FIXED AND MOV
ING CLUTTER
ITS THIRD ZERO TO THE LAND CLUTTER AS THE LAND CLUTTER RESIDUE STARTS TO DOMINATE THE OUTPUT
OF THE FIRST CANCELER 4HE ZERO LOCATIONS OF THE OPTIMUM -4) ARE SHOWN IN &IGURE AND CAN BE SEEN TO MOVE BETWEEN THE LAND CLUTTER AT ZERO DOPPLER TOWARD THE DOPPLER
OF THE CHAFF RETURNS AS THE RELATIVE LEVEL OF THE LAND CLUTTER BECOMES SMALL
Ó°£xÊ , ,Ê 1// ,Ê*)N MANY -4) RADAR APPLICATIONS THE CLUTTER TO NOISE RATIO IN THE RECEIVER WILL EXCEED THE
IMPROVEMENT FACTOR LIMIT OF THE SYSTEM EVEN WHEN TECHNIQUES SUCH AS SENSITIVITY TIME
CONTROL 34# IMPROVED RADAR RESOLUTION AND REDUCED ANTENNA GAIN CLOSE TO THE HORIZON
ARE USED TO REDUCE THE LEVEL OF CLUTTER RETURNS 4HE RESULTING CLUTTER RESIDUES AFTER THE -4)
CANCELER MUST THEREFORE BE FURTHER SUPPRESSED TO PREVENT SATURATION OF THE 00) DISPLAY
ANDOR AN EXCESSIVE FALSE ALARM RATE IN AN AUTOMATIC TARGET DETECTION !4$ SYSTEM
!GAINST SPATIALLY HOMOGENEOUS SOURCES OF CLUTTER SUCH AS RAIN SEA CLUTTER OR CORRI
DOR CHAFF A CELL AVERAGING CONSTANT FALSE ALARM RATE #! #&!2 PROCESSOR FOLLOWING
THE -4) FILTER WILL USUALLY PROVIDE GOOD SUPPRESSION OF THE CLUTTER RESIDUES 3PECIAL
FEATURES ARE SOMETIMES ADDED TO THE #! #&!2 SUCH AS GREATEST OF SELECTION OR TWO
PARAMETER SCALE AND SHAPE NORMALIZATION LOGIC IN ORDER TO IMPROVE ITS EFFECTIVENESS
AT CLUTTER BOUNDARIES IF THE PROBABILITY DISTRIBUTION OF THE CLUTTER AMPLITUDE IS NON
GAUSSIAN (OWEVER WHEN THE CLUTTER RETURNS ARE SIGNIFICANTLY NONHOMOGENEOUS AS IS
THE CASE FOR TYPICAL LAND CLUTTER RETURNS THE PERFORMANCE OF THE CELL AVERAGING #&!2
WILL NOT BE SATISFACTORY AND OTHER MEANS MUST BE IMPLEMENTED TO SUPPRESS THE OUTPUT
RESIDUES TO THE NOISE LEVEL
4HE TRADITIONAL SOLUTION TO THIS PROBLEM HAS BEEN TO DELIBERATELY REDUCE THE RECEIVER
DYNAMIC RANGE PRIOR TO THE -4) FILTER TO THE SAME VALUE AS THE MAXIMUM SYSTEM
IMPROVEMENT FACTOR 4HEORETICALLY THEN THE OUTPUT RESIDUE SHOULD BE AT OR BELOW THE
NORMAL RECEIVER NOISE LEVEL AND NO FALSE ALARMS WOULD BE GENERATED )N PRACTICE THE
INTRODUCTION OF )& LIMITING AGAINST THE GROUND CLUTTER RETURNS WILL RESULT IN AN ADDITIONAL
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IMPROVEMENT FACTOR RESTRICTION AS DISCUSSED IN 3ECTION #ONSEQUENTLY FOR THE
LIMITED )& DYNAMIC RANGE TO HAVE THE DESIRED EFFECT ON THE OUTPUT RESIDUES THE LIMIT
LEVEL MUST BE SET TO D" BELOW THE IMPROVEMENT FACTOR LIMIT OF THE LINEAR SYSTEM
4HE NET RESULT IS THAT SOME OF THE CLUTTER SUPPRESSION CAPABILITY OF THE -4) RADAR MUST
BE SACRIFICED IN EXCHANGE FOR CONTROL OF THE OUTPUT FALSE ALARM RATE
3INCE RETURNS FROM LAND CLUTTER SCATTERERS USUALLY ARE SPATIALLY FIXED AND THEREFORE
APPEAR AT THE SAME RANGE AND BEARING FROM SCAN TO SCAN IT HAS LONG BEEN RECOGNIZED
THAT A SUITABLE MEMORY CIRCUIT COULD BE USED TO STORE THE CLUTTER RESIDUES AND REMOVE
THEM FROM THE OUTPUT RESIDUE ON SUBSEQUENT SCANS BY EITHER SUBTRACTION OR GAIN NOR
MALIZATION 4HIS WAS THE BASIC PRINCIPLE OF THE SO CALLED AREA -4) AND MANY ATTEMPTS
HAVE BEEN MADE TO IMPLEMENT AN EFFECTIVE VERSION OF THIS CIRCUIT OVER AN EXTENDED SPAN
OF TIME 4HE MAIN HINDRANCE TO ITS SUCCESS HAS BEEN THE LACK OF APPROPRIATE MEMORY
TECHNOLOGY SINCE THE STORAGE TUBE LONG THE ONLY VIABLE CANDIDATE LACKS IN RESOLUTION
REGISTRATION ACCURACY SIMULTANEOUS READ AND WRITE CAPABILITY AND STABILITY 4HE DEVEL
OPMENT OF HIGH CAPACITY SEMICONDUCTOR MEMORIES IS THE TECHNOLOGICAL BREAKTHROUGH
THAT HAS MADE THE DESIGN OF A WORKING AREA -4) A REALITY 4HE AREA -4) IS BETTER KNOWN
TODAY AS A CLUTTER MAP BUT BOTH TERMS ARE USED
4HE CLUTTER MAP MAY BE CONSIDERED AS A TYPE OF #&!2 WHERE THE REFERENCE SAMPLES
WHICH ARE NEEDED TO ESTIMATE THE LEVEL OF THE CLUTTER OR CLUTTER RESIDUE ARE COLLECTED
IN THE CELL UNDER TEST ON A NUMBER OF PREVIOUS SCANS 3INCE AIRCRAFT TARGETS USUALLY
MOVE SEVERAL RESOLUTION CELLS FROM ONE SCAN TO THE NEXT IT IS UNLIKELY THAT THE REFERENCE
SAMPLES WILL BE CONTAMINATED BY A TARGET RETURN !LTERNATIVELY BY MAKING THE AVERAG
ING TIME IN TERMS OF PAST SCANS LONG THE EFFECT OF AN OCCASIONAL TARGET RETURN CAN BE
MINIMIZED !LTHOUGH THE PRIMARY PURPOSE OF THE CLUTTER MAP IS TO PREVENT FALSE ALARMS
DUE TO DISCRETE CLUTTER OR CLUTTER RESIDUES THAT ARE AT A FIXED LOCATION IT MAY ALSO BE
NECESSARY TO CONSIDER SLOWLY MOVING POINT CLUTTER IN THE CLUTTER MAP DESIGN EITHER TO
SUPPRESS BIRD RETURNS OR BECAUSE THE RADAR IS ON A MOVING PLATFORM EG A SHIP 4HE MEMORY OF A CLUTTER MAP IS USUALLY ORGANIZED IN A UNIFORM GRID OF RANGE AND
AZIMUTH CELLS AS ILLUSTRATED IN &IGURE %ACH MAP CELL WILL TYPICALLY HAVE TO
BITS OF MEMORY SO THAT IT WILL HANDLE THE FULL DYNAMIC RANGE OF SIGNALS AT ITS INPUT
WHICH MAKES IT POSSIBLE TO DETECT A STRONG TARGET FLYING OVER A POINT OF CLUTTER SOME
TIMES REFERRED TO AS SUPERCLUTTER VISIBILITY 4HE DIMENSIONS OF EACH CELL ARE A COMPRO
MISE BETWEEN THE REQUIRED MEMORY AND SEVERAL PERFORMANCE CHARACTERISTICS 4HESE ARE
THE MINIMUM TARGET VELOCITY THAT WILL NOT BE SUPPRESSED BY THE MAP SO CALLED CUTOFF
VELOCITY ITS TRANSIENT RESPONSE AND THE LOSS IN SENSITIVITY CAUSED BY THE CLUTTER MAP
SIMILAR TO A #&!2 LOSS 4HE MINIMUM CELL SIZE WILL BE CONSTRAINED BY THE SIZE OF THE
RADAR RESOLUTION CELL
&)'52% #LUTTER MAP CELL DEFINITION
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%ACH MAP CELL IS UPDATED BY THE RADAR RETURNS OR RESIDUES FALLING WITHIN ITS BORDERS
OR IN ITS VICINITY ON SEVERAL PREVIOUS SCANS 4O SAVE MEMORY THE CELLS ARE USUALLY
UPDATED BY USING A SIMPLE RECURSIVE SINGLE POLE FILTER OF THE FORM
YI A • YI A • X I
WHERE YI IS THE CLUTTER MAP AMPLITUDE FROM THE PREVIOUS SCAN YI IS THE UPDATED
CLUTTER MAP AMPLITUDE XI IS THE RADAR OUTPUT ON THE PRESENT SCAN AND THE CONSTANT
@ DETERMINES THE MEMORY OF THE RECURSIVE FILTER 4HE TEST FOR DETECTING A TARGET BASED
ON THE OUTPUT XI IS
XI q K4 • YI WHERE THE THRESHOLD CONSTANT K4 IS SELECTED TO GIVE THE REQUIRED FALSE ALARM RATE
!LTERNATIVELY THE RADAR OUTPUT CAN BE NORMALIZED ON THE BASIS OF THE CLUTTER MAP
XI
CONTENT TO OBTAIN AN OUTPUT ZI Y I WHICH CAN BE PROCESSED FURTHER IF REQUIRED
!NALOGOUSLY TO THE IMPLEMENTATION OF THE CELL AVERAGING #&!2 PROCESSOR THE AMPLI
TUDE XI CAN BE OBTAINED USING A LINEAR SQUARE LAW OR LOGARITHMIC DETECTOR
4HE LOSS IN DETECTABILITY DUE TO THE CLUTTER MAP IS ANALOGOUS TO THE #&!2 LOSS ANA
LYZED IN THE LITERATURE FOR MANY DIFFERENT CONDITIONS !N ANALYSIS OF THE CLUTTER MAP LOSS
FOR SINGLE HIT DETECTION USING A SQUARE LAW DETECTOR HAS BEEN PRESENTED BY .ITZBERG
4HESE AND OTHER RESULTS CAN BE SUMMARIZED INTO A SINGLE UNIVERSAL CURVE OF CLUTTER MAP
LOSS ,#- AS A FUNCTION OF THE CLUTTER MAP RATIO X,EFF AS SHOWN IN &IGURE WHERE
X DEFINES THE REQUIRED FALSE ALARM PROBABILITY ACCORDING TO 0F X AND ,EFF IS THE
EFFECTIVE NUMBER OF PAST OBSERVATIONS AVERAGED IN THE CLUTTER MAP DEFINED AS
,EFF A
A
&OR EXAMPLE FOR 0F AND @ THE CLUTTER MAP LOSS IS ,#- D" SINCE
X AND ,EFF FOR THIS CASE !LSO SHOWN IN &IGURE IS THE CURVE FOR THE CONVEN
TIONAL #! #&!2 WHERE ALL REFERENCE SAMPLES ARE EQUALLY WEIGHTED )F MORE THAN ONE
NOISE ANDOR CLUTTER AMPLITUDE IS USED TO UPDATE THE CLUTTER MAP CONTENT ON EACH SCAN
THE VALUE OF ,EFF SHOULD BE INCREASED PROPORTIONALLY )T SHOULD ALSO BE NOTED THAT MOST
RADARS BASE THEIR TARGET DETECTION ON MULTIPLE HITS USING SOME FORM OF VIDEO INTEGRA
TION AND THAT A CLUTTER MAP LOSS BASED ON THE SINGLE HIT RESULTS OF &IGURE COULD BE
MUCH TOO LARGE
!N ANALYSIS OF THE PERFORMANCE OF TYPICAL IMPLEMENTATIONS OF CLUTTER MAPS HAS BEEN
DISCUSSED IN +HOURY AND (OYLE &ROM THIS REFERENCE A TYPICAL TRANSIENT RESPONSE
CURVE IS SHOWN IN &IGURE FOR A SINGLE POINT CLUTTER SOURCE D" ABOVE THERMAL
NOISE THAT FLUCTUATES FROM SCAN TO SCAN ACCORDING TO A 2AYLEIGH PROBABILITY DENSITY
FUNCTION A FILTERING CONSTANT OF @ AND ASSUMING FOUR RETURNS NONCOHERENTLY
INTEGRATED IN EACH CLUTTER MAP CELL 4HE ABSCISSA IS IN RADAR SCANS AND THE ORDINATE IS
PROBABILITY OF DETECTION OF THE POINT CLUTTER SOURCE 3INCE THE CLUTTER POINT HAS THE SAME
AMPLITUDE STATISTICS AS THERMAL NOISE THE OUTPUT FALSE ALARM RATE APPROACHES 0F ASYMPTOTICALLY
!GAINST A SLOWLY MOVING SOURCE OF CLUTTER EG BIRDS THE PROBABILITY OF DETECTION
MAY INCREASE AS THE CLUTTER SOURCE CROSSES THE BOUNDARY BETWEEN TWO CLUTTER MAP CELLS
4O PREVENT THIS A SPREADING TECHNIQUE CAN BE USED THROUGH WHICH EACH CLUTTER MAP
CELL WILL BE UPDATEDˆNOT ONLY WITH RADAR RETURNS FALLING WITHIN ITS BOUNDARIES BUT ALSO
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&)'52% CLUTTER MAP
5NIVERSAL CURVE FOR DETERMINING DETECTABILITY LOSS CAUSED BY THE
BY USING RADAR RETURNS IN ADJACENT CELLS IN RANGE AND AZIMUTH 4HROUGH THE USE OF SUCH
SPREADING AN ADDITIONAL DEGREE OF CONTROL OVER THE CLUTTER MAP VELOCITY RESPONSE CAN
BE ACHIEVED
!N EXAMPLE OF THE VELOCITY RESPONSE OF A CLUTTER MAP INCLUDING SUCH SPREADING IS
SHOWN IN &IGURE 4HE RANGE EXTENT OF THE CLUTTER MAP CELL IS MS THE RADAR RESO
LUTION CELL IS MS N PULSES ARE NONCOHERENTLY INTEGRATED THE FILTERING CONSTANT IS
@ THE UPDATE INTERVAL IS S AND THE 3.2 D" /N EACH SCAN THE CLUTTER
MAP CELL IS UPDATED WITH THE RADAR AMPLITUDES IN THE FIVE RANGE CELLS FALLING WITHIN
THE CLUTTER MAP CELL AND WITH THE AMPLITUDE FROM ONE ADDITIONAL RADAR RESOLUTION CELL
BEFORE AND AFTER THE CLUTTER MAP CELL
&)'52% 4RANSIENT RESPONSE OF CLUTTER MAP DUE TO
3WERLING #ASE POINT CLUTTER MODEL
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6ELOCITY RESPONSE OF CLUTTER MAP
)T IS SEEN FROM &IGURE THAT THE VELOCITY RESPONSE CHARACTERISTIC OF THE CLUTTER
MAP FROM STOPBAND TO PASSBAND IS SOMEWHAT GRADUAL IN THIS PARTICULAR IMPLEMENTATION
4HIS IS PARTLY DUE TO THE LARGE SIZE OF THE CLUTTER MAP CELL RELATIVE TO THE RADAR RESOLU
TION ! FINER GRAIN MAP WITH ADDITIONAL SPREADING WOULD HAVE A MUCH BETTER VELOCITY
RESPONSE CHARACTERISTIC
! POTENTIAL PROBLEM WITH THE TYPE OF AMPLITUDE CLUTTER MAP DESCRIBED IN THIS SEC
TION IS THE FACT THAT A LARGE TARGET FLYING IN FRONT OF A SMALLER TARGET MAY CAUSE ENOUGH
BUILDUP IN THE MAP TO SUPPRESS THE SMALL TARGET /NE WAY TO OVERCOME THIS PROBLEM IN
A SYSTEM THAT INCLUDES AUTOMATIC TRACKING WOULD BE TO USE THE TRACK PREDICTION GATE TO
INHIBIT UPDATING OF THE CLUTTER MAP WITH NEW TARGET AMPLITUDES
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)N THE MID S SEVERAL RADAR RESEARCHERS HAD REALIZED THAT SIGNAL PROCESSING ALGO
RITHMS TO ESTIMATE THE UNAMBIGUOUS RADIAL VELOCITY OF A TARGET USING MULTIPLE 02&
DWELLS DURING THE TIME OF TARGET WERE BECOMING PRACTICAL 4HESE RADIAL VELOCITY ESTI
MATES COULD BE USED FOR IMPROVED FALSE ALARM CONTROL AGAINST SLOW MOVING TARGETS
SUCH AS BIRDS 7HEN SUCH RADIAL VELOCITY MEASUREMENTS ARE PAIRED WITH CORRE
SPONDING CROSS SECTION ESTIMATES A POWERFUL DISCRIMINANT FOR DISTINGUISHING BETWEEN
SLOW MOVING BIRDS AND LOW CROSS SECTION MISSILES BECOMES POSSIBLE USING THE SO
CALLED SENSITIVITY VELOCITY CONTROL 36# ALGORITHM
4HE 36# #ONCEPT 3ENSITIVITY VELOCITY CONTROL 36# IS USED WHEN A RADAR MUST
DETECT AIRCRAFT AND MISSILE TARGETS IN THE PRESENCE OF RETURNS FROM UNWANTED TARGETS
SUCH AS LARGE BIRDS OR BIRD FLOCKS 4HE CRITERIA TO ACCEPT OR REJECT TARGETS IS BASED ON A
COMBINATION OF THE RADIAL VELOCITY AND APPARENT 2#3 RADAR CROSS SECTION OF THE TARGET
RETURNS 4HE DESIRED TARGETS MAY HAVE AN 2#3 SMALLER THAN A SINGLE BIRD OR POSSIBLY
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A BIRD FLOCK IN A SINGLE RADAR RESOLUTION CELL 4HUS DISCRIMINATION REQUIRES A PARAME
TER IN ADDITION TO THE TARGET 2#3 4HE AVAILABLE PARAMETER IS TARGET RADIAL VELOCITY "IRDS
TYPICALLY FLY AT KNOTS OR LESS WHEREAS TARGETS OF CONCERN USUALLY HAVE AIRSPEEDS OF
KNOTS OR MORE )F THE RADAR CAN MAKE UNAMBIGUOUS RADAR DOPPLER MEASUREMENTS
OF EG o KNOTS WITH A SINGLE #0) COHERENT PROCESSING INTERVAL THE RADAR CAN
DETERMINE THE TRUE RADIAL VELOCITY OF EACH RADAR ECHO FROM RETURNS OF THREE OR MORE
CONSECUTIVE #0)S AT DIFFERENT 02&S
4HE ACCEPTANCE CRITERIA OF THE 36# ALGORITHM RELATES TO THE TYPE OF TARGET AIRCRAFT
MISSILE BIRD ETC BEING ACCEPTED OR REJECTED )N GENERAL THE CRITERIA ACCEPTS LARGE TAR
GETS HAVING LOW TO HIGH RADIAL VELOCITIES 4HE SMALLER THE APPARENT RADAR CROSS SECTION
OF THE TARGET THE HIGHER THE TRUE RADIAL VELOCITY MUST BE FOR ACCEPTANCE 4HE TRUE RADIAL
VELOCITY VERSUS APPARENT RADAR CROSS SECTION PROFILE IS INTENDED TO ACCEPT AIRCRAFT AND
MISSILES BUT REJECT BIRDS 4HEREFORE THREATENING TARGETS THAT HAVE HIGH RADIAL VELOCI
TIES BUT VERY SMALL 2#3 CAN BE INSTANTLY IDENTIFIED WHEREAS RETURNS FROM BIRDS WITH
THEIR SLOW RADIAL VELOCITIES CAN BE CENSORED ! TYPICAL 3#6 ACCEPTREJECT ALGORITHM IS
DEPICTED IN &IGURE 4O OBTAIN THE DOPPLER SPACE OF o KNOTS AMBIGUOUS RANGE 02&S MUST BE USED
4HIS REQUIRES APPROXIMATE 02&S OF (Z AT , BAND (Z AT 3 BAND AND
(Z AT 8 BAND UNAMBIGUOUS RANGES RESPECTIVELY NMI NMI AND NMI 4HE TRADEOFF FOR SELECTING 02&S IS THAT IN A DENSE TARGET ENVIRONMENT WHEN TRY
ING TO RESOLVE TRUE RADIAL VELOCITY USING DIFFERENT 02&S hGHOSTSve MAY BE CREATED
e h'HOSTSv OCCUR WHEN TARGETS OR NOISE PEAKS AT DIFFERENT UNAMBIGUOUS RANGES FOLD INTO THE SAME BUT INCORRECT
TRUE RANGE CELL 4HE VELOCITY RESOLUTION ALGORITHM THEN GIVES AN INCORRECT RESULT AND THE GHOSTS MAY BE DECLARED AS
THREATENING TARGETS
Ó°n™
-4) 2!$!2
)N ADDITION TO THE hGHOSTv PROBLEM MULTIPLE RANGE AMBIGUITIES LEAD TO TARGETS HAVING
TO COMPETE WITH CLUTTER AT ALL RANGES )N PARTICULAR TARGETS AT LONG DISTANCES HAVE TO
COMPETE WITH STRONG CLUTTER RETURNS IN THE FIRST OR SEVERAL RANGE INTERVALS
"ECAUSE OF THE GHOSTING PROBLEM IN ORDER TO MINIMIZE RANGE AMBIGUITIES WHILE
RETAINING ADEQUATE DOPPLER SPACE 2& FREQUENCIES OF -(Z OR LOWER ARE BEST
SUITED FOR THE 36# UNWANTED TARGET DISCRIMINATION TECHNIQUE
2ANGE AND 2ANGE 2ATE !MBIGUITY 2ESOLUTION 4O APPLY THE 36# ALGORITHM
TRUE RANGE AND RADIAL VELOCITY RANGE RATE MUST BE DETERMINED FROM THE RANGE AMBIG
UOUS AND DOPPLER AMBIGUOUS WAVEFORM 4HIS REQUIRES MULTIPLE DETECTIONS FROM THE
SAME TARGET !SSUME A DOPPLER FILTER BANK OF N PULSE &)2 FILTERS AND ASSUME A PROCESS
ING DWELL THAT CONSISTS OF THREE #0)S 4HE #0)S MUST USE DIFFERENT 02&S AND MAY ALSO
EMPLOY DIFFERENT 2& FREQUENCIES 4HE DIFFERENT 2& FREQUENCIES CHANGE TARGET 2#3
STATISTICS FROM 3WERLING TO 3WERLING AND THUS LESS RADAR ENERGY IS REQUIRED FOR HIGH
PROBABILITY OF DETECTION 4HE #0)S MUST HAVE SUFFICIENT TRANSMITTED PULSES SO THAT
N RETURNS ENOUGH TO FILL AN N PULSE FILTER WILL BE RECEIVED FROM THE MOST DISTANT TARGET
OF INTEREST AND THE MOST DISTANT CLUTTER AND ONE ADDITIONAL PULSE TO ENABLE VELOCITY
DETERMINATION MORE ON THIS LATER 4RUE 2ANGE $ETERMINATION 4HE MOST STRAIGHTFORWARD WAY TO DETECT A TARGET AND
SIMULTANEOUSLY DETERMINE ITS TRUE RANGE IS TO DETERMINE ON EACH #0) ALL hPRIMITIVEv
DETECTIONS AT THE OUTPUT OF THE DOPPLER FILTER BANK &OR THIS IT IS ASSUMED THAT EACH
DOPPLER FILTER OUTPUT IS PROCESSED THROUGH AN APPROPRIATE CLUTTER MAP THRESHOLD AND
CELL AVERAGING #&!2 TO CONTROL THE FALSE ALARM RATE &OR EACH PEAK DETECTION ADJACENT
AMPLITUDES WILL BE USED TO OBTAIN AN ACCURATE AMBIGUOUS RANGE ESTIMATE DENOTED R}I
WHERE THE SUBSCRIPT REFERS TO THE #0) NUMBER !LSO FROM THE SPECIFIC DOPPLER FILTER
CORRESPONDING TO THE PEAK DETECTION DESCRIBED ABOVE THE PHASE PI OF THE RETURN IS
SAVED )N ADDITION A CORRESPONDING PHASE P I OBTAINED FROM AN IDENTICAL SECOND DOP
PLER FILTER BANK TRAILING OR LEADING THE DETECTION FILTER BANK BY ONE PULSE REPETITION
INTERVAL 02) IS SAVED 4HIS EXPLAINS WHY A #0) OF N PULSES IS NEEDED TO IMPLEMENT
THE 36# CONCEPT &OR EACH PRIMITIVE DETECTION IN A #0) CALCULATE THE SET OF ALL POSSIBLE
TARGET RANGES OUT TO THE MAXIMUM INSTRUMENTED RANGE 2MAX
2} I R}I
M • 202) I
M MMAX
WHERE MMAX INT 2MAX 202) I
I WHERE 202) I IS THE AMBIGUOUS RANGE INTERVAL CORRESPONDING TO THE ITH #0) !FTER THE
PRIMITIVE DETECTIONS FROM ALL #0)S IN THE PROCESSING DWELL HAVE BEEN PROCESSED THE
VALUES OF 2} I FROM ALL #0)S ARE SORTED INTO A SINGLE LIST ! FINAL RANGE DETECTION AND
ITS TRUE RANGE IS THEN FOUND AS A CLUSTER OF THREE PRIMITIVE DETECTIONS HAVING POSSIBLE
RANGES WITHIN AN ERROR WINDOW OF TWO TO THREE TIMES THE STANDARD DEVIATION OF THE
AMBIGUOUS RANGE ESTIMATE
4RUE 2ADIAL 6ELOCITY $ETERMINATION &OR EACH TRUE TARGET DETECTION AN UNAM
BIGUOUS RADIAL VELOCITY ESTIMATE MUST NEXT BE DETERMINED USING A SIMILAR PROCE
DURE TO THAT DESCRIBED ABOVE FOR RANGE &OR THIS AN ACCURATE ESTIMATE F}D I OF THE
AMBIGUOUS TARGET RADIAL VELOCITY MUST BE OBTAINED AT THE RANGE CORRESPONDING TO
THE AMBIGUOUS PRIMITIVE TARGET DETECTION ON EACH #0) 4HIS FREQUENCY ESTIMATION
PROBLEM HAS BEEN STUDIED BY MANY AUTHORS WITH THE BEST APPROACH BEING DEFINED
Ó°™ä
2!$!2 (!.$"//+
BY THE MAXIMUM LIKELIHOOD ESTIMATE &OR A SINGLE PULSE SIGNAL TO NOISE RATIO 3
AND N PULSES IN A #0) THE #RAMER 2AO LOWER BOUND FOR THE ACCURACY OF THE DOPPLER
FREQUENCY ESTIMATE IS
SF
02& • P • 3 • N • N 3 • N • N 3INCE THE MAXIMUM LIKELIHOOD ESTIMATION PROCEDURE TENDS TO REQUIRE A TEDIOUS
COMPUTATIONAL BURDEN A SIMPLIFIED APPROACH FOR ESTIMATING THE DOPPLER FREQUENCY IS
HIGHLY DESIRABLE /NE SUCH APPROACH USING PHASE MEASUREMENTS OF THE DOPPLER FILTER
OUTPUT AT TIMES SEPARATED BY ONE INTERPULSE PERIOD WAS PRESENTED IN -C-AHON AND
"ARRETT 4HE NORMALIZED DOPPLER FREQUENCY ESTIMATE IS
FD I
Q
Q I
I
02&
•P
AND THE CORRESPONDING RADIAL VELOCITY IS
V}I FD I • L
)N MOST CASES OF INTEREST THE ACCURACY OF THIS ESTIMATE OF DOPPLER FREQUENCY IS AS
GOOD AS THE MAXIMUM LIKELIHOOD PROCEDURE %XPRESSED IN TERMS OF THE NUMERATOR OF
%Q WHICH WILL BE DENOTED BY K A SIMULATION OF THE PHASE DIFFERENCE ESTIMA
TOR USING DIFFERENT WEIGHTING FUNCTIONS FOR THE DOPPLER FILTER BANK ARE SUMMARIZED
IN &IGURE )T IS NOTED THAT THE PERFORMANCE OF THE PHASE DIFFERENCE ESTIMATION
PROCEDURE IS BEST WHEN MODERATE 4AYLOR WEIGHTING FUNCTIONS ARE USED &OR UNIFORM
WEIGHTING THE PROCEDURE WOULD BE SUBSTANTIALLY INFERIOR TO THE MAXIMUM LIKELIHOOD
APPROACH 4HE INCREASE IN THE CONSTANT K FOR THE MORE SEVERE WEIGHTING CASES IS THE
RESULT OF THE 3.2 LOSS RESULTING FROM THE USE OF WEIGHTING
5SING AN APPROACH SIMILAR TO THAT USED TO RESOLVE THE RANGE AMBIGUITY ALL POSSIBLE
RADIAL VELOCITIES ARE THEN ENUMERATED TO THE MAXIMUM NEGATIVE AND POSITIVE RADIAL
VELOCITY OF INTEREST ON EACH OF THE #0)S
6}I V}I
M • 6" I
M MMAX MMAX MMAX
WHERE MMAX INT6MAX 6" I
I )N THIS EQUATION 6" I 02&I • L IS THE BLIND VELOCITY FOR THE ITH #0) 4HE POS
SIBLE TARGET RADIAL VELOCITIES FOR ALL #0)S ARE THEN SORTED INTO A SINGLE LIST AND THE MOST
LIKELY TRUE RADIAL VELOCITY IS FOUND WHERE AT LEAST TWO POSSIBLE VELOCITIES FALL WITHIN AN
INTERVAL LESS THAN TWO OR THREE TIMES THE STANDARD DEVIATION OF THE DOPPLER FREQUENCY
ESTIMATE 4HE TIGHTNESS OF THE CLUSTER OF NEARLY IDENTICAL VELOCITIES IN CONJUNCTION WITH
THE NUMBER OF #0)S CONTRIBUTING TO THE CLUSTER CAN BE UTILIZED AS A MEASURE OF RELIABILITY
OF THE UNAMBIGUOUS RADIAL VELOCITY ESTIMATE
4HIS APPROACH WAS FIRST BROUGHT TO THE ATTENTION OF THE AUTHORS BY $R "EN #ANTRELL OF THE 53 .AVAL 2ESEARCH
,ABORATORY
Ó°™£
-4) 2!$!2
%&&"'''%'%$()$)!
-(+,
) $
(#&
'$
.
%'#, ) $
$!"'$
-"%', ) $
(!"'$
'#'% !%
%*$
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-
!& &)'52% 0ERFORMANCE OF PHASE DIFFERENCE DOPPLER FREQUENCY ESTIMATOR FOR DIFFERENT
WEIGHTING FUNCTIONS OF THE DOPPLER FILTER BANK
#OMMENTS 4HE ABOVE PROCEDURE FOR DETERMINING TRUE RANGE AND TRUE RADIAL VELOC
ITY HAS BEEN DESCRIBED FOR A DWELL OF THREE #0)S AND THE ASSUMPTION THAT EACH TARGET
WILL HAVE A RETURN FOR EACH OF THE THREE #0)S )N PRACTICE THIS ASSUMPTION IS NOT ALWAYS
VALID AND THE ACTUAL IMPLEMENTATION MAY CHOOSE FOR EXAMPLE TO HAVE THE DWELL CON
SIST OF FOUR OR FIVE #0)S WITH THE RANGE AND VELOCITY DETERMINATIONS BEING BASED ON
THE BEST GROUPING OF THREE RETURNS 4HE ACTUAL IMPLEMENTATION MUST BE BASED ON THE
PARAMETERS OF THE SYSTEM AND PERMISSIBLE TIME ALLOCATED FOR EACH DWELL
4HE 02&S OF THE #0)S SHOULD BE SELECTED TO MINIMIZE THE CHANCE OF FALSE RADIAL
VELOCITY DETERMINATIONS /NE METHOD OF SELECTING 02&S IS SIMILAR TO SELECTING PULSE
INTERVAL RATIOS FOR STAGGERED 02& OPERATION AS DESCRIBED IN 3ECTION &OR EXAM
PLE IF OPERATING AT AN AVERAGE 2& FREQUENCY OF -(Z AT AN AVERAGE 02& OF
(Z AMBIGUOUS VELOCITY OF KNOTS AND COVERING A VELOCITY RANGE OF INTEREST
OF o KNOTS THERE ARE APPROXIMATELY DOPPLER AMBIGUITIES TO COVER 5SING THE
FACTORS OF n n AS USED IN 02& STAGGER SELECTION THE INTERPULSE PERIODS OF THE
FOUR DIFFERENT 02&S WOULD BE IN THE RATIO OF 4HE AVERAGE OF THESE RATIOS
IS 4HE 02&S ARE CALCULATED AS q q q
AND q 4HE 02&S WOULD BE ABOUT AND (Z
Ó°£ÇÊ " - ,/" -Ê** ÊÊ
/"Ê/Ê, ,Ê-9-/ -4) RADAR SYSTEM DESIGN ENCOMPASSES MUCH MORE THAN SIGNAL PROCESSOR DESIGN
4HE ENTIRE RADAR SYSTEMˆTRANSMITTER ANTENNA AND OPERATIONAL PARAMETERSˆMUST BE
KEYED TO FUNCTION AS PART OF AN -4) RADAR &OR EXAMPLE EXCELLENT -4) CONCEPTS WILL
NOT PERFORM SATISFACTORILY UNLESS THE RADAR LOCAL OSCILLATOR IS EXTREMELY STABLE AND THE
Ó°™Ó
2!$!2 (!.$"//+
TRANSMITTER HAS VERY LITTLE PULSE TO PULSE FREQUENCY OR PHASE JITTER )N ADDITION THE
SYSTEM MUST SUCCESSFULLY OPERATE IN AN ENVIRONMENT THAT COMPRISES MANY UNWANTED
TARGETS SUCH AS BIRDS INSECTS AND AUTOMOBILES
(ARDWARE #ONSIDERATIONS )N THIS SECTION RULES AND FACTS RELATING TO -4) RADAR
DESIGN AS DEVELOPED DURING MANY YEARS OF WORK IN THE FIELD WILL BE SUMMARIZED
4HE RULES ARE AS FOLLOWS
/PERATE AT CONSTANT DUTY CYCLE
3YNCHRONIZE AC DC AND DC DC POWER CONDITIONERSo TO HARMONICS OF THE 02&
$ESIGN THE SYSTEM TO BE FULLY COHERENTp
0ROVIDE )& ,IMITERS PRIOR TO !$ CONVERTERS
"E WARY OF VIBRATION AND ACOUSTIC NOISE
4HE FACTS ARE AS FOLLOWS
4HE BASIC -4) CONCEPT DOES NOT REQUIRE A LONG TIME ON TARGET TO RESOLVE TARGETS FROM
FIXED CLUTTER )NSTEAD -4) SYSTEMS REJECT FIXED CLUTTER THROUGH A SUBTRACTION PROCESS
WHILE RETAINING MOVING TARGETS
4RANSMITTER INTRAPULSE ANOMALIES HAVE NO AFFECT ON -4) PERFORMANCE IF THEY REPEAT
PRECISELY PULSE TO PULSE
2ULE /PERATE AT CONSTANT DUTY CYCLE 4HE TRANSMITTER WHETHER THE TRANSMITTER
IS A SINGLE LARGE TUBE OR A DISTRIBUTED FUNCTION AS IN AN ACTIVE PHASED ARRAY WITH MANY
TRANSMIT RECEIVE ELEMENTS SHOULD BE OPERATED AT CONSTANT DUTY CYCLE 4HIS PERMITS
THE TRANSMITTER POWER SUPPLY TRANSIENT EFFECTS TO BE IDENTICAL PULSE TO PULSE AND ALSO
PARTICULARLY APPLICABLE TO SOLID STATE TRANSMIT DEVICES PERMITS THE DEVICE HEATING AND
COOLING TO BE IDENTICAL FROM PULSE TO PULSE 3OMETIMES CONSTANT DUTY CYCLE OPERATION IS
NOT POSSIBLE BUT THERE ARE VARIOUS TECHNIQUES THAT CAN BE USED TO APPROACH THIS DESIRED
CONDITION #ONSIDER AN -4$ WAVEFORM WHERE A #0) CONSISTING OF N PULSES IS TRANSMIT
TED WITH A CONSTANT 02) 4HE NEXT #0) USES A DIFFERENT 02) #ONSTANT DUTY CYCLE CAN BE
MAINTAINED BY CHANGING THE TRANSMITTED PULSE LENGTH IN PROPORTION TO THE CHANGE IN THE
02) )F PULSE COMPRESSION IS USED THE RANGE RESOLUTION OF THE COMPRESSED PULSE CAN BE
MAINTAINED BY CHANGING THE PULSE COMPRESSION WAVEFORM )F IT IS NECESSARY TO UTILIZE
PRECISELY THE SAME WAVEFORM AND 2& PULSE LENGTH FROM #0) TO #0) WITH FOR EXAMPLE
A KLYSTRON TRANSMITTER THE BEAM PULSE OF THE KLYSTRON CAN BE VARIED TO MAINTAIN CON
STANT BEAM DUTY CYCLE WHILE THE 2& PULSE LENGTH IS MAINTAINED CONSTANT 4HIS WASTES
PART OF THE BEAM PULSE ENERGY FOR THE LONGER 02)S BUT THE AVERAGE POWER LOADING ON
THE POWER SUPPLY REMAINS CONSTANT 4HE SAME TECHNIQUE CAN BE UTILIZED WITH SOLID
STATE DEVICES BY CHANGING THE DRAIN VOLTAGE PULSE DURATION WHILE HOLDING THE 2& PULSE
CONSTANT ! SECOND ORDER CORRECTION THAT HAS BEEN UTILIZED WHEN CHANGING BETWEEN
#0)S WITH DIFFERENT 02)S IS TO HAVE A TRANSITION 02) THAT IS THE AVERAGE OF THE TWO 02)S
7ITH PHASED ARRAY RADARS IF THE BEAM TRANSITION TIME BETWEEN #0)S TAKES LONGER THAN A
02) IT IS IMPORTANT TO KEEP THE TRANSMITTER PULSING AT A CONSTANT DUTY CYCLE DURING THE
TRANSITION TIME )F CONSTANT DUTY CYCLE CANNOT BE MAINTAINED OR WHEN STARTING TO RADIATE
o 0OWER CONDITIONERS ACCEPT EITHER AC OR DC INPUT AND PROVIDE A REGULATED DC OUTPUT
p h&ULLY COHERENTv IS DESCRIBED UNDER RULE -4) 2!$!2
Ó°™Î
AFTER DEAD TIME THE TRANSMITTER POWER SUPPLY AND HEATING EFFECTS MUST BE ALLOWED TO
SETTLE BEFORE GOOD -4) PERFORMANCE CAN BE EXPECTED 4HE DURATION OF THE SETTLING TIME
DEPENDS ON THE SYSTEM PARAMETERS AND THE REQUIREMENTS
2ULE 3YNCHRONIZE AC DC AND DC DC POWER CONDITIONERS TO HARMONICS OF THE
02& 7HEN AC DC ANDOR DC DC POWER CONDITIONERS ARE USED FOR VOLTAGES APPLIED TO
TRANSMITTING DEVICES THE FREQUENCY AND ITS HARMONICS OF THE CONVERTER MUST BE ATTEN
UATED SUFFICIENTLY SO THAT THEY DO NOT MODULATE THE PHASE OF THE TRANSMITTED PULSES )F
THE POWER CONDITIONER FREQUENCIES CANNOT BE SUFFICIENTLY ATTENUATED THEIR FREQUENCY
SHOULD BE SYNCHRONIZED TO A MULTIPLE OF THE 02& OF THE #0) SO THAT MODULATIONS REPEAT
PRECISELY PULSE TO PULSE AND THUS WILL CANCEL LIKE STATIONARY CLUTTER
2ULE $ESIGN THE SYSTEM TO BE FULLY COHERENT !LL FREQUENCIES AND TIMING SIGNALS
SHOULD BE GENERATED FROM A SINGLE MASTER OSCILLATOR $OING THIS MAKES THE ENTIRE SYS
TEM COHERENT AND MIXER PRODUCTS WILL BE IDENTICAL PULSE TO PULSE AND WILL THEREFORE
CANCEL IN THE -4) FILTERS 7HEN THIS COHERENCE OF ALL FREQUENCIES IS NOT MAINTAINED
CLUTTER RESIDUE WILL OCCUR AND MUST BE QUANTIFIED TO DETERMINE IF IT IS AT AN ACCEPTABLE
LEVEL /NE OF THE PROMINENT PLACES IN WHICH RESIDUE CAUSED BY UNSYNCHRONIZED LOCAL
OSCILLATORS HAS SHOWN UP IS IN PULSE COMPRESSION SIDELOBES )F THE PULSE COMPRESSION
SIDELOBES FROM FIXED CLUTTER RETURNS VARY FROM PULSE TO PULSE THEY DO NOT CANCEL 4HIS
COHERENCY ISSUE HAS BEEN FURTHER DISCUSSED BY 4AYLOR
2ULE 0ROVIDE )& ,IMITERS PRIOR TO !$ CONVERTERS -4) RADARS REQUIRE THAT )&
BANDPASS LIMITERS EXIST PRIOR TO AN !$ ANALOGDIGITAL CONVERTER 4HE LIMITER PREVENTS
ANY CLUTTER RETURN FROM EXCEEDING THE DYNAMIC RANGE OF THE !$ 4HIS REQUIREMENT
EXISTS FOR EITHER QUADRATURE ) 1 IN PHASE QUADRATURE SAMPLING OR DIRECT SAMPLING
WITH THE ) AND 1 DATA CONSTRUCTED AFTER THE !$ 4HE LIMITER MUST BE DESIGNED TO
MINIMIZE THE CONVERSION OF AMPLITUDE TO PHASE NO MATTER HOW MUCH THE SIGNAL LEVEL
EXCEEDS THE LIMIT LEVEL )F CLUTTER SATURATES THE !$ THE ) 1 DATA IS SIGNIFICANTLY COR
RUPTED 7HEN LIMITERS PREVENT !$ SATURATION THE SIGNALS ARE LIMITED IN A CONTROLLED
MANNER THAT STILL ENABLES GOOD CLUTTER REJECTION ABOUT OF THE TIME
2ULE "E WARY OF VIBRATION AND ACOUSTIC NOISE -ANY 2& DEVICES ARE SUSCEPTIBLE
TO BOTH VIBRATION AND ACOUSTIC NOISE !N AIR CONDITIONER FAN BLOWING ON WAVEGUIDE
HAS CAUSED DEGRADATION OF IMPROVEMENT FACTOR DUE TO PHASE MODULATION OF SIGNALS
6IBRATIONS CAN CAUSE PHASE MODULATION OF AN OSCILLATOR !COUSTIC NOISE CAN ORIGINATE
FROM COOLING FANS AND VIBRATIONS CAN COME FROM SHIPBOARD OR AIRBORNE RADAR PLAT
FORMS #OMPONENTS SUCH AS KLYSTRONS AND SOLID STATE MODULES CAN HAVE UNEXPECTED
SUSCEPTIBILITY TO VIBRATION 2& CONNECTORS MUST BE SECURE 3HOCK MOUNTS CAN BE USED
TO ISOLATE COMPONENTS FROM THE CABINET STRUCTURE )T IS RECOMMENDED THAT ALL 2& COM
PONENTS IN THEIR OPERATIONAL CONFIGURATION BE TESTED FOR PHASE STABILITY IN THE VIBRATION
ENVIRONMENT IN WHICH THEY WILL BE USED
&ACT 4HE BASIC -4) CONCEPT DOES NOT REQUIRE SUFFICIENT TIME ON TARGET TO RESOLVE
TARGETS FROM FIXED CLUTTER USING A LINEAR TIME INVARIANT FILTER )NSTEAD -4) SYSTEMS REJECT
FIXED CLUTTER THROUGH A SUBTRACTION PROCESS WHILE RETAINING MOVING TARGETS !N -4)
SYSTEM USING A TWO PULSE CANCELER REQUIRES THE TRANSMITTER TO TRANSMIT ONLY TWO SUC
CESSIVE IDENTICAL PULSES FOR THE SYSTEM TO BE ABLE TO REJECT STABLE FIXED CLUTTER 4HE
RADAR RETURNS FROM THE SECOND PULSE ARE SUBTRACTED FROM THE RETURNS FROM THE FIRST PULSE
Ó°™{
2!$!2 (!.$"//+
4HE RESULT FROM THIS SUBTRACTION PROCESS IS THAT THE FIXED CLUTTER IS REMOVED AND MOVING
TARGETS ARE RETAINED 4HE OUTPUT FROM THE FIRST PULSE IS NOT USED MAKING THIS TYPE OF -4)
FILTER TIME VARIANT /F COURSE THE CLUTTER FILTERS MAY BE MORE COMPLEX THAN A TWO PULSE
CANCELER e BUT THE PRINCIPLE STILL REMAINS THAT FIXED CLUTTER IS REJECTED BY THE ZEROS IN
THE CANCELER TRANSFER CHARACTERISTIC 4HIS ENABLES PHASED ARRAY RADARS TO HAVE GOOD CLUT
TER REJECTION WITH SHORT DWELLS
&ACT 4RANSMITTER INTRAPULSE ANOMALIES HAVE NO AFFECT ON -4) PERFORMANCE IF
THEY REPEAT PRECISELY PULSE TO PULSE 4RANSMITTED PULSES SHOULD BE IDENTICAL )T DOES
NOT MATTER IF THERE IS INTRAPULSE AMPLITUDE OR FREQUENCY MODULATION OF THE TRANSMITTED
PULSE AS LONG AS IT REPEATS PRECISELY FROM PULSE TO PULSE )F THE VOLTAGE OF THE TRANS
MITTER POWER SUPPLY VARIES PULSE TO PULSE THE TRANSMITTED PULSES WILL NOT BE IDENTI
CAL AND THE RESULTING VARIATIONS MUST BE QUANTIFIED TO DETERMINE IF THE LIMITATIONS ON
IMPROVEMENT FACTOR FALL WITHIN THE STABILITY BUDGET FOR THE SYSTEM (OWEVER IF THE ONLY
DIFFERENCE BETWEEN PULSES IS ABSOLUTE PHASE NOT INTRAPULSE VARIATIONS PULSE TO PULSE
SOME MITIGATION IS POSSIBLE /NE METHOD OF COMPENSATING FOR SMALL VARIATIONS IN THE
PHASE OF TRANSMITTER PULSES FOLLOWS ,INCOLN ,ABORATORY CHANGED THE ORIGINAL 4$72
WAVEFORM TO AN -4$ TYPE WAVEFORM 4HE ORIGINAL 4$72 WAVEFORM WAS CONSTANT
02& DURING EACH ANTENNA ROTATION AND PROCESSING WAS DONE WITH ELLIPTIC FILTERS 4HEY
THEN MODIFIED THE SYSTEM hxTO ACHIEVE D" CLUTTER SUPPRESSION USING A NEARBY
WATER TOWER FOR A TARGETv 4HE 4$72 USES A KLYSTRON TRANSMITTER TUBE 4YPICAL PHASE
PUSHING FOR A KLYSTRON DUE TO MODULATOR VOLTAGE CHANGE IS — FOR DELTA %% 4HE
STABILITY BUDGET ALLOCATED A D" LIMIT ON IMPROVEMENT FACTOR TO THE TRANSMITTER AND
THIS REQUIRED THAT THE RMS PULSE TO PULSE POWER SUPPLY VOLTAGE VARIATION BE LESS THAN
PART IN 4HE TRANSMITTER POWER SUPPLY COULD NOT MEET THIS REQUIREMENT WHEN
THE RADAR CHANGED 02& FROM #0) TO #0) AS REQUIRED BY AN -4$ WAVEFORM 4HEREFORE
THE ACTUAL PHASE OF EACH TRANSMITTED PULSE WAS MEASURED AND THIS MEASURED VALUE WAS
USED TO CORRECT THE PHASE OF THE RECEIVED SIGNALS FOR THAT 02) 4HIS TECHNIQUE CAUSES
SMALL PERTURBATIONS IN PHASE FROM WEATHER SIGNALS RECEIVED FROM AMBIGUOUS RANGES
BUT DOES NOT INTERFERE WITH VELOCITY ESTIMATES )T DOES DEGRADE THE IMPROVEMENT FACTOR
OF CLUTTER SIGNALS RECEIVED FROM AMBIGUOUS RANGES BUT FOR THE 4$72 OPERATION THAT
DEGRADATION WAS DEEMED ACCEPTABLE
%NVIRONMENTAL #ONSIDERATIONS 4HIS DISCUSSION CONTAINS ESSENTIAL INFORMA
TION FOR THOSE DESIGNING A MODERN SURVEILLANCE RADAR TO DETECT MAN MADE AIRBORNE
TARGETS 4HE LAWS OF PHYSICS COMBINED WITH THE ENVIRONMENT MAKE IT IMPOSSIBLE TO
DESIGN AN -4) SURVEILLANCE RADAR THAT DOES NOT HAVE COMPROMISES 4HE PROBLEMS
ARE RELATED TO THE UNWANTED RETURNS FROM BIRDS INSECTS AUTOMOBILES LONG RANGE
FIXED CLUTTER AND SHORT AND LONG RANGE WEATHER 4HE CURRENT STATE OF THE ART OF
RADAR CAN AMELIORATE THESE PROBLEMS BUT NOT WITHOUT SOME UNDESIRABLE SIDE EFFECTS
-ANY UNWANTED POINT TARGET RETURNS HAVE CHARACTERISTICS SIMILAR TO THE RETURNS FROM
WANTED TARGETS AND THE UNWANTED RETURNS MAY OUTNUMBER RETURNS FROM DESIRED TAR
GETS BY THE THOUSANDS
e 4HE CLUTTER FILTERS MUST BE DESIGNED BASED ON SYSTEM PARAMETERS TO REJECT THE RADIAL SPEED OF THE hFIXEDv CLUTTER
3EE 3ECTIONS AND )T HAS BEEN OBSERVED THAT SOME PHASED ARRAY RADARS HAVE POOR CLUTTER REJECTION WHICH IS OFTEN CAUSED BY FAILURE
TO FOLLOW RULE -4) 2!$!2
Ó°™x
4HE PROBLEMS ARE EXACERBATED WHEN ANOMALOUS OR DUCTED PROPAGATION OCCURS
ANOMALOUS PROPAGATION AS USED HEREIN IS WHEN THE RADAR ENERGY FOLLOWS THE CURVATURE
OF THE %ARTH THUS CAUSING DETECTION OF BOTH FIXED AND MOVING CLUTTER AT LONG RANGES &IGURE FROM 3HRADER SHOWS 00) PHOTOGRAPHS TAKEN WITH AN !232 RADAR
MOUNTED ON A FT TOWER IN FLAT COUNTRY NEAR !TLANTIC #ITY .EW *ERSEY 7ITH NORMAL
PROPAGATION THE EXPECTED LINE OF SIGHT IS ABOUT NMI BUT THE CLUTTER ACTUALLY GOES
OUT TO NMI 4HE BRIDGES ACROSS THE INTRACOASTAL WATERWAY CAN BE SEEN /N OCCASION
THE UNWANTED LONG RANGE CLUTTER AND WEATHER RETURNS COME FROM AMBIGUOUS RANGES
&)'52% !NOMALOUS PROPAGATION DUCTING A NMI MAXIMUM
RANGE AND B NMI MAXIMUM RANGE
Ó°™È
2!$!2 (!.$"//+
4HE RADAR SYSTEM MUST HAVE FEATURES TO COPE WITH THESE SITUATIONS &OR EXAMPLE IF PULSE
TO PULSE STAGGERING IS USED THE AMBIGUOUS RANGE CLUTTER WILL NOT CANCEL AND EITHER THE
02) MUST BE INCREASED OR THE 02) MUST BE MADE CONSTANT OVER THE AZIMUTH ANGLES FROM
WHICH THE AMBIGUOUS RANGE CLUTTER IS RECEIVED !ND BE FOREWARNED OF A PITFALL INTO WHICH
MANY RADAR DESIGNERS HAVE FALLEN &OR EXAMPLE WHEN PRESENTED WITH THE REQUIREMENT
TO TRACK TARGETS THE DESIGNER MAY NOT REALIZE THAT RADAR RETURNS FROM THE TARGETS OF
INTEREST MAY BE EMBEDDED IN SIMILAR RETURNS FROM THOUSANDS OF UNWANTED TARGETS
! TYPICAL LONG RANGE AIR TRAFFIC CONTROL RADAR HAS SUFFICIENT SENSITIVITY TO DETECT A
SINGLE LARGE BIRD SUCH AS A CROW SEAGULL OR VULTURE APPROXIMATE 2#3 OF SQUARE
METER AT A RANGE OF MILES )F THERE ARE MANY SUCH BIRDS IN THE RESOLUTION CELL OF THE
RADAR THEN THE COMPOSITE 2#3 INCREASES 4EN LARGE BIRDS IN A RESOLUTION CELL WILL HAVE
AN 2#3 OF SQUARE METER 7HEN MULTIPATH REFLECTIONS OCCUR SUCH AS OVER THE OCEAN
WHEN THE RADAR BEAM IS CENTERED AT THE HORIZON THERE CAN BE UP TO A D" ENHANCEMENT
OF THE 2#3 OF THE BIRDS GIVING AN APPARENT 2#3 GREATER THAN ONE SQUARE METER TO THE
FLOCK OF BIRDS )F THERE IS BIRD OR BIRD FLOCK PER SQUARE MILE THERE WILL BE ABOUT
BIRD RETURNS WITHIN MILES OF THE RADAR
4ECHNIQUES USED TO COUNTER UNWANTED TARGETS ARE AS FOLLOWS
3ENSITIVITY TIME CONTROL 34# USED FOR ELIMINATING LOW 2#3 TARGETS IN LOW 02&
RADARSˆTHAT IS RADARS THAT HAVE NO RANGE AMBIGUITIES UNDER NORMAL OPERATION
%NHANCED HIGH ANGLE GAIN ANTENNAS
4WO BEAM ANTENNASˆBEAM LIFTED ABOVE THE HORIZON FOR SHORT RANGE RECEPTION AND
THEN LOWERED TO HORIZON FOR LONG RANGE
-4$ TECHNIQUES USING CLUTTER MAPS !LSO COUNTING DETECTIONS IN SMALL RANGE
AZIMUTH SECTORS AND INCREASING DETECTION THRESHOLDS IN EACH SECTOR IF TOO MANY
DETECTIONS OCCUR
02&S HIGH ENOUGH SO THAT ALL TARGETS WITH RADIAL VELOCITIES BELOW KNOTS CAN BE
CENSORED
3ENSITIVITY VELOCITY CONTROL 36# WHICH CENSORS RADIALLY SLOW SMALL TARGETS
WHILE ACCEPTING RADIALLY FAST TARGETS AND LARGE TARGETS
#OMBINATIONS OF TECHNIQUES THROUGH ARE USED IN MOST AIR TRAFFIC CONTROL RADARS
WHERE THE SMALLEST TARGETS OF INTEREST HAVE AN 2#3 OF ONE SQUARE METER OR GREATER
4ECHNIQUES AND ARE USED WHEN THE DESIRED TARGETS MAY HAVE RADAR CROSS SECTIONS
SIMILAR TO OR SMALLER THAN A BIRD
4ECHNIQUE 34# IS THE TRADITIONAL METHOD OF SUPPRESSING BIRDS AND INSECTS IN A
RADAR WITH AN UNAMBIGUOUS RANGE 02& A 02& LOW ENOUGH SO THAT THE RANGE TO TARGETS
AND CLUTTER IS UNAMBIGUOUS 34# DECREASES THE SENSITIVITY OF THE RADAR AT SHORT RANGE
AND THEN INCREASES SENSITIVITY USUALLY USING A FOURTH POWER LAW AS RANGE INCREASES
4HIS HAS THE EFFECT OF NOT PERMITTING DETECTION OF TARGETS WITH APPARENT RADAR CROSS SEC
TIONS OF SAY LESS THAN SQUARE METER &IGURE SHOWS HOW EFFECTIVE 34# CAN BE
AGAINST BIRDS 4HESE 00) PHOTOS WERE TAKEN WITH AN , BAND !232 AIR ROUTE SURVEIL
LANCE RADAR IN /KLAHOMA .OTE THAT THE MAJORITY OF RETURNS FROM BIRDS WERE ELIMI
NATED BUT NOT &IGURE SHOWS THE EFFECT OF 34# AGAINST BATS AND INSECTSo
o $AYTIME BIRD RETURNS AND NIGHTTIME BAT AND INSECT RETURNS CAN OFTEN BE SEEN IN REAL TIMEˆTHE EXTENT DEPENDS ON THE
WEATHER AND TIME OF YEARˆON THE .%82!$ 732 $ WEATHER RADAR IMAGES ON THE ./!! )NTERNET SITES
-4) 2!$!2
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&)'52% 34# CAN GREATLY REDUCE THE NUMBER OF BIRDS DISPLAYED 2ANGE NMI A "IRDS SEEN WITH
-4) AND B BIRDS SEEN WITH -4) AND 34#
&)'52% )NSECTS WITH AND WITHOUT 34# AND RANGE MILES A BATS AND INSECTS SEEN WITH -4) AND
B BATS AND INSECTS SEEN WITH -4) AND 34#
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4HE TYPICAL DOPPLER RADAR IMAGES PRESENTED BY 46 WEATHER FORECASTERS OFTEN HAVE THE
BIRDS AND BATS AND INSECTS REMOVED BY HUMAN INTERVENTION
4ECHNIQUE 34# WORKS QUITE WELL FOR UNWANTED BIOLOGICAL RETURNS NEAR THE PEAK
OF THE RADAR BEAM BUT WHEN USED WITH A COSECANT SQUARED ANTENNA BEAM IT SOLVES ONE
PROBLEM BUT CREATES ANOTHER IT ALSO DECREASES SENSITIVITY TO DESIRED TARGETS AT HIGH
ELEVATION ANGLES WHERE THE ANTENNA GAIN IS LOW 4HE SOLUTION TO THIS PROBLEM IS TO BOOST
THE ANTENNA GAIN AT HIGH ELEVATION ANGLES TO BE CONSIDERABLY HIGHER THAN THE REQUIRE
MENT FOR THE COSECANT SQUARED PATTERN .OT ONLY DOES THIS COMPENSATE FOR THE USE OF
34# BUT ALSO ENHANCES THE TARGET TO CLUTTER SIGNAL RATIO FOR TARGETS AT HIGH ELEVATION
ANGLES THUS IMPROVING -4) PERFORMANCE 4HE PENALTY FOR THIS SOLUTION IS A LOSS IN THE
PEAK ANTENNA GAIN THAT CAN BE ACHIEVED !N ILLUSTRATION OF THIS APPROACH IS PROVIDED
IN &IGURE WHICH SHOWS BOTH THE !232 ANTENNA PATTERN AND THE CORRESPONDING
FREE SPACE COVERAGE
&)'52% !NTENNA ELEVATION PATTERN FOR THE !232 ANTENNA
A COMPARED WITH THE COSECANT SQUARED PATTERN AND B FREE SPACE
COVERAGE DIAGRAM
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4HE LOSS IN PEAK GAIN FOR THIS EXAMPLE DUE TO THE BOOST OF COVERAGE AT HIGH ANGLES
WAS ABOUT D" 4HE COMBINATION OF 34# WITH ENHANCED HIGH ANGLE COVERAGE DOES
QUITE WELL FOR INSECTS AND BIRDS BUT DOES NOT ELIMINATE AUTOMOBILE AND TRUCK RETURNS
6EHICLES HAVE 2#3S THAT EQUAL OR EXCEED THE 2#3 OF MANY DESIRED AIRCRAFT TARGETS
4ECHNIQUE 4HE TWO BEAM TECHNIQUE REDUCES THE RETURNS FROM VERY LOW ELEVA
TION ANGLES WHERE VEHICLE TRAFFIC AND MANY BIRDS BATS AND INSECTS IS ENCOUNTERED
4HE RADAR TRANSMITS ENERGY USING THE BASIC PATTERN BUT USES A HIGHER ANGLE BEAM
FOR RECEPTION AT SHORTER RANGES AND THE BASIC ANTENNA PATTERN FOR RECEIVING AT LONGER
RANGES &IGURE SHOWS UNDERNEATH THE TRANSMITTING FEED HORN A SECOND RECEIVE
ONLY ANTENNA FEED HORN FOR THE HIGH BEAM 4HE EFFECTIVE TWO WAY ANTENNA PATTERNS ARE
SHOWN IN &IGURE !S PREVIOUSLY MENTIONED THE ABOVE TECHNIQUES 34# TWO BEAM ANTENNAS AND
SOME VARIATION OF -4$ ARE CURRENTLY USED ON MANY AIR TRAFFIC CONTROL RADARS 4HE
TWO BEAM ANTENNAS ALSO UTILIZE SOME HIGH ANGLE GAIN ENHANCEMENT TO COUNTER THE
HIGH ANGLE EFFECTS OF 34#
4ECHNIQUE 4HE -4$ APPROACH IS DESCRIBED IN 3ECTION 4ECHNIQUE ! BRUTE FORCE TECHNIQUE USED TO ELIMINATE TARGETS WITH RADIAL
VELOCITIES OF LESS THAN APPROXIMATELY o KNOTS RESULTING IN A TOTAL REJECTION INTERVAL
OF KNOTS 4O KEEP THIS REJECTION OF VELOCITIES TO NO MORE THAN OF THE DOPPLER
SPACE AVAILABLE THE AMBIGUOUS VELOCITY MUST BE ABOUT KNOTS 4HIS REQUIRES
02&S OF (Z AT , BAND (Z AT 3 BAND AND AT 8 BAND UNAMBIGUOUS
RANGES RESPECTIVELY NMI NMI AND NMI 4HE MAIN CHALLENGE WITH THIS TECH
NIQUE IS THAT FIXED CLUTTER RETURNS FROM MANY RANGE AMBIGUITIES AS WELL AS ALL TARGETS
OF INTEREST FOLD INTO THE FIRST RANGE INTERVAL 4HUS EXCELLENT CLUTTER REJECTION MUST BE
PROVIDED TO PREVENT FOLDED CLUTTER FROM SUPPRESSING TARGETS OF INTEREST WHICH MAY
BE AT ANY TRUE RANGE
4ECHNIQUE 36# AS DESCRIBED IN 3ECTION IS USED WHEN IT IS NECESSARY TO
DISTINGUISH VERY LOW 2#3 TARGETS FROM LOW VELOCITY CLUTTER SUCH AS BIRDS INSECTS AND
SEA 3OMEWHAT LOWER 02&S CAN BE USED THAN THOSE USED FOR TECHNIQUE BECAUSE THE
&)'52% 4WO BEAM ANTENNA
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LOGIC PERMITS RETAINING MANY OF THE TARGETS WITH SMALLER RADIAL VELOCITIES IF THEIR 2#3
IS LARGE ENOUGH 36# STILL REJECTS BIRD CLUTTER BUT RETAINS FOR EXAMPLE THE FAST INCOM
ING THREATENING LOW 2#3 MISSILE WHILE ALSO RETAINING THE LARGER CROSS SECTION AIRCRAFT
WITH LOWER RADIAL VELOCITIES
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, ", Ê/Ê/ +1 !IRBORNE SEARCH RADARS WERE INITIALLY DEVELOPED FOR THE DETECTION OF SHIPS BY LONG RANGE
PATROL AIRCRAFT $URING THE LATTER PART OF 7ORLD 7AR )) AIRBORNE EARLY WARNING !%7
RADARS WERE DEVELOPED BY THE 53 .AVY TO DETECT LOW FLYING AIRCRAFT APPROACHING A
TASK FORCE BELOW THE RADAR COVERAGE OF THE SHIPS ANTENNA 4HE ADVANTAGE OF THE AIR
BORNE PLATFORM IN EXTENDING THE MAXIMUM DETECTION RANGE FOR AIR AND SURFACE TARGETS IS
APPARENT WHEN ONE CONSIDERS THAT THE RADAR HORIZON IS NMI FOR A FT ANTENNA MAST
COMPARED WITH APPROXIMATELY NMI FOR A FT AIRCRAFT ALTITUDE
4HE AIRCRAFT CARRIERnBASED % $ AIRCRAFT &IGURE USES !%7 RADAR AS THE PRIMARY
SENSOR IN ITS AIRBORNE TACTICAL DATA SYSTEM 4HESE RADARS WITH THEIR EXTENSIVE FIELD OF
VIEW ARE REQUIRED TO DETECT SMALL AIRBORNE TARGETS AGAINST A BACKGROUND OF SEA AND
LAND CLUTTER "ECAUSE THEIR PRIMARY MISSION IS TO DETECT LOW FLYING AIRCRAFT THEY CANNOT
ELEVATE THEIR ANTENNA BEAM TO ELIMINATE THE CLUTTER 4HESE CONSIDERATIONS HAVE LED TO
THE DEVELOPMENT OF AIRBORNE -4) !-4) RADAR SYSTEMS SIMILAR TO THOSE USED IN
SURFACE RADARS n DISCUSSED IN THE PRECEDING CHAPTER
4HE MISSION REQUIREMENTS FOR AN !%7 RADAR DRIVE THE NEED FOR — AZIMUTHAL COV
ERAGE AND LONG RANGE DETECTION CAPABILITY 4HE — AZIMUTHAL COVERAGE REQUIREMENT
IS BECAUSE THE !%7 RADAR SYSTEM IS GENERALLY REQUIRED TO PROVIDE THE FIRST DETECTION OF
AIRBORNE TARGETS WITHOUT ANY A PRIORI KNOWLEDGE OF THE LOCATION OF THESE TARGETS !%7
SYSTEMS HAVE GENERALLY BEEN DEVELOPED AT LOWER FREQUENCIESˆTHIS CAN BE UNDERSTOOD
BY REVIEWING THE SURVEILLANCE RADAR RANGE EQUATION
2MAX 0A !E S T
TS
P K4 &N , 3 . 7
3ECTIONS THROUGH AND WERE TAKEN PRIMARILY FROM THE SECOND EDITION OF THE 2ADAR (ANDBOOK #HAPTER AUTHORED BY &RED 3TAUDAHER WITH REVISIONS MADE BY *AMES $AY 4HE REMAINING SECTIONS OF THE CHAPTER WERE
AUTHORED BY *AMES $AY
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2!$!2 (!.$"//+
&)'52% % $ AIRBORNE EARLY WARNING !%7 AIRCRAFT SHOWING ROTODOME
HOUSING THE ANTENNA
WHERE TS IS THE SCAN TIME AND 7 IS THE SURVEILLANCE VOLUME COVERAGE REQUIREMENT PROD
UCT OF THE AZIMUTH AND ELEVATION ANGLES !S LONG AS THE BEAMWIDTHS OF THE RADAR IN AZIMUTH AND ELEVATION ARE SMALLER THAN
THE REGION TO BE SURVEILLED THIS EQUATION IS NOT DIRECTLY DEPENDENT UPON FREQUENCY
(OWEVER KEY PARAMETERS IN THIS EQUATION ARE DEPENDENT UPON FREQUENCY 0ARTICULARLY
PROPAGATION LOSSES FOR LOW ALTITUDE TARGETS AND TARGET 2#3 FOR SOME TARGET TYPES ARE
GENERALLY ADVANTAGEOUS FOR LOWER FREQUENCIES 4HE RESULT IS THAT !%7 SYSTEMS HAVE
BEEN DEVELOPED AT 5(& , BAND AND 3 BAND FREQUENCIES
!IRBORNE -4) RADAR SYSTEMS HAVE ALSO BEEN UTILIZED TO ACQUIRE AND TRACK TARGETS IN
INTERCEPTOR FIRE CONTROL SYSTEMS )N THIS APPLICATION THE SYSTEMS HAVE TO DISCRIMINATE
AGAINST CLUTTER ONLY IN THE VICINITY OF A PRESCRIBED TARGET 4HIS ALLOWS THE SYSTEM TO BE
OPTIMIZED AT THE RANGE AND ANGULAR SECTOR WHERE THE TARGET IS LOCATED -4) IS ALSO USED
TO DETECT MOVING GROUND VEHICLES BY RECONNAISSANCE AND TACTICAL FIGHTER AIRCRAFT
4HE ENVIRONMENT OF HIGH PLATFORM ALTITUDE MOBILITY AND SPEED COUPLED WITH
RESTRICTIONS ON SIZE WEIGHT AND POWER CONSUMPTION PRESENT A UNIQUE SET OF PROBLEMS
TO THE DESIGNER OF AIRBORNE -4) SYSTEMS 4HIS CHAPTER WILL BE DEVOTED TO CONSIDER
ATIONS UNIQUE TO THE AIRBORNE ENVIRONMENT
ΰÓÊ
"6 , Ê " -
,/" -
3EARCH RADARS GENERALLY REQUIRE n AZIMUTHAL COVERAGE 4HIS COVERAGE IS DIFFICULT
TO OBTAIN ON AN AIRCRAFT SINCE MOUNTING AN ANTENNA IN THE CLEAR PRESENTS MAJOR DRAG
STABILITY AND STRUCTURAL PROBLEMS 7HEN EXTENSIVE VERTICAL COVERAGE IS REQUIRED THE
AIRCRAFTS PLANFORM AND VERTICAL STABILIZER DISTORT AND SHADOW THE ANTENNA PATTERN
!NALYSIS OF TACTICAL REQUIREMENTS MAY SHOW THAT ONLY A LIMITED COVERAGE SECTOR IS
REQUIRED (OWEVER THIS SECTOR USUALLY HAS TO BE CAPABLE OF BEING POSITIONED OVER THE
FULL n RELATIVE TO THE AIRCRAFTS HEADING BECAUSE OF THE REQUIREMENTS FOR COVERAGE
ΰÎ
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&)'52% "OEING 7EDGETAIL AIRCRAFT SHOWING ANTENNAS MOUNTED
ABOVE THE FUSELAGE
WHILE REVERSING COURSE LARGE CRAB ANGLES WHEN HIGH WINDS ARE ENCOUNTERED THE NEED
TO POSITION GROUND TRACK IN RELATION TO WIND NONTYPICAL OPERATING SITUATIONS AND OPERA
TIONS REQUIREMENTS FOR COVERAGE WHILE PROCEEDING TO AND FROM THE STATION
(OWEVER IN THE S AND S A NUMBER OF SYSTEMS HAVE BEEN DEVELOPED THAT PRO
VIDE PHASED ARRAY PERFORMANCE IN AN AIRBORNE PLATFORM 4HE -ULTI 2OLE %LECTRONICALLY
3CANNED !RRAY -%3! RADAR DEVELOPED BY .ORTHROP 'RUMMAN ON A "OEING FOR THE !USTRALIAN 7EDGETAIL PROGRAM IS AN EXAMPLE SEE &IGURE !N ALTERNATE SOLU
TION THAT COMBINES MECHANICAL SCANNING IN CONJUNCTION WITH ELECTRONIC SCANNING IS IN
DEVELOPMENT WITH THE !.!09 RADAR FOR THE % $ AIRCRAFT FOLLOW UP TO THE 53
.AVYS % # AIRCRAFT ΰÎÊ , ",
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4HE PERFORMANCE OF AIRBORNE -4) SYSTEMS ARE PRIMARILY DETERMINED BY MOTION EFFECTS
INDUCED ON THE CLUTTER ECHOES PLATFORM MOTION ANTENNA SCANNING MOTION AND CLUTTER INTER
NAL MOTION THE PROCESSING TECHNIQUES USED TO ENHANCE TARGET DETECTION AND MAXIMIZE CLUT
TER CANCELLATION AND THE HARDWARE STABILITY LIMITATIONS OF THE RADAR 4HIS CHAPTER WILL DISCUSS
THE MOTION EFFECTS AS WELL AS THE PERFORMANCE OF VARIOUS PROCESSING TECHNIQUES
ΰ{Ê */",Ê"/" Ê Ê//1
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-4) DISCRIMINATES BETWEEN AIRBORNE MOVING TARGETS AND STATIONARY LAND OR SEA CLUTTER
(OWEVER IN THE AIRBORNE CASE THE CLUTTER MOVES WITH RESPECT TO THE MOVING AIRBORNE
PLATFORM )T IS POSSIBLE TO COMPENSATE FOR THE MEAN CLUTTER RADIAL VELOCITY BY USING
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&)'52% $EFINING GEOMETRY @¼
ANTENNA POINTING ANGLE @ LINE OF SIGHT ANGLE P ANGLE
FROM ANTENNA CENTERLINE 6G AIRCRAFT GROUND SPEED 6R RADIAL VELOCITY OF POINT TARGET 6" RADIAL
VELOCITY ALONG ANTENNA CENTERLINE BORESIGHT X ANTENNA AZIMUTH ANGLE X AZIMUTH ANGLE 2 GROUND RANGE TO POINT TARGET AND ( AIRCRAFT HEIGHT
TECHNIQUES SUCH AS TIME AVERAGED CLUTTER COHERENT AIRBORNE RADAR 4!##!2 4HIS
TECHNIQUE ATTEMPTS TO CENTER THE LARGEST RETURN FROM MAIN BEAM CLUTTER AT ZERO DOPPLER
FREQUENCY SUCH THAT A SIMPLE -4) FILTER ALSO CENTERED AT ZERO DOPPLER FREQUENCY WILL
CANCEL THE MAIN BEAM CLUTTER
!S SHOWN IN &IGURE THE APPARENT RADIAL VELOCITY OF THE CLUTTER IS 6R 6G COS @
WHERE 6G IS THE GROUND SPEED OF THE PLATFORM AND A IS THE ANGLE SUBTENDED BETWEEN THE LINE
OF SIGHT TO A POINT ON THE %ARTHS SURFACE AND THE AIRCRAFTS VELOCITY VECTOR &IGURE SHOWS
THE LOCI OF CONSTANT RADIAL VELOCITY ALONG THE SURFACE )N ORDER TO NORMALIZE THE FIGURE A FLAT
EARTH IS ASSUMED AND THE NORMALIZED RADIAL VELOCITY 6N 6R6G IS PRESENTED AS A FUNCTION OF
AZIMUTH ANGLE X AND NORMALIZED GROUND RANGE 2( WHERE ( IS THE AIRCRAFTS ALTITUDE
)NSTEAD OF A SINGLE CLUTTER DOPPLER FREQUENCY CORRESPONDING TO A CONSTANT RADIAL
VELOCITY 6" IN &IGURE DETERMINED BY THE ANTENNA POINTING ANGLE @ THE RADIAL
SEES A CONTINUUM OF VELOCITIES 4HIS RESULTS IN A FREQUENCY SPECTRUM AT A PARTICULAR
RANGE WHOSE SHAPE IS DETERMINED BY THE ANTENNA PATTERN THAT INTERSECTS THE SURFACE THE
REFLECTIVITY OF THE CLUTTER AND THE VELOCITY DISTRIBUTION WITHIN THE BEAM &URTHERMORE
SINCE 6R VARIES AS A FUNCTION OF RANGE AT A PARTICULAR AZIMUTH X THE CENTER FREQUENCY
AND SPECTRUM SHAPE VARY AS A FUNCTION OF RANGE AND AZIMUTH ANGLE X
7HEN THE ANTENNA IS POINTING AHEAD THE PREDOMINANT EFFECT IS THE VARIATION OF THE CEN
TER FREQUENCY CORRESPONDING TO THE CHANGE IN @ WITH RANGE 7HEN THE ANTENNA IS POINTING
!)2"/2.% -4)
ΰx
&)'52% ,OCI OF CONSTANT NORMALIZED RADIAL VELOCITY 6R6G AS A FUNC
TION OF AIRCRAFT RANGE TO HEIGHT RATIO 2( AND AZIMUTH ANGLE X
ABEAM THE PREDOMINANT EFFECT IS THE VELOCITY SPREAD ACROSS THE ANTENNA BEAMWIDTH 4HESE
ARE CLASSIFIED AS THE SLANT RANGE EFFECT AND THE PLATFORM MOTION EFFECT RESPECTIVELY
%FFECT OF 3LANT 2ANGE ON $OPPLER /FFSET 4HE ANTENNA BORESIGHT VELOCITY 6" IS
THE GROUND VELOCITY COMPONENT ALONG THE ANTENNA CENTERLINE BORESIGHT AND IS GIVEN
AS n6G COS @ )F THE CLUTTER SURFACE WERE COPLANAR WITH THE AIRCRAFT THIS COMPONENT
WOULD BE EQUAL TO 6G COS X AND WOULD BE INDEPENDENT OF RANGE 4HE RATIO OF THE
ACTUAL BORESIGHT VELOCITY TO THE COPLANAR BORESIGHT VELOCITY IS DEFINED AS THE NORMAL
IZED BORESIGHT VELOCITY RATIO
6"2 COS A COS F
COSY WHERE E IS THE DEPRESSION ANGLE OF THE ANTENNA CENTERLINE FROM THE HORIZONTAL &IGURE SHOWS THE VARIATION OF THE NORMALIZED BORESIGHT VELOCITY RATIO AS A FUNCTION OF SLANT RANGE
FOR A CURVED EARTH AND DIFFERENT AIRCRAFT ALTITUDES 4HE VARIATION IS FAIRLY RAPID FOR SLANT
RANGES LESS THAN NMI
)T IS DESIRABLE TO CENTER THE CLUTTER SPECTRUM IN THE NOTCH IE MINIMUM RESPONSE
REGION OF THE !-4) FILTER IN ORDER TO OBTAIN MAXIMUM CLUTTER REJECTION 4HIS CAN BE
ACCOMPLISHED BY OFFSETTING THE )& OR 2& FREQUENCY OF THE RADAR SIGNAL BY AN AMOUNT
EQUAL TO THE AVERAGE DOPPLER FREQUENCY OF THE CLUTTER SPECTRUM "ECAUSE THE CLUTTER
CENTER FREQUENCY VARIES WITH RANGE AND AZIMUTH WHEN THE RADAR IS MOVING IT IS NECES
SARY FOR THE FILTER NOTCH TO TRACK THE DOPPLER OFFSET FREQUENCY USING AN OPEN OR CLOSED
LOOP CONTROL SYSTEM SUCH AS 4!##!2 DESCRIBED BELOW
!N EXAMPLE OF A RECEIVED CLUTTER SPECTRUM GIVEN AN ANTENNA RESPONSE IS SHOWN
IN &IGURE A 4HE 4!##!2 FREQUENCY OFFSET THEN SHIFTS MAIN BEAM CLUTTER TO ZERO
DOPPLER AS SHOWN IN &IGURE B
ΰÈ
2!$!2 (!.$"//+
&)'52% .ORMALIZED BORESIGHT VELOCITY RATIO 6"2 AS A FUNCTION OF THE DIFFERENCE BETWEEN SLANT RANGE
2S AND AIRCRAFT ALTITUDE ( FOR DIFFERENT AIRCRAFT ALTITUDES
4!##!2 4HE -)4 ,INCOLN ,ABORATORY ORIGINALLY DEVELOPED 4!##!2 TO SOLVE
THE !-4) RADAR PROBLEM 4HE REQUIREMENTS AND THUS THE IMPLEMENTATION OF 4!##!2
CHANGE DEPENDING UPON THE TYPE OF CLUTTER CANCELLATION PROCESSING EMPLOYED !FTER
MANY OTHER APPROACHES IT WAS RECOGNIZED THAT IF ONE USED THE CLUTTER RETURN RATHER THAN
THE TRANSMIT PULSE TO PHASE LOCK THE RADAR TO THE CLUTTER FILTER ONE COULD CENTER THE CLUT
TER IN THE FILTER STOPBAND 4HE CLUTTER PHASE VARIES FROM RANGE CELL TO RANGE CELL OWING
TO THE DISTRIBUTION OF THE LOCATION OF THE SCATTERERS IN AZIMUTH (ENCE IT IS NECESSARY
TO AVERAGE THE RETURN FOR AS LONG AN INTERVAL AS POSSIBLE 4!##!2 IS USED TO DESCRIBE
THE CENTERING OF THE RETURNED CLUTTER SPECTRUM TO THE ZERO FILTER FREQUENCY 3INCE THE
TECHNIQUE COMPENSATES FOR DRIFT IN THE VARIOUS SYSTEM ELEMENTS AND BIASES IN THE MEAN
DOPPLER FREQUENCY DUE TO OCEAN CURRENTS CHAFF OR WEATHER CLUTTER IT IS USED IN SHIP
BOARD AND LAND BASED RADARS AS WELL AS AIRBORNE RADAR
! FUNCTIONAL BLOCK DIAGRAM OF AN AIRBORNE RADAR EMPLOYING 4!##!2 IS SHOWN IN
&IGURE 4HE CLUTTER ERROR SIGNAL IS OBTAINED BY MEASURING THE PULSE TO PULSE PHASE
SHIFT VD4P OF THE CLUTTER RETURN 4HIS PROVIDES A VERY SENSITIVE ERROR SIGNAL 4HE AVER
AGED ERROR SIGNAL CONTROLS A VOLTAGE CONTROLLED COHERENT MASTER OSCILLATOR #/-/
WHICH DETERMINES THE TRANSMITTED FREQUENCY OF THE RADAR 4HE #/-/ IS SLAVED TO
&)'52% #LUTTER 0OWER 3PECTRAL $ENSITY 03$ RESPONSE THROUGH ANTENNA PATTERN A WITHOUT
4!##!2 FREQUENCY OFFSET AND B WITH 4!##!2 FREQUENCY OFFSET
!)2"/2.% -4)
&)'52% 롂
"LOCK DIAGRAM OF A RADAR ILLUSTRATING THE SIGNAL FLOW PATH OF THE 4!##!2 CONTROL LOOP
THE SYSTEM REFERENCE OSCILLATOR FREQUENCY VIA THE AUTOMATIC FREQUENCY CONTROL !&#
LOOP SHOWN IN &IGURE 4HIS PROVIDES A STABLE REFERENCE IN THE ABSENCE OF CLUTTER
!N INPUT FROM THE AIRCRAFT INERTIAL NAVIGATION SYSTEM AND THE ANTENNA SERVO PROVIDE A
PREDICTED DOPPLER OFFSET 4HESE INPUTS ALLOW THE 4!##!2 SYSTEM TO PROVIDE A NARROW
BANDWIDTH CORRECTION SIGNAL
"ECAUSE OF THE NOISY NATURE OF THE CLUTTER SIGNAL THE NEED TO HAVE THE CONTROL SYSTEM
BRIDGE REGIONS OF WEAK CLUTTER RETURN AND THE REQUIREMENT NOT TO RESPOND TO THE DOP
PLER SHIFT OF A TRUE TARGET THE CONTROL SYSTEM USUALLY TRACKS THE AZIMUTH VARIATION OF
A SPECIFIC RADAR RANGE INTERVAL 4HE MAXIMUM RANGE OF THIS INTERVAL IS CHOSEN SO THAT
CLUTTER WILL BE THE DOMINANT SIGNAL WITHIN THE INTERVAL 4HE MINIMUM RANGE IS CHOSEN
TO EXCLUDE SIGNALS WHOSE AVERAGE FREQUENCY DIFFERS SUBSTANTIALLY FROM THE FREQUENCY
IN THE REGION OF INTEREST
!LTERNATE APPROACHES TO PROVIDING THIS FREQUENCY OFFSET CAN BE IMPLEMENTED WITH
DIGITAL EXCITERS OR ON RECEIVE &OR SOME APPLICATIONS IT MAY BE NECESSARY TO USE MULTIPLE
CONTROL LOOPS EACH ONE COVERING A SPECIFIC RANGE INTERVAL OR TO VARY THE OFFSET FRE
QUENCY IN RANGE 4HIS IS POSSIBLE IF THE FREQUENCY OFFSET IS IMPLEMENTED ON RECEIVE BUT
NOT ON TRANSMIT !T ANY PARTICULAR RANGE THE FILTER NOTCH IS EFFECTIVELY AT ONE FREQUENCY
AND THE CENTER FREQUENCY OF THE CLUTTER SPECTRUM AT ANOTHER 4HE DIFFERENCE BETWEEN
THESE FREQUENCIES RESULTS IN A DOPPLER OFFSET ERROR AS SHOWN IN &IGURE 4HE CLUTTER
SPECTRUM WILL EXTEND INTO MORE OF THE FILTER PASSBAND AND THE CLUTTER IMPROVEMENT
FACTOR WILL BE DEGRADED 4HE REQUIRED ACCURACY FOR THE 4!##!2 CONTROL LOOP CAN BE
RELAXED IF THE -4) FILTER IS AN ADAPTIVE FILTER SUCH AS WITH SPACE TIME ADAPTIVE PROCESS
ING DISCUSSED LATER IN THIS CHAPTER 4HIS IS BECAUSE THE ADAPTIVE FILTER WILL ADJUST TO THE
RECEIVED SIGNALS AND OPTIMIZE CLUTTER CANCELLATION
7ITHOUT ADAPTIVE ADJUSTMENT &IGURE SHOWS THE IMPROVEMENT FACTOR FOR SINGLE
AND DOUBLE DELAY CANCELERS AS A FUNCTION OF THE RATIO OF THE NOTCH OFFSET ERROR TO THE
PULSE REPETITION FREQUENCY 02& FOR DIFFERENT CLUTTER SPECTRAL WIDTHS &ORTUNATELY THE
PLATFORM MOTION SPECTRUM IS NARROW IN THE FORWARD SECTOR OF COVERAGE WHERE OFFSET
ERROR IS MAXIMUM !N OFFSET ERROR OF ONE HUNDREDTH OF THE 02& WOULD YIELD A D"
IMPROVEMENT FACTOR FOR A DOUBLE CANCELER WITH AN INPUT CLUTTER SPECTRUM WHOSE WIDTH
ΰn
2!$!2 (!.$"//+
&)'52% %FFECT OF DOPPLER OFFSET ERROR FR 02&
WAS OF THE 02& )F THE RADAR FREQUENCY WERE '(Z 02& K(Z AND GROUND SPEED
KT THE NOTCH WOULD HAVE TO BE HELD WITHIN KT OR 6G
"ECAUSE OF THESE REQUIREMENTS AND THE WIDTH OF THE PLATFORM MOTION SPECTRUM STAG
GER 02& SYSTEMS MUST BE CHOSEN PRIMARILY ON THE BASIS OF MAINTAINING THE STOPBAND
RATHER THAN FLATTENING THE PASSBAND 3IMILARLY HIGHER ORDER DELAY LINE FILTERS WITH OR
WITHOUT FEEDBACK ARE SYNTHESIZED ON THE BASIS OF STOPBAND REJECTION 4HE LIMITING CASE
IS THE NARROWBAND FILTER BANK WHERE EACH INDIVIDUAL FILTER CONSISTS OF A SMALL PASSBAND
THE BALANCE BEING STOPBAND
)MPROVEMENT FACTOR IS AN IMPORTANT METRIC BUT IN ADDITION TO THIS AVERAGE METRIC
DEFINED ACROSS ALL DOPPLER FREQUENCIES IT IS OFTEN IMPORTANT TO CHARACTERIZE THE PERFOR
MANCE AS A FUNCTION OF DOPPLER FREQUENCY PARTICULARLY WITH COHERENT DOPPLER FILTERING
IMBEDDED IN THE PROCESSING CHAIN 7ITH PERFORMANCE CHARACTERIZED VERSUS DOPPLER
&)'52% )MPROVEMENT FACTOR ) VERSUS NORMALIZED DOPPLER OFFSET R¼
E AS A FUNCTION OF CLUTTER
SPECTRUM WIDTH R C
ΰ™
!)2"/2.% -4)
FREQUENCY THE RADAR DESIGN CAN THEN BE EVALUATED THROUGH THE COMPLETE DETECTION CHAIN
AND OPTIMIZED IN CONJUNCTION WITH ANY MULTIPLE 02& STAGGER WAVEFORMS UTILIZED TO
BRIDGE -4) BLIND REGIONS
0LATFORM -OTION %FFECT 4O AN AIRBORNE RADAR A CLUTTER SCATTERER APPEARS TO HAVE A
RADIAL VELOCITY THAT DIFFERS FROM THE ANTENNA BORESIGHT RADIAL VELOCITY AT THE SAME RANGE BY
6E 6R
6"
6G COS A 6G COS A
6G ;COS A 6X SIN Q
COSA Q =
6Y SIN Q
FOR SMALL VALUES OF P AND DEPRESSION ANGLE E WHERE 6X IS THE HORIZONTAL COMPONENT
OF VELOCITY PERPENDICULAR TO THE ANTENNA BORESIGHT AND 6Y IS THE COMPONENT ALONG THE
ANTENNA BORESIGHT P IS THE AZIMUTHAL ANGLE FROM THE ANTENNA BORESIGHT OR THE INTERSEC
TION OF THE VERTICAL PLANE CONTAINING THE BORESIGHT WITH THE GROUND 4HE CORRESPONDING
DOPPLER FREQUENCY WHEN @ IS A FEW BEAMWIDTHS FROM GROUND TRACK IS
FD 6X
6
SIN Q y X Q
L
L
4HIS PHENOMENON RESULTS IN A PLATFORM MOTION CLUTTER POWER SPECTRUM THAT IS WEIGHTED
BY THE ANTENNAS TWO WAY POWER PATTERN IN AZIMUTH 4HE TRUE SPECTRUM MAY BE APPROX
IMATED BY A GAUSSIAN SPECTRUM
( F E
¤ FD
³
¥¦ S PM´µ
E
¤6 Q
³
¥ X LS ´
¦
PMµ
y ' Q
'P THE TWO WAY POWER PATTERN OF THE ANTENNA IS WHEN P PA WHERE PA IS
THE HALF POWER BEAMWIDTH WHICH CAN BE APPROXIMATED BY KA A BEING THE EFFECTIVE
HORIZONTAL APERTURE WIDTH 4HUS
E
¤6X
³
¦¥ A S PMµ´
OR
S PM 6X
A
WHERE 6X AND A ARE IN CONSISTENT UNITS 4HIS VALUE IS LOWER THAN ONES DERIVED BY OTHER
AUTHORS (OWEVER IT AGREES WITH MORE EXACT ANALYSIS OF ANTENNA RADIATION PATTERNS
AND EXPERIMENTAL DATA ANALYZED BY & 3TAUDAHER
! MORE EXACT VALUE OF THE PARAMETER RPM MAY BE OBTAINED BY MATCHING A TWO WAY
POWER PATTERN OF INTEREST WITH THE GAUSSIAN APPROXIMATION AT A SPECIFIC POINT ON THE PAT
TERN DETERMINING THE STANDARD DEVIATION OF P BY USING STATISTICAL TECHNIQUES OR FITTING
ΰ£ä
2!$!2 (!.$"//+
&)'52% %FFECT OF PLATFORM MOTION ON THE -4) IMPROVEMENT FACTOR
AS A FUNCTION OF THE FRACTION OF THE HORIZONTAL ANTENNA APERTURE DISPLACED PER
INTERPULSE PERIOD 6X4PA
THE PATTERN AND USING NUMERICAL METHODS 4HE CALCULATION OF THE IMPROVEMENT FACTOR
CAN BE PERFORMED BY AVERAGING THE RESULTANT RESIDUE POWER OBTAINED BY SUMMING THE
SIGNAL PHASORS AT SPECIFIC VALUES OF P FROM NULL TO NULL OF THE ANTENNA PATTERN
&IGURE SHOWS THE EFFECT OF PLATFORM MOTION ON THE -4) IMPROVEMENT FACTOR AS
A FUNCTION OF THE APERTURE DISPLACED IN THE PLANE OF THE APERTURE PER INTERPULSE PERIOD 4P
! DISPLACEMENT REDUCES THE DOUBLE DELAY IMPROVEMENT FACTOR TO D" 4HIS COR
RESPONDS TO A SPEED OF KT IF THE SYSTEM HAS A 02& OF (Z AND A FT ANTENNA
APERTURE &OR A SINGLE DELAY SYSTEM THE DISPLACEMENT HAS TO BE HELD TO FOR A
D" PERFORMANCE LIMIT
ΰxÊ */",‡"/" ÊÊ
"* -/" Ê 4HE DELETERIOUS EFFECTS OF PLATFORM MOTION CAN BE REDUCED BY PHYSICALLY OR ELECTRONI
CALLY DISPLACING THE ANTENNA PHASE CENTER ALONG THE PLANE OF THE APERTURE 4HIS IS REFERRED
TO AS THE DISPLACED PHASE CENTER ANTENNA $0#! TECHNIQUEn )N ADDITION SOME FORMS
OF SPACE TIME ADAPTIVE PROCESSING ARE EXPRESSLY DEVELOPED TO IMPROVE CLUTTER CANCELLA
TION WITH AN ADAPTIVE FILTER ELECTRONICALLY DISPLACING THE ANTENNA PHASE CENTER
%LECTRONICALLY $ISPLACED 0HASE #ENTER !NTENNA &IGURE A SHOWS THE
PULSE TO PULSE PHASE ADVANCE OF AN ELEMENTAL SCATTERER AS SEEN BY THE RADAR RECEIVER
!)2"/2.% -4)
&)'52% MOTION
ΰ££
0HASOR DIAGRAM SHOWING THE RETURN FROM A POINT SCATTERER DUE TO PLATFORM
4HE AMPLITUDE % OF THE RECEIVED SIGNAL IS PROPORTIONAL TO THE TWO WAY ANTENNA FIELD
INTENSITY 4HE PHASE ADVANCE IS
H P FD4P P 6X4P SIN Q
L
WHERE FD DOPPLER SHIFT OF SCATTERER %Q 4P INTERPULSE PERIOD
&IGURE B SHOWS A METHOD OF CORRECTING FOR THE PHASE ADVANCE G !N IDEALIZED
CORRECTION SIGNAL %C IS APPLIED LEADING THE RECEIVED SIGNAL BY n AND LAGGING THE NEXT
RECEIVED SIGNAL BY n &OR EXACT COMPENSATION THE FOLLOWING RELATION WOULD HOLD
%C % TAN H £ Q TAN
P 6X4P SIN Q
L
4HIS ASSUMES A TWO LOBE ANTENNA PATTERN SIMILAR TO THAT IN A MONOPULSE TRACKING
RADAR 4WO RECEIVERS ARE USED ONE SUPPLYING A SUM SIGNAL 3P AND THE OTHER A
DIFFERENCE SIGNAL $P 4HE DIFFERENCE SIGNAL IS USED TO COMPENSATE FOR THE EFFECTS
OF PLATFORM MOTION
)F THE SYSTEM IS DESIGNED TO TRANSMIT THE SUM PATTERN 3P AND RECEIVE BOTH 3P AND
A DIFFERENCE PATTERN $P THEN AT THE DESIGN SPEED THE RECEIVED SIGNAL 3P $P CAN BE
APPLIED AS THE CORRECTION SIGNAL 4HE ACTUAL CORRECTION SIGNAL USED TO APPROXIMATE %C IS
K 3P $P WHERE K IS THE RATIO OF THE AMPLIFICATION IN THE SUM AND DIFFERENCE CHANNELS
OF THE RECEIVER
! UNIFORMLY ILLUMINATED MONOPULSE ARRAY HAS THE DIFFERENCE SIGNAL $ IN QUADRA
TURE WITH THE SUM AND HAS THE AMPLITUDE RELATIONSHIP
¤ P7
³
$Q £Q TAN ¥
SIN Q´
¦ L
µ
WHERE 7 IS THE DISTANCE BETWEEN THE PHASE CENTERS OF THE TWO HALVES OF THE ANTENNA
(ENCE A CHOICE OF 7 6X4P AND K WOULD IDEALLY RESULT IN PERFECT CANCELLATION
)N PRACTICE A SUM PATTERN IS CHOSEN BASED ON THE DESIRED BEAMWIDTH GAIN AND
SIDELOBES FOR THE DETECTION SYSTEM REQUIREMENTS 4HEN THE DIFFERENCE PATTERN $P IS
SYNTHESIZED INDEPENDENTLY BASED ON THE RELATIONSHIP REQUIRED AT DESIGN RADAR PLATFORM
ΰ£Ó
2!$!2 (!.$"//+
SPEED AND ALLOWABLE SIDELOBES 4HE TWO PATTERNS MAY BE REALIZED BY COMBINING THE
ELEMENTS IN SEPARATE CORPORATE FEED STRUCTURES
&IGURE SHOWS THE IDEALIZED IMPROVEMENT FACTOR AS A FUNCTION OF NORMALIZED
APERTURE MOVEMENT FOR A DOUBLE DELAY CANCELER 4HE IMPROVEMENT FACTOR SHOWN IS
THE IMPROVEMENT FACTOR FOR A POINT SCATTERER AVERAGED OVER THE NULL TO NULL ANTENNA
BEAMWIDTH )N ONE CASE THE GAIN RATIO K IS OPTIMIZED AT EACH VALUE OF PULSE TO PULSE
DISPLACEMENT )N THE OTHER COMPENSATED CASE THE OPTIMUM GAIN RATIO K IS APPROXIMATED
BY THE LINEAR FUNCTION OF INTERPULSE PLATFORM MOTION K6X
! BLOCK DIAGRAM OF THE DOUBLE DELAY SYSTEM IS SHOWN IN &IGURE ! SINGLE DELAY
SYSTEM WOULD NOT HAVE THE SECOND DELAY LINE AND SUBTRACTOR 4HE NORMALLY REQUIRED
CIRCUITRY FOR MAINTAINING COHERENCE GAIN AND PHASE BALANCE AND TIMING IS NOT SHOWN
4HE SPEED CONTROL 6X IS BIPOLAR AND MUST BE CAPABLE OF REVERSING THE SIGN OF THE $P
SIGNAL IN EACH CHANNEL WHEN THE ANTENNA POINTING ANGLE CHANGES FROM THE PORT TO THE
STARBOARD SIDE OF THE AIRCRAFT
&)'52% -4) IMPROVEMENT FACTOR FOR $0#! COMPENSATION AS A
FUNCTION OF THE FRACTION OF THE HORIZONTAL PHASE CENTER SEPARATION 7 THAT
THE HORIZONTAL ANTENNA APERTURE IS DISPLACED PER INTERPULSE PERIOD 6X4P7
7 A WHERE A IS THE HORIZONTAL APERTURE LENGTH
ΰ£Î
!)2"/2.% -4)
&)'52% 3IMPLIFIED DOUBLE DELAY $0#! MECHANIZATION
4HE HYBRID AMPLIFIER SHOWN HAS TWO INPUT TERMINALS THAT RECEIVE 3P AND J$P
AND AMPLIFY THE $P CHANNEL BY K6X RELATIVE TO THE 3P CHANNEL 4HE OUTPUT TER
MINALS PRODUCE THE SUM AND DIFFERENCE OF THE TWO AMPLIFIED INPUT SIGNALS "ECAUSE
$0#! COMPENSATES FOR THE COMPLEX SIGNAL BOTH AMPLITUDE AND PHASE INFORMATION
MUST BE RETAINED 4HEREFORE THESE OPERATIONS USUALLY OCCUR AT 2& OR )& $IGITAL
COMPENSATION CAN BE USED IF SYNCHRONOUS DETECTION AND ANALOG TO DIGITAL !$
CONVERSION ARE PERFORMED AND THE COMPONENTS ARE TREATED AS COMPLEX PHASORS
&URTHERMORE THE OPERATIONS MUST BE LINEAR UNTIL THE SUM SIGNAL AND DIFFERENCE SIG
NALS HAVE BEEN PROCESSED BY THE HYBRID AMPLIFIER !FTER THIS SINGLE PULSE COMBINA
TION THE ACTUAL DOUBLE CANCELLATION CAN BE PERFORMED BY ANY CONVENTIONAL -4)
PROCESSING TECHNIQUES
0OWER IN THE !NTENNA 3IDELOBES !IRBORNE SYSTEMS ARE LIMITED IN THEIR ABILITY
TO REJECT CLUTTER DUE TO THE POWER RETURNED BY THE ANTENNA SIDELOBES 4HE FULL n
AZIMUTHAL PATTERN SEES VELOCITIES FROM 6G TO 6G 4HE COMPENSATION CIRCUITS OFFSET
THE VELOCITY BY AN AMOUNT CORRESPONDING TO THE ANTENNA BORESIGHT VELOCITY 6" BUT THE
TOTAL RANGE OF DOPPLER FREQUENCIES CORRESPONDING TO 6G IS OBTAINED BECAUSE OF ECHOES
RECEIVED VIA THE SIDELOBES &OR AIRBORNE SYSTEMS WITH LOW 02&S THESE DOPPLER FRE
QUENCIES CAN COVER SEVERAL MULTIPLES OF THE 02& SO THAT THE SIDELOBE POWER IS FOLDED
INTO THE FILTER 4HIS LIMITATION IS A FUNCTION OF THE ANTENNA POINTING ANGLE THE -4) FILTER
RESPONSE AND THE SIDELOBE PATTERN )F THE SIDELOBES ARE RELATIVELY WELL DISTRIBUTED IN
AZIMUTH A MEASURE OF PERFORMANCE CAN BE OBTAINED BY AVERAGING THE POWER RETURNED
BY THE SIDELOBES
4HE LIMITING IMPROVEMENT FACTOR DUE TO SIDELOBES IS
P
)SL LIMIT + ¯ ' Q DQ
P
¯SL ' Q DQ
WHERE THE LOWER INTEGRAL IS TAKEN OUTSIDE THE MAIN BEAM REGION -AIN BEAM EFFECTS
WOULD BE INCLUDED IN THE PLATFORM MOTION IMPROVEMENT FACTOR 4HE CONSTANT + IS THE
NOISE NORMALIZATION FACTOR FOR THE -4) FILTER + FOR SINGLE DELAY AND FOR DOUBLE
DELAY 'P IS THE TWO WAY POWER OF THE ANTENNA IN THE PLANE OF THE GROUND SURFACE
4HE $0#! PERFORMANCE DESCRIBED IN THE PRECEDING SUBSECTION CAN BE ANALYZED ON
THE BASIS OF RADIATION PATTERNS OR THE EQUIVALENT APERTURE DISTRIBUTION FUNCTION )F THE
RADIATION PATTERN IS USED THE COMPOSITE PERFORMANCE MAY BE OBTAINED EITHER BY APPLY
ING THE PATTERN FUNCTIONS OVER THE ENTIRE n PATTERN OR BY COMBINING THE IMPROVEMENT
롣{
2!$!2 (!.$"//+
FACTORS FOR THE $0#! MAIN BEAM AND THE SIDELOBE REGIONS IN THE SAME MANNER AS PARAL
LEL IMPEDANCES ARE COMBINED
) TOTAL ) SL
) $0#!
)F THE APERTURE DISTRIBUTION IS USED THE SIDELOBE EFFECTS ARE INHERENT IN THE ANALYSIS
#ARE MUST BE TAKEN HOWEVERˆIF THE ARRAY OR REFLECTOR FUNCTION IS USED WITHOUT CON
SIDERING THE WEIGHTING OF THE ELEMENTAL PATTERN OR THE FEED DISTRIBUTION THE INHERENT
SIDELOBE PATTERN CAN OBSCURE THE MAIN BEAM COMPENSATION RESULTS
!GAIN THE PERFORMANCE VERSUS DOPPLER FREQUENCY IS IMPORTANT FOR EVALUATING
OVERALL RADAR DETECTION PERFORMANCE !NTENNA SIDELOBE LIMITED PERFORMANCE CAN BE
APPROXIMATED BY PERFORMING THE LOWER INTEGRAL OF %Q OVER THOSE ANGLES THAT MAP
INTO A GIVEN DOPPLER FILTERS PASSBAND 4HE NOISE NORMALIZATION TERM K MUST ALSO BE
MODIFIED TO REFLECT THE CASCADED NOISE GAIN OF THE -4) AND DOPPLER FILTER BANK AS
.
. G K £ 7I I . £ 7I 7I COS P K .
I . £ 7I 7I COS P K . K.
I FOR THREE PULSE -4) AND CASCADED . PULSE DOPPLER FILTER BANK WHERE 7I ARE THE DOP
PLER FILTER WEIGHTS OR
.
. G K £ 7I I . £ 7I 7I COSP K . K.
I FOR TWO PULSE -4) AND CASCADED . PULSE DOPPLER FILTER BANK
ΰÈÊ - ‡"/" Ê "*
-/"
&IGURE A SHOWS A TYPICAL ANTENNA MAIN BEAM RADIATION PATTERN AND THE RESPONSE OF
A POINT SCATTERER FOR TWO SUCCESSIVE PULSES WHEN THE ANTENNA IS SCANNING )T IS SEEN THAT
THE SIGNALS RETURNED WOULD DIFFER BY $'P 4HIS RESULTS IN IMPERFECT CANCELLATION DUE
TO SCANNING 4HE AVERAGE EFFECT ON THE IMPROVEMENT FACTOR CAN BE OBTAINED BY INTEGRAT
ING THIS DIFFERENTIAL EFFECT $'P OVER THE MAIN BEAMS
)SCAN ¯
Q
Q
\ ' Q \ DQ
Q
¯ Q \ 'Q 4PQ
' Q \ DQ
FOR SINGLE DELAY CANCELLATION
A
)SCAN ¯
Q
¯ Q \ 'Q 4PQ
Q
Q
\ ' Q \ DQ
' Q
' Q 4PQ \ DQ
FOR DOUBLE DELAY CANCELLATIONN
B
WHERE P NULL OF MAIN BEAM
'P TWO WAY VOLTAGE PATTERN
롣x
!)2"/2.% -4)
&)'52% !NTENNA SCANNING EFFECTS A AS SEEN BY THE ANTENNA RADIATION PATTERN DUE TO THE APPARENT
Q Q 4P B AS SEEN BY THE APERTURE ILLUMINATION FUNCTION DUE
CHANGE IN AZIMUTH OF THE SCATTERER Q TO THE APPARENT MOTION V XQ OF THE SCATTERER RELATIVE TO THE ANTENNA AT POSITION X AND C STEP SCAN
COMPENSATION OF TWO RECEIVED PHASORS
)N ORDER TO TREAT SCANNING MOTION IN THE FREQUENCY DOMAIN THE APPARENT CLUTTER
VELOCITY SEEN BY THE SCANNING ANTENNA IS EXAMINED TO DETERMINE THE DOPPLER FREQUENCY
%ACH ELEMENT OF AN ARRAY OR INCREMENTAL SECTION OF A CONTINUOUS APERTURE CAN BE CON
SIDERED AS RECEIVING A DOPPLER SHIFTED SIGNAL DUE TO THE RELATIVE MOTION OF THE CLUTTER
4HE POWER RECEIVED BY THE ELEMENT IS PROPORTIONAL TO THE TWO WAY APERTURE POWER
DISTRIBUTION FUNCTION &X AT THE ELEMENT
)N ADDITION TO THE VELOCITY SEEN BY ALL ELEMENTS BECAUSE OF THE MOTION OF THE PLAT
FORM EACH ELEMENT SEES AN APPARENT CLUTTER VELOCITY DUE TO ITS ROTATIONAL MOTION AS
ILLUSTRATED IN &IGURE B 4HE APPARENT VELOCITY VARIES LINEARLY ALONG THE APERTURE
(ENCE THE TWO WAY APERTURE DISTRIBUTION IS MAPPED INTO THE FREQUENCY DOMAIN 4HE
RESULTING POWER SPECTRUM DUE TO THE ANTENNA SCANNING IS
¤L F³
( F & ¥ ´
¦ Q µ
a F a
AQ
L
WHERE Q ANTENNA ROTATION RATE
A HORIZONTAL ANTENNA APERTURE
4HIS SPECTRUM CAN BE APPROXIMATED BY A GAUSSIAN DISTRIBUTION WITH STANDARD DEVIATION
F
AQ
Q
S C R y N
QA
L
WHERE K AND A ARE IN THE SAME UNITS PA IS THE ONE WAY HALF POWER BEAMWIDTH AND N
IS THE NUMBER OF HITS PER BEAMWIDTH 4HE APPROXIMATION PA y KA IS REPRESENTATIVE OF
AN ANTENNA DISTRIBUTION YIELDING ACCEPTABLE SIDELOBE LEVELS
)T CAN BE SEEN THAT THE ANTENNA PATTERN PULSE TO PULSE DIFFERENTIAL GAIN IS
$' Q D' Q
D' Q $Q Q 4P
DQ
DQ
ΰ£È
2!$!2 (!.$"//+
4HIS SUGGESTS THAT A CORRECTION SIGNAL IN THE REVERSE SENSE TO $'P BE APPLIED
AS SHOWN IN &IGURE C (ALF THE CORRECTION IS ADDED TO ONE PULSE AND HALF SUBTRACTED
FROM THE OTHER SO THAT
#ORRECTION SIGNAL Q4P D £ Q
$' Q
DQ
D £Q
Q4P £Q
DQ
WHERE 3P WAS SUBSTITUTED FOR 'P 4HE RADAR TRANSMITS A SUM PATTERN 3P AND
RECEIVES ON THE DIFFERENCE PATTERN $P SO THAT THE RECEIVED SIGNAL IS PROPORTIONAL TO
THE PRODUCT OF THE TWO )F THE SIGNAL RECEIVED ON THE DIFFERENCE PATTERN IS USED AS THE
CORRECTION WE HAVE
%C $P 3P
"Y COMPARING %QS AND WE SEE THAT FOR %C TO APPROXIMATE THE CORRECTION
SIGNAL THE DIFFERENCE PATTERNS SHOULD BE
D £Q
$Q Q4P
DQ
4HE DERIVATIVE OF THE SUM PATTERN IS SIMILAR TO A DIFFERENCE PATTERN IN THAT IT IS POSITIVE
AT THE MAIN BEAM NULL P DECREASES TO ZERO ON THE ANTENNA CENTERLINE AND THEN GOES
NEGATIVE UNTIL P
2EFERRING TO &IGURE ONE OBSERVES THAT THE MECHANIZATION FOR SCAN COMPENSA
TION IS FUNDAMENTALLY SIMILAR TO THE $0#! MECHANIZATION EXCEPT THAT THE DIFFERENCE
SIGNAL IS APPLIED IN PHASE WITH THE SUM SIGNAL AND AMPLIFIED BY AN AMOUNT DETERMINED
BY THE ANTENNA ROTATION PER INTERPULSE PERIOD
4HE SIGNALS REQUIRED IF THE TRANSMISSION SIGNAL 3P THAT APPEARS IN EACH CHANNEL
IS NEGLECTED ARE 3Q o LQ4P $Q WHERE L IS THE RATIO OF THE AMPLIFICATION IN THE TWO
CHANNELS CHOSEN TO MAXIMIZE THE CLUTTER REJECTION 4HE REQUIRED DIFFERENCE PATTERN
SLOPE IS DETERMINED BY THE DERIVATIVE OF THE SCAN PATTERN WHICH DIFFERS FROM THE $0#!
CRITERION 4HIS TECHNIQUE IS KNOWN AS STEP SCAN COMPENSATION BECAUSE THE SYSTEM ELEC
TRONICALLY POINTS THE ANTENNA SLIGHTLY AHEAD OF AND BEHIND OF BORESIGHT EACH PULSE SO
THAT A LEADING AND LAGGING PAIR ARE TAKEN FROM SUCCESSIVE RETURNS TO OBTAIN THE EFFECT OF
THE ANTENNA REMAINING STATIONARY
&IGURE SHOWS THE IMPROVEMENT OBTAINED BY $ICKEY AND 3ANTA FOR SINGLE
DELAY CANCELLATION
#OMPENSATION 0ATTERN 3ELECTION 3ELECTION OF THE COMPENSATION PATTERN
DEPENDS ON THE LEVEL OF SYSTEM PERFORMANCE REQUIRED THE TYPE OF -4) FILTERING USED THE
PLATFORM VELOCITY SCAN RATE AND THE CHARACTERISTICS REQUIRED BY NORMAL RADAR PARAMETERS
SUCH AS RESOLUTION DISTORTION GAIN SIDELOBES ETC &OR INSTANCE AN EXPONENTIAL PATTERN
AND ITS CORRESPONDING DIFFERENCE PATTERN ARE EXCELLENT FOR SINGLE DELAY CANCELLATION
$0#! BUT ARE UNSATISFACTORY WHEN DOUBLE DELAY CANCELLATION IS USED 4HIS IS BECAUSE
THE SINGLE DELAY CANCELER REQUIRES THE BEST MATCH BETWEEN THE ACTUAL PATTERN AND THE
REQUIRED PATTERN NEAR BORESIGHT WHEREAS DOUBLE CANCELLATION REQUIRES THE BEST MATCH
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&)'52% -4) IMPROVEMENT FACTOR FOR A
STEP SCAN COMPENSATION OF A SINGLE DELAY CANCELER
AS A FUNCTION OF THE NUMBER OF HITS PER BEAMWIDTH
4HE ANTENNA PATTERN IS SIN X X
ON THE BEAM SHOULDER 3TEP SCAN COMPENSATION USUALLY REQUIRES THE DIFFERENCE PATTERN
PEAKS TO BE NEAR THE NULLS OF THE SUM PATTERN TO MATCH
'RISSETTI ET AL HAVE SHOWN THAT FOR STEP SCAN COMPENSATION THE IMPROVEMENT FACTOR
FOR SINGLE DELAY CANCELLATION INCREASES AS A FUNCTION OF THE NUMBER OF HITS AT D"
DECADE FOR THE FIRST DERIVATIVE TYPE STEP SCAN COMPENSATION AT THE RATE OF D"
DECADE AND WITH FIRST AND SECOND DERIVATIVE COMPENSATION AT THE RATE OF D"DECADE
(ENCE FOR A GROUND BASED SYSTEM THAT IS LIMITED BY SCAN RATE ONE SHOULD IMPROVE THE
COMPENSATION PATTERN RATHER THAN USE A HIGHER ORDER -4) CANCELER (OWEVER AIRBORNE
SYSTEMS ARE PRIMARILY LIMITED BY PLATFORM MOTION AND REQUIRE BOTH BETTER CANCELERS AND
COMPENSATION FOR OPERATION IN A LAND CLUTTER ENVIRONMENT )N THE SEA CLUTTER ENVIRON
MENT THE SYSTEM IS USUALLY DOMINATED BY THE SPECTRAL WIDTH OF THE VELOCITY SPECTRUM OR
PLATFORM MOTION RATHER THAN SCANNING 4HE APPLICABILITY OF $0#! OR STEP SCAN COMPEN
SATION IN THE LATTER CASE IS DEPENDENT ON THE PARTICULAR SYSTEM PARAMETERS
4HE COMPENSATION REQUIRED BY $'P CAN BE DETERMINED FROM A 4AYLORS SERIES EXPANSION OF 'P )N THE PRE
CEDING DISCUSSION WE USED THE FIRST DERIVATIVE 5SING HIGHER ORDER TERMS GIVES AN IMPROVED CORRECTION SIGNAL
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AN UNCOMPENSATED DOUBLE CANCELER (OWEVER THE PERFORMANCE OF A $0#! SYSTEM IS
SIGNIFICANTLY REDUCED WHEN IT IS SCANNED 4HIS IS DUE TO THE SCANNING MODULATION ON THE
DIFFERENCE PATTERN USED FOR PLATFORM MOTION COMPENSATION
3INCE THE $0#! APPLIES THE DIFFERENCE PATTERN IN QUADRATURE TO THE SUM PATTERN TO
COMPENSATE FOR PHASE ERROR AND STEP SCAN APPLIES THE DIFFERENCE PATTERN IN PHASE TO COM
PENSATE FOR AMPLITUDE ERROR IT IS POSSIBLE TO COMBINE THE TWO TECHNIQUES BY PROPERLY
SCALING AND APPLYING THE DIFFERENCE PATTERN BOTH IN PHASE AND IN QUADRATURE 4HE SCALING
FACTORS ARE CHOSEN TO MAXIMIZE THE IMPROVEMENT FACTOR UNDER CONDITIONS OF SCANNING
AND PLATFORM MOTION
4HE RELATIONSHIPS FOR A DOUBLE DELAY THREE PULSE !-4) ARE SHOWN IN THE PHASOR
DIAGRAM IN &IGURE 4HE PHASE ADVANCE BETWEEN THE FIRST PAIR OF PULSES FIRST AND
SECOND PULSE FOR THE THREE PULSE -4) RECEIVED BY THE SUM PATTERN 3 IS
H P 4P § ¤
6 SIN Q L ¨¨ X ¥¦
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SIN
W R 4P ³
W 4P
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AND THE PHASE ADVANCE BETWEEN THE SECOND PAIR OF PULSES SECOND AND THIRD PULSE FOR
THE THREE PULSE -4) IS
H P 4P § ¤
6 SIN Q L ¨¨ X ¥¦
©
SIN
W R 4P ³
W 4P
¤
6Y ¥ COS R
´µ
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³¶
COS Q ´ ·
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&)'52% 0HASOR DIAGRAM FOR SIMULTANEOUS SCANNING AND MOTION
COMPENSATION
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WHERE P IS THE DIRECTION OF THE CLUTTER CELL WITH RESPECT TO THE ANTENNA POINTING ANGLE
WHEN THE SECOND PULSE IS RECEIVED AND VR IS THE ANTENNA SCAN RATE 4HE SUBSCRIPTS ON
THE RECEIVED SIGNALS 3I AND $I INDICATE THE PULSE RECEPTION SEQUENCE
4HE DIFFERENCE PATTERN $ IS USED TO GENERATE AN IN PHASE CORRECTION FOR SCAN
NING MOTION AND A QUADRATURE CORRECTION FOR PLATFORM MOTION 4HIS PROCESS YIELDS
THE SET OF RESULTANT SIGNALS 2IJ WHERE THE SUBSCRIPT I DENOTES THE PULSE PAIR AND THE
SUBSCRIPT J DENOTES THE COMPONENT OF THE PAIR "ECAUSE G DOES NOT EQUAL G DIF
FERENT WEIGHTING CONSTANTS ARE REQUIRED FOR EACH PULSE PAIR 4HE VALUES OF K FOR THE
QUADRATURE CORRECTION OF THE FIRST PULSE PAIR K FOR THE QUADRATURE CORRECTION FOR
THE SECOND PULSE PAIR L FOR THE IN PHASE CORRECTION FOR THE FIRST PULSE PAIR AND L
FOR THE SECOND PULSE PAIR ARE OPTIMIZED BY MINIMIZING THE INTEGRATED RESIDUE POWER
OVER THE SIGNIFICANT PORTION OF THE ANTENNA PATTERN USUALLY CHOSEN BETWEEN THE FIRST
NULLS OF THE MAIN BEAM
&IGURE SHOWS THE SUM AND DIFFERENCE MAIN BEAM PATTERNS FOR AN APERTURE
WAVELENGTHS LONG &IGURE SHOWS THE RESIDUE FOR THE CASE WHEN THE FRACTION
OF THE HORIZONTAL APERTURE WIDTH A TRAVELED PER INTERPULSE PERIOD 4P 6N 6X4PA IS
EQUAL TO AND WHEN THE NUMBER OF WAVELENGTHS THAT THE APERTURE TIP ROTATES PER
INTERPULSE PERIOD 7N AVR4PK IS EQUAL TO 4HE CORRESPONDING IMPROVEMENT
FACTOR IS D"
4HE IMPROVEMENT FACTOR IS SHOWN IN &IGURE FOR A RANGE OF NORMALIZED PLATFORM
MOTION 6N AS A FUNCTION OF NORMALIZED SCANNING DISPLACEMENTS 7N 4HE NONSCANNING
CASE IS SHOWN AS 7N 4HE IMPROVEMENT FACTORS WERE COMPUTED FOR THE WAVE
LENGTH APERTURE PATTERNS SHOWN IN &IGURE !NDREWS HAS DEVELOPED AN OPTIMIZATION PROCEDURE FOR PLATFORM MOTION COMPEN
SATION THAT ROTATES THE PHASORS DIRECTLY RATHER THAN BY USING A QUADRATURE CORRECTION 4HE
PROCEDURE DETERMINES THE ANTENNA FEED COEFFICIENTS FOR TWO COMPENSATION PATTERNS ONE
OF WHICH #P IS ADDED TO THE SUM PATTERN 3P AND FED TO THE UNDELAYED CANCELER
&)'52% 3UM AND DIFFERENCE PATTERNS USED TO DETERMINE $0#! PERFORMANCE
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AS SHOWN IN &IGURE 4HE PROCEDURE WAS DEVELOPED FOR A SINGLE DELAY CANCELER AND
A NONSCANNING ANTENNA !NDREWS USED THE PROCEDURE TO MINIMIZE THE RESIDUE POWER
OVER THE FULL ANTENNA PATTERN WHICH INCLUDES THE MAIN BEAM AND SIDELOBE REGIONS
&)'52% $0#! IMPROVEMENT FACTOR VERSUS NORMALIZED PLATFORM MOTION 6N AS A FUNCTION OF NORMAL
IZED SCANNING MOTION 7N
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MOTION PARALLEL TO THE ANTENNA APERTURE 4!##!2 REMOVES THE AVERAGE COMPONENT
OF PLATFORM MOTION PERPENDICULAR TO THE APERTURE 4HE FORMER 7HEELER ,ABORATORIES
DEVELOPED THE #OINCIDENT 0HASE #ENTER 4ECHNIQUE #0#4 TO REMOVE THE SPECTRAL
SPREAD DUE TO THE VELOCITY COMPONENT PERPENDICULAR TO THE APERTURE AND DUE TO THE
COMPONENT PARALLEL TO THE APERTURE 2EMOVAL OF THE COMPONENT PARALLEL TO THE APERTURE
USES THE $0#! PATTERN SYNTHESIS TECHNIQUE DESCRIBED IN !NDERSON WHICH CREATES TWO
SIMILARLY SHAPED ILLUMINATION FUNCTIONS WHOSE PHASE CENTERS ARE PHYSICALLY DISPLACED
2EMOVAL OF THE COMPONENT PERPENDICULAR TO THE APERTURE IS ACCOMPLISHED BY A NOVEL
EXTENSION OF THIS CONCEPT
4HE FIRST TERM OF %Q FOR SPECTRAL WIDTH DUE TO PLATFORM MOTION APPROACHES ZERO AS
THE ANTENNA POINTS AHEAD (OWEVER THE SECOND TERM OF %Q DOMINATES AS THE ANTENNA
APPROACHES WITHIN A FEW BEAMWIDTHS OF THE AIRCRAFTS GROUND TRACK )N THIS REGION
FD y
6Y
Q 6YQ SIN y
L
L
WHICH YIELDS A SINGLE SIDED SPECTRUM THAT IS SIGNIFICANTLY NARROWER THAN THE SPECTRUM
ABEAM &OR MODERATE PLATFORM SPEEDS AND LOWER FREQUENCY 5(& RADARS THIS EFFECT
IS NEGLIGIBLE AND COMPENSATION IS NOT REQUIRED
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7HEN IT IS NECESSARY TO COMPENSATE FOR THIS EFFECT THE PHASE CENTER OF THE ANTENNA
MUST BE DISPLACED AHEAD OF THE APERTURE AND BEHIND THE APERTURE FOR ALTERNATE RECEIVE
PULSES SO THAT THE PHASE CENTERS ARE COINCIDENT FOR A MOVING PLATFORM 4HIS TECHNIQUE
CAN BE EXTENDED TO MORE THAN TWO PULSES BY USING THE NECESSARY PHASE CENTER DIS
PLACEMENTS FOR EACH PULSE )N ORDER TO MAINTAIN THE EFFECTIVE 02& THE DISPLACEMENT
MUST COMPENSATE FOR THE TWO WAY TRANSMISSION PATH 4O ACCOMPLISH THIS DISPLACEMENT
NEAR FIELD ANTENNA PRINCIPLES ARE UTILIZED ! DESIRED APERTURE DISTRIBUTION FUNCTION IS
SPECIFIED 4HE NEAR FIELD AMPLITUDE AND PHASE ARE CALCULATED AT A GIVEN DISTANCE FROM
THE ORIGIN )F THIS FIELD IS USED AS THE ACTUAL ILLUMINATION FUNCTION A VIRTUAL APERTURE IS
CREATED WITH THE DESIRED DISTRIBUTION FUNCTION AT THE SAME DISTANCE BEHIND THE PHYSICAL
ANTENNA &IGURE A SHOWS THE PHASE AND AMPLITUDE DISTRIBUTION REQUIRED TO FORM
A UNIFORM VIRTUAL DISTRIBUTION DISPLACED BEHIND THE PHYSICAL APERTURE )T CAN BE SHOWN
THAT IF THE PHASE OF THE ILLUMINATION FUNCTION IS REVERSED E` E THE DESIRED VIRTUAL
DISTRIBUTION FUNCTION IS DISPLACED AHEAD OF THE APERTURE AS SHOWN IN &IGURE B
)N PRACTICE PERFORMANCE IS LIMITED BY THE ABILITY TO PRODUCE THE REQUIRED ILLUMINA
TION FUNCTION !S THE DISPLACEMENT INCREASES A LARGER PHYSICAL APERTURE SIZE IS REQUIRED
TO PRODUCE THE DESIRED VIRTUAL APERTURE SIZE OWING TO BEAM SPREADING 4HIS CAN BE SEEN
IN &IGURE 4HE EFFECTIVENESS OF THE CORRECTION VARIES WITH ELEVATION ANGLE SINCE THE
&)'52% #0#4 CONCEPT SHOWING DISPLACEMENT OF THE PHASE CEN
TER A BEHIND THE PHYSICAL APERTURE AND B AHEAD OF THE PHYSICAL APER
TURE #OURTESY OF (AZELTINE )NC
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&)'52% #0#4 CANCELLATION RATIO IN DECIBELS AS A FUNCTION OF RELATIVE INTERPULSE
MOTION AND BEAM POINTING DIRECTION #OURTESY OF (AZELTINE )NC
ACTUAL DISPLACEMENT ALONG THE LINE OF SLIGHT VARIES WITH ELEVATION ANGLE 4HIS EFFECT IS
MORE PRONOUNCED AT HIGHER AIRCRAFT SPEEDS AND HIGHER RADAR FREQUENCIES ! CHANGE IN
THE MAGNITUDE OF THE CORRECTION FACTOR OR EVEN THE COMPENSATION PATTERN WITH RANGE
HEIGHT AND VELOCITY COULD BE UTILIZED TO RETAIN PERFORMANCE
&IGURE ILLUSTRATES THE THEORETICAL -4) PERFORMANCE OF A #0#4 SYSTEM AS A
FUNCTION OF BEAM POINTING DIRECTION AND INTERPULSE MOTION NORMALIZED TO THE INTERPULSE
MOTION USED TO DESIGN THE COMPENSATION PATTERN #ANCELLATION RATIO IS DEFINED AS THE
RATIO OF INPUT CLUTTER POWER TO OUTPUT CLUTTER RESIDUE POWER 4HE PEAK ON THE — AXIS
IS TYPICAL OF THE OPTIMIZED $0#! PERFORMANCE ILLUSTRATED IN &IGURE ΰ™Ê -* ‡/ Ê */6 ÊÊ
"/" Ê "* -/"
)NTRODUCTION 3EVERAL METHODS HAVE BEEN DESCRIBED TO COMPENSATE FOR ANTENNA
MOTION !LL THESE TECHNIQUES ARE APPLIED IN THE RADAR DESIGN PHASE FOR A SPECIFIC SET OF
OPERATIONAL PARAMETERS #ONTROLS USUALLY AUTOMATIC ARE PROVIDED TO ADJUST WEIGHTS
FOR OPERATIONAL CONDITIONS AROUND THE DESIGN VALUE
4HE DEVELOPMENT OF DIGITAL RADAR TECHNOLOGY AND ECONOMICAL HIGH SPEED PROCESSORS
ALLOWS THE USE OF DYNAMIC SPACE TIME ADAPTIVE ARRAY PROCESSING 34!0 WHEREBY
A SET OF ANTENNA PATTERNS THAT DISPLACE THE PHASE CENTER OF THE ARRAY BOTH ALONG AND
ORTHOGONAL TO THE ARRAY ARE CONTINUALLY SYNTHESIZED TO MAXIMIZE THE SIGNAL TO CLUTTER
RATIO 3PATIAL ADAPTIVE ARRAY PROCESSING COMBINES AN ARRAY OF SIGNALS RECEIVED AT THE
SAME INSTANT OF TIME THAT ARE SAMPLED AT THE DIFFERENT SPATIAL LOCATIONS CORRESPONDING
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TO THE ANTENNA ELEMENTS 4EMPORAL ADAPTIVE ARRAY PROCESSING COMBINES AN ARRAY OF
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THAT ARE SAMPLED AT DIFFERENT INSTANCES OF TIME SUCH AS SEVERAL INTERPULSE PERIODS FOR
AN ADAPTIVE -4) 3PACE TIME ADAPTIVE ARRAY PROCESSING COMBINES A TWO DIMENSIONAL
ARRAY OF SIGNALS SAMPLED AT DIFFERENT INSTANCES OF TIME AND AT DIFFERENT SPATIAL LOCATIONS
34!0 IS A FAIRLY BROAD TOPIC THAT HAS APPLICABILITY BEYOND THIS CHAPTER ON AIRBORNE
-4) RADAR 4HE PRIMARY MOTIVATION FOR 34!0 IS TO IMPROVE CLUTTER CANCELLATION PERFOR
MANCE AND TO BETTER INTEGRATE A RADARS SPATIAL PROCESSING ANTENNA SIDELOBE CONTROL AND
SIDELOBE JAMMING CANCELLATION WITH ITS TEMPORAL CLUTTER CANCELLATION PROCESSING
4HE APPLICABILITY OF 34!0 TO IMPROVING CLUTTER CANCELLATION MUST BE ASSESSED SPE
CIFICALLY IN THE CONTEXT OF THE KEY PERFORMANCE LIMITERS TO AIRBORNE -4) RADAR CLUT
TER CANCELLATION AS DESCRIBED AT THE START OF THIS CHAPTER 34!0 CAN IMPROVE A RADARS
MOTION COMPENSATION PERFORMANCE AND IS MORE ROBUST THAN NONADAPTIVE TECHNIQUES
IN ADDRESSING GENERALLY NON DISPERSIVE ERRORS IN THE RADAR FRONT END 34!0 WILL NOT
DIRECTLY ADDRESS CLUTTER INTERNAL MOTION EFFECTS ANTENNA SCANNING MOTION EFFECTS OR
OTHER HARDWARE STABILITY IMPACTS TO CLUTTER CANCELLATION PERFORMANCE 2ADAR DESIGNERS
NEED TO ASSESS THE KEY LIMITATIONS IN A SPECIFIC APPLICATION BEFORE JUMPING TO THE CON
CLUSION THAT 34!0 WILL IMPROVE PERFORMANCE
34!0S ABILITY TO INTEGRATE CLUTTER CANCELLATION TEMPORAL AND SPATIAL INTERFERENCE
CANCELLATION CAN BE QUITE IMPORTANT TO MANY RADAR SYSTEMS WHETHER THEY TYPICALLY HAVE TO
DEAL WITH INTENTIONAL JAMMING INTERFERENCE OR UNINTENTIONAL OR CASUAL ELECTROMAGNETIC
INTERFERENCE %-) 34!0 GETS AWAY FROM CASCADED SOLUTIONS SUCH AS ANALOG SIDELOBE
CANCELLERS FOLLOWED BY DIGITAL $0#! ANDOR -4) FILTERSˆTHAT DO NOT GENERALLY CREATE AN
OPTIMUM INTERFERENCE CANCELLATION SOLUTION
/PTIMAL !DAPTIVE 7EIGHTS -C'UFFIN 4HE OPTIMAL LINEAR ESTIMATE IS DETER
MINED BY REQUIRING THE ADAPTED ESTIMATION ERROR BE ORTHOGONAL TO THE OBSERVED VEC
TOR R 3TEADY STATE CONDITIONS ARE ASSUMED IN THIS DERIVATION THUS THE CONDITION FOR
ORTHOGONALITY IS
%[R D ] WHERE %[] IS THE EXPECTATION D IS THE ESTIMATION ERROR AND IS THE COMPLEX CONJUGATE
4HE ADAPTIVELY WEIGHTED ESTIMATE IS OBTAINED BY WEIGHTING THE RECEIVED SIGNAL VECTOR
BY THE ESTIMATE OF THE ADAPTIVE WEIGHTS
S} W} g R
7ITH D DEFINED AS THE DESIRED SIGNAL A MAIN BEAM TARGET THE ESTIMATION ERROR IS
OBTAINED FROM THE FOLLOWING EQUATION 4HEN SUBSTITUTING %Q INTO AND SOLV
ING FOR THE ADAPTIVE WEIGHT ESTIMATE YIELDS THE DESIRED CONDITION FOR OPTIMAL ADAPTIVE
WEIGHTING
E S} D W} g R D
%[R D
R g W} ] %[R D ] 2R W}
OR
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WHERE 2R %[R Rg] 4HE DESIRED SIGNAL D CAN BE EXPRESSED IN TERMS OF S THE SIGNAL
VECTOR OF A TARGET LOCATED IN THE MAIN BEAM AND B THE UNADAPTED BEAM WEIGHT VECTOR
D Bg S 4HIS IS THEN SUBSTITUTED INTO %Q W} 2R 2 S B
%QUATION IS EQUIVALENT TO THE MINIMUM MEAN SQUARE ERROR WEIGHT EQUATION
GIVEN BY 7IDROW WHICH HAS BEEN SHOWN TO BE THE OPTIMUM SET THAT MAXIMIZES
THE SIGNAL TO INTERFERENCE RATIO (OWEVER COMPLEX VARIABLES ARE EMPLOYED HERE RATHER
THAN REAL VARIABLES 4HE INTERFERENCE COVARIANCE MATRIX IS FURTHER DESCRIBED IN TERMS OF
THE INDIVIDUAL NOISE JAMMING CLUTTER AND SIGNAL CONTRIBUTIONS
2R . )
+:
23
WHERE . IS RECEIVER NOISE POWER +: IS THE COVARIANCE MATRIX FOR CLUTTER TEMPORALLY COR
RELATED PLUS JAMMING SPATIALLY CORRELATED AND 2S IS THE SIGNAL COVARIANCE MATRIX
4AXONOMY OF 34!0 !RCHITECTURES 7ARD 4HE APPLICATION OF THE ADAPTIVE
WEIGHT EQUATION FROM %Q IN A RADAR SYSTEM PROVIDES NUMEROUS OPTIONS AND COM
PLICATIONS 4HE OPTIONS RANGE FROM A FULLY ADAPTIVE SOLUTION ACROSS ALL AVAILABLE ANTENNA
ELEMENTS AND ALL PULSES IN A COHERENT PROCESSING INTERVAL #0) TO REDUCED DEGREES OF
FREEDOM SOLUTIONS IN ORDER TO BE PRACTICAL 4HE FULLY ADAPTIVE SOLUTION ALSO ENCOUNTERS
PROBLEMS IN THE REAL WORLD WHERE THE INTERFERENCE ENVIRONMENT IS NOT WELL BEHAVED
EG HOMOGENOUS CLUTTER )N ADDITION "RENNANS RULE INDICATES THAT TO ACHIEVE AN
ADAPTIVE SOLUTION WITHIN D" OF THE OPTIMUM ANSWER REQUIRES . . IS THE NUMBER OF
DEGREES OF FREEDOM INDEPENDENT INTERFERENCE SAMPLES CONTRIBUTING TO THE ADAPTIVE
WEIGHT ESTIMATE 7ITH ANTENNA ARRAY SIZES IN TENS TO HUNDREDS OF ELEMENTS AND #0)
LENGTHS OF TENS TO HUNDREDS OF PULSES THE NUMBER OF DEGREES OF FREEDOM CAN QUICKLY
GET QUITE LARGE RESULTING IN NOT ONLY FAIRLY COMPLEX ADAPTIVE WEIGHT PROCESSING BUT
ALSO THE MORE DIFFICULT PROBLEM OF OBTAINING ADEQUATE SAMPLE SUPPORT FROM CLUTTER AND
JAMMING INTERFERENCE FOR A GIVEN ADAPTIVE WEIGHT SOLUTION
!S SUCH IT IS IMPORTANT TO EXPLORE VARIOUS 34!0 ARCHITECTURE OPTIONS IMBEDDED IN A
RADAR DESIGN SOLUTION 4O BEGIN A FULLY ADAPTIVE ARRAY ARCHITECTURE IS SHOWN IN &IGURE 4HIS IS FOR A LINEAR ARRAY ANTENNA WITH A DISTRIBUTED TRANSMITTER AND DIGITAL RECEIVERS CON
NECTED TO EACH ANTENNA ELEMENT 4HE ADAPTIVE WEIGHT SOLUTION IS DEVELOPED BASED ON AT
LEAST ¾ . ¾ - VECTOR SAMPLES R OF LENGTH - ANTENNA ELEMENTS BY . PULSES 4HE
ADAPTIVE WEIGHT SOLUTION IS DEVELOPED AND APPLIED TO THE RECEIVED SIGNALS FROM THE SAME
ANTENNA ELEMENTS AND PULSES OF DATA 4HE ADAPTIVE WEIGHTED RESPONSE IS TYPICALLY PRO
CESSED THROUGH DOPPLER FILTERING COHERENT INTEGRATION PRIOR TO DETECTION PROCESSING
7ARD DESCRIBES THE POSSIBLE 34!0 ARCHITECTURES IN THE CONTEXT OF A GENERALIZED
TRANSFORMATION MATRIX FOLLOWED BY THE ASSOCIATED 34!0 PROCESSING 4HE FOUR CATEGORIES
OF 34!0 ARCHITECTURES ARE ORGANIZED IN &IGURE 4HE TRADES FOR AN APPROPRIATE 34!0
DESIGN SOLUTION MUST BE MADE IN THE CONTEXT OF THE TYPE AND SIZE OF THE ANTENNA APERTURE
UNDER CONSIDERATION THE WAVEFORMS UNDER CONSIDERATIONˆPARTICULARLY THE NUMBER OF
PULSES PER #0)ˆAND MOST IMPORTANTLY THE INTERFERENCE TO BE CANCELLED CLUTTER AND JAM
MING )N GENERAL FOR THE TRANSFORMATION AND DEGREES OF FREEDOM REDUCTION TO BE USEFUL
THE RESULTANT DEGREES OF FREEDOM MUST BE GREATER THAN THE INTERFERENCE RANK
0RE $OPPLER %LEMENTAL !NTENNA 34!0 #ONCEPTUALLY THE SIMPLEST REDUCTION
IN DEGREES OF FREEDOM IS OBTAINED BY REDUCING THE NUMBER OF TEMPORAL DEGREES OF
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FREEDOM IN 34!0 WHILE STILL PROCESSING THE FULL APERTURE SPATIALLY 4HIS IS SIMILAR TO
A CONVENTIONAL -4) OR $0#! ARCHITECTURE CASCADED WITH DOPPLER FILTERING 7E CALL
THIS ARCHITECTURE A PRE DOPPLER ELEMENTAL LEVEL 34!0 ARCHITECTURE &OR A THREE PULSE
VERSION OF THIS ARCHITECTURE THERE ARE - DEGREES OF FREEDOM )N THIS ARCHITECTURE
PLATFORM MOTION COMPENSATION TAKES THE GENERAL FORM OF ADJUSTING THE ANTENNAS PHASE
CENTER OVER THE THREE TEMPORALLY SEPARATED BEAMS
! BASIC BLOCK DIAGRAM OF A RADAR INCORPORATING PRE DOPPLER ELEMENTAL LEVEL SPACE
TIME ADAPTIVE ARRAY PROCESSING IS SHOWN IN &IGURE !N INDIVIDUAL DUPLEXER IS
PLACED BETWEEN EACH TRANSMITTERS CHANNELIZED OUTPUT AND ITS CORRESPONDING ANTENNA
ELEMENT 0ROVISION COULD BE INCLUDED FOR ELECTRONIC BEAM STEERING USING HIGH POWER
PHASE SHIFTERS OR TRANSMIT MODULES WITH LOW POWER BEAM STEERING
/N RECEIVE EACH DUPLEXER OUTPUT IS SENT TO ITS OWN DIGITAL RECEIVER 4HE DIGITAL
RECEIVER OUTPUTS ARE PASSED THROUGH 02) DELAYS TO YIELD TEMPORALLY DISPLACED DATA
SAMPLES ! FULL COMPLEMENT OF ELEMENTS AND TIME DELAYED SIGNALS ARE SAMPLED AND
USED TO GENERATE THE ADAPTIVE WEIGHTS 6ARIOUS ALGORITHMS ARE POSSIBLE TO GENERATE THE
ESTIMATE OF THE ADAPTIVE WEIGHTS FROM %Q 4HE FAIRLY SIMPLE ,EAST -EAN 3QUARED
ALGORITHM GENERALLY YIELDS FAIRLY SLOW CONVERGENCE RATES /THER ALGORITHMS CAN
SPEED UP THE ADAPTATION RATE BUT A MORE COMPLEX MECHANIZATION IS REQUIRED %XAMPLES
INCLUDE A 2ECURSIVE ,EAST 3QUARED ALGORITHM 1 2 DECOMPOSITION WITH 'RAM 3CHMIDT
ORTHOGONALIZATION OR A (OUSEHOLDER 4RANSFORMATION 4HE ADAPTIVE WEIGHTS ARE THEN
APPLIED TO THE RECEIVED SIGNALS AND BEAMFORMED TO GENERATE THREE SUM CHANNEL DETEC
TION BEAMS UNDELAYED ONE 02) DELAYED AND TWO 02) DELAYED BEAMS 4HESE BEAMS
ARE IN TURN ADDED TOGETHER TO FORM THE FINAL 34!0 WEIGHTED DETECTION BEAM
! SIMPLISTIC VIEW OF HOW THESE THREE BEAMS PERFORM MOTION COMPENSATION IS ILLUS
TRATED IN &IGURE FOR THE CASE WHERE THE APERTURE IS PARALLEL WITH THE RADARS PLATFORM
VELOCITY VECTOR 4HE FIRST PULSE RETURNS PHASE CENTER IS ADVANCED BY APERTURE WEIGHT
ING THE SECOND PULSE RETURNS PHASE CENTER IS ESSENTIALLY UNCHANGED FROM THE QUIESCENT
WEIGHTS AND THE THIRD PULSE RETURNS PHASE CENTER IS RETARDED BY APERTURE WEIGHTING
'IVEN IDEAL ANTENNA PATTERNS AND AN APERTURE LARGE ENOUGH TO ADJUST THE PHASE CENTERS
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" " " " &)'52% !PERTURE CONTROL FOR PLATFORM MOTION COMPENSATION
FOR THE GIVEN PLATFORM MOTION THESE THREE APERTURES APPEAR AS IF THEY ARE STATIONARY
WITH RESPECT TO EACH OTHER #LUTTER CANCELLATION ACROSS THESE THREE PULSES IS NO LONGER
LIMITED BY PLATFORM MOTION EFFECTSˆTHE PRIMARY GOAL OF PLATFORM MOTION COMPENSATION
TECHNIQUES
/F COURSE THIS SIMPLEST CONDITION IS ONLY ILLUSTRATIVE AS GENERALLY THE ANTENNA ELE
MENTS DO NOT BEHAVE EXACTLY THE SAME AND THE PLATFORM MOTION COMPENSATION MUST DEAL
WITH MOTION NOT ONLY IN THE PLANE OF THE APERTURE BUT ALSO ORTHOGONAL TO THE APERTURE
0RE $OPPLER "EAM 3PACE 34!0 4HE FIRST TYPE OF TRANSFORMATION TO BE CONSID
ERED IS SPATIALLY ORIENTED RESULTING IN BEAM SPACE 34!0 ARCHITECTURES 4HIS TRANSFOR
MATION IS TYPICALLY REQUIRED FOR MANY LARGE APERTURES 4HE TRANSFORMATIONS CAN RANGE
FROM SIMPLE COLUMN BEAMFORMING TO OVERLAPPED SUBARRAYS TO BEAM SPACE TRANSFOR
MATIONS SUCH AS A "UTLER MATRIX 4HE GENERAL GOAL IS TO REDUCE THE SPATIAL DEGREES OF
FREEDOM WHILE STILL PROVIDING ACCESS TO ARRAY RESPONSES THAT ALLOW FOR ADEQUATE CLUTTER
CANCELLATION AND BEAMS THAT CAN BE USED TO CANCEL DIRECTIONAL INTERFERENCE AS WELL 4HE
RESULTING BEAM RESPONSES MUST SPAN THE CLUTTER AND JAMMING INTERFERENCE SPATIALLY IN
ORDER FOR THIS TYPE OF TRANSFORMATION TO BE EFFECTIVE &OR EXAMPLE IF A RADARS CLUT
TER CANCELLATION PERFORMANCE IS DRIVEN BY MAIN BEAM CLUTTER RESIDUE DUE TO PLATFORM
MOTION EFFECTS THE BEAM RESPONSES MUST SPAN THE RADARS MAIN BEAM AND PROVIDE
DEGREES OF FREEDOM TO ALLOW FOR MOTION COMPENSATION IN THE ARRAY MAIN BEAM )N ADDI
TION TO CANCEL DIRECTION INTERFERENCE JAMMING OR CASUAL %-) THE BEAM RESPONSES
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MUST ALSO SPAN THE SPATIAL DIRECTIONS OF THAT INTERFERENCE !N EXAMPLE OF A SIMPLE
TRANSFORMATION OF THIS TYPE WOULD BE SIDELOBE CANCELER ARCHITECTURE WHERE THE BEAM
TRANSFORMATION WOULD GENERATE A SUM CHANNEL MAIN BEAM AND SELECT ELEMENTS FROM THE
APERTURE AS SIDELOBE CANCELLERS
0OST $OPPLER %LEMENT !NTENNA 34!0 4HE SECOND TYPE OF TRANSFORMATION
LEADS TO WHAT ARE CALLED POST DOPPLER 34!0 ARCHITECTURES !S THE NAME IMPLIES THE
ANTENNA ELEMENT SIGNALS ARE FIRST DOPPLER FILTERED AND THEN PROCESSED THROUGH 34!0
4HE MOTIVATION FOR THIS TYPE OF ARCHITECTURE IS THAT THE RESULTANT 34!0 SOLUTIONS CAN
INDEPENDENTLY ADDRESS A SUBSET OF THE CLUTTER INTERFERENCE PROBLEM ISOLATED TO CLUTTER
THAT REMAINS IN A SINGLE DOPPLER FILTER 4HIS TECHNIQUE MAY BE MORE EFFECTIVE FOR RADAR
SYSTEMS WHERE THE CLUTTER ENVIRONMENT AND WAVEFORM SELECTION LEAD TO UNAMBIGUOUS
CLUTTER RETURNS WITHIN THE RADARS 02& 4WO EXAMPLE CONDITIONS THE FIRST WITH AMBIGU
OUS DOPPLER CLUTTER AND THE SECOND WITH UNAMBIGUOUS DOPPLER CLUTTER ARE SHOWN IN
&IGURE 4HE FIGURE SHOWS THOSE ANTENNA ANGLES WHERE THE CLUTTER DOPPLER RESPONSE
REMAINS AFTER FILTERING THROUGH A SINGLE DOPPLER FILTER &IGURE A SHOWS THE RESPONSE
FOR AN AMBIGUOUS 02& OF (Z AND &IGURE B SHOWS THE RESPONSE FOR AN UNAM
BIGUOUS 02& OF (Z FOR A 5(& RADAR 4HIS FIGURE HIGHLIGHTS THAT EVEN WITH DOP
PLER PROCESSING A GIVEN DOPPLER FILTER MAY STILL INCLUDE CLUTTER RETURNS FROM A NUMBER
OF DISCONTIGUOUS ANGULAR INTERVALS 4HE ADVANTAGES OF THIS TRANSFORMATION FROM 02)
TO DOPPLER SPACE ON OVERALL 34!0 PERFORMANCE VERSUS A PRE DOPPLER ARCHITECTURE ARE
MORE DRAMATIC IN THE UNAMBIGUOUS DOPPLER CLUTTER CASE
02) STAGGERED DOPPLER FILTER OUTPUTS ARE REQUIRED TO MAINTAIN A SET OF TEMPORAL DEGREES
OF FREEDOM IN THIS ARCHITECTURE 4HE BLOCK DIAGRAM IS MODIFIED TO THAT SHOWN IN &IGURE WITH MULTIPLE DOPPLER FILTER BANKS ON EACH ANTENNA ELEMENT AND 02) DELAY
0OST $OPPLER "EAM 3PACE 34!0 4HE FINAL CATEGORY RESULTS FROM IMPLEMENT
ING BOTH DOPPLER AND SPATIAL TRANSFORMATIONS PRIOR TO 34!0 PROCESSING
4HE APPROPRIATE ARCHITECTURE SOLUTION DEPENDS UPON THE RADAR DESIGN CONSTRAINTS
4HE NUMBER OF ANTENNA ELEMENTS AND BEAMFORMING REQUIREMENTS ARE KEY DRIVERS IN THE
&)'52% !NTENNA POINTING ANGLES WHERE CLUTTER DOPPLER MAP TO A SINGLE DOPPLER FILTERS PASSBAND
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%LEMENT SPACE POST DOPPLER 34!0 ARCHITECTURE
DECISION WHETHER TO TRANSFORM FROM ELEMENTS TO BEAMS OR SUBARRAYS 4HE WAVEFORMS
AND CLUTTER CANCELLATION REQUIREMENTS ARE KEY DRIVERS IN THE DECISION WHETHER TO PER
FORM 34!0 ON SIGNALS BEFORE OR AFTER DOPPLER FILTERING )N ADDITION THE OVERALL TRANS
FORMATION DECISIONS TO REDUCE DEGREES OF FREEDOM ARE DRIVEN BY THE INTERFERENCE RANK
FOR THE RADAR PROBLEM /NE CAUTION IN THE DESIGN PROCESS IS THAT IF THE TRANSFORMATION
IS FIXED IN THE RADAR DESIGN IT IS IMPORTANT TO HAVE EXCESS DEGREES OF FREEDOM BEYOND
THE TOTAL INTERFERENCE RANK
)MPLEMENTATION #ONSIDERATIONS !S DISCUSSED ABOVE TRANSFORMATIONS AND TECH
NIQUES TO REDUCE THE NUMBER OF DEGREES OF FREEDOM IN THE 34!0 SOLUTION ARE IMPORTANT
NOT ONLY DUE TO PROCESSING REQUIREMENTS BUT ALSO BECAUSE OF THE NEED FOR SAMPLE SUP
PORT ON THE ORDER OF TWO TIMES THE NUMBER OF DEGREES OF FREEDOM FOR ADEQUATE 34!0
PERFORMANCE
4HE BASIC HARDWARE REQUIREMENTS FOR GOOD CLUTTER CANCELLATION REMAIN UNCHANGED
FROM CONVENTIONAL CLUTTER CANCELLATION ARCHITECTURESˆLOW PHASE NOISE LOW PULSE
JITTER ETC 4HE REQUIREMENTS ON THE HARDWARE MAY BECOME MORE STRINGENT BECAUSE
THE 34!0 ARCHITECTURE ALLOWS THE RADAR DESIGNER TO ACHIEVE HIGHER THEORETICAL CLUTTER
CANCELLATION PERFORMANCE LEVELS )N ADDITION TO THE ABOVE TEMPORALLY BASED HARDWARE
REQUIREMENTS THERE ARE ALSO SECOND ORDER SPATIALLY BASED HARDWARE REQUIREMENTS !S
ILLUSTRATED IN &IGURE PLATFORM MOTION COMPENSATION RESULTS IN DIFFERENT APERTURE
WEIGHTING FOR SUCCESSIVE PULSES IN A 34!0 SOLUTION !LTHOUGH GENERALLY SPEAKING
WELL MATCHED SPATIAL CHANNELS ANTENNA AND RECEIVER ARE DRIVEN BY JAMMING CANCELLA
TION AND ANTENNA SIDELOBE LEVELS A SECOND ORDER REQUIREMENT RESULTS FROM THE NEED FOR
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PLATFORM MOTION COMPENSATION )F ANTENNA AND RECEIVER CHANNELS ARE NOT WELL MATCHED
THE RESULTANT SUM CHANNEL BEAMS FORMED FROM DIFFERENT APERTURE ILLUMINATION FUNCTIONS
&IGURE WILL NOT BE MATCHED WELL ENOUGH TO PROVIDE MAIN BEAM AND SIDELOBE
CLUTTER CANCELLATION
0ERFORMANCE #OMPARISONS 'IVEN THE NUMBER OF 34!0 ARCHITECTURES AND COR
RESPONDING RADAR SYSTEM DESIGN SOLUTIONS GENERAL 34!0 PERFORMANCE COMPARISONS ARE
DIFFICULT TO COME BY )N GENERAL 34!0 PROVIDES A ROBUST SOLUTION TO DEAL WITH CLUTTER
AND JAMMING INTERFERENCE AND HELPS ALLEVIATE HARDWARE MISMATCH EFFECTS WITHIN REA
SON AMPLITUDE AND PHASE ADJUSTMENTS ARE APPLIED TO ANTENNA ELEMENT AND TIME DIS
PLACED RETURNS 'ENERALLY TO ADDRESS TIME DELAY ADAPTIVE WEIGHTING MORE COMPLEXITY
IS REQUIRED WITH A THIRD DIMENSION FOR ADAPTIVE WEIGHTSˆhFAST TIMEv OR RETURNS FROM
ADJACENT SAMPLED RANGE CELLS 4HIS EXTENSION CAN BE EXTREMELY COMPUTATIONALLY INTEN
SIVE AND FURTHER BURDEN THE SAMPLE SUPPORT PROBLEM ALLUDED TO PREVIOUSLY
7HEN EVALUATING A RADAR DESIGN AND TRADING OFF VARIOUS WAVEFORMS AND 34!0 PRO
CESSING TECHNIQUES IT IS IMPORTANT TO INCLUDE IN THE ANALYSIS KEY DRIVERS SUCH AS SIGNAL
BANDWIDTH CLUTTER INTERNAL MOTION PLATFORM MOTION ANTENNA SCANNING MOTION THE
AMOUNT OF SAMPLE SUPPORT AVAILABLE FROM NONHOMOGENOUS AND NONSTATIONARY CLUTTER
ENVIRONMENTS AND OTHER EFFECTS SUCH AS LARGE TARGET SAMPLES EFFECTING THE ADAPTIVE
WEIGHT SOLUTION
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!N AIRBORNE SEARCH RADAR SYSTEM MAY BE OPERATED AT AN ALTITUDE SO THAT THE RADAR HORI
ZON IS APPROXIMATELY AT THE MAXIMUM RANGE OF INTEREST 4HIS RESULTS IN SEA OR GROUND
CLUTTER BEING PRESENT AT ALL RANGES OF INTEREST /THER CLUTTER SOURCES SUCH AS RAIN AND
CHAFF MAY COEXIST WITH THE SURFACE CLUTTER )N MOST INSTANCES THESE SOURCES ARE MOV
ING AT A SPEED DETERMINED BY THE MEAN WIND ALOFT AND HAVE A MEAN DOPPLER FREQUENCY
SIGNIFICANTLY DIFFERENT FROM THAT OF THE SURFACE CLUTTER )F THE -4) FILTER IS TRACKING THE
SURFACE CLUTTER THE SPECTRA OF THE SOURCES WITH A DIFFERENT MEAN DOPPLER FREQUENCY LIE
IN THE PASSBAND OF THE -4) FILTER ! KT DIFFERENTIAL IN A 5(& SYSTEM CORRESPONDS
TO (Z WHICH WOULD GENERALLY BE OUTSIDE OF THE TRADITIONAL !-4) NOTCH FILTER IN A
(Z 02& SYSTEM ! SINGLE DELAY SECONDARY CANCELER CAN BE CASCADED WITH EITHER
A SINGLE DELAY OR A DOUBLE DELAY PRIMARY CANCELER 4HE PRIMARY CANCELER TRACKS THE
MEAN SURFACE VELOCITY AND REJECTS SURFACE CLUTTER 4HE SINGLE DELAY CANCELER TRACKS THE
SECONDARY SOURCE AND REJECTS IT 3INCE THE PASS AND REJECTION BANDS OF THE TWO CANCEL
ERS OVERLAP THE -4) IMPROVEMENT FACTOR FOR EACH CLUTTER SOURCE IS A FUNCTION OF THEIR
SPECTRAL SEPARATION
&IGURE SHOWS THE IMPROVEMENT FACTOR FOR A DOUBLE CANCELER WHICH CONSISTS OF
TWO SINGLE CANCELERS EACH TRACKING ONE OF THE SPECTRA )T CAN BE SEEN THAT AS THE SEPARA
TION VARIES FROM TO OF THE 02& THE PERFORMANCE DEGRADES FROM THAT EQUIVALENT TO
A DOUBLE CANCELER TO THE PERFORMANCE OF A SINGLE CANCELER AT HALF OF THE 02&
4HE TRIPLE CANCELER HAS A DOUBLE DELAY CANCELER TRACKING THE PRIMARY SPECTRA AND A
SINGLE DELAY CANCELER TRACKING THE SECONDARY SPECTRA 4HE PERFORMANCE OF THE PRIMARY
SYSTEM VARIES FROM THAT OF A TRIPLE CANCELER TO A LEVEL LESS THAN THAT OF A DOUBLE CANCELER
4HE SECONDARY SYSTEM PERFORMANCE VARIES FROM THAT OF A TRIPLE CANCELER TO A PERFOR
MANCE LEVEL LOWER THAN THAT OF A SINGLE CANCELER
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TRACKING TWO SPECTRA AS A FUNCTION OF THE NORMALIZED SPECTRA SEPARATION
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8* Ê/Ê, ,Ê-9-/ 4HE !.!09 RADAR DEVELOPED BY ,OCKHEED -ARTIN FOR THE 53 .AVY IS AN EXAMPLE
OF AN !-4) RADAR SYSTEM UTILIZED FOR AN AIRBORNE EARLY WARNING RADAR MISSION +EY
FEATURES OF THIS SYSTEM INCLUDE A SOLID STATE DISTRIBUTED TRANSMITTER A MECHANICALLY AND
ELECTRONICALLY SCANNED ROTATING ANTENNA DIGITAL RECEIVERS SPACE TIME ADAPTIVE PRO
CESSING DIGITAL PULSE COMPRESSION AND COHERENT INTEGRATION AND AUXILIARY PROCESSING
AIMED AT SUPPORTING THE 34!0 SAMPLE SELECTION PROCESS
4HE !.!09 RADAR ADDRESSES THE !%7 RADAR SURVEILLANCE COVERAGE REQUIREMENTS
DISCUSSED AT THE BEGINNING OF THIS CHAPTER UTILIZING A MECHANICALLY AND ELECTRONICALLY
STEERABLE ANTENNA LOCATED IN A ROTODOME 4HERE ARE THREE SCANNING MODES OF OPERATION
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MECHANICALLY SCANNED WITH AN OPERATOR SELECTABLE SCAN RATE AZIMUTH ELECTRONI
CALLY SCANNED WITH THE MECHANICAL BORESITE PROVIDED AS AN INPUT TO THE RADAR AND MECHANICALLY SCANNED WITH ADDITIONAL ELECTRONIC SCANNING WITHIN AN OPERATOR SELECT
ABLE AZIMUTH REGION
4HE TRANSMIT WAVEFORM INCLUDES 4!##!2 MODULATION TO CENTER MAINBEAM CLUTTER
AT ZERO DOPPLER FREQUENCY (OWEVER BECAUSE THE RADAR IMPLEMENTS ADAPTIVE CLUTTER
CANCELLATION 34!0 THE REQUIREMENTS ON 4!##!2 ARE SIGNIFICANTLY LESS COMPLEX
THAN FOR LEGACY RADAR SYSTEMS 4HERE IS NO NEED TO INCLUDE CLOSED LOOP ADJUSTMENTS TO
THE 4!##!2 MODULATION FREQUENCY 4HE OPTIMIZATION OF THE !-4) CLUTTER CANCELLA
TION FILTER IS ACHIEVED IN THE 34!0 PROCESSING AS OPPOSED TO ADJUSTING THE LOCATION OF
MAIN BEAM CLUTTER TO FIT A FIXED !-4) FILTER
)N ORDER TO IMPLEMENT 34!0 AND ELECTRONIC SCANNING IN THIS RADAR ALL ELEMENTS
OF THE PHASED ARRAY ANTENNA ARE PROCESSED ON TRANSMIT AND RECEIVE 4HE SOLID STATE
TRANSMITTER PROVIDES LOW POWER PHASE SHIFT CONTROL FOR ELECTRONIC STEERING FOLLOWED BY
POWER AMPLIFICATION IN EACH OF CHANNELS 4HESE ARE CONNECTED TO THE ELEMENTS
OF THE PHASED ARRAY THROUGH AN CHANNEL ROTARY COUPLER 4HE TRANSMITRECEIVE ISOLA
TION ON ALL CHANNELS IS PROVIDED THROUGH CIRCULATORS 4HE CHANNELS ARE PROCESSED
SEPARATELY THROUGH RECEIVERS FINALLY FEEDING THE 34!0 SUBSYSTEM WITH DIGITAL
BASEBAND SIGNALS
4HE RADAR PERFORMS PLATFORM MOTION COMPENSATION ELECTRONICALLY AS PART OF THE
34!0 ARCHITECTURE 4HE RADAR IMPLEMENTS AN ELEMENT SPACE PRE DOPPLER 34!0 ARCHI
TECTURE !DAPTIVE WEIGHTS ARE GENERATED AND APPLIED TO THE RECEIVE CHANNELS FORM
ING THREE BEAMS 3UM $ELTAAZ AND /MNI BY WEIGHTING AND SUMMING THE RECEIVE
CHANNELS OVER THREE PULSES TO PROVIDE SIMULTANEOUS CLUTTER AND JAMMING CANCELLATION
4HE ADAPTIVE WEIGHT ALGORITHM IS MATCHED TO THE RADARS OPERATING PARAMETERS AND IS
AUGMENTED WITH ADAPTIVE KNOWLEDGEnAIDED SAMPLING SCHEMES TO MAXIMIZE PERFOR
MANCE IN A COMPLEX HETEROGENEOUS CLUTTER AND JAMMING INTERFERENCE ENVIRONMENT
$OPPLER FILTERING IS PERFORMED AFTER DIGITAL BEAMFORMING
/THER FUNCTIONS DISCUSSED IN THIS CHAPTER ARE NOT REQUIRED FOR THIS RADAR APPLICATION
BECAUSE THEY DO NOT LIMIT PERFORMANCE %XAMPLES INCLUDE SCANNING MOTION COMPENSA
TION AND MULTIPLE SPECTRA !-4) CLUTTER CANCELLATION
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VOL 0'!% PP n *UNE 2 3 "ERKOWITZ ED -ODERN 2ADAR !NALYSIS %VALUATION AND 3YSTEM $ESIGN .EW 9ORK
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4HE PRIMARY BENEFIT OF PULSE DOPPLER RADAR IS ITS ABILITY TO DETECT SMALL AMPLITUDE MOV
ING TARGET RETURNS AGAINST AN OVERWHELMINGLY LARGE AMPLITUDE CLUTTER BACKGROUND
.OMENCLATURE 2ADARS THAT RELY ON THE DOPPLER EFFECT TO ENHANCE TARGET DETEC
TION ARE CALLED DOPPLER RADARS 4HE DOPPLER EFFECT MANIFESTS ITSELF WHEN THERE IS
A RELATIVE RANGE RATE OR RADIAL VELOCITY BETWEEN THE RADAR AND THE TARGET 7HEN THE
RADARS TRANSMIT SIGNAL IS REFLECTED FROM SUCH A TARGET THE CARRIER FREQUENCY OF THE
RETURN SIGNAL WILL BE SHIFTED !SSUMING A MONOSTATIC RADAR IE COLLOCATED TRANSMIT
TER AND RECEIVER THE ROUNDTRIP DISTANCE IS TWICE THE DISTANCE BETWEEN THE TRANSMITTER
AND THE TARGET 4HE DOPPLER FREQUENCY SHIFT FD IS A FUNCTION OF THE CARRIER WAVELENGTH
K AND THE RELATIVE RADIAL VELOCITY RANGE RATE BETWEEN THE RADAR AND THE TARGET 6RELATIVE
AND IS WRITTEN AS FD 6RELATIVEK WHERE K CF IS THE WAVELENGTH C IS THE SPEED OF
LIGHT AND F IS THE CARRIER FREQUENCY 7HEN THE TARGET IS MOVING AWAY FROM THE RADAR
THE RELATIVE RADIAL VELOCITY OR RANGE RATE IS DEFINED TO BE POSITIVE AND RESULTS IN A
NEGATIVE DOPPLER SHIFT
$OPPLER RADARS CAN BE EITHER CONTINUOUS WAVE #7 o OR PULSED RADARS #7 RADARS
SIMPLY OBSERVE THE DOPPLER SHIFT BETWEEN THE CARRIER FREQUENCY OF THE RETURN SIGNAL
RELATIVE TO THE TRANSMIT SIGNAL 0ULSED SYSTEMS MEASURE DOPPLER BY USING A COHERENT
TRAIN OF PULSES WHERE THERE IS A FIXED OR DETERMINISTIC PHASE RELATIONSHIP OF THE CARRIER
FREQUENCY BETWEEN EACH SUCCESSIVE RADIO FREQUENCY 2& PULSE #OHERENCE CONCEN
TRATES THE ENERGY IN THE FREQUENCY SPECTRUM OF THE PULSE TRAIN AROUND DISTINCT SPECTRAL
LINES SEPARATED BY THE PULSE REPETITION FREQUENCY 02& 4HIS SEPARATION INTO SPECTRAL
LINES ALLOWS FOR DISCRIMINATION OF DOPPLER SHIFTS
$OPPLER RADARS USING PULSED TRANSMISSIONS ARE MORE COMPLEX THAN #7 RADARS BUT
THEY OFFER SIGNIFICANT ADVANTAGES -OST IMPORTANT IS THE TIME GATING OF THE RECEIVER
$AVID ( -OONEY AND 7ILLIAM ! 3KILLMAN WROTE THIS CHAPTER FOR THE FIRST EDITION 7ILLIAM ( ,ONG
JOINED THE AUTHORS FOR THE SECOND EDITION *OHN 0 3TRALKA AND 7ILLIAM ' &EDARKO UPDATED THE MATERIAL
FOR THIS EDITION
o 4O ASSIST THE READER ABBREVIATIONS USED THROUGHOUT THIS CHAPTER ARE DEFINED IN A LIST AT THE END OF THE CHAPTER
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4IME GATING ALLOWS THE BLANKING OF DIRECT TRANSMITTER LEAKAGE INTO THE RECEIVER 4HIS
PERMITS THE USE OF A SINGLE ANTENNA FOR TRANSMIT AND RECEIVE WHICH OTHERWISE WOULD
NOT BE FEASIBLE FOR #7 RADAR DUE TO EXCESSIVE TRANSMITRECEIVE ISOLATION REQUIREMENTS
0ULSED RADARS CAN ALSO USE RANGE GATING A SPECIFIC FORM OF TIME GATING WHICH DIVIDES
THE INTERPULSE PERIOD INTO CELLS OR RANGE GATES 4HE DURATION OF EACH CELL IS TYPICALLY
LESS THAN OR EQUAL TO THE INVERSE OF THE TRANSMIT PULSE BANDWIDTH 2ANGE GATING HELPS
ELIMINATE EXCESS RECEIVER NOISE FROM COMPETING WITH TARGET RETURNS AND ALLOWS RANGE
MEASUREMENT WITH PULSE DELAY RANGING IE MEASURING THE TIME BETWEEN TRANSMISSION
OF A PULSE AND RECEPTION OF THE TARGET ECHO 0ULSED TRANSMISSION DOPPLER RADARS HAVE HISTORICALLY BEEN CATEGORIZED AS MOVING
TARGET INDICATION -4) OR PULSE DOPPLER -4) TYPICALLY ELIMINATES CLUTTER BY PASSING
THE RECEIVED RETURNS FROM MULTIPLE COHERENT PULSES THROUGH A FILTER WITH A STOPBAND
PLACED IN SPECTRAL REGIONS OF HEAVY CLUTTER CONCENTRATIONS -OVING TARGETS WITH DOP
PLER FREQUENCIES OUTSIDE THE STOPBAND ARE PASSED ONTO DETECTION PROCESSING 0ULSE
DOPPLER RADARS ON THE OTHER HAND RESOLVE AND ENHANCE TARGETS WITHIN A PARTICULAR
DOPPLER BAND WHILE REJECTING CLUTTER AND OTHER RETURNS OUTSIDE THE DOPPLER BAND OF
INTEREST 4HIS IS TYPICALLY ACCOMPLISHED WITH A CONTIGUOUS BANK OF DOPPLER FILTERS
FORMED BETWEEN TWO OF THE COHERENT PULSE TRAINS SPECTRAL LINES ONE OF WHICH IS THE
CENTRAL LINE 2ANGE GATING PRECEDES THE DOPPLER FILTER BANK 4HE BANDWIDTH OF EACH
DOPPLER FILTER IS INVERSELY PROPORTIONAL TO THE DURATION OF THE COHERENT PULSE TRAIN THAT
IS PROCESSED TO FORM THE DOPPLER FILTER BANK 4HIS PROCESS FORMS A MATCHED FILTER TO
THE ENTIRE PULSE TRAIN -4) AND PULSE DOPPLER RADARS SHARE THE FOLLOWING CHARACTERISTICS
L
L
#OHERENT TRANSMISSION AND RECEPTION THAT IS EACH TRANSMITTED PULSE AND THE RECEIVER
LOCAL OSCILLATOR ARE SYNCHRONIZED TO A FREE RUNNING HIGHLY STABLE OSCILLATOR
#OHERENT PROCESSING TO REJECT MAIN BEAM CLUTTER ENHANCE TARGET DETECTION AND AID
IN TARGET DISCRIMINATION OR CLASSIFICATION
-4) RADARS CAN ALSO BE IMPLEMENTED USING A DOPPLER FILTER BANK BLURRING THE HISTORIC
DELINEATION BETWEEN -4) AND PULSE DOPPLER RADARS !S A RESULT THIS BOOK WILL DEFINE
-4) RADARS AS THOSE RADARS WHOSE 02& IS SUFFICIENTLY LOW ENOUGH TO PROVIDE AN UNAM
BIGUOUS RANGE MEASUREMENT VIA PULSE DELAY RANGING OVER THE RADARS INSTRUMENTED
RANGE 4HE UNAMBIGUOUS RANGE 2U IS GIVEN BY CF2 WHERE C IS THE SPEED OF LIGHT
AND F2 IS THE 02& 2ADARS WITH 02&S THAT RESULT IN RANGE AMBIGUITIES WITHIN THE RANGE
COVERAGE OF INTEREST WILL BE REFERRED TO AS PULSE DOPPLER RADARS AND WILL BE THE FOCUS
OF THIS CHAPTER
!PPLICATIONS 0ULSE DOPPLER IS APPLIED PRINCIPALLY TO RADAR SYSTEMS REQUIRING
THE DETECTION OF MOVING TARGETS IN A SEVERE CLUTTER ENVIRONMENT 4ABLE LISTS TYPI
CAL APPLICATIONS AND REQUIREMENTSn 4HIS CHAPTER WILL DEAL PRINCIPALLY WITH AIRBORNE
APPLICATIONS ALTHOUGH THE BASIC PRINCIPLES CAN ALSO BE APPLIED TO THE SURFACE BASED
CASE /NLY MONOSTATIC RADARS WILL BE CONSIDERED
02&S 0ULSED RADARS THAT EMPLOY DOPPLER ARE DIVIDED INTO THREE BROAD 02& CAT
EGORIES LOW MEDIUM AND HIGH ! LOW 02& RADAR IS ONE IN WHICH THE RANGES OF INTEREST
ARE UNAMBIGUOUS WHILE THE RADIAL VELOCITIES DOPPLER FREQUENCIES ARE USUALLY HIGHLY
AMBIGUOUS !S DISCUSSED PREVIOUSLY THIS TYPE OF RADAR IS CALLED MOVING TARGET INDICA
TION -4) -4) RADARS ARE GENERALLY NOT CATEGORIZED AS PULSE DOPPLER RADARS ALTHOUGH
THE PRINCIPLES OF OPERATION ARE SIMILAR
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4!",% 0ULSE $OPPLER !PPLICATIONS AND 2EQUIREMENTS
2ADAR !PPLICATION
2EQUIREMENTS
!IRBORNE OR SPACEBORNE SURVEILLANCE
,ONG DETECTION RANGE ACCURATE RANGE DATA
!IRBORNE INTERCEPTOR OR FIRE CONTROL
-EDIUM DETECTION RANGE ACCURATE RANGE VELOCITY AND
ANGLE DATA
'ROUND BASED SURVEILLANCE
-EDIUM DETECTION RANGE ACCURATE RANGE DATA
"ATTLEFIELD SURVEILLANCE
SLOW MOVING TARGET DETECTION
-EDIUM DETECTION RANGE ACCURATE RANGE VELOCITY DATA
-ISSILE SEEKER
3HORT DETECTION RANGE ACCURATE VELOCITY AND ANGLE RATE DATA
MAY NOT NEED TRUE RANGE INFORMATION
3URFACE BASED WEAPON CONTROL
3HORT RANGE ACCURATE RANGE VELOCITY DATA
-ETEOROLOGICAL
'OOD VELOCITY RESOLUTION
-ISSILE WARNING
3HORT DETECTION RANGE VERY LOW FALSE ALARM RATE
4HE CONVERSE OF A LOW 02& RADAR IS A HIGH 02& RADAR THAT CAN MEASURE DOPPLER
UNAMBIGUOUSLY OVER THE SPAN OF RADIAL VELOCITIES OF INTEREST BUT IS USUALLY HIGHLY
AMBIGUOUS IN RANGE ! MEDIUM 02& RADAR HAS BOTH RANGE AND DOPPLER AMBIGUI
TIESn ! BLEND OF MEDIUM AND HIGH 02& KNOWN AS HIGH MEDIUM 02& WHICH WILL
BE DISCUSSED LATER IS CHARACTERIZED AS HAVING ONLY A SINGLE AMBIGUITY FOR THE RADIAL
VELOCITIES OF INTEREST &OR THIS CHAPTER A PULSE DOPPLER RADAR IS CHARACTERIZED AS HAVING
A 02& ANYWHERE WITHIN THE MEDIUM TO HIGH 02& REGIME THAT RESULTS IN AMBIGUOUS
RANGE MEASUREMENTS DURING A COHERENT PROCESSING INTERVAL
! COMPARISON OF -4) AND PULSE DOPPLER RADARS IS SHOWN IN 4ABLE 0REVIOUSLY
UNDEFINED TERMS WILL BE DEFINED THROUGHOUT THE CHAPTER 4HE TABLE ASSUMES AN AIRBORNE
RADAR APPLICATION DESIGNED TO DETECT OTHER AIRCRAFT 3UCH AN APPLICATION IS COMMONLY
REFERRED TO AS AIR TO AIR
4!",% #OMPARISON OF -4) AND 0ULSE $OPPLER 2ADARS FOR !IR TO !IR
!DVANTAGES
$ISADVANTAGES
,OW 02&
-4)
RANGE UNAMBIGUOUS
DOPPLER AMBIGUOUS
#AN SORT CLUTTER FROM TARGETS ON BASIS
OF RANGE &RONT END SENSITIVITY TIME
CONTROL 34# SUPPRESSES SIDELOBE
DETECTIONS AT SHORT RANGES AND REDUCES
DYNAMIC RANGE REQUIREMENTS
-ULTIPLE BLIND SPEEDS 5SUALLY
DOES NOT MEASURE RADIAL TARGET
VELOCITY 0OOR GROUND MOVING
TARGET REJECTION
-EDIUM 02&
0ULSE $OPPLER
RANGE AMBIGUOUS
DOPPLER AMBIGUOUS
0ERFORMANCE AT ALL TARGET ASPECTS
'OOD GROUND MOVING TARGET REJECTION
-EASURES RADIAL VELOCITY ,ESS RANGE
ECLIPSING THAN IN HIGH 02&
3IDELOBE CLUTTER CAN LIMIT
PERFORMANCE !MBIGUITY
RESOLUTION REQUIRED ,OW ANTENNA
SIDELOBES NECESSARY 2EJECTION
OF SIDELOBE RETURNS OF DISCRETE
GROUND TARGETS NEEDED
(IGH 02&
0ULSE $OPPLER
RANGE AMBIGUOUS
DOPPLER UNAMBIGUOUS
!LLOWS THERMAL NOISE LIMITED
DETECTION OF TARGETS WITH HIGH RADIAL
VELOCITIES 3INGLE DOPPLER BLIND
ZONE AT ZERO VELOCITY 'OOD GROUND
MOVING TARGET REJECTION -EASURES
RADIAL VELOCITY
,IMITED LOW RADIAL VELOCITY TARGET
DETECTION 2ANGE ECLIPSING ,ARGE
NUMBER OF RANGE AMBIGUITIES
PRECLUDE PULSE DELAY RANGING
(IGH STABILITY REQUIREMENTS DUE
TO RANGE FOLDING
{°{
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4!",% 4YPICAL 6ALUES FOR AN 8 BAND '(Z !IRBORNE &IRE #ONTROL 2ADAR
0ULSE $OPPLER 7AVEFORM
-EDIUM 02&
(IGH MEDIUM 02&
(IGH 02&
02&
4RANSMIT $UTY #YCLE
K(Z
K(Z
K(Z
4ABLE PROVIDES THE SPAN OF 02&S AND CORRESPONDING TRANSMIT DUTY CYCLES RATIO
OF TRANSMIT PULSE WIDTH TO INTERPULSE PERIOD FOR THE VARIOUS PULSE DOPPLER WAVEFORMS
USED IN A 8 BAND AIRBORNE FIRE CONTROL RADAR +EEP IN MIND THAT THE OPERATING FREQUENCY
OF THE RADAR ALONG WITH ITS REQUIRED RANGE AND RADIAL VELOCITY COVERAGE DETERMINES
WHETHER A 02& IS CONSIDERED MEDIUM HIGH MEDIUM OR HIGH !LSO MODERN MULTI
FUNCTION RADARS ARE TYPICALLY CAPABLE OF UTILIZING WAVEFORMS FROM THE VARIOUS 02&
CATEGORIES IN ORDER TO CARRY OUT THEIR DIVERSE MISSIONS
0ULSE $OPPLER 3PECTRUM 4HE TRANSMITTED SPECTRUM OF A PULSE DOPPLER RADAR CON
SISTS OF DISCRETE LINES AT THE CARRIER FREQUENCY F AND AT SIDEBAND FREQUENCIES F o IF2 WHERE
F2 IS THE 02& AND I IS AN INTEGER 4HE ENVELOPE OF THE SPECTRUM IS DETERMINED BY THE PULSE
SHAPE &OR THE RECTANGULAR PULSES USUALLY EMPLOYED A SINX X SPECTRUM IS OBTAINED
5SING A CONSTANT VELOCITY AIRBORNE RADAR THE RECEIVED SPECTRUM FROM A STATIONARY
TARGET HAS LINES THAT ARE DOPPLER SHIFTED PROPORTIONALLY TO THE RADIAL VELOCITY BETWEEN THE
RADAR PLATFORM AND THE TARGET 4HE TWO WAY DOPPLER SHIFT IS GIVEN BY FD 62K COSX
WHERE K IS THE RADAR WAVELENGTH 62 IS THE RADAR PLATFORM SPEED AND X IS THE ANGLE
BETWEEN THE VELOCITY VECTOR AND THE LINE OF SIGHT TO THE TARGET .OTE THAT THE RELATIVE
RADIAL VELOCITY RANGE RATE TO THE STATIONARY TARGET IS 6RELATIVE 62 COSX WHICH MAKES
THE LATER EQUATION FOR DOPPLER SHIFT CONSISTENT WITH THE ONE PRESENTED AT THE BEGINNING
OF THE CHAPTER )LLUSTRATED IN &IGURE IS THE RECEIVED PULSED SPECTRUM WITH RETURNS
FROM DISTRIBUTED CLUTTER SUCH AS THE GROUND OR WEATHER AND FROM DISCRETE TARGETS SUCH
AS AIRCRAFT AUTOMOBILES TANKS ETC
&IGURE SHOWS THE UNFOLDED SPECTRUM IE NO SPECTRAL FOLDOVER FROM ADJACENT
02& LINES IN THE CASE OF HORIZONTAL MOTION OF THE RADAR PLATFORM WITH A SPEED 62
4HE CLUTTER FREE REGION IS DEFINED AS THAT PORTION OF THE SPECTRUM IN WHICH NO GROUND
CLUTTER CAN EXIST ! CLUTTER FREE REGION USUALLY DOES NOT EXIST WITH MEDIUM 02&S
DUE TO DOPPLER FOLDING 4HE SIDELOBE CLUTTER REGION 62K IN WIDTH CONTAINS GROUND
CLUTTER POWER FROM THE SIDELOBES OF THE ANTENNA ALTHOUGH THIS CLUTTER POWER MAY BE
BELOW THE NOISE LEVEL IN PART OF THE REGION 4HE MAIN BEAM CLUTTER REGION LOCATED AT
F 62K COSX CONTAINS THE STRONG RETURN FROM THE MAIN BEAM OF THE ANTENNA
&)'52% #LUTTER AND TARGET FREQUENCY SPECTRUM FROM A HORIZONTALLY MOVING PLATFORM
05,3% $/00,%2 2!$!2
&)'52% {°x
5NFOLDED SPECTRUM WITH NO CLUTTER POSITIONING
STRIKING THE GROUND AT A SCAN ANGLE OF X MEASURED FROM THE VELOCITY VECTOR 2AIN AND
CHAFF CLUTTER MAY ALSO BE LARGE WHEN THE MAIN BEAM ILLUMINATES A RAIN OR CHAFF CLOUD
-OTION DUE TO WINDS MAY DISPLACE ANDOR SPREAD THE RETURN IN FREQUENCY
!LTITUDE LINE CLUTTER IS DUE TO THE RADAR RETURN FROM GROUND CLUTTER AT NEAR NORMAL
INCIDENCE DIRECTLY BELOW THE RADAR PLATFORM AND IS AT ZERO DOPPLER IF THERE IS NO VERTICAL
COMPONENT OF PLATFORM VELOCITY ! DISCRETE TARGET RETURN IN THE MAIN BEAM IS SHOWN AT
F4 F 62 K COSX 64 K COSX4 WHERE THE TARGET SPEED IS 64 WITH AN ANGLE
X4 BETWEEN THE TARGET VELOCITY VECTOR AND THE RADAR TARGET LINE OF SIGHT 4HE COMPONENTS
OF THE SPECTRUM SHOWN IN &IGURE WILL ALSO VARY WITH RANGE AS DISCUSSED LATER .OTE
THAT THE DIRECTION OF 64 COSX4 IS ASSUMED TO BE THE OPPOSITE OF 62 COSX RESULTING IN
A RELATIVE RANGE RATE OF 6RELATIVE 64 COSX4 62 COSX WHICH IS CONSISTENT WITH THE
DEFINITION FOR DOPPLER SHIFT STATED AT THE BEGINNING OF THE CHAPTER
&IGURE ILLUSTRATES THE VARIOUS CLUTTER DOPPLER FREQUENCY REGIONS AS A FUNCTION
OF THE ANTENNA MAIN BEAM AZIMUTH AND RELATIVE RADAR AND TARGET VELOCITIES AGAIN
FOR AN UNFOLDED SPECTRUM 4HE ORDINATE IS THE RADIAL OR LINE OF SIGHT COMPONENT OF
TARGET VELOCITY IN UNITS OF RADAR PLATFORM VELOCITY SO THE MAIN BEAM CLUTTER REGION
IS AT ZERO VELOCITY AND THE SIDELOBE CLUTTER REGION FREQUENCY BOUNDARIES VARY SINU
SOIDALLY WITH ANTENNA AZIMUTH 4HUS THE FIGURE SHOWS THE DOPPLER REGIONS IN WHICH
THE TARGET BECOMES CLEAR OF SIDELOBE CLUTTER &OR EXAMPLE IF THE ANTENNA MAIN BEAM
AZIMUTH ANGLE IS AT ZERO ANY HEAD ON TARGET 64 COSX4 IS CLEAR OF SIDELOBE
CLUTTER WHEREAS IF THE RADAR IS IN TRAIL BEHIND THE TARGET X4 — AND X — THE
TARGETS RADIAL VELOCITY HAS TO BE GREATER THAN TWICE THAT OF THE RADAR TO BECOME CLEAR
OF SIDELOBE CLUTTER
4HE SIDELOBE CLEAR AND CLUTTER REGIONS CAN ALSO BE EXPRESSED IN TERMS OF THE ASPECT
ANGLE WITH RESPECT TO THE TARGET AS SHOWN IN &IGURE (ERE COLLISION GEOMETRY
IS ASSUMED IN WHICH THE RADAR AND TARGET AIRCRAFT FLY STRAIGHT LINE PATHS TOWARD AN
INTERCEPT POINT THE LOOK ANGLE OF THE RADAR X AND THE ASPECT ANGLE OF THE TARGET X4 ARE
CONSTANT FOR A GIVEN SET OF RADAR AND TARGET SPEEDS 62 AND 64 RESPECTIVELY 4HE CENTER OF
THE DIAGRAM IS THE TARGET AND THE ANGLE TO THE RADAR ON THE CIRCUMFERENCE IS THE ASPECT
ANGLE 4HE ASPECT ANGLE AND LOOK ANGLES SATISFY THE EQUATION 62 SINX 64 SINX4
{°È
2!$!2 (!.$"//+
./4% 7IDTH OF ALTITUDE LINE AND MAIN BEAM CLUTTER REGIONS VARIES WITH CONDITIONS AZIMUTH IS MEASURED
FROM RADAR PLATFORM VELOCITY VECTOR TO THE ANTENNA BORESIGHT OR TO THE LINE OF SIGHT TO THE TARGET
HORIZONTAL MOTION CASE
&)'52% #LUTTER AND CLUTTER FREE REGIONS AS A FUNCTION OF TARGET VELOCITY AND AZIMUTH
WHICH IS DEFINED AS A COLLISION COURSE 4HE TARGET ASPECT ANGLE IS ZERO FOR A HEAD ON
CONDITION AND — FOR A TAIL CHASE 4HE ASPECT ANGLE CORRESPONDING TO THE BOUNDARY
BETWEEN THE SIDELOBE CLUTTER REGION AND THE SIDELOBE CLEAR REGION IS A FUNCTION OF THE
RELATIVE RADAR TARGET VELOCITY RATIO AND IS SHOWN IN &IGURE FOR FOUR CASES #ASE IS
WHERE THE RADAR AND TARGET SPEEDS ARE EQUAL AND THE TARGET CAN BE SEEN CLEAR OF SIDELOBE
CLUTTER IN A HEAD ON ASPECT OUT TO — ON EITHER SIDE OF THE TARGETS VELOCITY VECTOR
3IMILARLY #ASES THROUGH SHOW CONDITIONS WHERE THE TARGETS SPEED IS AND
TIMES THE RADARS SPEED IN WHICH CASE THE TARGET CAN BE SEEN CLEAR OF SIDELOBE CLUT
TER OVER A REGION OF UP TO o— RELATIVE TO THE TARGETS VELOCITY VECTOR !GAIN THESE
CONDITIONS ARE FOR AN ASSUMED COLLISION COURSE !S IS EVIDENT THE ASPECT ANGLE OF THE
TARGET CLEAR OF SIDELOBE CLUTTER IS ALWAYS FORWARD OF THE BEAM ASPECT
!MBIGUITIES AND 02& 3ELECTION 0ULSE DOPPLER RADARS ARE AMBIGUOUS IN RANGE
AND POSSIBLY DOPPLER !S MENTIONED EARLIER THE UNAMBIGUOUS RANGE 2U IS GIVEN BY
CF2 WHERE C IS THE SPEED OF LIGHT AND F2 IS THE 02&
)F THE AIRBORNE TARGET RADIAL VELOCITY TO BE OBSERVED IS BETWEEN 64 MAX OPENING FOR
OPENING TARGETS POSITIVE RANGE RATE AND 64 MAX CLOSING FOR CLOSING TARGETS NEGATIVE
RANGE RATE THEN THE MINIMUM VALUE OF 02& F2 MIN WHICH IS UNAMBIGUOUS IN VELOCITY
IN BOTH MAGNITUDE AND SENSE IE POSITIVE AND NEGATIVE IS
F2 MIN 64 MAX CLOSING 64 MAX OPENING 6G L
WHERE 6G IS THE UPPER LIMIT FOR GROUND MOVING TARGET REJECTION 6 REFERS TO THE SPEED
OR THE MAGNITUDE OF THE RANGE RATE
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&)'52% 3IDELOBE CLUTTER CLEAR REGIONS VERSUS TARGET ASPECT ANGLE .OTE THE TARGET IS AT THE CENTER OF THE
PLOT WITH THE RADAR PLATFORM ON THE CIRCUMFERENCE
(OWEVER SOME PULSE DOPPLER RADARS EMPLOY A 02& THAT IS UNAMBIGUOUS IN VELOC
ITY MAGNITUDE ONLY IE F2 MIN ;MAX64 MAX CLOSING 64 MAX OPENING 6G= K AND RELY ON
DETECTIONS IN MULTIPLE 02&S DURING THE TIME ON TARGET TO RESOLVE THE SIGN AMBIGUITY IN
DOPPLER 4HESE RADARS CAN BE DESCRIBED AS HIGH MEDIUM 02& AND CAN BE CONSIDERED
TO BE IN THE HIGH 02& CATEGORY IF THE OLDER DEFINITION OF HIGH 02& NO VELOCITY AMBI
GUITY IS EXTENDED TO ALLOW ONE VELOCITY AMBIGUITY THAT OF DOPPLER SENSE 4HE LOWER
02& EASES THE MEASUREMENT OF TRUE RANGE WHILE RETAINING THE HIGH 02& ADVANTAGE OF
A SINGLE BLIND SPEED REGION NEAR ZERO DOPPLER (IGH MEDIUM 02& IS BECOMING MORE
PREVALENT IN MODERN AIRBORNE RADARS FOR AIR TO AIR SEARCH
4HE CHOICE BETWEEN HIGH AND MEDIUM 02& INVOLVES A NUMBER OF CONSIDERATIONS
SUCH AS TRANSMITTER DUTY CYCLE LIMIT PULSE COMPRESSION AVAILABILITY SIGNAL PROCESSING
CAPABILITY MEASUREMENT ACCURACY REQUIREMENTS ETC BUT OFTEN DEPENDS ON THE
NEED FOR ALL ASPECT TARGET DETECTABILITY !LL ASPECT COVERAGE REQUIRES GOOD PERFOR
MANCE IN TAIL CHASE WHERE THE TARGET DOPPLER IS IN THE SIDELOBE CLUTTER REGION NEAR
THE ALTITUDE LINE )N A HIGH 02& RADAR THE RANGE FOLDOVER MAY LEAVE LITTLE CLEAR
REGION IN THE RANGE DIMENSION THUS DEGRADING TARGET DETECTABILITY "Y USING A LOWER
OR MEDIUM 02& THE CLEAR REGION IN RANGE IS INCREASED AT THE EXPENSE OF VELOCITY
FOLDOVER FOR HIGH DOPPLER TARGETS THAT ARE IN THE CLUTTER FREE REGION IN HIGH 02& !S
AN EXAMPLE &IGURE SHOWS THE CLUTTER PLUS NOISE TO NOISE RATIO IN RANGE DOPPLER
COORDINATES FOR TWO DIFFERENT 8 BAND WAVEFORMS AT SIMILAR ALTITUDES AND AIRCRAFT
VELOCITIES 4HE RANGE DIMENSION REPRESENTS THE UNAMBIGUOUS RANGE INTERVAL 2U AND
THE FREQUENCY DIMENSION REPRESENTS THE 02& INTERVAL WITH THE MAIN BEAM CLUTTER
ALTITUDE LINE AND SIDELOBE CLUTTER REGIONS CLEARLY DISCERNIBLE )N BOTH WAVEFORMS
THE MAIN BEAM CLUTTER RETURN IS POSITIONED TO $# THROUGH CLUTTER POSITIONING VIA AN
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#LUTTER PLUS NOISE TO NOISE RATIO IN RANGE DOPPLER SPACE
OFFSET APPLIED TO THE TRANSMIT FREQUENCY 4HE MEDIUM 02& SPECTRUM 02& K(Z
CONTAINS A RANGE DOPPLER REGION IN WHICH THE SIDELOBE CLUTTER IS BELOW THERMAL NOISE
AND IN WHICH GOOD TAIL ASPECT TARGET DETECTABILITY CAN BE ACHIEVED 4HE K(Z HIGH
MEDIUM 02& WAVEFORM HAS A MUCH MORE SEVERE CLUTTER FOLDING AND TAIL ASPECT
TARGETS WOULD COMPETE WITH SIDELOBE CLUTTER AT NEARLY ALL RANGES BUT THE CLUTTER FREE
REGION IS MUCH LARGER
"ECAUSE THE CLUTTER IS FOLDED IN BOTH RANGE AND DOPPLER WITH MEDIUM 02& A NUM
BER OF 02&S MAY BE REQUIRED TO OBTAIN A SATISFACTORY PROBABILITY OF SUFFICIENT DETECTIONS
TO RESOLVE THE RANGE AND DOPPLER AMBIGUITIES 4HE MULTIPLE 02&S MOVE THE RELATIVE
LOCATION OF THE CLEAR REGIONS SO THAT ALL ASPECT TARGET COVERAGE IS ACHIEVED 3INCE THE
SIDELOBE CLUTTER GENERALLY COVERS THE DOPPLER REGION OF INTEREST THE RATIO OF THE REGION
WITH SIDELOBE CLUTTER BELOW NOISE RELATIVE TO THE TOTAL RANGE DOPPLER SPACE IS A FUNCTION
OF THE RADAR ALTITUDE SPEED AND ANTENNA SIDELOBE LEVEL
)F A HIGH 02& WAVEFORM IS USED THE CLEAR RANGE REGION DISAPPEARS BECAUSE THE
SIDELOBE CLUTTER FOLDS IN RANGE INTO THE UNAMBIGUOUS RANGE INTERVAL ASSUMING THE TAR
GET DOPPLER IS SUCH THAT IT STILL COMPETES WITH THE SIDELOBE CLUTTER (OWEVER IN THOSE
DOPPLER REGIONS FREE OF SIDELOBE CLUTTER AS SHOWN IN &IGURE AND &IGURE TARGET
DETECTABILITY IS LIMITED ONLY BY THERMAL NOISE INDEPENDENT OF RADAR ALTITUDE SPEED
AND SIDELOBE LEVEL 4HIS REQUIRES SYSTEM STABILITY SIDEBANDS TO BE WELL BELOW NOISE FOR
THE WORST CASE MAIN BEAM CLUTTER 4HUS ALTHOUGH MEDIUM 02& PROVIDES ALL ASPECT
TARGET COVERAGE THE TARGET IS POTENTIALLY COMPETING WITH SIDELOBE CLUTTER AT ALL ASPECTS
WHEREAS WITH HIGH 02& A TARGET CAN BECOME CLEAR OF SIDELOBE CLUTTER AT ASPECT ANGLES
FORWARD OF THE BEAM ASPECT
&OR TARGETS WITH SUFFICIENT RADIAL VELOCITY HIGH 02& IS TYPICALLY MORE EFFICIENT THAN
MEDIUM 02& 4HE TRANSMIT PULSE WIDTH IS USUALLY LIMITED BY THE TRANSMITTERS ABILITY TO
PRESERVE THE PULSE AMPLITUDE AND PHASE CHARACTERISTICS OVER THE DURATION OF THE TRANSMIT
PULSE &OR A FIXED TRANSMIT PULSE WIDTH AND PEAK POWER A WAVEFORM WITH A HIGHER 02&
WILL HAVE A HIGHER TRANSMIT DUTY CYCLE RESULTING IN A HIGHER AVERAGE TRANSMIT POWER &OR
A GIVEN COHERENT PROCESSING TIME MORE ENERGY IS PLACED ON THE TARGET WHICH IMPROVES
DETECTABILITY &OR THIS REASON HIGH 02& IS USED FOR LONG RANGE SEARCH OF HIGH SPEED
CLOSING TARGETS
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2ANGE 'ATING 2ANGE GATING DIVIDES THE TIME BETWEEN TRANSMIT PULSES INTO MUL
TIPLE CELLS OR RANGE GATES 2ANGE GATING ELIMINATES EXCESS RECEIVER NOISE AND CLUTTER
FROM COMPETING WITH THE SIGNAL AND PERMITS TARGET TRACKING AND RANGE MEASUREMENT
4HE RANGE GATE IS TYPICALLY MATCHED TO THE BANDWIDTH OF THE TRANSMIT PULSE )N A SURVEIL
LANCE RADAR A NUMBER OF RECEIVER GATES ARE USED TO DETECT TARGETS THAT MAY APPEAR AT
ANY RANGE WITHIN THE INTERPULSE PERIOD &IGURE ILLUSTRATES THE GENERAL CASE WHERE THE
GATE SPACING SS THE GATE WIDTH SG AND THE TRANSMITTED PULSE ST ARE ALL UNEQUAL 3ELECTING
ST SG MAXIMIZES TARGET RETURN SIGNAL TO NOISE RATIO AND AS A RESULT RANGE PERFORMANCE
3ELECTING SG SS CREATES OVERLAPPED RANGE GATES AND REDUCES THE RANGE GATE STRADDLE
LOSS 3ECTION BUT CAN INCREASE THE POSSIBILITY OF RANGE GHOSTS UNLESS CONTIGUOUS
DETECTIONS FROM STRADDLED TARGET RETURNS ARE hCLUMPEDv PRIOR TO THE AMBIGUITY RESOLU
TION 3ECTION 7ITH RANGE GATING THE RANGE MEASUREMENT ACCURACY IS ON THE ORDER
OF THE RANGE GATE SIZE MMS BUT THIS CAN BE IMPROVED TO A FRACTION OF THE GATE
WIDTH BY AMPLITUDE CENTROIDING
4IMELINE $EFINITIONS 0ULSE DOPPLER RADAR WORKS ON SEVERAL DIFFERENT TIME
SCALES 6ARIOUS ORGANIZATIONS HAVE THEIR OWN NOMENCLATURE FOR TIME BASED PARAMETERS
4HEREFORE THE TIMELINE DEFINITIONS USED THROUGHOUT THIS CHAPTER ARE DEFINED HERE
&IGURE ILLUSTRATES THE DIFFERENT TIME SCALES 3TARTING AT THE LOWEST LEVEL A SERIES
OF COHERENT PULSES ARE TRANSMITTED AT A PULSE REPETITION FREQUENCY 02& 4HE TIME
BETWEEN THE PULSES IS THE INTERPULSE PERIOD )00 WHICH IS SIMPLY THE INVERSE OF THE
02& 4HE RECEIVE PORTION OF THE )00 IS BROKEN UP INTO RANGE GATES 4HE TRANSMIT DUTY
CYCLE IS THE TRANSMIT PULSE WIDTH DIVIDED BY THE )00 4HE TRAIN OF PULSES IS CALLED THE
COHERENT PROCESSING INTERVAL #0) 4HE COHERENT PROCESSING FORMS A BANK OF DOPPLER
&)'52% %XAMPLE OF RANGE GATES WITH OVERLAP EQUALLY SPACED IN THE INTERPULSE PERIOD
SB REPRESENTS THE EXTRA BLANKING TIME AFTER THE TRANSMIT PULSE TO ALLOW FOR RECEIVERPROTECTOR RECOVERY
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&)'52% 0ULSE DOPPLER DWELL TIMELINE
FILTERS FOR EACH RANGE GATE RESULTING IN A RANGE DOPPLER MAP FOR A #0) SIMILAR TO THAT
SHOWN IN &IGURE 3EVERAL #0)S WITH THE SAME 02& BUT POSSIBLY DIFFERENT TRANSMIT CARRIER FREQUEN
CIES CAN BE NONCOHERENTLY COMBINED VIA POSTDETECTION INTEGRATION 0$) )F FREQUENCY
MODULATION &- RANGING IS USED ALL THE #0)S THAT ARE NONCOHERENTLY INTEGRATED MUST
HAVE THE SAME &- SLOPE 4HE GROUPING OF #0)S IS A LOOK $ETECTIONS ARE DETERMINED
FOR THE RANGE DOPPLER CELLS IN A LOOK
-ULTIPLE LOOKS WITH DIFFERENT 02&S OR FREQUENCY MODULATIONS ARE USED TO RESOLVE
RANGE ANDOR DOPPLER AMBIGUITIES 4HIS GROUP OF LOOKS IS A DWELL ! DWELL IS ASSOCIATED
WITH A PARTICULAR ANTENNA LINE OF SIGHT OR BEAM POSITION 4ARGET REPORTS ARE GENERATED
FOR EACH DWELL
! BAR REFERS TO A LINE OF BEAM POSITIONS AT A CONSTANT ELEVATION )N SEARCH A MULTI
BAR RASTER SCANS THE BEAM OVER AN ASSIGNED AREA OR VOLUME TO CREATE A FRAME ! FRAME
MAY HAVE MULTIPLE BARS 4YPICALLY THE ANTENNA WILL VISIT EVERY BEAM POSITION ONCE
DURING A SEARCH FRAME
"ASIC #ONFIGURATION &IGURE SHOWS A REPRESENTATIVE CONFIGURATION OF A PULSE
DOPPLER RADAR UTILIZING DIGITAL SIGNAL PROCESSING UNDER THE CONTROL OF A MISSION PROCESSOR
)NCLUDED ARE THE ANTENNA RECEIVEREXCITER SIGNAL PROCESSOR AND DATA PROCESSOR 4HE
RADARS CONTROL PROCESSOR RECEIVES INPUTS FROM THE ON BOARD SYSTEMS SUCH AS THE INER
TIAL NAVIGATION SYSTEM ).3 AND OPERATOR CONTROLS VIA THE MISSION PROCESSOR AND
PERFORMS AS A MASTER CONTROLLER FOR THE RADAR HARDWARE
#OHERENT PROCESSING REQUIRES THAT ALL FREQUENCY DOWN CONVERSIONS INCLUDING THE
FINAL CONVERSION TO BASEBAND RETAIN THE COHERENT PHASE RELATIONSHIP BETWEEN TRANSMIT
TED AND RECEIVED PULSES !LL THE LOCAL OSCILLATORS ARE PHASE REFERENCED TO THE SAME MASTER
OSCILLATOR WHICH IS ALSO USED TO PRODUCE THE TRANSMITTED WAVEFORM 4HE IN PHASE )
AND QUADRATURE 1 COMPONENTS AT BASEBAND REPRESENT THE REAL AND IMAGINARY PARTS
RESPECTIVELY OF A COMPLEX NUMBER WHOSE COMPLEX ARGUMENT IN PHASOR NOTATION IS THE
PHASE DIFFERENCE BETWEEN THE TRANSMITTED AND RECEIVED PULSES 4HE COMPLEX MODULUS
OR MAGNITUDE IS PROPORTIONAL TO THE RECEIVED ECHO STRENGTH
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-ASTER /SCILLATOR 4HE MASTER OSCILLATOR PROVIDES A FREE RUNNING STABLE REFERENCE
SINUSOID ON WHICH THE SYSTEM SYNCHRONIZATION IS BASED
3YNCHRONIZER 4HE SYNCHRONIZER DISTRIBUTES PRECISELY TIMED STROBES AND CLOCKS FOR
THE VARIOUS COMPONENTS OF THE RADAR SYSTEM TO ENSURE THE TIME ALIGNMENT OF TRANSMIT
WAVEFORMS AND THE RECEPTION OF THEIR CORRESPONDING RETURNS 4HESE LOW JITTER TIMING
SIGNALS ARE USED TO ENABLE AND DISABLE THE TRANSMIT POWER AMPLIFIER TO CREATE THE TRANS
MIT PULSE TRAIN BLANK THE RECEIVER DURING TRANSMISSION AND FORM THE RANGE GATES
2EFERENCE 'ENERATOR
LOCAL OSCILLATORS ,/S 4HE REFERENCE GENERATOR OUTPUTS FIXED FREQUENCY CLOCKS AND
3YNTHESIZER 4HE SYNTHESIZER GENERATES THE TRANSMIT CARRIER FREQUENCY AND THE
FIRST LOCAL OSCILLATOR ,/ FREQUENCY &REQUENCY AGILITY IS PROVIDED TO THE TRANSMIT
AND ,/ SIGNALS
#LUTTER /FFSET 'ENERATOR 4HE CLUTTER OFFSET GENERATOR SHIFTS THE TRANSMIT CARRIER
SLIGHTLY SO THAT ON RECEIVE THE MAIN BEAM CLUTTER IS POSITIONED AT ZERO DOPPLER FRE
QUENCY OR $# DIRECT CURRENT AFTER BASEBANDING 4HE SAME EFFECT COULD BE OBTAINED
BY SHIFTING THE RECEIVER ,/ FREQUENCY 7ITH THE CLUTTER AT $# THE SPURIOUS SIGNALS
CAUSED BY CERTAIN RECEIVER NONLINEARITIES SUCH AS MIXER INTERMODULATION PRODUCTS AND
VIDEO HARMONICS ALSO FALL NEAR $# AND CAN BE FILTERED OUT ALONG WITH THE MAIN BEAM
CLUTTER 4HE FREQUENCY SHIFT APPLIED IS A FUNCTION OF THE ANTENNA MAIN BEAM LINE
OF SIGHT RELATIVE TO THE PLATFORMS VELOCITY VECTOR 4HIS PROCESS IS KNOWN AS CLUTTER
POSITIONING
/UTPUT 'ENERATOR 4HE OUTPUT GENERATES THE PULSED RADIO FREQUENCY 2& TRANSMIT
SIGNAL WHICH IS THE TRANSMIT DRIVE SIGNAL THAT IS AMPLIFIED BY THE POWER AMPLIFIER PRIOR
TO BEING FED TO THE TRANSMIT ANTENNA
!NTENNA 4HE ANTENNA CAN BE MECHANICALLY OR ELECTRONICALLY SCANNED -ODERN
PULSE DOPPLER RADARS HAVE MIGRATED TO THE USE OF ACTIVE ELECTRONICALLY SCANNED ARRAYS
!%3!S !%3!S CONTAIN TRANSMITRECEIVE 42 MODULES EACH COMPRISING A TRANS
MIT POWER AMPLIFIER AND A RECEIVE LOW NOISE AMPLIFIER ,.! ALONG WITH AN ATTENUATOR
AND PHASE SHIFTER AT EACH ANTENNA ELEMENT
)F THE SAME ANTENNA IS USED FOR TRANSMIT AND RECEIVE A DUPLEXER MUST BE INCLUDED
4HIS DUPLEXER IS USUALLY A PASSIVE DEVICE SUCH AS A CIRCULATOR WHICH EFFECTIVELY
SWITCHES THE ANTENNA BETWEEN THE TRANSMITTER AND RECEIVER #ONSIDERABLE POWER MAY
BE COUPLED TO THE RECEIVER SINCE TYPICALLY NO MORE THAN TO D" OF ISOLATION MAY
BE EXPECTED FROM FERRITE CIRCULATORS
!NTENNAS MAY FORM VARIOUS BEAMS 4HE TRANSMIT BEAM CAN BE FORMED WITH UNIFORM
APERTURE ILLUMINATION TO MAXIMIZE THE AMOUNT OF ENERGY ON TARGET WHEREAS THE RECEIVE
SUM 3 BEAM IS TYPICALLY FORMED WITH A LOW SIDELOBE TAPER TO MINIMIZE THE RETURNS
FROM GROUND CLUTTER 4HE 3 BEAM IS USED FOR TARGET DETECTION AND ACTING AS A SPATIAL FILTER
IS THE FIRST LINE OF DEFENSE AGAINST CLUTTER AND INTERFERENCE IN THE SIDELOBE REGION 4O
FACILITATE TARGET TRACKING ANGLE MEASUREMENTS WITH ACCURACIES FINER THAN THE ANTENNA
BEAMWIDTH ARE USUALLY REQUIRED ! TECHNIQUE TO OBTAIN SUCH ANGLE MEASUREMENTS OF
A TARGET ON A SINGLE PULSE IS CALLED MONOPULSE -ONOPULSE CAN BE CHARACTERIZED AS
AMPLITUDE OR PHASE WITH PHASE BEING PREFERABLE DUE TO ITS ADVANTAGE IN ANGLE ACCURACY
FOR A GIVEN SIGNAL TO NOISE RATIO 0HASE MONOPULSE USES A DELTA OR DIFFERENCE BEAM
05,3% $/00,%2 2!$!2
{°£Î
WHICH IS ESSENTIALLY FORMED BY DIVIDING THE APERTURE INTO TWO HALVES AND SUBTRACTING
THE CORRESPONDING PHASE CENTERS -ONOPULSE BEAMS DELTA AZIMUTH $!: AND DELTA
ELEVATION $%, ARE FORMED TO PROVIDE PHASE MONOPULSE AZIMUTH AND ELEVATION ANGLE
MEASUREMENTS 3ELF CALIBRATION ROUTINES CONTROLLED BY THE CONTROL PROCESSOR ENSURE
THAT THE PHASE AND AMPLITUDE MATCH OF THE RECEIVER CHANNELS ENABLES ACCURATE MONO
PULSE MEASUREMENTS ! GUARD BEAM WITH A NEAR OMNIDIRECTIONAL PATTERN IS FORMED FOR
SIDELOBE DETECTION BLANKING AS DISCUSSED IN 3ECTION 2ECEIVER0ROTECTOR 20 4HE RECEIVERPROTECTOR IS A LOW LOSS FAST RESPONSE
HIGH POWER SWITCH THAT PREVENTS THE TRANSMITTER OUTPUT FROM THE ANTENNAS DUPLEXER
FROM DAMAGING THE SENSITIVE RECEIVER FRONT END &AST RECOVERY IS REQUIRED TO MINIMIZE
DESENSITIZATION IN THE RANGE GATES FOLLOWING THE TRANSMITTED PULSE 20S CAN BE IMPLE
MENTED WITH A GAS DISCHARGE TUBE IN WHICH A GAS IS IONIZED BY HIGH POWER 2& ! DIODE
LIMITER CAN BE USED INSTEAD OF OR IN CONJUNCTION WITH THE GAS DISCHARGE TUBE 4HE 20
CAN BE REFLECTIVE OR ABSORPTIVE BUT MUST HAVE LOW INSERTION LOSS TO MINIMIZE IMPACT
ON RECEIVE CHAIN NOISE FIGURE
#LUTTER !UTOMATIC 'AIN #ONTROL #!'# 4HE #!'# ATTENUATOR IS USED BOTH FOR
SUPPRESSING TRANSMITTER LEAKAGE FROM THE 20 INTO THE RECEIVER SO THE RECEIVER IS NOT
DRIVEN INTO SATURATION WHICH COULD LENGTHEN RECOVERY TIME AFTER THE TRANSMITTER IS
TURNED OFF AND FOR CONTROLLING THE INPUT SIGNAL LEVELS INTO THE RECEIVER 4HE RECEIVED
LEVELS ARE KEPT BELOW SATURATION LEVELS TYPICALLY WITH A CLUTTER !'# IN SEARCH AND A
TARGET !'# IN SINGLE TARGET TRACK TO PREVENT SPURIOUS SIGNALS WHICH DEGRADE PERFOR
MANCE FROM BEING GENERATED
.OISE !UTOMATIC 'AIN #ONTROL .!'# 4HE .!'# ATTENUATOR IS USED TO SET THE
THERMAL NOISE LEVEL IN THE RECEIVER TO SUPPORT THE REQUIRED DYNAMIC RANGE AS DISCUSSED
IN 3ECTION 4HE ATTENUATION IS COMMANDED BASED ON MEASUREMENTS OF THE NOISE
DURING PERIODIC CALIBRATION
$IGITAL 0REPROCESSING 4HE ADVENT OF HIGH SPEED HIGH DYNAMIC RANGE ANALOG
TO DIGITAL CONVERTERS !$S ALLOWS )& SAMPLING AND DIGITAL BASEBANDING 4HE DIGITAL
)& SAMPLED OUTPUT OF THE RECEIVER IS DOWNCONVERTED TO BASEBAND $# VIA A DIGITAL
PRODUCT DETECTOR $0$ 3UPERIOR )1 IMAGE REJECTION IS AN ADVANTAGE OF A $0$
4HE ) AND 1 SIGNALS ARE PASSED THROUGH THE DIGITAL PORTION OF THE PULSE MATCHED
FILTER 4HE COMBINATION OF THE )& MATCHED FILTER AND THE DIGITAL MATCHED FILTER FORM THE
RECEIVERS SINGLE PULSE MATCHED FILTER
$IGITAL 3IGNAL 0ROCESSING &OLLOWING DIGITAL PREPROCESSING IS A DOPPLER FIL
TER BANK FOR MAIN BEAM CLUTTER REJECTION AND COHERENT INTEGRATION 2& INTERFERENCE
2&) THAT IS PULSED AND ASYNCHRONOUS TO THE RADAR TIMING CAN OFTEN BE DETECTED
PRIOR TO THE COHERENT INTEGRATION 2ANGE )00 CELLS WHERE 2&) IS DETECTED ARE THEN
hREPAIREDv TO PREVENT CORRUPTION OF THE OUTPUT SPECTRUM 4HE FILTER BANK IS USUALLY
REALIZED BY USING THE FAST &OURIER TRANSFORM &&4 HOWEVER THE DISCRETE &OURIER
TRANSFORM $&4 CAN BE USED WHEN THE NUMBER OF FILTERS IS SMALL !PPROPRIATE
WEIGHTING IS EMPLOYED TO REDUCE THE FILTER SIDELOBES 4HE AMOUNT OF WEIGHTING CAN
BE CHOSEN ADAPTIVELY BY SENSING THE PEAK SIGNAL LEVELS USUALLY MAIN BEAM CLUTTER
AND SELECTING THE DOPPLER WEIGHTING DYNAMICALLY
)F PULSE COMPRESSION MODULATION IS USED ON THE TRANSMIT PULSE TO INCREASE ENERGY ON
TARGET PULSE COMPRESSION CAN BE PERFORMED DIGITALLY EITHER BEFORE OR AFTER THE DOPPLER
{°£{
2!$!2 (!.$"//+
FILTER BANK 4HE ADVANTAGE OF PULSE COMPRESSION AFTER THE FILTER BANK IS THAT THE EFFECTS OF
DOPPLER ON PULSE COMPRESSION CAN BE LARGELY REMOVED BY TAILORING THE PULSE COMPRES
SION TO THE DOPPLER OFFSET OF EACH DOPPLER FILTER (OWEVER THIS INCREASES THE TOTAL AMOUNT
OF SIGNAL PROCESSING REQUIRED
4HE ENVELOPE AT THE OUTPUT OF THE &&4 IS FORMED WITH A LINEAR ) 1 OR SQUARE
LAW ) 1 DETECTOR (ISTORICALLY LINEAR DETECTORS WERE USED TO MANAGE DYNAMIC
RANGE IN FIXED POINT PROCESSORS 3QUARE LAW DETECTORS ARE PREFERRED FOR SOME MODERN
FLOATING POINT PROCESSORS 0OSTDETECTION INTEGRATION 0$) MAY BE USED WHERE EACH
RANGE GATE DOPPLER FILTER OUTPUT IS LINEARLY SUMMED OVER SEVERAL #0)S &OR EACH RANGE
DOPPLER CELL IN THE 3 CHANNEL THE 0$) OUTPUT IS COMPARED WITH A DETECTION THRESHOLD
DETERMINED BY A CONSTANT FALSE ALARM RATE #&!2 PROCESSn #ELLS WITH AMPLITUDES
GREATER THAN THE #&!2 THRESHOLD ARE LABELED AS DETECTIONS
3IMILAR PROCESSING IS DONE IN THE $!: AND $%, CHANNELS WITH EXCEPTIONS AS SHOWN IN
&IGURE &OR THOSE RANGE DOPPLER CELLS WITH DECLARED DETECTIONS THE IMAGINARY PART
OF THE $!:3 AND $%,3 RATIOS ARE USED FOR PHASE COMPARISON MONOPULSE TO ESTIMATE THE
AZIMUTH AND ELEVATION ANGLES RESPECTIVELY RELATIVE TO THE CENTER OF THE 3 MAIN BEAM
4HE ANGLE ESTIMATES ARE COMPUTED FOR EACH COHERENT LOOK AND THEN AVERAGED OVER THE
NUMBER OF #0)S NONCOHERENTLY INTEGRATED VIA 0$)
4HE GUARD CHANNEL IS PROCESSED SIMILAR TO THE 3 CHANNEL 4HE GUARD CHANNELS PUR
POSE IS TO BLANK SIDELOBE DETECTIONS AS DESCRIBED IN 3ECTION 0OSTPROCESSING &OLLOWING THE #&!2 IS DETECTION EDITING WHICH CONTAINS THE SIDE
LOBE DISCRETE REJECTION LOGIC &OLLOWING DETECTION EDITING RANGE AND VELOCITY AMBI
GUITY RESOLVERS WORK OVER SEVERAL LOOKS WITHIN A DWELL 4HE FINAL DETECTION OUTPUTS
ALONG WITH THEIR CORRESPONDING UNAMBIGUOUS RANGE VELOCITY AND ANGLE MEASUREMENTS
AND THEIR ESTIMATED ACCURACIES ARE PASSED TO THE MISSION PROCESSOR FOR TRACKING AND
OPERATOR DISPLAY
{°ÓÊ *1- Ê "** ,Ê 1// ,
'ENERAL #LUTTER RETURNS FROM VARIOUS SCATTERERS HAVE A STRONG INFLUENCE ON THE DESIGN
OF A PULSE DOPPLER RADAR AS WELL AS AN EFFECT ON THE PROBABILITY OF DETECTION OF POINT TARGETS
#LUTTER SCATTERERS INCLUDE TERRAIN BOTH LAND AND SEA WEATHER RAIN SNOW ETC AND CHAFF
3INCE THE ANTENNAS GENERALLY USED IN PULSE DOPPLER RADARS HAVE A SINGLE RELATIVELY HIGH
GAIN MAIN BEAM MAIN BEAM CLUTTER MAY BE THE LARGEST SIGNAL HANDLED BY THE RADAR WHEN
IN A DOWN LOOK CONDITION 4HE NARROW BEAM LIMITS THE FREQUENCY EXTENT OF THIS CLUTTER
TO A RELATIVELY SMALL PORTION OF THE DOPPLER SPECTRUM 4HE REMAINDER OF THE ANTENNA PAT
TERN CONSISTS OF SIDELOBES WHICH RESULT IN SIDELOBE CLUTTER 4HIS CLUTTER IS GENERALLY MUCH
SMALLER THAN THE MAIN BEAM CLUTTER BUT COVERS MUCH MORE OF THE FREQUENCY DOMAIN 4HE
SIDELOBE CLUTTER FROM THE GROUND DIRECTLY BELOW THE RADAR THE ALTITUDE LINE IS FREQUENTLY
LARGE OWING TO A HIGH REFLECTION COEFFICIENT AT STEEP GRAZING ANGLES THE LARGE GEOMETRIC
AREA AND THE SHORT RANGE 2ANGE PERFORMANCE IS DEGRADED FOR TARGETS IN THE SIDELOBE CLUTTER
REGION WHEREVER THE CLUTTER IS NEAR OR ABOVE THE RECEIVER NOISE LEVEL -ULTIPLE 02&S MAY
BE USED TO MOVE THE TARGET WITH RESPECT TO THE SIDELOBE CLUTTER IN THE RANGE DOPPLER MAP
THUS AVOIDING COMPLETELY BLIND RANGES OR BLIND FREQUENCIES DUE TO HIGH CLUTTER LEVELS 4HIS
RELATIVE MOTION OCCURS DUE TO THE RANGE AND DOPPLER FOLDOVER FROM RANGE ANDOR DOPPLER
AMBIGUITIES )F ONE 02& FOLDS SIDELOBE CLUTTER AND A TARGET TO THE SAME APPARENT RANGE AND
DOPPLER A SUFFICIENT CHANGE OF 02& WILL SEPARATE THEM
05,3% $/00,%2 2!$!2
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'ROUND #LUTTER IN A 3TATIONARY 2ADAR 7HEN THE RADAR IS FIXED WITH RESPECT
TO THE GROUND BOTH STATIONARY MAIN BEAM AND SIDELOBE CLUTTER RETURNS OCCUR AT ZERO
DOPPLER OFFSET FROM THE TRANSMIT CARRIER FREQUENCY 4HE SIDELOBE CLUTTER IS USUALLY
SMALL COMPARED WITH MAIN BEAM CLUTTER AS LONG AS SOME PART OF THE MAIN BEAM
STRIKES THE GROUND 4HE CLUTTER CAN BE CALCULATED AS IN A PULSED RADAR THEN FOLDED IN
RANGE AS A FUNCTION OF THE 02&
'ROUND #LUTTER IN A -OVING 2ADAR 7HEN THE RADAR IS MOVING WITH A VELOCITY
62 THE CLUTTER IS SPREAD OVER THE FREQUENCY DOMAIN AS ILLUSTRATED IN &IGURE FOR THE
SPECIAL CASE OF HORIZONTAL MOTION 4HE FOLDOVER IN RANGE AND DOPPLER IS ILLUSTRATED
IN &IGURE FOR A MEDIUM 02& RADAR WHERE THE CLUTTER IS AMBIGUOUS IN BOTH RANGE
AND DOPPLER 4HE RADAR PLATFORM IS MOVING TO THE RIGHT AT KT WITH A DIVE ANGLE
OF — 4HE NARROW ANNULI ISO RANGE CONTOURS DEFINE THE GROUND AREA THAT CONTRIBUTES
TO CLUTTER IN THE SELECTED RANGE GATE 4HE FIVE NARROW HYPERBOLIC BANDS ISO DOPPLER
CONTOURS DEFINE THE AREA THAT CONTRIBUTES TO CLUTTER IN THE SELECTED DOPPLER FILTER
4HE SHADED INTERSECTIONS REPRESENT THE AREA OR CLUTTER PATCHES THAT CONTRIBUTES TO
THE RANGE GATE DOPPLER FILTER CELL %ACH CLUTTER PATCH CONTRIBUTES CLUTTER POWER AS A
FUNCTION OF THE ANTENNA GAIN IN THE DIRECTION OF THE CLUTTER PATCH AND THE REFLECTIVITY
OF THE CLUTTER PATCH
4HE MAIN BEAM ILLUMINATES THE ELLIPTICAL AREA TO THE LEFT OF THE GROUND TRACK 3INCE
THIS AREA LIES ENTIRELY WITHIN THE FILTER AREA THE MAIN BEAM CLUTTER FALLS WITHIN THIS FILTER
AND ALL OTHER FILTERS RECEIVE SIDELOBE CLUTTER &OUR RANGE ANNULI ARE INTERSECTED BY THE
MAIN BEAM ELLIPSE SO THE MAIN BEAM CLUTTER IN THIS RANGE GATE IS THE VECTOR SUM OF
THE SIGNALS RECEIVED FROM ALL FOUR CLUTTER PATCHES /WING TO THIS HIGH DEGREE OF RANGE
FOLDOVER ALL RANGE GATES WILL HAVE APPROXIMATELY EQUAL CLUTTER
&)'52% 0LAN VIEW OF RANGE GATE AND DOPPLER FILTER AREAS 2ADAR ALTITUDE FT VELOCITY KT TO RIGHT DIVE ANGLE — RADAR WAVELENGTH CM 02& K(Z RANGE GATE WIDTH MS
RANGE GATE DOPPLER FILTER AT K(Z BANDWIDTH K(Z BEAMWIDTH — CIRCULAR MAIN BEAM AZIMUTH — DEPRESSION ANGLE —
{°£È
2!$!2 (!.$"//+
)F THE MAIN BEAM WERE SCANNED — IN AZIMUTH WITH THE SAME RADAR PLATFORM
KINEMATICS THE MAIN BEAM CLUTTER WOULD SCAN IN DOPPLER FREQUENCY SO THAT IT WOULD
APPEAR IN THE SELECTED FILTER TEN TIMES TWICE FOR EACH HYPERBOLIC BAND )N BETWEEN
THE FILTER WOULD RECEIVE SIDELOBE CLUTTER FROM ALL DARKENED INTERSECTIONS 7ITH THE USE
OF THE PROPER CLUTTER OFFSET WHICH WOULD VARY AS A FUNCTION OF MAIN BEAM AZIMUTH
ON THE TRANSMIT FREQUENCY AS DESCRIBED IN 3ECTION THE DOPPLER OF THE MAIN BEAM
CLUTTER RETURN WILL BE ZERO OR $#
#LUTTER 2ETURN 'ENERAL %QUATIONS 4HE CLUTTER TO NOISE RATIO FROM A SINGLE
CLUTTER PATCH WITH INCREMENTAL AREA D! AT A RANGE 2 IS
# .
0AV'4 '2 L S D!
P 2 ,# K4S "N
WHERE 0AV AVERAGE TRANSMIT POWER
'4 TRANSMIT GAIN IN PATCH DIRECTION
'2 RECEIVE GAIN IN PATCH DIRECTION
K OPERATING WAVELENGTH
R CLUTTER BACKSCATTER COEFFICIENT
,# LOSSES APPLICABLE TO CLUTTER
K "OLTZMANNS CONSTANT r 7(Z+
4S SYSTEM NOISE TEMPERATURE +
"N DOPPLER FILTER BANDWIDTH
,# REFERS TO LOSSES THAT APPLY TO DISTRIBUTED SURFACE CLUTTER AS OPPOSED TO DISCRETE
RESOLVABLE TARGETS 4HESE LOSSES WILL BE DISCUSSED IN 3ECTION 4HE CLUTTER TO NOISE RATIO FROM EACH RADAR RESOLUTION CELL IS THE INTEGRAL OF %Q OVER THE DOPPLER AND RANGE EXTENT OF EACH OF THE AMBIGUOUS CELL POSITIONS ON THE
GROUNDn 5NDER CERTAIN SIMPLIFIED CONDITIONS THE INTEGRATION CAN BE CLOSED FORM BUT IN GENERAL NUMERIC INTEGRATION IS REQUIRED
-AIN BEAM #LUTTER 4HE NET MAIN BEAM CLUTTER TO NOISE POWER IN A SINGLE RANGE
GATE IN THE RECEIVER CAN BE APPROXIMATED FROM %Q BY SUBSTITUTING THE RANGE GATES
CS
INTERSECTED AREA COS
@ 2PAZ WITHIN THE MAIN BEAM ON THE GROUND FOR D! AND SUM
MING OVER ALL AMBIGUITIES OF THAT RANGE GATE THAT ARE WITHIN THE MAIN BEAM
'4 '2S # 0AV L QAZ CT £
. P ,# K4S "N
2 COSA
4HE SUMMATION LIMITS ARE THE LOWER AND UPPER EDGES IN THE ELEVATION DIMENSION OF THE
SMALLER OF THE TRANSMIT AND RECEIVE BEAMS
WHERE PAZ AZIMUTH HALF POWER BEAMWIDTH RADIANS
S COMPRESSED PULSE WIDTH
@ GRAZING ANGLE AT CLUTTER PATCH
4HE REMAINING TERMS ARE AS DEFINED FOLLOWING %Q )F THE MAIN BEAM IS POINTED BELOW THE HORIZON THE MAIN BEAM CLUTTER SPECTRAL WIDTH
$F DUE TO PLATFORM MOTION MEASURED D" DOWN FROM THE PEAK IS APPROXIMATELY
$F 62 ª
Q COSF SINQ L «¬ "
Q " COSF COSQ CT SIN F COSQ ¹
º
H COSF
»
05,3% $/00,%2 2!$!2
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WHERE 62 RADAR GROUND SPEED
K 2& WAVELENGTH
P" D" ONE WAY ANTENNA AZIMUTH BEAMWIDTH RADIANS
E MAIN BEAM DEPRESSION ANGLE RELATIVE TO LOCAL HORIZONTAL RADIANS
P MAIN BEAM AZIMUTH ANGLE RELATIVE TO THE HORIZONTAL VELOCITY RADIANS
S COMPRESSED PULSE WIDTH
H RADAR ALTITUDE
7HEN THE MAGNITUDE OF THE MAIN BEAM AZIMUTH ANGLE IS GREATER THAN HALF OF THE AZI
MUTH BEAMWIDTH \ Q \ q Q " THE MAIN BEAM CLUTTER POWER SPECTRAL DENSITY CAN BE
MODELED WITH A GAUSSIAN SHAPE WITH A STANDARD DEVIATION RC $F
-AIN BEAM #LUTTER &ILTERING )N A PULSE DOPPLER RADAR UTILIZING DIGITAL SIGNAL
PROCESSING MAIN BEAM CLUTTER IS REJECTED BY EITHER A COMBINATION OF A DELAY LINE CLUT
TER CANCELER -4) FILTER FOLLOWED BY A DOPPLER FILTER BANK OR BY A FILTER BANK WITH LOW
FILTER SIDELOBES WHICH ARE ACHIEVED VIA WEIGHTING )N EITHER CASE THE FILTERS AROUND
THE MAIN BEAM CLUTTER ARE BLANKED TO MINIMIZE FALSE ALARMS ON MAIN BEAM CLUTTER 4HIS
BLANKED REGION IN DOPPLER IS KNOWN AS THE MAIN BEAM CLUTTER NOTCH
4HE CHOICE BETWEEN THESE OPTIONS IS A TRADE OFF OF QUANTIZATION NOISE AND COM
PLEXITY VERSUS THE FILTER WEIGHTING LOSS )F A CANCELER IS USED FILTER WEIGHTING CAN BE
RELAXED OVER THAT WITH A FILTER BANK ALONE SINCE THE CANCELER REDUCES THE DYNAMIC
RANGE REQUIREMENTS INTO THE DOPPLER FILTER BANK IF THE MAIN BEAM CLUTTER IS THE LARGEST
SIGNAL 7ITHOUT A CANCELER HEAVIER WEIGHTING IS NEEDED TO REDUCE SIDELOBES TO A LEVEL
SO THAT THE FILTER RESPONSE TO MAIN BEAM CLUTTER IS BELOW THE THERMAL NOISE LEVEL 4HIS
WEIGHTING INCREASES THE FILTER NOISE BANDWIDTH AND HENCE INCREASES THE LOSS IN SIGNAL
TO NOISE RATIO
#HOOSING THE PROPER WEIGHTING IS A COMPROMISE BETWEEN REJECTING MAIN BEAM
CLUTTER AND MAXIMIZING TARGET SIGNAL TO NOISE RATIO 4O DYNAMICALLY MAKE THIS COM
PROMISE THE FILTER WEIGHTING CAN BE ADAPTIVE TO THE MAIN BEAM CLUTTER LEVEL BY MEA
SURING THE PEAK RETURN LEVEL USUALLY MAIN BEAM CLUTTER OVER THE )00S AND SELECTING
OR COMPUTING THE BEST WEIGHTING TO APPLY ACROSS THE #0) !NOTHER TECHNIQUE THAT
IS APPLICABLE TO HIGH MEDIUM AND HIGH 02& IS TO GENERATE A HYBRID FILTER WEIGHT
ING BY CONVOLVING TWO WEIGHTING FUNCTIONS 4HE RESULT IS A FILTER WITH SIGNIFICANTLY
LESS WEIGHTING LOSS AND LOW FAR OUT SIDELOBES BUT AT A COST OF RELATIVELY HIGH NEAR
IN SIDELOBES
4O EVALUATE THE EFFECT OF MAIN BEAM CLUTTER ON TARGET DETECTION PERFORMANCE
THE CLUTTER TO NOISE RATIO MUST BE KNOWN FOR EACH FILTER WHERE TARGETS ARE TO BE
DETECTED ! GENERAL MEASURE THAT CAN BE EASILY APPLIED TO SPECIFIC CLUTTER LEVELS IS
THE IMPROVEMENT FACTOR ) 7HEN USING A DOPPLER FILTER BANK AS OPPOSED TO AN -4)
FILTER THE IMPROVEMENT FACTOR IS DEFINED FOR EACH DOPPLER FILTER AS THE RATIO OF THE
SIGNAL TO CLUTTER POWER AT THE OUTPUT OF THE DOPPLER FILTER TO THE SIGNAL TO CLUTTER
POWER AT THE INPUT 4HE SIGNAL IS ASSUMED TO BE AT THE CENTER OF THE DOPPLER FILTER
)NCORPORATING THE EFFECT OF FILTER WEIGHTING THE IMPROVEMENT FACTOR FOR A DOPPLER
FILTER IS GIVEN BY
) + . . §. ¶
¨£ !N ·
©N ¸
£ £ !N !M EXP [ §©P N M S C4 ¶¸ ] COS;P + N M .=
N M {°£n
2!$!2 (!.$"//+
WHERE !I )00 WEIGHT a I a . . NUMBER OF )00S IN #0)
RC STANDARD DEVIATION OF CLUTTER SPECTRUM
+ FILTER NUMBER + IS THE $# FILTER
4 INTERPULSE PERIOD
#LUTTER TRANSIENT 3UPPRESSION 7HEN THE 02& IS CHANGED FOR MULTIPLE
02& RANGING THE SLOPE IS CHANGED IN LINEAR &- RANGING OR THE 2& CARRIER IS
CHANGED THE TRANSIENT CHANGE IN THE CLUTTER RETURN MAY CAUSE DEGRADATION UNLESS IT IS
PROPERLY HANDLED 3INCE THE CLUTTER IS USUALLY AMBIGUOUS IN RANGE IN A PULSE DOPPLER
RADAR THE CLUTTER POWER INCREASES AT EACH INTERPULSE PERIOD )00 AS CLUTTER RETURN IS
RECEIVED FROM THE FARTHER AMBIGUITIES UNTIL THE HORIZON IS REACHED 4HIS PHENOMENON
IS CALLED SPACE CHARGING .OTE THAT ALTHOUGH AN INCREASING NUMBER OF CLUTTER RETURNS
ARE RECEIVED DURING THE CHARGING PERIOD THE VECTOR SUM MAY ACTUALLY DECREASE OWING
TO THE RANDOM PHASE RELATIONS OF THE RETURNS FROM DIFFERENT PATCHES
)F A CLUTTER CANCELER -4) FILTER IS USED THE OUTPUT CANNOT BEGIN TO SETTLE TO ITS
STEADY STATE VALUE UNTIL SPACE CHARGING IS COMPLETE 3OME SETTLING TIME MUST BE
ALLOWED BEFORE SIGNALS ARE PASSED TO THE FILTER BANK 4HEREFORE THE COHERENT INTEGRA
TION TIME AVAILABLE DURING EACH #0) IS REDUCED FROM THE TOTAL #0) TIME BY THE SUM OF
THE SPACE CHARGE TIME AND THE TRANSIENT SETTLING TIME 4HE CANCELER SETTLING TIME CAN
BE ELIMINATED BY PRECHARGING THE CANCELER WITH THE STEADY STATE INPUT VALUE 4HIS IS
DONE BY CHANGING THE CANCELER GAINS SO THAT ALL DELAY LINES ACHIEVE THEIR STEADY STATE
VALUES ON THE FIRST )00 OF DATA
)F NO CANCELER IS USED SIGNALS CAN BE PASSED TO THE FILTER BANK AFTER THE SPACE CHARGE
IS COMPLETE SO THAT THE COHERENT INTEGRATION TIME IS THE TOTAL #0) TIME MINUS THE SPACE
CHARGE TIME
!LTITUDE LINE #LUTTER "LANKING 4HE REFLECTION FROM THE EARTH DIRECTLY BENEATH
AN AIRBORNE PULSE RADAR IS CALLED ALTITUDE LINE CLUTTER "ECAUSE OF SPECULAR REFLEC
TION OVER SMOOTH TERRAIN THE LARGE GEOMETRIC AREA AND RELATIVELY SHORT RANGE THIS
SIGNAL CAN BE LARGE )T LIES WITHIN THE SIDELOBE CLUTTER REGION OF THE PULSE DOPPLER
SPECTRUM
"ECAUSE IT CAN BE MUCH LARGER THAN DIFFUSE SIDELOBE CLUTTER AND USUALLY HAS A
RELATIVELY NARROW SPECTRAL WIDTH ALTITUDE LINE CLUTTER IS OFTEN REMOVED EITHER BY A
SPECIAL #&!2 THAT PREVENTS DETECTION OF THE ALTITUDE LINE OR BY A TRACKER BLANKER
THAT REMOVES THESE REPORTS FROM THE FINAL OUTPUT )N THE CASE OF THE TRACKER BLANKER
A CLOSED LOOP TRACKER IS USED TO POSITION RANGE AND VELOCITY GATES AROUND THE ALTITUDE
RETURN AND BLANK THE AFFECTED RANGE DOPPLER REGION .OTE THAT AT VERY LOW ALTITUDES
THE ANGLES THAT SUBTEND THE FIRST RANGE GATE ON THE GROUND CAN BE QUITE BIG AND THE
SPECTRAL WIDTH WIDENS
3IDELOBE #LUTTER 4HE ENTIRE CLUTTER SPECTRUM CAN BE CALCULATED FOR EACH RANGE
GATE BY %Q IF THE ANTENNA PATTERN IS KNOWN IN THE LOWER HEMISPHERE )N PRELIMINARY
SYSTEM DESIGN THE EXACT GAIN FUNCTION MAY NOT BE KNOWN SO ONE USEFUL APPROXIMATION
IS THAT THE SIDELOBE RADIATION IS ISOTROPIC WITH A CONSTANT GAIN OF '3,
3IDELOBE $ISCRETES !N INHERENT CHARACTERISTIC OF AIRBORNE PULSE DOPPLER RADARS
IS THAT ECHOES FROM LARGE RESOLVABLE OBJECTS ON THE GROUND DISCRETES SUCH AS BUILD
INGS MAY BE RECEIVED THROUGH THE ANTENNA SIDELOBES AND APPEAR AS THOUGH THEY WERE
{°£™
05,3% $/00,%2 2!$!2
SMALLER MOVING TARGETS IN THE MAIN BEAM 4HIS IS A PARTICULARLY SEVERE PROBLEM IN
A MEDIUM 02& RADAR WHERE ALL ASPECT TARGET PERFORMANCE IS USUALLY DESIRED SINCE
THESE RETURNS COMPETE WITH TARGETS OF INTEREST )N A HIGH 02& RADAR THERE IS LITTLE IF ANY
RANGE REGION CLEAR OF SIDELOBE CLUTTER SUCH THAT THE SIDELOBE CLUTTER PORTION OF THE DOP
PLER SPECTRUM IS OFTEN NOT PROCESSED SINCE TARGET DETECTABILITY IS SEVERELY DEGRADED IN
THIS REGION &URTHER IN A HIGH 02& RADAR ESPECIALLY AT HIGHER ALTITUDES THE RELATIVE
AMPLITUDES OF THE DISTRIBUTED SIDELOBE CLUTTER AND THE DISCRETE RETURNS ARE SUCH THAT THE
DISCRETES ARE NOT VISIBLE IN THE SIDELOBE CLUTTER
4HE APPARENT RADAR CROSS SECTION 2#3 RAPP OF A SIDELOBE DISCRETE WITH AN 2#3
OF R IS RAPP R '3, WHERE '3, IS THE SIDELOBE GAIN RELATIVE TO THE MAIN BEAM 4HE
LARGER SIZE DISCRETES APPEAR WITH A LOWER DENSITY THAN THE SMALLER ONES AND A MODEL
COMMONLY ASSUMED AT THE HIGHER RADAR FREQUENCIES IS SHOWN IN 4ABLE 4HUS AS A
PRACTICAL MATTER M DISCRETES ARE RARELY PRESENT M ARE SOMETIMES PRESENT AND
M ARE OFTEN PRESENT
4WO MECHANIZATIONS FOR DETECTING AND ELIMINATING FALSE REPORTS FROM SIDELOBE DIS
CRETES ARE THE GUARD CHANNEL AND POSTDETECTION SENSITIVITY TIME CONTROL 34# 4HESE
ARE DISCUSSED IN THE PARAGRAPHS THAT FOLLOW
'UARD #HANNEL 4HE GUARD CHANNEL MECHANIZATION COMPARES THE OUTPUTS OF
TWO PARALLEL RECEIVING CHANNELS ONE CONNECTED TO THE MAIN ANTENNA AND THE SEC
OND TO A GUARD ANTENNA THE 3 AND 'UARD CHANNEL IN &IGURE RESPECTIVELY TO
DETERMINE WHETHER A RECEIVED SIGNAL IS IN THE MAIN BEAM OR THE SIDELOBESn 4HE
GUARD CHANNEL USES A BROAD BEAM ANTENNA THAT IDEALLY HAS A PATTERN ABOVE THE
MAIN ANTENNA SIDELOBES 4HE RETURNS FROM BOTH CHANNELS ARE COMPARED FOR EACH
RANGE DOPPLER CELL THAT HAD A DETECTION IN THE MAIN CHANNEL &OR THESE RANGE DOPPLER
CELLS WHEN THE GUARD CHANNEL RETURN IS GREATER THAN THAT OF THE MAIN CHANNEL THE
DETECTION IS REJECTED BLANKED )F THE MAIN CHANNEL RETURN IS HIGHER THE DETECTION
IS PASSED ON
! BLOCK DIAGRAM OF A GUARD CHANNEL MECHANIZATION IS SHOWN IN &IGURE !FTER
THE #&!2 WHICH IDEALLY WOULD BE IDENTICAL IN BOTH CHANNELS THERE ARE THREE THRESH
OLDS THE MAIN CHANNEL GUARD CHANNEL AND MAIN TO GUARD RATIO THRESHOLDS 4HE DETEC
TION LOGIC OF THESE THRESHOLDS IS ALSO SHOWN IN &IGURE 4HE BLANKING THAT OCCURS BECAUSE OF THE MAINGUARD COMPARISON AFFECTS THE
DETECTABILITY IN THE MAIN CHANNEL THE EXTENT OF WHICH IS A FUNCTION OF THE THRESH
OLD SETTINGS 4HE THRESHOLD SETTINGS ARE A TRADEOFF BETWEEN FALSE ALARMS DUE TO
SIDELOBE RETURNS AND DETECTABILITY LOSS IN THE MAIN CHANNEL !N EXAMPLE IS SHOWN
IN &IGURE FOR A NONFLUCTUATING TARGET WHERE THE ORDINATE IS THE PROBABILITY
OF DETECTION IN THE FINAL OUTPUT OF THE SIDELOBE BLANKER AND THE ABSCISSA IS THE
SIGNAL TO NOISE RATIO 3.2 IN THE MAIN CHANNEL 4HE QUANTITY " IS THE RATIO OF
THE GUARD CHANNEL 3.2 TO THE MAIN CHANNEL 3.2 AND IS ILLUSTRATED IN &IGURE 4!",% $ISCRETE #LUTTER -ODEL
2ADAR #ROSS 3ECTION M
$ENSITY PER SQUARE MILE
&)'52% '$
& & #'$
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&)'52% 0ROBABILITY OF DETECTION VERSUS SIGNAL TO NOISE RATIO WITH A GUARD CHANNEL
&)'52% -AIN AND GUARD ANTENNA PATTERNS
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2!$!2 (!.$"//+
" IS SMALL FOR A TARGET IN THE MAIN BEAM AND LARGE D" OR SO FOR A TARGET AT THE
SIDELOBE PEAKS )N THE EXAMPLE SHOWN THERE IS A D" DETECTABILITY LOSS DUE TO
THE GUARD BLANKING FOR TARGETS IN THE MAIN BEAM
)DEALLY THE GUARD ANTENNA GAIN PATTERN EXCEEDS THAT OF THE MAIN ANTENNA AT ALL ANGLES
IN SPACE EXCEPT FOR THE MAIN BEAM TO MINIMIZE DETECTIONS THROUGH THE SIDELOBES )F
NOT HOWEVER AS ILLUSTRATED IN &IGURE AND &IGURE RETURNS THROUGH THE SIDELOBE
PEAKS OF THE MAIN PATTERN ABOVE THE GUARD PATTERN HAVE A SIGNIFICANT PROBABILITY OF
DETECTION IN THE MAIN CHANNEL AND WOULD REPRESENT FALSE DETECTIONS
0OSTDETECTION 34# )N THE AMBIGUITY RESOLUTION AS THE OUTPUT RETURNS ARE
RANGE CORRELATED THEY ARE SUBJECTED TO POSTDETECTION 34# OR 2#3 THRESHOLDING
APPLIED INSIDE THE RANGE CORRELATION PROCESS 4ARGET RETURNS THAT RANGE CORRELATE
INSIDE THE 34# RANGE BUT FALL BELOW THE 34# THRESHOLD ARE LIKELY SIDELOBE DISCRETES
AND ARE BLANKED OR REMOVED FROM THE CORRELATION PROCESS AND KEPT FROM GHOSTING
WITH OTHER TARGETS 4HE BASIC LOGIC IS SHOWN IN &IGURE "ASICALLY THE #&!2 OUTPUT DATA IS
CORRELATED RESOLVED IN RANGE THREE TIMES %ACH CORRELATOR CALCULATES UNAMBIGUOUS
RANGE USING - OUT OF THE . SETS OF DETECTION DATA EG THREE DETECTIONS REQUIRED
OUT OF EIGHT 02&S .O DOPPLER CORRELATION IS USED SINCE THE DOPPLER IS AMBIGUOUS
4HE RESULTS OF THE FIRST TWO CORRELATIONS ARE USED TO BLANK ALL OUTPUTS THAT ARE LIKELY
TO BE SIDELOBE DISCRETES FROM THE FINAL RANGE CORRELATOR (ERE THREE RANGE CORRELA
TORS ARE USED IN WHICH THE FIRST THE ! CORRELATOR RESOLVES THE RANGE AMBIGUITIES
WITHIN SOME NOMINAL RANGE SAY NM BEYOND WHICH SIDELOBE DISCRETES ARE NOT
LIKELY TO BE DETECTED ! SECOND CORRELATOR THE " CORRELATOR RESOLVES THE RANGE
AMBIGUITIES OUT TO THE SAME RANGE BUT BEFORE A TARGET CAN ENTER THE " CORRELATOR
ITS AMPLITUDE IS THRESHOLDED BY A RANGE VARYING THRESHOLD THE 34# THRESHOLD ! RANGE GATE BY RANGE GATE COMPARISON IS MADE OF THE CORRELATIONS IN THE ! AND "
CORRELATORS AND IF A RANGE GATE CORRELATES IN ! AND NOT IN " THAT GATE IS BLANKED
OUT OF THE THIRD CORRELATOR THE # CORRELATOR 4HE # CORRELATOR RESOLVES THE RANGE
AMBIGUITIES WITHIN THE MAXIMUM RANGE OF INTEREST !N ALTERNATIVE MECHANIZATION
IS TO REPLACE THE RANGE VARYING 34# WITH AN EQUIVALENT 2#3 THRESHOLD INSIDE THE
RANGE CORRELATION PROCESS 4HE 2#3 IS COMPUTED FOR EACH POSSIBLE UNFOLDED RANGE
STARTING FROM THE SHORTEST RANGE AND COMPARED TO THE 2#3 THRESHOLD $ETECTIONS
THAT RANGE CORRELATE BUT ARE BELOW THE 2#3 THRESHOLD ARE PREVENTED FROM COR
RELATING WITH OTHER DETECTS AND ALL OF THEIR UNFOLDED RANGES ARE ALSO PREVENTED
FROM CORRELATING 4HE PRINCIPLE BEHIND THE POSTDETECTION 34# APPROACH IS ILLUSTRATED IN &IGURE WHERE THE RETURN OF A TARGET IN THE MAIN BEAM AND A LARGE DISCRETE TARGET IN THE SIDE
LOBES IS PLOTTED VERSUS UNAMBIGUOUS RANGE THAT IS AFTER THE RANGE AMBIGUITIES HAVE
BEEN RESOLVED !LSO SHOWN ARE THE NORMAL #&!2 THRESHOLD AND THE 34# THRESHOLD
VERSUS RANGE ! DISCRETE RETURN IN THE SIDELOBES IS BELOW THE 34# THRESHOLD AND A
RETURN IN THE MAIN BEAM IS ABOVE THE THRESHOLD SUCH THAT THE SIDELOBE DISCRETE CAN BE
RECOGNIZED AND BLANKED WITHOUT BLANKING THE TARGET IN THE MAIN BEAM 4HE 34# ONSET
RANGE REPRESENTS THE RANGE AT WHICH A LARGE DISCRETE TARGET IN THE SIDELOBES EXCEEDS THE
#&!2 THRESHOLD
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$OPPLER PROCESSING SEPARATES MOVING TARGETS FROM CLUTTER AND ALLOWS THEM TO BE
DETECTED WHILE ONLY COMPETING AGAINST THERMAL NOISE ASSUMING THAT THE TARGETS HAVE
SUFFICIENT RADIAL VELOCITY 62K AND THE 02& IS HIGH ENOUGH FOR AN UNAMBIGUOUS
CLUTTER SPECTRUM #OHERENCE THE CONSISTENCY OF PHASE OF A SIGNALS CARRIER FREQUENCY
FROM ONE PULSE TO THE NEXT IS CRUCIAL FOR DOPPLER PROCESSING 7ITHOUT CAREFUL SYSTEM
DESIGN AMPLITUDE AND PHASE INSTABILITIES DURING THE COHERENT INTEGRATION TIME WILL
BROADEN THE MAIN BEAM CLUTTER SPECTRUM AND RAISE THE NOISE FLOOR THAT CLUTTER FREE TAR
GETS MUST COMPETE WITH FOR DETECTION .ONLINEARITIES IN THE SYSTEM CAN ALSO CAUSE
DISCRETE SPURIOUS SPECTRAL SIGNALS THAT CAN BE MISTAKEN AS TARGETS 4HE INSTANTANEOUS
DYNAMIC RANGE OF THE SYSTEM GOVERNS THE SYSTEM LINEARITY AND HENCE SENSITIVITY IN A
STRONG CLUTTER ENVIRONMENT 4HE DRIVING FACTOR UPON STABILITY REQUIREMENTS IS WHEN THE
MAIN BEAM CLUTTER LEVEL IS AT THE SATURATION POINT OF THE RECEIVER
$YNAMIC 2ANGE $YNAMIC RANGE AS DISCUSSED HERE CAN BE REFERRED TO AS INSTAN
TANEOUS DYNAMIC RANGE AND IS THE LINEAR REGION ABOVE THERMAL NOISE OVER WHICH THE
RECEIVER AND SIGNAL PROCESSOR OPERATE BEFORE ANY SATURATION CLIPPING OR GAIN LIMITING
OCCURS )F SATURATIONS OCCUR SPURIOUS SIGNALS THAT DEGRADE PERFORMANCE MAY BE GENER
ATED &OR EXAMPLE IF MAIN BEAM CLUTTER SATURATES SPURIOUS FREQUENCIES CAN APPEAR
IN THE DOPPLER PASSBAND NORMALLY CLEAR OF MAIN BEAM CLUTTER AND THIS MAY GENERATE
FALSE TARGET REPORTS !N AUTOMATIC GAIN CONTROL !'# FUNCTION IS OFTEN EMPLOYED TO
PREVENT SATURATIONS ON EITHER MAIN BEAM CLUTTER IN SEARCH OR THE TARGET IN 3INGLE 4ARGET
4RACK MODE (OWEVER THE USE OF !'# DEGRADES THE SYSTEMS SENSITIVITY SO LARGE
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INSTANTANEOUS DYNAMIC RANGE IS PREFERABLE )F SATURATIONS OCCUR IN A RANGE GATE DURING
AN INTEGRATION PERIOD AN OPTION IN A MULTIPLE RANGE GATED SYSTEM IS SIMPLY TO BLANK
DETECTION REPORTS FROM THAT GATE 7HEN A -4) FILTER IS NOT USED THE DOPPLER FILTER BANK
FOR EACH RANGE GATE CAN BE EXAMINED TO DETERMINE IF THERE ARE ANY DETECTIONS DUE
TO SPURIOUS SIGNALS FROM LARGE CLUTTER WITH SUBSEQUENT EDITING OF THESE DETECTIONS IF
THE MEASURED CLUTTER TO NOISE RATIO EXCEEDS THE DYNAMIC RANGE 3IMILAR LOGIC CAN BE
APPLIED TO SATURATED RANGE GATES TO DETERMINE IF THE LARGEST SIGNAL IN THE FILTER BANK IS
IN THE PASSBAND OR REPRESENTS SATURATED CLUTTER RETURNS 3ATURATED RETURNS WITH THE PEAK
SIGNAL IN THE DOPPLER PASSBAND CAN REPRESENT VALID TARGETS AT SHORT RANGES AND NEED NOT
BE SUBJECTED TO THE SIDELOBE BLANKING LOGIC
4HE MOST STRESSING DYNAMIC RANGE REQUIREMENT IS DUE TO MAIN BEAM CLUTTER WHEN
SEARCHING FOR A SMALL LOW FLYING TARGETS (ERE FULL SENSITIVITY MUST BE MAINTAINED IN
THE PRESENCE OF THE CLUTTER TO MAXIMIZE THE PROBABILITY OF DETECTING THE TARGET
4HE DYNAMIC RANGE REQUIREMENT OF A PULSE DOPPLER RADAR AS DETERMINED BY MAIN
BEAM CLUTTER IS A FUNCTION NOT ONLY OF THE BASIC RADAR PARAMETERS SUCH AS POWER ANTENNA
GAIN ETC BUT OF RADAR ALTITUDE ABOVE THE TERRAIN AND THE RADAR CROSS SECTION 2#3 OF
LOW FLYING TARGETS !S AN EXAMPLE &IGURE SHOWS THE MAXIMUM CLUTTER TO NOISE
RATIO #.MAX THAT APPEARS IN THE AMBIGUOUS RANGE INTERVAL IE AFTER RANGE FOLDING FOR
A MEDIUM 02& RADAR AS A FUNCTION OF RADAR ALTITUDE AND THE RANGE OF THE INTERSECTION OF
THE PEAK OF THE MAIN BEAM WITH THE GROUND .OTE THAT THE CLUTTER TO NOISE RATIO IS A RMS
POWER RATIO MEASURED AT THE !$ CONVERTER ! PEAK POWER RATIO WOULD BE D" HIGHER
&)'52% $YNAMIC RANGE EXAMPLE
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2!$!2 (!.$"//+
4HE AMPLITUDE OF CLUTTER RETURNS FLUCTUATE OVER TIME AND ARE MODELED AS A STOCHASTIC
PROCESS 4HE CLUTTER TO NOISE RATIO REPRESENTS THE MEAN VALUE OF THIS PROCESS OVER TIME
&IGURE ASSUMES A PENCIL BEAM ANTENNA PATTERN AND A CONSTANT GAMMA MODEL FOR
CLUTTER REFLECTIVITY 4HE ANTENNA BEAM IS POINTED AT THE GROUND CORRESPONDING TO THE
RANGE OF THE TARGET !T LONGER RANGES SMALL LOOK DOWN ANGLES CLUTTER DECREASES WITH
INCREASING RADAR ALTITUDE SINCE RANGE FOLDING IS LESS SEVERE OWING TO LESS OF THE MAIN
BEAM INTERSECTING THE GROUND !T SHORTER RANGES CLUTTER INCREASES WITH RADAR ALTITUDE
SINCE THE CLUTTER PATCH SIZE ON THE GROUND INCREASES 7HILE &IGURE IS FOR A MEDIUM
02& RADAR SIMILAR CURVES RESULT FOR A HIGH 02& RADAR
!LSO SHOWN IN &IGURE IS THE SINGLE SCAN PROBABILITY OF DETECTION 0D VERSUS
RANGE FOR A GIVEN 2#3 TARGET IN A RECEIVER WITH UNLIMITED DYNAMIC RANGE )F IT IS
DESIRED TO HAVE THE LOW FLYING TARGET REACH AT LEAST SAY AN 0D BEFORE ANY GAIN
LIMITING IE THE USE OF !'# OCCURS THE DYNAMIC RANGE REQUIREMENT IS DRIVEN BY THE
MAIN BEAM CLUTTER LEVELS #.MAX OF D" AT FT D" AT FT AND D" AT
FT FOR THIS EXAMPLE 4HE HIGHER THE DESIRED PROBABILITY OF DETECTION OR THE LOWER
THE RADAR ALTITUDE THE MORE DYNAMIC RANGE IS REQUIRED &URTHER IF THE SPECIFIED TARGET
2#3 IS REDUCED THE DYNAMIC RANGE REQUIREMENT FOR THE SAME DESIRED 0D INCREASES AS
THE 0D VERSUS RANGE CURVE IN &IGURE SHIFTS TO THE LEFT
)N A PULSE DOPPLER RADAR USING DIGITAL SIGNAL PROCESSING THE !$ CONVERTERS ARE
USUALLY SELECTED TO HAVE A DYNAMIC RANGE THAT MEETS OR EXCEEDS THE USABLE DYNAMIC
RANGE SET BY THE MAXIMUM CLUTTER TO NOISE RATIO #.MAX AND THE SYSTEM STABILITY 4HE
PEAK DYNAMIC RANGE DEFINED AS THE MAXIMUM PEAK SINUSOIDAL SIGNAL LEVEL RELATIVE TO
THE RMS THERMAL NOISE LEVEL THAT CAN BE PROCESSED LINEARLY IS RELATED TO THE NUMBER OF
AMPLITUDE BITS IN THE !$ CONVERTER BY
¤ . !$ AMP ³
§ 3MAX ¶
LOG
¥ ;NOISE=
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QUANTA µ
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WHERE ;3MAX.=D" MAXIMUM INPUT PEAK SINUSOIDAL LEVEL RELATIVE TO RMS NOISE D"
.!$ AMP
NUMBER OF AMPLITUDE BITS NOT INCLUDING SIGN BIT IN THE !$
CONVERTER
;NOISE=QUANTA RMS THERMAL NOISE VOLTAGE LEVEL AT THE !$ CONVERTER QUANTA
4HE RMS THERMAL NOISE VOLTAGE LEVEL AT THE !$ CONVERTER IS GIVEN IN TERMS OF QUANTA
! SINGLE QUANTA REFERS TO A UNIT QUANTIZATION LEVEL OF THE !$ CONVERTER
&ROM THE RELATIONSHIP DESCRIBED ABOVE AND ASSUMING THE !$ CONVERTER LIMITS THE
DYNAMIC RANGE THE !$ CONVERTER SIZE CAN NOW BE DETERMINED !DDITIONAL MARGIN TO
ALLOW FOR MAIN BEAM CLUTTER FLUCTUATIONS ABOVE THE MEAN VALUE ALSO NEEDS TO BE CON
SIDERED 3INCE MAIN BEAM CLUTTER TIME FLUCTUATION STATISTICS ARE HIGHLY DEPENDENT ON
THE TYPE OF CLUTTER BEING OBSERVED SUCH AS SEA CLUTTER OR CLUTTER FROM AN URBAN AREA AND
ARE GENERALLY UNKNOWN A VALUE OF TO D" ABOVE THE RMS VALUE IS OFTEN ASSUMED
FOR THE MAXIMUM PEAK LEVEL THIS ALSO INCLUDES THE D" DIFFERENCE BETWEEN THE RMS
AND PEAK VALUES OF A SINUSOIDAL SIGNAL 4HUS THE REQUIRED NUMBER OF AMPLITUDE BITS IN
THE !$ CONVERTER AS DETERMINED BY THE MAIN BEAM CLUTTER IS
§;# .
MAX =D"
. !$ AMP q #%), ¨
¨
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LOG §©;NOISE=QUANTA ¶¸ ¶
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WHERE #%),X IS THE SMALLEST INTEGER q X 4HE INSTANTANEOUS DYNAMIC RANGE SUPPORTED
BY AN !$ CONVERTER IMPROVES ABOUT D" PER BIT
&OR THE EXAMPLE CITED IN &IGURE WHERE THE MAXIMUM #. IS D" AT A FT
RADAR ALTITUDE AND WITH A FLUCTUATION MARGIN OF D" AND THERMAL NOISE AT QUANTA
D" THE !$ CONVERTER REQUIRES AT LEAST AMPLITUDE BITS PLUS A SIGN BIT FOR A TOTAL
OF BITS TO ACHIEVE THE PEAK !$ DYNAMIC RANGE OF D" 4HE UPPER PORTION OF
&IGURE ILLUSTRATES THIS CASE 4HE LOWER PORTION OF &IGURE WILL BE USED IN THE
STABILITY DISCUSSION TO FOLLOW
3TABILITY 4O ACHIEVE THE THEORETICAL CLUTTER REJECTION AND TARGET DETECTION AND
TRACKING PERFORMANCE OF A PULSE DOPPLER SYSTEM THE REFERENCE FREQUENCIES TIMING SIG
NALS AND SIGNAL PROCESSING CIRCUITRY MUST BE EXTREMELY STABLEn )N MOST CASES THE
MAJOR CONCERN IS WITH SHORT TERM RATHER THAN LONG TERM STABILITY ,ONG TERM STABILITY
MAINLY AFFECTS VELOCITY OR RANGE ACCURACY OR SPURIOUS SIGNALS DUE TO 02& HARMONICS
BUT IS RELATIVELY EASY TO MAKE ADEQUATE 3HORT TERM STABILITY REFERS TO VARIATIONS WITHIN
THE ROUND TRIP RADAR ECHO TIME OR DURING THE SIGNAL COHERENT INTEGRATION TIME 4HE MOST
SEVERE STABILITY REQUIREMENTS RELATE TO THE GENERATION OF SPURIOUS MODULATION SIDEBANDS
ON THE MAIN BEAM CLUTTER WHICH RAISE THE SYSTEM NOISE FLOOR OR CAN APPEAR AS TARGETS AT
THE DETECTORS 4HUS THE MAXIMUM RATIO OF MAIN BEAM CLUTTER TO SYSTEM NOISE MEASURED
AT THE RECEIVER OUTPUT #. INCLUDING THE FLUCTUATION MARGIN AS DISCUSSED ABOVE IS THE
PREDOMINANT PARAMETER THAT DETERMINES STABILITY REQUIREMENTS
4ARGET RETURNS COMPETE WITH CLUTTER RETURNS AND NOISE FOR DETECTION 3UPPOSE DESIRED
TARGETS HAVE SUFFICIENT RADIAL SPEED SO THAT THEY LIE IN THE CLUTTER FREE REGION OF DOPPLER
FREQUENCY WHEN A PULSE DOPPLER WAVEFORM IS USED 4HESE TARGETS NOW HAVE TO COMPETE
ONLY WITH SYSTEM NOISE 4HIS NOISE CAN BE BOTH ADDITIVE AND MULTIPLICATIVE !DDITIVE
NOISE TENDS TO MASK MULTIPLICATIVE NOISE IN LOW PERFORMANCE RADARS
!DDITIVE NOISE SOURCES CAN BE EXTERNAL TO THE RADAR SUCH AS ATMOSPHERIC NOISE
SKY TEMPERATURE GROUND NOISE BLACK BODY RADIATION AND JAMMERS OR THEY CAN BE
INTERNAL SUCH AS THERMAL NOISE 4HERMAL NOISE IS ALSO KNOWN AS *OHNSON NOISE AND
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GAUSSIAN NOISE THE LATTER TERM ARISING FROM THE GAUSSIAN STATISTICS OF ITS VOLTAGE PROB
ABILITY DENSITY FUNCTION 4HERMAL NOISE IS ALWAYS PRESENT IN THE RADAR RECEIVER AND IS
THE ULTIMATE LIMIT ON RADAR SENSITIVITY 4HE ABSOLUTE LEVEL OF ADDITIVE NOISE SOURCES IS
DETERMINED BY THE SOURCE AND ITS RELATION TO THE RADAR 0ROPER SYSTEM DESIGN CAN REDUCE
THERMAL NOISE TO A LEVEL WHERE MULTIPLICATIVE NOISE CAN BECOME SIGNIFICANT IN LIMITING
THE RADAR SENSITIVITY
-ULTIPLICATIVE NOISE IS CHARACTERIZED BY EITHER A TIME VARYING AMPLITUDE AMPLI
TUDE MODULATION !- OR A TIME VARYING PHASE PHASE MODULATION 0- OR FREQUENCY
MODULATION &- 4HE ABSOLUTE LEVEL DEPENDS ON THE STRENGTH OF THE SIGNAL CARRIER
ON WHICH THE NOISE SOURCE IS RIDING -ULTIPLICATIVE NOISE SOURCES ARE FREQUENCY INSTA
BILITIES POWER SUPPLY RIPPLE AND NOISE F NOISE TIMING JITTER AND UNWANTED MIXER
PRODUCTS DISCRETES OR SPURS -ULTIPLICATIVE NOISE MODULATES RADAR RETURNS BY VARYING
THEIR AMPLITUDE OR PHASE AND IS PRESENT ON ALL RADAR RETURNS BEING MOST APPARENT ON
LARGE RETURNS SUCH AS MAIN BEAM CLUTTER 4HE RESULT IN THE SPECTRAL DOMAIN IS SPURIOUS
MODULATION SIDEBANDS 2ANDOM MULTIPLICATIVE NOISE BROADENS THE SPECTRUM OF THE CAR
RIER FREQUENCY $ISCRETE MULTIPLICATIVE NOISE SOURCES GENERATE DISCRETE SPECTRAL LINES
THAT CAN CAUSE FALSE ALARMS
3YSTEM STABILITY IS CHARACTERIZED BY THE OVERALL TWO WAY TRANSMIT AND RECEIVE
COMPOSITE SYSTEM FREQUENCY RESPONSE WHICH IS THE RETURN OF A NONFLUCTUATING TARGET
AS A FUNCTION OF DOPPLER FREQUENCY 3YSTEM FREQUENCY RESPONSE SHOULD BE DEFINED BY
THE DOPPLER PASSBAND 4HE FOCUS OF THIS SECTION WILL BE THE STABILITY REQUIREMENTS FOR
DOPPLER FREQUENCIES SEPARATED ENOUGH FROM THE CARRIER TO BE OUTSIDE THE GROUND MOV
ING TARGET NOTCH 4HE CONCERN IN THIS REGION IS WHITE PHASE NOISE WHICH DETERMINES THE
PHASE NOISE FLOOR ,OW FREQUENCY IE CLOSER TO THE CARRIER STABILITY IS MORE APPLICABLE
TO AIR TO GROUND PULSE DOPPLER MODES SUCH AS '-4) AND 3!2
4HE LOCATION OF AN INSTABILITY SOURCE WITHIN THE SYSTEM WILL DETERMINE WHETHER IT IS
IMPARTED UPON A RETURN SIGNAL VIA THE TRANSMIT PATH RECEIVE PATH OR BOTH )NSTABILITIES
EITHER ON TRANSMIT OR RECEIVE ARE CALLED INDEPENDENT 4HOSE IMPOSED ON BOTH TRANSMIT
AND RECEIVE ARE COMMON
!MPLITUDE INSTABILITIES CAUSED BY !- TEND TO BE CONSIDERED INDEPENDENT SINCE
THE ,/S DRIVE THE MIXERS IN THE RECEIVER INTO COMPRESSION !LSO TRANSMITTERS WORK
MOST EFFICIENTLY WHEN DRIVEN INTO COMPRESSION IE WHERE THE POWER AMPLIFIER IS SATU
RATED AND PROVIDES A CONSTANT OUTPUT POWER LEVEL REGARDLESS OF SMALL DEVIATIONS ON THE
INPUT )NSTABILITIES DUE TO 0- OF WHICH &- IS A SPECIAL CASE TEND TO DOMINATE THOSE
DUE TO !- !S SUCH THE FOCUS WILL BE ON PHASE DISTURBANCES RANDOM PHASE NOISE AND
DISCRETE SINUSOIDAL SIGNALS SPURIOUS SIGNALS 2ANDOM 0HASE .OISE 2ANDOM PHASE NOISE RIDING ON A LARGE SIGNAL CAN MASK
WEAK TARGET RETURNS 4HE OBJECT IS TO SPECIFY SYSTEM PHASE NOISE SO THAT IT IS WELL BELOW
THE THERMAL NOISE WHEN A LARGE SIGNAL AT THE !$ SATURATION LEVEL IS PRESENT IN THE
RECEIVER ! SIGNAL AT !$ SATURATION IS THE LARGEST SIGNAL THAT CAN BE LINEARLY PROCESSED
BY THE RADAR RECEIVER 4HEN THE RADAR SENSITIVITY IS LIMITED BY THERMAL NOISE ALWAYS
PRESENT PLUS A SMALL INCREASE IN THE TOTAL NOISE LEVEL CAUSED BY THE PHASE NOISE
4HE PHASE NOISE OF OSCILLATORS AND OTHER COMPONENTS IS TYPICALLY SPECIFIED AS THE
MULTIPLICATIVE NOISE THAT RIDES ON A CONTINUOUS WAVEFORM OR #7 PHASE NOISE )N PULSE
DOPPLER RADAR TRANSMIT GATING INTERRUPTS THE CONTINUOUS WAVEFORM TO PRODUCE A PULSED
WAVEFORM 'ATED PHASE NOISE IS THE RESULT OF GATING #7 PHASE NOISE 4HE SPECTRUM OF
A PULSED GATED SIGNAL IS DIFFERENT FROM #7 4HE RESULTING NOISE THE GATED NOISE CAN
BE MUCH DIFFERENT FROM THE #7 NOISE ESPECIALLY FOR LOW DUTY CYCLE WAVEFORMS AND
NOISE CLOSE TO THE CARRIER )T IS PREFERABLE TO MAKE NOISE MEASUREMENTS ON EQUIPMENT
{°Ó™
05,3% $/00,%2 2!$!2
UNDER THE SAME GATING CONDITIONS THAT WILL BE USED IN THE RADAR SYSTEM 3OME DEVICES
SUCH AS HIGH POWER TRANSMITTERS CANNOT OPERATE CONTINUOUSLY AND ONLY GATED NOISE
MEASUREMENTS ARE POSSIBLE 4HE GATED PHASE NOISE SPECTRUM IS THE SUMMATION OF THE
#7 PHASE NOISE SPECTRUM REPLICAS CENTERED AT FREQUENCIES o NF2 WHERE F2 IS THE 02&
AND N IS AN INTEGER 4HE TOTAL GATED PHASE NOISE IN THE 02& BANDWIDTH F2 EQUALS THE TOTAL
#7 PHASE NOISE IN THE TRANSMIT PULSE BANDWIDTH )N TERMS OF STABILITY REQUIREMENTS THE
SYSTEM REQUIREMENTS ARE DERIVED USING GATED PHASE NOISE WHICH IN TURN IS CONVERTED TO
A #7 VALUE FOR SPECIFYING COMPONENTS SUCH AS OSCILLATORS 4HE #7 PHASE NOISE FLOOR
IS SMALLER BY A FACTOR OF THE RATIO OF THE 02& TO THE TRANSMIT BANDWIDTH WHEN THE #7
PHASE NOISE IS ASSUMED TO BE WHITE
3ENSITIVITY LOSS DUE TO PHASE NOISE IS QUANTIFIED BY THE INCREASE IN THE SYSTEM NOISE
FLOOR IN THE hCLUTTER FREEv DOPPLER FILTERS DUE TO THE PHASE NOISE SIDEBANDS ON A LARGE
SIGNAL SUCH AS MAIN BEAM CLUTTER 3ENSITIVITY LOSS IS THE AMOUNT BY WHICH THE TOTAL
NOISE THERMAL PLUS PHASE EXCEEDS THE THERMAL NOISE LEVEL AS SHOWN IN %Q !
GATED PHASE NOISE TO THERMAL NOISE RATIO OF D" RESULTS IN AN APPROXIMATELY D"
SENSITIVITY LOSS 4HIS ASSUMES A WORST CASE SCENARIO WITH THE MAIN BEAM CLUTTER RETURN
AT THE !$ SATURATION LEVEL #!'# DISCUSSED IN 3ECTION IS TYPICALLY USED TO REGU
LATE THE MEAN CLUTTER TO A LEVEL BELOW !$ SATURATION TYPICALLY BY THE AMOUNT OF THE
EXPECTED CLUTTER FLUCTUATION LEVEL 7ITH #!'# SENSITIVITY LOSS WILL BE LESS THAN OR
EQUAL TO THE CALCULATED WORST CASE VALUE
¤
;3ENSITIVITY ,OSS=D" LOG ¥
¦
'ATED 0HASE .OISE 0OWER $ENSITY³
4HERMAL .OISE 0OWER $ENSIITY ´µ
4ABLE CONTAINS A CALCULATION OF THE PHASE NOISE FLOOR REQUIREMENTS FOR AN
K(Z 02& WAVEFORM #LUTTER LEVELS THAT REQUIRE A BIT SIGN PLUS AMPLITUDE
BITS !$ CONVERTER ARE ASSUMED AS SHOWN IN &IGURE 4HE TRANSMIT PULSE DURATION
IS MS RESULTING IN A TRANSMIT PULSE BANDWIDTH OF APPROXIMATELY -(Z SINCE
NO PULSE COMPRESSION IS USED 4HE RMS THERMAL NOISE POWER IS THE THERMAL NOISE FLOOR
WITHIN THE RECEIVE PORTION OF )00 4HIS POWER LEVEL IS GIVEN IN DECIBELS WITH RESPECT
TO THE CARRIER AMPLITUDE D"C 4HE THERMAL NOISE DENSITY IS OBTAINED BY DIVIDING THIS
POWER BY THE 02& BANDWIDTH 4HE MAXIMUM GATED PHASE NOISE FLOOR IS SET TO BE D"
BELOW THE THERMAL NOISE FLOOR FOR AT MOST A D" SENSITIVITY LOSS 4HE #7 PHASE NOISE
FLOOR IS THEN OBTAINED BY MULTIPLYING BY THE 02& TO TRANSMIT BANDWIDTH RATIO
4!",% #7 0HASE .OISE $ENSITY &LOOR #ALCULATION
0ARAMETER
4HERMAL .OISE 0OWER AT !$
6ALUE ;D"=
5NITS
D"C
02& "ANDWIDTH
D"(Z
4HERMAL .OISE $ENSITY &LOOR AT !$
0HASE .OISE TO 4HERMAL .OISE 2ATIO
D"C(Z
D"
'ATED 0HASE .OISE $ENSITY &LOOR
02& TO 4RANSMIT "ANDWIDTH 2ATIO
D"C(Z
D"
#7 0HASE .OISE $ENSITY &LOOR
D"C(Z
#OMMENT
BIT !$ SIGN BITS THERMAL
NOISE SET AT QUANTA
K(Z 02& WAVEFORM
-ARGIN FOR AT MOST D"
SENSITIVITY LOSS
-(Z TRANSMIT PULSE BANDWIDTH
MS PULSE WIDTH W NO 0#
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4!",% .OTIONAL 3UBSYSTEM 0HASE .OISE !LLOCATION
!LLOCATION
0ERCENTAGE
D"
!DJUSTMENT FOR
#OMMON 3OURCE ;D"=
2EQUIREMENT ;D"C(Z=
4RANSMITTER
!%XCITER
02ECIVER
3YNCHRONIZER
3YSTEM
3UBSYSTEM
4HE SYSTEM LEVEL #7 PHASE NOISE FLOOR REQUIREMENT D"C(Z IS ALLOCATED
TO THE CONTRIBUTING HARDWARE UNITS 4HE PERCENTAGES ARE BASED ON EXPERIENCE AND NEGO
TIATIONS WITH THE SUBSYSTEM DESIGNERS ! POSSIBLE ALLOCATION IS PROVIDED IN 4ABLE $ISCRETES 3OME SOURCES OF DISCRETE SIDEBANDS ARE RIPPLE ON POWER SUPPLIES AND
THE PICKUP OF DIGITAL CLOCKS )T IS DESIRABLE TO KEEP THE INTEGRATED DISCRETE SIDEBANDS
BELOW NOISE AT THE #&!2 INPUT TO PREVENT DETECTING THESE DISCRETES AND PRODUCING FALSE
ALARMS !LL COHERENT AND POSTDETECTION INTEGRATION MUST BE ACCOUNTED FOR WHEN WE
SPECIFY DISCRETE PHASE NOISE REQUIREMENTS
#OMMON DISCRETES ARE AFFECTED BY THE TIME DELAY BETWEEN THE PORTION IMPARTED
ON THE TRANSMIT AND THAT ON RECEIVE 4HE TIME DELAY CHANGES THE CORRELATION BETWEEN
THE PHASE OF THE SPURIOUS MODULATING FREQUENCY FROM THE TRANSMIT PATH WITH THE PHASE
FROM THE RECEIVE PATH 4HIS CAN RELIEVE THE COMMON DISCRETE LEVEL REQUIREMENT FOR
LOW 02& OR -4) WAVEFORMS THAT ARE RANGE UNAMBIGUOUS (OWEVER FOR HIGHLY RANGE
AMBIGUOUS MEDIUM 02& AND HIGH 02& WAVEFORMS THE ASSUMPTION IS MADE THAT THE
NOISE COMMON TO TRANSMIT AND RECEIVE ADDS NONCOHERENTLY IN THE DOWNCONVERSION
PROCESS !S A RESULT THE COMMON DISCRETE POWER INCREASES BY D"
4ABLE PROVIDES THE CALCULATION FOR THE SYSTEM REQUIREMENTS FOR INDEPENDENT
AND COMMON DISCRETE LEVELS !S IN 4ABLE A MAXIMUM CLUTTER LEVEL REQUIRING A
BIT !$ IS ASSUMED AND THE RMS THERMAL NOISE LEVEL AT THE !$ CONVERTER IS SET
TO QUANTA 4O FORM THE DOPPLER FILTERS PULSES ARE COHERENTLY INTEGRATED
4!",% $ISCRETE ,EVEL 2EQUIREMENT #ALCULATION
0ARAMETER
4HERMAL .OISE 0OWER AT !$
6ALUE ;D"= 5NITS
#OMMENT
D"C BIT !$ SIGN BITS THERMAL NOISE
SET AT QUANTA
.UMBER OF 0ULSES
#OHERENTLY )NTEGRATED
D"
)00S INTEGRATED PER #0)
$OPPER &ILTER 7EIGHTING
D"
D" $OLPH #HEBYSHEV WEIGHTING LOSS
.UMBER OF #0)S
.ONCOHERENTLY
)NTEGRATED
D"
0$) OF #0)S PER ,OOK LOG.PDI
4HERMAL .OISE 0OWER AT #&!2
D"C %FFECTIVE NOISE LEVEL AFTER INTEGRATION
4OTAL
)NTEGRATION
'AIN
$ISCRETE TO 4HERMAL .OISE -ARGIN
D"
)NDEPENDENT $ISCRETE 2EQUIREMENT
D"C
#OMMON $ISCRETE 2EQUIREMENT
D"C D" LESS THAN )NDEPENDENT $ISCRETE
0ROVIDES LOW 0&! DUE TO DISCRETES
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4O REDUCE DOPPLER FILTER SIDELOBES A D" $OLPH #HEBYSHEV WEIGHTING IS APPLIED
WHICH REDUCES THE COHERENT INTEGRATION 3.2 GAIN BY ABOUT D" &OR DETECTION
THREE #0)S ARE INTEGRATED NONCOHERENTLY VIA 0$) FOR AN APPROXIMATE INTEGRATION GAIN
IN D" OF LOG.0$) OR D" 4HIS RESULTS IN A THERMAL NOISE LEVEL OF D"C
AT THE DETECTOR ! DISCRETE TO THERMAL NOISE MARGIN OF D" IS USED TO PROVIDE A LOW
0&! DUE TO DISCRETES 4HE COMMON DISCRETE REQUIREMENT IS MADE D" MORE STRINGENT
RELATIVE TO THE INDEPENDENT REQUIREMENT AS DISCUSSED ABOVE
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-EDIUM AND HIGH MEDIUM 02& WAVEFORMS USUALLY USE MULTIPLE DISCRETE 02& RANGING
TO RESOLVE RANGE AMBIGUITIES WHILE LINEAR &- RANGING IS COMMONLY EMPLOYED WHEN
HIGH 02& WAVEFORMS ARE USED
-ULTIPLE $ISCRETE 02& 2ANGING 4HE TECHNIQUES FOR CALCULATING TRUE RANGE
FROM SEVERAL AMBIGUOUS MEASUREMENTS GENERALLY INVOLVE SEQUENTIAL MEASUREMENT OF
THE AMBIGUOUS RANGE IN EACH 02& FOLLOWED BY AN UNFOLDING AND CORRELATION PROCESS
4HE UNFOLDING CREATES A VECTOR OF POSSIBLE RANGES FOR EACH VALID DETECTION BY ADDING A
SET OF INTEGERS ; x += TIMES THE UNAMBIGUOUS RANGE INTERVAL
2UNFOLD 2AMBIGUOUS
C
;
F2
+=
WHERE THE UNAMBIGUOUS RANGE INTERVAL CF2 WITH C SPEED OF LIGHT AND F2 02&
4HE SET OF INTEGERS ;x+= ARE REFERRED TO AS THE RANGE AMBIGUITY NUMBERS WITH + DETER
MINED BY THE MAXIMUM RANGE OF INTEREST + #%),;2MAX F2 C= 2ANGE CORRELATION
OCCURS WHEN THE UNFOLDED DETECTIONS ARE SCANNED AND A CORRELATION WINDOW IS APPLIED
ACROSS LOOKS AS SHOWN IN &IGURE )N THIS EXAMPLE THE CORRELATED TARGET RANGE
HAS AN AMBIGUITY NUMBER OF TH TIME AROUND ECHO ON 02& AND AN AMBIGUITY
!"#!%#
$ $"
#!%
$ $"!"$!#" !
"
!"
!!# &)'52% 2ANGE CORRELATION EXAMPLE WITH 02&S
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NUMBER OF ON 02&S AND 4HE )00 LENGTHS OFTEN EXPRESSED IN RANGE GATES PER )00
ARE USUALLY KEPT RELATIVELY PRIME NO COMMON FACTORS EXCEPT THE NUMBER TO PERMIT
UNAMBIGUOUS RANGING AT THE MAXIMUM POSSIBLE RANGE
4HE LOGIC FOR CORRELATION REQUIRES AT LEAST - DETECTIONS ACROSS THE . 02&S IN A
DWELL TO DECLARE A TARGET REPORT WITH - TYPICALLY q FOR MEDIUM AND HIGH MEDIUM
02& WAVEFORMS 2ANGE GHOSTS OCCUR IF THE CORRELATED RANGE DOES NOT REPRESENT THE
TRUE TARGET RANGE AND TYPICALLY OCCUR WHEN THERE IS MORE THAN ONE DETECTION PER LOOK
2ANGE GHOSTS CAN ALSO OCCUR IF A TARGET DETECTION ON A SINGLE LOOK CORRELATED WITH OTHER
DISSIMILAR TARGETS OR IF MULTIPLE RANGE CORRELATIONS OCCURRED ON A SET OF DETECTIONS
CORRESPONDING TO A SINGLE UNIQUE TARGET IE MULTIPLE UNFOLDED RANGES FELL WITHIN THE
CORRELATION WINDOW /NE METHOD FOR EFFICIENTLY SCANNING AND CORRELATING THE UNFOLDED DETECTIONS
INVOLVES COARSE BINNING AS SHOWN IN &IGURE (ERE AMBIGUOUS DETECTIONS ARE
FIRST AMPLITUDE CENTROIDED AND THEN UNFOLDED AS DISCUSSED PREVIOUSLY BUT WITH THE
RESULTS STORED IN AN ARRAY WHOSE ELEMENTS ARE THE COARSE BINS 4HESE BINS HAVE A SIZE
LESS THAN OR EQUAL TO THE SHORTEST )00 AND CORRELATION INVOLVES SCANNING IDENTICAL BINS
ACROSS ALL OF THE 02&S IN THE DWELL AND APPLYING A CORRELATION WINDOW )N THE EXAMPLE
SHOWN IN &IGURE THE BINS ARE SET TO NINE RANGE GATES SHORTEST )00 LENGTH AND THE
FIFTH COARSE BIN CONTAINS DETECTIONS ACROSS THE THREE 02&S THAT FALL WITHIN THE CORRELA
TION WINDOW OF o RANGE GATES "LANK OR EMPTY BINS OCCUR WHEN THE UNFOLDED RANGE
FALLS OUTSIDE A PARTICULAR COARSE BIN INTERVAL +EY ADVANTAGES TO THIS APPROACH ARE THE
ABILITY TO CHANGE THE RANGE CORRELATION WINDOW DYNAMICALLY AND PERFORM MOTION COM
PENSATION EASILY FOR THE RANGE CHANGE ACROSS THE DWELL DUE TO RADAR PLATFORM MOTION
ANDOR THE TARGETS MOTION IF THE UNAMBIGUOUS DOPPLER HAS BEEN RESOLVED PRIOR TO THIS
PROCESS !DDITIONALLY THE RANGE GATE SIZES DO NOT NEED TO STAY THE SAME ACROSS THE
SET OF 02&S USED IN THE DWELL IN THIS CASE THE AMBIGUOUS RANGE GATE MEASUREMENTS
ON EACH LOOK ARE FIRST CONVERTED TO COMMON DISTANCE UNITS EG METERS PRIOR TO THE
UNFOLDING AND SCANNINGCORRELATION PROCESSES
%'$#'*(,)-"',' (%
)'! %%*(,+*#( #'!*
()*#'*#/#**+.
+"*"()+*+
' (%)'!*
&#!,(,* ' (%)'!*
&#!,(,*
' (%)'!*
&#!,(,* ())%+#('-#'( '!+*
&)'52% 2ANGE CORRELATION USING COARSE BINNING ON UNFOLDED CENTROIDED AMBIGUOUS DETECTIONS )N
THIS EXAMPLE RANGE GATE SIZE IS THE SAME FOR ALL THREE 02&S
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!DDITIONAL CRITERIA CAN BE USED TO REJECT RANGE GHOSTS SUCH AS SELECTING THE CORRE
LATED RANGE WITH THE HIGHEST - OF . VALUE SELECTING THE DETECTIONS BASED ON THE MINI
MUM VARIANCE ACROSS THE - DETECTIONS OR USING MAXIMUM LIKELIHOOD TECHNIQUES
4HE COMPUTED RADAR CROSS SECTION 2#3 OF CORRELATIONS CAN ALSO BE USED IN THE
CORRELATION PROCESS TO REJECT SIDELOBE DISCRETE DETECTIONS AS DESCRIBED IN 3ECTION POSTDETECTION 34# 4HE GHOSTING PROBLEM CAN BE MITIGATED FURTHER BY A COMBINATION OF DOPPLER ANDOR
MONOPULSE BINNING 2ESOLVING THE DOPPLER AMBIGUITIES FIRST PRIOR TO RANGE CORRELA
TION WILL REDUCE THE SET OF DETECTIONS TO THOSE WITHIN THE DOPPLER CORRELATION WINDOW
&OR CASES WHERE THIS IS NOT FEASIBLE GENERALLY THE LOWER MEDIUM 02&S UTILIZING BOTH
RANGE AND DOPPLER CORRELATION WILL REDUCE GHOSTS 5SING MONOPULSE MEASUREMENTS TO
SEGREGATE AND BIN TARGETS THAT ARE DISTINGUISHABLE IN ANGLE CAN ALSO REDUCE GHOSTING
WHEN THERE ARE A SIGNIFICANT NUMBER OF DETECTIONS IN A DWELL
! TYPICAL MEDIUM OR HIGH MEDIUM 02& PULSE DOPPLER WAVEFORM CYCLES THROUGH
. UNIQUE 02&S IN A PROCESSING DWELL . TYPICALLY BEING TO 4HE MEDIUM 02&S
GENERALLY COVER NEARLY AN OCTAVE IN FREQUENCY FOR GOOD DOPPLER VISIBILITY AND GROUND
MOVING TARGET REJECTION (OWEVER HIGH MEDIUM 02&S HAVE INHERENTLY GOOD DOPPLER
VISIBILITY SINCE THEY ARE AMBIGUOUS IN SIGN ONLY SO THE SPAN OF THE 02&S IN A SET OF
. 02&S IS USUALLY MUCH LESS THAN AN OCTAVE !DDITIONAL CONSTRAINTS ON 02& SELECTION
FOR BOTH WAVEFORMS INCLUDE GOOD VISIBILITY IN SIDELOBE CLUTTER WHERE SOME 02&S MAY
BE OBSCURED BY CLUTTER IN PORTIONS OF THE AMBIGUOUS RANGE INTERVAL AND MINIMIZATION
OF GHOSTS IN THE AMBIGUITY RESOLUTION PROCESSING
$OPPLER !MBIGUITY 2ESOLUTION 2ESOLUTION OF THE UNAMBIGUOUS DOPPLER VELOCITY
IS NEEDED FOR MEDIUM 02& WAVEFORMS AND IT IS GENERALLY DONE WITH A SIMILAR UNFOLDING
AND CORRELATION TECHNIQUE AS DESCRIBED PREVIOUSLY FOR RANGE AMBIGUITIES !S SHOWN IN
&IGURE VELOCITY UNFOLDING OF DETECTIONS INVOLVES ADDING A SET OF SIGNED INTEGERS
!
#!$
!$ "" #$ ! &)'52% $OPPLER VELOCITY CORRELATION PERFORMED ON TWO DETECTIONS ACROSS TWO LOOKS !MBIGUOUS
DETECTIONS ARE UNFOLDED OUT TO A MAXIMUM POSITIVE AND NEGATIVE VELOCITY
{°Î{
2!$!2 (!.$"//+
TIMES THE 02& VELOCITY FIRST BLIND SPEED TO EACH MEASURED AMBIGUOUS RADIAL VELOCITY
AS FOLLOWS
6UNFOLD F2 L ¤ &CENTROID
¥¦ . &&4
; *
³
+ =´
µ
WHERE F2K IS THE FIRST BLIND SPEED 02& VELOCITY &CENTROID IS THE AMPLITUDE CEN
TROIDED DOPPLER FILTER NUMBER .&&4 IS THE NUMBER OF FILTERS IN THE DOPPLER FILTER BANK
AND ; * x x += REPRESENTS THE SET OF DOPPLER AMBIGUITY NUMBERS COVERING THE
MAXIMUM NEGATIVE AND POSITIVE DOPPLER VELOCITIES FOR THE TARGETS OF INTEREST &OR
CASES WHERE THERE ARE ONLY A FEW AMBIGUITIES IN DOPPLER DOPPLER CORRELATION MAY BE
PERFORMED PRIOR TO OR IN CONJUNCTION WITH RANGE CORRELATION TO MINIMIZE GHOSTING
(IGH 02& 2ANGING 2ANGE AMBIGUITY RESOLUTION IN HIGH 02& IS PERFORMED BY
MODULATING THE TRANSMITTED SIGNAL AND OBSERVING THE PHASE SHIFT OF THE MODULATION
ON THE RETURN ECHO -ODULATION METHODS INCLUDE VARYING THE 02& EITHER CONTINU
OUSLY OR IN DISCRETE STEPS VARYING THE 2& CARRIER WITH EITHER LINEAR OR SINUSOIDAL
&- OR SOME FORM OF PULSE MODULATION SUCH AS PULSE WIDTH MODULATION 07PULSE POSITION MODULATION 00- OR PULSE AMPLITUDE MODULATION 0!- /F THESE
MODULATION TECHNIQUES 07- AND 00- MAY HAVE LARGE ERRORS BECAUSE OF CLIPPING
OF THE RECEIVED MODULATION BY ECLIPSING OR STRADDLING DISCUSSED IN 3ECTION AND
0!- IS DIFFICULT TO MECHANIZE IN BOTH THE TRANSMITTER AND THE RECEIVER #ONSEQUENTLY
THEY WILL NOT BE FURTHER CONSIDERED HERE
,INEAR #ARRIER &- ,INEAR FREQUENCY MODULATION &- OF THE CARRIER CAN BE USED
TO MEASURE RANGE 4HE MODULATION AND DEMODULATION TO OBTAIN RANGE ARE THE SAME AS
USED IN FREQUENCY MODULATED CONTINUOUS WAVE &- #7 RADAR BUT THE TRANSMISSION
REMAINS PULSED
3UPPOSE THE DWELL TIME IS DIVIDED INTO TWO LOOKS )N THE FIRST LOOK NO &- IS APPLIED
AND THE DOPPLER SHIFT OF THE TARGET IS MEASURED )N THE SECOND LOOK THE TRANSMITTER
FREQUENCY IS VARIED LINEARLY AT A RATE F IN ONE DIRECTION IE INCREASING OR DECREASING
IN FREQUENCY $URING THE ROUNDTRIP TIME TO THE TARGET THE LOCAL OSCILLATOR HAS CHANGED
FREQUENCY SO THE TARGET RETURN HAS A FREQUENCY SHIFT IN ADDITION TO THE DOPPLER SHIFT THAT
IS PROPORTIONAL TO RANGE 4HE DIFFERENCE IN THE FREQUENCY $F OF THE TARGET RETURN BETWEEN
THE TWO LOOKS IS FOUND AND THE TARGET RANGE CALCULATED FROM
2
C$F
F
4HE PROBLEM WITH ONLY TWO &- SEGMENTS DURING A DWELL IS THAT WITH MORE THAN A
SINGLE TARGET IN THE ANTENNA BEAMWIDTH RANGE GHOSTS RESULT &OR EXAMPLE WITH TWO TAR
GETS PRESENT AT DIFFERENT DOPPLERS THE TWO FREQUENCIES OBSERVED DURING THE &- PERIOD
CANNOT BE UNAMBIGUOUSLY PAIRED WITH THE TWO FREQUENCIES OBSERVED DURING THE NO &PERIOD 4O MITIGATE THIS PROBLEM A THREE SEGMENT SCHEME IS USED WITH THE FOLLOWING
SEGMENTS NO &- &- UP AND &- DOWN 4HE RANGE IS FOUND BY SELECTING RETURNS FROM
EACH OF THE THREE SEGMENTS THAT SATISFY THE RELATIONS
F F F
F F F
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4!",% 4HREE SLOPE &- 2ANGING %XAMPLE
4HERE ARE TWO TARGETS ! AND " &- SLOPE -(ZS
4ARGET
!
"
2ANGE NMI
$OPPLER FREQUENCY K(Z
&- SHIFT K(Z
/BSERVED &REQUENCIES
F NO &- K(Z
F &- UP K(Z
F &- DOWN K(Z
0OSSIBLE SETS THAT SATISFY THE RELATIONS SHOWN IN %Q AND %Q ARE
F
F
F
F
F
F
4ARGET
2ANGE NMI
9ES
.O
.O
9ES
WHERE F F AND F ARE THE FREQUENCIES OBSERVED DURING THE NO &- &- UP AND
&- DOWN SEGMENTS RESPECTIVELY 4HE RANGE THEN IS FOUND FROM %Q WHERE
$F F
F
OR F
F OR
F
F
!N EXAMPLE IS SHOWN IN 4ABLE )F MORE THAN TWO TARGETS ARE ENCOUNTERED DURING A DWELL TIME GHOSTS AGAIN RESULT AS
ONLY . SIMULTANEOUSLY DETECTED TARGETS CAN BE RESOLVED GHOST FREE WHERE . IS THE
NUMBER OF &- SLOPES (OWEVER THIS PROBLEM IS NOT SEVERE IN PRACTICE SINCE MULTIPLE
TARGETS IN A SINGLE BEAMWIDTH ARE USUALLY A TRANSIENT PHENOMENON
4HE ACCURACY OF THE RANGE MEASUREMENT IMPROVES AS THE &- SLOPE INCREASES SINCE
THE OBSERVED FREQUENCY DIFFERENCES CAN BE MORE ACCURATELY MEASURED 4HE &- SLOPE IS
HOWEVER LIMITED BY CLUTTER SPREADING CONSIDERATIONS SINCE DURING THE &- PERIODS THE
CLUTTER IS SMEARED IN FREQUENCY AND CAN APPEAR IN FREQUENCY REGIONS NORMALLY CLEAR OF
CLUTTER ! NO &- &- UP DOUBLE &- UP SCHEME IS RECOMMENDED TO PREVENT DESIRED
TARGETS FROM COMPETING WITH MAIN BEAM CLUTTER 2ANGE ACCURACIES ON THE ORDER OF OR
MILES CAN BE REASONABLY ACHIEVED
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-
-ODERN MULTIFUNCTION PULSE DOPPLER RADARS UTILIZE VARIOUS MODES TO ACCOMPLISH TASKS
SUCH AS SEARCH AND TRACK %ACH MODE USES CERTAIN WAVEFORMS OPTIMIZED FOR THE DETEC
TION AND MEASUREMENT OF VARIOUS TARGET CHARACTERISTICS
&OR EXAMPLE THE RADAR OPERATOR MIGHT SELECT A SEARCH MODE AND SPECIFY A SEARCH
VOLUME THAT THE RADAR WILL RASTER SCAN AS SHOWN IN &IGURE 6ALID DETECTIONS IN
SEARCH ARE THEN CONVERTED TO TRACKS IN THE RADAR COMPUTER 4HESE TRACKS NEED TO BE
UPDATED BY A TRACK MODE ON A REGULAR BASIS DEPENDING ON THE TRACK ACCURACY REQUIRED
(IGH TRACK ACCURACY IS NEEDED FOR THREATENING TARGETS OR THOSE THAT NEED A FIRE CONTROL
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SOLUTION IN ORDER TO ENGAGE AS OPPOSED TO NONTHREATENING TARGETS WHERE A GENERAL SITU
ATIONAL AWARENESS IS SUFFICIENT AND HIGH ACCURACY IS NOT REQUIRED
3EARCH 4HE TWO PRIMARY SEARCH MODES ARE !UTONOMOUS 3EARCH AND #UED 3EARCH
)N !UTONOMOUS 3EARCH THE OPERATOR SELECTS A RANGE AZIMUTH AND ELEVATION COVERAGE
AND THE RADAR SEARCHES EACH BEAM POSITION THAT COVERS THIS VOLUME ONCE PER FRAME 4HE
TIME IT TAKES TO COMPLETE A FRAME IS KNOWN AS THE REVISIT OR FRAME TIME 4HE FRAME TIME
SHOULD BE MINIMIZED TO ENHANCE THE CUMULATIVE PROBABILITY OF DETECTION OF TARGETS
-ODERN RADAR SYSTEMS CAN TAKE ADVANTAGE OF ON AND OFF BOARD CUES TO INCREASE
THE PROBABILITY OF ACQUIRING A TARGET USING #UED 3EARCH ! #UED 3EARCH MODE ADJUSTS
THE SEARCH VOLUME AND WAVEFORM SELECTION ACCORDING TO THE ACCURACY OF THE CUES
PARAMETERS
2ADARS WITH ELECTRONICALLY SCANNED ARRAY %3! ANTENNAS CAN INTERLEAVE OTHER FUNC
TIONS TRACK UPDATES #UED 3EARCH CALIBRATIONS ETC WITH !UTONOMOUS 3EARCH 4HE
RADAR COMPUTERS RESOURCE MANAGER MUST ENSURE THAT THE MAXIMUM FRAME TIME IS NOT
EXCEEDED WITH THE INCLUSION OF THESE OTHER FUNCTIONS DURING A SEARCH FRAME
&OR AIRBORNE PULSE DOPPLER RADARS !UTONOMOUS 3EARCH CAN HAVE TWO SUBMODES
&ORWARD ASPECT AND !LL ASPECT 3EARCH &ORWARD ASPECT 3EARCH IS DESIGNED TO DETECT
HEAD ON ENGAGEMENT TARGETS WITH HIGH CLOSING SPEEDS THAT ARE NOT COMPETING AGAINST
MAIN BEAM OR SIDELOBE CLUTTER &ORWARD ASPECT 3EARCH USES HIGH DUTY HIGH 02& WAVE
FORMS TO MAXIMIZE THE ENERGY ON TARGET AND PROVIDE LONG DETECTION RANGE &ORWARD
ASPECT 3EARCH WAVEFORMS INCLUDE 6ELOCITY 3EARCH 63 (IGH 02& 2ANGE 7HILE 3EARCH
(273 AND !LERT#ONFIRM !LL ASPECT 3EARCH CAN BE EITHER A SINGLE HIGH MEDIUM 02&
WAVEFORM THAT HAS ACCEPTABLE PERFORMANCE FOR TARGETS THAT ARE COMPETING WITH SIDELOBE
CLUTTER OR THE COMBINATION OF &ORWARD ASPECT 3EARCH HIGH 02& WAVEFORMS INTERLEAVED
WITH MEDIUM 02& WAVEFORMS DESIGNED TO DETECT TARGETS COMPETING WITH SIDELOBE CLUT
TER SUCH AS -EDIUM 02& 2ANGE 7HILE 3EARCH -273 6ELOCITY 3EARCH 63 IS A HIGH 02& SEARCH WAVEFORM THAT MEASURES DOPPLER FRE
QUENCY UNAMBIGUOUSLY WITH THE POSSIBLE EXCEPTION OF SENSE BUT DOES NOT MEASURE
RANGE 4HIS IS THE CLASSIC HIGH 02& WAVEFORM 4HE TRANSMIT DUTY CYCLE IS MAXIMIZED
TO INCREASE DETECTION RANGE 4HE RECEIVER MAY BE RANGE GATED TO MATCH THE BANDWIDTH
OF THE TRANSMIT WAVEFORM BUT RANGE MEASUREMENT IS NOT ATTEMPTED
! 63 DWELL WILL CONSIST OF A SINGLE LOOK AT A GIVEN 02& 4HE COHERENT INTEGRATION
TIME IS MAXIMIZED WITHIN THE LIMITS OF THE MAXIMUM EXPECTED TARGET RADIAL ACCELERATION
63 IS OPTIMIZED FOR 3WERLING ) AND ))) TARGET AMPLITUDE FLUCTUATION STATISTICS AND THE
CUMULATIVE PROBABILITY OF DETECTION OF INCOMING TARGETS OVER SEVERAL SEARCH FRAMES
(IGH 02& 2ANGE 7HILE 3EARCH ,IKE 63 (273 IS A HIGH 02& WAVEFORM
(OWEVER LINEAR CARRIER &- RANGING IS USED TO OBTAIN A RANGE MEASUREMENT AS DESCRIBED
IN 3ECTION 4HIS RANGE MEASUREMENT COMES AT THE EXPENSE OF FRAME TIME WITH THE
ADDITION OF VARIOUS &- SLOPES FOR EACH DWELL 4HE ACCURACY OF THIS RANGE MEASUREMENT
IS DEPENDENT UPON THE LINEAR &- RANGING SLOPES
!LERT#ONFIRM 4HE BEAM AGILITY OF %3! BASED RADARS ALLOWS THE USE OF SEQUEN
TIAL DETECTION TECHNIQUES ! SIMPLIFICATION OF SUCH TECHNIQUES IS KNOWN AS !LERT
#ONFIRM 4HE GOAL OF !LERT#ONFIRM IS TO PROVIDE HIGH SENSITIVITY WHILE MANAGING
FALSE ALARMS AND MINIMIZING THE SEARCH FRAME TIME "Y TRANSMITTING A LONGER #ONFIRM
DWELL FOR RANGING ONLY AT BEAM POSITIONS WHERE A SHORTER DWELL !LERT HAS DETECTED
05,3% $/00,%2 2!$!2
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TARGETS !LERT#ONFIRM PROVIDES THE RANGE MEASUREMENT OF CLASSIC (273 WAVEFORMS
WITHOUT THE FRAME TIME EXPENSE OF TRANSMITTING LINEAR &- RANGING DWELLS EVERY BEAM
POSITION 4HE #ONFIRM DWELL CAN ALSO BE USED TO CONTROL FALSE ALARMS PERMITTING THE
!LERT DWELL TO BE MORE SENSITIVE THAN CLASSIC 63
4HE !LERT PHASE IS USED TO SEARCH EACH BEAM POSITION OF THE FRAME FOR THE PRESENCE
OF A TARGET ! 63 WAVEFORM IS USED WITH A LOW DETECTION THRESHOLD AND A CORRESPONDING
FALSE ALARM TIME ON THE ORDER OF A FEW SECONDS 4HE LOWER DETECTION THRESHOLD INCREASES
SENSITIVITY 7HEN AN !LERT DWELL DECLARES A DETECTION A #ONFIRM DWELL IS SCHEDULED
FOR THAT !LERT DWELLS BEAM POSITION )F MONOPULSE MEASUREMENTS ARE AVAILABLE ON THE
!LERT DETECTION THE #ONFIRM BEAM CAN BE CENTERED ON THE DETECTION TO DECREASE BEAM
SHAPE LOSS 4HE #ONFIRM DWELL IS TYPICALLY A (273 WAVEFORM AND ONLY EXAMINES
DOPPLER FILTERS WITHIN A WINDOW CENTERED ABOUT THE FILTER OF THE !LERT DETECTION CUE 4HE
#ONFIRM DWELL MUST PRODUCE A DETECTION CORRESPONDING TO THE !LERT DETECTION IN ORDER
FOR A VALID DETECTION DECLARATION 4HE #ONFIRM DWELL IS USED TO MANAGE FALSE ALERTS
AND PROVIDE A RANGE MEASUREMENT FOR TARGET DETECTIONS 4HE !LERT AND #ONFIRM DETEC
TION THRESHOLDS ARE DESIGNED TO ACHIEVE OVERALL FALSE ALARM TIME EQUAL TO CONVENTIONAL
SEARCH ONE EVERY FEW MINUTES !LONG WITH USING THE SAME 02& IN !LERT AND #ONFIRM
THE TIME BETWEEN THESE DWELLS OR LATENCY SHOULD BE MINIMIZED TO PREVENT A VALID !LERT
DETECTION FROM BEING ECLIPSED DURING THE #ONFIRMATION DWELL
,OW LATENCY ALSO ALLOWS THE USE OF #ORRELATED !LERT#ONFIRM (ERE A 3WERLING
) TARGET 2#3 FLUCTUATION MODEL IS ASSUMED 4HIS IMPLIES THAT WHEN THE SAME 2& CAR
RIER FREQUENCY IS USED FOR !LERT AND #ONFIRM THE TARGET 2#3 WILL BE RELATIVELY CONSTANT
BETWEEN THE TWO DWELLS PROVIDING ADDITIONAL RANGE ENHANCEMENT IN TERMS OF THE
CUMULATIVE PROBABILITY OF DETECTION
-EDIUM 02& 2ANGE 7HILE 3EARCH ! MEDIUM 02& WAVEFORM IS USED TO DETECT
TARGETS COMPETING WITH SIDELOBE CLUTTER THAT WOULD BE UNDETECTABLE IN (273 -273
ALLOWS THE DETECTION OF NOSE ASPECT TARGETS AT WIDE SCAN ANGLES THAT ARE CROSSING THE
RADAR LINE OF SIGHT SUCH THAT THEIR LOW CLOSING VELOCITY PLACES THEM IN SIDELOBE CLUT
TER AND TAIL ASPECT TARGETS IN LEAD PURSUIT ENGAGEMENTS AN ATTACK GEOMETRY WHERE THE
NOSE OF THE ATTACKING AIRCRAFT IS POINTED AHEAD OF THE TARGETS PRESENT POSITION -273
PROVIDES COMPLETE SITUATIONAL AWARENESS PERCEPTION OF THE SURROUNDING TACTICAL ENVI
RONMENT BUT DOES NOT HAVE THE MAXIMUM DETECTION RANGE PROVIDED BY THE HIGHER DUTY
CYCLE OF (273 FOR THERMAL NOISE LIMITED TARGETS
4HE -273 WAVEFORM USES - OF . DETECTION PROCESSING A TYPICAL WAVEFORM
MIGHT BE OF %ACH -273 DWELL IS MADE UP OF . LOOKS EACH WITH A DIFFERENT 02&
$ETECTION IS REQUIRED ON AT LEAST - LOOKS TO RESOLVE TARGET RANGE AND RANGE RATE UNAM
BIGUOUSLY 4HE DETECTION THRESHOLDS ARE SET TO PROVIDE APPROXIMATELY ONE FALSE ALARM
PER MINUTE
4HE EFFECTIVENESS OF -273 IS DEPENDENT ON THE ABILITY TO DETECT TARGETS AT THE REQUIRED
RANGES WHILE SIMULTANEOUSLY REJECTING DISCRETE CLUTTER DETECTIONS ,OW TWO WAY ANTENNA
SIDELOBES ALONG WITH THE COMBINATION OF TECHNIQUES DISCUSSED IN 3ECTION SUCH AS
GUARD CHANNEL BLANKING AND POSTDETECTION 34# ARE USED TO MITIGATE SIDELOBE CLUTTER
DISCRETE FALSE ALARMS
-273 ALSO USES PULSE COMPRESSION TO DECREASE THE AMOUNT OF SIDELOBE CLUTTER THAT
TARGETS MUST COMPETE WITH 4HE LOWER 02& REDUCES ECLIPSING AND THE AMOUNT OF CLUT
TER RANGE FOLDING 4RANSMIT CARRIER FREQUENCY DIVERSITY DWELL TO DWELL FORCES 3WERLING
) AND ))) TARGET FLUCTUATION STATISTICS AND IMPROVES CUMULATIVE PROBABILITY OF DETEC
TION PERFORMANCE &REQUENCY DIVERSITY LOOK TO LOOK WITHIN A DWELL PRODUCES 3WERLING
)) AND )6 STATISTICS AND IS BETTER SUITED FOR HIGH SINGLE SCAN PROBABILITY OF DETECTION
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-273 CAN ALSO BE IMPLEMENTED WITH A HIGH MEDIUM 02& WHICH IS CHARACTERIZED
BY THE WAVEFORMS DOPPLER COVERAGE BEING UNAMBIGUOUS IN DOPPLER MAGNITUDE BUT
NOT DOPPLER SENSE FOR THE MAXIMUM TARGET DOPPLER OF INTEREST 4HE RESULTING SINGLE
BLIND SPEED DUE TO MAIN BEAM CLUTTER PERMITS AS WIDE OF A CLUTTER REJECTION NOTCH
AS REQUIRED TO REJECT MAIN BEAM CLUTTER OR GROUND MOVING TARGETS AND STILL NOT RESULT
IN DOPPLER BLIND SPEEDS FOR TARGETS OF INTEREST - OF . RANGING PROVIDES BETTER RANGE
MEASUREMENT ACCURACY THAN LINEAR &- RANGING USED IN (273 4HE 02&S USED IN A
DWELL MUST BE CHOSEN TO RESOLVE THE HIGH NUMBER OF RANGE AMBIGUITIES WITHIN THE
INSTRUMENTED RANGE
4RACK 4ARGET TRACKING IS DONE BY MAKING RANGE RANGE RATE AND AZIMUTH AND ELEVA
TION ANGLE MEASUREMENTS ON TARGETS 2ANGE MEASUREMENTS ARE OBTAINED USING RANGE GAT
ING AND CENTROIDING ON THE TARGET RETURN WITH RANGE AMBIGUITIES BEING RESOLVED WITHIN THE
TRACKER 2ANGE RATE IE DOPPLER MEASUREMENTS ARE FORMED WITH A CENTROID ON THE TARGETS
DOPPLER RETURN IN THE FILTER BANK !NGLE MEASUREMENTS CAN BE OBTAINED USING MONOPULSE
SEQUENTIAL LOBING OR CONICAL SCAN WITH MONOPULSE BEING THE PROMINENT CHOICE IN MOD
ERN RADARS 4HE TRACKER CREATES WINDOWS OR GROUPS OF CONTIGUOUS RANGE DOPPLER CELLS
AROUND EACH OF THESE MEASUREMENTS IN ORDER TO ASSOCIATE DETECTIONS WITH EXISTING TRACKS
4HE TRACKER USUALLY IMPLEMENTED WITH A NINE STATE POSITION VELOCITY AND ACCELERATION
+ALMAN FILTER ESTIMATES TARGET MOTION IN AN INERTIAL COORDINATE SYSTEM
-ULTIPLE 4ARGET 4RACKING -44 CAN BE ACCOMPLISHED IN SEVERAL WAYS /NE
METHOD 4RACK 7HILE 3CAN OR 473 IS TO USE THE NORMAL SEARCH MODE WITH &- OR
MULTIPLE 02& RANGING AND STORE THE RANGE ANGLE AND DOPPLER OF THE REPORTED DETEC
TIONS IN THE RADAR COMPUTER 4HESE DETECTIONS ARE THEN USED TO FORM AND UPDATE TRACK
FILES 4HE ANTENNA SCANS IN A NORMAL SEARCH PATTERN AND A SCAN TO SCAN CORRELATION IS
MADE ON THE DETECTIONS THAT UPDATE THE TRACK FILES !LTHOUGH TRACKING ACCURACIES ARE
LESS THAN CAN BE ACHIEVED IN A DEDICATED SINGLE TARGET TRACK MULTIPLE TARGETS CAN BE
TRACKED SIMULTANEOUSLY OVER A LARGE VOLUME OF SPACE
! SECOND METHOD OF -ULTIPLE 4ARGET 4RACKING 0AUSE 7HILE 3CAN PARTICULARLY
APPLICABLE TO %3! BASED RADARS IS TO SCAN IN A NORMAL SEARCH PATTERN PAUSE ON
EACH SEARCH DETECTION AND ENTER A 3INGLE 4ARGET 4RACK MODE FOR A BRIEF PERIOD 4HE
ADVANTAGE IS THAT THE RESULTING RANGE ANGLE AND DOPPLER MEASUREMENTS ARE MORE
ACCURATE THAN THOSE MADE WITH A SCANNING ANTENNA BUT THE TIME TO SEARCH A VOLUME
IN SPACE IS INCREASED
4RANSITION TO 4RACK OR 4RACK !CQUISITION IS USED TO CONFIRM SEARCH TARGET DETEC
TIONS AND PROVIDE IMPROVED RANGE ACCURACY WHEN NEEDED )F THE TARGET IS SUCCESSFULLY
ACQUIRED A TRACK FILE IN THE RADAR COMPUTER IS INITIATED 4HE 4RACK !CQUISITION WAVE
FORMS PARAMETERS DEPEND UPON THE TYPE OF SEARCH WAVEFORM THAT PRODUCED THE TARGET
DETECTION 4HE 4RACK !CQUISITION WAVEFORMS THRESHOLDS ARE SET TO REJECT FALSE ALARMS
AND REDUCE THE FALSE TRACK INITIATION RATE TO LESS THAN ONE PER HOUR
&OR 4RACK !CQUISITION A SEARCH DETECTION FROM 63 WOULD REQUIRE A (273 WAVE
FORM TO OBTAIN A RANGE MEASUREMENT (273 AND !LERT#ONFIRM WAVEFORMS ARE FOLLOWED
BY RANGE GATED HIGH 02& DWELLS USING - ON . RANGING TO ACHIEVE THE NECESSARY RANGE
ACCURACY FOR SINGLE 02& TRACK UPDATES 4HE UNAMBIGUOUS (273 RANGE MEASUREMENT OF
THE SEARCH DETECTION IS USED TO HELP RESOLVE THE RANGE AMBIGUITY &OR -273 DETECTIONS
ANOTHER -273 DWELL IS USED FOR 4RACK !CQUISITION /NCE THE TRACK FILE IS INITIATED SEVERAL
RAPID TRACK UPDATES ARE USED TO FIRMLY ESTABLISH THE TRACK
7HEN DOING 3INGLE 4ARGET 4RACK UPDATES A SINGLE 02& WAVEFORM CAN BE USED
4HE RANGE ANDOR DOPPLER AMBIGUITIES ARE RESOLVED IN SEARCH AND IF NECESSARY IN THE
4RANSITION TO 4RACK PHASE "Y USING THE UNAMBIGUOUS RANGE AND VELOCITY PREDICTIONS
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OF THE TARGET PROVIDED BY THE TRACKER A SINGLE 02& CAN BE CHOSEN SUCH THAT RANGE AND
DOPPLER ECLIPSING IS AVOIDED WITH HIGH PROBABILITY 4HE LENGTH OF THE DWELL IS ADAPTED
TO PROVIDE SUFFICIENT ENERGY ON TARGET SO THAT ITS RETURN SIGNAL TO NOISE RATIO WILL PRO
VIDE THE NECESSARY MEASUREMENT ACCURACIES REQUIRED BY THE TRACKER 4HIS ADAPTIVE
TRACK UPDATE WAVEFORM ALLOWS THE SEARCH REVISIT TIME TO BE MAINTAINED WHILE TRACKING
MULTIPLE TARGETS
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4HE RADAR RANGE EQUATION IS USED TO DETERMINE THE PERFORMANCE OF PULSE DOPPLER RADAR
4HE RADAR RANGE EQUATION MUST INCLUDE LOSSES BOTH SYSTEM AND ENVIRONMENTAL THAT
WILL DEGRADE THE STRENGTH OF RETURN SIGNALS AT THE DETECTOR 0ROBABILITY OF DETECTION 0D
DEPENDS ON TARGET SIGNAL TO NOISE RATIO AND PROBABILITY OF FALSE ALARM 0&! WHICH
ITSELF IS A FUNCTION OF WAVEFORM 4HE FALSE ALARM PROBABILITY DETERMINES THE DETECTION
THRESHOLD AND IS REFERENCED TO AN INDIVIDUAL RANGE DOPPLER CELL 4HIS PER CELL PROBABIL
ITY IS DERIVED FROM THE SPECIFIED FALSE REPORT TIME FOR THE SYSTEM
2ADAR 2ANGE %QUATION )N THE DOPPLER REGION WHERE THE SIGNAL DOES NOT FALL IN
CLUTTER PERFORMANCE IS LIMITED ONLY BY SYSTEM NOISE 4HE SIGNAL TO NOISE POWER RATIO
IN THE RANGE DOPPLER CELL AT THE DETECTOR PRIOR TO POSTDETECTION INTEGRATION FOR A TARGET
AT RANGE 2 IS GIVEN BY
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WHERE 2O RANGE AT WHICH 3.2 IS EQUAL TO R4 TARGET RADAR CROSS SECTION
,4 LOSSES APPLICABLE TO THE TARGET
4HE REMAINING TERMS ARE AS DEFINED FOLLOWING %Q 4HE NET LOSS ,4 USED TO COM
PUTE 3.2 FOR A TARGET IS GENERALLY HIGHER THAN THE NET LOSS ,# USED TO COMPUTE #.2
IN %Q ,4 INCLUDES LOSSES SUCH AS ECLIPSING AND RANGE GATE STRADDLE DOPPLER FILTER
STRADDLE #&!2 AND GUARD BLANKING THAT ARE APPLICABLE TO RESOLVABLE TARGETS BUT NOT
TO DISTRIBUTED CLUTTER
4HE TARGET 3.2 REPRESENTS THE ENVELOPE ) 1 FOR A LINEAR DETECTOR OR ) 1
FOR A SQUARE LAW DETECTOR OF THE TARGET RETURN COMPARED TO THAT OF JUST NOISE 4HE ENVE
LOPE IS MEASURED AFTER THE ENTIRE COHERENT MATCHED FILTER PROCESS IE TRANSMIT PULSE
MATCHED FILTER PULSE COMPRESSION AND COHERENT DOPPLER FILTERING 4HEREFORE 3.2 IS
ASSOCIATED WITH A SINGLE #0)
,OSSES 3OME OF THE LOSSES INHERENT IN BUT NOT NECESSARILY UNIQUE TO PULSE DOP
PLER RADARS THAT EMPLOY DIGITAL SIGNAL PROCESSING ARE DISCUSSED BELOW 3OME OF THE
LOSSES MAY BE INCORPORATED INTO THE OTHER VARIABLES IN THE RADAR RANGE EQUATION #ARE
MUST BE TAKEN TO ACCOUNT FOR ALL OF THE SYSTEM LOSSES WHILE AVOIDING REDUNDANCIES
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-OST FRONT END LOSSES ARE APPLICABLE TO BOTH TARGETS AND CLUTTER ,OSSES APPLICABLE
ONLY TO TARGETS WILL BE INDICATED
2& 4RANSMIT ,OSS 4HIS LOSS ACCOUNTS FOR 2& OHMIC LOSSES BETWEEN THE TRANSMIT
TER OR 2& POWER AMPLIFIER AND THE ANTENNA RADIATOR WHICH CAN INCLUDE LOSSES FROM
CONNECTORS CIRCULATORS AND RADIATING ELEMENTS
2ADOME ,OSS -OST RADARS REQUIRE A RADOME TO PROTECT THE ANTENNA FROM ENVIRON
MENTAL ELEMENTS AND TO CONFORM TO THE PLATFORMS SHAPE 2ADOMES WILL HAVE A LOSS THAT
MAY DEPEND ON THE SCAN ANGLE OF THE ANTENNA 4HIS LOSS MUST BE ACCOUNTED FOR ON TRANSMIT
AND RECEIVE IE A TWO WAY LOSS 0ROPAGATION ,OSS 0ROPAGATION THROUGH THE ATMOSPHERE RESULTS IN A LOSS ESPE
CIALLY AT HIGHER RADAR CARRIER FREQUENCIES 4HIS LOSS IS A FUNCTION OF RANGE ALTITUDE AND
WEATHER )T IS ALSO A TWO WAY LOSS 0ROPAGATION LOSS IS MORE OF A ENVIRONMENTAL LOSS
THAN A SYSTEM LOSS BUT CAN BE GROUPED WITH THE OTHER LOSSES THAT MAKE UP NET LOSS IN
THE RADAR RANGE EQUATION
3CAN ,OSS "ROADSIDE ELECTRONICALLY SCANNED ARRAY ANTENNAS ARE SUBJECT TO REDUC
TION IN GAIN WHEN THE MAIN BEAM IS SCANNED OFF BROADSIDE 4HE PROJECTED AREA OF THE
%3! APERTURE DECREASES AS BEAM SCANS FROM BROADSIDE 0ROJECTED AREA DROPS AS COSINE
OF SCAN CONE ANGLE -UTUAL COUPLING BETWEEN RADIATING ELEMENTS FURTHER REDUCES THE
EFFECTIVE AREA 3CAN LOSS MUST BE ACCOUNTED FOR ON TRANSMIT AND RECEIVE
"EAMSHAPE ,OSS 4HIS TARGET SPECIFIC LOSS ACCOUNTS FOR THE LOSS IN GAIN WHEN THE
TARGET IS NOT LOCATED AT THE PEAK OF THE BEAM "EAMSHAPE LOSS IS DEFINED AS THE INCREASE
IN THE POWER OR THE 3.2 REQUIRED TO ACHIEVE THE SAME PROBABILITY OF DETECTION ON A TAR
GET SPREAD UNIFORMLY OVER THE SPECIFIED BEAM COVERAGE AS WOULD OCCUR WITH A TARGET AT
BEAM CENTER "EAMSHAPE LOSS IS USED PRIMARILY IN SEARCH DETECTION RANGE PERFORMANCE
CALCULATIONS
2& 2ECEIVE ,OSS 4HIS LOSS IS SIMILAR TO 2& 4RANSMIT ,OSS EXCEPT IT ACCOUNTS FOR
OHMIC LOSSES FROM THE ANTENNA FACE TO THE FIRST LOW NOISE AMPLIFIER 4HIS LOSS MAY BE
INCLUDED IN THE RECEIVE SYSTEM NOISE FIGURE OR SYSTEM TEMPERATURE VALUE
)& -ATCHED &ILTER ,OSS 4HE MATCHED FILTER FOR A PULSE DOPPLER WAVEFORM INCLUDES
THE ANALOG )& MATCHED FILTER IN THE RECEIVER AND ANY SUBSEQUENT DIGITAL INTEGRATION OF
!$ SAMPLES TO MATCH THE DURATION OF THE TRANSMIT PULSE )& MATCHED FILTER LOSS QUANTI
FIES HOW WELL THE ANALOG )& MATCHED FILTER COMPARES TO THE IDEAL MATCHED FILTER FOR THAT
POINT IN THE RECEPTION CHAIN
1UANTIZATION .OISE ,OSS 4HIS LOSS IS DUE TO THE NOISE ADDED BY THE !$ CONVER
SION PROCESS AND TO TRUNCATION DUE TO FINITE WORD LENGTHS IN THE SIGNAL PROCESSOR THAT
FOLLOW 4HIS LOSS CAN ALSO BE INCORPORATED INTO THE RECEIVER NOISE FIGURE VALUE
0ULSE #OMPRESSION -ISMATCH ,OSS 4HIS IS CAUSED BY THE INTENTIONAL MISMATCH
ING OF THE PULSE COMPRESSION FILTER TO REDUCE TIME RANGE SIDELOBES
%CLIPSING AND 2ANGE 'ATE 3TRADDLE ,OSS 4HE LARGE AMOUNT OF RANGE AMBIGUITY
INHERENT IN PULSE DOPPLER WAVEFORMS RESULTS IN THE POSSIBLE ECLIPSING OF TARGET RETURNS
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WHEN THE RECEIVER IS BLANKED DURING PULSE TRANSMISSION )N A MULTIPLE RANGE GATE SYS
TEM THE RETURNS MAY ALSO STRADDLE GATES REDUCING THE PULSE MATCHED FILTER OUTPUT OF
A SINGLE GATE "ECAUSE OF ECLIPSING AND RANGE GATE STRADDLE THE VALUE OF 2O GIVEN BY
%Q MAY FALL ANYWHERE BETWEEN ZERO AND A MAXIMUM VALUE DEPENDING ON THE
EXACT LOCATION OF THE TARGET RETURN WITHIN THE INTERPULSE PERIOD
&IGURE ILLUSTRATES THE EFFECT OF ECLIPSING AND RANGE GATE STRADDLE ON THE OUTPUT
OF THE PULSE MATCHED FILTER OVER THE )00 %ACH RANGE GATE IS ASSUMED TO BE MATCHED TO
THE TRANSMIT PULSE BANDWIDTH WHICH FOR UNMODULATED PULSES IE NO PULSE COMPRESSION
MODULATION IS THE INVERSE OF THE PULSE DURATION 4HEREFORE REFERRING TO &IGURE THE
GATE WIDTH SG EQUALS THE TRANSMITTED PULSE ST )N &IGURE THE )00 IS SG 4HE PLOTS ON
THE LEFT REPRESENT A RANGE GATE SPACING OF SS EQUAL TO SG 2ANGE GATE STRADDLE LOSS CAN BE
REDUCED BY THE USE OF OVERLAPPING GATES AT THE EXPENSE OF EXTRA HARDWARE AND PROCESS
ING 4HE RIGHTMOST PLOTS REPRESENT THE USE OF RANGE GATE OVERLAP SS SG 4HE
MAXIMUM PULSE MATCHED FILTER OUTPUT AS A FUNCTION OF RETURN DELAY IS SHOWN IN TERMS OF
RELATIVE VOLTAGE AND POWER 4HE hVOLTAGEv PLOT SHOWS THE CUMULATIVE EFFECT OF CONVOLV
ING THE RETURN PULSE WITH THE MATCHED FILTER OF EACH RANGE GATE &OR A SINGLE RANGE GATE
THIS IS SIMPLY THE CONVOLUTION OF TWO RECTANGULAR PULSES WHICH RESULTS IN A TRIANGULAR
RESPONSE 4O COMPUTE LOSS THE MATCHED FILTER OUTPUT IN TERMS OF POWER IE VOLTAGE
SQUARED MUST BE USED
7HEN THE 02& IS HIGH SO THAT MANY RANGE AMBIGUITIES OCCUR THE TARGET RANGE DELAY
MAY BE CONSIDERED TO BE RANDOM FROM FRAME TO FRAME WITH A UNIFORM DISTRIBUTION OVER
THE )00 ! MEASURE OF PERFORMANCE REDUCTION DUE TO ECLIPSING AND RANGE GATE STRADDLE
IS FOUND BY
5SING THE UNECLIPSED DETECTION CURVE 0D VS 3. FOR THE WAVEFORM AND SELECT
ING A PARTICULAR 3.2 OF INTEREST 3. ALONG WITH ITS CORRESPONDING PROBABILITY OF
DETECTION 0D 2EDUCE 3. BY A FACTOR RELATED TO THE RELATIVE OUTPUT hPOWERv OF THE MATCHED
FILTER AS A FUNCTION OF AMBIGUOUS RANGE WITHIN THE )00 3EE THE THIRD ROW OF PLOTS
IN &IGURE 7ITH THE REDUCED 3.2 DETERMINE THE NEW 0D AS A FUNCTION OF AMBIGUOUS RANGE
WITHIN THE )00 FROM THE UNECLIPSED DETECTION CURVE
!VERAGE THESE NEW 0D VALUES ACROSS THE )00
4HE RESULT WILL BE A NEW DETECTION CURVE INCLUDING THE AVERAGE EFFECT OF ECLIPSING AND
RANGE GATE STRADDLE &OR A FIXED 0D THE DIFFERENCE IN 3.2 BETWEEN THE UNECLIPSED AND
THE ECLIPSED DETECTION CURVES IS THE AVERAGE ECLIPSING AND RANGE GATE STRADDLE LOSS 4HIS
DIFFERENCE REPRESENTS THE AVERAGE INCREASE IN SIGNAL TO NOISE RATIO REQUIRED TO OBTAIN
THE SAME PROBABILITY OF DETECTION WITH ECLIPSING AND STRADDLE AS IN THE CASE WHERE
THE TRANSMIT PULSE IS RECEIVED BY A MATCHED GATE WITH NO STRADDLE 3INCE THE DETECTION
CURVE CHANGES SHAPE THE LOSS DEPENDS ON THE PROBABILITY OF DETECTION SELECTED WHICH
IS DEPICTED IN &IGURE &OR ACCURATE RESULTS ECLIPSING AND RANGE GATE STRADDLE LOSS
MUST BE COMPUTED TOGETHER
! LESS ACCURATE APPROXIMATION COMPARES THE AVERAGE SIGNAL TO NOISE RATIO OVER THE
INTERPULSE PERIOD WITH THE SIGNAL TO NOISE RATIO OF THE MATCHED CASE )N THE CASE OF .
CONTINUOUS RANGE GATES SPANNING THE DURATION OF THE )00 EACH OF WHICH ARE MATCHED TO
THE TRANSMIT PULSE WIDTH THE APPROXIMATE AVERAGE ECLIPSING AND STRADDLE LOSS IS
APPROXIMATE ECLIPSING AND RANGE GATE STRADDLLE LOSS .
. 4IME .ORMALIZED BY 2ANGE 'ATE $URATION
.O 2' /VERLAP TT TG TS TB )00 TG
4IME .ORMALIZED BY 2ANGE 'ATE $URATION
2' /VERLAP TT TG TS TB )00 TG
&)'52% #ONCEPT OF ECLIPSING AND RANGE GATE STRADDLE LOSS 4HE TOP ROW OF PLOTS SHOWS THE TRANSMIT PULSE FOR A SINGLE )00 OF A PULSE DOPPLER WAVEFORM WITH A
DUTY CYCLE OF 4HE SECOND ROW OF PLOTS SHOWS THE RELATIVE VOLTAGE OF THE MAXIMUM PULSE MATCHED FILTER -& OUTPUT AS A FUNCTION OF RANGE AMBIGUOUS TARGET RETURN
WITHIN THE )00 4HE THIRD ROW OF PLOTS SHOWS THE OUTPUT IN TERMS OF RELATIVE POWER
4RANSMIT 0ULSE
-& /UTPUT
h6OLTAGEv
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h0OWERv
4RANSMIT 0ULSE
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&)'52% #OMPARISON OF DETECTION PERFORMANCE WITH AND WITHOUT ECLIPSING AND RANGE GATE
STRADDLE LOSS 4HE APPROXIMATE PERFORMANCE USING %Q IS ALSO PROVIDED 4HE PERFORMANCE WITH
ECLIPSING AND RANGE GATE STRADDLE LOSS WITH THE USE OF OVERLAPPED RANGE GATES IS SHOWN
%Q ASSUMES AN UNMODULATED RECTANGULAR TRANSMIT PULSE SHAPE WITH THE RECEIVE
GATE MATCHED TO THE TRANSMIT PULSE WIDTH 4HERE IS NO RANGE GATE OVERLAP 4HE FIRST GATE
OF THE . RANGE GATES ARE BLANKED FOR THE TRANSMIT PULSE !S SHOWN IN &IGURE THIS
APPROXIMATION IS ONLY VALID FOR A 0D NEAR 4HERE ARE SEVERAL OTHER DETAILS THAT HAVE NOT BEEN INCLUDED IN &IGURE !S SHOWN
IN &IGURE A PORTION OF THE FIRST VALID RECEIVE RANGE GATE AND POSSIBLY A PORTION
OF THE LAST RANGE GATE IN THE )00 IS TYPICALLY BLANKED TO AVOID RECEIVING TRANSIENTS OF
THE TRANSMIT TO RECEIVE AND RECEIVE TO TRANSMIT SWITCHING !LSO IF PULSE COMPRES
SION MODULATION IS USED ON THE TRANSMIT PULSE THE RANGE GATE DURATION WILL BE REDUCED
TO MATCH THE TRANSMIT PULSE BANDWIDTH !LL OF THESE EFFECTS SHOULD BE INCLUDED WHEN
COMPUTING THE ECLIPSING AND RANGE GATE STRADDLE LOSS
$OPPLER &ILTER 7EIGHTING ,OSS 4HIS LOSS RESULTS FROM THE INCREASED NOISE BAND
WIDTH OF THE DOPPLER FILTERS THAT OCCURS BECAUSE OF FILTER SIDELOBE WEIGHTING 4HE LOSS
CAN ALSO BE ACCOUNTED FOR BY AN INCREASE OF THE DOPPLER FILTER NOISE BANDWIDTH INSTEAD
OF AS A SEPARATE LOSS
$OPPLER &ILTER 3TRADDLE ,OSS 4HIS LOSS IS DUE TO A TARGET NOT ALWAYS BEING IN THE
CENTER OF A DOPPLER FILTER )T IS COMPUTED BY ASSUMING A UNIFORMLY DISTRIBUTED TARGET DOP
PLER OVER ONE FILTER SPACING AND IS A FUNCTION OF THE DOPPLER FILTER SIDELOBE WEIGHTING 4HIS
LOSS CAN BE REDUCED AT THE EXPENSE OF INCREASED PROCESSING BY ZERO PADDING THE COLLECTED
DATA AND PERFORMING A HIGHER POINT &&4 TO FORM HIGHLY OVERLAPPED DOPPLER FILTERS
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#&!2 ,OSS 4HIS LOSS IS CAUSED BY AN IMPERFECT ESTIMATE OF THE DETECTION THRESH
OLD COMPARED WITH THE IDEAL THRESHOLD 4HE FLUCTUATION IN THE ESTIMATE NECESSITATES
THAT THE MEAN THRESHOLD BE SET HIGHER THAN THE IDEAL HENCE A LOSS )T IS ONLY APPLICABLE
TO TARGETS
'UARD "LANKING ,OSS 4HIS TARGET SPECIFIC LOSS IS THE DETECTABILITY LOSS IN THE MAIN
CHANNEL CAUSED BY SPURIOUS BLANKING FROM THE GUARD CHANNEL 3EE &IGURE 0ROBABILITY OF &ALSE !LARM 2ADAR DETECTION PERFORMANCE IS DETERMINED BY
THE DETECTION THRESHOLD WHICH IN TURN IS SET TO PROVIDE A SPECIFIED PROBABILITY OF
FALSE ALARMn !S DESCRIBED IN 3ECTION PULSE DOPPLER RADARS OFTEN EMPLOY
A MULTILOOK DETECTION CRITERION TO RESOLVE RANGE AMBIGUITIES 4HIS CAN BE ACCOM
PLISHED WITH LINEAR &- RANGING AS IN THE (273 WAVEFORM OR - OF . RANGING USED
BY -273 4HESE AMBIGUITY RESOLUTION TECHNIQUES DICTATE HOW THE PROBABILITY OF
FALSE ALARM PER RANGE DOPPLER CELL IS COMPUTED 4HESE CALCULATIONS ASSUME A NOISE
LIMITED ENVIRONMENT
&OR (273 DIFFERENT LINEAR &- SLOPES ARE APPLIED TO LOOKS THROUGH M OF A M LOOK
DWELL WHERE M IS TYPICALLY 4HE 02& IS HIGH ENOUGH FOR AT MOST ONLY A DOPPLER SIGN
AMBIGUITY $ETECTIONS IN LOOKS THROUGH M MUST CORRELATE IN DOPPLER WITH DETECTIONS
IN THE FIRST LOOK WHICH HAS NO SLOPE ! DOPPLER CORRELATION WINDOW IS SET EQUAL TO
THE MAXIMUM DOPPLER OFFSET DUE TO LINEAR &- RANGING FROM A TARGET AT THE MAXIMUM
INSTRUMENTED RANGE &OR DOPPLER ONLY CORRELATION THE 0&! PER RANGE DOPPLER CELL TO
PROVIDE A SPECIFIED FALSE REPORT TIME IS
³
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WHERE .R NUMBER OF INDEPENDENT RANGE SAMPLES PROCESSED PER )00
.F NUMBER OF INDEPENDENT DOPPLER FILTERS VISIBLE IN THE DOPPLER PASSBAND
NUMBER OF UNBLANKED FILTERS&&4 WEIGHTING FACTOR
4D TOTAL DWELL TIME OF THE MULTIPLE 02&S INCLUDING POSTDETECTION INTEGRATION
IF ANY SPACE CHANGE AND ANY DEAD TIME
N NUMBER OF LOOKS IN A DWELL TIME
M NUMBER OF DETECTIONS REQUIRED FOR A TARGET REPORT FOR A TYPICAL (273
DWELL N AND M ¤ M³
¥¦ N´µ BINOMIAL COEFFICIENT N;MN M =
4&2 FALSE REPORT TIME PER -ARCUMS DEFINITION WHERE THE PROBABILITY IS
THAT AT LEAST ONE FALSE REPORT WILL OCCUR IN THE FALSE REPORT TIME THIS
CAN BE RELATED TO THE AVERAGE TIME 4!6' BETWEEN FALSE REPORTS BY
4&2 y 4!6' LN
.&- K&- MAX2MAXC NUMBER OF INDEPENDENT DOPPLER FILTERS IN THE DOPPLER
CORRELATION WINDOW
K&- MAX STEEPEST LINEAR &- SLOPE MAGNITUDE
2MAX MAXIMUM INSTRUMENTED RANGE
{°{x
05,3% $/00,%2 2!$!2
!LERT#ONFIRM INCREASES SENSITIVITY BY ALLOWING MORE FALSE ALARMS IN !LERT AND RELY
ING ON #ONFIRM TO REJECT THOSE FALSE ALERTS 4HE !LERT#ONFIRM COMBINATION IS DESIGNED
TO PROVIDE THE SAME FALSE REPORT TIME 4&2 AS A CONVENTIONAL WAVEFORM ! SPECIFIED
FRACTIONAL INCREASE & IN FRAME TIME ACCOUNTS FOR THE EXECUTION OF #ONFIRM DWELLS TO
REJECT FALSE !LERT DETECTIONS & IS ON THE ORDER OF n 7HEN USING A 63 !LERT AND A
LOOK (273 #ONFIRM THE PROBABILITY OF FALSE ALARM PER RANGE DOPPLER CELL 0&! A AND
0&! C FOR !LERT AND #ONFIRM RESPECTIVELY IS
0&! A 4D A LN . R A . F A4&2 A
& ³
¤ 4D C LN 0&! C r
. R C ¥¦ . F CUE . && ´µ
4&2
WHERE 4D A TOTAL !LERT DWELL TIME
.R A NUMBER OF INDEPENDENT RANGE SAMPLES PROCESSED PER )00 IN !LERT
.F A NUMBER OF INDEPENDENT DOPPLER FILTERS VISIBLE IN THE !LERT DOPPLER
PASSBAND
4&2 A 4D C & !LERT FALSE REPORT TIME
4D C TOTAL #ONFIRM DWELL TIME
& FRACTIONAL INCREASE IN FRAME TIME ALLOCATED TO #ONFIRM n
.R C NUMBER OF INDEPENDENT RANGE SAMPLES PROCESSED PER )00 IN #ONFIRM
.F CUE NUMBER OF INDEPENDENT DOPPLER FILTERS IN THE #ONFIRM WINDOW CENTERED
ABOUT THE DOPPLER OF THE !LERT DETECTION CUE
.&- NUMBER OF INDEPENDENT DOPPLER FILTERS IN #ONFIRM LINEAR &- RANGING
DOPPLER CORRELATION WINDOW
4&2 OVERALL !LERT#ONFIRM FALSE REPORT TIME
4HE - OF . RANGING USED IN -273 REQUIRES CORRELATION IN RANGE AND CAN BE VIEWED
AS A BINARY DETECTOR -273 IS TYPICALLY A MEDIUM 02& WAVEFORM WITH RANGE AND DOP
PLER AMBIGUITIES $OPPLER IS USED FOR CLUTTER MITIGATION IN EACH LOOK AND THE DOPPLER
AMBIGUITY MAY NOT NEED TO BE RESOLVED SINCE THE TRACKER CAN DETERMINE RANGE RATE FROM
SUCCESSIVE DWELLS ! TYPICAL -273 - OF . CORRELATION WOULD BE THREE DETECTIONS OUT
OF EIGHT LOOKS IE M AND N &OR RANGE ONLY CORRELATION THE 0&! IN EACH RANGE
DOPPLER CELL IS GIVEN BY
M
§
¶
¨¨ 4D LN ··
0&! . F ¨¤ M³
·
¨¥¦ N´µ . RU4&2 ·
©
¸
WHERE .RU NUMBER OF INDEPENDENT RANGE SAMPLES IN THE OUTPUT UNAMBIGUOUS RANGE
INTERVAL DISPLAY RANGERANGE GATE SIZE
{°{È
2!$!2 (!.$"//+
&OR BETTER FALSE ALARM REJECTION DOPPLER CORRELATION CAN BE USED FOR -273 )N THE
CASE WHERE BOTH RANGE AND DOPPLER CORRELATION ARE USED THE REQUIRED 0&! IS
M
§
¶
¨
·
4D LN ·
0&! ¨
¨¤ M³
M ·
¨¥¦ N´µ . FU . RU4&27 ·
©
¸
WHERE .FU NUMBER OF INDEPENDENT DOPPLER FILTERS IN THE UNAMBIGUOUS DOPPLER REGION
7 WIDTH IN DOPPLER FILTERS OF THE CORRELATION WINDOW APPLIED TO DETECTIONS
FOLLOWING INITIAL DETECTION
0ROBABILITY OF $ETECTION 5SING THE 0&! PER RANGE DOPPLER CELL THE PROBABILITY
OF DETECTION 0D OF A GIVEN LOOK CAN BE DETERMINED FOR A GIVEN TARGET 3.2 THE NUM
BER OF #0)S NONCOHERENTLY INTEGRATED .PDI AND THE TARGET 2#3 FLUCTUATION MODEL
ASSUMED 4HE INVERSE PROBLEM OF DETERMINING THE REQUIRED 3.2 FOR A GIVEN 0D CAN BE
SOLVED VIA APPROXIMATIONS 5NIVERSAL DETECTION EQUATIONS HAVE BEEN PUBLISHED THAT
PROVIDE REASONABLY ACCURATE RESULTS AND ARE REPRODUCED HERE !GAIN THE ASSUMPTION
THAT TARGETS ARE IN A GAUSSIAN NOISE LIMITED ENVIRONMENT IS MADE
&OR A SINGLE LOOK WITH .PDI #0)S NONCOHERENTLY INTEGRATED AND A SPECIFIED 0&! PER
RANGE DOPPLER CELL THE 0D AS A FUNCTION OF 3.2 FOR A -ARCUM NONFLUCTUATING TARGET
CAN BE APPROXIMATED AS
0D 3.2 0&! . PDI ¤
ERFC ¥
¦
LN; 0&! 0&! =
. PDI
. PDI 3.2
. PDI
³
´µ
WHERE ERFCq IS THE COMPLEMENTARY ERROR FUNCTION 4HE REQUIRED 3.2 AS A FUNCTION OF
0D FOR A -ARCUM TARGET IS APPROXIMATED AS
3.2 REQD 0D 0&! . PDI H
. PDI
H
. PDI
. PDI
WHERE
H
LN; 0&! 0&! = SIGN 0D
LN; 0D 0D =
&OR 3WERLING FLUCTUATING TARGET MODELS THE 0D AND REQUIRED 3.2 CAN BE APPROXI
MATED RESPECTIVELY AS
§
¨+ 0 .
. PDI
M
&!
PDI
0D 3.2 0&! . PDI NE + M ¨
.
PDI
¨
3.2 ¨©
NE
§ + M 0D NE . PDI
3.2 0D 0&! . PDI NE ¨
+ M 0D NE
¨©
NE
NE
¶
·
NE ·
·
·¸
¶ N
· E
·¸ . PDI
{°{Ç
05,3% $/00,%2 2!$!2
WHERE
ª ­­ .
PDI
NE «
­
­¬ . PDI
FOR 3WERLING ) TARGGET CHI SQUARED DISTRIBUTION WITH DEGRESSS OF FREEDOM
FOR 3WERLING )) TARGET CHI SQUARED DISTRIBUTION WITH . PDI DEGRESS OF FREEDOM
FOR 3WERLING ))) TARGET CHI SQUARRED DISTRIBUTION WITH DEGRESS OF FREEDOM
FOR 3WERLING )6 TARGET CHI SQUARED DISTRIIBUTION WITH . PDI DEGRESS OF FREEDOM
¤ D X³
+M X D 0 ¥
CHI SQUARED DISTRIBUTION SURVIVAL FUNCTION
¦ ´µ
+M P D INVERSE CHI SQUARED DISTRIBUTION SURVIVAL FUNCTION
X
G A X
¯ TA E T DT REGULARIZED LOWER INCOMPLETE GAMMA FUNCTION
0A X c
' A
T A E T DT
¯
4HE INTEGRAL OF THE CHI SQUARED DISTRIBUTION +MX D AND ITS INVERSE +M P D ARE OFTEN
INCLUDED IN MATHEMATICAL COMPUTATION SOFTWARE PACKAGES
7HEN - OF . DETECTION IE BINARY DETECTION IS USED WITHIN A DWELL THE PROBABIL
ITY OF DETECTION FOR EACH LOOK 0D LOOK IS USED TO COMPUTE THE PROBABILITY OF DETECTION
FOR A DWELL 0D DWELL 7HEN A DWELL REQUIRES M DETECTIONS OUT OF N LOOKS FOR A TARGET
DECLARATION THE 0D DWELL IS
N
¤ K³
0D DWELL £ ¥ ´ 0DK LOOK 0D LOOK N K
¦ Nµ
K M
&OR !LERT#ONFIRM DETECTION PERFORMANCE THE 0D FOR THE !LERT DWELL AND THE 0D
FOR THE #ONFIRM DWELL ARE INDIVIDUALLY COMPUTED AS A FUNCTION OF 3.2 #ARE MUST
BE TAKEN TO NORMALIZE THE 3.2 TO ACCOUNT FOR DIFFERENCES IN DOPPLER FILTER BANDWIDTH
BETWEEN THE !LERT AND #ONFIRM WAVEFORMS 4HE MULTIPLICATION OF NORMALIZED PROB
ABILITY OF DETECTION CURVE FOR THE !LERT DWELL WITH THAT OF THE #ONFIRM DWELL RESULTS
IN AN ESTIMATE OF THE COMPOSITE 0D VS 3. CURVE FOR !LERT#ONFIRM -ORE ACCURATE
RESULTS MUST INCLUDE THE EFFECTS OF LATENCY BETWEEN THE !LERT AND #ONFIRM DWELLS
3EARCH DETECTION PERFORMANCE IS OFTEN CHARACTERIZED BY THE CUMULATIVE PROBABIL
ITY OF DETECTION 0D CUM WHICH IS DEFINED AS THE PROBABILITY THAT THE RADAR WILL DETECT
A CLOSING TARGET AT LEAST ONCE BY THE TIME THE TARGET HAS CLOSED TO A SPECIFIED RANGE
0D CUM IS ONLY DEFINED FOR CLOSING TARGETS 4HE CUMULATIVE PROBABILITY OF DETECTION FOR
THE KTH SCAN OR FRAME IS
K
0D CUM ;K = “ ; 0D SS ;I==
I 0D CUM ;K = 0D SS ;K = 0D CUM ;K =
WHERE 0D SS;K= IS THE SINGLE SCAN PROBABILITY OF DETECTION ON THE KTH SCAN 4HE ACCUMULA
TION OF SINGLE SCAN PROBABILITY OF DETECTIONS IS STARTED AT A RANGE WHERE THE TARGETS 0D SS
IS APPROXIMATELY 4HERE IS AN OPTIMAL SEARCH FRAME TIME FOR CUMULATIVE DETECTION
PERFORMANCE ! BALANCE MUST BE ACHIEVED ! SHORT FRAME TIME LIMITS THE AMOUNT OF
ENERGY PLACED ON TARGET PER DWELL AND LOWERS THE SINGLE SCAN 0D ! LONG FRAME TIME
ALLOWS THE TARGET TO CLOSE IN RANGE MORE BETWEEN REVISITS THUS LOWERING THE BENEFIT
OF THE ACCUMULATION &IGURE ILLUSTRATES THE DIFFERENCE BETWEEN SINGLE SCAN AND
CUMULATIVE PROBABILITY OF DETECTION
{°{n
2!$!2 (!.$"//+
!#&##
$$#%
!#"" !
&)'52% 3INGLE SCAN VS CUMULATIVE 0D AS A FUNCTION OF RANGE FOR A FIXED
RADIAL VELOCITY MOVING TARGET
#LUTTER LIMITED #ASE 4HE FOREGOING DISCUSSION ASSUMED THAT THE TARGET FELL
IN THE NOISE LIMITED IE CLUTTER FREE PART OF THE DOPPLER BAND )F THE TARGET FALLS
IN THE SIDELOBE CLUTTER REGION THE RANGE PERFORMANCE WILL BE DEGRADED SINCE THE
TOTAL INTERFERENCE POWER SYSTEM NOISE PLUS CLUTTER AGAINST WHICH THE TARGET MUST
COMPETE IS INCREASED 4HE FOREGOING DISCUSSION CAN BE APPLIED TO THE SIDELOBE CLUT
TER REGION HOWEVER BY INTERPRETING 2O AS THE RANGE WHERE THE SIGNAL IS EQUAL TO
SIDELOBE CLUTTER PLUS SYSTEM NOISEn 4HE #&!2 LOSS MAY ALSO BE HIGHER OWING
TO THE INCREASED VARIABILITY OF THE THRESHOLD WHEN THE CLUTTER VARIES OVER THE TARGET
DETECTION REGION -ORE ACCURATE CALCULATIONS OF DETECTION PERFORMANCE IN THE SIDE
LOBE CLUTTER LIMITED CASE SHOULD INCLUDE THE PROPER CLUTTER 2#3 FLUCTUATION MODELS
AND #&!2 TECHNIQUES
-/Ê"Ê
!%3!
!$
!'#
!#!'#
#&!2
#.2
#0)
#7
$!:
$%,
D"C
$#
$&4
, 6/" -
ACTIVE ELECTRONICALLY SCANNED ARRAY
ANALOG TO DIGITAL
AUTOMATIC GAIN CONTROL
AMPLITUDE MODULATION
CLUTTER AUTOMATIC GAIN CONTROL
CONSTANT FALSE ALARM RATE
CLUTTER TO NOISE POWER RATIO
COHERENT PROCESSING INTERVAL
CONTINUOUS WAVE
DELTA AZIMUTH ANTENNA BEAM USED FOR MONOPULSE ANGLE ESTIMATION
DELTA ELEVATION ANTENNA BEAM USED FOR MONOPULSE ANGLE ESTIMATION
DECIBELS WITH RESPECT TO THE CARRIER
DIRECT CURRENT
DISCRETE &OURIER TRANSFORM
05,3% $/00,%2 2!$!2
{°{™
$0$
DIGITAL PRODUCT DETECTOR
%3!
ELECTRONICALLY SCANNED ARRAY
&&4
FAST &OURIER TRANSFORM
&FREQUENCY MODULATION
&- #7 FREQUENCY MODULATED CONTINUOUS WAVE
(273 HIGH 02& RANGE WHILE SEARCH
)
INPHASE
)&
INTERMEDIATE FREQUENCY
).3
INERTIAL NAVIGATION SYSTEM
)00
INTERPULSE PERIOD
,.!
LOW NOISE AMPLIFIER
,/
LOCAL OSCILLATOR
-&
MATCHED FILTER
-273 MEDIUM 02& RANGE WHILE SEARCH
-4)
MOVING TARGET INDICATION
-44
MULTIPLE TARGET TRACKING
.!'# NOISE AUTOMATIC GAIN CONTROL
0!PULSE AMPLITUDE MODULATION
0D
PROBABILITY OF DETECTION
0#
PULSE COMPRESSION
0$)
POSTDETECTION INTEGRATION NONCOHERENT INTEGRATION
0&!
PROBABILITY OF FALSE ALARM
0PHASE MODULATION
00PULSE POSITION MODULATION
02&
PULSE REPETITION FREQUENCY
07- PULSE WIDTH MODULATION
1
QUADRATURE
2#3
RADAR CROSS SECTION
2&)
RADIO FREQUENCY INTERFERENCE
RMS
ROOT MEAN SQUARE
2&
RADIO FREQUENCY
20
RECEIVER PROTECTOR
273
RANGE WHILE SEARCH
3
SUM RECEIVE ANTENNA BEAM PRIMARY BEAM USED FOR DETECTION
3,"
SIDELOBE BLANKER
3.2
SIGNAL TO NOISE POWER RATIO
34#
SENSITIVITY TIME CONTROL
473
TRACK WHILE SCAN
42
TRANSMITRECEIVE
63
VELOCITY SEARCH
, ,
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)N SPITE OF MORE THAN A HALF CENTURY OF IMPROVEMENTS IN RADAR PERFORMANCE AND
RELIABILITY THE EFFORT REQUIRED FOR DEPLOYMENT OPERATION AND MAINTENANCE OF MOST
RADARS IS SUBSTANTIAL &URTHERMORE THE POWER APERTURE PRODUCT IS NEVER AS LARGE AS
DESIRED 4HE FORWARD PROJECTED AREA AS WELL AS AVIONICS WEIGHT IS VERY COSTLY IN MOST
FIGHTER AIRCRAFT PARAMETERS 4HESE PARAMETERS HAVE MOTIVATED USERS BUYERS AND
DESIGNERS TO WANT MORE FUNCTIONS IN A SINGLE RADAR AND ITS COMPLEMENTARY PROCESSING
SUITE !S A RESULT MOST MODERN FIGHTER RADARS ARE MULTIFUNCTIONALˆPROVIDING RADAR
NAVIGATION LANDING AIDS DATA LINK AND %LECTRONIC #OUNTER -EASURES %#- FUNC
TIONS 4HE PRIMARY ENABLER FOR MULTIFUNCTIONAL RADAR IS SOFTWARE DEFINED SIGNAL
AND DATA PROCESSING FIRST INTRODUCED IN THE MID Sn 3OFTWARE PROGRAMMABILITY
ALLOWS MANY RADAR SYSTEM MODES TO BE PERFORMED USING THE SAME 2& HARDWARE )N
ADDITION MODERN NAVIGATION AIDS WORK SO WELL THAT EACH RADAR MODE IS DEFINED BY
ITS EARTH SITUATION GEOMETRY WITH ALMOST ALL WAVEFORM PARAMETERS SET BY LOCAL EARTH
CONDITIONS 4HE MODERN RADAR OFTEN IS NET CENTRIC USING AND PROVIDING DATA TO A
COMMUNICATIONS NETWORK AND WHERE SUITABLY EQUIPPED HAS ITS OWN )NTERNET PROTOCOL
)0 ADDRESS
-ULTIFUNCTIONALITY IS NOT DEPENDENT ON ANTENNA TYPE )N FACT THE MECHANICALLY
SCANNED !.!0' AND RADARS HAVE DEMONSTRATED MULTIFUNCTIONALITY IN
COMBAT (OWEVER MULTIFUNCTIONALITY IS FACILITATED BY !CTIVE %LECTRONICALLY 3CANNED
!NTENNA !%3! ARRAYS 4HE MULTIFUNCTIONAL !%3! RADAR IN THE &! %& FIGHTER IS
SHOWN WITH A PROTECTIVE COVER OVER THE ARRAY IN &IGURE 4HE !%3! IS SHAPED AND
CANTED UPWARD TO AID IN SOME MODES AND TO MINIMIZE REFLECTIONS TO ENEMY RADARS
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4HIS CHAPTER ADDRESSES WHAT SIGNALS ARE EMITTED AND WHY THEY ARE NEEDED IN A
-ULTIFUNCTIONAL &IGHTER !IRCRAFT 2ADAR -&!2 4HE WHY BEGINS WITH TYPICAL MIS
SIONS WHICH SHOWS THE GEOMETRY THAT GIVES RISE TO EACH RADAR MODE AND WAVEFORM
LISTS REPRESENTATIVE RADAR MODES AND SHOWS TYPICAL MODERN AIRBORNE RADAR MODE INTER
LEAVING AND TIMING 4HE ANSWER TO WHAT IS PROVIDED BY TYPICAL WAVEFORM VARIATIONS
AND A FEW EXAMPLES 4HE EXAMPLES ARE NOT FROM ANY SINGLE RADAR BUT ARE A COMPOSITE
OF MODERN RADARS 4HE GENERAL -&!2 IDEA IS ILLUSTRATED IN &IGURE )T SHOWS TIME
MULTIPLEXED OPERATIONS FOR AIR TO AIR ! ! AIR TO SURFACE ! 3 ELECTRONIC WARFARE
%7 AND COMMUNICATION FROM THE SAME RADIO FREQUENCY 2& HARDWARE AND PROCESS
ING COMPLEX OFTEN OVER MOST OF THE MICROWAVE BAND 3OMETIMES MULTIPLE FUNCTIONS
CAN BE PERFORMED SIMULTANEOUSLY IF A COMMON WAVEFORM IS USED
4HE ANTENNA APERTURE USUALLY HAS MULTIPLE PHASE CENTERS ENABLING MEASUREMENT FOR
3PACE 4IME !DAPTIVE 0ROCESSING 34!0 $ISPLACED 0HASE #ENTER !NTENNA $0#!
&)'52% -&!2 INTERLEAVES ! 3 ! ! AND %7 FUNCTIONS ADAPTED -5,4)&5.#4)/.!, 2!$!2 3934%-3 &/2 &)'(4%2 !)2#2!&4
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PROCESSING CONVENTIONAL MONOPULSE ANGLE TRACKING JAMMER NULLING AND OUT OF BAND
ANGLE OF ARRIVAL !/! ESTIMATION 4HE OPTIMUM PLACEMENT OF PHASE CENTERS IS AN
IMPORTANT DESIGN TRADEOFF ! PHASE CENTER IS AN ANTENNA APERTURE CHANNEL WHICH IS OFF
SET IN SPACE AND PROVIDES A PARTIALLY OR FULLY INDEPENDENT MEASUREMENT OF AN INCOMING
ELECTROMAGNETIC WAVEFRONT &OR EXAMPLE A ONE DIMENSIONAL PHASE MONOPULSE HAS TWO
PHASE CENTERS A TWO DIMENSIONAL PHASE MONOPULSE HAS FOUR PHASE CENTERS $0#! HAS
TWO OR MORE PHASE CENTERS A RADAR WITH A GUARD HORN FOR SIDELOBE SUPPRESSION HAS TWO
PHASE CENTERS AND AN ADAPTIVE ARRAY MAY HAVE MANY PHASE CENTERSn 34!0 IS AN
EXTENSION OF THE CLASSIC THEORY FOR A MATCHED FILTER IN THE PRESENCE OF NONnWHITE NOISE
WHICH INCLUDES BOTH TIME AND SPACE
/VERALL WEAPON SYSTEM REQUIREMENTS USUALLY FAVOR 8 OR +U BAND FOR THE OPERATING
FREQUENCY OF A -&!2 )N ADDITION THE -&!2 APERTURES AND ASSOCIATED TRANSMITTER ARE
USUALLY THE LARGEST ON AN AIRCRAFT AND HENCE CAN CREATE THE HIGHEST %FFECTIVE 2ADIATED
0OWER %20 FOR JAMMING ADVERSARY RADARS AND DATA LINKS WHERE THESE ARE IN BAND
-ULTIFUNCTIONAL 2ADAR !RCHITECTURE !N EXAMPLE -&!2 BLOCK DIAGRAM IS
SHOWN IN &IGURE 4HE MODERN INTEGRATED AVIONIC SUITE CONCEPT BLURS THE BOUNDARIES
BETWEEN TRADITIONAL RADAR FUNCTIONS AND OTHER SENSORS COUNTERMEASURES WEAPONS AND
COMMUNICATIONS SEE &IGURES AND LATER IN THE CHAPTER 4HERE IS A MICROWAVE
AND 2& SUITE AN ELECTRO OPTICAL INFRARED ULTRAVIOLET %/ SUITE A STORES MANAGEMENT
SUITE A CONTROLS AND DISPLAYS SUITE A MULTIPLY REDUNDANT VEHICLE MANAGEMENT SUITE
AND A MULTIPLY REDUNDANT PROCESSOR COMPLEX
%ACH MICROWAVE ANDOR 2& APERTURE MAY HAVE SOME EMBEDDED SIGNAL CONDITIONING
BUT THEN MAY BE MULTIPLEXED TO STANDARDIZED COMMON DESIGN 2& FILTER FREQUENCY REF
ERENCE ANALOG TO DIGITAL CONVERSION !$ INPUT OUTPUT )/ AND CONTROL MODULES !
SIMILAR DESIGN CONCEPT IS USED FOR THE ELECTRO OPTICAL %/ SENSORS STORES MANAGEMENT
&)'52% -&!2 MERGED WITH OTHER SENSORS ADAPTED
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VEHICLE MANAGEMENT PILOT VEHICLE INTERFACE AND INTEGRATED CORE PROCESSING SUITE 4HERE
IS SUBSTANTIAL DATA TRAFFIC BETWEEN THE CORE PROCESSING AND THE SENSORS TO PROVIDE POINT
ING CUEING TRACKING AND MULTISENSOR FUSION OF DETECTIONS 4HE AIM OF THIS APPROACH IS
TO PROVIDE A SHARED POOL OF COMPUTATIONAL RESOURCES WHICH MAY BE FLEXIBLY ALLOCATED
BETWEEN SENSORS AND FUNCTIONS
4HE SENSORS MAY CONTAIN DEDICATED MOTION SENSING BUT LONG TERM NAVIGATION IS PRO
VIDED BY THE VEHICLE MANAGEMENT GLOBAL POSITIONING SYSTEM AND INERTIAL NAVIGATION SYS
TEM '03).3 4HE ON RADAR MOTION SENSING MUST SENSE POSITION TO A FRACTION OF THE
TRANSMITTED WAVELENGTH OVER THE COHERENT PROCESSING INTERVAL 4HIS IS USUALLY DONE WITH
INERTIAL SENSORS SUCH AS ACCELEROMETERS AND GYROS WITH VERY HIGH SAMPLING RATES !N
INERTIAL NAVIGATION SYSTEM ESTIMATES THE POSITION OF THE AIRCRAFT IN A WORLDWIDE COORDINATE
SPACE BY INTEGRATING THE OUTPUTS OF THE GYROS AND ACCELEROMETERS TYPICALLY USING +ALMAN
FILTERING TECHNIQUES !CCUMULATED ERRORS IN SUCH A SYSTEM CAN BE CORRECTED BY USING '03
UPDATES AS WELL AS KNOWN REFERENCE POINTS MEASURED WITH THE RADAR OR %/ SENSORS
4HERE MAY BE DOZENS OR HUNDREDS OF STORED PROGRAM DEVICES DISTRIBUTED THROUGHOUT
THE AVIONICS 4HESE LOWER LEVEL FUNCTIONAL SUITES ARE CONNECTED BY STANDARDIZED BUS
SES WHICH MAY BE FIBER OPTIC OR WIRED 4HE PROGRAMMABLE DEVICES ARE CONTROLLED BY
SOFTWARE OPERATING ENVIRONMENTS INVOKING PROGRAMS 4HE ARCHITECTURE OBJECTIVE IS TO
HAVE STANDARD INTERFACES FEW UNIQUE ASSEMBLIES AND SINGLE LEVEL MAINTENANCE
4HE SUITE OF MICROWAVE AND 2& APERTURES IN A FIGHTER AIRCRAFT MIGHT APPEAR AS
SHOWN IN &IGURE !S MANY AS APERTURES MAY BE DISTRIBUTED THROUGHOUT THE VEHI
CLE PERFORMING RADAR DATA LINK NAVIGATION MISSILE WARNING DIRECTION FINDING JAM
MING OR OTHER FUNCTIONS OVER A FREQUENCY RANGE COVERING SEVERAL DECADES 4HERE ARE
APERTURES DISTRIBUTED OVER THE AIRCRAFT THAT POINT FORWARD AND AFT RIGHT AND LEFT AS WELL
AS UP AND DOWN 3OME APERTURES WILL BE SHARED FOR COMMUNICATIONS RADIO NAVIGATION
AND IDENTIFICATION #.) AS WELL AS IDENTIFICATION FRIEND OR FOE )&& DUE TO COMPATIBLE
FREQUENCIES AND GEOMETRIES $ATA LINKS SUCH AS *4)$3,INK AND ,INK CAN SHARE
APERTURES WITH '03 AND , BAND SATELLITE COMMUNICATIONS , 3!4#/- %7 APERTURES
MUST BE BROADBAND BY NATURE AND CAN BE SHARED WITH RADAR WARNING RECEIVERS 272
RADAR AUXILIARIES AND SOME TYPES OF #.)S
&)'52% -&!2 2& APERTURES SHARE LOW LEVEL 2& ADAPTED -5,4)&5.#4)/.!, 2!$!2 3934%-3 &/2 &)'(4%2 !)2#2!&4
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-&!2 PROCESSING ADAPTED 4HE APERTURES ARE SIGNAL CONDITIONED CONTROLLED AND INTERFACED THROUGH BUSSES IN THE
AIRCRAFT WITH REMAINING PROCESSING PERFORMED EITHER IN A COMMON PROCESSOR COMPLEX
AS SHOWN IN &IGURE OR IN FEDERATED PROCESSORS DISTRIBUTED THROUGHOUT THE AIRCRAFT
/NE IMPORTANT CLASS OF STANDARDIZED MODULES CONTAINS BASIC TIMING AND PROGRAMMABLE
EVENT GENERATORS 0%' THAT CREATE ACCURATE TIMING FOR 0ULSE 2EPETITION &REQUENCIES
02&S ANALOG TO DIGITAL CONVERSION !$ SAMPLING PULSE AND CHIP WIDTHS BLANK
ING GATES BEAM REPOINTING COMMANDS AND OTHER SYNCHRONIZED REAL TIME INTERRUPTS !
SECOND CLASS CONTAINS 2& AND INTERMEDIATE FREQUENCY )& AMPLIFICATION AND MIXING
! THIRD CLASS CONTAINS LOW NOISE FREQUENCY SYNTHESIZERS WHICH MAY INCLUDE $IRECT
$IGITAL FREQUENCY 3YNTHESIS $$3 !$ CONVERTERS AND CONTROL INTERFACE MODULES ARE
THE FINAL CLASS "USSING PROTOCOLS AND SPEEDS MUST HAVE ADEQUATE RESERVES TO INSURE
FAIL SAFE REAL TIME OPERATION
4HE FUNCTIONAL BLOCK DIAGRAM AND OPERATION OF A SPECIFIC SENSOR MODE IS THEN OVER
LAID ON THIS HARDWARE AND SOFTWARE INFRASTRUCTURE ! SPECIFIC MODE IS IMPLEMENTED IN AN
APPLICATIONS PROGRAM IN THE SAME SENSE THAT WORD PROCESSING IS ON A PERSONAL COMPUTER
0# #ARRYING THE ANALOGY FURTHER COMMON EXPERIENCE WITH THE UNRELIABILITY OF 0#
HARDWARE AND SOFTWARE REQUIRES THAT A SYSTEM OF THE TYPE DEPICTED IN &IGURE MUST
BE REDUNDANT ERROR CHECKING TRUSTED FAIL SAFE IN THE PRESENCE OF FAULTS AND EMBODY
STRICT PROGRAM EXECUTION SECURITY 4HIS IS A VERY CHALLENGING SYSTEM ENGINEERING TASK
%XHAUSTIVE MATHEMATICAL ASSURANCE AND SYSTEM TESTING IS REQUIRED WHICH IS COMPLETELY
DIFFERENT FROM CURRENT COMMERCIAL PERSONAL COMPUTER PRACTICE
! NOTIONAL -&!2 INTEGRATED CORE PROCESSING COMPLEX WITH ITS CORRESPONDING INTER
FACES SIMILAR TO THAT SHOWN IN &IGURE IS SHOWN IN &IGURE WHERE THERE ARE
MULTIPLE REDUNDANT PROCESSING ARRAYS THAT CONTAIN STANDARDIZED MODULES CONNECTED IN
A NON BLOCKING SWITCHED NETWORK )NTERNAL AND EXTERNAL BUSSES CONNECT THE INDIVIDUAL
PROCESSING ARRAYS TO EACH OTHER AS WELL AS TO THE OTHER SUITES SENSORS CONTROLS AND
DISPLAYS
5SUALLY THERE ARE BOTH PARALLEL ELECTRICAL SIGNAL BUSSES AS WELL AS SERIAL FIBER
OPTIC BUSSES DEPENDING ON SPEED AND TOTAL LENGTH IN THE AIRCRAFT 4HE SIGNAL AND DATA
PROCESSOR COMPLEX CONTAINS MULTIPLE PROCESSOR AND MEMORY ENTITIES WHICH MIGHT BE
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ON A SINGLE CHIP OR ON SEPARATE CHIPS DEPENDING ON YIELD COMPLEXITY SPEED CACHE
SIZE AND SO ON %ACH PROCESSOR ARRAY MAY CONSIST OF PROGRAMMABLE SIGNAL PROCESSORS
030 GENERAL PURPOSE PROCESSORS '00 BULK MEMORY "- INPUT OUTPUT )/ AND
A MASTER CONTROL UNIT -#5 4HE 030S PERFORM SIGNAL PROCESSING ON ARRAYS OF SENSOR
DATA 4HE '00S PERFORM PROCESSING IN WHICH THERE ARE LARGE NUMBERS OF CONDITIONAL
BRANCHES 4HE -#5 ISSUES PROGRAMS TO 030S '00S AND "- AS WELL AS MANAGES
OVERALL EXECUTION AND CONTROL 4YPICAL PROCESSING SPEED IS -)03 MILLIONS OF
INSTRUCTIONS PER SECOND PER CHIP BUT MIGHT BE ')03 BILLIONS OF INSTRUCTIONS PER
SECOND IN THE NEAR FUTURE #LOCK FREQUENCIES ARE LIMITED BY ON CHIP SIGNAL PROPAGA
TION BUT ARE UP TO '(Z GIGAHERTZ AND COULD BE '(Z IN THE NEAR FUTURE 3ENSOR
PROCESSING HAS ARRIVED AT THE POINT WHERE THE CONCEPTION OF SUCCESSFUL ALGORITHMS IS
MORE IMPORTANT THAN THE COMPUTATIONAL HORSEPOWER NECESSARY TO CARRY THEM OUT
-&!2 3OFTWARE 3TRUCTURE )MPROPER OPERATION OF MANY FIGHTER SYSTEMS
CAN BE HAZARDOUS !S PREVIOUSLY MENTIONED THE SOFTWARE MUST BE EXHAUSTIVELY
TESTED ERROR CHECKED MATHEMATICALLY TRUSTED FAILSAFE IN THE PRESENCE OF FAULTS
AND EMBODY STRICT PROGRAM EXECUTION SECURITY /NE OF THE MOST IMPORTANT ASPECTS
IS RIGID ADHERENCE TO A STRUCTURED PROGRAM ARCHITECTURE !N OBJECT BASED HIERARCHI
CAL STRUCTURE WHERE EACH LEVEL IS SUBORDINATE TO THE LEVEL ABOVE AND SUBPROGRAMS
ARE CALLED IN STRICT SEQUENCE IS NECESSARY )T ALSO REQUIRES AMONG OTHER THINGS
THAT SUBPROGRAMS NEVER CALL THEMSELVES RECURSIVE CODE OR ANY OTHERS AT THEIR
EXECUTION LEVEL 3UBPROGRAMS OBJECTS ARE CALLED RECEIVE EXECUTION PARAMETERS
FROM THE LEVEL ABOVE THE PARENT AND RETURN RESULTS BACK TO THE CALLING LEVEL !N
EXAMPLE OF SUCH A SOFTWARE STRUCTURE IS SHOWN IN &IGURES AND 4HE SOFTWARE
WOULD BE EXECUTED IN THE HARDWARE SHOWN IN &IGURE &)'52% -&!2 STRUCTURED SOFTWARE
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-&!2 PRIORITY SCHEDULING
!N -&!2 CAN SUPPORT MANY ACTIVITIES OR MODES CONCURRENTLY BY INTERLEAVING
THEIR RESPECTIVE DATA COLLECTIONS 3URVEILLANCE TRACK UPDATES AND GROUND MAPS ARE
EXAMPLES OF SUCH ACTIVITIES 4HE SOFTWARE NEEDED TO SUPPORT EACH ACTIVITY IS MAPPED TO
A SPECIFIC CLIENT MODULE AS SHOWN IN &IGURE %ACH CLIENT MODULE IS RESPONSIBLE FOR
MAINTAINING ITS OWN OBJECT DATABASE AND FOR REQUESTING USE OF THE APERTURE 2EQUESTS
ARE MADE BY SUBMITTING ANTENNA JOB REQUESTS THAT SPECIFY BOTH THE WAVEFORM TO BE USED
HOW TO DO IT AND THE PRIORITY AND URGENCY OF THE REQUEST
! SCHEDULER EXECUTES DURING EACH DATA COLLECTION INTERVAL AND DECIDES WHAT TO DO
NEXT BASED ON THE PRIORITIES AND URGENCIES OF THE ANTENNA JOB REQUESTS THAT HAVE BEEN
RECEIVED 4HIS KEEPS THE APERTURE BUSY AND RESPONSIVE TO THE LATEST ACTIVITY REQUESTS
&OLLOWING THE SELECTION OF THE ANTENNA JOB BY THE SCHEDULER THE FRONT END TRANSMIT AND
RECEIVE HARDWARE IS CONFIGURED AND IN PHASE AND QUADRITURE )1 DATA IS COLLECTED AND
SENT TO THE SIGNAL PROCESSORS 4HERE THE DATA IS PROCESSED IN A MANNER DEFINED BY THE
SENSOR MODE AND THE SIGNAL PROCESSING RESULTS ARE RETURNED TO THE CLIENT THAT REQUESTED
THEM 4HIS TYPICALLY RESULTS IN DATABASE UPDATES ANDOR NEW ANTENNA JOB REQUESTS FROM
THE CLIENT .EW ACTIVITIES CAN BE ADDED AT ANY TIME USING THIS MODULAR APPROACH
!LTHOUGH THIS STRUCTURE IS COMPLEX AND THE SOFTWARE ENCOMPASSES MILLIONS OF LINES
OF CODE MODERN -&!2 SOFTWARE INTEGRITY CAN BE MAINTAINED WITH STRICT CONTROL OF
INTERFACES FORMAL CONFIGURATION MANAGEMENT PROCESSES AND FORMAL VERIFICATION AND
VALIDATION SOFTWARE TOOLS )N ADDITION MOST SUBPROGRAMS ARE DRIVEN BY READ ONLY
TABLES AS SHOWN IN &IGURE SO THAT THE EVOLUTION OF AIRCRAFT TACTICS CAPABILITIES AND
HARDWARE DO NOT REQUIRE REWRITES OF VALIDATED SUBPROGRAMS 3OFTWARE VERSIONS BUILDS
ARE UPDATED EVERY YEAR THROUGHOUT THE LIFETIME OF THE SYSTEM WHICH MAY BE DECADES
%ACH SUBPROGRAM MUST HAVE TABLE DRIVEN ERROR CHECKING AS WELL -ANY LOWER LEVELS ARE
NOT SHOWN IN &IGURES AND THERE MAY BE SEVERAL THOUSAND SUBPROGRAMS IN ALL
2ANGE $OPPLER 3ITUATION -ODERN RADARS HAVE THE LUXURY OF INTERLEAVING MOST
OF THE MODES SUGGESTED IN &IGURE IN REAL TIME AND SELECTING THE BEST AVAILABLE TIME
OR AIRCRAFT POSITION TO INVOKE EACH MODE AS THE MISSION REQUIRES 4HE GEOMETRY THAT MUST BE SOLVED EACH TIME IS SHOWN IN &IGURE 4HE FIGHTER
AIRCRAFT PULSE DOPPLER GEOMETRY IS CENTERED AROUND THE AIRCRAFT TRAVELING AT A VELOCITY
6A AND AT AN ALTITUDE H ABOVE THE %ARTHS SURFACE 4HE RADAR PULSE REPETITION FREQUENCY
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&)'52% 3TRIKE FIGHTER PULSE DOPPLER GEOMETRY 02& GIVES RISE TO A SERIES OF RANGE AND DOPPLER X Y Z AMBIGUITIES AS
SHOWN IN &IGURE WHICH INTERCEPT THE %ARTHS SURFACE AS RANGE hRINGSv AND ISO
DOPPLER hHYPERBOLASv BECAUSE THE %ARTH IS A ROUGH GEOID CONSTANT RANGE AND DOPPLER
CONTOURS ARE NOT ACTUALLY RINGS OR HYPERBOLAS 4HE RADAR ANTENNA PATTERN INTERCEPTS THE
LIMB OF THE %ARTH USUALLY IN BOTH THE MAIN BEAM AND SIDELOBES ! TARGET IN THE MAIN
BEAM AT RANGE 2T AND VELOCITY 6T MAY HAVE TO BE OBSERVED IN THE PRESENCE OF BOTH
RANGE AND DOPPLER AMBIGUITIES /NLY THE TARGETS LINE OF SIGHT VELOCITY 6TLOS IS OBSERV
ABLE ON A SHORT TERM BASIS 4HE RADAR DESIGNERS PROBLEM IS TO SELECT THE BEST WAVEFORM
IN THIS TARGET CLUTTER GEOMETRY (ISTORICALLY THESE WAVEFORMS WERE SELECTED AHEAD OF
TIME AND BUILT INTO THE RADAR HARDWARE AND SOFTWARE -OST MODERN AIRBORNE RADARS
SOLVE THIS GEOMETRY IN REAL TIME AND CONTINUOUSLY SELECT THE BEST AVAILABLE FREQUENCY
02& PULSEWIDTH TRANSMIT POWER SCAN PATTERN ETC
5NFORTUNATELY THE SPECIFICS OF THE WAVEFORM ARE UNPREDICTABLE EVEN TO THE RADAR
WITHOUT EXACT KNOWLEDGE OF THE AIRCRAFT TARGET EARTH VELOCITY GEOMETRY SET AND MODE
OF OPERATION REQUESTED BY THE OPERATOR OR MISSION SOFTWARE 4HIS MAKES TESTING QUITE
DIFFICULT FORTUNATELY TEST EQUIPMENT HAS COME A LONG WAY (ARDWARE IN THE LOOP TEST
ING USING REAL TIME SIMULATION OF THE ENTIRE GEOMETRY AND EXTERNAL WORLD IN THE RADAR
INTEGRATION LABORATORY IS COMMONLY EMPLOYED
!CTIVE %LECTRONICALLY 3CANNED !RRAY !%3! !LTHOUGH MULTIFUNCTIONAL RADARS
HAVE BEEN DEPLOYED WITH MECHANICALLY SCANNED AND ELECTRONICALLY SCANNED ANTENNAS
FULLY MULTIFUNCTIONAL RADARS USE !CTIVE %LECTRONICALLY 3CANNED !RRAYS !%3! WHICH
CONTAIN A TRANSMIT RECEIVE CHANNEL 42 FOR EACH RADIATOR 4HE ADVANTAGES OF !%3!
ARE FAST ADAPTIVE BEAM SHAPING AND AGILITY IMPROVED POWER EFFICIENCY IMPROVED
MODE INTERLEAVING SIMULTANEOUS MULTIPLE WEAPON SUPPORT AND REDUCED OBSERVABIL
ITYn 0ERHAPS HALF THE COST AND COMPLEXITY OF AN !%3! IS IN THE 42 CHANNELS 4HAT
SAID HOWEVER THE FEED NETWORK BEAM STEERING CONTROLLER "3# !%3! POWER SUPPLY
AND COOLING SUBSYSTEM AIR OR LIQUID ARE EQUALLY IMPORTANT -5,4)&5.#4)/.!, 2!$!2 3934%-3 &/2 &)'(4%2 !)2#2!&4
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! MAJOR ENABLER FOR !%3!S IS THE STATE OF THE ART IN MICROWAVE INTEGRATED CIRCUITS
4HIS HAS FOLLOWED THE DRAMATIC COST AND PERFORMANCE GAINS AVAILABLE IN MOST SEMICON
DUCTOR TECHNOLOGIES %ACH 42 CHANNEL HAS SELF DIAGNOSIS FEATURES WHICH CAN DETECT
FAILURE AND COMMUNICATE THAT TO THE BEAM STEERING CONTROLLER FOR FAILURE COMPENSATION
!%3!S CAN ACCOMMODATE UP TO FAILURES WITH VERY LITTLE DEGRADATION IF PROPERLY
COMPENSATED IN THE "3#
&ROM AN -&!2 POINT OF VIEW THE IMPORTANT PARAMETERS ARE VOLUMETRIC DENSITIES
HIGH ENOUGH TO SUPPORT LESS THAN WAVELENGTH SPACING RADIATED POWER DENSITIES HIGH
ENOUGH TO SUPPORT WATTS PER SQ CM RADIATED TO PRIME POWER EFFICIENCIES GREATER
THAN BANDWIDTH OF SEVERAL '(Z ON TRANSMIT AND ALMOST TWICE THAT BANDWIDTH ON
RECEIVE PHASE AND AMPLITUDE CALIBRATION AND CONTROL ADEQUATE TO PROVIDE AT LEAST n D"
RMS SIDELOBES AMPLITUDE CONTROL ADEQUATE TO PROVIDE D" POWER MANAGEMENT NOISE
PERFORMANCE ADEQUATE TO SUPPORT THE SUBCLUTTER VISIBILITY REQUIREMENTS AND FINALLY SUF
FICIENT STORAGE AND COMPUTING TO ALLOW BEAM REPOINTINGADJUSTMENT IN A FRACTION OF
MSEC &AST BEAM ADJUSTMENT REQUIRES HIGH SPEED BUSSES TO EACH 42 CHANNEL
/NE OF THE PRINCIPAL ADVANTAGES OF AN !%3! IS THE ABILITY TO MANAGE BOTH POWER
AND SPATIAL COVERAGE ON A SHORT TERM BASIS S OF MSEC /FTEN ANOTHER ADVANTAGE IS
THAT BOTH THE NOISE FIGURE IS LOWER AND RADIATED POWER IS HIGHER FOR A GIVEN AMOUNT OF
PRIME POWER 4HIS IS BECAUSE THE 2& PATH LENGTHS CAN BE MUCH SHORTER WHICH USUALLY
LEADS TO LOWER FRONT END LOSSES %ACH RADIATING ELEMENT IS USUALLY DESIGNED TO BE VERY
BROADBAND AND IS DRIVEN BY A 42 CHANNEL IN A TYPICAL !%3! ARRAY 4HERE ARE TYPI
CALLY A FEW THOUSAND CHANNELS IN AN -&!2 !%3! %ACH CHANNEL CONTAINS FIRST LEVEL
POWER REGULATION FILTERING LOGIC CALIBRATION TABLES AS WELL AS THE OBVIOUS 2& FUNC
TIONS 3OME CHANNELS IN THE ARRAY ARE DEDICATED TO OTHER FUNCTIONS SUCH AS CALIBRATION
JAMMER NULLING SIDELOBE BLANKING CLOSE IN MISSILE DATALINK OUT OF BAND DIRECTION
FINDING ETC !LSO THERE ARE USUALLY SOME CHANNELS AT THE EDGE OF THE ARRAY THAT
ARE PASSIVE AND IMPROVE THE SIDELOBES AND 2#3 PATTERN
&IGURE SHOWS THE COMPARISON BETWEEN A CONVENTIONAL MECHANICALLY SCANNED
RADAR WITH THE LOW NOISE AMPLIFIER AND A HIGH POWER TRAVELING WAVE TUBE TRANSMIT
TER MOUNTED OFF THE GIMBAL VERSUS A REAL TIME ADAPTED !%3! WITH TWO DIFFERENT SCAN
REGIMES FOR THE SAME AMOUNT OF INPUT PRIME POWER !%3! PERFORMANCE FALLS OFF FOR
LARGE SCAN COVERAGE BECAUSE OF THE LOWER PROJECTED APERTURE AREA FOR A FIXED MOUNTING AS
SHOWN IN &IGURE ! MECHANICAL SCAN HAS THE SAME PROJECTED AREA IN ALL DIRECTIONS AND
LARGE SCAN ANGLES MARGINALLY REDUCE RADOME LOSSES WHICH RESULTS IN SLIGHTLY IMPROVED
LARGE ANGLE PERFORMANCE .ONETHELESS !%3! PERFORMANCE IS USUALLY SUPERIOR INSIDE
&)'52% %XAMPLE !%3! MANAGEMENT COMPARISON ADAPTED x°£ä
2!$!2 (!.$"//+
A on AZIMUTH SCAN 5SUALLY A FIGHTER CANT ENGAGE AT LONG RANGE OUTSIDE THIS
AZIMUTH FOR KINEMATIC REASONS
4HE PERFORMANCE DIFFERENCES DEPICTED IN &IGURE ARE THE RESULT OF THREE FACTORS
THE INSTALLED APERTURE CAN BE LARGER IN NET PROJECTED AREA AT THE AIRCRAFT IN FLIGHT
HORIZONTAL DUE TO ELIMINATION OF GIMBAL SWING SPACE HIGHER RADIATED POWER DUE TO
LOWER LOSSES AND BETTER EFFICIENCY AND LOWER LOSSES BEFORE THE LOW NOISE AMPLI
FIER 4HE OTHER MAJOR ADVANTAGE IS THAT SEARCH VOLUME CAN BE CHANGED DYNAMICALLY TO
FIT THE INSTANT TACTICAL SITUATION AS SUGGESTED IN &IGURE 4HE FEED NETWORK IS MUNDANE BUT CRITICALLY IMPORTANT )N SINGLE TUBE TRANSMIT
TERS THE FEED IS HEAVY BECAUSE IT MUST CARRY HIGH POWER AT LOW LOSS !%3! FEEDS USE
SMALLER COAX STRIPLINE MICROSTRIP OR 2& MODULATED LIGHT IN FIBER OPTICS FOR TRANSMIT
AND RECEIVE 2& SINCE LESS THAN WATTS 2& OR OPTICAL IS USUALLY REQUIRED (OWEVER
SIGNIFICANT $# POWER IS STILL REQUIRED FOR 2& FEED DISTRIBUTION AMPLIFIERS BECAUSE THOU
SANDS MUST BE DRIVEN #OST WEIGHT AND COMPLEXITY IS STILL AN ISSUE BECAUSE MULTIPLE
PHASE CENTERS NECESSARY FOR ADAPTIVE ARRAY PERFORMANCE REQUIRE MULTIPLE MANIFOLDS
5SUALLY ONCE A SUBARRAY IS FORMED IN THE MANIFOLDS IT IS DIGITIZED AND MULTIPLEXED FOR
ADAPTIVE SIGNAL PROCESSING
!NOTHER IMPORTANT FUNCTION IS BEAM STEERING CONTROL "3# 4HE "3# DOES ARRAY
CALIBRATION FAILED ELEMENT COMPENSATION PHASE AND AMPLITUDE SETTING FOR BEAM
STEERING AS WELL AS SPACE TIME ADAPTIVE OPERATIONn 4HE "3# IS USUALLY REALIZED
WITH A COMBINATION OF GENERAL PURPOSE PROCESSING OF THE TYPE FOUND IN A PERSONAL
COMPUTER WITH VERY HIGH SPEED INCREMENTAL PHASE AND AMPLITUDE CALCULATION AND 42
MODULE INTERFACE HARDWARE "OTH SCANNING AND ADAPTIVE OPERATION REQUIRE VERY LOW
LATENCY IE THE TIME BETWEEN THE SENSED NEED AND THE FIRST PULSE AT THE TARGET IS USUALLY
MSEC BEAM CONTROL IN A HIGH SPEED AIRCRAFT PLATFORM
,ASTLY THE !%3! REQUIRES A VERY SIGNIFICANT POWER SUPPLY 0OWER SUPPLIES HAVE
A HISTORY OF BEING HEAVY HOT AND UNRELIABLE %VEN THE BEST SYSTEMS STILL HAVE OVERALL
POWER EFFICIENCIES PRIME POWER IN TO 2& OUT IN SPACE IN THE n REGION IN SPITE
OF YEARS OF DEVELOPMENT 4HE TYPICAL !%3! REQUIRES LOW VOLTAGE AND HIGH CURRENT
AT THE 42 CHANNEL 4HIS FORCES LARGE CONDUCTORS IN THE ABSENCE OF HIGH POWER LIGHT
WEIGHT SUPERCONDUCTORS NOT AVAILABLE AT THIS WRITING )T ALSO REQUIRES VERY LOW VOLTAGE
DROP RECTIFIERS AND REGULATORS #OOLING IS GENERALLY A SIGNIFICANT PERFORMANCE BURDEN
5SUALLY THE POWER SUPPLIES ARE DISTRIBUTED TO IMPROVE RELIABILITY AND FAULT TOLERANCE
/FTEN POWER CONVERTERS ARE OPERATED AT SWITCHING FREQUENCIES UP TO SEVERAL HUNDRED
MEGAHERTZ TO REDUCE THE SIZE OF MAGNETICS AND FILTER COMPONENTS AND SOMETIMES THE
SWITCHING FREQUENCIES ARE SYNCHRONIZED TO THE RADAR MASTER CLOCK
x°ÓÊ /9* Ê--" -Ê
Ê"
-
!IR TO 3URFACE -ISSION 0ROFILE 4HE MODE STRUCTURE OF ANY MODERN FIGHTER AIR
CRAFT ARISES FROM MISSION PROFILES /NE TYPICAL MISSION PROFILE FOR AN AIR TO SURFACE
! 3 STRIKE IS SHOWN IN &IGURE 4HE MISSION PROFILE BEGINS WITH A TAKEOFF CON
TINUES THROUGH FLIGHT TO A TARGET AND ULTIMATELY RETURNS TO THE STARTING POINT !LONG THE
WAY THE AIRCRAFT USES A VARIETY OF MODES TO NAVIGATE SEARCH AND ACQUIRE TARGETS TRACK
TARGETS DELIVER WEAPONS ASSESS BATTLE DAMAGE ENGAGE IN COUNTERMEASURES AND MONI
TOR AND CALIBRATE ITS PERFORMANCE !%3!S HAVE DEMONSTRATED SIMULTANEOUS MULTIPLE
WEAPON DELIVERIES
-5,4)&5.#4)/.!, 2!$!2 3934%-3 &/2 &)'(4%2 !)2#2!&4
&)'52% x°££
4YPICAL AIR TO SURFACE MISSION PROFILE !IR TO 3URFACE -ODE 3UITE 4HE MISSION NATURALLY CREATES THE NEED FOR AN AIR
TO SURFACE MODE SUITE FOR FIGHTER RADAR AS SHOWN IN &IGURE %ACH GENERAL CAT
EGORY OF OPERATION CONTAINS MODES PRIMARILY FOR THAT FUNCTION BUT MODES WILL OFTEN
BE INVOKED DURING OTHER PARTS OF THE MISSION 7ITHIN EACH MODE SHOWN IN &IGURE THERE IS OPTIMIZATION FOR THE PARTICULAR COMBINATION OF ALTITUDE RANGE TO THE TARGET
ANTENNA FOOTPRINT ON THE %ARTHS SURFACE RELATIVE TARGET AND CLUTTER DOPPLER DWELL TIME
AVAILABLE PREDICTED TARGET STATISTICAL BEHAVIOR TRANSMITTED FREQUENCY AND DESIRED RESO
LUTION /BVIOUSLY EACH MODE MUST NOT COMPROMISE SOME REQUIRED LEVEL OF MISSION
STEALTHn ! MODERN FIGHTER IS NET CENTRIC AND EXCHANGES SUBSTANTIAL INFORMATION WITH
OTHER SYSTEMS "OTH THE FIGHTERS WINGMAN SUPPORT AIRCRAFT AND SURFACE NODES MAY
EXCHANGE COMPLETE DATA AND TASKING IN REAL TIME TO FACILITATE A MISSION 4HE FIGHTER
AND ITS WINGMAN WILL COORDINATE MODE TASKING SO THAT DURING A HIGH RESOLUTION GROUND
MAP WHICH COULD TAKE A MINUTE TO FORM THE WINGMAN MIGHT BE PERFORMING AN AIR TO
AIR SEARCH AND TRACK TO PROTECT BOTH OF THEM
&)'52% &IGHTER AIRCRAFT AIR TO SURFACE RADAR MODE SUITE x°£Ó
2!$!2 (!.$"//+
3OME MODES ARE USED FOR SEVERAL OPERATIONAL CATEGORIES SUCH AS REAL BEAM MAP
2"- FIXED TARGET TRACK &44 DOPPLER BEAM SHARPENING $"3 AND SYNTHETIC APER
TURE RADAR 3!2 USED NOT ONLY FOR NAVIGATION BUT ALSO FOR ACQUISITION AND WEAPON
DELIVERY TO FIXED TARGETSn 3!2 MAY ALSO BE USED TO DETECT TARGETS IN EARTHWORKS OR
TRENCHES COVERED WITH CANVAS AND A SMALL AMOUNT OF DIRT WHICH ARE INVISIBLE TO %/
OR )2 SENSORS 3IMILARLY AIR TO SURFACE RANGING ! 3 2ANGE AND PRECISION VELOCITY
UPDATE 065 MAY BE USED FOR WEAPON SUPPORT TO IMPROVE DELIVERY ACCURACY AS WELL
AS NAVIGATION 4ERRAIN FOLLOWING AND TERRAIN AVOIDANCE 4&4! IS USED FOR NAVIGATION AT VERY
LOW ALTITUDES OR IN MOUNTAINOUS TERRAIN 3EA SURFACE SEARCH 333 SEA SURFACE TRACK
334 AND INVERSE SYNTHETIC APERTURE RADAR )3!2 WHICH WILL BE DESCRIBED LATER IN
THE CHAPTER ARE USED PRIMARILY FOR THE ACQUISITION AND RECOGNITION OF SHIP TARGETS
'ROUND MOVING TARGET INDICATION '-4) AND GROUND MOVING TARGET TRACKING '-44
ARE USED PRIMARILY FOR THE ACQUISITION AND RECOGNITION OF SURFACE VEHICLE TARGETS BUT
ALSO FOR RECOGNIZING LARGE MOVEMENTS OF SOLDIERS AND MATERIALS IN A BATTLE SPACE (IGH
POWER JAMMING (I0WR*AM IS A COUNTERMEASURE AVAILABLE FROM !%3!S DUE TO THEIR
NATURAL BROADBAND BEAM AGILE HIGH GAIN AND HIGH POWER ATTRIBUTES !%3!S ALSO ALLOW
LONG RANGE AIR TO SURFACE DATA LINKS ! 3 $ATA ,INK THROUGH THE RADAR PRIMARILY FOR
MAP IMAGERY "ECAUSE THERE MAY BE THOUSANDS OF WAVELENGTHS AND A GAIN OF MILLIONS
THROUGH A RADAR AUTOMATIC GAIN CONTROL AND CALIBRATION !'##!, IS USUALLY REQUIRED
FAIRLY OFTEN -ODES OPTIMIZED FOR THIS FUNCTION ARE INVOKED THROUGHOUT A MISSION
7AVEFORM 6ARIATIONS BY -ODE !LTHOUGH THE SPECIFIC WAVEFORM IS HARD TO PRE
DICT TYPICAL WAVEFORM VARIATIONS CAN BE TABULATED BASED ON OBSERVED BEHAVIOR OF A
NUMBER OF EXISTING ! 3 RADAR SYSTEMS 4ABLE SHOWS THE RANGE OF PARAMETERS THAT
CAN BE OBSERVED AS A FUNCTION OF RADAR MODE 4HE PARAMETER RANGES LISTED ARE 02&
PULSE WIDTH DUTY CYCLE PULSE COMPRESSION RATIO INDEPENDENT FREQUENCY LOOKS PULSES
PER COHERENT PROCESSING INTERVAL #0) TRANSMITTED BANDWIDTH AND TOTAL PULSES IN A
4IME /N 4ARGET 4/4 /BVIOUSLY MOST RADARS DO NOT CONTAIN ALL OF THIS VARIATION BUT MODES EXIST IN MANY
FIGHTER AIRCRAFT WHICH REPRESENT A GOOD FRACTION OF THE PARAMETER RANGE -OST FIGHTER
RADARS ARE FREQUENCY AGILE SINCE THEY WILL BE OPERATED IN CLOSE PROXIMITY TO SIMILAR OR
IDENTICAL SYSTEMS 4HE FREQUENCY USUALLY CHANGES IN A CAREFULLY CONTROLLED COMPLETELY
COHERENT MANNER DURING A #0) 4HIS CAN BE A WEAKNESS FOR CERTAIN KINDS OF JAMMING
SINCE THE PHASE AND FREQUENCY OF THE NEXT PULSE IS PREDICTABLE 3OMETIMES TO COUNTER
ACT THIS WEAKNESS THE FREQUENCY SEQUENCE IS PSEUDORANDOM FROM A PREDETERMINED SET
WITH KNOWN AUTOCORRELATION PROPERTIES FOR EXAMPLE &RANK #OSTAS 6ITERBI 0 CODES
! MAJOR DIFFICULTY WITH COMPLEX WIDEBAND FREQUENCY CODING IS THAT THE PHASE SHIFT
ERS IN A PHASE SCANNED ARRAY MUST BE CHANGED ON AN INTRA OR INTER PULSE BASIS GREATLY
COMPLICATING BEAM STEERING CONTROL AND ABSOLUTE 42 CHANNEL PHASE DELAY !NOTHER
CHALLENGE IS MINIMIZING POWER SUPPLY PHASE PULLING WHEN 02&S AND PULSEWIDTHS VARY
OVER MORE THAN RANGE -&!2 SYSTEMS NOT ONLY HAVE A WIDE VARIATION IN 02&
AND PULSEWIDTH BUT ALSO USUALLY EXHIBIT LARGE INSTANT AND TOTAL BANDWIDTH #OUPLED
WITH THE LARGE BANDWIDTH IS THE REQUIREMENT FOR LONG COHERENT INTEGRATION TIMES 4HIS
REQUIREMENT NATURALLY LEADS TO EXTREME STABILITY MASTER OSCILLATORS AND ULTRA LOW NOISE
SYNTHESIZERS
!IR TO !IR -ISSION 0ROFILE *UST AS WITH AN AIR TO SURFACE MISSION THE MODE
STRUCTURE OF A MODERN FIGHTER AIRCRAFT AIR TO AIR MISSION ARISES FROM ITS PROFILE ! TYPI
CAL MISSION PROFILE FOR AIR TO AIR ! ! IS SHOWN IN &IGURE 4HE MISSION PROFILE
-5,4)&5.#4)/.!, 2!$!2 3934%-3 &/2 &)'(4%2 !)2#2!&4
4!",% x°£Î
4YPICAL 7AVEFORM 0ARAMETERS ! 3 -ODES 2ADAR
-ODES
02&
K(Z
0ULSE
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$UTY
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#OMP
2ATIO
&REQ
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4RANSMITTED
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-AP
n
n
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n
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n
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n
$OPPLER
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n
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n
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n
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n
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3!2
n
n
n
n
n
nK
n
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! 3 2ANGE
n
n
n
n
n
n
n
n
065
n
n
n
n
n
n
n
n
4&4!
n
n
n
n
n
n
n
n
3EA 3URFACE
3EARCH
n
n
n
n
n
n
n
n
)NVERSE
3!2
n
n
n
n
n
n
n
n
'-4)
n
n
n
n
n
n
n
n
&IXED
4ARGET
4RACK
n
n
n
n
n
n
n
n
'-44
n
n
n
n
n
n
n
n
3EA 3URFACE
4RACK
n
n
n
n
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n
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(I0WR *AM
n
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BEGINS WITH AN AIRFIELD OR CARRIER TAKEOFF CONTINUES THROUGH FLIGHT PENETRATING INTO
AN ENEMY BATTLE SPACE SEARCHES FOR AIR TARGETS TO ATTACK AND ULTIMATELY RETURNS TO
THE STARTING POINT !LONG THE WAY THE AIRCRAFT USES A VARIETY OF MODES TO NAVIGATE
EXCHANGE DATA WITH COMMAND CONTROL COMMUNICATIONS INTELLIGENCE SURVEILLANCE
&)'52% 4YPICAL ! ! MISSION PROFILE
x°£{
2!$!2 (!.$"//+
RECONNAISSANCE #)32 ASSETS SEARCH AND ACQUIRE AIRBORNE TARGETS TRACK AND SEPARATE
BENIGN TARGETS FROM THREATS DELIVER WEAPONS ESCAPE AND ENGAGE IN COUNTERMEASURES
MONITOR AND CALIBRATE ITS PERFORMANCE AND RETURN TO BASE
!IR TO !IR -ODE 3UITE 3IMILARLY THE ! ! MISSION NATURALLY CREATES THE NEED FOR
A CORRESPONDING MODE SUITE FOR THE RADAR AS SHOWN IN &IGURE !T THE RADAR SEN
SOR AND AIR TO AIR MODE SOFTWARE LEVEL THERE IS ADAPTIVE TASK PRIORITIZATION TO INSURE THAT
THE HIGHEST PROCESSOR PRIORITIZED PILOT SELECTED THREAT IS SERVICED FIRST 0ASSIVE MODES
ARE INTERLEAVED WITH ACTIVE OPERATION TO IMPROVE SURVIVABILITY AND PASSIVE TRACKING AND
)$ %ACH MODE SHOWN IN &IGURE IS OPTIMIZED IN REAL TIME FOR THE PARTICULAR COMBI
NATION OF ALTITUDE RANGE TO THE TARGET DENSITY OF TARGET THREATS ANTENNA FOOTPRINT ON THE
%ARTHS SURFACE RELATIVE TARGET AND CLUTTER DOPPLER DWELL TIME AVAILABLE PREDICTED TARGET
STATISTICAL BEHAVIOR TRANSMITTED FREQUENCY AND DESIRED RESOLUTION 4HE MODE CATEGORY hAUTONOMOUS AND CUED SEARCHv CONTAINS THE MODES MOST COM
MONLY ASSOCIATED WITH FIGHTER RADARS 4HERE ARE USUALLY TWO RANGE GATED HIGH PULSE REP
ETITION FREQUENCY (02& MODES VELOCITY SEARCH 63 PRIMARILY DEDICATED TO LONGEST
RANGE DETECTION AND RANGE WHILE SEARCH 273 WHICH USES SOME FORM OF &- RANGING
TO ESTIMATE TARGET RANGE 4HERE IS A MEDIUM 02& -02& MODE WHICH PROVIDES ALL
ASPECT VELOCITY RANGE SEARCH 623 AT THE EXPENSE OF POORER LONG RANGE PERFORMANCE
)N ADDITION THERE ARE TWO PASSIVE MODES PASSIVE SEARCH AND RANGING IN WHICH THE
RADAR DETECTS AND ESTIMATES RANGE AND ANGLE TO AN EMITTER OR BISTATICALLY WINGMAN OR
SUPPORT AIRCRAFT ILLUMINATED TARGET AND %3- SHARED APERTURE IN WHICH THE 2& AND PRO
CESSOR COMPLEX DETECTS ESTIMATES WAVEFORM PARAMETERS AND RECORDS THEM FOR FUTURE
USE 0ASSIVE SEARCH MAY BE COMBINED WITH CUED BURST RANGING TO BETTER ESTIMATE EMIT
TER LOCATION %XTENDED VOLUME SEARCH IS A MODE USED WITH CUEING FROM ANOTHER ON OR
OFF BOARD SENSOR IN WHAT NORMALLY WOULD BE AN UNFAVORABLE GEOMETRY
-ANY MODES AND FUNCTIONS ARE SHARED IN COMMON WITH ! 3 ESPECIALLY COUNTERMEA
SURES AND PERFORMANCE MONITORING %XTREMELY IMPORTANT IN BOTH MODES IS IMPLEMENTA
TION OF EMISSIONS CONTROL TO MINIMIZE THE ABILITY OF THE ADVERSARY TO DETECT TRACK AND
ATTACK USING THE RADAR EMISSION 7ITHOUT CARE THESE EMISSIONS CAN EASILY SERVE AS A
STRONG GUIDANCE SIGNAL FOR A HOSTILE ANTIRADIATION MISSILE !2- !NTENNA APERTURES
THAT HAVE MULTIPLE INDEPENDENT PHASE CENTERS CAN PERFORM BOTH ADAPTIVE CLUTTER CANCEL
LATION AS WELL AS JAMMER CANCELLATION WITH SUITABLE HARDWARE AND SOFTWARE n
&)'52% ! ! MODE SUITE
x°£x
-5,4)&5.#4)/.!, 2!$!2 3934%-3 &/2 &)'(4%2 !)2#2!&4
4HE SUBSUITE OF MULTI TARGET TRACK -44 CONTAINS CONVENTIONAL TRACK WHILE SCAN
473 PASSIVE TRACKING OF EMITTERS OR ECHOES FROM BISTATIC ILLUMINATION MISSILE TRACK
ING WITH OR WITHOUT A MISSILE DATALINK OR BEACON AND SEVERAL MODES TO RECOGNIZE
TARGET NUMBER AND TYPE RAID ASSESSMENT AND NONCOOPERATIVE TARGET RECOGNITION USU
ALLY INCORRECTLY CALLED TARGET IDENTIFICATION 4HE FIGHTER AND WINGMAN WILL COORDINATE
MODES THROUGH THE NET SO THAT BOTH HAVE SITUATIONAL AWARENESS DURING THE LONG TIME
SPAN REQUIRED TO PROVIDE TARGET RECOGNITION
!NOTHER IMPORTANT FIGHTER CATEGORY IS WEAPON SUPPORT -ISSILE UPDATE IS THE MEA
SUREMENT OF MISSILE AND TARGET POSITION VELOCITY AND ACCELERATION TO ALLOW STATISTICALLY
INDEPENDENT MEASUREMENTS FOR TRANSFER ALIGNMENT AS WELL AS MISSILE STATE OF HEALTH
-ISSILE UPDATE PROVIDES THE LATEST TARGET INFORMATION AND FUTURE DYNAMICS PREDICTION
BY DATA LINK )2 MISSILE SLAVING CO ALIGNS RADAR AND SEEKER 3INCE GUN EFFECTIVE RANGES
ARE VERY SHORT GUN RANGING CAUSES THE RADAR TO SENSE THE GUN FIELD OF FIRE PREDICTS
ANGLE RATE AND MEASURES RANGE TO A TARGET FOR TENTATIVE GUNFIRE )T MAY ALSO TRACK GUN
ROUNDS DURING FIRE
4HERE ARE THOUSANDS OF ELECTRICAL DEGREES OF PHASE BETWEEN FREE SPACE AND THE !$
CONVERTERS 4HE COMBINATION OF TEMPERATURE TIME AND MANUFACTURING TOLERANCES GIVES
RISE TO THE NEED FOR SELF CALIBRATION TEST FAULT DETECTION FAILURE DIAGNOSIS AND NEEDED
CORRECTIONS WHICH ARE PERFORMED BY A SUBSUITE OF PERFORMANCE MONITOR SOFTWARE
4IMING 3TRUCTURE 4HE SIGNIFICANCE OF THE REMAINING PARAMETERS IN 4ABLES AND CAN BEST BE ILLUSTRATED WITH A TIMING STRUCTURE TYPICAL OF FIGHTER RADARS &IGURE SHOWS A MODERN RADAR TIMING STRUCTURE IN A SEQUENCE OF PROGRESSIVELY
EXPANDED TIMELINES 4HE FIRST ROW OF &IGURE SHOWS A TYPICAL SCAN CYCLE COVERING
THE REQUIRED VOLUME OF INTEREST FOR A SPECIFIC MODE 4HE TIME SPAN FOR A FULL SCAN CYCLE
MIGHT BE TO SECONDS )NSIDE THE TOTAL SCAN CYCLE TIME THERE MAY BE SEVERAL BARS OF
A SCANNED REGION OF SPACE WITH A TIME SPAN OF A FEW TENTHS OF A SECOND ! BAR IS A SCAN
SEGMENT ALONG A SINGLE ANGULAR TRAJECTORY AS SHOWN IN &IGURE LATER IN THE CHAPTER
4!",% 4YPICAL 7AVEFORM 0ARAMETERS ! ! -ODES
4OTAL
0ULSES
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n
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&)'52% 4YPICAL -&!2 TIMING SEQUENCES #OURTESY 3CI4ECH 0UBLISHING
%ACH BAR CONSISTS OF MULTIPLE BEAM POSITIONS OF A FEW TENS OF MILLISECONDS EACH WHICH
ARE COMPUTED ON THE FLY TO OPTIMALLY COVER THE SELECTED VOLUME %ACH BEAM CYCLE IN TURN
MAY CONTAIN ONE OR MORE RADAR MODES OR SUBMODES SUCH AS THOSE CONTAINED IN 4ABLES OR AND DEPICTED IN THE LOWEST LINE OF &IGURE 4HE MODES MAY NOT BE INVOKED EACH
TIME DEPENDING ON THE GEOMETRY BETWEEN THE AIRCRAFT AND THE INTENDED TARGET SET
4HE MODE TIME IS BROKEN UP INTO COHERENT PROCESSING INTERVALS #0)S ! COHER
ENT PROCESSING INTERVAL IS SEGMENTED AS SHOWN IN THE BOTTOM ROW OF &IGURE 4HE
PARTICULAR EXAMPLE SHOWN IS TRACKING THAT MIGHT BE USED IN &44 '-44 065 OR ! '
2ANGING AS SHOWN PREVIOUSLY IN &IGURE AND LATER IN &IGURES AND )T
CONSISTS OF A FREQUENCY CHANGE SETTLING TIME PASSIVE RECEIVING TO BE SURE THE BAND ISNT
JAMMED CALIBRATE THAT DOESNT INTENTIONALLY RADIATE BUT OFTEN THERE IS SOME 2& LEAKAGE
RADIATED AN AUTOMATIC GAIN CONTROL !'# INTERVAL IN WHICH A NUMBER OF PULSES ARE
TRANSMITTED TO SET THE RECEIVER GAIN AND FINALLY TWO INTERVALS IN WHICH RANGE DOPPLER AND
ANGLE DISCRIMINANTS ARE FORMED 4HESE #0)S OFTEN BUT NOT ALWAYS HAVE CONSTANT POWER
FREQUENCY SEQUENCE 02& SEQUENCE PULSEWIDTH PULSE COMPRESSION AND BANDWIDTH x°ÎÊ ‡Ê"
Ê
- ,*/" -ÊEÊ76 ",-
!IR TO !IR 3EARCH !CQUISITION AND 4RACKˆ -EDIUM 02& )T MAY BE INSTRUC
TIVE TO EXAMINE HOW SEVERAL MODES ARE GENERATED AND PROCESSED TO UNDERSTAND WHY THE
WAVEFORMS MUST BE THE WAY THEY ARE -EDIUM 02& TRADES LONG RANGE DETECTION PERFOR
MANCE SEE &IGURE LATER IN THE CHAPTER FOR ALL ASPECT TARGET DETECTION /FTEN
HIGH AND MEDIUM 02& WAVEFORMS ARE INTERLEAVED ON ALTERNATE SCANS SEE &IGURE TO
IMPROVE TOTAL PERFORMANCE !FTER YEARS OF SEARCHING FOR AN OPTIMUM SET MOST
MODERN MEDIUM 02& MODES HAVE DEVOLVED TO A RANGE OF 02&S BETWEEN AND K(Z
IN A DETECTION SET OF FOR THE TIME ON TARGET n 4HESE 02&S ARE CHOSEN TO MINIMIZE
RANGE AND VELOCITY BLIND ZONES WHILE SIMULTANEOUSLY ALLOWING UNAMBIGUOUS RESOLU
TION OF TARGET RANGE AND DOPPLER RETURNS IN A SPARSE TARGET SPACE 2ANGE BLIND
ZONES ARE THOSE RANGES IN WHICH A TARGET IS ECLIPSED BY THE TRANSMITTED PULSE 6ELOCITY
OR DOPPLER BLIND ZONES ARE THOSE VELOCITIES OR DOPPLERS THAT ARE EXCLUDED DUE TO THE
-5,4)&5.#4)/.!, 2!$!2 3934%-3 &/2 &)'(4%2 !)2#2!&4
x°£Ç
MAIN BEAM CLUTTER AND GROUND MOVING TARGET FILTER REJECTION NOTCH 4ARGET DETEC
TION REQUIRES DETECTIONS IN AT LEAST OF THE 02&S WITH ALL 02&S CLEAR AT MAXIMUM
RANGE 4HE 02& SELECTION CRITERIA USUALLY REQUIRES THAT THE 02& SET IS CLEARˆIN
OTHER WORDS AT LEAST A SPECIFIED NUMBER TYPICALLY OF 02&S MUST HAVE AN ABOVE
THRESHOLD RETURN ECHO FOR THE MINIMUM SPECIFIED TARGET FOR THE FULL SPECIFIED RANGE
DOPPLER COVERAGE
! TYPICAL PROCESSING BLOCK DIAGRAM IS GIVEN IN &IGURE %ACH 02& PROCESSING
INTERVAL IS DIFFERENT BUT THEY AVERAGE OUT TO AN OPTIMUM AS SHOWN LATER IN &IGURE "OTH MAIN AND GUARD CHANNEL PROCESSING IS REQUIRED TO REJECT FALSE TARGETS 3OME
34!0 PROCESSING MAY HAVE BEEN PERFORMED BEFORE THIS PROCESS BUT TRADITIONAL SIDE
LOBE AND MAIN BEAM CLUTTER IS LESS OF A LIMIT THAN GROUND MOVING TARGETS WHICH HAVE
VERY LARGE CROSS SECTIONS AND EXO DOPPLERS IE DOPPLER FAR ENOUGH OUT OF MAIN BEAM
CLUTTER THAT DETECTION IS NOT LIMITED BY THE CLUTTER RETURN -02& USUALLY HAS A SMALL
AMOUNT OF PULSE COMPRESSION TO WHICH STILL MAY REQUIRE DOPPLER COMPEN
SATION -AIN AND GUARD CHANNELS ARE PROCESSED IN THE SAME WAY /BVIOUSLY THE TWO
SPECTRA ARE QUITE DIFFERENT AND SEPARATE FALSE ALARM AND NOISE ENSEMBLE ESTIMATES ARE
MADE 4HIS LEADS TO SEPARATE THRESHOLD SETTINGS -ULTIPLE CHANNELS ARE USED TO ESTIMATE
INTERFERENCE AND SELECT %##- STRATEGY -AIN CHANNEL DETECTIONS ARE EXAMINED FOR
'-4S AND CENTROIDED IN RANGE AND DOPPLER BECAUSE A RETURN IN RANGE OR DOPPLER MAY
STRADDLE MULTIPLE BINS THE CENTROID OF THOSE RETURNS IN MULTIPLE BINS MUST BE ESTIMATED
FROM THE AMPLITUDE IN EACH BIN AND THE NUMBER OF BINS STRADDLED 4HE GUARD CHANNEL
IS DETECTED AND THE THRESHOLDED RESULTS ARE USED TO GATE THE MAIN CHANNEL RESULTS FOR THE
FINAL HIT MISS COUNT 'ENUINE TARGETS ARE RESOLVED IN RANGE AND DOPPLER PRESENTED TO A
DISPLAY AND USED FOR 473 CORRELATION AND TRACKING
&ALSE ALARMS ARE A CRITICAL ISSUE IN MOST RADAR MODES 4HESE ARE USUALLY SUPPRESSED
FOR THERMAL NOISE BY CONSTANT FALSE ALARM RATE THRESHOLDING COINCIDENCE DETECTION
AND POST DETECTION INTEGRATION WITH FREQUENCY AGILITY #LUTTER FALSE ALARMS ARE SUP
PRESSED BY ADAPTIVE APERTURE TAPERING LOW NOISE FRONT END HARDWARE WIDE DYNAMIC
RANGE !$S CLUTTER REJECTION FILTERING INCLUDING 34!0 PULSE COMPRESSION SIDELOBE
SUPPRESSION DOPPLER FILTER SIDELOBE CONTROL GUARD CHANNEL PROCESSING RADOME REFLEC
TION LOBE COMPENSATION ANGLE RATIO TESTS SEE &IGURE AND THE hFRINGE REGIONv FOR
AN EXAMPLE ANGLE RATIO TEST AND ADAPTIVE 02& SELECTION
&)'52% 4YPICAL -02& PROCESSING ADAPTED COURTESY 3CI4ECH 0UBLISHING
x°£n
2!$!2 (!.$"//+
&)'52% -EDIUM 02& RANGE VELOCITY BLIND ZONES
-02& 4YPICAL 2ANGE $OPPLER "LIND -AP &OR EXAMPLE A TYPICAL -02& SET
FOR 8 BAND WITH RANGE DOPPLER COVERAGE OF KMn K(Z IS SHOWN IN &IGURE 4HIS SET IS FOR A n ANTENNA BEAMWIDTH OWNSHIP IE THE RADAR CARRYING FIGHTER
VELOCITY OF MS AND AN ANGLE OFF THE VELOCITY VECTOR OF n 4HE 02& SET IS AND K(Z (ISTORICALLY A 02& SET WAS
CALCULATED DURING DESIGN AND REMAINED FIXED DURING DEPLOYMENT -ODERN MULTIFUNC
TIONAL RADAR COMPUTING IS SO ROBUST THAT 02& SETS CAN BE SELECTED IN REAL TIME BASED
ON SITUATION GEOMETRY AND LOOK ANGLE 4HE SET WHICH GENERATED &IGURE ON THE
AVERAGE IS CLEAR ON OUT OF 02&S FOR A SINGLE TARGET %XCEPT FOR TWO SMALL DOPPLER
REGIONS ALL THE 02&S ARE CLEAR AT MAXIMUM RANGE WHICH PROVIDES MAXIMUM DETEC
TION AND MINIMUM LOSS AT THE DESIGN RANGE &OR SOME PULSE COMPRESSION WAVEFORMS
THE ECLIPSING LOSS IS ALMOST LINEAR AND PARTIAL OVERLAP STILL ALLOWS SHORTER RANGE DETEC
TION %CLIPSING LOSS IS THAT DIMINISHMENT OF RECEIVED POWER WHEN THE RECEIVER IS
OFF DURING THE TRANSMITTED PULSE )T IS OFTEN THE LARGEST SINGLE LOSS IN HIGH DUTY RATIO
WAVEFORMS 4HE BAD NEWS IS THAT THE AVERAGE DETECTION POWER LOSS IS SLIGHTLY OVER
D" SEE &IGURE -02& 3ELECTION !LGORITHMS /BVIOUSLY SELECTING 02&S IN REAL TIME REQUIRES
SEVERAL RULES TO GET CLOSE TO A FINAL SET 4HIS IS FOLLOWED BY SMALL ITERATIONS TO PICK THE
OPTIMUM SET &OR MEDIUM 02& BOTH RANGE AND VELOCITY BLIND ZONES ARE IMPORTANT &IRST THE SOFTWARE MUST PICK A CENTRAL 02& ABOUT WHICH ALL THE OTHER 02&S ARE DEVIA
TIONS TO FILL OUT THE DESIRED VISIBILITY CRITERIA 3ECOND THE 02& SET SHOULD ALL BE CLEAR AT
THE MAXIMUM DESIGN RANGE SO THAT DETECTION LOSSES ARE AT A MINIMUM
&IGURE SHOWS ONE EXAMPLE CRITERIA FOR SELECTING THE CENTRAL 02& IE THE HIGH
EST PROBABILITY OF VISIBILITY 06 )N THE EXAMPLE THE PRODUCT 06 OF THE RANGE 02
AND DOPPLER 0$ TARGET VISIBILITY PROBABILITIES FOR A SINGLE 02& PEAKS AT APPROXIMATELY
AND THUS THE OTHER 02&S MUST FILL IN TO REACH CLEAR OR HIGHER 4HERE ARE SEVERAL
-5,4)&5.#4)/.!, 2!$!2 3934%-3 &/2 &)'(4%2 !)2#2!&4
&)'52% x°£™
-EDIUM 02& CENTRAL 02& SELECTION EXAMPLE
OTHER FACTORS TO BE CONSIDERED DOPPLER AND RANGE BLIND ZONES AND ECLIPSING AND SIDE
LOBE CLUTTER %VEN WITH 34!0 SIDELOBE CLUTTER IS A MAJOR LIMITATION "OTH SIDELOBE
AND MAIN BEAM CLUTTER CAN BE MINIMIZED BY NARROW DOPPLER ANDOR RANGE BINS IE
RESOLUTION CELLS WHICH IMPLY LONGER DWELL TIMES AND HIGHER TRANSMIT BANDWIDTH
/NE EXAMPLE METHOD FOR SELECTING A SET OF 02&S FOR -02& IS GIVEN IN %Q 4HE
BASIC IDEA IS TO FIND A TIME INTERVAL 4! REPRESENTING THE DESIRED MAXIMUM CLEAR RANGE
AND THEN TO CHOOSE A SET OF 02)S IN WHICH ALL WILL BE CLEAR AT MAXIMUM RANGE 4HIS CAN
BE ACHIEVED BY DIVIDING 4! BY AN INTEGER TYPICALLY TO 4HIS SET WILL GENERALLY NOT
PROVIDE CLEAR OVER THE RANGE DOPPLER SPACE 4HE EVEN DIVISOR 02)S CAN BE PERTURBED
ITERATIVELY BY A SMALL AMOUNT TO ACHIEVE THE DESIRED VISIBILITY 4HE NORMALIZED TARGET SIG
NAL TO NOISE RATIO 40 VARIES DRAMATICALLY WITH STRADDLE AND ECLIPSING LOSSES FOR EXAMPLE
SEE &IGURE 4HE FUNCTION TO BE OPTIMIZED IS A THRESHOLDED VERSION OF 40K OR J
&)'52% %XAMPLE 2'(02& ECLIPSING AND STRADDLE NEAR MAXIMUM RANGE
x°Óä
2!$!2 (!.$"//+
&OR EXAMPLE THE THRESHOLD SCHEME MIGHT BE D" 3.2 PER 02) AND OUT OF FOR ALL 02)S /FTEN MULTIPLE AND DIFFERENT THRESHOLDS ARE USED FOR EACH #0) AND 02)
,OWER THRESHOLDS ARE ALLOWABLE FOR HIGHER NUMBERS OF TOTAL HITS )T SHOULD BE NOTED
THAT ECLIPSING AND STRADDLING AND SO ON HAVE MUCH LESS EFFECT AT CLOSER RANGES WHERE
THERE IS USUALLY MORE THAN ENOUGH 3.2 !NOTHER SERENDIPITOUS EFFECT OF THIS SELECTION
TECHNIQUE IS THAT AS AN INDIVIDUAL 02) RANGE CLEAR REGION GETS SMALLER THE DOPPLER CLEAR
REGION GETS LARGER FILLING IN THE BLIND ZONES IN BOTH DIMENSIONS
¤2
4! r ¥ C
¦ C
4!
³
02) J T P´ 02) K # r K
#
µ
40K OR J F R #
6 ;MOD F 02) K OR J = r 2BLIND ;MODR 02) K OR J =
R BLIND
4!
r J
DJ
WHERE 2C IS MAXIMUM DESIGN CLEAR RANGE
C IS THE VELOCITY OF LIGHT • MS
S P IS TRANSMITTED PULSE WIDTH K AND J ARE INDICES EG x
# IS AN ODD INTEGER EG # IS AN EVEN INTEGER EG CJ IS A SMALL PERTURBATION EG z YIELDING VISIBILITY 6BLIND IS A FUNCTION OF F DESCRIBING ECLIPSING AND STRADDLING
2BLIND IS A FUNCTION OF R DESCRIBING ECLIPSING AND STRADDLING
# IS A CONSTANT REPRESENTING THE REMAINDER OF THE RANGE EQUATION
F IS FREQUENCY R IS RANGE MOD IS MODULO THE FIRST VARIABLE BY THE SECOND
2ANGE 'ATED (IGH 02& 2ANGE GATED HIGH 02& 2'(02& PERFORMANCE IS
DRAMATICALLY BETTER FOR DETECTION OF HIGHER SPEED CLOSING TARGETS 2ANGE GATES
ARE OFTEN SMALLER THAN RANGE RESOLUTION CELLS OR BINS 2'(02& PRODUCES THE LONGEST
DETECTION RANGE AGAINST CLOSING LOW CROSS SECTION TARGETS 5LTRA LOW NOISE FREQUENCY
REFERENCES ARE REQUIRED TO IMPROVE SUBCLUTTER VISIBILITY ON LOW 2#3 TARGETS EVEN USING
34!0 2ANGE GATING DRAMATICALLY IMPROVES SIDELOBE CLUTTER REJECTION WHICH ALLOWS
OPERATION AT LOWER OWNSHIP ALTITUDES 0RINCIPAL LIMITATIONS OF 2'(02& CLOSING TARGET
DETECTION PERFORMANCE ARE ECLIPSING A RADAR RETURN WHEN THE RECEIVER IS OFF DURING THE
TRANSMITTED PULSE AND RANGE GATE STRADDLE LOSSES THE RANGE GATE SAMPLING TIME MISSES
THE PEAK OF THE RADAR RETURN &IGURE SHOWS 40I WITH ECLIPSING AND STRADDLE LOSSES
NEAR MAXIMUM RANGE FOR A HIGH PERFORMANCE 2'(02& 4HIS MODE IS OPTIMIZED FOR LOW
CROSS SECTION TARGETS OUT TO JUST BEYOND KM MAXIMUM RANGE 4HE PARTICULAR EXAMPLE
HAS OVERLAPPING RANGE GATES TO MINIMIZE STRADDLE LOSS AND TWO 02&S TO ALLOW AT LEAST
ONE CLEAR 02& NEAR MAXIMUM RANGE 4HE 02&S ARE K(Z AND K(Z $UTY
RATIO IS WITH D" REQUIRED DETECTION 3.2 !VERAGED OVER ALL POSSIBLE TARGET POSI
TIONS AND CLOSING DOPPLERS THE LOSSES FOR THIS MODE ARE A SURPRISINGLY SMALL D"
4HE RANGE DOPPLER BLIND ZONES PLOT IS SHOWN IN &IGURE CORRESPONDING TO THE
&IGURE WAVEFORM #OMPARED TO THE MEDIUM 02& PLOT SHOWN IN &IGURE THE
CLEAR REGION AND CORRESPONDING LOSSES IS DRAMATICALLY BETTER 5NFORTUNATELY RANGE
IS VERY AMBIGUOUS .ORMALLY A 2'(02& RANGE WHILE SEARCH 273 MODE IS INTER
LEAVED WITH THE HIGHEST PERFORMANCE VELOCITY SEARCH 63 MODE TO RANGE ON PREVI
OUSLY DETECTED TARGETS
/FTEN 273 IS 2'(02& WITH THREE PHASES IN WHICH A CONSTANT FREQUENCY AND TWO
CHIRP LINEAR &- FREQUENCIES TRIANGULAR UP DOWN OR UP STEEPER UP ARE USED TO RESOLVE
RANGE AND DOPPLER IN A SPARSE TARGET SPACE !T LOW ALTITUDES SIDELOBE CLUTTER EVEN
WITH 34!0 PROCESSING LIMITS PERFORMANCE FOR ALL TARGETS BUT ESPECIALLY OPENING TARGETS
-5,4)&5.#4)/.!, 2!$!2 3934%-3 &/2 &)'(4%2 !)2#2!&4
x°Ó£
&)'52% 2'(02& RANGE VELOCITY BLIND ZONES CORRESPONDING TO &IGURE WAVEFORMS
4HIS LIMITATION LEADS TO THE NEED FOR ANOTHER MODE INTERLEAVED WITH 2'(02&
&ORTUNATELY THE TIMELINE FOR OPENING TARGETS IS MUCH LONGER NET SPEED IS LESS AND THE
ENGAGEMENT RANGE IS MUCH SHORTER WEAPON CLOSURE RATES ARE TOO SLOW /FTEN IN GENERAL SEARCH -02& 623 MEDIUM 02& VELOCITY RANGE SEARCH IS
INTERLEAVED WITH (02& 63 AND 273 AS SHOWN IN &IGURE TO PROVIDE ALL ASPECT
DETECTION 5NFORTUNATELY BOTH 273 AND 623 HAVE POORER MAXIMUM DETECTION RANGE
2'(02& CAN PROVIDE ALL ASPECT DETECTION BUT TAIL PERFORMANCE IS DRAMATICALLY POORER
DUE TO SIDELOBE CLUTTER %VEN WITH 34!0 WHICH SIGNIFICANTLY IMPROVES SIDELOBE CLUTTER
REJECTION LOW ALTITUDE TAIL ASPECT DETECTION FOR 2'(02& IS POORER &)'52% (IGH AND MEDIUM 02& INTERLEAVE FOR ALL ASPECT DETECTION
x°ÓÓ
2!$!2 (!.$"//+
&)'52% #OMPARISON OF HIGH AND MEDIUM 02&
!N EXAMPLE COMPARISON OF (02& AND -02& AS A FUNCTION OF ALTITUDE FOR A GIVEN
MAXIMUM TRANSMITTER POWER POWER APERTURE PRODUCT AND TYPICAL ANTENNA AND RADOME
INTEGRATED SIDELOBE RATIO IS SHOWN IN &IGURE !T HIGH ALTITUDE AND NOSE ON THERE IS
MORE THAN AN D" DIFFERENCE CAUSED BY BLIND ZONES STRADDLE FOLDED CLUTTER PROCESS
ING AND THRESHOLDING LOSSES 2'(02& 3ELECTION !LGORITHMS &IRST AS IN THE -02& CASE ALL 02&S SHOULD BE
CLEAR AT THE MAXIMUM DESIGN RANGE 3ECOND ALL 02&S SHOULD BE CLEAR TO THE MAXIMUM
DOPPLER OF INTEREST /NE POSSIBLE SELECTION CRITERIA IS GIVEN IN %Q !LTHOUGH THE
DETAILS ARE QUITE DIFFERENT THE BASIC PHILOSOPHY IN 02& SELECTION IS TO OPTIMIZE LONG
RANGE CLEAR REGIONS
4! r 2C
C
THEN 02) T P AND 02) ! r L
§ 4 ¶
AND ) CEIL ¨ ! ·
6A 6T
© 02) ! ¸
§C r T P
4!
AND 02) 02) r ¨
)
© 2C
¶
·
¸
WHERE 2C IS MAXIMUM DESIGN CLEAR RANGE
C IS THE VELOCITY OF LIGHT r MS
SP IS TRANSMITTED PULSE WIDTH K IS TRANSMITTED WAVELENGTH
CEIL IS THE NEXT INTEGER ABOVE THE VALUE OF THE VARIABLE
6A AND 6T ARE THE MAXIMUM VELOCITIES OF INTEREST FOR AIRCRAFT AND TARGET RESPECTIVELY
.ONCOOPERATIVE !IR 4ARGET 2ECOGNITION -&!2 TARGET RECOGNITION 4)$
RECOGNIZES TARGET TYPE BUT NOT UNIQUE IDENTIFICATION 4HERE ARE COOPERATIVE TARGET
-5,4)&5.#4)/.!, 2!$!2 3934%-3 &/2 &)'(4%2 !)2#2!&4
x°ÓÎ
IDENTIFICATION METHODS SUCH AS *4)$3 )&& AND 2& TAGGING THAT CAN BE UNIQUE 4)$
DEPENDS ON DETECTING FEATURES OF THE RADAR SIGNATURE IN FUSION WITH EMISSIONS AND
OTHER SENSORS 4HE FIVE MOST COMMON 4)$ SIGNATURES ARE MONOPULSE EXTENT SIMILAR
TO THE EXAMPLE SHOWN IN &IGURE RESONANCES HIGH RESOLUTION RANGE (22
PROFILES DOPPLER SPREAD STEPPED FREQUENCY WAVEFORM MODULATION OR MULTIFRE
QUENCY 3&7--&2 WHICH CAN BE TRANSFORMED INTO A RANGE PROFILE AND INVERSE
SYNTHETIC APERTURE RADAR )3!2 -ONOPULSE EXTENT ALLOWS ESTIMATION OF LENGTH
AND WIDTH AS WELL AS SEPARATION OF CLOSELY SPACED AIRCRAFT ! HIGH RANGE RESOLUTION
PROFILE ALSO ALLOWS THE SEPARATION OF TARGETS FLYING IN CLOSE FORMATION AS WELL AS THE
SEPARATION OF A MISSILE FROM A TARGET ! HIGH RANGE RESOLUTION PROFILE ON A SINGLE
TARGET CAN ALLOW RECOGNITION ASSUMING THE TARGET ATTITUDE IS KNOWN OR HAS BEEN
GUESSED ,ENGTH WIDTH AND LOCATION OF MAJOR SCATTERING FEATURES CAN BE PROJECTED
INTO A RANGE PROFILE IF THE ATTITUDE IS KNOWN 4HE NUMBER OF TYPES OF MAJOR CIVILIAN
AND MILITARY AIRCRAFT AND SHIPS IS AT MOST A FEW THOUSAND EASILY STORABLE IN MEMORY
5NFORTUNATELY RECOGNITION IS LIMITED TO BROAD CATEGORIES RATHER THAN -)' -
VERSUS -)' 3 EVEN THOUGH THERE ARE SIGNIFICANT DIFFERENCES THAT AIR SHOW VISI
TORS CAN EASILY SEE 4HE BASIC NOTION OF DOPPLER RESONANCES STEPPED 3&7- AND MULTIFREQUENCY
-&2 SIGNATURES IS MODULATION EITHER BY REFLECTIONS FROM MOVING PARTS EG ENGINE
COMPRESSOR TURBINE ROTOR OR PROPELLER BLADES OR BY INTERACTIONS FROM SCATTERERS ALONG
THE AIRCRAFT OR VEHICLE EG FUSELAGE WING ANTENNAS OR STORES 3&7--&2 SIGNA
TURES ARE CLOSELY RELATED TO HIGH RANGE RESOLUTION SIGNATURES A &OURIER TRANSFORM EASILY
CONVERTS ONE TO THE OTHER AND THEY SUFFER THE SAME ATTITUDE ESTIMATION LIMITATIONS 4HE
PRINCIPAL ADVANTAGE TO -&2 IS THAT MANY DEPLOYED RADARS HAVE MULTIPLE CHANNELS AND
SWITCHING BETWEEN THEM ON A SINGLE TARGET IS RELATIVELY EASY ! SIMPLIFIED VERSION OF
THE RECOGNITION PROCESS IS SUMMARIZED IN &IGURE $OPPLER SIGNATURES REQUIRE HIGH DOPPLER RESOLUTION WHICH IS USUALLY EASILY ACHIEVED
AND LIMITED ONLY BY DWELL TIME 4HE INDIVIDUAL SCATTERERS WHICH GIVE RISE TO DOPPLER
SPREAD ARE SMALL AND SO RECOGNITION IS USUALLY LIMITED TO A FRACTION TYPICAL OF
MAXIMUM RANGE *ET ENGINE MODULATION *%- A SUBSET OF DOPPLER SIGNATURES IS AN
EXCELLENT TARGET RECOGNITION METHOD %VEN AIRCRAFT WHICH USE THE SAME ENGINE TYPE
OFTEN HAVE VARIATIONS IN THE ENGINE APPLICATION SUCH AS THE NUMBER OF COMPRESSOR
BLADES OR NUMBER OF ENGINES WHICH ALLOWS UNIQUE TYPE RECOGNITION 4HE REAL PICTURE
OF *%- IS NOT SO CLEAN BECAUSE OF MULTIPLE ON AIRCRAFT BOUNCES STRADDLING AND SPEED
VARIATIONS BUT CENTROIDING OF EACH LINE IMPROVES THE SIGNATURE ESTIMATE 4HE LAST
METHOD OF 4)$ )3!2 WILL BE DEALT WITH IN ANOTHER SECTION )3!2 WORKS WELL ON BOTH
AIRCRAFT AND SHIPS ! TYPICAL TAIL HEMISPHERE AIR TO AIR )3!2 IS SHOWN IN &IGURE &)'52% .ONCOOPERATIVE TARGET RECOGNITION SUBMODES
x°Ó{
2!$!2 (!.$"//+
&)'52% ! ! )3!2 EXAMPLE 4! "
4HE FUSION OF THE RECOGNITION OF EACH OF THE SIGNATURES ABOVE PROVIDES EXCELLENT
NONCOOPERATIVE RECOGNITION
7EATHER !VOIDANCE -ANY AIRCRAFT HAVE SEPARATE WEATHER RADARS 7EATHER
AVOIDANCE IS NORMALLY INCORPORATED INTO MODERN FIGHTER RADARS 4HE NORMAL OPERATING
FREQUENCY FOR A FIGHTER RADAR HAS NOT BEEN CONSIDERED OPTIMUM FOR WEATHER DETECTION
AND AVOIDANCEˆPRIMARILY DUE TO LACK OF PENETRATION DEPTH INTO A STORM AND REDUCED
OPERATING RANGE (OWEVER WITH COMPLEX ATMOSPHERIC ATTENUATION COMPENSATION AND
DOPPLER METHODS WEATHER CAN BE DETECTED WELL ENOUGH TO ALLOW WARNING AND AVOID
ANCE OF STORMS 4HE PRINCIPAL CHALLENGE IS COMPENSATING FOR BACKSCATTER FROM THE
LEADING EDGE OF A STORM AND ADJUSTING FOR ATTENUATION TO SEE FAR ENOUGH INTO A STORM TO
EVALUATE ITS SEVERITY 4HE BACKSCATTER FROM EACH CELL IS MEASURED THE POWER REMAINING
IS CALCULATED THE ATTENUATION IN THE NEXT CELL IS ESTIMATED AND THEN THE BACKSCATTER IN
THE NEXT CELL IS MEASURED AND SO ON 7HEN THE POWER IN THE CELLS DROPS TO THE NOISE
LEVEL THOSE CELLS BEHIND IT ARE DECLARED BLIND 3INCE PENETRATION RANGE INTO A STORM IS
NOT GREAT THE -&!2 WEATHER MODE USUALLY HAS PROVISIONS TO MARK THE LAST VISIBLE OR
RELIABLE RANGE ON THE WEATHER DISPLAY 4HIS IS SO THE PILOT DOES NOT FLY INTO A DARK AREA
BELIEVING THERE IS NO WEATHER
!IR $ATA ,INKS 4HE -&!2 IS PART OF A NETWORK OF SENSORS AND INFORMA
TION SOURCES #)32 NET SOMETIMES CALLED THE 'LOBAL )NFORMATION 'RID ')' ! MAJOR USE OF RADAR AND AIRCRAFT DATA LINKS IS TO PROVIDE TOTAL SITUATIONAL AWARENESS
"Y USING ON BOARD AND OFF BOARD SENSOR FUSION A TOTAL AIR AND GROUND PICTURE
CAN BE PRESENTED IN THE COCKPIT 4HIS PICTURE CAN BE A COMBINATION OF DATA FROM
-5,4)&5.#4)/.!, 2!$!2 3934%-3 &/2 &)'(4%2 !)2#2!&4
x°Óx
OTHER RADAR SENSORS WINGMAN OR SUPPORT AIRCRAFT ON SIMILAR PLATFORMS TO REPORTS BY
OBSERVERS WITH BINOCULARS "ECAUSE THE MODERN FIGHTER IS NET CENTRIC USING EVERYTHING
AVAILABLE ON AND OFF BOARD THE AIRCRAFT NET CENTRIC OPERATION REQUIRES DRAMATICALLY
HIGHER LEVELS OF DATA EXCHANGE AND FUSION OF DATA FOR PRESENTATION TO THE OPERATOR
2ADAR MODES CAN BE SCHEDULED BETWEEN MULTIPLE AIRCRAFT IN REAL TIME THROUGH THE
DATA LINKS
4HE TWO MAIN USES FOR DATA LINKS ASSOCIATED WITH HIGH PERFORMANCE AIRCRAFT ARE
HIGH BANDWIDTH IMAGERY TRANSMISSION FROM A WEAPON OR SENSOR PLATFORM TO A SECOND
PLATFORM OR GROUND STATION AND LOW BANDWIDTH TRANSMISSION OF CONTEXT TARGETING DATA
GUIDANCE AND HOUSEKEEPING COMMANDSn 4HE LARGEST QUANTITY OF DATA LINKS ARE
ASSOCIATED WITH WEAPONS 4HE WAVEFORM SELECTED TO TRANSMIT THIS AND OTHER DATA MUST
NOT COMPROMISE THE SIGNATURE OF THE PLATFORM AT EITHER END OF THE LINK n
4HERE ARE NUMEROUS DATA LINKS ON FIGHTERS 4ABLE SHOWS AIR DATA LINKS THAT MIGHT
BE ON A FIGHTER PLATFORM )N SPITE OF THIS FACT THE RADAR OR PART OF ITS APERTURE IS OFTEN
USED FOR A DATA LINK ESPECIALLY TO MISSILES ON THE FLY AND IN RESPONSE TO PEACETIME
AIR TRAFFIC CONTROL INTERROGATIONS 0ULSE AMPLITUDE INCLUDING ON OFF PULSE POSITION
PHASE SHIFT AND FREQUENCY SHIFT MODULATION ARE COMMONLY USED ,INKS MAY BE UNIDI
RECTIONAL OR BIDIRECTIONAL 3OME MISSILES REQUIRE SEMI ACTIVE ILLUMINATION AS WELL AS
REFERENCE SIGNALS AND MIDCOURSE COMMAND DATA DERIVED FROM MISSILE AND TARGET TRACK
ING 4HE DATA TO AND FROM THE MISSILE IS OFTEN AN ENCRYPTED PHASE CODE IN OR NEAR THE
RADAR OPERATING BAND )N SOME CASES THE FREQUENCY CHANNEL IS RANDOMLY SELECTED AT
THE FACTORY AND HARDWIRED INTO THE MISSILE &REQUENCY CHANNELS ARE TYPICALLY SELECTED
OR COMMUNICATED TO THE RADAR IMMEDIATELY BEFORE LAUNCH )F THE DATA LINK FREQUENCY IS
WELL BELOW THE RADAR BAND USUALLY A SMALL NUMBER OF RADIATORS AT THAT LOWER FREQUENCY
ARE IMBEDDED IN THE RADAR APERTURE )F THE FREQUENCY IS CLOSE ENOUGH TO THE RADAR BAND
THE RADAR APERTURE OR A SEGMENT OF THE APERTURE IS USED
2ADAR !PERTURE $ATALINKING (ISTORICALLY DATALINK FUNCTIONS EMBEDDED IN
-&!2S HAVE BEEN USED FOR THE MIDCOURSE GUIDANCE OF MISSILES !N EMERGING APPLICA
TION IS THE USE OF THE RADAR APERTURE AS A HIGH POWER HIGH GAIN PRIMARY DATALINK ANTENNA
4!",% !IR $ATA ,INKS
,INK
&REQ "AND
$ATA 2ATE KBS
%##-
!2# !2# !2# !2# 4!$),
*4)$3
*4)$3 ,%4
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4!$)83
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4#$,
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6(&
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n
n
n n n
n n (IGH
(IGH
-ODERATE
-ODERATEn(IGH
-ODERATEn(IGH
-ODERATE
-ODERATE
-ODERATEn(IGH
-ODERATE
-ODERATEn(IGH
(IGH
-ODERATE
x°ÓÈ
2!$!2 (!.$"//+
WHERE DATALINK TRANSMISSION AND RECEPTION ARE INTERLEAVED WITH OTHER MODES 4HE PRIN
CIPAL LIMITATION OF MOST GENERAL PURPOSE DATALINK EQUIPMENT IS THE LOW POWER APERTURE
PERFORMANCE ASSOCIATED WITH OMNIDIRECTIONAL OFTEN SHARED ANTENNA APERTURES AND LIM
ITED POWER LEVELS 4HIS CONSTRAINS ACHIEVABLE DATA TRANSFER RATES REGARDLESS OF CHANNEL
BANDWIDTH !N ASSOCIATED PROBLEM IS VULNERABILITY TO INTERCEPT AND JAMMING INHERENT IN
WIDEBEAM APERTURES !N 8 OR +U BAND -&!2 CAN EMIT POWER LEVELS IN THE MULTI KILO
WATT RANGE WITH MAIN BEAM BEAMWIDTHS OF A FEW DEGREES AFFORDING HIGH DATA RATES AND
SIGNIFICANT RESISTANCE TO JAMMING AND INTERCEPT 4RANSMIT DATA RATES OF OVER -BPS
AND RECEIVE DATA RATES OF UP TO 'BPS HAVE BEEN DEMONSTRATED USING A PRODUCTION !%3!
AND A MODIFIED #OMMON $ATA ,INK #$, WAVEFORM -ODELING USING REPRESENTATIVE
-&!2 PARAMETERS INDICATES THAT PERFORMANCE BOUNDS ARE AT SEVERAL 'BPS THROUGHPUT
OVER DISTANCES IN EXCESS OF NAUTICAL MILES SUBJECT TO -&!2 PERFORMANCE PLATFORM
ALTITUDE TROPOSPHERIC CONDITIONS AND FORWARD SCATTERING EFFECTS
)MPLEMENTATION REQUIRES ACCURATE ANTENNA POINTING SINCE THERE IS RELATIVE MOTION
WITH RESPECT TO THE OTHER END OF THE LINK /NE TECHNIQUE INVOLVES THE USE OF AN OUT OF
BAND DATALINK CHANNEL EG *4)$3 TO CARRY '03 POSITION UPDATES $OPPLER SHIFTING
DUE TO LINK GEOMETRY DYNAMICS MUST BE ACTIVELY COMPENSATED ! RELATED ISSUE IS SYN
CHRONIZATION IN TIME TO ALLOCATE TRANSMISSION AND RECEPTION WINDOWS AND TO SYNCHRONIZE
TIMEBASES 7HEN EXISTING WAVEFORMS MUST BE USED THIS CAN PRESENT CHALLENGES %XISTING
APERTURE SCHEDULING ALGORITHMS CAN THEN ALLOCATE TIME FOR TRANSMISSION OR RECEPTION
4O ACHIEVE VERY HIGH THROUGHPUTS PHASE LINEARITY IN TRANSMIT AND RECEIVE PATHS
IS CRITICAL SINCE DATA TRANSMISSION WAVEFORMS RELY ON MODULATION THAT IS EVERY BIT AS
COMPLEX AS MANY RADAR MODES 4HIS CAN ALSO IMPACT CHOICE OF TAPER FUNCTION BECAUSE
ANGULAR VARIATIONS IN PHASE ACROSS THE MAIN BEAM WAVEFRONT MAY INCUR PERFORMANCE
PENALTIES 7HERE THE -&!2 IS PHASE STEERED APERTURE FILL AND SIDELOBE STEERING EFFECTS
CONSTRAIN USABLE APERTURE BANDWIDTH SIMILAR TO 3!2 LIMITATIONS 4HE LATTER IS BECAUSE
THE ELEMENT PHASE ANGLES REQUIRED TO POINT THE MAIN BEAM ARE NOT THE SAME AS THOSE FOR
THE OUTER SIDELOBES OF THE MODULATION USED
,OW BANDWIDTH DATA LINKS CAN USE ALL THE RADAR BANDWIDTH TO IMPROVE ENCRYPTION
AND SIGNAL TO JAM RATIOS (OWEVER THE DATA LINK ON A WEAPON IS TRAVELING TO THE TARGET
WHICH WILL INEVITABLY ATTEMPT TO PROTECT ITSELF 7HEN THE WEAPON IS NEAR THE TARGET
THE SIGNAL TO JAM RATIO CAN BE VERY UNFAVORABLE !NTENNA JAMMER NULLING IS USUALLY
REQUIRED SINCE TRANSMITTING MORE POWER TO BURN THROUGH MAY NOT BE POSSIBLE #LEARLY
THE DATA FROM AND TO A WEAPON MUST ALSO BE SUFFICIENTLY ENCRYPTED TO PREVENT TAKE OVER
OF THE WEAPON IN FLIGHT
4IME SYNCHRONIZED WITH A RADAR TRANSMISSION ON A DIFFERENT SET OF BEAMS ANDOR FRE
QUENCIES MESSAGES ARE SENT TO ONE OR MORE MISSILES ON THE FLY TO THE TARGETS /BVIOUSLY
ALL THE RANDOM FREQUENCY DIVERSITY SPREAD SPECTRUM AND ENCRYPTION NECESSARY FOR
ROBUST COMMUNICATION SHOULD BE INCORPORATED INTO THE MESSAGE %ACH MISSILE MAY
ANSWER BACK AT A KNOWN BUT RANDOMIZED OFFSET FREQUENCY AND TIME WITH IMAGE OR
HOUSEKEEPING DATA !GAIN A WAVEFORM AS ROBUST AS POSSIBLE IS USED BUT SINCE THE BASE
BAND DATA AND LINK GEOMETRY MAY BE QUITE DIFFERENT THE DATA COMPRESSION DIVERSITY
AND ENCRYPTION MAY BE DIFFERENT
4HE MISSILE DATALINK WAVEFORM USUALLY MUST BE STEALTHY AND GREATLY ATTENUATED IN
THE DIRECTION OF THE TARGET SINCE ONE COUNTERMEASURES STRATEGY IS A DECEPTION REPEATER
JAMMER AT THE TARGET (IGH ACCURACY TIME AND FREQUENCY SYNCHRONIZATION INCLUDING
RANGE OPENING AND DOPPLER EFFECTS BETWEEN BOTH ENDS OF THE LINK CAN DRAMATICALLY
REDUCE THE EFFECTIVENESS OF JAMMING BY NARROWING THE SUSCEPTIBILITY WINDOW 4IME
AND FREQUENCY SYNCHRONIZATION ALSO MINIMIZES ACQUISITION OR REACQUISITION TIME
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!N AIRCRAFT USING A DATA LINK IS MOVING WITH RESPECT TO THE OTHER END OF THE LINK
SO THE LINK GEOMETRY IS CONTINUALLY CHANGING IN TIME FREQUENCY ASPECT AND ATTITUDE
4HE SIGNAL PROCESSOR WILL GENERATE WAVEFORMS FOR TRANSMISSION BY THE SEEKER OR DATA
LINK )T WILL ALSO MEASURE TARGET RANGE ANGLE DOPPLER AND SO ON AND PROVIDE THOSE TO
THE OTHER PLATFORM 4HE -&!2 SIGNAL PROCESSOR SENDS MOTION SENSING AND NAVIGATION
ESTIMATES TO CORRECT MEASUREMENTS TO TRACK ENCODE AND DECODE DATALINK MESSAGES
AND TO PERFORM JAMMER NULLING
"EACON 2ENDEZVOUS AND 3TATION +EEPING -OST MODERN MILITARY AIRCRAFT
DEPEND ON IN FLIGHT REFUELING FOR MANY MISSIONS 4HIS REQUIRES RENDEZVOUS WITH TANKER
AIRCRAFT DURING ALL WEATHER CONDITIONS AS WELL AS STATION KEEPING UNTIL AIRCRAFT CURRENTLY
IN LINE FOR REFUELING DEPART 4HIS MAY INVOLVE DETECTING A CODED BEACON ON THE TANKER
SKIN TRACKING TANKERS AND OTHER AIRCRAFT AT CLOSE RANGE 3TATION KEEPING RANGES CAN BE
BETWEEN AND S OF METERS 3PECIAL SHORT RANGE RADAR MODES ARE USUALLY USED FOR
THIS PURPOSE ,OW POWER SHORT PULSE OR &- #7 WAVEFORMS ARE OFTEN USED /NE METER
ACCURACY AND METER MINIMUM RANGE IS USUALLY REQUIRED FOR BLIND TANKING
(IGH 0OWER !PERTURE *AMMING 4HE BASIC NOTION BEHIND -&!2 HIGH POWER
APERTURE JAMMING IS SUGGESTED IN &IGURE ! THREAT EMITTER WHETHER SURFACE OR AIRBORNE IS FIRST DETECTED AND RECOGNIZED
BY THE SPHERICAL COVERAGE RADAR WARNING RECEIVER 272 FUNCTION POSSIBLY JUST AN
APPLICATION OVERLAY ON THE 2& AND PROCESSING INFRASTRUCTURE SHOWN IN &IGURE )F THE INTERCEPT IS INSIDE THE RADAR FIELD OF VIEW &/6 FINE ANGLE OF ARRIVAL !/!
AND POSSIBLY BURST RANGING ARE PERFORMED WITH THE PRIMARY RADAR APERTURE AS SHOWN
IN THE TOP PORTION OF &IGURE (IGH GAIN ELECTRONIC SUPPORT MEASURES %3- ARE
THEN PERFORMED AND RECORDED ON THE EMITTER MAIN BEAM OR SIDELOBES USING THE NOSE
APERTURE )F IT IS DETERMINED FROM AN ON BOARD THREAT TABLE CURRENT RULES OF ENGAGE
MENT OR MISSION PLAN HIGH POWER DENSITY JAMMING BASED ON THE CORRESPONDING
ON BOARD TECHNIQUES TABLE MAY BE INITIATED USING THE HIGH GAIN NOSE APERTURE
&)'52% -&!2 %#- EXAMPLE
x°Ón
2!$!2 (!.$"//+
"ECAUSE THE ADVERSARY RADAR MAY ALSO BE A -&!2 THREAT TABLES WILL BE REQUIRED TO
CATEGORIZE THEM BY THEIR APPARENT STATISTICAL NATURE /LD STYLE MATCHING BY 02& PULSE
WIDTH AND PULSE TRAIN ENVELOPE WONT WORK VERY WELL BECAUSE WAVEFORMS VARY SO
MUCH 4HE TYPICAL NOSE APERTURE RADARnBASED EFFECTIVE RADIATED PEAK POWER %200
CAN EASILY EXCEED D"7 WHICH IS NORMALLY MORE THAN ENOUGH TO PLAY HOB WITH THREAT
RADARS &OR EXAMPLE ASSUMING A '(Z IN BAND SIGNAL n D"I THREAT SIDELOBE
AND n D"7 THREAT SENSITIVITY A JAMMING PULSE D" ABOVE MINIMUM SENSITIVITY
CAN BE GENERATED AT KM /BVIOUSLY IN THE NEAR SIDELOBES OR MAIN BEAM THE RANGE
FOR A D" PULSE WILL BE MUCH GREATER
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Ê
- ,*/" -ÊEÊ76 ",-
4ERRAIN &OLLOWING 4ERRAIN !VOIDANCE 4HE NEXT EXAMPLE IS TERRAIN FOLLOWING
TERRAIN AVOIDANCE 4&4! SHOWN IN &IGURE )N TERRAIN FOLLOWING 4& THE ANTENNA
SCANS SEVERAL VERTICAL BARS ORIENTED ALONG THE AIRCRAFT VELOCITY VECTOR AND GENERATES AN
ALTITUDE RANGE PROFILE THAT IS SOMETIMES DISPLAYED TO THE PILOT ON AN % SCAN DISPLAY
$EPENDING ON THE AIRCRAFTS MANEUVERING CAPABILITIES THERE IS A CONTROL PROFILE G
ACCELERATION MANEUVER CONTROL LINE SHOWN AS AN UPWARD CURVING LINE IN THE UPPER RIGHT
OF &IGURE n )F THIS CONCEPTUAL LINE INTERCEPTS THE TERRAIN ANYWHERE IN RANGE AN
AUTOMATIC UP MANEUVER IS PERFORMED 4HERE IS ALSO A CONCEPTUAL PUSHOVER LINE NOT
SHOWN IN THE FIGURE WHICH CAUSES A CORRESPONDING DOWN MANEUVER 4HE CONTROL PRO
FILE IN MODERN AIRCRAFT IS AUTOMATIC BECAUSE A HUMAN PILOT DOES NOT HAVE THE REFLEXES
TO AVOID ALL POSSIBLE DETECTED OBSTACLES
)N TERRAIN AVOIDANCE 4! THE ANTENNA SCAN IS IN A HORIZONTAL PLANE SHOWN IN THE
UPPER LEFT OF &IGURE 3EVERAL ALTITUDE PLANE CUTS ARE ESTIMATED AND PRESENTED TO
&)'52% 4&4! MODE EXAMPLE ADAPTED COURTESY 3CI4ECH 0UBLISHING
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THE PILOT ON AN AZIMUTH RANGE DISPLAY SHOWN IN THE LOWER RIGHT OF &IGURE 4HE
TERRAIN AVOIDANCE SCAN PATTERN SHOWS ALL THE TERRAIN THAT IS NEAR OR ABOVE THE FLIGHT
ALTITUDE AND ONE CUT BELOW AT A SET CLEARANCE ALTITUDE FT TYPICALLY &IGURE LOWER LEFT AND LOWER RIGHT SHOWS THE SITUATION GEOMETRY OF AN AIRCRAFT FLYING TOWARD
TWO HILLS AND THE CORRESPONDING ALTITUDE CUTS DISPLAYED TO THE PILOT 4HIS ALLOWS EITHER
MANUAL OR AUTOMATIC TURNING FLIGHT TO MAINTAIN A LOWER ALTITUDE
4&4! ALLOWS AN AIRCRAFT TO PENETRATE AT LOW ALTITUDE USING THE TERRAIN AS MASKING
THUS PREVENTING EARLY DETECTION 4&4! IS AN IMPORTANT ASPECT OF STEALTH EVEN WHEN THE
ALTITUDE IS NOT ALL THAT LOW BECAUSE LOWER ALTITUDES PROVIDE SOME TERRAIN OBSCURATION
AND MANY OTHER COMPETING TARGETS WITH SIMILAR CROSS SECTIONS
4ERRAIN (EIGHT %STIMATION 3OME OF THE FEATURES OF 4&4! ARE THE REQUIRED SCAN
PATTERN THE NUMBER OF INDEPENDENT FREQUENCY LOOKS REQUIRED TO OBTAIN A VALID ESTIMATE
OF THE HEIGHT OF A POSSIBLY SCINTILLATING OBJECT ALONG THE FLIGHT PATH AND THE RANGE COV
ERAGE "ECAUSE TERRAIN HEIGHT IS ESTIMATED THROUGH AN ELEVATION MEASUREMENT ANGLE
ACCURACY IS CRITICAL 4HE RANGE COVERAGE ALTHOUGH SHORT REQUIRES MULTIPLE OVERLAPPING
BEAMS AND MULTIPLE WAVEFORMS /NE METHOD FOR CALCULATING TERRAIN HEIGHT IS SHOWN IN
&IGURE )T CONSISTS OF MEASURING THE CENTROID AND EXTENT OF EACH INDIVIDUAL BEAM
POSITION OVER MANY PULSES AND ESTIMATING THE TOP OF THE TERRAIN IN EACH BEAM AS SHOWN
IN THE FIGURE 4HE CALCULATION IS SUMMARIZED IN %Q ª£ 3I r $I ¹
­
­
0R £ \ 3I \ POWER RECEIVED #R 2E « I
º CENTROID
0R
I
­
­
»
¬
£ \ $I \
%R I
#R EXTENT SQUARED 4 #R r %R TERRAIN TOP ESTIMATE
0R
WHERE 3I IS A SINGLE SUM MONOPULSE MEASUREMENT $I IS THE CORRESPONDING ELEVATION
DIFFERENCE MONOPULSE MEASUREMENT
5SUALLY THE RANGE ELEVATION PROFILE IS MEASURED IN MULTIPLE SEGMENTS WITH SEPARATE
02&S AND PULSEWIDTHS 4HE LOWEST 02& IS USED TO MEASURE THE LONGEST RANGE PORTION
OF THE PROFILE AT THE TOP OF THE ELEVATION SCAN )T USES THE LARGEST PULSE COMPRESSION RATIO
n %ACH BEAM POSITION OVERLAPS BY AS MUCH AS AND MULTIPLE FREQUENCY
&)'52% 4ERRAIN HEIGHT ESTIMATION #OURTESY 3CI4ECH 0UBLISHING
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LOOKS IN EACH BEAM CREATE AS MANY AS INDEPENDENT LOOKS 4HE SHORTEST RANGE AT THE
BOTTOM OF THE ELEVATION SCAN USES A SHORT PULSE WITH NO PULSE COMPRESSION AND A MUCH
HIGHER 02& BUT THE SAME NUMBER OF LOOKS 4HE PULSES IN A 4/4 ARE ALL THE PULSES THAT
ILLUMINATE A SINGLE SPOT FROM THE OVERLAPPING BEAMS %ACH OVERLAPPING BEAM MUST BE
COMPENSATED FOR THE ANTENNA LOOK ANGLE BEFORE THE BEAMS CAN BE SUMMED FOR A TERRAIN
HEIGHT ESTIMATE FROM ALL THE BEAMS 4HE RADAR CROSS SECTION OF THE TERRAIN COULD BE
QUITE LOW EG SNOW COVERED LEVEL TREELESS TERRAIN SO SOME PULSES MAY BE INTEGRATED
COHERENTLY TO IMPROVE SIGNAL TO NOISE RATIO FOR A #0) OF UP TO PULSES AS SHOWN IN THE
4&4! ENTRY IN 4ABLE 4ERRAIN $ATABASE -ERGING &OR THE PURPOSES OF SAFETY AS WELL AS STEALTH ACTIVE
RADAR MEASUREMENTS ARE MERGED WITH A PRESTORED TERRAIN DATABASE &IGURE SHOWS
THE GENERAL CONCEPT OF MERGED 4&4! MEASUREMENTS WITH STORED DATA
!CTIVE RADAR MEASUREMENTS ARE MADE OUT TO A FEW MILES 4HE INSTANT USE TERRAIN DATA
BASE EXTENDS OUT TO PERHAPS TEN MILES 4HE TERRAIN DATABASE CANNOT BE COMPLETELY CURRENT
AND MAY CONTAIN CERTAIN SYSTEMATIC ERRORS &OR EXAMPLE THE DATABASE CANNOT CONTAIN
THE HEIGHT OF WIRES STRUNG BETWEEN TOWERS OR STRUCTURES ERECTED SINCE THE DATABASE WAS
PREPARED &OR THE LOWEST POSSIBLE FLIGHT PROFILES WITH LESS THAN n PROBABILITY OF CRASH
PER MISSION THE PRESTORED DATA IS MERGED AND VERIFIED WITH ACTIVE RADAR MEASUREMENTS
,OW CRASH PROBABILITIES MAY ALSO REQUIRE SOME HARDWARE AND SOFTWARE REDUNDANCY )N
ADDITION AS THE AIRCRAFT FLIES DIRECTLY OVER A PIECE OF TERRAIN COMBINED TERRAIN PROFILE IS
VERIFIED BY A RADAR ALTIMETER FUNCTION 4%2#/-4%202/- IN THE 2& AND PROCESSOR
COMPLEX 5SUALLY THE PRESTORED DATA IS GENERATED AT THE REQUIRED RESOLUTION BEFORE A
MISSION FROM THE WORLDWIDE DIGITAL TERRAIN ELEVATION DATABASE $4%$ 3EA 3URFACE 3EARCH !CQUISITION AND 4RACK 3EA SURFACE SEARCH ACQUISITION
AND TRACK ARE ORIENTED TOWARD THREE TYPES OF TARGETS SURFACE SHIPS SUBMARINES SNORKEL
ING OR NEAR THE SURFACE AND SEARCH AND RESCUE 4RACKING MAY BE PRELIMINARY TO ATTACK
WITH ANTISHIP WEAPONS !LTHOUGH MOST SHIPS ARE LARGE RADAR TARGETS THEY MOVE RELA
TIVELY SLOWLY COMPARED TO LAND VEHICLES AND AIRCRAFT )N ADDITION SEA CLUTTER EXHIBITS
BOTH CURRENT AND WIND DRIVEN MOTION AS WELL AS hSPIKYv BEHAVIOR 4HESE FACTS OFTEN
REQUIRE HIGH RESOLUTION AND MULTIPLE LOOKS IN FREQUENCY OR TIME TO ALLOW SMOOTHING OF
SEA CLUTTER FOR STABLE DETECTION AND TRACK )F THE TARGET IS A SIGNIFICANT SURFACE VES
SEL THEN 2#3 MIGHT BE M AND A M RANGE RESOLUTION MIGHT BE USED FOR SEARCH
&)'52% 4&4! TERRAIN MERGING #OURTESY 3CI4ECH 0UBLISHING
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2ANGE PROFILE SHIP RECOGNITION
AND ACQUISITION )F THE TARGET IS A PERISCOPE OR PERSON IN A LIFE RAFT THEN M RESOLU
TION MIGHT BE USED SINCE THE 2#3 MIGHT BE LESS THAN M AND SMOOTHING IS ESPECIALLY
IMPORTANT $0#! AND DOPPLER PROCESSING IS OFTEN INTERLEAVED WITH TRADITIONAL BRIGHT
D" OR GREATER ABOVE BACKGROUND TARGET DETECTION ,OWER 02&S ARE USUALLY USED
WHICH IMPLY RELATIVELY HIGH PULSE COMPRESSION RATIOS AS SHOWN IN 4ABLE 3CAN
RATES ARE OFTEN SLOW WITH ONE BAR TAKING SECONDS
! HIGH RANGE RESOLUTION PROFILE CAN BE USED TO RECOGNIZE A SHIP JUST AS WITH AN
AIRCRAFT )T NATURALLY HAS THE SAME WEAKNESS PREVIOUSLY MENTIONED AND THE ASPECT
OR ATTITUDE MUST BE KNOWN )F THE ATTITUDE IS KNOWN THEN THE MAJOR SCATTERERS CAN BE
MAPPED INTO A RANGE PROFILE AND CORRELATED WITH THE SHIP POWER RETURN IN EACH CELL !N
EXAMPLE OF A SHIP RANGE PROFILE IS SHOWN IN &IGURE 4HESE PROFILES ARE USUALLY
GENERATED IN TRACK WHEN THE PROFILE IS STABILIZED IN RANGE
4HE WAKE OF A SURFACE SHIP OR SUBMARINE NEAR THE SURFACE PROVIDES A SUBSTANTIAL
CROSS SECTION OVER TIME BUT REQUIRES SURFACE STABILIZED INTEGRATION OVER nS OF
SECONDS %ARTHS SURFACE STABILIZED INTEGRATION CAN BE DONE USING A MOTION COM
PENSATED DOPPLER BEAM SHARPENING $"3 MODE
)NVERSE 3!2 ! FAR MORE RELIABLE METHOD OF SHIP RECOGNITION IS INVERSE SYNTHETIC
APERTURE RADAR )3!2 4HE BASIC NOTION IS THAT THE MOTION OF A RIGID OBJECT CAN BE
RESOLVED INTO A TRANSLATION AND ROTATION WITH RESPECT TO THE LINE OF SIGHT TO THE TARGET 4HE
ROTATION GIVES RISE TO A DIFFERENTIAL RATE OF PHASE CHANGE ACROSS THE OBJECT 4HE PHASE
HISTORY DIFFERENCES CAN BE MATCH FILTERED TO RESOLVE INDIVIDUAL SCATTERERS IN A RANGE CELL
#ONCEPTUALLY SUCH A MATCHED FILTER IS NO DIFFERENT THAN A FILTER USED TO MATCH A PHASE
CODED PULSE COMPRESSION WAVEFORM 4HIS IS THE BASIS OF ALL 3!2 2#3 RANGE IMAGING
OBSERVED GEOMETRIC TARGET ACCELERATION TURNTABLE IMAGING AND )3!2
! SHIP IN OPEN WATER EXHIBITS ROLL PITCH AND YAW MOTIONS ABOUT ITS CENTER OF GRAV
ITY CG &OR EXAMPLE &IGURE SHOWS A ROLLING MOTION OF o n THAT MIGHT BE
EXHIBITED BY A SHIP IN CALM SEAS 4HE ROLL MOTION MIGHT HAVE A PERIOD OF SECONDS
4HE MOTION OF ALMOST ALL THE SCATTERERS ON A LARGE COMBATANT ARE MOVING IN ARCS OF
CIRCLES PROJECTED AS SEGMENTS OF ELLIPSES TO A RADAR OBSERVER &OR A RADAR OBSERVER THE
CHANGE IN RANGE D2 ASSOCIATED WITH A ROLL MOVEMENT IS A FUNCTION OF THE HEIGHT H
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&)'52% )NVERSE 3!2 NOTION
OF THE SCATTERER ABOVE THE CENTER OF GRAVITY 4HE APPROXIMATE RANGE RATE FOR EACH SCAT
TERER IN ROLLING PITCH YAW MOTION AT A HEIGHT H IS THE TIME DERIVATIVE OF 2 SHOWN IN
&IGURE &OR A GIVEN DESIRED CROSS RANGE RESOLUTION WITH REASONABLE SIDELOBES $RC
A MUST BE EQUAL TO $RC K &OR THE EXAMPLE FT CROSS RANGE RESOLUTION IS OBTAINABLE
WITH A SECOND OBSERVATION TIME 4HE CORRESPONDING DOPPLER AND DOPPLER RATES ARE
ALSO GIVEN IN &IGURE &OR A SHIP WHOSE PRINCIPAL SCATTERERS ARE LESS THAN FT ABOVE THE CENTER OF GRAVITY
THE DOPPLERS WILL BE IN THE RANGE OF o (Z AT 8 BAND WITH A RATE OF CHANGE OF UP TO
o (ZS !S LONG AS THE IMAGE RESOLUTION IS NOT TOO GREAT EACH RANGE DOPPLER BIN CAN
BE MATCH FILTERED USING THE HYPOTHESIZED MOTION FOR EACH SCATTERER AND AN IMAGE CAN
BE FORMED ON THE SHIP %ACH RANGE BIN MAY CONTAIN MULTIPLE SCATTERERS FROM THE SHIP
IN A GIVEN ROLL PLANE AND THEY MAY BE DISTINGUISHED BY THEIR DIFFERING PHASE HISTORY
(OWEVER SCATTERERS IN THE PITCH AXIS AT THE SAME RANGE AND ROLL HEIGHT CANNOT BE SEPA
RATED !LTHOUGH PITCH AND YAW MOTIONS ARE SLOWER THEY ALSO EXIST AND ALLOW SEPARATION
IN OTHER SIMILAR PLANES
2EASONABLY GOOD IMAGES COUPLED WITH EXPERIENCED RADAR OPERATORS ALLOW RECOGNI
TION OF MOST SURFACE COMBATANTS 2ECOGNITION AIDS USING PRESTORED SHIP PROFILES ALLOW
IDENTIFICATION TO HULL NUMBER IN MANY CASES !N EXAMPLE OF A SINGLE )3!2 IMAGE OF
A LANDING ASSAULT SHIP IS GIVEN IN &IGURE 4HE RADAR IN THIS CASE IS ILLUMINATING
&)'52% 3INGLE )3!2 SHIP IMAGE
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THE SHIP FROM THE BOW AT KM AND n GRAZING 4HE BRIGHT SCATTERERS EXHIBIT CROSS
RANGE SIDELOBES WHICH CAN BE PARTIALLY REDUCED BY SENSING LARGE RETURNS THEN APPLY
ING AMPLITUDE WEIGHTING AND DISPLAY COMPRESSION AS HAS BEEN DONE IN THIS IMAGE
)NTEGRATION OF MULTIPLE )3!2 IMAGES DRAMATICALLY IMPROVES QUALITY
!IR TO 'ROUND 2ANGING !IR TO GROUND RANGING IS USED MOST OFTEN FOR TARGET
ING OF GUNS DUMB BOMBS AND MISSILES WITH SHORT RANGE SEEKERS AGAINST FIXED OR
SLOW MOVING TARGETS 4HE TARGET IS DETECTED AND DESIGNATED IN SOME OTHER MODE
SUCH AS '-4) $"3 3!2 OR 333 4HE DESIGNATED TARGET IS TRACKED IN RANGE AND
ANGLE TO PROVIDE A MORE ACCURATE DISTANCE AND ANGLE TO THE TARGET 4HE TRACKING
MAY BE OPEN OR CLOSED LOOP 4HE ESTIMATES ARE THEN PROVIDED TO THE WEAPON BEFORE
AND AFTER LAUNCH $EPENDING ON DISTANCE ANOTHER DESIGNATOR SUCH AS A LASER AND
THE RADAR MAY BE ALTERNATELY SLAVED TO ONE ANOTHER "OTH THE RADAR AND THE OTHER
DESIGNATOR MAY BE SUBJECT TO ATMOSPHERIC REFRACTION ESPECIALLY AT LOW ALTITUDES
WHICH IS SOMETIMES ESTIMATED AND COMPENSATED
0RECISION 6ELOCITY 5PDATE 0RECISION VELOCITY UPDATE 065 IS USED FOR NAVIGA
TION CORRECTION TO AN INERTIAL PLATFORM !LTHOUGH '03 UPDATES ARE COMMONLY USED TO
PROVIDE NAVIGATION IN MANY SITUATIONS A MILITARY AIRCRAFT CANNOT DEPEND SOLELY ON ITS
AVAILABILITY &URTHERMORE INERTIAL SENSORS ARE USED TO FILL IN BETWEEN '03 MEASURE
MENTS EVEN UNDER THE BEST CIRCUMSTANCES )NERTIAL SENSORS ARE EXTREMELY GOOD OVER
SHORT SPAN TIMES BUT VELOCITY DRIFT IS A MAJOR LONG TIME ERROR SOURCE EG KMH
ACCUMULATES M ERROR PER MINUTE ! RADAR MODE MAY REQUIRE POSITION TO KM
FOR PROPER OPERATION
065 GENERALLY USES THREE OR MORE ANTENNA BEAM POSITIONS IN WHICH IT MAKES A
VELOCITY MEASUREMENT AS SHOWN IN &IGURE 4HIS MODE DIRECTLY EMULATES DEDI
CATED RADAR DOPPLER NAVIGATORS 4HERE IS A THREE STAGE VELOCITY MEASUREMENT PROCESS
&IRST THE SURFACE IS AUTOMATICALLY ACQUIRED IN RANGE 3ECOND A FINE RANGE MEASUREMENT
IS MADE OFTEN USING MONOPULSE DISCRIMINANTS AND RANGE CENTROIDING SIMILAR TO THAT
SHOWN IN %Q 4HIRD A LINE OF SIGHT VELOCITY MEASUREMENT 6,/3 USING DOPPLER
ANDOR RANGE RATE IS MADE ALSO USING CENTROIDING "ECAUSE TERRAIN MAY BE RISING OR FALL
ING AT THE ILLUMINATED PATCHES GIVING RISE TO VELOCITY ERRORS TERRAIN SLOPE IS ESTIMATED
AND USED TO CORRECT THE ESTIMATED VELOCITY
&)'52% CONCEPT
0RECISION VELOCITY UPDATE
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! +ALMAN FILTER A RECURSIVE FILTER THAT ADAPTIVELY COMBINES MODELS OF TARGET MEA
SUREMENTS AND OF ERRORS IS EMPLOYED TO PROVIDE A BETTER ESTIMATE OF AIRCRAFT VELOCITY
!LTHOUGH THIS PROCEDURE CAN BE PERFORMED OVER LAND OR WATER SEA CURRENTS MAKE OVER
WATER MEASUREMENTS FAR LESS ACCURATE 4HIS VELOCITY MEASUREMENT PROVIDES IN FLIGHT
TRANSFER ALIGNMENT OF THE VARIOUS INERTIAL PLATFORMS AIRCRAFT WEAPONS AND RADAR ! SET
OF OUTPUTS IS PROVIDED TO THE MISSION MANAGEMENT COMPUTER FUNCTION INCLUDING .ORTH
%AST $OWN .%$ VELOCITY ERRORS AND ESTIMATES OF STATISTICAL ACCURACIES
3NIFF OR 0ASSIVE ,ISTENING -OST MODES HAVE A PRECURSOR SUBPROGRAM CALLED
SNIFF WHICH LOOKS FOR PASSIVE DETECTIONS IN A TENTATIVE OPERATING CHANNEL BEFORE ANY
RADAR EMISSIONS IN THAT CHANNEL 4HE DETECTIONS COULD BE A FRIENDLY INTERFEROR A JAMMER
OR AN INADVERTENT INTERFEROR SUCH AS A FAULTY CIVILIAN COMMUNICATIONS TRANSPONDER
4HIS LAST EXAMPLE IS THE MOST COMMON IN THE AUTHORS EXPERIENCE )T IS NOT UNCOMMON
FOR A FAULTY TRANSPONDER TO APPEAR AS A MILLION SQUARE METER TARGET
$OPPLER "EAM 3HARPENING $"3 $"3 IS VERY SIMILAR TO SYNTHETIC APER
TURE RADAR 3!2 SINCE BOTH USE THE DOPPLER SPREAD ACROSS THE ANTENNA MAIN BEAM TO
CREATE HIGHER RESOLUTION IN THE CROSS BEAM DIRECTION 4HE PRINCIPAL DIFFERENCE IS
THE AMOUNT OF ANGULAR COVERAGE BEAM SCANNING RESOLUTION DATA GATHERING TIME AND
ACCURACY OF MATCHED FILTERING IN EACH RANGE DOPPLER CELL ! $"3 MAP MAY TAKE A SEC
OND TO GATHER OVER AN ANGLE OF n $EPENDING ON THE ANGLE FROM THE AIRCRAFT VELOCITY
VECTOR A 3!2 MAP OF A FEW FEET RESOLUTION MAY TAKE TENS OF SECONDS TO GATHER AT 8
BAND $"3 AND 3!2 ARE COMPARED IN A QUALITATIVE WAY IN &IGURE !S THE BEAM IS POSITIONED CLOSER TO THE VELOCITY VECTOR THE DOPPLER SPREAD IS SMALLER
AND SO COHERENT DWELL TIMES MUST INCREASE FOR THE SAME RESOLUTION 5SUALLY THERE IS A
TRANSITION FROM SHORTER COHERENT PROCESSING INTERVALS #0)S AND LONGER POST DETECTION
INTEGRATIONS 0$)S TO LONGER #0)S AND SHORTER 0$)S AS THE BEAM APPROACHES THE AIR
CRAFT VELOCITY VECTOR .EAR NOSE ON DWELL TIMES BECOME PROHIBITIVE AND THE SCAN CENTER
IS FILLED WITH REAL BEAM MAPPING 4HE REAL BEAM USES THE SAME RANGE RESOLUTION BUT
BECAUSE RETURNS FROM THE ENTIRE BEAM ARE USED SOME AMPLITUDE EQUALIZATION IS REQUIRED
TO PROVIDE UNIFORM CONTRAST AND BRIGHTNESS ACROSS THE WHOLE MAP 3OME EFFORT IS MADE
&)'52% $OPPLER BEAM SHARPENING $"3 COMPARISON TO 3!2
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$"3 PROCESSING ADAPTED COURTESY 3CI4ECH 0UBLISHING
TO MATCH FILTER BOTH IN RANGE CLOSURE AND PHASE HISTORY THE DOPPLER SPREAD SINCE ISO
RANGE AND ISO DOPPLERS ARE NOT CLOSE TO ORTHOGONAL NEAR THE AIRCRAFT VELOCITY VECTOR SEE
&IGURE 3!2 ON THE OTHER HAND IS USUALLY FULLY MATCHED RELATIVE TO THE DESIRED
RESOLUTION AND PHASE HISTORY IN EVERY RANGE DOPPLER CELL
&IGURE SHOWS THE SIGNAL PROCESSING THAT MIGHT BE FOUND IN $"3 MODE )T
CONSISTS OF MULTIPLE TIME AROUND ECHO -4!% SUPPRESSION AMPLITUDE WEIGHTING TO
IMPROVE SIDELOBES PRESUMMATION AN &&4 FILTER BANK MAGNITUDE DETECTION IN EACH
USABLE FILTER OUTPUT PLACEMENT OF EACH FILTER OUTPUT IN THE CORRECT GROUND STABILIZED
LOCATION FOLLOWED BY POST DETECTION INTEGRATION AND SCALING FOR THE DISPLAY FOR CON
STANT BRIGHTNESS AND DYNAMIC RANGE $EPENDING ON GRAZING ANGLE AMBIGUOUS RETURNS
MAY COMPETE WITH THE REGION TO BE IMAGED /FTEN A COMBINATION OF SENSITIVITY TIME
CONTROL 34# AND PULSE TO PULSE PHASE CODING IS USED TO REJECT MULTIPLE TIME AROUND
ECHOES -4!% 4HE AMOUNT OF PRESUMMATION 02%35- AND POST DETECTION
INTEGRATION 0$) AS A FUNCTION OF BEAM POSITION OFF THE VELOCITY VECTOR IS SHOWN IN THE
LOWER RIGHT OF &IGURE &OR EACH DIFFERENT ANGLE THERE IS A DIFFERENT DOPPLER SPREAD
ACROSS THE BEAM 4HEREFORE IN ORDER TO MAINTAIN A CONSTANT BEAM SHARPENING RATIO
DIFFERENT AMOUNTS OF PRESUMMING MUST BE USED FOR EACH BEAM POSITION 0RESUMMING
IS THE FORMATION OF AN UNFOCUSSED SYNTHETIC BEAM IE THERE IS LITTLE OR NO ATTEMPT TO
MATCH THE EXACT PHASE HISTORY OF SURFACE POINTS INSIDE THE REAL ANTENNA BEAM BY WHAT
IS ESSENTIALLY A LOWPASS FILTER 4HIS WOULD RESULT IN DIFFERENT TARGET BRIGHTNESS AND CON
TRAST IF IT WERE NOT COMPENSATED BY APPLYING A CORRESPONDING POST DETECTION INTEGRATION
0$) FOR EACH ANGLE AS SHOWN IN &IGURE -ULTIPLE FREQUENCY LOOKS ARE USED TO REDUCE SPECKLE IN THE IMAGE AND SO SEVERAL
DIFFERENT FREQUENCIES ARE 0$)ED 4HE #0) IS THE PRESUM RATIO TIMES THE NUMBER OF FILTER
SAMPLES n IS TYPICAL %ACH #0) MAY HAVE MINOR CHANGES IN THE 02& TO SIM
PLIFY PROCESSING AND COMPENSATE FOR AIRCRAFT MANEUVERS 4HE AIRCRAFT MAY TRAVEL FT
DURING THE GATHERING TIME 4HERE IS CONSIDERABLE TRANSPORT DELAY IN MOST 3!2 AND
$"3 PROCESSING AS A RESULT PROCESSED RETURNS MUST BE RECTIFIED IE COMPENSATED FOR
GEOMETRIC DISTORTION MOTION COMPENSATED AND MAPPED INTO THE PROPER SPACE ANGLE
AND RANGE POSITION 3INCE $"3 USUALLY MAPS A LARGE AREA TO PROVIDE OVERALL GROUND
SITUATIONAL AWARENESS THE TOTAL RANGE COVERAGE IS OFTEN COVERED IN MULTIPLE ELEVATION
BEAMS AND RANGE SWATHS 4HIS IS TRANSPARENT TO THE OPERATOR BUT REQUIRES DIFFERENT
02&S PULSEWIDTHS FILTER SHAPES AND DWELL TIMES
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!LTHOUGH AN -&!2 CONTAINS A VERY STABLE TIME REFERENCE UNCERTAINTIES IN THE RATE
OF CHANGE OF TERRAIN HEIGHT REFRACTION WINDS ALOFT AND VERY LONG COHERENT INTEGRATION
TIMES FORCE THE MEASUREMENT OF THE CLUTTER DOPPLER ERROR VERSUS PREDICTED FREQUENCY TO
MAINTAIN PROPER FOCUS AND BIN REGISTRATION AS SHOWN IN THE UPPER RIGHT IN &IGURE ! SIMILAR FUNCTION IS PERFORMED IN 3!2 AS WELL
3YNTHETIC !PERTURE 2ADAR !S IS THE CASE FOR $"3 3!2 IS A MULTIRATE FILTERING
PROBLEM IE A CASCADE OF FILTERS IN WHICH THE INPUT SAMPLING RATE IS HIGHER THAN THE
OUTPUT SAMPLING RATE AS SHOWN IN &IGURE WHICH REQUIRES VERY CAREFUL ATTENTION TO
RANGE AND AZIMUTH FILTER SIDELOBES 4YPICALLY THE SPACING OF INDIVIDUAL PULSES ON THE
GROUND IS CHOSEN TO BE MUCH CLOSER THAN THE DESIRED ULTIMATE RESOLUTION 4HIS ALLOWS
LINEAR RANGE CLOSURE AND PHASE CORRECTION SINCE EACH POINT ON THE SURFACE MOVES A
SIGNIFICANT FRACTION OF A RANGE CELL PULSE TO PULSE n 4HE INPUT SIGNAL POINT
! IN &IGURE IS SHOWN AS A SPECTRUM AT ! FOLDED ABOUT THE 02& ON THE LEFT IN
&IGURE 3UBSEQUENTLY PRESUMMATION IS APPLIED WHICH FORMS AN UNFOCUSSED SYNTHETIC BEAM
OR FILTER INSIDE THE MAIN BEAM GROUND RETURN POINT " IN &IGURE WHICH IMPROVES
AZIMUTH SIDELOBES AND NARROWS THE SPECTRUM AS SUGGESTED IN THE CENTER GRAPH SHOWN
IN &IGURE 4HE PRESUMMER OUTPUT IS RESAMPLED AT A LOWER RATE F3 CONSISTENT WITH
ACCEPTABLE FILTER ALIASING 4HEN RANGE PULSE COMPRESSION IS PERFORMED ASSUMING THE
TRANSMITTED PULSE IS VERY LONG COMPARED TO THE RANGE SWATH )F CHIRP LINEAR &- IS USED
PART OF THE hSTRETCHv PULSE COMPRESSION PROCESSING IS PERFORMED IN THE RANGE COMPRES
SION FUNCTION WITH THE REMAINDER PERFORMED IN POLAR FORMAT PROCESSING 4HE DECHIRPED
AND PARTIALLY FILTERED OR COMPRESSED OUTPUT SHOWN AT POINT # IN &IGURE MAY BE
RESAMPLED AGAIN AT A NEW F3 AS INDICATED IN THE RIGHT GRAPH SHOWN IN &IGURE POINT
# )N ANY CASE AZIMUTH VARIABLE PHASE ADJUSTMENT AND BIN MAPPING WHICH COMPEN
SATES FOR CHANGES IN MEASUREMENT SPACE ANGLES AND RANGE CLOSURE SINCE SIGNIFICANT
MOTION OCCURS DURING THE DATA GATHERING TIME MUST BE PERFORMED BEFORE AZIMUTH FILTER
ING SOMETIMES CALLED COMPRESSION BECAUSE IT IS SIMILAR TO PHASE MATCHED PULSE COM
PRESSION 4HE OUTPUT OF AZIMUTH COMPRESSION IS SHOWN AT POINT # 4HE COMPLEX 3!2
OUTPUT MAP MUST BE CHECKED FOR DEPTH OF FOCUS AND USUALLY REQUIRES AUTOFOCUS SINCE
BOTH ATMOSPHERIC EFFECTS AND LOCALLY RISING OR FALLING TERRAIN MAY CAUSE DEFOCUSING
3UBSEQUENT TO REFOCUSING THE MAP IS MAGNITUDE DETECTED AND HISTOGRAM AVERAGED TO
MAINTAIN UNIFORM BRIGHTNESS 4HE MAP IS INTEGRATED WITH OTHER LOOKS WHICH REQUIRES
&)'52% 3!2 PROCESSING ADAPTED COURTESY 3CI4ECH 0UBLISHING
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3!2 -ULTIRATE &ILTERING ADAPTED COURTESY 3CI4ECH 0UBLISHING
GEOMETRICAL CORRECTION AND MOTION COMPENSATION 4HE TOTAL MAP DYNAMIC RANGE CAN
EASILY BE GREATER THAN D" 4HE TYPICAL COCKPIT DISPLAY IS LIMITED TO n D" AND
DYNAMIC RANGE COMPRESSION SUCH AS CONVERTING MAP AMPLITUDES INTO THEIR LOGARITHMS
IS OFTEN PERFORMED
$"3 OR 3!2 02& 0ULSE ,ENGTH AND #OMPRESSION 3ELECTION &OR EACH 3!2
OR $"3 GEOMETRY THE TRANSMITTED PULSE WIDTH PULSE REPETITION INTERVAL AND PULSE
COMPRESSION RATIO MUST BE CALCULATED /NE POSSIBLE SET OF SELECTION CRITERIA IS GIVEN
IN %Q 5SUALLY THE LAST RANGE AMBIGUITY BEFORE THE RANGE SWATH IS CHOSEN TO BE OUTSIDE
THE MAIN BEAM FAR ENOUGH TO BE AT LEAST D" DOWN INCLUDING 2 EFFECTS /FTEN IN
3!2 THE TRANSMITTED PULSE IS MUCH LARGER THAN THE RANGE SWATH 2SWATH #LEARLY IN
EACH OF THE CASES THE NEAREST INTEGRAL CLOCK INTERVAL AND NEAREST CONVENIENT PULSE
COMPRESSION RATIO IS SELECTED BECAUSE THE VALUES IN %Q WILL BE CLOCK INTEGERS ONLY
BY COINCIDENCE
0ULSE 2EPETITION )NTERVAL 02) r 2
L
q 02) q
r 6A r 5 r "AZ r SINQ
2MIN 2SWATH
C
0ULSE 7IDTH 2P a $UTYMAX r 02) r C
-INIMUM !LLOWABLE !MBIGUOUS 2ANGE
2MIN y H r CSC D 5 r "EL 2ANGE 3WATH IS 'EOMETRY AND )NSTRUMENTATION $EPENDENT
2SWATH a H r ;CSC D "EL CSCD "EL =
AND 2SWATH a 2MAXSWATH
2P
WHERE K IS TRANSMITTED WAVELENGTH H IS THE AIRCRAFT ALTITUDE
"AZ "EL ARE THE AZIMUTH ELEVATION HALF POWER BEAMWIDTHS
P D ARE THE ANGLES BETWEEN THE VELOCITY VECTOR AND ANTENNA BEAM CENTER
2 IS THE DISTANCE TO THE FIRST RANGE BIN 6A IS THE AIRCRAFT VELOCITY
2SWATH IS THE RANGE SWATH LENGTH 2MAXSWATH IS MAXIMUM INSTRUMENTED RANGE SWATH
2MIN IS THE RANGE TO THE CLOSEST ALLOWABLE AMBIGUITY $UTYMAX IS ALLOWABLE DUTY RATIO
2P IS THE TRANSMITTED PULSE LENGTH IN DISTANCE UNITS C IS THE VELOCITY OF LIGHT
5 5 ARE BEAMWIDTH MULTIPLIERS AT PREDEFINED POWER ROLLOFF
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2!$!2 (!.$"//+
&OR EXAMPLE ASSUME 6A MS K M H M P D "AZ
"EL 5 5 2SWATH KM 2MIN KM DESIRED MAPPING RANGE 2 KM
$UTYMAX SELECTING A FIRST GUESS FOR 2P M THEN 02) MSEC
2MIN IS THE EQUIVALENT OF MSEC AND THE NEXT ALLOWABLE AMBIGUITY WOULD BE PAST THE
SWATH AT MSEC THEREFORE A 02) OF OR MSEC COULD BE USED WITH A TRANSMITTED
PULSE OF APPROXIMATELY OR MSEC RESPECTIVELY
'ROUND -OVING 4ARGET )NDICATION '-4) AND 4RACK '-44 '-4) IS
THE DETECTION AND ACQUISITION OF GROUND MOVING TARGETS '-4) AND '-44 RADAR
MODES HAVE A DIFFERENT SET OF CHALLENGES &IRST TARGET DETECTION IS USUALLY THE EASY
PART THE 2#3 OF MOST ANTHROPOGENIC OBJECTS AND MANY NATURAL MOVING TARGETS IS
LARGE n M 5NFORTUNATELY THERE ARE MANY STATIONARY OBJECTS WITH MOVING
PARTS SUCH AS VENTILATORS FANS WATER COURSES AND POWER LINES THAT LEAD TO APPARENT
FALSE ALARMS /FTEN SLOW MOVING VEHICLES HAVE FAST MOVING PARTS EG HELICOP
TERS AND AGRICULTURAL IRRIGATORS -OST AREAS HAVE LARGE NUMBERS OF VEHICLES AND SCATTERERS THAT COULD BE VEHICLES )T IS
TYPICAL TO HAVE UP TO BONA FIDE '-4S IN THE FIELD OF VIEW 0ROCESSING CAPACITY
MUST BE ADEQUATE TO HANDLE AND DISCRIMINATE THOUSANDS OF HIGH 3.2 THRESHOLD CROSSINGS
AND HUNDREDS OF MOVING TARGETS OF INTEREST 5SUALLY MULTI HYPOTHESIS TRACKING FILTERS
WILL BE FOLLOWING SEVERAL HUNDRED '-4S OF INTEREST SIMULTANEOUSLY )N MOST CASES ALL
TARGETS MUST BE TRACKED AND THEN RECOGNIZED ON THE BASIS OF DOPPLER SPECTRUM HELICOPTERS
VS WHEELED VEHICLES VS TRACKED VEHICLES VS SCANNING ANTENNAS RATE OF MEASURED LOCA
TION CHANGE VENTILATOR LOCATIONS DONT CHANGE AND CONSISTENT TRAJECTORY EG MPH
WHERE THERE ARE NO ROADS IS IMPROBABLE FOR A SURFACE VEHICLE )N ADDITION VEHICLES OF
INTEREST MAY HAVE RELATIVELY LOW RADIAL VELOCITIES REQUIRING ENDOCLUTTER PROCESSING IE
FAR ENOUGH INSIDE MAIN BEAM CLUTTER THAT DETECTION IS LIMITED FOR DOPPLER ONLY FILTERING ! PROCESSING BLOCK DIAGRAM FOR '-4) IS SHOWN IN &IGURE !LTHOUGH THERE
ARE ALTERNATE WAYS TO PERFORM ENDOCLUTTER PROCESSING A MULTIPLE PHASE CENTERnBASED
&)'52% 0UBLISHING
'ROUND MOVING TARGET DETECTION PROCESSING ADAPTED COURTESY 3CI4ECH
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PROCESSING SCHEME IS GIVEN IN &IGURE -ULTIPLE CHANNELS OR PHASE CENTERS ARE
DIGITIZED AND PULSE COMPRESSED 0ERIODIC CALIBRATION SIGNALS ARE USED TO CREATE A GAIN
PHASE AND BEAM STEERING CORRECTION TABLE FOR ALL FREQUENCIES ANTENNA BEAM STEERING
AND CHANNELS WHICH ARE THEN APPLIED TO THE DIGITIZED MEASUREMENTS IN EACH CHANNEL
-OTION COMPENSATION TO A FRACTION OF A WAVELENGTH FOR PLATFORM MANEUVERS OR DEVIA
TIONS IS APPLIED TO THE DATA ! COARSE TWO DIMENSIONAL &&4 IS PERFORMED FOLLOWED BY
SPACE TIME ADAPTIVE CALCULATIONS AND FILTER WEIGHTING IS APPLIED TO REJECT SOME CLUT
TER AND JAMMING (IGH RESOLUTION DOPPLER FILTERING IS PERFORMED IN A CONVENTIONAL
&&4 PERHAPS WITH $0#! CLUTTER CANCELLATION $OPPLER FILTER OUTPUTS ARE USED
TO FORM MAIN BEAM CLUTTER ERROR DISCRIMINANTS FOR PRECISELY MEASURING DOPPLER CENTER
FREQUENCY TO PROVIDE FRACTION OF WAVELENGTH MOTION COMPENSATION -AIN BEAM CLUTTER
IS NOT IN THE SAME FREQUENCY LOCATION FOR EACH RANGE BIN AND SO FILTER OUTPUT ORDER MUST
BE ADJUSTED TO PRESENT A COMMON INPUT TO THE THRESHOLD DETECTOR 4HE DOPPLER FILTER
BANK OUTPUTS ALSO ARE APPLIED TO A MULTILEVEL THRESHOLD DETECTOR FOR GROUND MOVING
TARGET DETECTION SIMILAR TO THOSE DESCRIBED IN h'ROUND -OVING 4ARGET 4HRESHOLDINGv
3UM AND DIFFERENCE DISCRIMINANT FUNCTIONS ARE FORMED AND STORED IN BUFFER STORAGE FOR
EACH DETECTED MOVING TARGET TO IMPROVE TARGET TRACKING AND GEOLOCATION ACCURACY
/FTEN 02&S ARE AMBIGUOUS IN BOTH RANGE AND DOPPLER BUT UNAMBIGUOUS INSIDE
THE MAIN BEAM AND NEAR SIDELOBES IE THERE IS ONLY ONE RANGE OR DOPPLER AMBIGU
ITY INTERVAL IN THE MAIN BEAM AND NEAR SIDELOBES 02& SELECTION IS SIMILAR TO ! !
-02& 5SUALLY FEWER 02&S ARE USED FOUR OR FIVE ARE TYPICAL ! RANGE AMBIGU
ITY MAY BE IN THE MAIN BEAM AT LOW GRAZING ANGLES 4WO OUT OF FOUR OR THREE OUT
OF FIVE IS USUALLY THE FINAL DETECTION CRITERIA 02&S TYPICALLY ARE n K(Z #ODED
WAVEFORMS ARE OFTEN USED TO REJECT AMBIGUOUS RETURNS OUTSIDE THE ANTENNA MAIN
BEAM THAT COMPETE WITH THE REGION OF INTEREST ! FT RANGE CELL SIZE IS OFTEN USED
TO MATCH THE SMALLEST VEHICLE OF INTEREST AND TO REDUCE BACKGROUND CLUTTER 'ROUND
MOVING TARGET RECOGNITION MAY REQUIRE FT RESOLUTION !NTENNA ILLUMINATION
MUST BE GROUND STABILIZED SINCE THE AIRCRAFT WILL ENGAGE IN BOTH INTENTIONAL AND
UNINTENTIONAL MANEUVERS
'ROUND -OVING 4ARGET 4HRESHOLDING 4HE TYPICAL MULTILEVEL THRESHOLD HAS
SEVERAL UNIQUE FEATURES )N ADDITION TO THE OBVIOUS ALERT CONFIRM PROPERTIES A DOUBLE
THRESHOLDING METHOD IN WHICH A LOWER FIRST THRESHOLD NOMINATES RADAR RETURNS AS POS
SIBLE TARGETS TO BE CONFIRMED BY A RETURN OBSERVATION WITH A HIGHER THRESHOLD IT ALSO
USES MULTIPLE PHASE CENTER DISCRIMINANTS AS WELL AS NEAR SIDELOBE THRESHOLD MULTIPLI
ERS %VEN WITH 34!0 THE NON GAUSSIAN NATURE OF CLUTTER REQUIRES HIGHER THRESHOLDS IN
THE MAIN BEAM AND NEAR SIDELOBES 4HRESHOLD CROSSINGS ARE CORRELATED IN RANGE AND
DOPPLER AND BUFFERED ALONG WITH CORRESPONDING PHASE CENTER DISCRIMINANTS WHICH ARE
PRESENTED TO TRACKING FILTERS OR ACTIVITY COUNTERS
4HERE ARE THREE REGIONS OF THRESHOLDING MAIN BEAM CLUTTER LIMITED DETECTION NEAR
SIDELOBE CLUTTER LIMITED DETECTION AND THERMAL NOISE LIMITED DETECTION .EAR SURFACE
TARGETS OF INTEREST WILL OFTEN HAVE RADIAL VELOCITIES OF A FEW MILES PER HOUR FOR LONG
PERIODS OF TIME WHICH FORCES THE DETECTION OF GROUND MOVING TARGETS WELL INTO MAIN
BEAM CLUTTER 0HASE MONOPULSE $0#! OR 34!0 PROCESSING ALLOWS THE FIRST ORDER
CANCELLATION OF CLUTTER FOR MANY SLOW MOVING TARGETS 5NFORTUNATELY CLUTTER DOES NOT
ALWAYS HAVE WELL BEHAVED STATISTICAL TAILS AND TO MAINTAIN A CONSTANT FALSE ALARM RATE
THE THRESHOLD MUST BE RAISED FOR ENDOCLUTTER TARGETS 4HE OUTPUT OF THE DOPPLER FILTER
BANK MIGHT BE THOUGHT OF AS A TWO DIMENSIONAL RANGE DOPPLER IMAGE 4HERE WILL STILL BE
PARTS OF MAIN BEAM CLUTTER THAT ARE COMPLETELY DISCARDED EXCEPT FOR MOTION COMPENSA
TION BECAUSE CLUTTER CANCELLATION IS INADEQUATE
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!N EXAMPLE THRESHOLDING SCHEME BASED ON THESE CONCEPTS IS SHOWN IN &IGURE 4HE RANGE DOPPLER SPACE IS BROKEN UP INTO A GRID OF RANGE BINS AND DOPPLER FILTERS AS
SHOWN IN THE FIGURE %ACH CELL IN THE GRID MIGHT BE ¾ RANGE DOPPLER BINS WITH GRID CELLS TOTAL 3OME GRID LOCATIONS CLOSE TO MAIN BEAM CLUTTER -,# IN FIGURE ARE
USED FOR FORMING MAIN BEAM CLUTTER DISCRIMINANTS ONLY AND ARE OTHERWISE DISCARDED
4HE BINS IN THE EXAMPLE IN EACH GRID CELL ARE ENSEMBLE AVERAGED %! IN SUM AND
DIFFERENCE CHANNELS 4HE POWER IN EACH BIN IN A GRID CELL IN THE CLEAR THERMAL NOISE
LIMITED REGION IS COMPARED TO A THRESHOLD 04(%! WHICH IS A FUNCTION OF THE %!
IN THAT GRID CELL )N THE ENDOCLUTTER NEAR SIDELOBE REGION A DISCRIMINANT #S IS FORMED
AND USED TO PROVIDE ADDITIONAL CLUTTER CANCELLATION PRIOR TO THRESHOLDING !GAIN THE
THRESHOLD 04(%! IS A FUNCTION OF THE %! IN THAT GRID CELL AND A PRIORI KNOWLEDGE OF
THE CLUTTER STATISTICS !LTHOUGH ONLY ONE THRESHOLD IS DESCRIBED TWO ARE ACTUALLY USED
BEFORE HITS AND THEIR CORRESPONDING DISCRIMINANTS ARE PASSED TO THE TRACK FILES !LL LOW
THRESHOLD HITS ARE PASSED TO ACTIVITY COUNTERS !S COMPLEX AS THIS THRESHOLDING SCHEME
SEEMS TO BE IT IS VERY DETECTION POWER EFFICIENT
4YPICAL '-4 7EAPON $ELIVERY !S MENTIONED PREVIOUSLY MISSILE GUIDANCE
REQUIRES TRACKING OF BOTH TARGETS AND MISSILES ALSO BULLETS IN GUN LAYING RADAR GUN LAY
ING IS A TERM INVENTED BY THE 5+ DURING 77)) FOR RADAR POINTING OF ANTIAIRCRAFT GUNS 2ANGE ACCURACY IS AT LEAST AN ORDER OF MAGNITUDE BETTER THAN ANGLE ACCURACY 3OME
METHOD MUST BE USED TO IMPROVE ANGLE ACCURACY FOR WEAPON DELIVERY !N EXAMPLE PRO
CESSING DIAGRAM FOR '-4 WEAPON DELIVERY IS SHOWN IN &IGURE )N THIS CASE THREE
DIFFERENT CLASSES OF TARGET OR MISSILE ARE TRACKED ! SINGLE WAVEFORM MAY BE USED TO TRACK
STATIONARY ENDO AND EXOCLUTTER MOVING TARGETS AND MISSILES OR BULLETS %ACH CLASS OF
RETURN BASED ON ITS RANGE AND DOPPLER LOCATION IS SEPARATELY TRACKED AND GEOLOCATED
4HERE ARE SEVERAL COMMON TYPES OF GEOLOCATION MANY OF THEM ARE BASED ON USING
EITHER $4%$ OR CARTOGRAPHIC DATA /NE METHOD USING CARTOGRAPHIC DATA IS SHOWN
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4YPICAL '-4 WEAPON GUIDANCE ADAPTED COURTESY 3CI4ECH 0UBLISHING
IN &IGURE !N ERROR ELLIPSE AND ITS CORRESPONDING ECCENTRICITY ARE CALCULATED FOR
EACH TARGET )F THE ECCENTRICITY IS LESS THAN SOME ARBITRARY THRESHOLD EG RELA
TIVE THE MINIMUM PERPENDICULAR DISTANCE IS CALCULATED FOR ROAD SEGMENTS INSIDE THE
SIGMA ELLIPSE !S SHOWN IN THE FIGURE THE PERPENDICULAR INTERCEPT MAY NOT LIE INSIDE
THE ROAD SEGMENT AND WILL BE DISCARDED 4HE MINIMUM DISTANCE FOR VALID ROAD SEGMENT
DISTANCES WILL BE SELECTED AS THE '-4 LOCATION )F THE ECCENTRICITY IS GREATER THAN THE
THRESHOLD THE ROAD SEGMENTS THAT HAVE A MAJOR ELLIPSE AXIS INTERCEPT INSIDE SIGMA
ARE COMPARED AND THE MINIMUM DISTANCE IS SELECTED /BVIOUSLY SOME OTHER SCREENING
MUST ALSO BE APPLIED &OR EXAMPLE SOME ROADS CANNOT SUPPORT HIGH SPEEDS AND TANKS
DO NOT HAVE TO BE ON ROADS
! COMMON 3!2 -4) DISPLAY MAY BE PRESENTED TO THE OPERATOR )N ADDITION GUID
ANCE COMMANDS OR ERRORS ARE DERIVED FROM THE MEASUREMENTS AND PROVIDED TO DOWN
LINKS TO EITHER MISSILES ON THE FLY OR GUN DIRECTING COMPUTERS FOR THE NEXT ROUNDS
3HORT TERM COHERENT CHANGE DETECTION MAY BE USED TO SEPARATE STATIONARY TARGETS FROM
SLOW MOVING ENDOCLUTTER TARGETS 3HORT TERM COHERENT CHANGE DETECTION IS A METHOD IN
WHICH TWO COHERENT 3!2 MAPS TAKEN WITHIN A FEW HOURS OF ONE ANOTHER AT THE SAME
FREQUENCY ARE REGISTERED AND CROSS CORRELATED PIXEL BY PIXEL 4HE FAST MOVING TARGET
CATEGORY USUALLY INCLUDES BOTH TARGETS AND BULLETS OR MISSILES
&)'52% #ARTOGRAPHIC ASSISTED '-4 GEOLOCATION
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2!$!2 (!.$"//+
-ISSILE 0ERFORMANCE !SSESSMENT 4RACK AND 5PDATE -ISSILE MIDCOURSE GUID
ANCE USUALLY CONSISTS OF ASSESSING THE MISSILE PERFORMANCE MEASUREMENT OF THE TARGET
AND MISSILE LOCATION PREDICTION OF THE PATH OF EACH AND UPDATING THE RESULTING DATA TO
THE MISSILE FOR THE BEST FUTURE INTERCEPT OF THE TARGET )T MAY ALSO INCLUDE THE MOST CURRENT
ESTIMATE OF THE TARGET TYPE AND ATTITUDE FOR BEST FUZING 4HE MISSILE USUALLY SENDS DATA
ABOUT ITS STATE OF HEALTH OWNSHIP MEASUREMENTS REMAINING FUEL AMOUNTS AND TARGET
ACQUISITION IF ANY 7HEN THE MISSILE IS CLOSE TO THE DATA LINK AIRCRAFT WHICH MAY OR MAY
NOT BE THE LAUNCHING PLATFORM COMMUNICATION IS OFTEN THROUGH AN APERTURE OTHER THAN IN
THE MAIN -&!2 !S THE DISTANCE GETS GREATER THE PRIMARY -&!2 APERTURE IS USED !S THE
DATA LINK AIRCRAFT MANEUVERS THE APERTURE THAT HAS THE LARGEST PROJECTED AREA IN THE DIREC
TION OF THE MISSILE IS USED 4HE BANDWIDTH TO THE MISSILE IS VERY LOW AND CAN BE REDUNDANT
AND HIGHLY ENCRYPTED TO PROVIDE GOOD ANTIJAM !* PROTECTION )F IT CONTAINS IMAGERY
THE UPLINK BANDWIDTH FROM THE MISSILE IS RELATIVELY LARGE AND WILL HAVE COMPARATIVELY
LOWER !* PERFORMANCE !N ADAPTIVE -&!2 PRIMARY APERTURE CAN IMPROVE A WIDER BAND
MISSILE UPLINK !* IF THE JAMMER IS OFFSET FROM THE TARGET !T THE MISSILE END THE MISSILE
ANTENNA CAN HAVE JAMMER NULLING TO IMPROVE DOWNLINK !* !'# #ALIBRATE AND 3ELF 4EST 5SUALLY AT THE BEGINNING OF A NEW MODE THE
END OF EACH SCAN BAR OR ONCE PER SECOND THE CALIBRATE AND SELF TEST SUBPROGRAM IS
INVOKED BY THE OPERATIONAL FLIGHT PROGRAM /&0 EXECUTIVE ! SEQUENCE OF SUBROUTINES
IS EXECUTED THAT MEASURES PHASE AND GAIN UNBALANCE BETWEEN CHANNELS USING A SIGNAL
INJECTED ON THE ANTENNA 4HIS IS USUALLY DONE OVER A RANGE OF INPUT AMPLITUDES FREQUEN
CIES AND !'# SETTINGS BECAUSE OF THE NONLINEAR CHARACTERISTICS OF MOST 2& FRONT ENDS
!LSO FOR MODES LIKE 4&4! A FULL SET OF OFF ANGLE DIAGNOSTICS IS PERFORMED WHICH
TESTS THE INTEGRITY OF THE ENTIRE MEASUREMENT PROCESSING AND FLIGHT CONTROL CHAIN OFTEN
ENOUGH TO KEEP THE PROBABILITY OF A FAILURE INDUCED CRASH PER FLIGHT BELOW n IN THE
PRESENCE OF JAMMING OR COMPONENT FAILURES
)N ADDITION THERE ARE INITIATED BUILT IN TESTS AT TWO LEVELS AN OPERATIONAL READINESS
TEST PERFORMED AS PART OF MISSION INITIATION AND A FAULT ISOLATION TEST PERFORMED BY THE
MAINTENANCE CREW IN RESPONSE TO AN OPERATOR DEFICIENCY REPORT "OTH TESTS TAKE LONGER
AND ARE MORE EXHAUSTIVE )N THE BEST CASE THE SPECIFIC FLIGHT LINE OR A FIRST LEVEL MAIN
TENANCE REPLACEABLE ASSEMBLY IS IDENTIFIED WITH HIGH PROBABILITY 3UCH ASSEMBLIES ARE
THEN SENT TO A DEPOT FOR REPLACEMENT REPAIR FAILURE TRACKING ANDOR RECLAMATION &OR
ASSEMBLIES THAT HAVE A VERY LOW FAILURE RATE IT IS USUALLY CHEAPER TO REPLACE AND RECLAIM
RATHER THAN REPAIR EVEN WHEN THE ASSEMBLY IS VERY EXPENSIVE
, ,
-
3HORT COURSE NOTES AND OTHER PAPERS CAN USUALLY BE OBTAINED FROM THE AUTHORS OR THE COURSE SPONSOR FOR
A SMALL FEE !LL OF THE AUTHORS PAPERS REFERENCED ARE AVAILABLE IN !DOBE !CROBAT FORMAT SUBJECT ONLY
TO COPYRIGHT RESTRICTIONS BY E MAIL REQUEST DAVIDLYNCHJR IEEEORG AND CARLOKOPP IINETNETAU
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4HE FUNCTION OF A RADAR RECEIVER IS TO AMPLIFY FILTER DOWNCONVERT AND DIGITIZE THE
ECHOES OF THE RADAR TRANSMISSION IN A MANNER THAT WILL PROVIDE THE MAXIMUM DISCRIMI
NATION BETWEEN DESIRED ECHO SIGNALS AND UNDESIRED INTERFERENCE 4HE INTERFERENCE COM
PRISES NOT ONLY THE SELF NOISE GENERATED IN THE RADAR RECEIVER BUT ALSO THE ENERGY RECEIVED
FROM GALACTIC SOURCES NEIGHBORING RADARS AND COMMUNICATION EQUIPMENT AND POSSIBLY
JAMMERS 4HE PORTION OF THE RADARS OWN RADIATED ENERGY THAT IS SCATTERED BY UNDESIRED
TARGETS SUCH AS RAIN SNOW BIRDS INSECTS ATMOSPHERIC PERTURBATIONS AND CHAFF MAY
ALSO BE CLASSIFIED AS INTERFERENCE AND IS COMMONLY CATEGORIZED AS CLUTTER 7HERE AIR
BORNE RADARS ARE USED FOR ALTIMETERS OR MAPPING OTHER AIRCRAFT ARE UNDESIRED TARGETS AND
THE GROUND IS THE DESIRED TARGET )N THE CASE OF WEATHER RADARS GROUND BUILDINGS AND
AIRCRAFT ARE CLUTTER AND RAIN OR SNOW IS THE DESIRED TARGET -ORE COMMONLY RADARS ARE
INTENDED FOR DETECTION OF AIRCRAFT MISSILES SHIPS SURFACE VEHICLES OR PERSONNEL AND THE
REFLECTION FROM WEATHER SEA OR GROUND IS CLASSIFIED AS CLUTTER INTERFERENCE
!LTHOUGH THE BOUNDARIES OF THE RADAR RECEIVER ARE SOMEWHAT ARBITRARY THIS CHAPTER
WILL CONSIDER THOSE ELEMENTS IDENTIFIED IN &IGURE AS THE RECEIVER 4HE RADAR EXCITER
GENERATES THE TRANSMIT WAVEFORMS AS WELL AS LOCAL OSCILLATOR ,/ CLOCK AND TIMING
SIGNALS 3INCE THIS FUNCTION IS USUALLY TIGHTLY COUPLED TO A RADAR RECEIVER IT IS ALSO
SHOWN IN &IGURE AND WILL BE DISCUSSED IN THIS CHAPTER 4HE PURPOSE OF &IGURE IS
TO ILLUSTRATE THE FUNCTIONS TYPICAL OF A MODERN RADAR RECEIVER AND EXCITER
6IRTUALLY ALL RADAR RECEIVERS OPERATE ON THE SUPERHETERODYNE PRINCIPLE SHOWN
IN &IGURE 4HROUGH THIS ARCHITECTURE THE RECEIVER FILTERS THE SIGNAL TO SEPARATE
DESIRED TARGET SIGNALS FROM UNWANTED INTERFERENCE !FTER MODEST 2& AMPLIFICA
TION THE SIGNAL IS SHIFTED TO AN INTERMEDIATE FREQUENCY )& BY MIXING WITH A LOCAL
OSCILLATOR ,/ FREQUENCY -ORE THAN ONE CONVERSION STAGE MAY BE NECESSARY TO
REACH THE FINAL )& WITHOUT ENCOUNTERING SERIOUS IMAGE OR SPURIOUS FREQUENCY PROB
LEMS IN THE MIXING PROCESS 4HE SUPERHETERODYNE RECEIVER VARIES THE ,/ FREQUENCY TO
FOLLOW ANY DESIRED TUNING VARIATION OF THE TRANSMITTER WITHOUT DISTURBING THE FILTERING
AT )& 4HIS SIMPLIFIES THE FILTERING OPERATION AS THE SIGNALS OCCUPY A WIDER PERCENTAGE
4HIS CHAPTER INCORPORATES MATERIAL WRITTEN BY *OHN 7 4AYLOR *R FOR THE FIRST AND SECOND EDITIONS AND UPDATED
BY -ICHAEL 9EOMANS FOR THIS EDITION
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BANDWIDTH AT THE )& FREQUENCY 4HESE ADVANTAGES HAVE PROVEN TO BE SO SIGNIFICANT
THAT COMPETITIVE FORMS OF RECEIVERS HAVE VIRTUALLY DISAPPEARED
)N CONVENTIONAL ANTENNA SYSTEMS THE RECEIVER INPUT SIGNAL IS DERIVED FROM THE
DUPLEXER WHICH PERMITS A SINGLE ANTENNA TO BE SHARED BETWEEN TRANSMITTER AND
RECEIVER )N ACTIVE ARRAY SYSTEMS THE RECEIVER INPUT IS DERIVED FROM THE RECEIVE BEAM
FORMING NETWORK !CTIVE ARRAY ANTENNAS INCLUDE LOW NOISE AMPLIFIERS PRIOR TO FORMING
THE RECEIVE BEAMS ALTHOUGH THESE ARE GENERALLY CONSIDERED TO BE ANTENNA RATHER THAN
RECEIVER COMPONENTS THEY WILL BE DISCUSSED IN THIS CHAPTER
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4HE BLOCK DIAGRAM SHOWN IN &IGURE INCLUDES SENSITIVITY TIME CONTROL 34#
ATTENUATION AT THE 2& INPUT !LTERNATIVELY ADJUSTABLE 2& ATTENUATION MAY BE USED
%ITHER FORM PROVIDES INCREASED DYNAMIC RANGE ABOVE THAT PROVIDED BY THE ANALOG
TO DIGITAL !$ CONVERTERS 2& ATTENUATION IS DESCRIBED IN MORE DETAIL IN 3ECTION 4HE 34# ATTENUATOR IS FOLLOWED BY AN 2& AMPLIFIER OFTEN REFERRED TO AS A LOW NOISE
AMPLIFIER ,.! 4HIS AMPLIFIER PROVIDES SUFFICIENT GAIN WITH A LOW NOISE FIGURE TO
MINIMIZE THE SUBSEQUENT DEGRADATION OF THE OVERALL RADAR NOISE FIGURE BY SUBSEQUENT
COMPONENTS )F SUFFICIENT GAIN IS PROVIDED IN THE ANTENNA PRIOR TO THE RECEIVER IT MAY
BE POSSIBLE TO ELIMINATE THIS GAIN STAGE 4HE 2& FILTER PROVIDES REJECTION OF OUT OF BAND
INTERFERENCE INCLUDING REJECTION AT THE 2& IMAGE FREQUENCY !FTER DOWNCONVERSION TO
)& A BANDPASS FILTER PROVIDES REJECTION OF UNWANTED SIGNALS AND SETS THE RECEIVER ANA
LOG PROCESSING BANDWIDTH !DDITIONAL GAIN IS PROVIDED AT )& TO OVERCOME LOSSES AND
RAISE THE SIGNAL LEVEL REQUIRED FOR SUBSEQUENT PROCESSING AND TO SET THE CORRECT SIGNAL
LEVEL INTO THE !$ CONVERTERS !N )& LIMITER PROVIDES GRACEFUL LIMITING OF LARGE SIGNALS
THAT WOULD OTHERWISE OVERLOAD THE !$ CONVERTERS
4HE TWO DOMINANT METHODS OF DIGITIZATION )& SAMPLING AND ANALOG )1 DEMODULA
TION WITH BASEBAND !$ CONVERSION ARE INCLUDED FOR ILLUSTRATION IN &IGURE THOUGH
IN GENERAL RECEIVERS WILL NOT INCLUDE BOTH TECHNIQUES 0RIOR TO THE AVAILABILITY OF AFFORD
ABLE DIGITAL SIGNAL PROCESSING A NUMBER OF FUNCTIONS SUCH AS MONOPULSE COMPARISON
CURRENTLY PERFORMED IN THE DIGITAL DOMAIN WERE PERFORMED USING ANALOG PROCESSING
WITHIN THE RECEIVER 2EADERS INTERESTED IN THE DETAILS OF THESE ANALOG PROCESSING TECH
NIQUES WILL FIND DETAILS IN THE FIRST AND SECOND EDITIONS OF THIS HANDBOOK !LL BUT THE SIMPLEST OF RADARS REQUIRE MORE THAN ONE RECEIVER CHANNEL &IGURE SHOWS A SINGLE RECEIVER CHANNEL THAT MAY BE REPLICATED ANY NUMBER OF TIMES DEPENDING
ON THE RADAR SYSTEM REQUIREMENTS -ONOPULSE RADARS TYPICALLY INCLUDE THREE RECEIVER
CHANNELS SUM DELTA AZIMUTH AND DELTA ELEVATION CHANNELS USED TO PROVIDE IMPROVED
ANGLE ACCURACY !DDITIONALLY MANY MILITARY RADAR SYSTEMS INCLUDE A SIDELOBE BLANKER
OR SEVERAL SIDELOBE CANCELER CHANNELS TO COMBAT JAMMING 3INCE THE ADVENT OF DIGITAL
BEAMFORMING RADAR SYSTEMS THE NUMBER OF RECEIVER CHANNELS REQUIRED HAS INCREASED
DRAMATICALLY WITH SOME SYSTEMS NOW REQUIRING HUNDREDS OF RECEIVER CHANNELS )N
THESE MULTICHANNEL RECEIVER SYSTEMS CLOSE MATCHING AND TRACKING OF GAIN AND PHASE IS
REQUIRED 2ECEIVER CHANNEL TRACKING AND EQUALIZATION ARE DISCUSSED IN 3ECTION 4HE STABLE LOCAL OSCILLATOR 34!,/ BLOCK PROVIDES THE LOCAL OSCILLATOR FREQUENCIES
FOR DOWNCONVERSION IN THE RECEIVER AND UPCONVERSION IN THE EXCITER &OR TRUE COHERENT
OPERATION THE 34!,/ IS LOCKED TO A LOW FREQUENCY REFERENCE SHOWN BY THE REFERENCE
OSCILLATOR IN &IGURE THAT IS USED AS THE BASIS FOR ALL CLOCKS AND OSCILLATORS SUCH AS THE
COHERENT LOCAL OSCILLATOR #/(/ WITHIN THE RECEIVER AND EXCITER 4HE CLOCK GENERATOR
PROVIDES CLOCKS TO THE !$ CONVERTERS AND THE DIRECT DIGITAL SYNTHESIZER AND PROVIDES
THE BASIS FOR THE SIGNALS THAT DEFINE THE RADAR TRANSMIT AND RECEIVE INTERVALS
4HE DIRECT DIGITAL SYNTHESIZER IN &IGURE IS USED TO GENERATE THE TRANSMIT WAVE
FORMS AT AN )& FREQUENCY PRIOR TO UPCONVERSION TO THE 2& OUTPUT FREQUENCY &ILTERING
IN THE EXCITER IS REQUIRED TO REJECT ALIASED SIGNALS FROM THE DIRECT DIGITAL SYNTHESIZER AND
UNWANTED MIXER PRODUCTS 2& GAIN IS TYPICALLY REQUIRED TO PROVIDE A SUFFICIENT DRIVE
LEVEL TO THE TRANSMITTER OR PHASED ARRAY ANTENNA
!LMOST ALL MODERN RADAR SYSTEMS USE DIGITAL SIGNAL PROCESSING TO PERFORM A VARIETY
OF FUNCTIONS INCLUDING PULSE COMPRESSION AND THE DISCRIMINATION OF DESIRED TARGETS FROM
INTERFERENCE ON THE BASIS OF VELOCITY OR THE CHANGE IN PHASE FROM ONE PULSE TO THE NEXT
0REVIOUSLY PULSE COMPRESSION WAS PERFORMED USING ANALOG PROCESSING WITH DISPERSIVE
DELAY LINES TYPICALLY SURFACE ACOUSTIC WAVE 3!7 DEVICES !NALOG PULSE COMPRES
SION HAS LARGELY BEEN REPLACED BY PULSE COMPRESSION USING DIGITAL SIGNAL PROCESSING
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)N THE CASE OF VERY WIDEBAND WAVEFORMS ANALOG STRETCH PROCESSING SEE 3ECTION MAY
BE USED TO REDUCE THE SIGNAL BANDWIDTH BEFORE SUBSEQUENT DIGITAL SIGNAL PROCESSING
4HE RECEIVER DISCUSSED HEREIN FOCUSES ON THOSE FUNCTIONS THAT PROVIDE ANALOG PRO
CESSING AND DIGITIZATION OF THE INDIVIDUAL PULSE SIGNALS WITH THE MINIMUM OF DISTORTION
ENABLING SUBSEQUENT DIGITAL SIGNAL PROCESSING TO MAXIMIZE THE PERFORMANCE OF THE
RADAR 4HE DIGITAL SIGNAL PROCESSING FUNCTION IS NOT NORMALLY CONSIDERED TO BE PART OF
THE RECEIVER
È°ÓÊ "- Ê Ê 9 ‡, Ê
" - ,/" 2ECEIVERS GENERATE INTERNAL NOISE THAT MASKS WEAK SIGNALS BEING RECEIVED FROM THE RADAR
TRANSMISSIONS 4HIS NOISE CONTRIBUTION WHICH CAN BE EXPRESSED AS EITHER A NOISE TEM
PERATURE OR A NOISE FIGURE IS ONE OF THE FUNDAMENTAL LIMITATIONS ON THE RADAR RANGE
4HE NOISE TEMPERATURE OR NOISE FIGURE OF THE RADAR RECEIVER HAS BEEN REDUCED
TO THE POINT THAT IT NO LONGER REPRESENTS A DOMINANT INFLUENCE IN CHOOSING BETWEEN
AVAILABLE ALTERNATIVES )T IS A PARADOX THAT A NOISE PARAMETER IS USUALLY THE FIRST CHAR
ACTERISTIC SPECIFIED FOR A RADAR RECEIVER YET FEW RADARS EMPLOY THE LOWEST NOISE
RECEIVER AVAILABLE BECAUSE SUCH A CHOICE REPRESENTS TOO GREAT A SACRIFICE IN OTHER
PERFORMANCE PARAMETERS
#OST IS RARELY A CONSIDERATION IN REJECTING A LOWER NOISE ALTERNATIVE ! REDUCTION IN
REQUIREMENTS FOR ANTENNA GAIN OR TRANSMITTER POWER INVARIABLY PRODUCES COST SAVINGS
FAR IN EXCESS OF ANY ADDED COST OF A LOWER NOISE RECEIVER /THER VITAL PERFORMANCE
CHARACTERISTICS THAT GENERALLY DICTATE THE CHOICE OF RECEIVER FRONT END INCLUDE
L
L
L
$YNAMIC RANGE AND SUSCEPTIBILITY TO OVERLOAD
)NSTANTANEOUS BANDWIDTH AND TUNING RANGE
0HASE AND AMPLITUDE STABILITY
! DIRECT COMPROMISE MUST BE MADE BETWEEN THE NOISE FIGURE AND THE DYNAMIC RANGE
OF A RECEIVER 4HE INTRODUCTION OF AN 2& AMPLIFIER IN FRONT OF THE MIXER NECESSARILY
INVOLVES RAISING THE SYSTEM NOISE LEVEL AT THE MIXER TO MAKE THE NOISE CONTRIBUTION OF
THE MIXER ITSELF INSIGNIFICANT %VEN IF THE 2& AMPLIFIER ITSELF HAS MORE THAN ADEQUATE
DYNAMIC RANGE THE MIXER DYNAMIC RANGE HAS BEEN COMPROMISED AS INDICATED BELOW
2ATIO OF FRONT END NOISE TO MIXER NOISE
3ACRIFICE IN MIXER DYNAMIC RANGE
$EGRADATION OF SYSTEM NOISE TEMPERATURE DUE
TO MIXER NOISE
%XAMPLE %XAMPLE %XAMPLE D"
D"
D"
D"
D"
D"
D"
D"
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4HE SAME CONSIDERATIONS APPLY TO THE SETTING OF THE NOISE LEVEL AT THE INPUT TO THE
!$ CONVERTERS 4RADITIONALLY THE NOISE CONTRIBUTION OF THE !$ CONVERTER WAS CON
SIDERED BY THE SYSTEM ENGINEERS AS A SEPARATE CONTRIBUTION TO THE OVERALL RADAR SYSTEM
NOISE DISTINCT FROM RECEIVER NOISE AND WAS ACCOUNTED FOR AT THE SYSTEM LEVEL 4ODAY IT
HAS BECOME COMMON TO INCLUDE THE !$ CONVERTER NOISE AS PART OF THE OVERALL RECEIVER
NOISE #ONSEQUENTLY IT IS IMPORTANT TO UNDERSTAND WHETHER OR NOT THE CONTRIBUTION OF
THE !$ CONVERTER IS INCLUDED IN THE SPECIFICATION FOR THE NOISE FIGURE OF A RECEIVER
2!$!2 2%#%)6%23
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)N ACTIVE ARRAY ANTENNAS AND MANY CONVENTIONAL ANTENNAS LOW NOISE AMPLIFIERS
,.!S ESTABLISH THE SYSTEM NOISE FLOOR PRIOR TO THE RECEIVER INPUT 4HE NOISE FROM THE
ANTENNA IS USUALLY SET WELL ABOVE THE RECEIVER NOISE FLOOR SUCH THAT THE RECEIVER HAS
ONLY A SMALL IMPACT ON OVERALL SYSTEM NOISE !GAIN THE TRADE OFF MUST BE PERFORMED
BETWEEN SYSTEM DYNAMIC RANGE AND NOISE FIGURE
$EFINITIONS $YNAMIC 2ANGE REPRESENTS THE RANGE OF SIGNAL STRENGTH OVER
WHICH THE RECEIVER WILL PERFORM AS EXPECTED )T REQUIRES THE SPECIFICATION OF A
MINIMUM LEVEL TYPICALLY THE NOISE FLOOR THE MAXIMUM LEVEL THAT CAN BE HANDLED
WITH SOME ALLOWABLE DEVIATION FROM THE IDEAL RESPONSE AND THE TYPE OF SIGNAL TO
BE HANDLED 4HESE PARAMETERS ARE DEFINED THROUGH A VARIETY OF CHARACTERISTICS AS
DESCRIBED BELOW
-ODERN RADARS SYSTEMS INCREASINGLY RELY SOLELY ON LINEAR RECEIVER CHANNELS FOL
LOWED BY DIGITAL SIGNAL PROCESSING PROVIDING BOTH INCREASED FLEXIBILITY AND NEAR
IDEAL SIGNAL DETECTION CHARACTERISTICS 0REVIOUSLY A VARIETY OF LIMITING OR LOGARITHMIC
RECEIVER APPROACHES WERE USED TO PERFORM VARIOUS SIGNAL PROCESSING FUNCTIONS 4HESE
RECEIVERS MUST DEFINE AN ALLOWABLE ERROR IN THEIR OUTPUTS RELATIVE TO THEIR IDEAL NONLIN
EAR RESPONSE
2ECEIVERS THAT INCLUDE SOME FORM OF GAIN CONTROL MUST DISTINGUISH BETWEEN INSTAN
TANEOUS DYNAMIC RANGE AND THE TOTAL DYNAMIC RANGE THAT IS ACHIEVED AS A RESULT OF
PROGRAMMED GAIN VARIATION
2ECEIVER )NPUT .OISE ,EVEL "ECAUSE MANY RADAR SYSTEMS INCLUDE LOW NOISE
AMPLIFIERS PRIOR TO THE INPUT OF THE RECEIVER IT IS IMPORTANT TO UNDERSTAND AND SPECIFY
THE NOISE LEVEL AT THE RECEIVER INPUT 4HIS NOISE LEVEL IS SET BY THE ANTENNA NOISE TEM
PERATURE AND ITS TOTAL EFFECTIVE NOISE GAIN OR LOSS 4HE NOISE LEVEL CAN BE SPECIFIED EITHER
AS AN RMS POWER IN A SPECIFIED BANDWIDTH OR AS A NOISE POWER SPECTRAL DENSITY
3YSTEM .OISE 4HE SYSTEM NOISE LEVEL IS THE COMBINED ANTENNA AND RECEIVER NOISE
4YPICALLY THE RECEIVER INPUT NOISE WILL EXCEED THAT OF THE NOISE DUE TO THE RECEIVER
ITSELF SO THAT THE RECEIVER HAS ONLY A SMALL IMPACT ON THE SYSTEM NOISE TEMPERATURE OR
NOISE FIGURE 4HUS WHEN DEFINING DYNAMIC RANGE PARAMETERS SUCH AS SIGNAL TO NOISE
RATIO IT IS IMPORTANT TO SPECIFY WHETHER THE NOISE LEVEL BEING REFERENCED IS THE RECEIVER
NOISE OR TOTAL SYSTEM NOISE
-INIMUM 3IGNAL OF )NTEREST -INIMUM SIGNAL DEFINITIONS SUCH AS MINIMUM
DETECTABLE SIGNAL OR MINIMUM DISCERNABLE SIGNAL HAVE BEEN USED IN THE PAST HOW
EVER THESE DEFINITIONS HAVE BECOME LESS COMMON DUE TO THE EXTENSIVE USE OF DIGITAL
SIGNAL PROCESSING TECHNIQUES $IGITAL SIGNAL PROCESSING OF THE RECEIVER OUTPUT ALLOWS
THE DETECTION OF SIGNALS WELL BELOW THE RECEIVER NOISE FLOOR AND THE MINIMUM DETECT
ABLE LEVEL DEPENDS ON THE NATURE OF THE PROCESSING PERFORMED
3IGNAL TO .OISE 2ATIO 3.2 3.2 IS THE RATIO OF THE SIGNAL LEVEL TO THAT OF THE
NOISE 3.2 IS TYPICALLY EXPRESSED IN DECIBELS D" 4HE MAXIMUM RECEIVER 3.2 IS
SET BY THE NOISE CONTRIBUTION AND MAXIMUM SIGNAL CAPABILITY OF EVERY COMPONENT
IN THE CHAIN HOWEVER SINCE THE LIMITING TECHNOLOGY IS OFTEN THE !NALOG TO $IGITAL
!$ CONVERTER THE PRECEDING COMPONENTS AND GAIN STRUCTURE ARE OFTEN CHOSEN SUCH
THAT THE MAXIMUM 3.2 IS DRIVEN BY THE PERFORMANCE OF THE !$ CONVERTER -ORE
DETAILS OF THE RELATIONSHIP BETWEEN !$ CONVERTER AND RECEIVER 3.2 ARE INCLUDED IN
3ECTIONS AND È°È
2!$!2 (!.$"//+
3PURIOUS &REE $YNAMIC 2ANGE 3&$2 3&$2 IS THE RATIO OF THE MAXIMUM SIG
NAL LEVEL TO THAT OF LARGEST SPURIOUS SIGNAL CREATED WITHIN THE RECEIVER 3&$2 IS TYPI
CALLY EXPRESSED IN DECIBELS D" 4HIS PARAMETER IS DETERMINED BY A VARIETY OF FACTORS
INCLUDING THE MIXER INTERMODULATION SPURIOUS DESCRIBED IN MORE DETAIL IN 3ECTION
THE SPURIOUS CONTENT OF THE RECEIVER LOCAL OSCILLATORS THE PERFORMANCE OF THE !$
CONVERTER AND THE MANY SNEAK PATHS THAT MAY RESULT IN UNWANTED SIGNALS COUPLING ONTO
THE RECEIVER SIGNAL PATH
)NTERMODULATION $ISTORTION )-$ )NTERMODULATION DISTORTION IS A NONLINEAR PRO
CESS THAT RESULTS IN GENERATION OF FREQUENCIES THAT ARE LINEAR COMBINATIONS OF THE FUN
DAMENTAL FREQUENCIES OF THE INPUT SIGNALS 3ECOND AND THIRD ORDER INTERMODULATION ARE
THE MOST COMMONLY SPECIFIED AND THE PERFORMANCE OF THE RECEIVER IS USUALLY SPECIFIED
IN TERMS OF TWO TONE SECOND AND THIRD ORDER INPUT INTERCEPT POINTS 4HE INTERCEPT POINT
IS THE EXTRAPOLATED LEVEL AT WHICH THE POWER IN THE INTERMODULATION PRODUCT EQUALS THAT
OF THE TWO FUNDAMENTAL SIGNALS
&OR INPUT SIGNALS AT FREQUENCIES F AND F SECOND ORDER INTERMODULATION DISTORTION
PRODUCES SIGNALS AT FREQUENCIES F n F F F F AND F 4HIRD ORDER INTERMODU
LATION DISTORTION PRODUCES SIGNALS AT FREQUENCIES F n F F n F F F F F F
AND F &OR NARROW BAND SIGNALS ONLY THE THIRD ORDER PRODUCTS F n F AND F n F FALL
IN BAND AND CONSEQUENTLY THIRD ORDER DISTORTION IS TYPICALLY THE PRIMARY CONCERN 4HE
POWER LEVELS OF THESE THIRD ORDER INTERMODULATION PRODUCTS ARE GIVEN BY
0 F F D"M 0F D"M
0F D"M
0)0 D"M
0 F F D"M 0F D"M
0F D"M
0)0 D"M
WHERE 0F D"M POWER OF INPUT SIGNAL AT FREQUENCY F IN D"M
0F D"M POWER OF INPUT SIGNAL AT FREQUENCY F IN D"M
0)0D"M THIRD ORDER INTERCEPT POINT IN D"M
)NTERMODULATION CAN RESULT IN A VARIETY OF UNDESIRABLE EFFECTS SUCH AS
L
L
L
)NTERMODULATION OF CLUTTER RETURNS CAUSING BROADENING OF CLUTTER DOPPLER WIDTH
RESULTING IN THE MASKING OF TARGETS
5NWANTED IN BAND SIGNALS DUE TO OUT OF BAND INTERFERING SIGNALS RESULTING IN
FALSE TARGETS
)NTERMODULATION PRODUCTS FROM IN BAND SIGNALS THAT CANNOT BE READILY CANCELLED
THROUGH LINEAR CANCELLATION TECHNIQUES RESULTING IN SUSCEPTIBILITY TO JAMMERS
)NTERMODULATION DISTORTION OCCURS THROUGHOUT THE RECEIVER CHAIN #ONSEQUENTLY THE
RECEIVER WILL HAVE A SIGNIFICANTLY DIFFERENT INPUT INTERCEPT POINT DEPENDING ON THE
SIGNAL FREQUENCY RELATIVE TO THE RADIO FREQUENCY 2& )& AND VIDEO FILTER BANDWIDTHS
)T IS THEREFORE IMPORTANT TO DISTINGUISH BETWEEN THE REQUIREMENTS FOR IN BAND AND
OUT OF BAND INTERMODULATION DISTORTION AS DIFFERENT SIGNALS HAVE DIFFERENT EFFECTS ON
THE RECEIVER
#ROSS -ODULATION $ISTORTION #ROSS MODULATION OCCURS AS A RESULT OF THIRD ORDER
INTERMODULATION WHEREBY THE AMPLITUDE MODULATION !- OF ONE SIGNAL TYPICALLY AN
UNWANTED INTERFERENCE SIGNAL IN THE OPERATING 2& BAND BUT USUALLY OUTSIDE THE TUNED
SIGNAL BANDWIDTH IS TRANSFERRED ONTO THE DESIRED SIGNAL
2!$!2 2%#%)6%23
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4HE RESULTANT PERCENT !- MODULATION D ON THE DESIRED SIGNAL IS GIVEN BY
D U
0)0
05
05
WHERE U PERCENT !- MODULATION OF THE UNWANTED SIGNAL
05 POWER OF UNWANTED SIGNAL
0)0 THIRD ORDER INTERCEPT POINT
#ROSS MODULATION CAN RESULT IN THE MODULATION OF CLUTTER AND TARGET RETURNS DUE TO
LARGE AMPLITUDE MODULATED OUT OF BAND INTERFERENCES RESULTING IN POOR CLUTTER CANCEL
LATION AND POOR RANGE SIDELOBE PERFORMANCE
D" #OMPRESSION 0OINT 4HE INPUT D" COMPRESSION POINT OF A RECEIVER
IS A MEASURE OF THE MAXIMUM LINEAR SIGNAL CAPABILITY AND IS DEFINED AS THE INPUT
POWER LEVEL AT WHICH THE RECEIVER GAIN IS D" LESS THAN THE SMALL SIGNAL LINEAR GAIN
2ECEIVER GAIN COMPRESSION CAN RESULT FROM COMPRESSION IN AMPLIFIERS MIXERS AND
OTHER COMPONENTS THROUGHOUT THE RECEIVER CHAIN 4YPICALLY THE RECEIVER IS DESIGNED
TO PROVIDE CONTROLLED GAIN COMPRESSION THROUGH A LIMITING STAGE AT THE FINAL )& AS
DESCRIBED IN 3ECTION !NALOG TO $IGITAL #ONVERTER &ULL 3CALE 4HE !$ CONVERTER FULL SCALE LEVEL DETER
MINES THE MAXIMUM LEVEL THAT CAN BE DIGITIZED 2ECEIVERS TYPICALLY PROVIDE CONTROLLED
LIMITING 3ECTION TO PREVENT THE SIGNAL LEVEL FROM EXCEEDING THE FULL SCALE LEVEL
OF THE !$ CONVERTER 0RACTICAL CONSIDERATIONS MEAN THAT THE HARD LIMIT LEVEL IS TYPI
CALLY SET D" BELOW FULL SCALE TO PREVENT OVERLOAD AS A RESULT OF COMPONENT TOLERANCE
VARIATIONS
4YPES OF 3IGNALS 6ARIOUS TYPES OF SIGNALS ARE OF INTEREST IN DETERMINING
DYNAMIC RANGE REQUIREMENTS DISTRIBUTED TARGETS POINT TARGETS WIDEBAND NOISE JAM
MING AND NARROW BAND INTERFERENCE )F THE RADAR EMPLOYS A PHASE CODED SIGNAL THE
ELEMENTS OF THE RECEIVER PRECEDING THE DECODER WILL NOT RESTRICT THE DYNAMIC RANGE
OF A POINT TARGET AS SEVERELY AS THEY WILL FOR DISTRIBUTED CLUTTER THE TIME BANDWIDTH
PRODUCT OF THE CODED PULSE INDICATES THE ADDED DYNAMIC RANGE THAT THE DECODER WILL
EXTRACT FROM THE POINT TARGETS #ONVERSELY IF THE RADAR INCORPORATES AN EXCESSIVELY
WIDE BANDWIDTH 2& AMPLIFIER ITS DYNAMIC RANGE MAY BE SEVERELY RESTRICTED DUE TO
WIDEBAND NOISE INTERFERENCE
7HEN LOW NOISE AMPLIFIERS ,.!S ARE INCLUDED IN THE ANTENNA PRIOR TO FORMING
THE RECEIVE BEAMS THE ANTENNA SIDELOBE LEVELS ACHIEVED ARE DEPENDENT UPON THE DEGREE
TO WHICH GAIN AND PHASE CHARACTERISTICS ARE SIMILAR IN ALL ,.!S $YNAMIC RANGE HAS
AN EXAGGERATED IMPORTANCE IN SUCH CONFIGURATIONS BECAUSE MATCHING NONLINEAR CHAR
ACTERISTICS IS IMPRACTICAL 4HE EFFECT OF STRONG INTERFERENCEˆMOUNTAIN CLUTTER OTHER
RADAR PULSES OR ELECTRONIC COUNTERMEASURES %#- ˆENTERING THROUGH THE SIDELOBES
WILL BE EXAGGERATED IF IT EXCEEDS THE DYNAMIC RANGE OF THE ,.!S BECAUSE SIDELOBES
WILL BE DEGRADED 4HE ,.!S ARE WIDEBAND DEVICES VULNERABLE TO INTERFERENCE OVER
THE ENTIRE RADAR OPERATING BAND AND OFTEN OUTSIDE THIS BAND ALTHOUGH OFF FREQUENCY
INTERFERENCE IS FILTERED IN SUBSEQUENT STAGES OF THE RECEIVER STRONG INTERFERENCE SIGNALS
CAN CAUSE CLUTTER RETURNS IN THE ,.! TO BE DISTORTED DEGRADING THE EFFECTIVENESS OF
DOPPLER FILTERING AND CREATING FALSE ALARMS 4HIS PHENOMENON IS DIFFICULT TO ISOLATE AS
THE CAUSE OF FALSE ALARMS IN SUCH RADARS OWING TO THE NONREPETITIVE CHARACTER OF MANY
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SOURCES OF INTERFERENCE )N MODERN RADAR ARCHITECTURES THAT EMPLOY DIGITAL BEAMFORM
ING NONLINEARITY AT ANY STAGE OF THE RECEIVER CHANNEL WILL CREATE SIMILAR PROBLEMS
3YSTEM CALIBRATION TECHNIQUES AND ADAPTIVE BEAMFORMING TECHNIQUES CAN COM
PENSATE FOR LINEAR GAIN AND PHASE DEVIATIONS HOWEVER AS FOR THE CASE OF THE ,.!
NONLINEARITIES DESCRIBED ABOVE COMPENSATION FOR NONLINEAR CHARACTERISTICS IS EITHER
IMPRACTICAL OR IMPOSSIBLE WHEN THE CAUSE OF THE NONLINEAR DISTORTION IS OUTSIDE THE
DIGITIZED BANDWIDTH
%VALUATION ! THOROUGH EVALUATION OF ALL ELEMENTS OF THE RECEIVER IS NEC
ESSARY TO PREVENT UNANTICIPATED DEGRADATION OF NOISE FIGURE OR DYNAMIC RANGE
)NADEQUATE DYNAMIC RANGE MAKES THE RADAR RECEIVER VULNERABLE TO INTERFERENCE
WHICH CAN CAUSE SATURATION OR OVERLOAD MASKING OR HIDING THE DESIRED SIGNALS
! TABULAR FORMAT FOR SUCH A COMPUTATION A TYPICAL EXAMPLE OF WHICH IS SHOWN IN
4ABLE WILL PERMIT THOSE COMPONENTS THAT CONTRIBUTE SIGNIFICANT NOISE OR RESTRICT
THE DYNAMIC RANGE TO BE QUICKLY IDENTIFIED h4YPICALv VALUES ARE INCLUDED IN THE
TABLE FOR PURPOSES OF ILLUSTRATION
"ANDPASS &ILTER
!MPLIFIER
!'# !TTENUATOR
,IMITER
)NPUT
!$ #ONVERTER
-IXER
#OMPONENT
D"
.OISE &IGURE
#OMPONENT 'AIN
D"
#OMPONENT /UTPUT
D"M
RD /RDER )NTERCEPT
#OMPONENT /UTPUT D" D"M
#OMPRESSION 0OINT
#UMULATIVE 'AIN
D"
#UMULATIVE
D"
.OISE &IGURE
#UMULATIVE /UTPUT
D"M
RD /RDER )NTERCEPT
#UMULATIVE /UTPUT D" D"M
#OMPRESSION 0OINT
2ECEIVER .OISE ,EVEL
D"M(Z
3YSTEM .OISE ,EVEL
D"M(Z
"ANDWIDTH
-(Z
!$ 3.2 IN
D"
.YQUIST "7
!$ #ONVERTER
-(Z
3AMPLE 2ATE
!$ &ULL 3CALE ,EVEL
D"M
!$ .OISE ,EVEL
D"M(Z
3YSTEM .OISE 2ELATIVE
D"
TO !$ .OISE
-AXIMUM 0OINT #LUTTER D"M
OR 4ARGET ,EVEL
"ANDPASS &ILTER
5NITS
!MPLIFIER
.OISE AND $YNAMIC 2ANGE #HARACTERISTICS
34# !TTENUATOR
4!",% +
%
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$EFINITIONS 4HE INSTANTANEOUS BANDWIDTH OF A COMPONENT IS THE FREQUENCY BAND
OVER WHICH THE COMPONENT CAN SIMULTANEOUSLY PROCESS TWO OR MORE SIGNALS TO WITHIN A
SPECIFIED ACCURACY 7HEN THE TERM INSTANTANEOUS BANDWIDTH IS USED AS A RADAR RECEIVER
PARAMETER IT REFERS TO THE RESULTING BANDWIDTH SET BY THE COMBINATION OF 2& )& VIDEO
AND DIGITAL FILTERING THAT OCCURS WITHIN THE RECEIVER
7HEN THE RADAR RECEIVER EMPLOYS STRETCH PROCESSING DEFINED LATER IN THIS SEC
TION THE 2& PROCESSING BANDWIDTH IS SIGNIFICANTLY LARGER THAN THE )& BANDWIDTH
#ONSEQUENTLY THE TERM INSTANTANEOUS BANDWIDTH CAN BE CONFUSING #ONFUSION CAN BE
AVOIDED BY USING THE TERMS 2& WAVEFORM BANDWIDTH ,/ LINEAR &- CHIRP BANDWIDTH
AND )& PROCESSING BANDWIDTH 4HE RELATIONSHIP BETWEEN 2& ,/ AND )& BANDWIDTHS
USED IN STRETCH PROCESSING IS EXPLAINED IN MORE DETAIL LATER
4HE TUNING RANGE IS THE FREQUENCY BAND OVER WHICH THE COMPONENT MAY OPERATE
WITHOUT DEGRADING THE SPECIFIED PERFORMANCE 4UNING IS TYPICALLY ACCOMPLISHED BY
ADJUSTING THE LOCAL OSCILLATOR FREQUENCY AND ADJUSTING THE 2& FILTERING CHARACTERIS
TICS 4HE FREQUENCY RANGE OVER WHICH THE RADAR OPERATES IS OFTEN REFERRED TO AS THE
OPERATING BANDWIDTH
)MPORTANT #HARACTERISTICS 4HE ENVIRONMENT IN WHICH A RADAR MUST OPERATE
INCLUDES MANY SOURCES OF ELECTROMAGNETIC RADIATION WHICH CAN MASK THE RELATIVELY
WEAK RETURNS FROM ITS OWN TRANSMISSION 4HE SUSCEPTIBILITY TO SUCH INTERFERENCE IS
DETERMINED BY THE ABILITY OF THE RECEIVER TO SUPPRESS THE INTERFERING FREQUENCIES IF THE
SOURCES HAVE NARROW BANDWIDTH OR TO RECOVER QUICKLY IF THEY ARE MORE LIKE IMPULSES IN
CHARACTER /NE MUST BE CONCERNED WITH THE RESPONSE OF THE RECEIVER IN BOTH FREQUENCY
AND TIME DOMAINS
'ENERALLY THE CRITICAL RESPONSE IS DETERMINED IN THE )& PORTION OF THE RECEIVER THIS
WILL BE DISCUSSED IN 3ECTION (OWEVER ONE CANNOT IGNORE THE 2& PORTION OF THE
RECEIVER MERELY BY MAKING IT HAVE WIDE BANDWIDTH 3ECTION DISCUSSED HOW EXCES
SIVELY WIDE BANDWIDTH CAN PENALIZE DYNAMIC RANGE IF THE INTERFERENCE IS WIDEBAND
NOISE %VEN MORE LIKELY IS AN OUT OF BAND SOURCE OF STRONG INTERFERENCE EG OTHER
RADARS 46 STATIONS OR MICROWAVE COMMUNICATION LINKS THAT IF ALLOWED TO REACH THIS
POINT CAN EITHER OVERLOAD THE MIXER OR BE CONVERTED TO )& BY ONE OF THE SPURIOUS
RESPONSES OF THE MIXER
)DEAL MIXERS IN A SUPERHETERODYNE RECEIVER ACT AS MULTIPLIERS PRODUCING AN OUTPUT
PROPORTIONAL TO THE PRODUCT OF THE TWO INPUT SIGNALS %XCEPT FOR THE EFFECT OF NONLINEARI
TIES AND UNBALANCE THESE MIXERS PRODUCE ONLY TWO OUTPUT FREQUENCIES EQUAL TO THE SUM
AND THE DIFFERENCE OF THE TWO INPUT FREQUENCIES 4HE NONLINEARITIES AND IMBALANCE OF
MIXERS IS DESCRIBED IN MORE DETAIL IN 3ECTION 4HE BEST RADAR RECEIVER IS ONE WITH THE NARROWEST 2& INSTANTANEOUS BANDWIDTH COM
MENSURATE WITH THE RADIATED SPECTRUM AND HARDWARE LIMITATIONS AND WITH GOOD FREQUENCY
AND IMPULSE RESPONSES ! WIDE TUNING RANGE PROVIDES FLEXIBILITY TO ESCAPE INTERFERENCE
BUT IF THE INTERFERENCE IS INTENTIONAL AS IN THE CASE OF JAMMING A CHANGE IN 2& FRE
QUENCY ON A PULSE TO PULSE BASIS MAY BE REQUIRED USING SWITCHABLE OR ELECTRONICALLY
TUNED FILTERS )F THE 2& FILTERING IS LOCATED PRIOR TO 2& AMPLIFICATION THE FILTER INSERTION
LOSS WILL HAVE A D" FOR D" IMPACT ON THE RECEIVER NOISE FIGURE ANOTHER SACRIFICE IN NOISE
TEMPERATURE TO ACHIEVE MORE VITAL OBJECTIVES 9TTRIUM IRON GARNET 9)' FILTERS AND PIN
DIODE SWITCHED FILTERS HAVE BEEN USED TO PROVIDE THE NECESSARY FREQUENCY AGILITY
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3TRETCH 0ROCESSING 3TRETCH PROCESSING IS A TECHNIQUE FREQUENTLY USED TO PRO
CESS WIDE BANDWIDTH LINEAR &- WAVEFORMS 4HE ADVANTAGE OF THIS TECHNIQUE IS THAT IT
ALLOWS THE EFFECTIVE )& SIGNAL BANDWIDTH TO BE SUBSTANTIALLY REDUCED ALLOWING DIGITIZA
TION AND SUBSEQUENT DIGITAL SIGNAL PROCESSING AT MORE READILY ACHIEVABLE SAMPLE RATES
"Y APPLYING A SUITABLY MATCHED CHIRP WAVEFORM TO THE RECEIVER FIRST ,/ COINCIDENT
WITH THE EXPECTED TIME OF ARRIVAL OF THE RADAR RETURN THE RESULTANT )& WAVEFORM HAS
A SIGNIFICANTLY REDUCED BANDWIDTH FOR TARGETS OVER A LIMITED RANGE WINDOW OF INTER
EST 0ROVIDED THAT THE LIMITED RANGE WINDOW CAN BE TOLERATED A SUBSTANTIALLY REDUCED
PROCESSING BANDWIDTH ALLOWS MORE ECONOMICAL !$ CONVERSION AND SUBSEQUENT DIGITAL
SIGNAL PROCESSING )T ALSO ALLOWS A GREATER DYNAMIC RANGE TO BE ACHIEVED WITH LOWER
RATE !$ CONVERTERS THAN WOULD BE ACHIEVABLE IF DIGITIZATION OF THE ENTIRE 2& SIGNAL
BANDWIDTH WERE PERFORMED
)F THE ,/ CHIRP RATE IS SET EQUAL TO THE RECEIVED SIGNAL CHIRP RATE OF A POINT TARGET
THE RESULTANT OUTPUT IS A CONSTANT FREQUENCY TONE AT THE OUTPUT OF THE STRETCH PROCESSOR
RECEIVER WITH FREQUENCY $T"4 WHERE $T IS THE DIFFERENCE IN TIME BETWEEN THE RECEIVED
SIGNAL AND THE ,/ CHIRP SIGNAL AND "4 IS THE WAVEFORM CHIRP SLOPE CHIRP BANDWIDTH
PULSE WIDTH 4ARGET DOPPLER IS MAINTAINED THROUGH THE STRETCH PROCESSING PRODUCING
AN OUTPUT FREQUENCY OFFSET EQUAL TO THE DOPPLER FREQUENCY THOUGH THE WIDE PERCENTAGE
BANDWIDTH OFTEN USED MEANS THAT THE DOPPLER FREQUENCY CAN CHANGE SIGNIFICANTLY OVER
THE DURATION OF THE PULSE
)GNORING THE EFFECT OF TARGET DOPPLER THE REQUIRED 2& SIGNAL BANDWIDTH IS EQUAL TO
THE TRANSMITTED WAVEFORM BANDWIDTH 'IVEN THE 2& SIGNAL BANDWIDTH "2 THE RECEIVED
PULSE WIDTH 42 AND THE RANGE INTERVAL $4 THE REQUIRED ,/ REFERENCE WAVEFORM DURA
TION IS GIVEN BY
4, 42
$4
THE ,/ REFERENCE CHIRP WAVEFORM BANDWIDTH IS GIVEN BY
", 42
$4
"2
42
AND THE )& PROCESSING BANDWIDTH IS GIVEN BY
") È°{Ê ,
$4
"
42 2
6 ,Ê," /Ê
#ONFIGURATION 4HE RADAR FRONT END CONSISTS OF A LOW NOISE AMPLIFIER ,.! AND
BANDPASS FILTER FOLLOWED BY A DOWNCONVERTER 4HE RADAR FREQUENCY IS DOWNCONVERTED
TO AN )& WHERE FILTERS WITH SUITABLE BANDPASS CHARACTERISTICS ARE PHYSICALLY REALIZ
ABLE 4HE MIXER ITSELF AND THE PRECEDING CIRCUITS ARE GENERALLY RELATIVELY BROADBAND
4UNING OF THE RECEIVER BETWEEN THE LIMITS SET BY THE PRESELECTOR OR MIXER BANDWIDTH
IS ACCOMPLISHED BY CHANGING THE ,/ FREQUENCY /CCASIONALLY RECEIVERS WILL INCLUDE
FILTERING BEFORE THE ,.! IN ORDER TO LIMIT THE EFFECTS OF INTERMODULATION DISTORTION THAT
CAN OCCUR IN THE ,.! %VEN WHEN FILTERING IS INCLUDED BEFORE THE ,.! A SECOND FILTER
IS OFTEN STILL REQUIRED BETWEEN THE ,.! AND THE MIXER IN ORDER TO REJECT THE AMPLIFIER
NOISE AT THE IMAGE FREQUENCY 7ITHOUT THIS FILTER THE NOISE CONTRIBUTION OF A BROADBAND
,.! WOULD BE DOUBLED
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4HE RECEIVER FRONT END MAY ALSO INCLUDE A LIMITER USED TO PROTECT THE RECEIVER CIR
CUITRY FROM DAMAGE DUE TO HIGH POWER THAT MAY OCCUR EITHER FROM LEAKAGE DURING
TRANSMIT MODE OR AS A RESULT OF INTERFERENCE FROM ANOTHER SYSTEM SUCH AS A RADAR AT CLOSE
RANGE &RONT END LIMITERS ARE DISCUSSED IN MORE DETAIL IN 3ECTION 4HE RADAR OR RECEIVER FRONT END OFTEN INCLUDES SOME FORM OF GAIN OR ATTENUATION CON
TROL AS SHOWN IN &IGURE 'AIN CONTROL IS DESCRIBED IN MORE DETAIL IN 3ECTION %FFECT OF #HARACTERISTICS ON 0ERFORMANCE .ONCOHERENT PULSE RADAR PERFOR
MANCE IS AFFECTED BY FRONT END CHARACTERISTICS IN THREE WAYS .OISE INTRODUCED BY THE
FRONT END INCREASES THE RADAR NOISE TEMPERATURE DEGRADING SENSITIVITY AND LIMITS THE
MAXIMUM RANGE AT WHICH TARGETS ARE DETECTABLE &RONT END SATURATION ON STRONG SIGNALS
MAY LIMIT THE MINIMUM RANGE OF THE SYSTEM OR ITS ABILITY TO HANDLE STRONG INTERFERENCE
&INALLY THE FRONT END SPURIOUS PERFORMANCE AFFECTS THE SUSCEPTIBILITY TO OFF FREQUENCY
INTERFERENCE
#OHERENT RADAR PERFORMANCE IS EVEN MORE AFFECTED BY SPURIOUS MIXER CHARACTERIS
TICS 2ANGE AND VELOCITY ACCURACY IS DEGRADED IN PULSE DOPPLER RADARS STATIONARY TARGET
CANCELLATION IS IMPAIRED IN -4) MOVING TARGET INDICATION RADARS AND RANGE SIDELOBES
ARE RAISED IN HIGH RESOLUTION PULSE COMPRESSION SYSTEMS
3PURIOUS $ISTORTION OF 2ADIATED 3PECTRUM )T IS A SURPRISE TO MANY RADAR ENGI
NEERS THAT COMPONENTS OF THE RADAR RECEIVER CAN CAUSE DEGRADATION OF THE RADIATED
TRANSMITTER SPECTRUM GENERATING HARMONICS OF THE CARRIER FREQUENCY OR SPURIOUS DOP
PLER SPECTRA BOTH OF WHICH ARE OFTEN REQUIRED TO BE D" OR MORE BELOW THE CARRIER
(ARMONICS CAN CREATE INTERFERENCE IN OTHER ELECTRONIC EQUIPMENT 3PURIOUS DOPPLER
SPECTRA LEVELS ARE DICTATED BY REQUIREMENTS TO SUPPRESS CLUTTER INTERFERENCE THROUGH
DOPPLER FILTERING
(ARMONICS ARE GENERATED BY ANY COMPONENT THAT BECOMES NONLINEAR WHEN SUB
JECTED TO THE POWER LEVEL CREATED BY THE TRANSMITTER AND THAT PASSES THOSE HARMONICS TO
THE ANTENNA 'ASEOUS OR DIODE RECEIVER PROTECTORS ARE DESIGNED TO BE NONLINEAR DURING
THE TRANSMITTED PULSE AND REFLECT THE INCIDENT ENERGY BACK TOWARD THE ANTENNA )SOLATORS
OR CIRCULATORS ARE OFTEN EMPLOYED TO ABSORB MOST OF THE REFLECTED FUNDAMENTAL BUT THEY
ARE GENERALLY MUCH LESS EFFECTIVE AT THE HARMONICS -OREOVER THESE FERRITE DEVICES ARE
NONLINEAR DEVICES AND CAN GENERATE HARMONICS
3PURIOUS DOPPLER SPECTRA ARE CREATED BY ANY PROCESS THAT DOES NOT REOCCUR IDENTI
CALLY ON EACH TRANSMITTED PULSE 'ASEOUS RECEIVER PROTECTORS IONIZE UNDER TRANSMITTER
POWER LEVELS BUT THERE IS SOME SMALL STATISTICAL VARIATION IN THE INITIATION OF IONIZA
TION ON THE LEADING EDGE OF THE PULSE AND IN ITS SUBSEQUENT DEVELOPMENT )N RADARS
DEMANDING HIGH CLUTTER SUPPRESSION IN EXCESS OF D" IT HAS SOMETIMES BEEN FOUND
NECESSARY TO PREVENT THIS VARIABLE REFLECTED POWER FROM BEING RADIATED BY USE OF BOTH
A CIRCULATOR AND AN ISOLATOR IN THE RECEIVE PATH
3PURIOUS 2ESPONSE OF -IXERS 4HE IDEAL MIXER ACTS AS A MULTIPLIER PRODUCING AN
OUTPUT PROPORTIONAL TO THE PRODUCT OF THE TWO INPUT SIGNALS 4HE INPUT 2& SIGNAL AT FRE
QUENCY F2 IS FREQUENCY SHIFTED OR MODULATED BY THE ,/ SIGNAL AT FREQUENCY F, "ALANCED
MIXERS ARE USED TO MINIMIZE CONVERSION LOSS AND UNWANTED SPURIOUS RESPONSES )N
ACTIVE MIXERS MODULATION IS PERFORMED USING TRANSISTORS AND IN PASSIVE MIXERS THE
MODULATION IS PERFORMED USING 3CHOTTKY BARRIER DIODES OR OTHER SOLID STATE DEVICES
EG -%3&%4 WHERE INCREASED DYNAMIC RANGE IS REQUIRED
4HE RESULTING OUTPUT SIGNAL FREQUENCIES F, F2 AND F, n F2 ARE THE SUM AND DIFFERENCE
OF THE TWO INPUT FREQUENCIES )N PRACTICE ALL MIXERS PRODUCE UNWANTED INTERMODULATION
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SPURIOUS RESPONSES WITH FREQUENCIES NF, MF2 WHERE M AND N ARE INTEGERS AND THE
DEGREE TO WHICH THESE SPURIOUS PRODUCTS IMPACT THE RADAR PERFORMANCE DEPENDS UPON THE
TYPE OF MIXER AND THE OVERALL RADAR PERFORMANCE REQUIREMENTS !NALYSIS OF MIXER SPURI
OUS LEVELS IS NONTRIVIAL AND THE RECEIVER DESIGNER TYPICALLY REQUIRES TABULATED DATA GENER
ATED THROUGH MIXER CHARACTERIZATION MEASUREMENTS TO PREDICT MIXER SPURIOUS LEVELS
!DVANCES IN MIXER TECHNOLOGY HAVE RESULTED IN A WIDE VARIETY OF COMMERCIALLY
AVAILABLE DEVICES EMPLOYING BALANCED DOUBLE BALANCED AND DOUBLE DOUBLE BALANCED
TOPOLOGIES COVERING A WIDE RANGE OF 2& ,/ AND )& FREQUENCIES AND A RANGE OF PER
FORMANCE CHARACTERISTICS
-IXER 3PURIOUS %FFECTS #HART ! GRAPHICAL DISPLAY OF MIXER SPURIOUS COMPO
NENTS UP TO THE SIXTH ORDER IS SHOWN IN &IGURE 4HIS CHART ALLOWS IDENTIFICATION OF
THOSE COMBINATIONS OF INPUT FREQUENCIES AND BANDWIDTHS THAT ARE FREE OF STRONG LOW
ORDER SPURIOUS COMPONENTS 3UCH CHARTS ARE MOST USEFUL IN DETERMINING OPTIMUM )& AND
,/ FREQUENCIES DURING THE INITIAL DESIGN PHASE /NCE THE FREQUENCY PLAN HAS BEEN DETER
MINED COMPUTER ANALYSIS OF SPURIOUS RESPONSES IS TYPICALLY USED TO ENSURE SPURIOUS FREE
PERFORMANCE OVER THE ENTIRE RANGE OF ,/ FREQUENCIES AND 2& AND )& BANDWIDTHS
4HE HEAVY LINE IN &IGURE REPRESENTS THE DESIRED SIGNAL AND SHOWS THE VARIATION
OF NORMALIZED OUTPUT FREQUENCY ( n , ( WITH NORMALIZED INPUT FREQUENCY ,(
!LL OTHER LINES ON THE CHART REPRESENT THE UNWANTED SPURIOUS SIGNALS 4O SIMPLIFY
USE OF THE CHART THE HIGHER INPUT FREQUENCY IS DESIGNATED BY ( AND THE LOWER INPUT
FREQUENCY BY ,
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INPUT FREQUENCY
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IS ILLUSTRATED BY MEANS OF THE REGION MARKED ! WHICH REPRESENTS THE WIDEST AVAILABLE
SPURIOUS FREE BANDWIDTH CENTERED AT ,( 4HE AVAILABLE 2& PASSBAND IS FROM
TO AND THE CORRESPONDING )& PASSBAND IS FROM TO (OWEVER SPURI
OUS )& FREQUENCIES OF ( n , AND ( n , ARE GENERATED AT THE EXTREMES
OF THE 2& PASSBAND !NY EXTENSION OF THE INSTANTANEOUS 2& BANDWIDTH WILL PRODUCE
OVERLAPPING )& FREQUENCIES A CONDITION THAT CANNOT BE CORRECTED BY )& FILTERING 4HE
( n , AND ( n , SPURIOUS FREQUENCIES LIKE ALL SPURIOUS )& FREQUENCIES ARISE FROM
CUBIC OR HIGHER ORDER INTERMODULATION
4HE AVAILABLE SPURIOUS FREE BANDWIDTH IN ANY OF THE DESIGNATED REGIONS IS ROUGHLY
OF THE CENTER FREQUENCY OR ( n , ( 4HUS RECEIVERS REQUIRING A WIDE BAND
WIDTH SHOULD USE A HIGH )& FREQUENCY CENTERED IN ONE OF THESE REGIONS &OR )& FREQUEN
CIES BELOW ( n , ( THE SPURIOUS FREQUENCIES ORIGINATE FROM HIGH ORDER TERMS
IN THE POWER SERIES MODEL AND ARE CONSEQUENTLY LOW ENOUGH IN AMPLITUDE THAT THEY
CAN OFTEN BE IGNORED &OR THIS REASON A LOW )& GENERALLY PROVIDES BETTER SUPPRESSION
OF SPURIOUS RESPONSES
4HE SPURIOUS EFFECTS CHART ALSO DEMONSTRATES SPURIOUS INPUT RESPONSES /NE OF THE
STRONGER OF THESE OCCURS AT POINT " WHERE THE ( n , PRODUCT CAUSES A MIXER OUTPUT IN
THE )& PASSBAND WITH AN INPUT FREQUENCY AT !LL THE PRODUCTS OF THE FORM .( n ,
PRODUCE POTENTIALLY TROUBLESOME SPURIOUS RESPONSES 4HESE FREQUENCIES MUST BE FIL
TERED AT 2& TO PREVENT THEIR REACHING THE MIXER )F SUFFICIENT FILTERING CANNOT BE APPLIED
PRIOR TO THE MIXING PROCESS SPURIOUS PRODUCTS THAT FALL WITHIN THE OPERATING BAND WILL
NO LONGER BE FILTERABLE WHICH WILL SERIOUSLY DEGRADE SYSTEM PERFORMANCE
3PURIOUS RESPONSES NOT PREDICTED BY THE CHART OCCUR WHEN TWO OR MORE 2& INPUT SIG
NALS PRODUCE OTHER FREQUENCIES BY INTERMODULATION THAT LIE WITHIN THE 2& PASSBAND
)MAGE 2EJECT -IXER ! CONVENTIONAL MIXER HAS TWO INPUT RESPONSES AT POINTS
ABOVE AND BELOW THE ,/ FREQUENCY WHERE THE FREQUENCY SEPARATION EQUALS THE )& 4HE
UNUSED RESPONSE KNOWN AS THE IMAGE IS SUPPRESSED BY THE IMAGE REJECT OR SINGLE
SIDEBAND MIXER SHOWN IN &IGURE 4HE 2& HYBRID PRODUCES A n PHASE DIFFERENTIAL
BETWEEN THE ,/ INPUTS TO THE TWO MIXERS 4HE EFFECT OF THIS PHASE DIFFERENTIAL ON THE
)& OUTPUTS OF THE MIXERS IS A n SHIFT IN ONE SIDEBAND AND A n SHIFT IN THE OTHER
4HE )& HYBRID ADDING OR SUBTRACTING ANOTHER n DIFFERENTIAL CAUSES THE HIGH SIDEBAND
SIGNALS TO ADD AT ONE OUTPUT PORT AND TO SUBTRACT AT THE OTHER 7HERE WIDE BANDWIDTHS
ARE INVOLVED THE )& HYBRID IS OF THE ALL PASS TYPE )N PRACTICE IMAGE REJECT MIXERS OFTEN
DO NOT PROVIDE SUFFICIENT REJECTION OF THE IMAGE RESPONSE ALONE WITHOUT FILTERING )N
THIS CASE THEY CAN BE USED IN CONJUNCTION WITH AN IMAGE REJECTION FILTER REDUCING THE
MAGNITUDE OF REJECTION REQUIRED BY THE FILTER
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#HARACTERISTICS OF !MPLIFIERS AND -IXERS .OISE FIGURE AMPLIFIER GAIN MIXER
CONVERSION LOSS D" COMPRESSION POINT AND THIRD ORDER INTERCEPT POINT ARE THE MOST
COMMON PERFORMANCE PARAMETERS SPECIFIED FOR AMPLIFIERS AND MIXERS /CCASIONALLY A
SECOND ORDER INTERCEPT POINT SPECIFICATION IS ALSO REQUIRED FOR VERY WIDE BANDWIDTH SIG
NALS )T SHOULD BE NOTED THAT FOR AMPLIFIERS COMPRESSION POINT AND THIRD ORDER INTERCEPT
ARE USUALLY SPECIFIED AT THEIR OUTPUT WHEREAS FOR MIXERS THESE PARAMETERS ARE USUALLY
SPECIFIED AT THEIR INPUT
!DDITIONAL SPECIFICATIONS FOR MIXERS INCLUDE ,/ DRIVE POWER PORT TO PORT ISOLATION
AND SINGLE TONE INTERMODULATION LEVELS 4HE ,/ DRIVE POWER SPECIFICATION DEFINES HOW
MUCH ,/ POWER IS REQUIRED BY THE MIXER TO MEET ITS SPECIFIED PERFORMANCE LEVELS
4YPICALLY THE HIGHER THE ,/ POWER THE HIGHER THE D" COMPRESSION POINT AND THIRD
ORDER INTERCEPT POINT 2ADAR RECEIVERS OFTEN REQUIRE HIGH ,/ DRIVE LEVEL MIXERS IN
ORDER TO MEET THE CHALLENGING DYNAMIC RANGE REQUIREMENTS 4HE PORT TO PORT ISOLATION
IS USED TO DETERMINE THE POWER LEVEL COUPLED DIRECTLY BETWEEN THE MIXER PORTS WITHOUT
FREQUENCY TRANSLATION 4HE SINGLE TONE INTERMODULATION LEVELS SPECIFY THE LEVELS OF
THE NF, MF2 SPURIOUS SIGNALS AS DISCUSSED PREVIOUSLY
È°xÊ " Ê"- /",&UNCTIONS OF THE ,OCAL /SCILLATOR 4HE SUPERHETERODYNE RECEIVER UTILIZES ONE
OR MORE LOCAL OSCILLATORS AND MIXERS TO CONVERT THE SIGNAL TO AN INTERMEDIATE FRE
QUENCY THAT IS CONVENIENT FOR FILTERING AND PROCESSING OPERATIONS 4HE RECEIVER CAN
BE TUNED BY CHANGING THE FIRST ,/ FREQUENCY WITHOUT DISTURBING THE )& SECTION OF THE
RECEIVER 3UBSEQUENT SHIFTS IN INTERMEDIATE FREQUENCY ARE OFTEN ACCOMPLISHED WITHIN
THE RECEIVER BY ADDITIONAL ,/S GENERALLY OF FIXED FREQUENCY 4HESE ,/S ARE GENER
ALLY ALSO USED IN THE EXCITER TO UPCONVERT MODULATED WAVEFORMS TO 2& FOR OUTPUT TO
THE TRANSMITTER
)N MANY EARLY RADARS THE ONLY FUNCTION OF THE LOCAL OSCILLATORS WAS CONVERSION OF
THE INPUT SIGNAL FREQUENCY TO THE CORRECT INTERMEDIATE FREQUENCY -ANY MODERN RADAR
SYSTEMS HOWEVER COHERENTLY PROCESS A SERIES OF RETURNS FROM A TARGET 4HE LOCAL OSCIL
LATORS ACT ESSENTIALLY AS A TIMING STANDARD BY WHICH THE SIGNAL DELAY IS MEASURED TO
EXTRACT RANGE INFORMATION ACCURATE TO WITHIN A SMALL FRACTION OF A WAVELENGTH 4HE
PROCESSING DEMANDS A HIGH DEGREE OF PHASE STABILITY THROUGHOUT THE RADAR
34!,/ )NSTABILITY 4HE FIRST LOCAL OSCILLATOR GENERALLY REFERRED TO AS A STABLE
LOCAL OSCILLATOR 34!,/ TYPICALLY HAS THE GREATEST EFFECT ON RECEIVER EXCITER STABILITY
HOWEVER WHEN EVALUATING THE OVERALL PERFORMANCE OTHER CONTRIBUTIONS SHOULD NOT BE
NEGLECTED !DVANCES IN STATE OF THE ART 34!,/ OSCILLATOR PERFORMANCE AND THE STRIN
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ALL OSCILLATORS AND TIMING JITTER OF !$ CONVERTER AND $! CONVERTER CLOCKS AND 42
STROBES MAY BE SIGNIFICANT
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IZED BY AGING AND ENVIRONMENTAL EFFECTS SPECIFIED IN TERMS OF FREQUENCY DRIFT AND
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)T SHOULD BE NOTED THAT MEASUREMENTS OF PHASE NOISE ARE TYPICALLY PERFORMED BY
MEASUREMENT OF DOUBLE SIDEBAND NOISE THE SUM OF THE POWER IN BOTH THE UPPER AND
LOWER SIDEBANDS BUT MORE TYPICALLY REPORTED AND SPECIFIED AS SINGLE SIDEBAND 33"
VALUES $OUBLE SIDEBAND NOISE CAN BE TRANSLATED TO A SINGLE SIDEBAND VALUE BY SUB
TRACTING D" 5NEQUAL SIDEBAND POWER CAN ONLY RESULT FROM ADDITIVE SIGNALS OR NOISE
OR CORRELATED AMPLITUDE AND PHASE NOISE COMPONENTS
!MPLITUDE MODULATION !- OF THE 34!,/ IS TYPICALLY NOT A SIGNIFICANT FACTOR AS
IT IS USUALLY AT A LOWER LEVEL THAN THE PHASE NOISE AT SMALL OFFSET FREQUENCIES FROM CAR
RIER AND CAN BE FURTHER REDUCED THROUGH LIMITING -ODERN MIXERS TYPICALLY PROVIDE A
SIGNIFICANT REDUCTION IN THE EFFECT OF 34!,/ AMPLITUDE MODULATION AS THEIR CONVERSION
GAIN IS RELATIVELY INSENSITIVE TO ,/ POWER VARIATION WHEN OPERATED AT THEIR SPECIFIED
DRIVE LEVEL
&OR SYSTEMS REQUIRING HIGH SENSITIVITY !- NOISE CAN BECOME DISRUPTIVE IF UNIN
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CAN OCCUR VIA SUBOPTIMUM COMPONENT BIAS TECHNIQUES WHERE HIGH AMPLITUDE SIGNALS
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A BENIGN ENVIRONMENT SOURCES OF UNWANTED PHASE MODULATION INCLUDE THE EFFECTS OF
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CIALLY IN AIRBORNE ENVIRONMENTS WHERE HIGH VIBRATION LEVELS ARE PRESENT 4HE VIBRATION
SENSITIVITY OF AN OSCILLATOR IS SPECIFIED BY THE FACTIONAL FREQUENCY VIBRATION SENSITIVITY
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2ANGE $EPENDENCE -OST MODERN RADARS USE THE 34!,/ IN BOTH THE RECEIVER
FOR DOWNCONVERSION AND THE EXCITER FOR UPCONVERSION 4HIS DOUBLE USE OF THE 34!,/
INTRODUCES A DEPENDENCE ON RANGE OF THE CLUTTER AND EXAGGERATES THE EFFECT OF CERTAIN
UNINTENTIONAL PHASE MODULATION COMPONENTS BY D" THE CRITICAL FREQUENCIES BEING
THOSE WHICH CHANGE PHASE BY ODD MULTIPLES OF — DURING THE TIME PERIOD BETWEEN
TRANSMISSION AND RECEPTION OF THE CLUTTER RETURN FROM A SPECIFIED RANGE
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\ &2 FM \ SIN P FM 2 C SIN P FM4
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2 RANGE M
C PROPAGATION VELOCITY r MS
4 TIME DELAY 2C S
! SHORT TIME DELAY CAN TOLERATE MUCH HIGHER DISTURBANCES AT LOW MODULATION FRE
QUENCIES AS ILLUSTRATED BY THE TWO CASES IN &IGURE #ONSEQUENTLY THE EFFECTS OF
34!,/ STABILITY NEED TO BE COMPUTED FOR SEVERAL TIME DELAYS OR RANGES TO ENSURE SUF
FICIENT STABILITY EXISTS FOR THE INTENDED APPLICATION
#LOSE TO CARRIER PHASE MODULATION IS TYPICALLY DOMINATED BY THAT OF THE OSCILLATORS
DUE TO THE INHERENT FEEDBACK PROCESS WITHIN THE OSCILLATOR CIRCUITRY .OISE CONTRIBU
TORS WITHIN THE OSCILLATOR LOOP THAT EXHIBIT A F CHARACTERISTIC D"DECADE NOISE
SLOPE ARE ENHANCED BY D" VIA THE FEEDBACK MECHANISM WITH A RESULTING NET F CHARACTERISTIC D"DECADE NOISE SIGNATURE CLOSE TO CARRIER WITHIN THE OSCILLATOR LOOP
BANDWIDTH /UTSIDE THIS LOOP BANDWIDTH THE OSCILLATOR NOISE SIGNATURE RESUMES A F
SLOPE UNTIL REACHING A FLAT THERMAL NOISE FLOOR !T LARGER FREQUENCY OFFSETS SIGNIFICANT
NOISE CONTRIBUTIONS CAN RESULT FROM OTHER COMPONENTS SUCH AS AMPLIFIERS IN THE 34!,/
SIGNAL PATH $EPENDING ON THE LOCATION OF THESE AMPLIFIERS THEY MAY EITHER CREATE
PHASE MODULATION THAT IS COMMON TO BOTH THE RECEIVER AND EXCITER CORRELATED NOISE
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OR UNCOMMON NOISE IS NOT SUBJECT TO THE RANGE DEPENDENT FACTOR DESCRIBED ABOVE SO IT
MUST BE ACCOUNTED FOR SEPARATELY /THER SIGNIFICANT CONTRIBUTORS OF UNCOMMON NOISE
ARE THE NOISE ON THE EXCITER WAVEFORM BEFORE UPCONVERSION ALONG WITH AMPLIFIERS IN
THE RECEIVER AND EXCITER SIGNAL PATHS
4HE UNDESIRED 33" PHASE NOISE AFTER DOWNCONVERSION BY THE 34!,/ IS THE SUM OF
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AND SIGNAL PROCESSOR HAVE RESPONSES THAT ARE FUNCTIONS OF THE DOPPLER MODULATION FRE
QUENCY SO THE OUTPUT SPECTRUM CAN BE OBTAINED BY COMBINING THE RESPONSES OF THESE
FILTERS WITH THE SPECTRUM PRESENT AT THE MIXER INPUT )N -4) SYSTEMS IT IS COMMON TO
DESCRIBE THE ABILITY TO SUPPRESS CLUTTER IN TERMS OF AN -4) IMPROVEMENT FACTOR 4HE
-4) IMPROVEMENT FACTOR ) IS DEFINED AS THE SIGNAL TO CLUTTER RATIO AT THE OUTPUT OF
THE CLUTTER FILTER DIVIDED BY THE SIGNAL TO CLUTTER RATIO AT THE INPUT OF THE CLUTTER FILTER
AVERAGED UNIFORMLY OVER ALL TARGET RADIAL VELOCITIES OF INTEREST 4HE -4) IMPROVEMENT
FACTOR LIMITATION DUE TO THE 34!,/ MAY BE EXPRESSED AS THE RATIO OF THE 34!,/ POWER
TO THE TOTAL INTEGRATED POWER OF THE RETURN MODULATION SPECTRUM IT CREATES AT THE OUTPUT
OF THE -4) FILTERS &IGURE ILLUSTRATES THE EFFECT OF THE OVERALL FILTERING CONSISTING OF
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4HE INTEGRATED RESIDUE POWER DUE TO THE 34!-/ PHASE NOISE IS GIVEN BY
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MITTED AT A FIXED PULSE REPETITION FREQUENCY 02& AND DOPPLER PROCESSING IS PER
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4HE RESULTING SAMPLING OF THE RECEIVER OUTPUT AT THE 02& PRODUCES ALIASING OF THE PHASE
NOISE SPECTRUM PERIODICALLY AT THE 02& INTERVAL AS SHOWN IN &IGURE WHERE EACH
CURVE REPRESENTS THE PHASE NOISE AT THE OUTPUT OF THE RECEIVER INCLUDING THE EFFECTS
OF RECEIVER FILTERING AND OFFSET BY A MULTIPLE OF THE 02& FREQUENCY 4HE COMBINED
PHASE NOISE DUE TO EACH ALIASED COMPONENT IS CALCULATED USING %Q WITH THE RESULT
ILLUSTRATED IN &IGURE 4HIS SAMPLED PHASE NOISE SPECTRUM PROVIDES A METHOD FOR
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3INUSOIDAL -ODULATIONS 2ADAR PERFORMANCE IS AFFECTED BY BOTH RANDOM AND SINU
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THEIR RELATIONSHIP TO THE RADAR 02& AND THEIR MAGNITUDE RELATIVE TO THE RANDOM MODU
LATIONS %XAMPLES OF SUCH UNDESIRED SINUSOIDAL MODULATIONS ARE IN BAND UNFILTERABLE
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MUST BE CONCERNED WITH INTERNAL SIGNAL SOURCES -4) AND PULSE DOPPLER RADARS ARE
PARTICULARLY SUSCEPTIBLE TO ANY SUCH INTERNAL OSCILLATORS THAT ARE NOT COHERENT IE THAT
DO NOT HAVE THE SAME PHASE FOR EACH PULSE TRANSMISSION 4HE EFFECT OF THE SPURIOUS
SIGNAL IS THEN DIFFERENT FOR EACH RETURN AND THE ABILITY TO REJECT CLUTTER IS DEGRADED
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A SINGLE FREQUENCY REFERENCE 4HIS FULLY COHERENT ARCHITECTURE INSURES THAT BOTH THE
DESIRED FREQUENCIES AND ALL THE INTERNALLY GENERATED SPURIOUS SIGNALS ARE COHERENT
ELIMINATING THE DEGRADATION OF CLUTTER REJECTION
-ANY RADAR SYSTEMS ARE PSEUDO COHERENT 4HE SAME OSCILLATORS ARE USED IN BOTH
TRANSMIT AND RECEIVE BUT NOT NECESSARILY COHERENT WITH EACH OTHER 4HE RESULT IS THAT
THE PHASE OF THE TARGET REMAINS CONSTANT BUT THE PHASE OF MANY OF THE SPURIOUS SIGNALS
VARIES FROM PULSE TO PULSE )N THIS TYPE OF CONFIGURATION SIGNAL ISOLATION AND FREQUENCY
ARCHITECTURE IS CRITICAL TO MINIMIZE THE OCCURRENCE OF SPURIOUS SIGNALS THAT COULD ERRO
NEOUSLY BE INTERPRETED AS FALSE TARGETS
#/(/ AND 4IMING )NSTABILITY 4HE MAJORITY OF THIS DISCUSSION HAS FOCUSED
ON THE 34!,/ AS THE MAJOR CONTRIBUTOR TO RECEIVER STABILITY /THER CONTRIBUTORS
SUCH AS THE SECOND ,/ THE COHERENT OSCILLATOR #/(/ IF USED !$ AND $!
CONVERTER CLOCKS CAN ALL BECOME SIGNIFICANT !$ AND $! CONVERTER CLOCK JITTER
BECOMES INCREASINGLY SIGNIFICANT AS SAMPLE RATES AND )& FREQUENCIES ARE INCREASED
4HE EFFECTS OF !$ AND $! CONVERTER CLOCK PHASE NOISE AND JITTER IS DESCRIBED IN
3ECTIONS AND 4HE JITTER ON TIMING STROBES USED TO PERFORM TRANSMITRECEIVE
42 SWITCHING IS TYPICALLY LESS STRINGENT THAN THAT OF !$ CLOCKS AS IT DOES NOT HAVE
A DIRECT IMPACT ON THE SIGNAL PHASE (OWEVER IF COMPONENTS SUCH AS TRANSMITRECEIVE
SWITCHES OR POWER AMPLIFIERS HAVE A TRANSIENT PHASE RESPONSE OF SIGNIFICANT DURATION
TIME JITTER ON THE SWITCHING TIME CAN BE TRANSLATED INTO A PHASE MODULATION OF THE
TRANSMITTER OR RECEIVER SIGNAL
4OTAL 2ADAR )NSTABILITY 4HE PRIMARY SOURCES OF RADAR INSTABILITY ARE USUALLY THE
RECEIVER EXCITER COMMON PHASE NOISE RECEIVER AND EXCITER UNCOMMON PHASE NOISE
AND THE TRANSMITTER PHASE NOISE )F THE SPECTRA OF THESE COMPONENTS ARE AVAILABLE EITHER
THROUGH MEASUREMENTS OR THROUGH PREDICTIONS BASED ON SIMILAR DEVICES THE CONVOLU
TION OF RECEIVER EXCITER COMMON PHASE NOISE MODIFIED BY THE RANGE DEPENDENT EFFECT
WITH THE OTHER COMPONENTS PROVIDES AN ESTIMATE OF THE SPECTRUM OF RETURNS FROM STABLE
CLUTTER WHICH IS THEN MODIFIED BY THE RECEIVER FILTERS AND INTEGRATED TO OBTAIN THE RESI
DUE POWER CAUSED BY THESE CONTRIBUTORS 4HESE PROCEDURES ARE EMPLOYED TO DIAGNOSE
THE SOURCE OF RADAR INSTABILITY IN AN EXISTING RADAR OR TO PREDICT THE PERFORMANCE OF A
RADAR IN THE DESIGN STAGE AND TO ALLOW THE ALLOCATION OF STABILITY REQUIREMENTS TO CRITICAL
COMPONENTS OR SUBSYSTEMS WITHIN THE RADAR
-EASUREMENT OF TOTAL RADAR INSTABILITY CAN BE CONDUCTED WITH THE RADAR ANTENNA
SEARCH LIGHTING A STABLE POINT CLUTTER REFLECTOR THAT PRODUCES A SIGNAL RETURN CLOSE TO
BUT BELOW THE DYNAMIC RANGE LIMIT OF THE RECEIVER 3UITABLE CLUTTER SOURCES ARE DIF
FICULT TO FIND AT MANY RADAR SITES AND INTERRUPTION OF ROTATION OF THE ANTENNA TO CON
DUCT SUCH A TEST MAY BE UNACCEPTABLE AT OTHERS IN THIS CASE A MICROWAVE DELAY LINE
CAN BE EMPLOYED TO FEED A DELAYED SAMPLE OF THE TRANSMITTER PULSE INTO THE RECEIVER
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TER DOES NOT PRODUCE EQUAL IMPACT ON ALL PARTS OF THE RETURN PULSE AND GENERALLY HAS
MINIMAL EFFECT ON THE CENTER OF THE PULSE SO IT IS ESSENTIAL TO COLLECT DATA SAMPLES AT
A MULTIPLICITY OF POINTS ACROSS THE RETURN INCLUDING LEADING AND TRAILING EDGES 4HE
TOTAL RADAR INSTABILITY IS THE RATIO OF THE SUM OF THE MULTIPLICITY OF RESIDUE POWERS AT
THE OUTPUT OF THE DOPPLER FILTER TO THE SUM OF THE POWERS AT ITS INPUT DIVIDED BY THE
RATIO OF RECEIVER NOISE AT THESE LOCATIONS 3TABILITY IS THE INVERSE OF THIS RATIO BOTH ARE
GENERALLY EXPRESSED IN DECIBELS
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CAUSED BY PHASE MODULATION DURING THE LONG TRANSMITTED PULSE RATHER THAN SOLELY FROM
PULSE TO PULSE -EASUREMENT OF STABILITY OF SUCH RADARS MUST EMPLOY A VERY LARGE NUM
BER OF DATA POINTS TO OBTAIN AN ANSWER VALID FOR CLUTTER DISTRIBUTED IN RANGE
)N ADDITION TO THE AMPLITUDE AND PHASE NOISE OF THE RECEIVER EXCITER AND THE TRANS
MITTER MECHANICALLY SCANNING ANTENNAS PRODUCE A MODULATION THAT IS PREDOMINANTLY
!- 4HE COMBINED EFFECT IS THE SUM OF THE RESIDUE POWERS PRODUCED BY EACH COMPO
NENT INDIVIDUALLY
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2& FREQUENCIES REQUIRING A NUMBER OF ,/ FREQUENCIES THAT ARE TYPICALLY GENERATED
USING FREQUENCY SYNTHESIS &REQUENCY SYNTHESIS IS THE PROCESS OF CREATING ONE OR MORE
FREQUENCIES FROM A SINGLE REFERENCE FREQUENCY USING FREQUENCY MULTIPLICATION DIVI
SION ADDITION AND SUBTRACTION TO SYNTHESIZE THE REQUIRED FREQUENCIES 4HE FUNDAMENTAL
BUILDING BLOCK OF ANY FREQUENCY SYNTHESIS APPROACH IS THE OSCILLATOR #RYSTAL OSCILLATORS
HAVE HISTORICALLY BEEN THE MOST COMMON SOURCE TECHNOLOGY 6(& CRYSTAL OSCILLATORS
EMPLOYING DOUBLY ROTATED 3# )4 ETC CRYSTAL RESONATORS ARE ABLE TO SUPPORT HIGHER
POWER LEVELS THAN SINGLE AXIS CRYSTALS 4HIS ENABLES THEM TO ACHIEVE LOWER PHASE NOISE
AND IMPROVED VIBRATION IMMUNITY DUE TO PROPERTIES UNIQUE TO THE PARTICULAR AXIS OF
ROTATION &REQUENCY MULTIPLICATION OF THESE 6(& SOURCES IS OFTEN USED TO GENERATE THE
RADAR 2& FREQUENCIES REQUIRED HOWEVER THIS MULTIPLICATION PROCESS RESULTS IN INCREASE
IN PHASE NOISE PERFORMANCE BY LOG- D" WHERE - IS THE MULTIPLICATION FACTOR !
VARIETY OF OTHER SOURCE TECHNOLOGIES SUCH AS 3URFACE !COUSTIC 7AVE 3!7 OSCILLA
TORS HAVE BEEN EXPLOITED TO ACHIEVE IMPROVED PHASE NOISE PERFORMANCE 3!7 OSCIL
LATORS ENABLE LOWER FAR FROM CARRIER PHASE NOISE LARGELY DUE TO THEIR HIGHER FREQUENCY
OPERATION AND THE RESULTING LOWER FREQUENCY MULTIPLICATION FACTOR REQUIRED TO GENERATE
THE EQUIVALENT RADAR 2& OUTPUT FREQUENCIES
6ERY ACCURATE FREQUENCY TIMING IS OFTEN REQUIRED IN RADARS WHERE COORDINATION OR
HAND OFF FROM ONE RADAR TO ANOTHER OR COMMUNICATION TO A MISSILE IN FLIGHT IS REQUIRED
4HIS IS TYPICALLY THE CASE WHERE A SEARCH RADAR ACQUIRES A TARGET AND QUEUES A PRECI
SION TRACKING RADAR !CCURATE TIMING FOR THESE APPLICATIONS MAY BE ACHIEVED BY PHASE
LOCKING THE LOW PHASE NOISE RADAR OSCILLATORS TO A LOW FREQUENCY REFERENCE GENERATED
FROM EITHER A RUBIDIUM OSCILLATOR OR A '03 RECEIVER )N THIS CONFIGURATION THE LONG TERM
STABILITY OF THE REFERENCE OSCILLATOR IS SUPERIOR TO THAT OF THE RADAR OSCILLATOR AND THE
SHORT TERM STABILITY OF THE RADAR OSCILLATOR IS SUPERIOR TO THAT OF THE REFERENCE OSCILLATOR
4HE PHASE LOCK LOOP 0,, ARCHITECTURE IS ESTABLISHED TO EXPLOIT THE STRENGTHS OF BOTH
TECHNOLOGIES BY SELECTING A 0,, BANDWIDTH AT THE OFFSET FREQUENCY WHERE THE SOURCE
STABILITIES CROSS OVER &OR TYPICAL RADAR AND REFERENCE OSCILLATOR TECHNOLOGIES THIS USU
ALLY OCCURS IN THE (Z TO K(Z OFFSET REGION
&REQUENCY 3YNTHESIS 4ECHNIQUES 4HE MOST COMMON TECHNIQUES ARE DIRECT
SYNTHESIS DIRECT DIGITAL SYNTHESIS AND FREQUENCY MULTIPLICATION $IRECT SYNTHESIS IS
THE PROCESS OF GENERATING FREQUENCIES THROUGH THE MULTIPLICATION AND MIXING OF A
NUMBER OF SIGNALS AT DIFFERENT FREQUENCIES TO PRODUCE THE REQUIRED OUTPUT FREQUENCY
&REQUENCY MULTIPLICATION AND DIRECT DIGITAL SYNTHESIS ARE DESCRIBED IN 3ECTION #ONVENTIONAL PHASE LOCKED LOOP SYNTHESIZERS ARE OCCASIONALLY USED BUT THEIR FRE
QUENCY SWITCHING TIMES AND PHASE SETTLING RESPONSES ARE GENERALLY INADEQUATE TO MEET
THE STRINGENT RADAR RECEIVER EXCITER REQUIREMENTS 0HASE LOCKED LOOPS ARE MORE LIKELY
USED TO LOCK FIXED HIGH FREQUENCY OSCILLATORS TO STABLE LOW FREQUENCY REFERENCES TO
È°ÓÓ
2!$!2 (!.$"//+
ENSURE COHERENCE OF ALL OSCILLATORS WITHIN THE RECEIVER EXCITER AND OBTAIN AN OPTIMUM
BALANCE OF LONG AND SHORT TERM STABILITY
#OHERENCE !FTER &REQUENCY 3WITCHING ,ONG RANGE RADARS OFTEN TRANSMIT A SERIES
OF PULSES BEFORE RECEIVING RETURNS FROM THE FIRST IN THE SEQUENCE 0ULSES MAY BE TRANSMITTED
AT A NUMBER OF DIFFERENT OPERATING FREQUENCIES REQUIRING SWITCHING OF THE ,/ FREQUENCY
BETWEEN PULSES )F TARGET RETURNS ARE PROCESSED COHERENTLY THE PHASE OF THE ,/ SIGNAL
MUST BE CONTROLLED SUCH THAT EACH TIME IT SWITCHES TO A PARTICULAR FREQUENCY THE PHASE OF
THE ,/ IS THE SAME PHASE THAT IT WOULD HAVE BEEN HAD NO FREQUENCY SWITCHING OCCURRED
4HIS REQUIREMENT DRIVES THE ARCHITECTURE USED TO GENERATE ,/ FREQUENCIES 'ENERATING
ALL THE FREQUENCIES FROM A SINGLE REFERENCE FREQUENCY DOES NOT GUARANTEE PHASE COHER
ENCE WHEN FREQUENCY SWITCHING OCCURS 4HREE SOURCES OF PHASE AMBIGUITY ARE COMMON
FREQUENCY DIVIDERS DIRECT DIGITAL SYNTHESIZERS AND VOLTAGE CONTROLLED OSCILLATORS 6#/ &REQUENCY DIVIDERS PRODUCE AN OUTPUT SIGNAL THAT CAN HAVE ANY ONE OF . PHASES WHERE .
IS THE DIVIDE RATIO SWITCHING DIVIDERS CAN RESULT IN PHASE AMBIGUITY OF O . )F FREQUENCY
DIVIDERS ARE USED IN THE FREQUENCY SYNTHESIS PROCESS THEY MUST BE OPERATED CONSTANTLY
WITHOUT SWITCHING THE INPUT FREQUENCY OR DIVIDE RATIO TO AVOID THIS PHASE AMBIGUITY
$IRECT DIGITAL SYNTHESIZERS $$3S CAN BE USED EITHER TO GENERATE ,/ FREQUENCIES DIRECTLY
OR TO GENERATE MODULATED WAVEFORMS PRIOR TO UPCONVERSION 7HEN PULSE TO PULSE PHASE
COHERENCE IS REQUIRED THE STARTING PHASE IS RESET TO ZERO AT THE START OF EACH PULSE )F ALL THE
,/ FREQUENCIES USED ARE MULTIPLES OF THE PULSE REPLETION FREQUENCY THE RESULTING PHASE
WILL BE THE SAME FOR EACH PULSE 6#/S CAN BE USED TO CREATE A TUNABLE ,/ BUT ARE USUALLY
PHASE LOCKED TO ANOTHER STABLE SOURCE FOR IMPROVED STABILITY 4HE TUNING VOLTAGE DESIGN
AND FILTER CAPACITOR TECHNOLOGY USED TO ACHIEVE PHASE LOCK MUST BE CAREFULLY DESIGNED
TO ENSURE RAPID VOLTAGE AND STORED CHARGE TRANSITIONS /THERWISE THE 6#/ MAY PROPERLY
ACQUIRE AND ACHIEVE PHASE LOCK BUT THE RESIDUAL VOLTAGE DECAY FROM THE TRANSITION WILL
MANIFEST ITSELF IN AN INSIDIOUS PHASE AMBIGUITY CALLED POST TUNING DRIFT
3TRETCH 0ROCESSING )N STRETCH PROCESSING THE ,/ SIGNAL FREQUENCY IS MODULATED
WITH A CHIRP WAVEFORM SIMILAR TO THAT OF THE RECEIVED SIGNAL TO REDUCE THE BANDWIDTH
OF THE )& SIGNAL AS DESCRIBED IN 3ECTION 4HE WIDEBAND CHIRP WAVEFORM IS TYPICALLY
GENERATED BY PASSING A NARROWER BANDWIDTH LINEAR FREQUENCY MODULATION ,&- WAVE
FORM THROUGH A FREQUENCY MULTIPLIER THAT INCREASES BOTH THE OPERATING FREQUENCY AND
BANDWIDTH OF THE CHIRP WAVEFORM &REQUENCY MULTIPLIERS MULTIPLY THE PHASE DISTORTION
OF THE INPUT SIGNAL AND OFTEN HAVE SIGNIFICANT PHASE DISTORTION THEMSELVES $ISTORTION OF
THE ,/ CHIRP SIGNAL PHASE CAN HAVE A SIGNIFICANT EFFECT ON THE COMPRESSED PULSE PERFOR
MANCE EITHER DISTORTING THE COMPRESSED PULSE SHAPE OR DEGRADING SIDELOBE PERFORMANCE
3ECTION 0HASE ERRORS CAN BE MEASURED USING A TEST TARGET INJECTED INTO THE RECEIVER
AND MEASURING THE PHASE RIPPLE AT THE RECEIVER OUTPUT "Y PERFORMING THIS MEASUREMENT
WITH TARGETS INJECTED AT DIFFERENT SIMULATED RANGES THE ERRORS ASSOCIATED WITH THE RECEIVER
,/ AND TEST SIGNAL CAN BE SEPARATED #ORRECTION OF RECEIVER ,/ PHASE DISTORTION CAN BE
READILY CORRECTED WHEN USING A DIRECT DIGITAL SYNTHESIZER AS DESCRIBED IN 3ECTION È°ÈÊ Ê " /,"
3ENSITIVITY 4IME #ONTROL 34# 4HE SEARCH RADAR DETECTS RETURNS OF WIDELY DIF
FERING AMPLITUDES OFTEN SO GREAT THAT THE DYNAMIC RANGE OF A FIXED GAIN RECEIVER WILL
BE EXCEEDED $IFFERENCES IN RETURN STRENGTH ARE CAUSED BY DIFFERENCES IN RADAR CROSS
2!$!2 2%#%)6%23
È°ÓÎ
SECTIONS IN METEOROLOGICAL CONDITIONS AND IN RANGE 4HE EFFECT OF RANGE ON RADAR RETURN
STRENGTH OVERSHADOWS THE OTHER CAUSES AND CAN BE MITIGATED BY A TECHNIQUE KNOWN AS
SENSITIVITY TIME CONTROL WHICH CAUSES THE RADAR RECEIVER SENSITIVITY TO VARY WITH TIME IN
SUCH A WAY THAT THE AMPLIFIED RADAR RETURN STRENGTH IS INDEPENDENT OF RANGE
4IME SIDELOBES OF COMPRESSED PULSES IN RADARS THAT TRANSMIT CODED WAVEFORMS CAN
BE DEGRADED BY 34# 'RADUAL CHANGES CAN USUALLY BE TOLERATED BUT AT CLOSE RANGE THE
RATE OF CHANGE OF ATTENUATION CAN BE VERY LARGE -OST MODERN RADARS THAT INCLUDE 34#
USE DIGITAL 34# CONTROL WHICH CAN LEAD TO LARGE STEP SIZES AT CLOSE RANGE UNLESS HIGH
DIGITIZATION RATES ARE USED 4HE PHASE STABILITY OF THE 34# ATTENUATOR IS ALSO AN IMPOR
TANT CONSIDERATION AS EXCESSIVE PHASE VARIATION AS A FUNCTION OF ATTENUATION CAN HAVE A
DRAMATIC IMPACT ON RANGE SIDELOBES
#LUTTER -AP !UTOMATIC 'AIN #ONTROL )N SOME RADARS MOUNTAIN OR URBAN CLUT
TER CAN CREATE RETURNS THAT WOULD EXCEED THE DYNAMIC RANGE OF THE RECEIVER 4HE SPATIAL
AREA OCCUPIED BY SUCH CLUTTER IS TYPICALLY A VERY SMALL FRACTION OF THE RADAR COVERAGE
SO CLUTTER MAP !'# HAS BEEN USED AS AN ALTERNATIVE TO BOOSTING THE 34# CURVE 4HIS
TECHNIQUE USES A DIGITAL MAP TO RECORD THE MEAN AMPLITUDE OF THE CLUTTER IN EACH MAP
CELL OVER MANY SCANS AND ADDS RECEIVER ATTENUATION WHERE NECESSARY TO KEEP THE CLUTTER
RETURNS BELOW THE SATURATION LEVEL OF THE RECEIVER
0ROGRAMMABLE 'AIN #ONTROL 2EDUCED GAIN MAY BE DESIRABLE IN A VARIETY OF
SITUATIONS SUCH AS HIGH CLUTTER OR HIGH INTERFERENCE ENVIRONMENTS OR IN SHORT RANGE
MODES &IXED ATTENUATION IS OFTEN PREFERABLE TO 34# OR CLUTTER MAP CONTROL (IGH 02&
PULSE DOPPLER RADARS FOR EXAMPLE CANNOT TOLERATE 34# DUE TO THE RANGE AMBIGUITY
OF TARGETS !DDITIONAL ATTENUATION MAY BE PROGRAMMED EITHER MANUALLY VIA OPERATOR
CONTROL OR AUTOMATICALLY TO INCREASE THE RECEIVERS LARGE SIGNAL HANDLING CAPABILITY OR
TO REDUCE ITS SENSITIVITY
'AIN .ORMALIZATION 2ECEIVER GAIN CAN VARY DUE TO COMPONENT TOLERANCES FRE
QUENCY RESPONSE VARIATION WITH TEMPERATURE AND AGING !CCURATE RECEIVER GAIN CONTROL
IS REQUIRED FOR A VARIETY OF REASONS THAT INCLUDE TARGET RADAR CROSS SECTION MEASURE
MENT MONOPULSE ANGLE ACCURACY MAXIMIZING THE RECEIVER DYNAMIC RANGE AND NOISE
LEVEL CONTROL $IGITAL GAIN CONTROL PERMITS THE CALIBRATION OF RECEIVER GAIN BY INJECT
ING TEST SIGNALS DURING RADAR DEAD TIME OR DURING SOME SCHEDULED CALIBRATION INTERVAL
#ALIBRATION COEFFICIENTS CAN BE STORED AS A FUNCTION OF COMMANDED ATTENUATION OPERAT
ING FREQUENCY AND TEMPERATURE AS NEEDED -EASUREMENTS OVER TIME CAN ALSO BE USED
TO ASSESS COMPONENT AGING AND POTENTIALLY PREDICT RECEIVER FAILURE PRIOR TO DEGRADATION
BEYOND ACCEPTABLE LIMITS !CCURATE GAIN CONTROL IS ESSENTIAL FOR RECEIVER CHANNELS USED
TO PERFORM MONOPULSE ANGLE MEASUREMENTS WHERE AMPLITUDES RECEIVED IN TWO OR MORE
BEAMS SIMULTANEOUSLY ARE COMPARED TO ACCURATELY DETERMINE THE TARGETS POSITION IN
AZIMUTH OR ELEVATION 2ECEIVER DYNAMIC RANGE IS MAXIMIZED WITH ACCURATE GAIN CONTROL
AS TOO LITTLE GAIN CAN RESULT IN NOISE FIGURE DEGRADATION AND TOO MUCH GAIN RESULTS IN
LARGE SIGNALS EXCEEDING THE !$ CONVERTER FULL SCALE OR CREATING UNWANTED GAIN COM
PRESSION INTERMODULATION OR CROSS MODULATION DISTORTION
!UTOMATIC .OISE ,EVEL #ONTROL !NOTHER WIDELY EMPLOYED USE FOR !'# IS TO
MAINTAIN A DESIRED LEVEL OF RECEIVER NOISE AT THE !$ CONVERTER !S WILL BE DESCRIBED
IN 3ECTION TOO LITTLE NOISE RELATIVE TO THE QUANTIZATION INCREMENT OF THE !$ CON
VERTER CAUSES A LOSS IN SENSITIVITY 3AMPLES OF NOISE ARE TAKEN AT LONG RANGE OFTEN BEYOND
THE INSTRUMENTED RANGE OF THE RADAR OR DURING SOME SCHEDULED PERIOD )F THE RADAR HAS
È°Ó{
2!$!2 (!.$"//+
2& 34# PRIOR TO ANY AMPLIFICATION IT CAN BE SET TO FULL ATTENUATION TO MINIMIZE EXTER
NAL INTERFERENCE WITH MINIMAL AND PREDICTABLE EFFECT ON SYSTEM NOISE TEMPERATURE -OST
RADARS EMPLOY AMPLIFIERS PRIOR TO 34# SO THEY CANNOT ATTENUATE EXTERNAL INTERFERENCE WITH
OUT AFFECTING THE NOISE LEVEL 4HE NOISE LEVEL CALIBRATION ALGORITHM MUST BE DESIGNED TO
TOLERATE EXTERNAL INTERFERENCE AND RETURNS FROM RAINSTORMS OR MOUNTAINS AT EXTREME RANGE
!NOTHER CONCERN WITH AMPLIFICATION PRIOR TO 34# IS THAT THE NOISE LEVEL AT THE OUTPUT
OF THE 34# ATTENUATOR VARIES WITH RANGE !T CLOSE RANGE THE NOISE LEVEL INTO THE !$
CONVERTER MAY FALL BELOW THE QUANTIZATION INTERVAL !LSO A CONSTANT NOISE LEVEL AS A
FUNCTION OF RANGE AT THE RECEIVER OUTPUT IS DESIRABLE IN ORDER TO MAINTAIN A CONSTANT FALSE
ALARM RATE .OISE INJECTION AFTER THE 34# ATTENUATOR IS USED TO OVERCOME THIS PROBLEM
! NOISE SOURCE AND ATTENUATOR ARE OFTEN EMPLOYED AT )& TO INJECT ADDITIONAL NOISE TO
COMPENSATE FOR THE REDUCED NOISE AFTER THE 34# ATTENUATOR $IGITAL CONTROL OF THE NOISE
INJECTION IS SYNCHRONIZED WITH THE 34# ATTENUATION TO PROVIDE AN EFFECTIVE CONSTANT
NOISE LEVEL AT THE !$ CONVERTER INPUT
'AIN #ONTROL #OMPONENTS -OST MODERN RADARS PERFORM GAIN CONTROL DIGITALLY
$IGITAL CONTROL PERMITS CALIBRATION OF EACH ATTENUATION VALUE TO DETERMINE THE DIFFER
ENCE BETWEEN THE ACTUAL ATTENUATION AND THAT COMMANDED BY INJECTING TEST SIGNALS
DURING DEAD TIME
)N THE PAST GAIN CONTROLLED AMPLIFIERS WERE USED EXTENSIVELY TO CONTROL AND ADJUST
RECEIVER GAIN 2ECENTLY THIS APPROACH HAS LARGELY BEEN REPLACED USING DIGITAL SWITCHED
OR ANALOG VOLTAGE OR CURRENT CONTROLLED ATTENUATORS DISTRIBUTED THROUGHOUT THE RECEIVER
CHAIN 6ARIABLE ATTENUATORS HAVE A NUMBER OF ADVANTAGES OVER VARIABLE GAIN AMPLIFI
ERS THEY TYPICALLY PROVIDE BROADER BANDWIDTHS GREATER GAIN CONTROL ACCURACY GREATER
PHASE STABILITY IMPROVED DYNAMIC RANGE AND FASTER SWITCHING SPEED
4HE CHOICE BETWEEN VOLTAGE CONTROLLED AND SWITCHED ATTENUATION DEPENDS ON TRADE
OFFS BETWEEN PERFORMANCE OF A VARIETY OF PARAMETERS 3WITCHED ATTENUATORS GENERALLY
PROVIDE MAXIMUM ATTENUATION ACCURACY FASTER SWITCHING SPEED IMPROVED AMPLITUDE
AND PHASE STABILITY GREATER BANDWIDTH HIGHER DYNAMIC RANGE AND HIGHER POWER HAN
DLING CAPABILITY 6OLTAGE OR CURRENT CONTROLLED ATTENUATORS CONTROLLED VIA A $! CON
VERTER TYPICALLY PROVIDE IMPROVED RESOLUTION AND LOWER INSERTION LOSS
'AIN CONTROL ATTENUATORS ARE OFTEN INCORPORATED WITHIN THE RECEIVER AT BOTH 2& AND
)& 2& ATTENUATION IS USED TO PROVIDE INCREASED DYNAMIC RANGE IN THE PRESENCE OF LARGE
TARGET RETURNS "Y PLACING THE ATTENUATION AS CLOSE TO THE FRONT END AS POSSIBLE LARGE
SIGNALS CAN BE HANDLED BY MINIMIZING GAIN COMPRESSION INTERMODULATION OR CROSS
MODULATION DISTORTION IN THE MAJORITY OF RECEIVER COMPONENTS 4HE DISADVANTAGE OF
USING FRONT END ATTENUATION IS THAT IT WILL TYPICALLY HAVE A LARGER IMPACT ON RECEIVER
NOISE FIGURE THAN ATTENUATION PLACED LATER IN THE RECEIVER 4HIS IS NOT USUALLY AN ISSUE
WHEN THE INTENT OF ADDING ATTENUATION IS TO DESENSITIZE THE RECEIVER AS IS THE CASE FOR
34# "ACK END OR )& ATTENUATION IS OFTEN USED TO ADJUST THE GAIN OF THE RECEIVER TO
COMPENSATE FOR RECEIVER GAIN VARIATIONS DUE TO COMPONENT VARIATIONS WHERE RECEIVER
NOISE FIGURE DEGRADATION CANNOT BE TOLERATED
È°ÇÊ / , &ILTERING OF THE %NTIRE 2ADAR 3YSTEM &ILTERING PROVIDES THE PRINCIPAL MEANS
BY WHICH THE RADAR DISCRIMINATES BETWEEN TARGET RETURNS AND INTERFERENCE OF MANY
TYPES 4HE FILTERING IS PERFORMED BY A VARIETY OF FILTERS THROUGHOUT THE RECEIVER AND
È°Óx
2!$!2 2%#%)6%23
IN THE SUBSEQUENT DIGITAL SIGNAL PROCESSING -OST RADARS TRANSMIT MULTIPLE PULSES AT
A TARGET BEFORE THE ANTENNA BEAM IS MOVED TO A DIFFERENT DIRECTION AND THE MULTIPLE
RETURNS ARE COMBINED IN SOME FASHION 4HE RETURNS MAY BE COMBINED USING COHERENT
INTEGRATION OR VARIOUS DOPPLER PROCESSING TECHNIQUES INCLUDING -4) TO SEPARATE
DESIRED TARGETS FROM CLUTTER &ROM THE RADAR SYSTEM STANDPOINT THESE ARE ALL FILTER
ING FUNCTIONS AND IN MODERN RADAR SYSTEMS THESE FUNCTIONS ARE PERFORMED USING
DIGITAL SIGNAL PROCESSING ON THE RECEIVER OUTPUT ) AND 1 DATA 4HESE FUNCTIONS ARE
DISCUSSED IN OTHER CHAPTERS OF THIS HANDBOOK 4HE PURPOSE OF THE FILTERING WITHIN
THE RECEIVER IS TO REJECT OUT OF BAND INTERFERENCE AND DIGITIZE THE RECEIVED SIGNAL
WITH THE MINIMUM OF ERROR SO THAT OPTIMUM FILTERING CAN BE PERFORMED USING DIGITAL
SIGNAL PROCESSING
-ATCHED &ILTERING !LTHOUGH MATCHED FILTERING IS TYPICALLY NOW PERFORMED
WITHIN THE DIGITAL SIGNAL PROCESSING FUNCTION THE CONCEPT IS EXPLAINED HERE FOR COM
PLETENESS 4HE OVERALL FILTER RESPONSE OF THE SYSTEM IS CHOSEN TO MAXIMIZE THE RADAR
PERFORMANCE )F THE SIGNAL SPECTRUM 8V IN THE PRESENCE OF WHITE NOISE WITH POWER
SPECTRAL DENSITY . IS PROCESSED WITH A FILTER WITH FREQUENCY RESPONSE (V THE
RESULTING SIGNAL TO NOISE RATIO 3.2 AT TIME 4 IS GIVEN BY
C
c
8 V ( V E JW4 DV
P ¯ c
c
.
\ ( V \ DV
P ¯
c
4HE IDEAL FILTER RESPONSE FROM THE STANDPOINT OF MAXIMIZING 3.2 IS THE MATCHED FILTER
THAT MAXIMIZES THE 3.2 AT TIME 4- WHEN
( - V 8 V E JV4-
$EVIATIONS FROM THE IDEAL MATCHED FILTER RESPONSE (-V PRODUCE A REDUCTION IN
3.2 TERMED MISMATCH LOSS 4HIS LOSS CAN OCCUR FOR A NUMBER OF REASONS SUCH AS TARGET
DOPPLER OR BECAUSE A FILTER RESPONSE IS CHOSEN THAT IS DIFFERENT FROM THE MATCHED FILTER
RESPONSE IN ORDER TO MINIMIZE ANOTHER PARAMETER SUCH AS RANGE SIDELOBES
2ECEIVER FILTERING IS OFTEN MODIFIED FOR DIFFERENT WAVEFORMS USED 7HEN RADAR SYS
TEMS USE WAVEFORMS OF WIDELY VARYING BANDWIDTHS DIFFERENT )1 DATA RATES MAY BE
USED TO MINIMIZE THE DIGITAL SIGNAL PROCESSING THROUGHPUT REQUIREMENTS 7ITH DIFFER
ENT DATA RATES COMES THE NEED TO ADJUST THE RECEIVER FILTERING IN ORDER TO AVOID ALIASING
SIGNALS BEYOND THE .YQUIST RATE !LTHOUGH THESE RADARS ADJUST THEIR FILTERING TO THE
WAVEFORM BANDWIDTH THEY DO NOT TYPICALLY IMPLEMENT THE MATCHED FILTERING WITHIN THE
RECEIVER 4HIS FUNCTION IS USUALLY IMPLEMENTED IN DIGITAL SIGNAL PROCESSING
2ECEIVER &ILTERING &ILTERING IS REQUIRED AT VARIOUS POINTS THROUGHOUT THE RECEIVER
CHAIN INCLUDING 2& )& BASEBAND IF USED DIGITAL FILTERING PRIOR TO DECIMATION REDUC
TION OF THE SAMPLE RATE AND AS AN INTEGRAL PART OF )1 GENERATION
3ECTION DESCRIBED HOW SPURIOUS RESPONSES ARE GENERATED IN THE MIXING PROCESS
5NWANTED INTERFERENCE SIGNALS CAN BE TRANSLATED TO THE DESIRED INTERMEDIATE FREQUENCY
EVEN THOUGH THEY ARE WELL SEPARATED FROM THE SIGNAL FREQUENCY AT THE INPUT TO THE MIXER
4HE ABILITY OF THE RADAR TO SUPPRESS SUCH UNWANTED INTERFERENCE IS DEPENDENT UPON THE
FILTERING PRECEDING THE MIXER AS WELL AS ON THE QUALITY OF THE MIXER ITSELF
È°ÓÈ
2!$!2 (!.$"//+
4HE PRIMARY FUNCTION OF 2& FILTERING IS THE REJECTION OF THE IMAGE RESPONSE DUE TO
THE FIRST DOWNCONVERSION )MAGE REJECTION FILTERING CAN BE ALLEVIATED USING AN IMAGE
REJECT MIXER HOWEVER THE MAXIMUM REJECTION ACHIEVABLE BY IMAGE REJECT MIXERS IS
TYPICALLY INADEQUATE WITHOUT THE USE OF ADDITIONAL REJECTION THROUGH FILTERING 4HIS
IMAGE SUPPRESSION PROBLEM IS THE REASON WHY SOME RECEIVERS DO NOT TRANSLATE FROM THE
RECEIVED SIGNAL FREQUENCY DIRECTLY TO THE FINAL INTERMEDIATE FREQUENCY IN A SINGLE STEP
4HE OTHER SPURIOUS PRODUCTS OF A MIXER GENERALLY BECOME MORE SERIOUS IF THE RATIO
OF INPUT TO OUTPUT FREQUENCIES OF THE DOWNCONVERTER IS LESS THAN 4HE SPURIOUS
EFFECTS CHART &IGURE SHOWS THAT THERE ARE CERTAIN CHOICES OF FREQUENCY RATIO THAT
PROVIDE SPURIOUS FREE FREQUENCY BANDS APPROXIMATELY OF THE INTERMEDIATE FRE
QUENCY IN WIDTH "Y THE USE OF A HIGH FIRST )& ONE CAN ELIMINATE THE IMAGE PROBLEM
AND PROVIDE A WIDE TUNING BAND FREE OF SPURIOUS EFFECTS &ILTERING PRIOR TO THE MIXER
REMAINS IMPORTANT HOWEVER BECAUSE THE NEIGHBORING SPURIOUS RESPONSES ARE OF RELA
TIVELY LOW ORDER AND MAY PRODUCE STRONG OUTPUTS FROM THE MIXER 2& FILTERING IS ALSO
IMPORTANT AS IT REDUCES OUT OF BAND INTERFERENCE BEFORE IT CAN CAUSE INTERMODULATION OR
CROSS MODULATION DISTORTION WITHIN THE RECEIVER
)F THE RECEIVER OPERATING BANDWIDTH IS A LARGE PERCENTAGE OF THE 2& FREQUENCY SOME
FORM OF SWITCHED OR TUNABLE 2& FILTERING MAY BE REQUIRED SO THAT THE IMAGE RESPONSE IS
REJECTED AS IT MOVES THROUGH THE OPERATING BANDWIDTH 4HE CHOICE BETWEEN USING SWITCHED
OR TUNABLE FILTERING DEPENDS ON THE SWITCHING SPEED LINEARITY AND STABILITY REQUIREMENTS OF
THE RECEIVER 3WITCHED FILTERS PROVIDE THE FASTEST RESPONSE TIME WITH EXCELLENT LINEARITY AND
STABILITY BUT CAN BE BULKY AND SUFFER FROM THE ADDITIONAL LOSS OF THE SWITCH COMPONENTS
!N ALTERNATE APPROACH THAT IS SOMETIMES USED WITH LARGE OPERATING BANDWIDTHS IS
TO FIRST UPCONVERT THE INPUT 2& SIGNAL TO AN )& FREQUENCY HIGHER THAN THE 2& OPERATING
BAND 4HIS PROCESS VIRTUALLY ELIMINATES THE IMAGE RESPONSE PROBLEM ALLOWING THE USE
OF A SINGLE 2& FILTER SPANNING THE ENTIRE OPERATING BANDWIDTH .ARROW BANDWIDTH FILTER
ING CAN BE USED ON THE HIGH )& AS DEFINED BY THE SIGNAL BANDWIDTH BEFORE DOWNCONVER
SION TO A LOWER )& FOR DIGITIZATION OR BASEBAND CONVERSION
)& FILTERING IS THE PRIMARY FILTERING USED TO DEFINE THE RECEIVER BANDWIDTH PRIOR TO !$
CONVERSION IN RECEIVERS USING EITHER )& SAMPLING OR BASEBAND CONVERSION )N )& SAMPLING
RECEIVERS THE )& FILTER ACTS AS THE ANTI ALIASING FILTER AND LIMITS THE BANDWIDTH OF SIGNALS
ENTERING THE !$ CONVERTER )N RECEIVERS USING BASEBAND CONVERSION THE )& FILTER SETS THE
RECEIVER BANDWIDTH 3UBSEQUENT VIDEO FILTERING SHOULD BE OF GREATER BANDWIDTH TO PREVENT
THE INTRODUCTION OF )1 IMBALANCE DUE TO FILTER DIFFERENCES BETWEEN ) AND 1 CHANNELS
)N )& SAMPLING RECEIVERS DIGITAL FILTERING IS USUALLY THE PRIMARY MEANS OF SETTING THE
FINAL RECEIVER BANDWIDTH AND PROVIDES ANTI ALIAS REJECTION REQUIRED TO PREVENT ALIASING
IN THE DECIMATION OF THE )1 DATA RATE $IGITAL FILTERING CAN BE PRECISELY CONTROLLED
TAILORED TO ALMOST ANY DESIRED PASSBAND AND STOP BAND REJECTION REQUIREMENTS 4HE
DIGITAL FILTERS USED ARE TYPICALLY LINEAR PHASE &)2 FILTERS BUT THEY CAN ALSO BE TAILORED TO
COMPENSATE FOR VARIATIONS IN THE PASSBAND PHASE AND AMPLITUDE RESPONSES OF 2& AND
)& ANALOG FILTERS
&ILTER #HARACTERISTICS &ILTER RESPONSES ARE CHARACTERIZED FULLY BY EITHER THEIR
FREQUENCY RESPONSE (V OR THEIR IMPULSE RESPONSE HT HOWEVER THEY ARE USUALLY
SPECIFIED BY A VARIETY OF PARAMETERS AS DESCRIBED BELOW $IGITAL FILTERS MAY BE SPECI
FIED USING THE SAME MEASURES OR BECAUSE THEY CAN BE SPECIFIED EXACTLY THEY ARE FRE
QUENTLY SPECIFIED BY THEIR TRANSFER FUNCTION (Z OR IMPULSE RESPONSE HN +EY PASSBAND CHARACTERISTICS ARE INSERTION LOSS BANDWIDTH PASSBAND AMPLITUDE
AND PHASE RIPPLE AND GROUP DELAY "ANDWIDTHS ARE FREQUENTLY SPECIFIED IN TERMS OF
A D" BANDWIDTH HOWEVER IF A LOW PASSBAND VARIATION IS REQUIRED THE SPECIFIED
È°ÓÇ
2!$!2 2%#%)6%23
BANDWIDTH MAY BE FOR EXAMPLE SPECIFIED AS A D" OR D" BANDWIDTH 0ASSBAND
AMPLITUDE VARIATION RELATIVE TO THE INSERTION LOSS IS A KEY PARAMETER THAT HAS POTENTIAL
IMPACT ON RANGE SIDELOBES AND CHANNEL TO CHANNEL TRACKING 0HASE RIPPLE IF SPECIFIED
IS RELATIVE TO A BEST FIT LINEAR PHASE AND HAS SIMILAR EFFECTS AS AMPLITUDE RIPPLE 'ROUP
DELAY THE RATE OF CHANGE OF PHASE VS FREQUENCY IS IDEALLY CONSTANT FOR LINEAR PHASE
FILTERS 4HE ABSOLUTE VALUE OF GROUP DELAY DOES NOT IMPACT THE RANGE SIDELOBE PERFOR
MANCE HOWEVER THE RELATIVE GROUP DELAY BETWEEN CHANNELS MUST BE TIGHTLY CONTROLLED
OR COMPENSATED IN MONOPULSE SIDELOBE CANCELER AND DIGITAL BEAMFORMING SYSTEMS
!LTHOUGH STOPBAND REJECTION IS CLEARLY A KEY PARAMETER FILTERS WITH FAST ROLL OFF
MAY NOT PROVIDE THE REQUIRED PHASE AND IMPULSE RESPONSE CHARACTERISTICS &IGURE SHOWS THE MAGNITUDE RESPONSE OF SIX DIFFERENT FIFTH ORDER LOW PASS FILTERS WITH EQUAL
D" BANDWIDTH 4HE #HEBSHEV FILTERS AND D" RIPPLE HAVE FLAT PASSBAND
RESPONSE AND IMPROVED STOPBAND REJECTION RELATIVE TO THE REMAINING FILTERS HOWEVER
AS SHOWN IN &IGURE AND &IGURE THEY HAVE INFERIOR PHASE GROUP DELAY AND
IMPULSE RESPONSE CHARACTERISTICS
$IGITAL FILTERS CAN BE EITHER &INITE )MPULSE 2ESPONSE &)2 OR )NFINITE )MPULSE
2ESPONSE ))2 &)2 FILTERS ARE TYPICALLY PREFERRED AS THEIR FINITE RESPONSE IS DESIRABLE
ALONG WITH THEIR LINEAR PHASE CHARACTERISTIC 0HASE LINEARITY IS ACHIEVED WITH THE SYM
METRIC IMPULSE RESPONSE CONDITION DEFINED BY %Q OR THE ANTI SYMMETRIC IMPULSE
RESPONSE CONDITIONS DEFINED BY %Q HN H-
N
N x -
WHERE - IS THE LENGTH OF THE &)2 FILTER IMPULSE RESPONSE
HN H-
&)'52% N
-AGNITUDE RESPONSE OF LOWPASS FILTERS
N x -
È°Ón
2!$!2 (!.$"//+
&)'52% 'ROUP DELAY RESPONSE OF LOWPASS FILTERS
&)'52% .ORMALIZED IMPULSE RESPONSE OF LOWPASS FILTERS
2!$!2 2%#%)6%23
Ȱә
2ANGE 3IDELOBES %RRORS IN FILTER RESPONSES CAN PRODUCE DEGRADATION IN PULSE
COMPRESSION RANGE SIDELOBES 4HE EFFECT OF A FILTER RESPONSE ON RANGE OR TIME SIDELOBES
CAN BE SEEN BY TAKING THE FILTER IMPULSE RESPONSE HT AND ADDING TO THIS A DELAYED
IMPULSE RESPONSE LOG@ D" BELOW THE MAIN RESPONSE TO PRODUCE THE MODIFIED
RESPONSE HgT WHICH IS GIVEN BY
HgT HT
@ HT 4
5SING THE PROPERTY OF TIME SHIFTING OF THE &OURIER TRANSFORM THE RESULTANT FREQUENCY
RESPONSE IS GIVEN BY
( `V ( V
@ E JV4 ( V
4HUS FOR SMALL VALUES OF @ THE RESULTING MAGNITUDE AND PHASE RESPONSE IS THAT OF THE
ORIGINAL FILTER MODIFIED BY A SINUSOIDAL PHASE AND AMPLITUDE MODULATION AS GIVEN HERE
\ ( `V \ \ ( V \ A COSV4
Ž( `V Ž( V
@ SINV 4
4HEREFORE IF THERE ARE N RIPPLES ACROSS THE FILTER BANDWIDTH " THE RANGE SIDELOBE
OCCURS AT TIME 4 GIVEN BY
4 N"
!SSUMING A COMPRESSED PULSE WIDTH OF " VALUES OF N WILL PUT THE RANGE
SIDELOBE WITHIN THE MAIN LOBE OF THE TARGET RETURN RESULTING IN A DISTORTION OF THE
MAINLOBE RESPONSE
#HANNEL -ATCHING 2EQUIREMENTS 2ADAR RECEIVERS WITH MORE THAN ONE
RECEIVER CHANNEL TYPICALLY REQUIRE SOME DEGREE OF PHASE AND AMPLITUDE MATCHING
OR TRACKING BETWEEN CHANNELS )N ORDER TO OPERATE EFFECTIVELY SIDELOBE CANCELER
CHANNELS MUST TRACK VERY CLOSELY #ONSTANT OFFSETS IN GAIN OR PHASE DO NOT DEGRADE
SIDELOBE CANCELER PERFORMANCE BUT SMALL VARIATIONS IN PHASE AND AMPLITUDE ACROSS
THE BANDWIDTH CAUSE SIGNIFICANT DEGRADATION &OR EXAMPLE ACHIEVING A CANCELLATION
RATIO OF D" REQUIRES A GAIN TRACKING OF LESS THAN D" ACROSS THE RECEIVER BAND
WIDTH &ILTERS ARE THE MAIN SOURCE OF AMPLITUDE AND PHASE RIPPLE ACROSS THE SIGNAL
BANDWIDTH AS OTHER COMPONENTS SUCH AS AMPLIFIERS AND MIXERS ARE TYPICALLY RELA
TIVELY BROADBAND 4HE DEGREE OF TRACKING REQUIRED FOR SIDELOBE CANCELER OPERATION
WAS PREVIOUSLY ACHIEVED BY PROVIDING MATCHED SETS OF FILTERS WITH TIGHTLY TRACKING
AMPLITUDE AND PHASE RESPONSES -ODERN DIGITAL SIGNAL PROCESSING ALLOWS THE CORREC
TION OF THESE CHANNEL TO CHANNEL VARIATIONS USING &)2 EQUALIZATION 3ECTION OR
CORRECTION IN THE FREQUENCY DOMAIN IN THE DIGITAL SIGNAL PROCESSOR ALLOWING THE USE
OF LESS TIGHTLY CONTROLLED FILTERS
È°nÊ / ,!PPLICATIONS ,IMITERS ARE USED TO PROTECT THE RECEIVER FROM DAMAGE AND TO CON
TROL SATURATION THAT MAY OCCUR WITHIN THE RECEIVER 7HEN RECEIVED SIGNALS SATURATE
SOME STAGE OF THE RADAR RECEIVER THAT IS NOT EXPRESSLY DESIGNED TO COPE WITH SUCH A
È°Îä
2!$!2 (!.$"//+
SITUATION THE DISTORTIONS CAN RESULT IN SEVERELY DEGRADED RADAR PERFORMANCE AND THE
DISTORTION OF OPERATING CONDITIONS CAN PERSIST FOR SOME TIME AFTER THE SIGNAL DISAP
PEARS 6IDEO STAGES ARE MOST VULNERABLE AND TAKE LONGER TO RECOVER THAN )& STAGES
SO IT IS CUSTOMARY TO INCLUDE A LIMITER IN THE LAST )& STAGE DESIGNED TO QUICKLY REGAIN
NORMAL OPERATING CONDITIONS IMMEDIATELY FOLLOWING THE DISAPPEARANCE OF A LIMITING
SIGNAL ,IMITING PRIOR TO THE !$ CONVERTER ALSO PREVENTS THE DISTORTION THAT OCCURS
WHEN SIGNALS EXCEED FULL SCALE !LTHOUGH !$ CONVERTERS CAN OFTEN HANDLE MODEST
OVERLOAD WITH FAST RECOVERY THE DISTORTION THAT OCCURS DEGRADES SIGNAL PROCESSING SUCH
AS DIGITAL PULSE COMPRESSION AND CLUTTER REJECTION 7ITH )& LIMITING THESE HARMONICS
ARE FILTERED OUT USING BANDPASS FILTERING AFTER LIMITING PRIOR TO !$ CONVERSION MINI
MIZING THE DEGRADATION DUE TO LIMITING
!LL RADAR SYSTEMS CONTAIN SOME FORM OF 4RANSMIT2ECEIVE 42 DEVICE TO PROTECT
THE RECEIVE ELECTRONICS FROM THE HIGH POWER TRANSMIT SIGNAL )N MANY SYSTEMS AN 2&
FRONT END LIMITER IS ALSO REQUIRED IN ORDER TO PREVENT THE RECEIVER FROM BEING DAMAGED
BY HIGH INPUT POWER LEVELS FROM THE ANTENNA THAT MAY OCCUR AS A RESULT OF LEAKAGE FROM
THE 42 DEVICE DURING TRANSMIT MODE OR FROM INTERFERENCE DUE TO JAMMERS OR OTHER
RADAR SYSTEMS 4HESE LIMITERS ARE TYPICALLY DESIGNED TO LIMIT WELL ABOVE THE MAXIMUM
SIGNALS TO BE PROCESSED BY THE RECEIVER
)N THE PAST LIMITERS WERE USED TO PERFORM A VARIETY OF ANALOG SIGNAL PROCESSING
FUNCTIONS (ARD LIMITERS WITH AS MUCH AS D" OF LIMITING RANGE WERE USED WITH SOME
DESIGNED TO LIMIT ON RECEIVER NOISE !PPLICATIONS THAT UTILIZE HARD LIMITING INCLUDING
PHASE DETECTORS AND PHASE MONOPULSE RECEIVERS ARE DESCRIBED IN 3ECTION OF THE
SECOND EDITION OF THIS HANDBOOK -ODERN RADAR SYSTEMS ARE MOSTLY DESIGNED TO MAXI
MIZE THE LINEAR OPERATING REGION WITH LIMITERS USED ONLY TO HANDLE EXCESSIVELY LARGE
SIGNALS THAT INEVITABLY EXIST UNDER WORST CASE CONDITIONS
#HARACTERISTICS 4HE IDEAL LIMITER IS PERFECTLY LINEAR UP TO THE POWER LEVEL AT
WHICH LIMITING BEGINS FOLLOWED BY A TRANSITION REGION BEYOND WHICH THE OUTPUT POWER
REMAINS CONSTANT )N ADDITION THE INSERTION PHASE IS CONSTANT FOR ALL INPUT POWER LEV
ELS AND RECOVERY FROM LIMITING IS INSTANTANEOUS 4HE OUTPUT WAVEFORM FROM A BAND
PASS LIMITER IS SINUSOIDAL WHEREAS THE OUTPUT WAVEFORM FROM A BROADBAND LIMITER
APPROACHES A SQUARE WAVE $EVIATIONS FROM THE IDEAL CHARACTERISTICS CAN DEGRADE RADAR
PERFORMANCE IN A VARIETY OF WAYS
,INEARITY "ELOW ,IMITING /NE MAJOR DRAWBACK OF ADDING A LIMITER STAGE TO A
RECEIVER CHANNEL IS THAT IT IS INHERENTLY NONLINEAR 3INCE ANY PRACTICAL LIMITER HAS A
GRADUAL TRANSITION INTO LIMITING THE LIMITER IS OFTEN THE LARGEST CONTRIBUTOR TO RECEIVER
CHANNEL NONLINEARITY IN THE LINEAR OPERATING REGION AND CAN CAUSE SIGNIFICANT INTER
MODULATION DISTORTION OF IN BAND SIGNALS &OR THIS REASON THE PRIMARY LIMITING STAGE IS
USUALLY LOCATED AT THE FINAL )& STAGE WHERE MAXIMUM FILTERING OF OUT OF BAND INTERFER
ENCE HAS BEEN ACHIEVED 4HE LOWER OPERATING FREQUENCY ALSO ALLOWS IMPLEMENTATION OF
A LIMITER THAT MORE CLOSELY MATCHES THE IDEAL CHARACTERISTICS
,IMITING !MPLITUDE 5NIFORMITY .O SINGLE STAGE LIMITER WILL EXHIBIT A CONSTANT
OUTPUT OVER A WIDE RANGE OF INPUT SIGNAL AMPLITUDES /NE CAUSE IS APPARENT IF ONE
CONSIDERS THE EFFECT OF A SINGLE STAGE LIMITER HAVING A PERFECTLY SYMMETRICAL CLIPPING AT
VOLTAGES o% &OR A SINUSOIDAL INPUT THE OUTPUT SIGNAL AT THE THRESHOLD OF LIMITING IS
V %SINV T
2!$!2 2%#%)6%23
ȰΣ
AND WHEN THE LIMITER IS FULLY SATURATED AND THE OUTPUT WAVEFORM IS RECTANGULAR IT IS
GIVEN BY THE &OURIER SERIES
VO` % c SIN NVT
P N£
N
WHICH IS AN INCREASE OF LOG O D" IN THE POWER OF THE FUNDAMENTAL
)N PRACTICE THE AMPLITUDE PERFORMANCE IS ALSO DEGRADED BY CAPACITIVE COUPLING
BETWEEN INPUT AND OUTPUT OF EACH LIMITING STAGE CHARGE STORAGE IN TRANSISTORS AND
DIODES AND 2# TIME CONSTANTS THAT PERMIT CHANGES IN BIAS WITH SIGNAL LEVEL &OR THESE
REASONS TWO OR MORE LIMITER STAGES MAY BE CASCADED WHEN GOOD AMPLITUDE UNIFORMITY
IS REQUIRED OVER A WIDE DYNAMIC RANGE
0HASE 5NIFORMITY 4HE CHANGE OF INSERTION PHASE OF THE LIMITER WITH AMPLITUDE IS
LESS OF A CONCERN FOR MODERN RADAR SYSTEMS THAT OPERATE PRIMARILY IN THE LINEAR OPERAT
ING REGION (OWEVER MAINTAINING CONSTANT INSERTION PHASE DURING LIMITING PRESERVES
THE PHASE OF TARGET RETURNS IN THE PRESENCE OF LIMITING CLUTTER OR INTERFERENCE 4HE
CHANGE OF INSERTION PHASE WITH SIGNAL AMPLITUDE IS GENERALLY DIRECTLY PROPORTIONAL TO
THE FREQUENCY AT WHICH IT IS OPERATED
2ECOVERY 4IME 4HE RECOVERY TIME OF A LIMITER IS A MEASURE OF HOW QUICKLY THE
LIMITER RETURNS TO LINEAR OPERATION AFTER THE LIMITING SIGNAL IS REMOVED &AST RECOVERY IS
PARTICULARLY IMPORTANT WHEN THE RADAR IS EXPOSED TO IMPULSIVE INTERFERENCE
È°™Ê É+Ê
" 1/",-
!PPLICATIONS 4HE )1 DEMODULATOR ALSO REFERRED TO AS A QUADRATURE CHANNEL
RECEIVER QUADRATURE DETECTOR SYNCHRONOUS DETECTOR OR COHERENT DETECTOR PERFORMS FRE
QUENCY CONVERSION OF SIGNALS AT THE )& FREQUENCY TO A COMPLEX REPRESENTATION ) J1
CENTERED AT ZERO FREQUENCY 4HE BASEBAND IN PHASE ) AND QUADRATURE PHASE 1 SIGNALS
ARE DIGITIZED USING A PAIR OF !$ CONVERTERS PROVIDING A REPRESENTATION OF THE )& SIGNAL
INCLUDING PHASE AND AMPLITUDE WITHOUT LOSS OF INFORMATION 4HE RESULTING DIGITAL DATA CAN
THEN BE PROCESSED USING A WIDE VARIETY OF DIGITAL SIGNAL PROCESSING ALGORITHMS DEPEND
ING ON THE TYPE OF RADAR AND MODE OF OPERATION 0ROCESSING SUCH AS PULSE COMPRESSION
DOPPLER PROCESSING AND MONOPULSE COMPARISON ALL REQUIRE AMPLITUDE AND PHASE INFOR
MATION 4HE PREDOMINANCE OF DIGITAL SIGNAL PROCESSING IN MODERN RADAR SYSTEMS HAS LED
TO ALMOST UNIVERSAL NEED FOR .YQUIST RATE SAMPLED DATA )N MANY MODERN RADAR SYSTEMS
DIGITAL ) AND 1 DATA IS NOW GENERATED USING )& SAMPLING FOLLOWED BY DIGITAL SIGNAL PRO
CESSING USED TO PERFORM THE BASEBAND CONVERSION AS DESCRIBED IN 3ECTIONS AND )1 DEMODULATORS ARE STILL USED THOUGH THEIR USE IS INCREASINGLY LIMITED TO WIDER BAND
WIDTH SYSTEMS WHERE !$ CONVERTERS ARE NOT YET AVAILABLE WITH THE REQUIRED COMBINATION
OF BANDWIDTH AND DYNAMIC RANGE TO PERFORM )& SAMPLING
)MPLEMENTATION &IGURE SHOWS THE BASIC BLOCK DIAGRAM OF A )1 DEMODUAL
TOR 4HE )& SIGNAL DESCRIBED BY %Q IS SPLIT AND FED TO A PAIR OF MIXERS OR ANALOG
MULTIPLIERS 4HE MIXER ,/ PORTS ARE FED WITH A PAIR OF SIGNALS IN QUADRATURE GENERATED
FROM THE REFERENCE FREQUENCY SIGNAL OR COHERENT OSCILLATOR #/(/ AND REPRESENTED
È°ÎÓ
2!$!2 (!.$"//+
$ &)'52% !("$$
%#
$ !$ !("$$
%#
$ "$ !&%!#
*
"!(# # )#
'# !$ )1 DEMODULATOR
IN COMPLEX FORM IN %Q )GNORING ANY MIXER INSERTION LOSS OR LOSS ASSOCIATED WITH
THE )& SPLIT THE COMPLEX REPRESENTATION OF THE MIXER OUTPUT IS GIVEN BY %Q )DEAL
LOW PASS FILTERING REJECTS THE SECOND SUM FREQUENCY TERM OF %Q PRODUCING THE
)1 DEMODULATOR OUTPUT AS REPRESENTED BY %Q 6)& !3 SINV T P !3 J V T P
E
J
6#/(/ !2 §©SINV T
J COSV T ¶¸ J!2 E JV T
!3 !2 J;V V T P =
E
!3 !2 J;V V T P =
E
6)&6#/(/ !3 J V T P
E
E J V T P !2 E JV T 6)
!3 !2
COS;V
V T P =
J61 J
!3 !2
SIN;V
E J V T P
V T P = !3 !2 J §©V V T P ¶¸
E
)N IMPLEMENTING AN )1 DEMODULATOR IT IS IMPORTANT TO PROVIDE WELL BALANCED
) AND 1 CHANNELS IN ORDER TO MAXIMIZE IMAGE REJECTION AS EXPLAINED BELOW 4HE MIXERS
MUST HAVE $# COUPLED )& OUTPUT PORTS AND BE PRESENTED WITH A GOOD MATCH AT BOTH THE
WANTED LOW FREQUENCY OUTPUT AND THE UNWANTED SUM FREQUENCY ! MATCH AT THE SUM
FREQUENCY CAN BE PROVIDED USING A DIPLEXER FILTER 6IDEO FILTERING IS REQUIRED TO REJECT
THE SUM FREQUENCY MIXER OUTPUTS AND ALSO PROVIDES REJECTION OF WIDEBAND NOISE FROM
THE VIDEO AMPLIFIERS WHICH WOULD OTHERWISE ALIAS TO BASEBAND THROUGH THE !$ CON
VERTER SAMPLING PROCESS PRODUCING AN UNWANTED DEGRADATION OF RECEIVER NOISE FIGURE
6IDEO AMPLIFICATION IS OFTEN REQUIRED TO INCREASE THE SIGNAL LEVEL TO THE FULL SCALE SIGNAL
LEVEL OF THE !$ CONVERTER AND ALSO ALLOWS FOR IMPEDANCE MATCHING OF THE MIXER AND
!$ CONVERTER
4HE CONVENTION FOR THE ) AND 1 RELATIONSHIP IS THAT THE ) SIGNAL PHASE LEADS THE 1 SIG
NAL PHASE FOR RADAR SIGNALS WITH POSITIVE DOPPLER APPROACHING TARGETS &REQUENCY CON
VERSIONS WITHIN THE RECEIVER USING ,/ FREQUENCIES GREATER THAN THE 2& FREQUENCY WILL
CAUSE A DOPPLER FREQUENCY INVERSION SO EACH CONVERSION MUST BE CONSIDERED IN ORDER
TO ACHIEVE THE CORRECT SENSE OF ) AND 1 AT THE RECEIVER OUTPUT &ORTUNATELY AN INCORRECT
) AND 1 RELATIONSHIP CAN EASILY BE FIXED EITHER IN THE RECEIVER OR THE SIGNAL PROCESSOR
BY SWITCHING THE ) AND 1 DIGITAL DATA OR BY CHANGING THE SIGN OF EITHER ) OR 1
'AIN OR 0HASE )MBALANCE )F THE GAINS OF THE ) AND 1 CHANNELS ARE NOT EXACTLY
EQUAL OR IF THEIR #/(/ PHASE REFERENCES ARE NOT EXACTLY DEGREES APART AN INPUT
SIGNAL AT FREQUENCY V WILL CREATE AN OUTPUT AT BOTH THE DESIRED FREQUENCY V V AND
È°ÎÎ
2!$!2 2%#%)6%23
AT THE IMAGE FREQUENCY V V 4HE IMAGE SIGNALS GENERATED BY GAIN AND PHASE
IMBALANCE ARE GIVEN BY %Q AND %Q &OR SMALL ERRORS IF THE RATIO OF VOLTAGE
GAINS IS o $ OR IF THE PHASE REFERENCES DIFFER BY O o $ RADIANS THE RATIO OF THE
SPURIOUS IMAGE AT VD TO THE DESIRED OUTPUT OF VD IS $ IN VOLTAGE $ IN POWER OR
LOG $ IN DECIBELS
6)
J61 % COSV D T
$ ³ JV D T
%E
´µ
¤
J $ % SINV D T ¥
¦
¤
6)
J61 % COSV D T
$³
¤ $ ³ J¥V D T ´
$ COS ¥ ´ %E ¦ µ
¦ µ
J% SINV D T
$
%E JV D T
¤
J ¥V D T
¤ $³
SIN ¥ ´ %E ¦
¦ µ
$ P³
´µ
(ISTORICALLY ) AND 1 PHASE AND GAIN CORRECTIONS HAVE BEEN PERFORMED USING
ADJUSTMENTS IN THE ANALOG SIGNAL PATHS AS SHOWN IN &IGURE 'AIN ERRORS MAY
BE CORRECTED BY A CHANGE IN GAIN IN THE )& OR VIDEO STAGES OF EITHER OR BOTH ) AND 1
CHANNELS 6IDEO GAIN CONTROL MUST BE IMPLEMENTED WITH CARE AS IT CAN EXAGGERATE
THE NONLINEARITY OF THOSE STAGES 4HESE CORRECTIONS CAN NOW BE IMPLEMENTED MORE
PRECISELY IN THE DIGITAL DOMAIN
! MEASUREMENT OF THE SIGNAL SPECTRUM AT THE CENTER OF THE )& BANDWIDTH INDICATES
THE DEGREE OF GAIN AND PHASE IMBALANCE COMPENSATION (OWEVER AS THE FOLLOWING
DISCUSSION WILL EXPLAIN THE SUPPRESSION OF IMAGE ENERGY ACROSS THE )& BANDWIDTH MAY
BE SUBSTANTIALLY LESS THAN INDICATED BY THIS MEASUREMENT AT )& CENTER
4IME $ELAY AND &REQUENCY 2ESPONSE )MBALANCE )F THE RESPONSES OF THE
) AND 1 CHANNELS ARE NOT IDENTICAL ACROSS THE ENTIRE SIGNAL BANDWIDTH UNWANTED IMAGE
RESPONSES WILL OCCUR THAT ARE FREQUENCY DEPENDENT /PTIMUM BANDPASS FILTERING SHOULD
"
&'
!$ #
&
,
#*$&&
'%
'
"
&)'52% ' '
,
&
"$& !#( '#%
,
$#*% %"
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"
!$ #
#*$&&
'%
&'
)1 DEMODULATOR WITH GAIN PHASE $# OFFSET AND TIME DELAY ADJUSTMENTS
' '
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2!$!2 (!.$"//+
BE AT )& WHERE IT AFFECTS ) AND 1 CHANNELS IDENTICALLY NOT AT BASEBAND 6IDEO FILTER
BANDWIDTH SHOULD BE MORE THAN HALF THE )& BANDWIDTH AND CONTROLLED BY PRECISION
COMPONENTS IN ORDER TO MINIMIZE THE CREATION OF IMAGE SIGNALS 3UBSTITUTING $V FOR $
IN %Q AND %Q GIVES THE IMAGE COMPONENTS FOR FREQUENCY DEPENDENT GAIN AND
PHASE ERRORS 3IMILARLY SUBSTITUTING V $4 FOR $ IN %Q GIVES THE IMAGE COMPONENT
DUE TO TIME DELAY IMBALANCE IN THE ) AND 1 PATHS 3MALL TIME DELAY IMBALANCES CAN
BE CORRECTED BY ADDING TIME DELAY TO THE !$ SAMPLE CLOCK AS SHOWN IN &IGURE ,ARGE TIME DELAY CORRECTIONS SHOULD BE AVOIDED AS THEY CAN CAUSE PROBLEMS ALIGNING
THE ) AND 1 DIGITAL DATA 7HEN ADDING TIME DELAY TO THE SAMPLE CLOCK CARE MUST BE
TAKEN TO AVOID ADDING JITTER WHICH COULD DEGRADE THE !$ CONVERTER 3.2 PERFORMANCE
4IME DELAY CORRECTION CAN ALSO BE IMPLEMENTED EFFECTIVELY IN THE DIGITAL DOMAIN AND
IF FREQUENCY DEPENDENT PHASE AND AMPLITUDE IMBALANCE CORRECTION IS REQUIRED THIS IS
MOST EASILY AND EFFECTIVELY PERFORMED IN THE DIGITAL DOMAIN USING &)2 FILTERING OF THE
) AND 1 DATA OR BY PERFORMING CORRECTIONS IN THE FREQUENCY DOMAIN DATA AS PART OF THE
RADAR SIGNAL PROCESSING
.ONLINEARITY IN ) AND 1 #HANNELS #OMPONENT TOLERANCES OFTEN LEAD TO SOME
WHAT DIFFERENT NONLINEARITIES IN ) AND 1 WHICH CAN GENERATE THE VARIETY OF SPURIOUS
DOPPLER COMPONENTS
4HE IDEAL INPUT SIGNAL IS
6 !E JV D T )
J1
%ACH VIDEO CHANNEL RESPONSE CAN BE EXPRESSED AS A POWER SERIES &OR SIMPLICITY
ONLY SYMMETRICAL DISTORTION WILL BE CONSIDERED 4HE !$ OUTPUT INCLUDING A RESIDUAL
GAIN IMBALANCE OF $ IS
6g)1 6g) J6g1
6g) 6) A6 ) C6 )
6g1 $ 61 B61 D61
3UBSTITUTION OF %QS AND INTO %Q YIELDS THE AMPLITUDES OF THE SPECTRAL
COMPONENTS LISTED IN 4ABLE .OTE THAT IF THE NONLINEARITIES IN ) AND 1 WERE IDENTI
CAL A B C D SPURIOUS COMPONENTS AT V AND V WOULD NOT BE PRESENT AND THE
IMAGE V WOULD BE PROPORTIONAL TO INPUT SIGNAL AMPLITUDE 3PURIOUS AT ZERO DOPPLER
IS NOT DUE TO DC OFFSET IT IS THE RESULT OF EVEN ORDER NONLINEARITIES THAT WERE OMITTED
FROM THE ABOVE EQUATIONS 4HE NEGATIVE THIRD HARMONIC IS THE DOMINANT COMPONENT
PRODUCED BY NONLINEARITY
4!",% 3PURIOUS 3IGNAL #OMPONENTS 'ENERATED BY )1 .ONLINEARITY
3IGNAL &REQUENCY
!MPLITUDE OF 3PECTRAL #OMPONENT
V
V
V
)NPUT V
V
V
!C D !A B ! C D !$ ! A B ! C D ! $ !A B !C D !A B ! C D !C D 2!$!2 2%#%)6%23
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$# /FFSET 3MALL SIGNALS AND RECEIVER NOISE CAN BE DISTORTED BY AN OFFSET IN
THE MEAN VALUE OF THE !$ CONVERTER OUTPUT UNLESS THE DOPPLER FILTER SUPPRESSES THIS
COMPONENT
&ALSE ALARM CONTROL IN RECEIVERS WITHOUT DOPPLER FILTERS IS SOMETIMES DEGRADED BY
ERRORS OF A SMALL FRACTION OF THE LEAST SIGNIFICANT BIT ,3" SO CORRECTION IS PREFERABLY
APPLIED AT THE ANALOG INPUT TO THE !$ $# OFFSETS CAN BE MEASURED USING DIGITAL PRO
CESSING OF THE !$ CONVERTER OUTPUTS AND A CORRECTION APPLIED USING $! CONVERTERS
AS SHOWN IN &IGURE $# OFFSET CORRECTION CAN ALSO BE PERFORMED EFFECTIVELY IN THE
DIGITAL DOMAIN PROVIDED THAT THE $# OFFSET AT THE INPUT OF THE !$ CONVERTER IS NOT SO
LARGE THAT IT RESULTS IN A SIGNIFICANT LOSS OF AVAILABLE DYNAMIC RANGE
-ANY OF THE )1 DEMODULATOR ERRORS DESCRIBED ABOVE ARE EITHER REDUCED DRAMATI
CALLY OR ELIMINATED USING )& SAMPLING 4HIS ALONG WITH THE REDUCTION OF HARDWARE
REQUIRED ARE THE REASONS THAT )& SAMPLING DESCRIBED IN 3ECTIONS AND IS
BECOMING THE DOMINANT APPROACH
È°£äÊ "‡/"‡ /Ê " 6 ,/ ,4HE HIGH SPEED !$ CONVERTER IS A KEY COMPONENT IN RECEIVERS OF MODERN RADAR SYS
TEMS 4HE EXTENSIVE USE OF DIGITAL SIGNAL PROCESSING OF RADAR DATA HAS RESULTED IN A
DEMAND FOR CONVERTERS WITH BOTH STATE OF THE ART SAMPLING RATES AND DYNAMIC RANGE
!NALOG TO DIGITAL CONVERTERS TRANSFORM CONTINUOUS TIME ANALOG SIGNALS INTO DISCRETE
TIME DIGITAL SIGNALS 4HE PROCESS INCLUDES BOTH SAMPLING IN THE TIME DOMAIN CONVERT
ING FROM CONTINUOUS TIME TO DISCRETE TIME SIGNALS AND QUANTIZATION CONVERTING FROM
CONTINUOUS ANALOG VOLTAGES TO DISCRETE FIXED LENGTH DIGITAL WORDS "OTH THE SAMPLING
AND QUANTIZATION PROCESS PRODUCE ERRORS THAT MUST BE MINIMIZED IN ORDER TO LIMIT THE
RADAR PERFORMANCE DEGRADATION )N ADDITION A VARIETY OF OTHER ERRORS SUCH AS ADDITIVE
NOISE SAMPLING JITTER AND DEVIATION FROM THE IDEAL QUANTIZATION RESULT IN NON IDEAL
!$ CONVERSION
!PPLICATIONS 4HE CONVENTIONAL APPROACH OF USING A PAIR OF CONVERTERS TO DIGI
TIZE THE ) AND 1 OUTPUTS OF AN )1 DEMODULATOR IS IN MANY CASES BEING REPLACED BY
DIGITAL RECEIVER ARCHITECTURES WHERE A SINGLE !$ CONVERTER IS FOLLOWED BY DIGITAL
SIGNAL PROCESSING TO GENERATE ) AND 1 DATA $IGITAL RECEIVER TECHNIQUES ARE DESCRIBED
IN 3ECTION !LTHOUGH THE DIVIDING LINE IS ARBITRARY AND ADVANCING WITH THE STATE OF THE ART RADAR
RECEIVERS ARE OFTEN CLASSIFIED AS EITHER WIDEBAND OR HIGH DYNAMIC RANGE $IFFERENT
RADAR FUNCTIONS PUT A GREATER EMPHASIS ON ONE OR THE OTHER OF THESE PARAMETERS &OR
EXAMPLE IMAGING RADARS PUT A PREMIUM ON WIDE BANDWIDTH WHEREAS PULSE DOPPLER
RADARS REQUIRE HIGH DYNAMIC RANGE "ECAUSE RADARS ARE OFTEN REQUIRED TO OPERATE IN A
VARIETY OF MODES WITH DIFFERING BANDWIDTH AND DYNAMIC RANGE REQUIREMENTS IT IS NOT
UNCOMMON TO USE DIFFERENT TYPES OF !$ CONVERTER SAMPLING AT DIFFERENT RATES FOR THESE
DIFFERENT MODES
$ATA &ORMATS 4HE MOST FREQUENTLY USED DIGITAL FORMATS FOR !$ CONVERTERS ARE
S COMPLEMENT AND OFFSET BINARY
4HE S COMPLEMENT IS THE MOST POPULAR METHOD OF DIGITAL REPRESENTATION OF SIGNED
INTEGERS AND IS CALCULATED BY COMPLEMENTING EVERY BIT OF A GIVEN NUMBER AND ADDING ONE
È°ÎÈ
2!$!2 (!.$"//+
4HE MOST SIGNIFICANT BIT IS REFERRED TO AS THE SIGN BIT )F THE SIGN BIT IS THE VALUE IS POSI
TIVE IF IT IS THE VALUE IS NEGATIVE 4HE REPRESENTATION OF VOLTAGE IN S COMPLEMENT FORM
IS GIVEN BY
% K B.. B. . B. . •••
B
WHERE % ANALOG VOLTAGE
. NUMBER OF BINARY DIGITS
BI STATE OF ITH BINARY DIGIT
K QUANTIZATION VOLTAGE
/FFSET BINARY IS AN ALTERNATE CODING SCHEME IN WHICH THE MOST NEGATIVE VALUE IS
REPRESENTED BY ALL ZEROS AND THE MOST POSITIVE VALUE IS REPRESENTED BY ALL ONES :ERO IS
REPRESENTED BY A MOST SIGNIFICANT BIT -3" OF ONE FOLLOWED BY ALL ZEROS 4HE REPRE
SENTATION OF VOLTAGE IN OFFSET BINARY IS GIVEN BY
% K;B. . B. . B. . B=
•••
4HE 'RAY CODE IS ALSO USED IN CERTAIN HIGH SPEED !$ CONVERTERS IN ORDER TO
REDUCE THE IMPACT OF DIGITAL OUTPUT TRANSITIONS ON THE PERFORMANCE OF THE !$ CON
VERTER 4HE 'RAY CODE ALLOWS ALL ADJACENT TRANSITIONS TO BE ACCOMPLISHED BY THE CHANGE
OF A SINGLE DIGIT ONLY
$ELTA 3IGMA #ONVERTERS $ELTA SIGMA CONVERTERS DIFFER FROM CONVENTIONAL
.YQUIST RATE CONVERTERS BY COMBINING OVERSAMPLING WITH NOISE SHAPING TECHNIQUES TO
ACHIEVE IMPROVED 3.2 IN THE BANDWIDTH OF INTEREST .OISE SHAPING MAY BE EITHER LOW
PASS OR BANDPASS DEPENDING ON THE APPLICATION $ELTA SIGMA ARCHITECTURES PROVIDE POTEN
TIAL IMPROVEMENTS IN SPURIOUS FREE DYNAMIC RANGE 3&$2 AND 3.2 OVER CONVENTIONAL
.YQUIST CONVERTERS WHERE TIGHT TOLERANCES ARE REQUIRED TO ACHIEVE VERY LOW SPURIOUS
PERFORMANCE $IGITAL FILTERING AND DECIMATION IS REQUIRED TO PRODUCE DATA RATES THAT CAN
BE HANDLED BY CONVENTIONAL PROCESSORS 4HIS FUNCTION IS EITHER PERFORMED AS AN INTEGRAL
PART OF THE !$ CONVERTER FUNCTION OR CAN BE INTEGRATED INTO THE DIGITAL DOWNCONVERSION
FUNCTION USED TO GENERATE DIGITAL ) AND 1 DATA AS DESCRIBED IN 3ECTION 0ERFORMANCE #HARACTERISTICS 4HE PRIMARY PERFORMANCE CHARACTERISTICS OF !$
CONVERTERS ARE THE SAMPLE RATE OR USABLE BANDWIDTH AND RESOLUTION THE RANGE OVER
WHICH THE SIGNALS CAN BE ACCURATELY DIGITIZED 4HE RESOLUTION IS LIMITED BY BOTH NOISE
AND DISTORTION AND CAN BE DESCRIBED BY A VARIETY OF PARAMETERS
3AMPLE 2ATE 3AMPLING OF BAND LIMITED
SIGNALS IS PERFORMED WITHOUT ALIASING DISTORTION
PROVIDED THAT THE SAMPLE RATE FS IS GREATER THAN
TWICE THE SIGNAL BANDWIDTH AND PROVIDED THE SIG
NAL BANDWIDTH DOES NOT STRADDLE THE .YQUIST FRE
QUENCY FS OR ANY INTEGER MULTIPLE .FS )N CONVENTIONAL BASEBAND APPROACHES SAM
PLING IS USUALLY PERFORMED AT THE MINIMUM RATE TO
MEET THE .YQUIST CRITERIA 3INCE THE BASEBAND ) AND
1 SIGNALS HAVE BANDWIDTHS " EQUAL TO HALF THE
)& SIGNAL BANDWIDTH A SAMPLE RATE JUST GREATER THAN
THE )& BANDWIDTH IS REQUIRED SEE &IGURE &)'52% "ASEBAND SAMPLING
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2!$!2 2%#%)6%23
&)'52% )& SAMPLING IN SECOND .YQUIST REGION
&OR )& SAMPLING A FREQUENCY AT LEAST TWICE THE )& BANDWIDTH IS REQUIRED HOWEVER
OVERSAMPLING IS TYPICALLY EMPLOYED TO EASE ALIAS REJECTION FILTERING AND TO REDUCE THE
EFFECT OF !$ CONVERTER QUANTIZATION NOISE )& SAMPLING IS OFTEN PERFORMED WITH THE
SIGNAL LOCATED IN THE SECOND .YQUIST REGION AS SHOWN IN &IGURE OR IN HIGHER
.YQUIST REGIONS
3TATED 2ESOLUTION 4HE STATED RESOLUTION OF AN !$ CONVERTER IS THE NUMBER OF
OUTPUT DATA BITS PER SAMPLE 4HE FULL SCALE VOLTAGE RANGE OF A .YQUIST RATE CONVERTER
IS GIVEN BY 6&3 .1 WHERE . IS THE STATED RESOLUTION AND 1 IS THE LEAST SIGNIFICANT
BIT ,3" SIZE
3IGNAL TO .OISE 2ATIO 3.2 3.2 IS THE RATIO OF RMS SIGNAL AMPLITUDE TO RMS
!$ CONVERTER NOISE POWER &OR AN IDEAL !$ CONVERTER THE ONLY ERROR IS DUE TO QUAN
TIZATION 0ROVIDED THAT THE INPUT SIGNAL IS SUFFICIENTLY LARGE RELATIVE TO THE QUANTIZATION
SIZE AND UNCORRELATED TO THE SAMPLING SIGNAL THE QUANTIZATION ERROR IS ESSENTIALLY RAN
DOM AND IS ASSUMED TO BE WHITE 4HE RMS QUANTIZATION NOISE IS 1 AND SIGNAL
TO QUANTIZATION NOISE RATIO 31.2 OF AN IDEAL !$ CONVERTER IS GIVEN BY
31.2D" .
0RACTICAL !$ CONVERTERS HAVE ADDITIONAL SAMPLING ERRORS OTHER THAN QUANTIZATION
INCLUDING THERMAL NOISE AND APERTURE JITTER 0ROVIDED THAT THESE ADDITIONAL ERRORS CAN
BE CHARACTERIZED AS WHITE THEY CAN BE COMBINED WITH THE QUANTIZATION NOISE WITH A
RESULTING 3.2 LESS THAN THE THEORETICAL 3.2 OF THE IDEAL CONVERTER "ECAUSE VARIOUS
!$ CONVERTER ERROR MECHANISMS ARE DEPENDENT ON INPUT SIGNAL LEVEL AND FREQUENCY
IT IS IMPORTANT TO CHARACTERIZE DEVICES OVER THE FULL RANGE OF INPUT CONDITIONS TO BE
EXPECTED 4HE AVAILABLE SIGNAL TO NOISE RATIO OF STATE OF THE ART HIGH SPEED !$ CON
VERTERS HAS BEEN SHOWN TO FALL OFF BY ONE BIT D" FOR EVERY DOUBLING OF THE SAMPLE
RATE /VER SAMPLING OF THE SIGNAL FOLLOWED BY FILTERING AND DECIMATION PROVIDES AN
IMPROVEMENT OF ONE HALF BIT D" IN THE ACHIEVABLE SIGNAL TO NOISE RATIO FOR EACH
DOUBLING OF THE SAMPLE RATE 4HUS FOR HIGH DYNAMIC RANGE APPLICATIONS THE BEST PER
FORMANCE IS ACHIEVED USING A STATE OF THE ART !$ CONVERTER THAT HAS A MAXIMUM
SAMPLE RATE JUST SUFFICIENT FOR THE APPLICATION
3PURIOUS &REE $YNAMIC 2ANGE 3&$2 3&$2 IS THE RATIO OF THE SINGLE TONE SIG
NAL AMPLITUDE TO THE LARGEST SPURIOUS SIGNAL AMPLITUDE AND IS USUALLY STATED IN D"
3IMILAR TO 3.2 THE SPURIOUS PERFORMANCE OF AN !$ CONVERTER IS DEPENDENT ON THE
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2!$!2 (!.$"//+
INPUT SIGNAL FREQUENCY AND AMPLITUDE 4HE FREQUENCY OF SPURIOUS SIGNALS IS ALSO DEPEN
DENT ON THE INPUT SIGNAL FREQUENCY WITH THE HIGHEST VALUES TYPICALLY DUE TO LOW ORDER
HARMONICS OR THEIR ALIASES 7HEN USING )& SAMPLING WITH A SIGNIFICANT OVER SAMPLING
RATIO FS " THE WORST SPURIOUS SIGNALS MAY BE AVOIDED BY CHOOSING THE SAMPLE
FREQUENCY RELATIVE TO SIGNAL FREQUENCY SUCH THAT THE UNWANTED SPURIOUS SIGNALS FALL
OUTSIDE THE SIGNAL BANDWIDTH OF INTEREST )F THE WORST CASE SPURIOUS CAN BE AVOIDED THE
SPECIFIED 3&$2 IS LESS IMPORTANT THAN THE LEVELS OF THE SPECIFIC SPURIOUS COMPONENTS
THAT FALL WITHIN THE BANDWIDTH OF INTEREST !GAIN IT IS IMPORTANT TO CHARACTERIZE DEVICES
OVER THE RANGE OF EXPECTED OPERATING CONDITIONS
4HE IMPACT OF !$ CONVERTER SPURIOUS SIGNALS ON RADAR PERFORMANCE DEPENDS ON THE
TYPE OF WAVEFORMS BEING PROCESSED AND THE DIGITAL SIGNAL PROCESSING BEING PERFORMED
)N APPLICATIONS USING CHIRP WAVEFORMS WITH LARGE TIME BANDWIDTH PRODUCTS SPURIOUS
SIGNALS ARE LESS CRITICAL AS THEY ARE EFFECTIVELY REJECTED IN THE PULSE COMPRESSION PRO
CESS BECAUSE THEIR CODING DOES NOT MATCH THAT OF THE WANTED SIGNAL )N PULSE DOPPLER
APPLICATIONS SPURIOUS SIGNALS ARE OF MUCH GREATER CONCERN BECAUSE THEY CAN CREATE
COMPONENTS WITH DOPPLER AT A VARIETY OF FREQUENCIES THAT MAY NOT BE REJECTED BY THE
CLUTTER FILTERING
3IGNAL TO .OISE AND $ISTORTION 2ATIO 3).!$ 3).!$ IS THE RMS SIGNAL AMPLI
TUDE TO THE RMS VALUE OF THE !$ CONVERTER NOISE PLUS DISTORTION 4HE NOISE PLUS DIS
TORTION INCLUDES ALL SPECTRAL COMPONENTS EXCLUDING $# AND THE FUNDAMENTAL UP TO
THE .YQUIST FREQUENCY 3).!$ IS A USEFUL FIGURE OF MERIT FOR !$ CONVERTERS BUT IN
DIGITAL RECEIVER APPLICATIONS WHERE THE WORST SPURIOUS COMPONENTS MAY FALL OUTSIDE OF
THE BANDWIDTH OF INTEREST IT IS NOT NECESSARILY A KEY DISCRIMINATOR BETWEEN COMPETING
CONVERTERS FOR A SPECIFIC APPLICATION
%FFECTIVE .UMBER OF "ITS %./" 4HE TERM EFFECTIVE NUMBER OF BITS IS OFTEN USED
TO STATE THE TRUE PERFORMANCE OF AN !$ CONVERTER AND HAS BEEN STATED IN THE LITERATURE
IN TERMS OF 3).!$ AND 3.2 AS GIVEN BELOW #ONSEQUENTLY IT IS IMPORTANT TO DIFFER
ENTIATE BETWEEN DEFINITIONS WHEN USING THIS TERM
.EFF ;3).!$D"
= .EFF ;3.2D"
= 4WO 4ONE )NTERMODULATION $ISTORTION )-$ 4WO TONE INTERMODULATION DISTORTION
IS ALSO IMPORTANT IN RECEIVER APPLICATIONS 4ESTING IS PERFORMED WITH TWO SINUSOIDAL INPUT
SIGNALS OF UNEQUAL FREQUENCY AND LEVELS SET SUCH THAT THE SUM OF THE TWO INPUTS DOES
NOT EXCEED THE !$ CONVERTER FULL SCALE LEVEL 3IMILAR TO )-$ FOR AMPLIFIERS THE MOST
SIGNIFICANT DISTORTION IS USUALLY SECOND ORDER OR THIRD ORDER )-$ PRODUCTS (OWEVER
DUE TO THE COMPLEX NATURE OF THE DISTORTION MECHANISM IN !$ CONVERTERS THE AMPLITUDE
OF )-$ PRODUCTS IS NOT EASILY CHARACTERIZED AND PREDICTED BY THE MEASUREMENT OF AN
INPUT INTERCEPT POINT
)NPUT .OISE ,EVEL AND $YNAMIC 2ANGE !CCURATE SETTING OF THE !$ CON
VERTER INPUT NOISE LEVEL RELATIVE TO THE !$ CONVERTER NOISE IS CRITICAL TO ACHIEVING THE
OPTIMUM TRADE OFF BETWEEN DYNAMIC RANGE AND SYSTEM NOISE FLOOR 4OO HIGH A LEVEL
OF NOISE INTO THE !$ CONVERTER WILL DEGRADE THE AVAILABLE DYNAMIC RANGE TOO LOW
A LEVEL WILL DEGRADE THE OVERALL SYSTEM NOISE FLOOR 3UFFICIENT TOTAL NOISE SHOULD BE
APPLIED TO THE !$ CONVERTER INPUT TO RANDOMIZE OR hWHITENv THE QUANTIZATION NOISE
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! " ! $ " ! !#
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4HIS CAN BE ACHIEVED WITH RMS INPUT NOISE R EQUAL TO THE ,3" STEP SIZE 1 )N
ADDITION THE INPUT NOISE POWER SPECTRAL DENSITY SHOULD BE SUFFICIENT TO MINIMIZE THE
IMPACT ON SYSTEM NOISE DUE TO THE !$ CONVERTER NOISE 4HE IMPACT ON OVERALL NOISE
DUE TO QUANTIZATION NOISE IS GIVEN BY
R 1
R q1
R
R 4YPICAL OPERATING POINTS ARE IN THE RANGE OF R 1 TO R 1 WITH CORRESPONDING
NOISE POWER DEGRADATION DUE TO QUANTIZATION OF D" AND D" RESPECTIVELY
)N PRACTICE THE 3.2 OF HIGH SPEED CONVERTERS IS OFTEN SUCH THAT THE NOISE OF THE
!$ CONVERTER IS SIGNIFICANTLY GREATER THAN THE THEORETICAL QUANTIZATION NOISE )N ADDI
TION THE !$ CONVERTER INPUT SIGNAL NOISE BANDWIDTH MAY BE SIGNIFICANTLY LESS THAN THE
.YQUIST BANDWIDTH 4HIS IS A SIGNIFICANT FACTOR IN )& SAMPLING APPLICATIONS WHERE THE
)& NOISE BANDWIDTH IS OFTEN LESS THAN  OF THE .YQUIST BANDWIDTH )N THIS CASE THE TOTAL
INPUT AND !$ CONVERTER NOISE MUST BE SUFFICIENT TO WHITEN THE QUANTIZATION NOISE AND
THE POWER SPECTRAL DENSITY OF THE INPUT NOISE SHOULD BE SUFFICIENTLY GREATER THAN THAT OF
THE !$ CONVERTER AS ILLUSTRATED IN &IGURE )N SOME CASES OUT OF BAND NOISE MAY
BE ADDED TO WHITEN THE !$ CONVERTER QUANTIZATION NOISE AND SPURIOUS SIGNALS 4HE OUT
OF BAND NOISE IS THEN REJECTED THROUGH SUBSEQUENT DIGITAL SIGNAL PROCESSING
4HE RESULTING 3.2 OF THE SYSTEM AFTER DIGITAL FILTERING WITH RECEIVER BANDWIDTH "2
AND SAMPLE RATE FS IS GIVEN BY
3.2393 D" 3.2!$# D"
¤ F ³
LOG ¥ 3 ´
¦ "2 µ
LOG 3)& 3!$#
WHERE 3)&3!$# IS THE RATIO OF NOISE POWER SPECTRAL DENSITY OF THE !$ CONVERTER INPUT
SIGNAL TO THE POWER SPECTRAL DENSITY OF THE !$ CONVERTER 4HE DEGRADATION OF OVERALL
SENSITIVITY DUE TO THE !$ CONVERTER NOISE IS GIVEN BY
,D" LOG
3!$#3)&
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2!$!2 (!.$"//+
!$ #ONVERTER 3AMPLE #LOCK 3TABILITY 4HE STABILITY OF THE SAMPLE CLOCK IS
CRITICAL TO ACHIEVING THE FULL CAPABILITY OF AN !$ CONVERTER 3AMPLE TO SAMPLE VARIA
TION IN THE SAMPLING INTERVAL CALLED APERTURE UNCERTAINTY OR APERTURE JITTER PRODUCES
A SAMPLING ERROR PROPORTIONAL TO THE RATE OF CHANGE OF INPUT VOLTAGE &OR A SINUSOIDAL
INPUT SIGNAL THE 3.2 DUE TO APERTURE UNCERTAINTY ALONE IS GIVEN BY
3.2D" LOGO FR J
WHERE F INPUT SIGNAL FREQUENCY
RJ RMS APERTURE JITTER
3IMILARLY CLOSE TO CARRIER NOISE SIDEBANDS PRESENT ON THE SAMPLE CLOCK SIGNAL ARE
TRANSFERRED TO SIDEBANDS ON THE SAMPLED INPUT SIGNAL REDUCED BY LOG F F3 D"
&OR EXAMPLE IN AN )& SAMPLING APPLICATION WITH THE INPUT SIGNAL Ð OF THE SAMPLE
FREQUENCY THE CLOSE TO CARRIER PHASE NOISE OF THE SAMPLE CLOCK WILL BE TRANSFERRED TO
THE OUTPUT OF THE !$ CONVERTER OUTPUT DATA SIGNAL REDUCED BY D"
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4HE AVAILABILITY OF HIGH SPEED ANALOG TO DIGITAL CONVERTERS CAPABLE OF DIRECT SAM
PLING OF RADAR RECEIVER )& SIGNALS HAS RESULTED IN THE ALMOST UNIVERSAL ADOPTION OF
DIGITAL RECEIVER ARCHITECTURES OVER CONVENTIONAL ANALOG )1 DEMODULATION )N A DIGITAL
RECEIVER A SINGLE !$ CONVERTER IS USED TO DIGITIZE THE RECEIVED SIGNAL AND DIGITAL
SIGNAL PROCESSING IS USED TO PERFORM THE DOWNCONVERSION TO ) AND 1 BASEBAND SIG
NALS #ONTINUING ADVANCES IN SAMPLING SPEEDS ARE LEADING TO SAMPLING AT INCREASING
FREQUENCIES SOMETIMES ELIMINATING THE NEED FOR A SECOND DOWNCONVERSION WITH THE
POSSIBILITY APPROACHING OF SAMPLING DIRECTLY AT THE RADAR 2& FREQUENCY 4HE BENEFITS
OF )& SAMPLING OVER CONVENTIONAL ANALOG )1 DEMODULATION ARE
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L
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6IRTUAL ELIMINATION OF ) AND 1 IMBALANCE
6IRTUAL ELIMINATION OF $# OFFSET ERRORS
2EDUCED CHANNEL TO CHANNEL VARIATION
)MPROVED LINEARITY
&LEXIBILITY OF BANDWIDTH AND SAMPLE RATE
4IGHT FILTER TOLERANCE PHASE LINEARITY AND IMPROVED ANTI ALIAS FILTERING
2EDUCED COMPONENT COST SIZE WEIGHT AND POWER DISSIPATION
4HE USE OF A HIGH )& FREQUENCY IS DESIRABLE AS IT EASES THE DOWNCONVERSION AND
FILTERING PROCESS HOWEVER THE USE OF HIGHER FREQUENCIES PLACES GREATER DEMANDS ON
THE PERFORMANCE OF THE !$ CONVERTER $IRECT 2& SAMPLING IS CONSIDERED THE ULTI
MATE GOAL OF DIGITAL RECEIVERS WITH ALL THE TUNING AND FILTERING PERFORMED THROUGH
DIGITAL SIGNAL PROCESSING 4HE ADVANTAGE BEING THE ALMOST COMPLETE ELIMINATION OF
ANALOG HARDWARE (OWEVER NOT ONLY DOES THE !$ CONVERTER HAVE TO SAMPLE THE
2& DIRECTLY BUT UNLESS IT IS PRECEDED BY TUNABLE 2& PRESELECTOR FILTERS THE !$
CONVERTER INPUT MUST HAVE THE DYNAMIC RANGE TO HANDLE ALL OF THE SIGNALS PRES
ENT IN THE RADAR BAND SIMULTANEOUSLY 'ENERALLY THE INTERFERENCE POWER ENTERING
THE !$ CONVERTER IS PROPORTIONAL TO THE BANDWIDTH OF COMPONENTS IN FRONT OF THE
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!$ CONVERTER 4HE REQUIRED !$ CONVERTER 3.2 TO AVOID SATURATION ON THE INTERFER
ING SIGNALS IS GIVEN BY
¤ 0 # ³
3.2!$# D" LOG ¥ ) ´
¦ . !$# µ
WHERE
0) INTERFERENCE POWER AT !$ CONVERTER INPUT
# CREST FACTOR
.!$# !$ CONVERTER NOISE
4HE CREST FACTOR IS THE PEAK LEVEL THAT CAN BE HANDLED WITHIN THE FULL SCALE RANGE
OF THE !$ CONVERTER RELATIVE TO THE RMS INTERFERENCE LEVEL )T IS SET TO ACHIEVE A
SUFFICIENTLY HIGH PROBABILITY THAT FULL SCALE WILL NOT BE EXCEEDED &OR EXAMPLE WITH
GAUSSIAN NOISE A CREST FACTOR OF SETS THE PEAK LEVEL AT THE R LEVEL D" ABOVE
THE RMS LEVEL WITH A PROBABILITY OF THAT THE FULL SCALE IS NOT EXCEEDED ON
EACH !$ CONVERTER SAMPLE
3ETTING THE SYSTEM NOISE LEVEL POWER SPECTRAL DENSITY INTO THE !$ CONVERTER 2D"
ABOVE THE !$ CONVERTER NOISE GIVES
¤ F.
³
2 D" LOG ¥ S 393 ´
"
.
¦ )& !$# µ
WHERE
.393 SYSTEM NOISE AT !$ CONVERTER INPUT IN BANDWIDTH ")&
#OMBINING %Q AND GIVES THE REQUIRED 3.2 AS
¤ 0 # ")& ³
3.2!$# D" LOG ¥ )
¦ F3 . 393 ´µ
2 D"
4HE GENERATION OF BASEBAND ) AND 1 SIGNALS FROM THE )& SAMPLED !$ CONVERTER DATA
IS PERFORMED USING DIGITAL SIGNAL PROCESSING AND CAN BE IMPLEMENTED THROUGH A VARIETY
OF APPROACHES 4WO APPROACHES ARE DESCRIBED NEXT
$IGITAL $OWNCONVERSION 4HE DIGITAL DOWNCONVERSION APPROACH IS SHOWN IN
&IGURE 4HE SIGNAL IS SAMPLED BY THE !$ CONVERTER FREQUENCY SHIFTED TO BASE
BAND LOW PASS FILTERED AND DECIMATED TO PRODUCE )1 DIGITAL DATA 4HE SIGNAL SPECTRUM
AT EACH STAGE OF THE PROCESS IS SHOWN IN &IGURE )N CONTINUOUS TIME &IG A
FREQUENCY IS IN HERTZ AND IS REPRESENTED BY & )N DISCRETE TIME &IG BnE FRE
QUENCY IS IN RADIANS PER SAMPLE AND IS REPRESENTED BY V 4HE SPECTRUM OF THE ANA
LOG INPUT SIGNAL XT IS SHOWN IN &IGURE A WITH THE SIGNAL SPECTRUM CENTERED AT
& HERTZ 4HE SIGNAL IS SAMPLED BY THE !$ CONVERTER AT FREQUENCY &S PRODUCING THE
W CENTERED AT FREQUENCY V WITH THE
TIME SEQUENCE X N AND FREQUENCY SPECTRUM 8
IMAGE CENTERED AT V 4HE !$ CONVERTER OUTPUT SIGNAL IS THEN FREQUENCY SHIFTED BY
COMPLEX MULTIPLICATION WITH THE REFERENCE SIGNAL E JV N CORRESPONDING TO A REFERENCE
SIGNAL ROTATING AT V RADIANS PER SAMPLE CENTERING THE SIGNAL SPECTRUM 8V ABOUT
ZERO 4HE UNWANTED IMAGE IS RE CENTERED AT V IF V O OR V O IF V a O 4HE UNWANTED IMAGE IS THEN REJECTED USING THE &)2 FILTER WITH IMPULSE RESPONSE HN
PRODUCING OUTPUT X} N WITH SPECTRUM 8} V &INALLY THE SAMPLE RATE IS REDUCED BY
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&)'52% $IGITAL DOWNCONVERSION ARCHITECTURE
SELECTING EVERY $TH SAMPLE 0ROVIDED THE FILTER RESPONSE (V HAS SUFFICIENT REJECTION
FOR FREQUENCIES \V \ q P $ THERE WILL BE NEGLIGIBLE ALIASING AND LOSS OF INFORMATION IN
THE DECIMATION PROCESS
&)'52% $IGITAL DOWNCONVERSION SPECTRA
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2!$!2 2%#%)6%23
&)'52% (ILBERT TRANSFORMER ARCHITECTURE
(ILBERT 4RANSFORMER !N ALTERNATIVE DIGITAL RECEIVER ARCHITECTURE IS SHOWN IN
&IGURE WITH THE RELEVANT SIGNAL SPECTRA SHOWN IN &IGURE 4HE !$ CONVERTER
OUTPUT SIGNAL X N IS PROCESSED USING A (ILBERT TRANSFORMER COMPRISING &)2 FILTERS
HN AND HN WHERE THE FREQUENCY RESPONSES ARE GIVEN BY
\( V \ y \( V \ y \V V \ a "
AND
( V
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' V
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\V V \ a "
\V V \ a "
4HE FILTER OUTPUTS FORM THE DESIRED COMPLEX VALUED SIGNAL X N CENTERED AT FREQUENCY
V WHILE REJECTING THE IMAGE CENTERED AT V 4HE FINAL STAGE IS TO PERFORM A FREQUENCY
SHIFT AND SAMPLE RATE REDUCTION BY DECIMATING THE SIGNAL BY SELECTING EVERY $TH SAMPLE
&)'52% 3PECTRA OF (ILBERT TRANSFORMER RECEIVER
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)F THE SPECTRUM OF 8V IS CENTERED AT FREQUENCY V O K $ K THE DECIMATION
WILL CENTER THE SPECTRUM 9V ABOUT ZERO 0ROVIDED THE FILTER RESPONSES HAVE SUFFICIENT
REJECTION FOR FREQUENCIES \V o V \ q O $ THERE WILL BE NEGLIGIBLE ALIASING AND LOSS OF
INFORMATION IN THE DECIMATION PROCESS
)1 %RRORS $IGITAL ) AND 1 GENERATION DOES NOT PRODUCE SIGNALS WITHOUT ERROR
AS IS OFTEN STATED BUT INSTEAD ALLOWS THE GENERATION OF THESE SIGNALS WITH ERRORS
THAT ARE SUFFICIENTLY SMALL TO BE CONSIDERED NEGLIGIBLE 4HE PRIMARY CAUSE OF THE
IMBALANCE IS THE NON IDEAL FILTER RESPONSES !N INFINITE NUMBER OF TAPS WOULD BE
REQUIRED TO SET THE PASSBAND GAIN TO UNITY AND THE STOPBAND GAIN TO ZERO HOWEVER
FOR MOST APPLICATIONS SUFFICIENT PROCESSING RESOURCES ARE AVAILABLE TO REDUCE THE
ERRORS TO INSIGNIFICANT LEVELS &INITE LENGTH WORDS FOR FILTER COEFFICIENTS PRODUCE NON
IDEAL FILTER RESPONSES 4HE EFFECT ON PASSBAND RESPONSE IS TYPICALLY NEGLIGIBLE BUT
SIGNIFICANT DISTORTION OF THE FILTER STOPBAND REJECTION CAN OCCUR POTENTIALLY EFFECTING
)1 BALANCE
$IGITAL $OWNCONVERSION 5SING -ULTIRATE 0ROCESSING AND 0OLYPHASE
FILTERS 4HERE ARE MANY VARIATIONS TO THESE BASIC APPROACHES AND SPECIFIC IMPLE
MENTATIONS OFTEN UTILIZE EFFICIENT APPROACHES THAT MINIMIZE THE NUMBER OF CALCULA
TIONS REQUIRED WITH EMPHASIS ON REDUCING THE NUMBER OF MULTIPLICATIONS AS THESE
REQUIRE SIGNIFICANTLY MORE RESOURCES THAN ADDITIONS 4WO TECHNIQUES USED TO REDUCE
THE &)2 FILTER PROCESSING BURDEN ARE MULTIRATE PROCESSING AND POLYPHASE FILTERING
4HE DIGITAL DOWNCONVERSION APPROACH IS SHOWN IN &IGURE USING MULTIRATE PRO
CESSING 4HE FIRST &)2 FILTER HN PROVIDES SUFFICIENT REDUCTION TO PREVENT ALIASING
IN THE FIRST DECIMATION BY FACTOR $ THE SECOND FILTER HN PROVIDES ALIAS REDUCTION
FOR THE SECOND DECIMATION AND CAN ALSO BE USED TO CORRECT PASSBAND RIPPLE OR DROOP
DUE TO FILTER HN &OR LARGE DECIMATION FACTORS MORE THAN TWO DECIMATION STAGES
MAY BE USED
! POPULAR FILTER FOR THE FIRST STAGE IS THE #ASCADED )NTEGRATOR #OMB #)# DECIMA
TOR FILTER THAT CAN BE IMPLEMENTED WITHOUT MULTIPLIERS 4HESE FILTERS PROVIDE REJECTION IN
THE STOPBAND AT FREQUENCIES THAT ALIAS TO THE PASSBAND AS A RESULT OF DECIMATION 3INCE
THEY PROVIDE RELATIVELY LARGE PASSBAND DROOP AND SLOW STOPBAND REJECTION THEY ARE
GENERALLY FOLLOWED BY A &)2 FILTER THAT CAN BOTH CORRECT FOR #)# PASSBAND DROOP AND
&)'52% $IGITAL DOWNCONVERSION ARCHITECTURE
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2!$!2 2%#%)6%23
PROVIDE THE DESIRED STOPBAND REJECTION RESPONSE 4HE KTH ORDER #)# FILTER FOR DECIMA
TION FACTOR $ HAS TRANSFER FUNCTION
§$ ¶
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§ Z $ ¶
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+
! POLYPHASE FILTER IS A FILTER BANK THAT SPLITS AN INPUT SIGNAL INTO $ SUB BAND FILTERS
OPERATING AT A SAMPLE RATE REDUCED BY A FACTOR $ PROVIDING A COMPUTATIONALLY EFFICIENT
APPROACH TO PERFORMING THE &)2 FILTERING FOLLOWED BY DECIMATION IN A DIGITAL RECEIVER
2ATHER THAN COMPUTING ALL THE FILTER OUTPUT SAMPLES AND ONLY USING EVERY $TH SAMPLE
THE POLYPHASE APPROACH CALCULATES ONLY THOSE THAT ARE ACTUALLY USED &IGURE AND
%Q DEFINE HOW THE FILTER WITH IMPULSE RESPONSE HN FOLLOWED WITH DECIMATION
BY FACTOR $ IS IMPLEMENTED IN A POLYPHASE STRUCTURE 4HE INPUT SIGNAL XN IS DIVIDED
INTO $ PARALLEL PATHS BY THE hCOMMUTATOR v WHICH OUTPUTS SAMPLES IN TURN ROTATING IN A
COUNTERCLOCKWISE DIRECTION TO EACH OF THE &)2 FILTERS OPERATING AT THE REDUCED SAMPLE
RATE 4HE OUTPUTS OF THE &)2 FILTERS ARE SUMMED TO PRODUCE THE OUTPUT SIGNAL YM 4HIS
ARCHITECTURE IS BENEFICIAL AS IT PROVIDES AN APPROACH THAT CAN BE EASILY PARALLELIZED AT
RATE &8 $
PKN HK
N$
K x $
N x +
-ULTI #HANNEL 2ECEIVER #ONSIDERATIONS -ODERN RADAR SYSTEMS RARELY CON
TAIN ONLY ONE RECEIVER CHANNEL -ONOPULSE PROCESSING FOR EXAMPLE REQUIRES TWO
OR MORE CHANNELS TO PROCESS SUM AND DELTA SIGNALS !DDITIONALLY THE CHANNELS
MUST BE COHERENT SYNCHRONIZED IN TIME AND WELL MATCHED IN PHASE AND AMPLITUDE
$IGITAL BEAMFORMING SYSTEMS REQUIRE A LARGE NUMBER OF CHANNELS WITH SIMILAR
COHERENCE AND SYNCHRONIZATION REQUIREMENTS AND TIGHT PHASE AND AMPLITUDE TRACK
ING 4HE COHERENCE REQUIREMENT DICTATES THE RELATIVE PHASE STABILITY OF ,/ AND
!$ CONVERTER CLOCK SIGNALS USED FOR EACH RECEIVE CHANNEL 4HE TIME SYNCHRONIZA
TION REQUIREMENT MEANS THAT !$ CONVERTER CLOCK SIGNALS FOR EACH CHANNEL MUST
BE ALIGNED IN TIME AND DECIMATION MUST BE PERFORMED IN PHASE FOR EACH CHANNEL
0HASE AND AMPLITUDE IMBALANCE BETWEEN CHANNELS IS A RESULT OF VARIATION IN THE
&)'52% $ECIMATION USING POLYPHASE FILTERS
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2!$!2 (!.$"//+
ANALOG CIRCUITRY PRIOR TO AND WITHIN THE !$ CONVERTER )F THE )& FILTER BANDWIDTH IS
WIDE RELATIVE TO THE DIGITAL RECEIVER BANDWIDTH THE MAJORITY OF THE ERROR BETWEEN
CHANNELS WILL BE A CONSTANT GAIN AND PHASE OFFSET ACROSS THE RECEIVER BANDWIDTH
! SINGLE CORRECTION APPLIED AS A COMPLEX MULTIPLICATION OF )1 DATA WILL COR
RECT FOR GAIN AND PHASE OFFSETS AND IS USUALLY ADEQUATE TO PROVIDE THE REQUIRED
CHANNEL TRACKING FOR MONOPULSE APPLICATIONS 7HEN TIGHTER CHANNEL TRACKING IS
REQUIRED SUCH AS FOR SIDELOBE CANCELER OR DIGITAL BEAMFORMING APPLICATIONS &)2
FILTER EQUALIZATION CAN BE USED TO CORRECT FOR FREQUENCY DEPENDENT VARIATIONS ACROSS
THE RECEIVER BANDWIDTH &)2 FILTER EQUALIZATION CAN BE PERFORMED EITHER SUBSE
QUENT TO THE &)2 FILTERING USED TO GENERATE )1 DATA OR COMBINED WITH THESE FILTERS
)T SHOULD BE NOTED THAT TO CORRECT FOR FREQUENCY AND PHASE VARIATION ACROSS THE
RECEIVER BANDWIDTH REQUIRES &)2 FILTERS WITH COMPLEX COEFFICIENTS APPLIED EQUALLY
TO ) AND 1 DATA 2EAL VALUE COEFFICIENTS TYPICALLY USED IN )1 GENERATION PROVIDE FIL
TER RESPONSES SYMMETRICAL ABOUT ZERO FREQUENCY #ORRECTION OF )& FILTER FREQUENCY
RESPONSE ERRORS WILL IN GENERAL REQUIRE ASYMMETRIC FREQUENCY CORRECTION THAT CAN
ONLY BE PROVIDED AT BASEBAND USING COMPLEX COEFFICIENTS
4HE DEGREE TO WHICH THESE MULTIPLE RECEIVER CHANNELS MUST TRACK DEPENDS ON THE
SPECIFIC SYSTEM REQUIREMENTS !LTHOUGH MODERN SYSTEMS TYPICALLY INCLUDE SOME
DEGREE OF CHANNEL EQUALIZATION FUNCTION A REASONABLE DEGREE OF TRACKING BETWEEN GAIN
PHASE AND TIMING MUST BE MAINTAINED IN ORDER TO ALLOW THE CHANNEL EQUALIZATION TO
BE PERFORMED USING DIGITAL SIGNAL PROCESSING WITHOUT CONSUMING EXCESSIVE PROCESSING
RESOURCES !LSO THE RELATIVE STABILITY OF THE RADAR CHANNELS AS A FUNCTION OF TIME AND
TEMPERATURE MUST BE SUCH THAT THE CORRECTIONS CAN MAINTAIN ADEQUATE TRACKING DURING
THE TIME BETWEEN CALIBRATION INTERVALS
$IGITAL BEAMFORMING SYSTEMS REQUIRE A LARGE NUMBER OF RECEIVER CHANNELS )N THESE
APPLICATIONS SIZE WEIGHT POWER DISSIPATION AND COST ARE CRITICAL CONSIDERATIONS
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$IPLEX "ENEFITS $IPLEX OPERATION CONSISTS OF TWO RECEIVERS THAT SIMULTANEOUSLY
PROCESS RETURNS FROM TRANSMISSIONS ON DIFFERENT FREQUENCIES 4RANSMISSIONS ARE USU
ALLY NON OVERLAPPING IN TIME TO AVOID A D" INCREASE IN PEAK POWER AND BECAUSE MOST
RADAR TRANSMITTERS ARE OPERATED IN SATURATION AND SIMULTANEOUS TRANSMISSION AT MULTIPLE
FREQUENCIES WOULD PRODUCE SIGNIFICANT TRANSMITTED INTERMODULATION DISTORTION
4HE SENSITIVITY BENEFIT OF DIPLEX OPERATION FOR DETECTING 3WERLING TARGETS IS SHOWN
IN &IGURE INCREASING WITH PROBABILITY OF DETECTION 0$ &OR EXAMPLE DIPLEX OPER
ATION ACHIEVES 0$ WITH D" LESS TOTAL SIGNAL POWER THAN SIMPLEX !SSUMPTIONS
MADE IN DERIVING &IGURE ARE
2ETURNS ON THE TWO FREQUENCIES ARE ADDED IN VOLTAGE OR POWER PRIOR TO THE DETECTION
DECISION RATHER THAN BEING SUBJECTED TO INDIVIDUAL DETECTION DECISIONS
3EPARATION OF THE TWO FREQUENCIES IS SUFFICIENT TO MAKE THEIR 3WERLING FLUCTUA
TIONS INDEPENDENT 4HIS DEPENDS ON THE PHYSICAL LENGTH OF THE TARGET IN THE RANGE
DIMENSION K2 4HE MINIMUM FREQUENCY SEPARATION IS -(ZK2 M -(Z
WILL MAINTAIN THE DIPLEX BENEFIT FOR AIRCRAFT LONGER THAN M FT %QUAL ENERGY IS TRANSMITTED IN BOTH PULSES ! IMBALANCE SACRIFICES ONLY D"
OF THE BENEFIT AT 0$
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$IPLEX OPERATION IMPROVES THE SENSITIVITY OF THE RECEIVER
"OTH LINEAR AND ASYMMETRICAL NONLINEAR &- PRODUCE A RANGE ERROR AS A FUNCTION
OF DOPPLER DUE TO RANGE DOPPLER COUPLING 4HESE RANGE DISPLACEMENTS MUST MATCH IN
THE TWO RECEIVERS TO WITHIN A SMALL FRACTION OF THE COMPRESSED PULSE WIDTH OTHERWISE
THE SENSITIVITY BENEFITS OF DIPLEX OPERATION ARE NOT FULLY ACHIEVED AND RANGE ACCURACY
MAY BE DEGRADED
)MPLEMENTATION $IPLEX OPERATION CAN BE IMPLEMENTED WITH A VARIETY OF
APPROACHES #OMPLETE REPLICATION OF THE RECEIVER CHANNELS IS TYPICALLY THE MOST EXPEN
SIVE APPROACH AND MAY BE REQUIRED IF THE FREQUENCY SEPARATION IS VERY LARGE ! MORE
COMMON APPROACH IS SEPARATION OF THE FREQUENCIES AT THE FIRST )& AS THIS DOES NOT
REQUIRE COMPLETE DUPLICATION OF THE 2& FRONT END OR THE FIRST ,/ SIGNAL 3EPARATE SEC
OND LOCAL OSCILLATOR OR )1 DEMODULATOR REFERENCE FREQUENCIES CAN BE USED TO PROCESS
THE DIFFERENT FREQUENCIES 7ITH THE USE OF HIGH SPEED )& SAMPLING IT IS ALSO POSSIBLE
TO DIGITIZE BOTH SIGNALS SIMULTANEOUSLY USING A SINGLE !$ CONVERTER AND PERFORM THE
FREQUENCY SEPARATION USING DIGITAL SIGNAL PROCESSING 7HICHEVER APPROACH IS USED CARE
MUST BE TAKEN TO PROVIDE ADEQUATE DYNAMIC RANGE AND LINEARITY TO PREVENT INTERMODULA
TION DISTORTION FROM DEGRADING RADAR PERFORMANCE
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4HE EXCITER FUNCTION OF WAVEFORM GENERATION AND UPCONVERSION IS OFTEN TIGHTLY COUPLED
WITH THE RECEIVER FUNCTION 4HE REQUIREMENT FOR COHERENCE BETWEEN THE RECEIVER AND
EXCITER IS A MAJOR FACTOR FOR THIS TIGHT COUPLING AND THE USE OF THE SAME ,/ FREQUEN
CIES WITHIN THE RECEIVER AND EXCITER USUALLY RESULTS IN HARDWARE SAVINGS 3IMILAR TO
THE MIGRATION TO DIGITAL RECEIVER ARCHITECTURES THE EXCITER FUNCTIONALITY IS INCREASINGLY
BEING IMPLEMENTED USING DIGITAL APPROACHES
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$IRECT $IGITAL 3YNTHESIZER 4HE $IRECT $IGITAL 3YNTHESIZER $$3 PRODUCES
WAVEFORMS USING DIGITAL TECHNIQUES AND PROVIDES SIGNIFICANT IMPROVEMENTS IN STABIL
ITY PRECISION AGILITY AND VERSATILITY OVER ANALOG TECHNIQUES 4HE MAIN LIMITATIONS ARE
THE NOISE AND SPURIOUS SIGNALS AS DESCRIBED BELOW 4HE GENERAL $$3 ARCHITECTURE IS
SHOWN IN &IGURE 4HE DOUBLE ACCUMULATOR ARCHITECTURE COMPRISING THE FREQUENCY
AND PHASE ACCUMULATORS ENABLES THE GENERATION OF #7 LINEAR &- CHIRP NONLINEAR
PIECE WISE LINEAR &- FREQUENCY MODULATED AND PHASE MODULATED WAVEFORMS #7
WAVEFORMS ARE GENERATED BY APPLYING A CONSTANT FREQUENCY WORD DIGITIZED FREQUENCY
REPRESENTATION INPUT TO THE PHASE ACCUMULATOR CREATING A LINEAR PHASE SEQUENCE THAT IS
FIRST TRUNCATED THEN INPUT TO A COSINE OR SINE LOOKUP TABLE THAT OUTPUTS THE CORRESPOND
ING SINUSOIDAL SIGNAL VALUE TO THE DIGITAL TO ANALOG $! CONVERTER 4HE FREQUENCY
RESOLUTION IS DEPENDENT ON THE NUMBER OF BITS AND THE CLOCK FREQUENCY OF THE PHASE
ACCUMULATOR 4HE OUTPUT FREQUENCY IS GIVEN BY
FOUT - F FCLK
.F
WHERE
-F FREQUENCY WORD INPUT TO THE PHASE ACCUMULATOR
FCLK PHASE ACCUMULATOR CLOCK FREQUENCY
.E NUMBER OF BITS OF PHASE ACCUMULATOR
,INEAR &- OR CHIRP WAVEFORMS ARE GENERATED BY APPLYING A CONSTANT CHIRP SLOPE
WORD DIGITIZED CHIRP SLOPE REPRESENTATION TO THE INPUT OF THE FREQUENCY ACCUMULATOR
CREATING A QUADRATIC PHASE SEQUENCE AT THE OUTPUT OF THE PHASE REGISTER 0IECEWISE LINEAR
OR NONLINEAR &- WAVEFORMS CAN BE GENERATED BY APPLYING A TIME VARYING SLOPE INPUT
TO THE FREQUENCY REGISTER 4HE FREQUENCY ACCUMULATOR MAY BE CLOCKED EITHER AT THE SAME
RATE AS THE PHASE ACCUMULATOR OR AT A SUB MULTIPLE TO PROVIDE FINER CHIRP SLOPE RESOLU
TION )F BOTH ACCUMULATORS ARE CLOCKED AT THE SAME RATE THE CHIRP SLOPE IS GIVEN BY
$FOUT - 3 FCLK
.F
$T
WHERE
-3 CHIRP SLOPE WORD INPUT TO THE FREQUENCY ACCUMULATOR
.F NUMBER OF BITS OF FREQUENCY ACCUMULATOR
&REQUENCY MODULATED AND PHASE MODULATED WAVEFORMS CAN BE CREATED APPLYING TIME
VARYING INPUTS TO THE FREQUENCY MODULATION &- AND PHASE MODULATION 0- PORTS
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2!$!2 2%#%)6%23
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%RRORS SUCH AS PHASE TRUNCATION AND $! CONVERTER QUANTIZATION AND NONLINEARITY
PRODUCE SPURIOUS SIGNALS DUE TO THEIR DETERMINISTIC NATURE 4HE SPURIOUS SIGNAL FRE
QUENCIES GENERATED BY A $$3 CAN BE READILY PREDICTED AS THEY ARE A FUNCTION OF THE
DIGITAL ARCHITECTURE AND PROGRAMMED FREQUENCY 4HE SPURIOUS SIGNAL MAGNITUDES ARE
LESS PREDICTABLE AS THE MAGNITUDES OF THE DOMINANT SPURIOUS SIGNALS ARE A FUNCTION OF
THE $! CONVERTER NONLINEARITY
7HEN GENERATING #7 WAVEFORMS THE $! CONVERTER SEQUENCE REPEATS AFTER +
SAMPLES WHERE + EQUALS THE GREATEST COMMON DIVISOR OF .E AND -F 4HUS SPURIOUS
SIGNALS OCCUR ONLY AT FREQUENCIES
FSPUR NFCLK
+
N )N THE EXTREME CASE WHERE -F DOES NOT CONTAIN THE FACTOR THIS CREATES A SPURIOUS FRE
QUENCY SPACING OF FCLK .E &OR EXAMPLE WITH A '(Z CLOCK AND BIT FREQUENCY ACCU
MULATOR THE SPURIOUS FREQUENCY SPACING CAN BE AS CLOSE AS (Z )N MOST CASES SUCH
CLOSELY SPACED SPURIOUS SIGNALS CANNOT BE DIFFERENTIATED FROM NOISE #ONVERSELY CHOOS
ING VALUES OF -F THAT CONTAIN LARGE FACTORS OF . CREATES RELATIVELY LARGE SPURIOUS SPACING
&OR EXAMPLE USING A -(Z CLOCK ALLOWS THE GENERATION OF FREQUENCIES AT MULTIPLES OF
-(Z WITH ALL THE SPURIOUS COMPONENTS OCCURRING AT MULTIPLES OF -(Z
4HE IMPACT OF $$3 SPURIOUS SIGNALS ON RADAR PERFORMANCE DEPENDS ON THE NATURE
OF THE SPURIOUS SIGNALS AND THE TYPE OF RADAR PROCESSING INVOLVED !PPLICATIONS USING
CHIRP WAVEFORMS WITH LARGE TIME BANDWIDTH PRODUCTS ARE TYPICALLY LESS SENSITIVE TO
$$3 SPURIOUS SIGNALS SINCE THE $$3 SPURIOUS SIGNALS CHIRP AT A DIFFERENT RATE TO THAT
OF THE WANTED SIGNAL 4HE SPURIOUS SIGNALS ARE THUS REJECTED DURING PULSE COMPRESSION
)N PULSE DOPPLER APPLICATIONS SPURIOUS SIGNALS ARE OF MUCH GREATER CONCERN HOWEVER
THEIR EFFECTS CAN BE MITIGATED BY ENSURING THAT THE $$3 GENERATES EACH WAVEFORM FROM
THE SAME INITIAL CONDITIONS 2ESTARTING THE $$3 FOR EVERY PULSE GUARANTEES THAT THE
SAME DIGITAL SEQUENCE WILL BE INPUT TO THE $! CONVERTER FOR EACH PULSE 4HE RESULT IS A
$$3 OUTPUT THAT ONLY CONTAINS SPECTRAL COMPONENTS AT MULTIPLES OF THE 02&
4ECHNIQUES HAVE BEEN PROPOSED OR INCORPORATED INTO $$3 DEVICES THAT REDUCE SPU
RIOUS LEVELS BY ADDING DITHERING TO REDUCE THE EFFECTS OF LIMITED WORD LENGTHS 4HE
EFFECT OF THESE TECHNIQUES AND THE SPURIOUS SIGNALS THAT THEY ARE DESIGNED TO MITIGATE
SHOULD BE CONSIDERED CAREFULLY AS THEY MAY BE DETRIMENTAL TO RADAR PERFORMANCE 4HE
USE OF DITHERING WILL RANDOMIZE THE SPURIOUS SIGNAL RESULTING IN PULSE TO PULSE VARIA
TIONS IN THE DIGITAL SEQUENCE OUTPUT TO THE $! CONVERTER A RESULT THAT IS UNDESIRABLE IN
PULSE DOPPLER APPLICATIONS
4RULY RANDOM ERRORS ARE NOT GENERATED BY THE DIGITAL PORTION OF THE $$3 4HE ONLY
NONDETERMINISTIC ERRORS ARE A RESULT OF THE $! CONVERTER PERFORMANCE IN THE FORM OF
INTERNAL CLOCK JITTER OR ADDITIVE THERMAL NOISE AND THE EFFECT OF THE PHASE NOISE ON THE
INPUT CLOCK SIGNAL
)NTERNAL $! CONVERTER CLOCK JITTER PRODUCES PHASE MODULATION OF THE OUTPUT SIGNAL
PROPORTIONAL TO THE OUTPUT FREQUENCY 3IMILARLY PHASE NOISE PRESENT ON THE CLOCK INPUT
SIGNAL IS TRANSFERRED TO THE OUTPUT SIGNAL REDUCED BY LOG FOUT FCLK D" $! CON
VERTER ADDITIVE THERMAL NOISE IS INDEPENDENT OF OUTPUT SIGNAL FREQUENCY AND PRODUCES
BOTH PHASE AND AMPLITUDE NOISE COMPONENTS
&REQUENCY -ULTIPLIERS &REQUENCY MULTIPLICATION ALLOWS SIGNALS TO BE INCREASED
IN BOTH FREQUENCY AND BANDWIDTH &REQUENCY MULTIPLICATION IS FREQUENTLY USED IN GEN
ERATING LOCAL OSCILLATOR #7 FREQUENCIES WHERE ALL FREQUENCIES ARE TYPICALLY BASED ON A
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LOW FREQUENCY REFERENCE 4HEY ALSO PROVIDE THE CAPABILITY FOR WIDE BANDWIDTH CHIRP
WAVEFORMS THAT CANNOT BE GENERATED DIRECTLY USING AVAILABLE $$3 DEVICES &REQUENCY
MULTIPLIERS OPERATE AS SHOWN IN &IGURE BY MULTIPLYING THE PHASE OF THE INPUT
SIGNAL BY THE INTEGER MULTIPLICATION FACTOR - 3INCE IN PRACTICE THE PROCESS TYPICALLY
INCLUDES SOME FORM OF LIMITING THE OUTPUT AMPLITUDE !T GENERALLY HAS A LOWER AMPLI
TUDE VARIATION THAN THE INPUT SIGNAL AMPLITUDE !T "ECAUSE THE MULTIPLICATION PROCESS MULTIPLIES UP THE VARIATIONS IN THE SIGNAL PHASE
BY FACTOR - INPUT PHASE NOISE AND SPURIOUS PHASE MODULATIONS ARE INCREASED BY
LOG- D" 3IMILARLY VARIATIONS IN THE PHASE OF THE SIGNAL AS A FUNCTION OF FRE
QUENCY ARE MULTIPLIED UP 4HESE VARIATIONS ARE PRODUCED DURING SIGNAL FILTERING AND
MAY BE PRESENT ON THE INPUT SIGNAL &OR CHIRP WAVEFORMS THIS CAN RESULT IN A SIGNIFICANT
DEGRADATION IN THE RANGE SIDELOBE PERFORMANCE !LSO PRACTICAL MULTIPLIERS MAY HAVE A
SIGNIFICANT PHASE VARIATION AS A FUNCTION OF FREQUENCY )F THE INPUT SIGNAL PHASE DISTOR
TION IS GIVEN BY
¤ P NF ³
E F A SIN ¥
¦ " ´µ
WHERE
A PEAK PHASE RIPPLE
" WAVEFORM INPUT BANDWIDTH
N NUMBER OF CYCLES OF PHASE RIPPLE
THE RESULTING OUTPUT DISTORTION PRODUCES RANGE SIDELOBES AT TIMES oN -" AND MAGNITUDE
LOG-A RELATIVE TO THE MAIN BEAM OF THE TARGET RETURN !S AN EXAMPLE GENERAT
ING A CHIRP WAVEFORM THAT HAS RANGE SIDELOBES BETTER THAN D" USING AN r MULTIPLIER
REQUIRES THAT THE INPUT SIGNAL HAS LESS THAN DEGREES PEAK PEAK PHASE RIPPLE
&REQUENCY MULTIPLIERS CAN BE IMPLEMENTED USING A VARIETY OF TECHNIQUES SUCH AS
USING STEP RECOVERY DIODE MULTIPLIERS OR USING PHASE LOCKED LOOPS 7HERE WIDE PERCENT
AGE BANDWIDTH AND FAST SETTLING IS REQUIRED THE MOST COMMON TECHNIQUE IS TO CASCADE A
SERIES OF FREQUENCY DOUBLERS OR LOW ORDER MULTIPLIERS 4HIS TYPE OF MULTIPLIER CAN ALSO
PROVIDE NEAR IDEAL PHASE NOISE PERFORMANCE BUT HAS SIGNIFICANT PHASE MODULATION AS A
FUNCTION OF FREQUENCY AS IT CONTAINS FILTERS BETWEEN EACH STAGE OF MULTIPLICATION
0REDISTORTION OF THE MULTIPLIER INPUT WAVEFORM IS OFTEN USED IN ORDER TO PRODUCE
WIDEBAND CHIRP WAVEFORMS WITH LOW RANGE SIDELOBE PERFORMANCE )F THE MULTIPLIER
IS CHARACTERIZED BY AN OUTPUT PHASE DISTORTION AS A FUNCTION OF INPUT FREQUENCY GIVEN
BY E V THEN A PREDISTORTION OF THE INPUT SIGNAL BY PHASE E V - WILL EQUALIZE THE
MULTIPLIER RESPONSE 0REDISTORTION CAN BE PERFORMED VERY PRECISELY BY ADDING THE PHASE
MODULATION VIA THE $$3 THAT IS USED TO GENERATE THE CHIRP WAVEFORM
7AVEFORM 5PCONVERSION 5PCONVERSION OF EXCITER WAVEFORMS IS SIMILAR TO
DOWNCONVERSION WITHIN THE RECEIVER !LSO SIMILAR PRACTICAL CONSIDERATIONS OF MIXER
SPURIOUS AND IMAGE REJECTION APPLY 4HE ONE SIGNIFICANT ADDITIONAL CHALLENGE IS THE
REJECTION OF THE ,/ LEAKAGE ,/ REJECTION TYPICALLY IMPOSES TIGHT FILTER REJECTION
REQUIREMENTS ON THE 2& FILTERS AND FOR WIDE TUNABLE RANGES SWITCHED FILTERS ARE
OFTEN REQUIRED
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!S DIGITAL PROCESSING HAS INCREASED IN SPEED AND DIGITAL HARDWARE HAS DECREASED IN COST
AND SIZE RADARS HAVE BECOME MORE AND MORE AUTOMATED SO THAT AUTOMATIC DETECTION
AND TRACKING !$4 SYSTEMS ARE ASSOCIATED WITH ALMOST ALL BUT THE SIMPLEST OF RADARS
)N THIS CHAPTER AUTOMATIC DETECTION AUTOMATIC TRACKING AND SENSOR INTEGRATION
TECHNIQUES FOR SURVEILLANCE RADARS ARE DISCUSSED )NCLUDED IN THE DISCUSSION ARE VARI
OUS NONCOHERENT INTEGRATORS THAT PROVIDE TARGET ENHANCEMENT THRESHOLDING TECHNIQUES
FOR FALSE ALARMS AND TARGET SUPPRESSION AND ALGORITHMS FOR ESTIMATING TARGET POSITION
AND RESOLVING TARGETS 4HEN AN OVERVIEW OF THE ENTIRE TRACKING SYSTEM IS GIVEN FOL
LOWED BY A DISCUSSION OF ITS VARIOUS COMPONENTS SUCH AS TRACK INITIATION CORRELATION
LOGIC TRACKING FILTER AND MANEUVER FOLLOWING LOGIC &INALLY THE CHAPTER CONCLUDES
WITH A DISCUSSION OF SENSOR INTEGRATION AND RADAR NETTING INCLUDING BOTH COLOCATED AND
MULTISITE SYSTEMS
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)N THE S -ARCUM APPLIED STATISTICAL DECISION THEORY TO RADAR AND LATER 3WERLING
EXTENDED THE WORK TO FLUCTUATING TARGETS 4HEY INVESTIGATED MANY OF THE STATISTICAL
PROBLEMS ASSOCIATED WITH THE NONCOHERENT DETECTION OF TARGETS IN GAUSSIAN NOISE
.OTE )F THE INPHASE AND QUADRATURE COMPONENTS ARE GAUSSIAN DISTRIBUTED THE ENVE
LOPE IS 2AYLEIGH DISTRIBUTED AND THE POWER IS EXPONENTIALLY DISTRIBUTED -ARCUMS
MOST IMPORTANT RESULT WAS THE GENERATION OF CURVES OF PROBABILITY OF DETECTION 0$ VER
SUS SIGNAL TO NOISE RATIO 3. FOR A DETECTOR THAT SUMS . ENVELOPE DETECTED SAMPLES
EITHER LINEAR OR SQUARE LAW UNDER THE ASSUMPTION OF EQUAL SIGNAL AMPLITUDES 7HEREAS
FOR A PHASED ARRAY THE EQUAL AMPLITUDE ASSUMPTION IS VALID FOR A ROTATING RADAR THE
RETURNED SIGNAL AMPLITUDE IS MODULATED BY THE ANTENNA PATTERN AS THE BEAM SWEEPS OVER
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THE TARGET -ANY AUTHORS HAVE INVESTIGATED VARIOUS DETECTORS COMPARING DETECTION PER
FORMANCE AND ANGULAR ESTIMATION RESULTS WITH OPTIMAL VALUES AND MANY OF THESE RESULTS
ARE PRESENTED LATER IN THIS SECTION
)N THE ORIGINAL WORK ON DETECTORS THE ENVIRONMENT WAS ASSUMED KNOWN AND HOMO
GENEOUS SO THAT FIXED THRESHOLDS COULD BE USED (OWEVER A REALISTIC RADAR ENVIRON
MENT EG CONTAINING LAND SEA AND RAIN WILL CAUSE AN EXORBITANT NUMBER OF FALSE
ALARMS FOR A FIXED THRESHOLD SYSTEM THAT DOES NOT UTILIZE EXCELLENT COHERENT PROCESSING
4HREE MAIN APPROACHESˆADAPTIVE THRESHOLDING NONPARAMETRIC DETECTORS AND CLUTTER
MAPSˆHAVE BEEN USED TO SOLVE THE NONCOHERENT FALSE ALARM PROBLEM "OTH ADAPTIVE
THRESHOLDING AND NONPARAMETRIC DETECTORS ARE BASED ON THE ASSUMPTION THAT HOMO
GENEITY EXISTS IN A SMALL REGION ABOUT THE RANGE CELL THAT IS BEING TESTED 4HE ADAP
TIVE THRESHOLDING METHOD ASSUMES THAT THE NOISE DENSITY IS KNOWN EXCEPT FOR A FEW
UNKNOWN PARAMETERS EG THE MEAN AND THE VARIANCE 4HE SURROUNDING REFERENCE
CELLS ARE THEN USED TO ESTIMATE THE UNKNOWN PARAMETERS AND A THRESHOLD BASED ON THE
ESTIMATED DENSITY IS OBTAINED .ONPARAMETRIC DETECTORS OBTAIN A CONSTANT FALSE ALARM
RATE #&!2 BY RANKING ORDERING THE SAMPLES FROM SMALLEST TO LARGEST THE TEST SAMPLE
WITH THE REFERENCE CELLS 5NDER THE HYPOTHESIS THAT ALL THE SAMPLES TEST AND REFER
ENCE ARE INDEPENDENT SAMPLES FROM AN UNKNOWN DENSITY FUNCTION THE RANK OF THE TEST
SAMPLE IS UNIFORM AND CONSEQUENTLY A THRESHOLD THAT YIELDS #&!2 CAN BE SET #LUTTER
MAPS STORE AN AVERAGE BACKGROUND LEVEL FOR EACH RANGE AZIMUTH CELL ! TARGET IS THEN
DECLARED IN A RANGE AZIMUTH CELL IF THE NEW VALUE EXCEEDS THE AVERAGE BACKGROUND LEVEL
BY A SPECIFIED AMOUNT
/PTIMAL $ETECTOR 4HE RADAR DETECTION PROBLEM IS A BINARY HYPOTHESIS
TESTING PROBLEM IN WHICH ( DENOTES THE HYPOTHESIS THAT NO TARGET IS PRESENT AND (
IS THE HYPOTHESIS THAT THE TARGET IS PRESENT 7HILE SEVERAL CRITERIA IE DEFINITIONS OF
OPTIMALITY CAN BE USED TO SOLVE THIS PROBLEM THE MOST APPROPRIATE FOR RADAR IS THE
.EYMAN 0EARSON 4HIS CRITERION MAXIMIZES THE PROBABILITY OF DETECTION 0$ FOR A GIVEN
PROBABILITY OF FALSE ALARM 0FA BY COMPARING THE LIKELIHOOD RATIO , DEFINED BY %Q TO AN APPROPRIATE THRESHOLD 4 THAT DETERMINES THE 0FA ! TARGET IS DECLARED PRESENT IF
, X
XN P X
P X
XN\ (
q4
XN \ ( WHERE PX x XN\( AND PX x XN\( ARE THE JOINT PROBABILITY DENSITY FUNCTIONS OF
THE N OBSERVATIONS XI UNDER THE CONDITIONS OF TARGET PRESENCE AND TARGET ABSENCE RESPEC
TIVELY &OR A LINEAR ENVELOPE DETECTOR THE SAMPLES HAVE A 2AYLEIGH DENSITY UNDER (
AND A 2ICEAN DENSITY UNDER ( AND THE LIKELIHOOD RATIO DETECTOR REDUCES TO
N
¤!X ³
“ ) ¥¦ SI I ´µ q 4
I WHERE ) IS THE MODIFIED "ESSEL FUNCTION OF ZERO ORDER R IS THE NOISE POWER AND !I IS
THE TARGET AMPLITUDE OF THE ITH PULSE AND IS PROPORTIONAL TO THE ANTENNA POWER PATTERN
&OR SMALL SIGNALS !I R THE DETECTOR REDUCES TO THE SQUARE LAW DETECTOR
N
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AND FOR LARGE SIGNALS !I R IT REDUCES TO THE LINEAR DETECTOR
N
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I &OR CONSTANT SIGNAL AMPLITUDE IE !I ! THESE DETECTORS WERE FIRST STUDIED BY
-ARCUM AND WERE STUDIED IN SUCCEEDING YEARS BY NUMEROUS OTHER PEOPLE 4HE MOST
IMPORTANT FACTS CONCERNING THESE DETECTORS ARE THE FOLLOWING
L
L
L
L
4HE DETECTION PERFORMANCES OF THE LINEAR AND SQUARE LAW DETECTORS ARE SIMILAR DIF
FERING ONLY BY LESS THAN D" OVER WIDE RANGES OF 0$ 0FA AND N
"ECAUSE THE SIGNAL RETURN OF A SCANNING RADAR IS MODULATED BY THE ANTENNA PATTERN TO
MAXIMIZE THE 3. WHEN INTEGRATING A LARGE NUMBER OF PULSES WITH NO WEIGHTING IE
!I ONLY OF THE PULSES BETWEEN THE HALF POWER POINTS SHOULD BE INTEGRATED
AND THE ANTENNA BEAM SHAPE FACTOR !"3& IS D" 4HE !"3& IS THE NUMBER BY
WHICH THE MIDBEAM 3. MUST BE REDUCED SO THAT THE DETECTION CURVES GENERATED FOR
EQUAL SIGNAL AMPLITUDES CAN BE USED FOR THE SCANNING RADAR
4HE COLLAPSING LOSS FOR THE LINEAR DETECTOR CAN BE SEVERAL DECIBELS GREATER THAN THE
LOSS FOR A SQUARE LAW DETECTOR SEE &IGURE 4HE COLLAPSING LOSS IS THE ADDITIONAL
SIGNAL REQUIRED TO MAINTAIN THE SAME 0$ AND 0FA WHEN UNWANTED NOISE SAMPLES ALONG
WITH THE DESIRED SIGNAL PLUS NOISE SAMPLES ARE INTEGRATED 4HE NUMBER OF SIGNAL SAM
PLES INTEGRATED IS . THE NUMBER OF EXTRANEOUS NOISE SAMPLES INTEGRATED IS - AND THE
COLLAPSING RATIO Q . - .
-OST AUTOMATIC DETECTORS ARE REQUIRED NOT ONLY TO DETECT TARGETS BUT ALSO TO MAKE ANGU
LAR ESTIMATES OF THE AZIMUTH POSITION OF THE TARGET 3WERLING CALCULATED THE STANDARD
DEVIATION OF THE OPTIMAL ESTIMATE BY USING THE #RAMER 2AO LOWER BOUND 4HE RESULTS
&)'52% #OLLAPSING LOSS VERSUS COLLAPSING RATIO FOR A PROBABILITY OF FALSE ALARM OF AND A PROB
ABILITY OF DETECTION OF AFTER ' 6 4RUNK Ú )%%% Ç°{
2!$!2 (!.$"//+
&)'52% #RAMER 2AO BOUND FOR ANGULAR ESTIMATES FOR FLUCTUATING AND NONFLUCTUATING TARGETS R
IS THE STANDARD DEVIATION OF THE ESTIMATION ERROR AND . IS THE NUMBER OF PULSES WITHIN THE D" BEAM
WIDTH WHICH IS P 4HE 3. IS THE VALUE AT THE CENTER OF THE BEAM AFTER 0 3WERLING Ú )%%% ARE SHOWN IN &IGURE WHERE A NORMALIZED STANDARD DEVIATION IS PLOTTED AGAINST THE
MIDBEAM 3. 4HIS RESULT HOLDS FOR A MODERATE OR LARGE NUMBER OF PULSES INTEGRATED
AND THE OPTIMAL ESTIMATE INVOLVES FINDING THE LOCATION WHERE THE CORRELATION OF THE
RETURNED SIGNAL AND THE DERIVATIVE OF THE ANTENNA PATTERN IS ZERO !LTHOUGH THIS ESTI
MATE IS RARELY IMPLEMENTED ITS PERFORMANCE IS APPROACHED BY SIMPLE ESTIMATES
0RACTICAL $ETECTORS -ANY DIFFERENT DETECTORS OFTEN CALLED INTEGRATORS ARE USED
TO ACCUMULATE THE RADAR RETURNS AS THE RADAR SWEEPS BY A TARGET ! FEW OF THE MOST
COMMON DETECTORS ARE SHOWN IN &IGURE 4HE FEEDBACK INTEGRATOR AND TWO POLE
FILTER ARE DETECTORS THAT MINIMIZE THE DATA STORAGE REQUIREMENTS 7HILE THESE DETEC
TORS MAY STILL BE FOUND IN OLDER RADARS THEY PROBABLY WOULD NOT BE IMPLEMENTED IN
NEW RADARS AND WILL NOT BE DISCUSSED IN THIS EDITION 4HOUGH ALL THE DETECTORS ARE
SHOWN IN &IGURE AS BEING CONSTRUCTED WITH SHIFT REGISTERS THEY WOULD NORMALLY BE
IMPLEMENTED WITH RANDOM ACCESS MEMORY 4HE INPUT TO THESE DETECTORS CAN BE LINEAR
VIDEO SQUARE LAW VIDEO OR LOG VIDEO "ECAUSE LINEAR VIDEO IS PROBABLY THE MOST COM
MONLY USED THE ADVANTAGES AND DISADVANTAGES OF THE VARIOUS DETECTORS WILL BE STATED
FOR THIS VIDEO
-OVING 7INDOW 4HE MOVING WINDOW IN &IGURE A PERFORMS A RUNNING SUM OF
N PULSES IN EACH RANGE CELL
3I 3I XI
XI N
WHERE 3I IS THE SUM AT THE ITH PULSE OF THE LAST N PULSES AND XI IS THE ITH PULSE 4HE PER
FORMANCE OF THIS DETECTOR FOR N y IS ONLY D" WORSE THAN THE OPTIMAL DETECTOR
GIVEN BY %Q 4HE DETECTION PERFORMANCE CAN BE OBTAINED BY USING AN !"3& OF
D" AND STANDARD DETECTION CURVES FOR EQUAL AMPLITUDE PULSES 4HE ANGULAR ESTIMATE
THAT IS OBTAINED BY EITHER TAKING THE MAXIMUM VALUE OF THE RUNNING SUM OR TAKING THE
MIDPOINT BETWEEN THE FIRST AND LAST CROSSINGS OF THE DETECTION THRESHOLD HAS A BIAS OF
N PULSES WHICH IS EASILY CORRECTED 4HE STANDARD DEVIATION OF THE ESTIMATION ERROR OF
BOTH THESE ESTIMATORS IS ABOUT PERCENT HIGHER THAN THE OPTIMAL ESTIMATE SPECIFIED
!54/-!4)# $%4%#4)/. 42!#+).' !.$ 3%.3/2 ).4%'2!4)/.
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&)'52% "LOCK DIAGRAMS OF VARIOUS DETECTORS 4HE LETTER # INDICATES
A COMPARISON S IS A DELAY AND LOOPS INDICATE FEEDBACK FROM ' 6 4RUNK
BY THE #RAMER 2AO BOUND ! DISADVANTAGE OF THIS DETECTOR IS THAT IT IS SUSCEPTIBLE TO
INTERFERENCE THAT IS ONE LARGE SAMPLE FROM INTERFERENCE CAN CAUSE A DETECTION 4HIS
PROBLEM CAN BE MINIMIZED BY USING SOFT LIMITING
4HE DETECTION PERFORMANCE DISCUSSED PREVIOUSLY IS BASED ON THE ASSUMPTION THAT THE
TARGET IS CENTERED IN THE MOVING WINDOW )N THE REAL SITUATION THE RADAR SCANS OVER THE
TARGET AND DECISIONS THAT ARE HIGHLY CORRELATED ARE MADE AT EVERY PULSE (ANSEN ANA
LYZED THIS SITUATION FOR . AND PULSES AND CALCULATED THE DETECTION THRESH
OLDS SHOWN IN &IGURE THE DETECTION PERFORMANCE SHOWN IN &IGURE AND THE
ANGULAR ACCURACY SHOWN IN &IGURE #OMPARING (ANSENS SCANNING CALCULATION WITH
THE SINGLE POINT CALCULATION ONE CONCLUDES THAT ABOUT D" OF IMPROVEMENT IS OBTAINED
BY MAKING A DECISION AT EVERY PULSE 4HE ANGULAR ERROR OF THE BEAM SPLITTING PROCEDURE
IS ABOUT PERCENT GREATER THAN THE OPTIMAL ESTIMATE &OR LARGE SIGNAL TO NOISE RATIOS
THE ACCURACY RMS ERROR OF THE BEAM SPLITTING AND MAXIMUM RETURN PROCEDURES WILL BE
LIMITED BY THE PULSE SPACING AND WILL APPROACH
S Q} $Q Ç°È
2!$!2 (!.$"//+
&)'52% 3INGLE SWEEP FALSE ALARM PROBABILITY 0FA VERSUS THRESHOLD FOR MOVING WINDOW
4HE NOISE IS 2AYLEIGH DISTRIBUTED WITH R AFTER 6 ' (ANSEN Ú )%%% WHERE $P IS THE ANGULAR ROTATION BETWEEN TRANSMITTED PULSES #ONSEQUENTLY IF THE NUM
BER OF PULSES PER BEAMWIDTH IS SMALL THE ANGULAR ACCURACY WILL BE POOR &OR INSTANCE
IF PULSES ARE SEPARATED BY BEAMWIDTH S Q} IS BOUNDED BY BEAMWIDTHS
(OWEVER IMPROVED ACCURACY CAN BE OBTAINED BY USING THE AMPLITUDES OF THE RADAR
RETURNS !N ACCURATE ESTIMATE OF THE TARGET ANGLE IS GIVEN BY
Q} Q
$Q
N ! !
A$Q
&)'52% $ETECTION PERFORMANCE OF THE ANALOG MOVING WINDOW DETECTOR FOR THE NO
FADING CASE AFTER 6 ' (ANSEN Ú )%%% !54/-!4)# $%4%#4)/. 42!#+).' !.$ 3%.3/2 ).4%'2!4)/.
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&)'52% !NGULAR ACCURACY OBTAINED WITH BEAM SPLITTING ESTIMATION PROCEDURE
FOR THE NO FADING CASE "ROKEN LINE CURVES ARE LOWER BOUNDS DERIVED BY 3WERLING AND
POINTS SHOWN ARE SIMULATION RESULTS AFTER 6 ' (ANSEN Ú )%%% WHERE
A BEAMWIDTH AND ! AND ! ARE THE TWO LARGEST AMPLITUDES OF THE RETURNED SAMPLES AND OCCUR AT
ANGLES P AND P P $P RESPECTIVELY "ECAUSE THE ESTIMATE SHOULD LIE BETWEEN P
AND P AND %Q WILL NOT ALWAYS YIELD SUCH AN ESTIMATE Q} SHOULD BE SET EQUAL TO P
IF Q} P AND Q} SHOULD BE EQUAL TO P IF Q} P 4HE ACCURACY OF THIS ESTIMATOR IS GIVEN
IN &IGURE FOR THE CASE OF N PULSES PER BEAMWIDTH 4HIS ESTIMATION PROCEDURE
CAN ALSO BE USED TO ESTIMATE THE ELEVATION ANGLE OF A TARGET IN MULTIBEAM SYSTEMS WHERE
P AND P ARE THE ELEVATION POINTING ANGLES OF ADJACENT BEAMS AND ! AND ! ARE THE
CORRESPONDING AMPLITUDES
"INARY )NTEGRATOR 4HE BINARY INTEGRATOR IS ALSO KNOWN AS THE DUAL THRESHOLD DETEC
TOR - OUT OF . DETECTOR OR RANK DETECTOR SEE h.ONPARAMETRIC $ETECTORS v LATER IN THIS
SECTION AND NUMEROUS INDIVIDUALS HAVE STUDIED ITn !S SHOWN IN &IGURE D THE
INPUT SAMPLES ARE QUANTIZED TO OR DEPENDING ON WHETHER OR NOT THEY ARE LESS THAN
A THRESHOLD 4 4HE LAST . ZEROS AND ONES ARE SUMMED WITH A MOVING WINDOW AND
COMPARED WITH A SECOND THRESHOLD 4 - &OR LARGE . THE DETECTION PERFORMANCE OF
THIS DETECTOR IS APPROXIMATELY D" LESS THAN THE MOVING WINDOW INTEGRATOR BECAUSE
OF THE HARD LIMITING OF THE DATA AND THE ANGULAR ESTIMATION ERROR IS ABOUT PERCENT
GREATER THAN THE #RAMER 2AO LOWER BOUND 3CHWARTZ SHOWED THAT WITHIN D" THE
OPTIMAL VALUE OF - FOR MAXIMUM 0$ IS GIVEN BY
- .
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2!$!2 (!.$"//+
&)'52% !NGULAR ACCURACY FOR TWO PULSES SEPARATED BY BEAMWIDTHS
WHEN 0FA AND 0$ 4HE OPTIMAL VALUE OF 0N THE PROBABILITY OF
EXCEEDING 4 WHEN ONLY NOISE IS PRESENT WAS CALCULATED BY $ILLARD AND IS SHOWN IN
&IGURE 4HE CORRESPONDING THRESHOLD 4 IS
4 R LN 0.
! COMPARISON OF THE OPTIMAL BEST VALUE OF - BINARY INTEGRATOR WITH VARIOUS OTHER
PROCEDURES IS GIVEN IN &IGURES AND FOR 0$ AND RESPECTIVELY
4HE BINARY INTEGRATOR IS USED IN MANY RADARS BECAUSE IT IS EASILY IMPLEMENTED
IT IGNORES INTERFERENCE SPIKES THAT CAUSE TROUBLE WITH INTEGRATORS THAT DIRECTLY USE
SIGNAL AMPLITUDE AND IT WORKS EXTREMELY WELL WHEN THE NOISE HAS A NON 2AYLEIGH
DENSITY &OR . COMPARISON OF THE OPTIMAL BINARY INTEGRATOR OUT OF ANOTHER
BINARY INTEGRATOR OUT OF AND THE MOVING WINDOW DETECTOR IN LOG NORMAL INTERFER
ENCE AN EXAMPLE OF A NON 2AYLEIGH DENSITY WHERE THE LOG OF THE RETURN HAS A GAUSSIAN
DENSITY IS SHOWN IN &IGURE 4HE OPTIMAL BINARY INTEGRATOR IS MUCH BETTER THAN
THE MOVING WINDOW INTEGRATOR 4HE OPTIMAL VALUES FOR LOG NORMAL INTERFERENCE WERE
CALCULATED BY 3CHLEHER AND ARE - AND FOR . AND RESPECTIVELY
"ATCH 0ROCESSOR 4HE BATCH PROCESSOR &IGURE E IS VERY USEFUL WHEN A LARGE
NUMBER OF PULSES ARE WITHIN THE D" BEAMWIDTH )F +. PULSES ARE IN THE D" BEAM
WIDTH + PULSES ARE SUMMED BATCHED AND EITHER A OR A IS DECLARED DEPENDING
ON WHETHER OR NOT THE BATCH IS LESS THAN A THRESHOLD 4 4HE LAST . ZEROS AND ONES ARE
!54/-!4)# $%4%#4)/. 42!#+).' !.$ 3%.3/2 ).4%'2!4)/.
&)'52% /PTIMUM VALUES OF 0. AS A FUNCTION OF THE SAMPLE SIZE N AND THE PROBABILITY OF FALSE
ALARM @ 2ICEAN DISTRIBUTION WITH 3. D" PER PULSE AFTER ' - $ILLARD Ú )%%% &)'52% #OMPARISON OF BINARY INTEGRATOR - OUT OF . WITH OTHER
INTEGRATION METHODS 0FA 0$ AFTER - 3CHWARTZ Ú )%%%
Ç°™
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2!$!2 (!.$"//+
&)'52% #OMPARISON OF BINARY INTEGRATOR - OUT OF . WITH
OTHER INTEGRATION METHODS 0FA 0$ AFTER - 3CHWARTZ
Ú )%%% SUMMED AND COMPARED WITH A SECOND THRESHOLD - !N ALTERNATIVE VERSION OF THIS DETEC
TOR IS TO PUT THE BATCH AMPLITUDES THROUGH A MOVING WINDOW DETECTOR
4HE BATCH PROCESSOR LIKE THE BINARY INTEGRATOR IS EASILY IMPLEMENTED IGNORES INTER
FERENCE SPIKES AND WORKS EXTREMELY WELL WHEN THE NOISE HAS A NON 2AYLEIGH DENSITY
&URTHERMORE THE BATCH PROCESSOR REQUIRES LESS STORAGE DETECTS BETTER AND ESTIMATES
&)'52% #OMPARISON OF VARIOUS DETECTORS IN LOG NORMAL R D"
INTERFERENCE . 0FA AFTER $ # 3CHLEHER Ú )%%% !54/-!4)# $%4%#4)/. 42!#+).' !.$ 3%.3/2 ).4%'2!4)/.
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ANGLES MORE ACCURATELY THAN THE BINARY INTEGRATOR &OR INSTANCE IF THERE WERE PULSES
ON TARGET ONE COULD BATCH PULSES QUANTIZE THIS RESULT TO A OR A AND DECLARE A TARGET
WITH A OUT OF OR OUT OF BINARY INTEGRATOR 4HE DETECTION PERFORMANCE OF THE
BATCH PROCESSOR FOR A LARGE NUMBER OF PULSES INTEGRATED IS APPROXIMATELY D" WORSE
THAN THE MOVING WINDOW 4HE BATCH PROCESSOR HAS BEEN SUCCESSFULLY IMPLEMENTED BY
THE !PPLIED 0HYSICS ,ABORATORY OF 4HE *OHNS (OPKINS 5NIVERSITY 4O OBTAIN AN ACCU
RATE AZIMUTH ESTIMATE Q} APPROXIMATELY PERCENT GREATER THAN THE LOWER BOUND
£ "IQI
Q} £ "I
IS USED WHERE "I IS THE BATCH AMPLITUDE AND PI IS THE AZIMUTH ANGLE CORRESPONDING TO
THE CENTER OF THE BATCH
&ALSE !LARM #ONTROL )N THE PRESENCE OF CLUTTER IF FIXED THRESHOLDS ARE USED WITH
THE PREVIOUSLY DISCUSSED INTEGRATORS AN ENORMOUS NUMBER OF DETECTIONS WILL OCCUR AND
WILL SATURATE AND DISRUPT THE TRACKING COMPUTER ASSOCIATED WITH THE RADAR SYSTEM &OUR
IMPORTANT FACTS SHOULD BE NOTED
L
L
L
L
! TRACKING SYSTEM SHOULD BE ASSOCIATED WITH THE AUTOMATIC DETECTION SYSTEM THE
ONLY EXCEPTION IS WHEN ONE DISPLAYS MULTIPLE SCANS OF DETECTIONS 4HE 0FA OF THE DETECTOR SHOULD BE MATCHED TO THE TRACKING SYSTEM TO PRODUCE THE
OVERALL LOWEST 3. REQUIRED TO FORM A TRACK WITHOUT INITIATING TOO MANY FALSE TRACKS
SEE &IGURE LATER IN THIS CHAPTER 2ANDOM FALSE ALARMS AND UNWANTED TARGETS EG STATIONARY TARGETS ARE NOT A PROB
LEM IF THEY ARE REMOVED BY THE TRACKING SYSTEM
3CAN TO SCAN PROCESSING CAN BE USED TO REMOVE STATIONARY POINT CLUTTER OR MOVING
TARGET INDICATION -4) CLUTTER RESIDUES
/NE CAN LIMIT THE NUMBER OF FALSE ALARMS WITH A FIXED THRESHOLD SYSTEM BY SETTING
A VERY HIGH THRESHOLD 5NFORTUNATELY THIS WOULD REDUCE TARGET SENSITIVITY IN REGIONS OF
LOW NOISE CLUTTER RETURN 4HREE MAIN APPROACHESˆADAPTIVE THRESHOLD NONPARAMET
RIC DETECTORS AND CLUTTER MAPSˆHAVE BEEN USED TO REDUCE THE FALSE ALARM PROBLEM
!DAPTIVE THRESHOLDING AND NONPARAMETRIC DETECTORS ASSUME THAT THE SAMPLES IN THE
RANGE CELLS SURROUNDING THE TEST CELL CALLED REFERENCE CELLS ARE INDEPENDENT AND IDENTI
CALLY DISTRIBUTED &URTHERMORE IT IS USUALLY ASSUMED THAT THE TIME SAMPLES ARE INDEPEN
DENT "OTH KINDS OF DETECTORS TEST WHETHER THE TEST CELL HAS A RETURN SUFFICIENTLY LARGER
THAN THE REFERENCE CELLS #LUTTER MAPS ALLOW VARIATION IN SPACE BUT THE CLUTTER MUST BE
STATIONARY OVER SEVERAL TYPICALLY TO SCANS #LUTTER MAPS STORE AN AVERAGE BACK
GROUND LEVEL FOR EACH RANGE AZIMUTH CELL ! TARGET IS THEN DECLARED IN A RANGE AZIMUTH
CELL IF THE NEW VALUE EXCEEDS THE AVERAGE BACKGROUND LEVEL BY A SPECIFIED AMOUNT
!DAPTIVE 4HRESHOLDING 4HE BASIC ASSUMPTION OF THE ADAPTIVE THRESHOLDING TECH
NIQUE IS THAT THE PROBABILITY DENSITY OF THE NOISE IS KNOWN EXCEPT FOR A FEW UNKNOWN
PARAMETERS 4HE SURROUNDING REFERENCE CELLS ARE THEN USED TO ESTIMATE THE UNKNOWN
PARAMETERS AND A THRESHOLD BASED ON THE ESTIMATED PARAMETERS IS OBTAINED 4HE SIM
PLEST ADAPTIVE DETECTOR SHOWN IN &IGURE IS THE CELL AVERAGE #&!2 CONSTANT
FALSE ALARM RATE INVESTIGATED BY &INN AND *OHNSON )F THE NOISE HAS A 2AYLEIGH DEN
SITY PX X EXP XR R ONLY THE PARAMETER R R IS THE NOISE POWER NEEDS TO
BE ESTIMATED AND THE THRESHOLD IS OF THE FORM 4 +3XI +N P S} WHERE S} IS THE
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2!$!2 (!.$"//+
&)'52% #ELL AVERAGING #&!2 4HE LETTER # INDICATES A COMPARISON FROM ' 6 4RUNK
ESTIMATE OF R (OWEVER SINCE 4 IS SET BY AN ESTIMATE S} IT HAS SOME ERROR AND MUST BE
SLIGHTLY LARGER THAN THE THRESHOLD THAT ONE WOULD USE IF R WERE KNOWN EXACTLY A PRIORI
4HE RAISED THRESHOLD CAUSES A LOSS IN TARGET SENSITIVITY AND IS REFERRED TO AS A #&!2
LOSS 4HIS LOSS HAS BEEN CALCULATED AND IS SUMMARIZED IN 4ABLE !S CAN BE SEEN
FOR A SMALL NUMBER OF REFERENCE CELLS THE LOSS IS LARGE BECAUSE OF THE POOR ESTIMATE OF
R #ONSEQUENTLY ONE WOULD PREFER TO USE A LARGE NUMBER OF REFERENCE CELLS (OWEVER
IF ONE DOES THIS THE HOMOGENEITY ASSUMPTION IE ALL THE REFERENCE CELLS ARE STATISTI
CALLY SIMILAR MIGHT BE VIOLATED ! GOOD RULE OF THUMB IS TO USE ENOUGH REFERENCE CELLS
SO THAT THE #&!2 LOSS IS BELOW D" AND AT THE SAME TIME NOT LET THE REFERENCE CELLS
EXTEND OVER A RANGE INTERVAL THAT VIOLATES THE HOMOGENOUS BACKGROUND ASSUMPTION
5NFORTUNATELY FOR A SPECIFIC RADAR THIS MIGHT NOT BE FEASIBLE
)F THERE IS UNCERTAINTY ABOUT WHETHER OR NOT THE NOISE IS 2AYLEIGH DISTRIBUTED IT IS
BETTER TO THRESHOLD INDIVIDUAL PULSES AND USE A BINARY INTEGRATOR AS SHOWN IN &IGURE 4HIS DETECTOR IS TOLERANT OF VARIATIONS IN THE NOISE DENSITY BECAUSE BY SETTING + TO YIELD
A WITH PROBABILITY A 0FA y CAN BE OBTAINED BY USING A OUT OF DETECTOR
7HILE NOISE MAY BE NON 2AYLEIGH IT WILL PROBABLY BE VERY 2AYLEIGH LIKE OUT TO THE
4!",% #&!2 ,OSS FOR 0FA AND 0$ .UMBER OF 0ULSES
)NTEGRATED
,OSS FOR 6ARIOUS .UMBERS OF 2EFERENCE #ELLS IN D"
AFTER 2 , -ITCHELL AND * & 7ALKER Ú )%%% c
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&)'52% )MPLEMENTATION OF A BINARY INTEGRATOR 4HE LETTER # INDICATES A COMPARISON
FROM ' 6 4RUNK
TENTH PERCENTILE &URTHERMORE ONE CAN USE FEEDBACK BASED ON SEVERAL SCANS OF DATA
TO CONTROL + IN ORDER TO MAINTAIN A DESIRED 0FA ON EITHER A SCAN OR A SECTOR BASIS 4HIS
DEMONSTRATES A GENERAL RULE TO MAINTAIN A LOW 0FA IN VARIOUS ENVIRONMENTS ADAPTIVE
THRESHOLDING SHOULD BE PLACED IN FRONT OF THE INTEGRATOR
)F THE NOISE POWER VARIES FROM PULSE TO PULSE AS IT WOULD IN JAMMING WHEN FRE
QUENCY AGILITY IS EMPLOYED ONE MUST #&!2 EACH PULSE AND THEN INTEGRATE 7HILE THE
BINARY INTEGRATOR PERFORMS THIS TYPE OF #&!2 ACTION ANALYSIS HAS VERIFIED THAT THE
RATIO DETECTOR SHOWN IN &IGURE IS A BETTER DETECTOR 4HE RATIO DETECTOR SUMS SIGNAL
TO NOISE RATIOS AND IS SPECIFIED BY
N
X J
I
£ M
I §X J K
M £ © I
K XI J K ¶¸
WHERE XIJ IS THE ITH ENVELOPE DETECTED PULSE IN THE JTH RANGE CELL AND M IS THE NUMBER
OF REFERENCE CELLS 4HE DENOMINATOR IS THE MAXIMUM LIKELIHOOD ESTIMATE OF S I THE
NOISE POWER PER PULSE 4HE RATIO DETECTOR WILL DETECT TARGETS EVEN THOUGH ONLY A FEW
RETURNED PULSES HAVE A HIGH SIGNAL TO NOISE RATIO 5NFORTUNATELY THIS WILL ALSO CAUSE
THE RATIO DETECTOR TO DECLARE FALSE ALARMS IN THE PRESENCE OF NARROW PULSE INTERFERENCE
4O REDUCE THE NUMBER OF FALSE ALARMS WHEN NARROW PULSE INTERFERENCE IS PRESENT THE
INDIVIDUAL POWER RATIOS CAN BE SOFT LIMITED TO A SMALL ENOUGH VALUE SO THAT INTERFER
ENCE WILL CAUSE ONLY A FEW FALSE ALARMS ! COMPARISON OF THE RATIO DETECTOR WITH OTHER
COMMONLY USED DETECTORS IS SHOWN IN &IGURES AND FOR NONFLUCTUATING AND
FLUCTUATING TARGETS ! TYPICAL PERFORMANCE IN SIDELOBE JAMMING WHEN THE JAMMING
LEVEL VARIES BY D" PER PULSE IS SHOWN IN &IGURE "Y EMPLOYING A SECOND TEST TO
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&)'52% 2ATIO DETECTOR FROM ' 6 4RUNK
IDENTIFY THE PRESENCE OF NARROW PULSE INTERFERENCE A DETECTION PERFORMANCE APPROXI
MATELY HALFWAY BETWEEN THE LIMITING AND NONLIMITING RATIO DETECTORS CAN BE OBTAINED
)F THE NOISE SAMPLES HAVE A NON 2AYLEIGH DENSITY SUCH AS THE CHI SQUARE DENSITY OR
LOG NORMAL DENSITY IT IS NECESSARY TO ESTIMATE MORE THAN ONE PARAMETER AND THE ADAP
TIVE DETECTOR IS MORE COMPLICATED 5SUALLY TWO PARAMETERS ARE ESTIMATED THE MEAN
AND THE VARIANCE AND A THRESHOLD OF THE FORM 4 M} +S} IS USED 4HE SAMPLED MEAN
IS EASILY OBTAINED (OWEVER THE USUAL ESTIMATE OF THE STANDARD DEVIATION
WHERE
§
S} ¨ £ XI
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M} £ XI
.
&)'52% #URVES OF PROBABILITY OF DETECTION VERSUS SIGNAL TO NOISE RATIO PER PULSE FOR THE
CELL AVERAGING #&!2 RATIO DETECTORS LOG INTEGRATOR AND BINARY INTEGRATOR NONFLUCTUATING TARGET
. M REFERENCE CELLS AND 0FA FROM ' 6 4RUNK AND 0 + (UGHES
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!54/-!4)# $%4%#4)/. 42!#+).' !.$ 3%.3/2 ).4%'2!4)/.
&)'52% #URVES OF PROBABILITY OF DETECTION VERSUS SIGNAL TO NOISE RATIO FOR THE CELL
AVERAGING #&!2 RATIO DETECTORS LOG INTEGRATOR AND BINARY INTEGRATOR 2AYLEIGH PULSE TO PULSE
FLUCTUATING TARGET . M REFERENCE CELLS AND 0FA FROM ' 6 4RUNK AND 0 +
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IS SOMEWHAT MORE DIFFICULT TO IMPLEMENT CONSEQUENTLY THE MEAN DEVIATE DEFINED BY
S ! £ \ XI
M} \
IS SOMETIMES USED BECAUSE OF ITS EASE OF IMPLEMENTATION AND BECAUSE IT IS MORE ROBUST
)T SHOULD BE NOTED THAT THE #&!2 LOSS ASSOCIATED WITH A TWO PARAMETER THRESHOLD IS
LARGER THAN THOSE ASSOCIATED WITH A ONE PARAMETER THRESHOLD SEE 4ABLE AND FOR
THAT REASON A TWO PARAMETER THRESHOLD IS RARELY USED
&)'52% #URVES OF PROBABILITY OF DETECTION VERSUS SIGNAL TO NOISE RATIO FOR THE CELL
AVERAGING #&!2 RATIO DETECTORS LOG INTEGRATOR AND BINARY INTEGRATOR 2AYLEIGH PULSE TO PULSE
FLUCTUATIONS M REFERENCE CELLS 0FA AND MAXIMUM JAMMING TO NOISE RATIO D"
FROM ' 6 4RUNK AND 0 + (UGHES
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2!$!2 (!.$"//+
)F THE NOISE SAMPLES ARE CORRELATED NOTHING CAN BE DONE TO THE BINARY INTEGRATOR TO
YIELD A LOW 0FA 4HUS IT SHOULD NOT BE USED IN THIS SITUATION (OWEVER IF THE CORRELATION
TIME IS LESS THAN A BATCHING INTERVAL THE BATCH PROCESSOR WILL YIELD A LOW 0FA WITHOUT
MODIFICATIONS
4ARGET 3UPPRESSION 4ARGET SUPPRESSION IS THE LOSS IN DETECTABILITY CAUSED BY OTHER
TARGETS OR CLUTTER RESIDUES IN THE REFERENCE CELLS "ASICALLY THERE ARE TWO APPROACHES TO
SOLVING THIS PROBLEM REMOVE LARGE RETURN FROM THE CALCULATION OF THE THRESHOLDn OR
DIMINISH THE EFFECTS OF LARGE RETURNS BY EITHER LIMITING OR USING LOG VIDEO 4HE TECHNIQUE
THAT SHOULD BE USED IS A FUNCTION OF THE PARTICULAR RADAR SYSTEM AND ITS ENVIRONMENT
2ICKARD AND $ILLARD PROPOSED A CLASS OF DETECTORS $+ WHERE THE + LARGEST SAMPLES
ARE CENSORED REMOVED FROM THE REFERENCE CELLS ! COMPARISON OF $ NO CENSORING
WITH $ AND $ FOR A 3WERLING TARGET AND A SINGLE SQUARE LAW DETECTED PULSE IS SHOWN
IN &IGURE WHERE . IS THE NUMBER OF REFERENCE CELLS A IS THE RATIO OF THE POWER OF
THE INTERFERING TARGET TO THE TARGET IN THE TEST CELL AND THE BRACKETED PAIR M N INDICATES
THE 3WERLING MODELS OF THE TARGET AND THE INTERFERING TARGET RESPECTIVELY !S SHOWN
IN &IGURE WHEN ONE HAS AN INTERFERING TARGET THE 0$ DOES NOT APPROACH AS 3.
INCREASES !NOTHER APPROACH THAT CENSORS SAMPLES IN THE REFERENCE CELL IF THEY EXCEED
A THRESHOLD IS BRIEFLY DISCUSSED IN THE h.ONPARAMETRIC $ETECTORv SUBSECTION
&INN INVESTIGATED THE PROBLEM OF THE REFERENCE CELLS SPANNING TWO CONTINUOUS DIF
FERENT hNOISEv FIELDS EG THERMAL NOISE SEA CLUTTER ETC /N THE BASIS OF THE SAMPLES
HE ESTIMATED THE STATISTICAL PARAMETERS OF THE TWO NOISE FIELDS AND THE SEPARATION POINT
BETWEEN THEM 4HEN ONLY THOSE REFERENCE CELLS THAT ARE IN THE NOISE FIELD CONTAINING
THE TEST CELL ARE USED TO CALCULATE THE ADAPTIVE THRESHOLD
!N ALTERNATIVE APPROACH FOR INTERFERING TARGETS IS TO USE LOG VIDEO "Y TAKING THE
LOG LARGE SAMPLES IN THE REFERENCE CELLS WILL HAVE LESS EFFECT THAN LINEAR VIDEO ON THE
THRESHOLD 4HE LOSS ASSOCIATED WITH USING LOG VIDEO RATHER THAN LINEAR VIDEO IS D"
&)'52% $ETECTION PROBABILITY VERSUS 3.2 FOR A 3WERLING #ASE PRIMARY TARGET
AFTER * 4 2ICKARD AND ' - $ILLARD Ú )%%% !54/-!4)# $%4%#4)/. 42!#+).' !.$ 3%.3/2 ).4%'2!4)/.
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&)'52% "LOCK DIAGRAM OF CELL AVERAGING LOG #&!2 RECEIVER AFTER 6 ' (ANSEN
AND * 2 7ARD Ú )%%% FOR PULSES INTEGRATED AND D" FOR PULSES INTEGRATED !N IMPLEMENTATION
OF THE LOG #&!2 IS SHOWN IN &IGURE )N MANY SYSTEMS THE ANTILOG SHOWN IN
&IGURE IS NOT TAKEN 4O MAINTAIN THE SAME #&!2 LOSS AS FOR LINEAR VIDEO THE
NUMBER OF REFERENCE CELLS -LOG FOR THE LOG #&!2 SHOULD EQUAL
-LOG -LIN
WHERE -LIN IS THE NUMBER OF REFERENCE CELLS FOR LINEAR VIDEO 4HE EFFECT OF TARGET SUPPRES
SION WITH LOG VIDEO IS DISCUSSED LATER IN THIS SECTION SEE 4ABLE LATER IN THE CHAPTER .ONPARAMETRIC $ETECTORS 5SUALLY NONPARAMETRIC DETECTORS OBTAIN #&!2 BY RANK
ING THE TEST SAMPLE WITH THE REFERENCE CELLS 2ANKING MEANS THAT ONE ORDERS THE
SAMPLES FROM THE SMALLEST TO THE LARGEST AND REPLACES THE SMALLEST WITH RANK THE NEXT
SMALLEST WITH RANK AND THE LARGEST WITH RANK N 5NDER THE HYPOTHESIS THAT
ALL THE SAMPLES ARE INDEPENDENT SAMPLES FROM AN UNKNOWN DENSITY FUNCTION THE TEST
SAMPLE HAS EQUAL PROBABILITY OF TAKING ON ANY OF THE N VALUES &OR INSTANCE REFERRING TO
THE RANKER IN &IGURE THE TEST CELL IS COMPARED WITH OF ITS NEIGHBORS 3INCE IN THE
SET OF SAMPLES THE TEST SAMPLE HAS EQUAL PROBABILITY OF BEING THE SMALLEST SAMPLE OR
EQUIVALENTLY ANY OTHER RANK THE PROBABILITY THAT THE TEST SAMPLE TAKES ON VALUES IS ! SIMPLE RANK DETECTOR IS CONSTRUCTED BY COMPARING THE RANK WITH A THRESHOLD
+ AND GENERATING A IF THE RANK IS LARGER A OTHERWISE 4HE S AND S ARE SUMMED IN A
MOVING WINDOW 4HIS DETECTOR INCURS A #&!2 LOSS OF ABOUT D" BUT ACHIEVES A FIXED
0FA FOR ANY UNKNOWN NOISE DENSITY AS LONG AS THE TIME SAMPLES ARE INDEPENDENT 4HIS
DETECTOR WAS INCORPORATED INTO THE !243 ! POSTPROCESSOR USED IN CONJUNCTION WITH THE
&EDERAL !VIATION !DMINISTRATION AIRPORT SURVEILLANCE RADAR !32 4HE MAJOR SHORTCOM
ING OF THIS DETECTOR IS THAT IT IS FAIRLY SUSCEPTIBLE TO TARGET SUPPRESSION EG IF A LARGE
TARGET IS IN THE REFERENCE CELLS THE TEST CELL CANNOT RECEIVE THE HIGHEST RANKS )F THE TIME SAMPLES ARE CORRELATED THE RANK DETECTOR WILL NOT YIELD #&!2 ! MOD
IFIED RANK DETECTOR CALLED THE MODIFIED GENERALIZED SIGN TEST -'34 MAINTAINS
A LOW 0FA AND IS SHOWN IN &IGURE 4HIS DETECTOR CAN BE DIVIDED INTO THREE PARTS
A RANKER AN INTEGRATOR IN THIS CASE A TWO POLE FILTER AND A THRESHOLD DECISION
PROCESS ! TARGET IS DECLARED WHEN THE INTEGRATED OUTPUT EXCEEDS TWO THRESHOLDS
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&)'52% 2ANK DETECTOR OUTPUT OF A COMPARATOR # IS EITHER A ZERO OR A
ONE FROM ' 6 4RUNK
4HE FIRST THRESHOLD IS FIXED EQUALS L 4+ IN &IGURE AND YIELDS 0FA WHEN THE REFERENCE CELLS ARE INDEPENDENT AND IDENTICALLY DISTRIBUTED 4HE SECOND
THRESHOLD IS ADAPTIVE AND MAINTAINS A LOW 0FA WHEN THE REFERENCE SAMPLES ARE COR
RELATED 4HE DEVICE ESTIMATES THE STANDARD DEVIATION OF THE CORRELATED SAMPLES WITH
THE MEAN DEVIATE ESTIMATOR WHERE EXTRANEOUS TARGETS IN THE REFERENCE CELLS HAVE
BEEN EXCLUDED FROM THE ESTIMATE BY USE OF A PRELIMINARY THRESHOLD 4
4HE BASIC DISADVANTAGES OF ALL NONPARAMETRIC DETECTORS ARE THAT THEY HAVE
RELATIVELY LARGE #&!2 LOSSES THEY HAVE PROBLEMS WITH CORRELATED SAMPLES AND
ONE LOSES AMPLITUDE INFORMATION WHICH CAN BE A VERY IMPORTANT DISCRIMINANT
BETWEEN TARGET AND CLUTTER &OR EXAMPLE A LARGE RETURN CROSS SECTION q M IN
A CLUTTER AREA IS PROBABLY JUST CLUTTER BREAKTHROUGH 3EE h2ADAR $ETECTION !CCEPTANCEv
IN 3ECTION #LUTTER -APPING ! CLUTTER MAP USES ADAPTIVE THRESHOLDING WHERE THE THRESHOLD
IS CALCULATED FROM THE RETURN IN THE TEST CELL ON PREVIOUS SCANS RATHER THAN FROM THE SUR
ROUNDING REFERENCE CELLS ON THE SAME SCAN 4HIS TECHNIQUE HAS THE ADVANTAGE IN THAT
FOR ESSENTIALLY STATIONARY ENVIRONMENTS EG LAND BASED RADAR AGAINST GROUND CLUTTER
THE RADAR HAS INTERCLUTTER VISIBILITYˆIT CAN SEE BETWEEN LARGE CLUTTER RETURNS ,INCOLN
,ABORATORY IN ITS MOVING TARGET DETECTOR -4$ USED A CLUTTER MAP FOR THE ZERO DOP
PLER FILTER VERY EFFECTIVELY 4HE DECISION THRESHOLD 4 FOR THE ITH CELL IS
4 ! 3I WHERE THE CLUTTER IS ESTIMATED USING A SIMPLE FEEDBACK INTEGRATOR
3 I + 3I 8I
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-ODIFIED GENERALIZED SIGN TEST PROCESSOR AFTER ' 6 4RUNK ET AL WHERE 3I IS THE AVERAGE BACKGROUND LEVEL 8I IS THE RETURN IN THE ITH CELL + IS THE FEED
BACK VALUE THAT DETERMINES THE MAP TIME CONSTANT AND ! IS THE CONSTANT THAT DETERMINES
THE 0FA )N THE -4$ USED FOR THE !32 APPLICATION + IS WHICH EFFECTIVELY AVERAGES
THE LAST EIGHT SCANS 4HE PURPOSE OF THE CLUTTER MAP IS TO DETECT IN CLUTTER FREE AREAS
CROSSING TARGETS THAT WOULD HAVE BEEN REMOVED BY THE DOPPLER PROCESSING 4HE MAIN
UTILITY OF CLUTTER MAPS IS WITH FIXED FREQUENCY LAND BASED RADARS 7HILE CLUTTER MAPS
CAN BE USED WITH FREQUENCY AGILE RADARS AND ON MOVING PLATFORMS EG RADARS ON
SHIPS THEY ARE NOT NEARLY AS EFFECTIVE IN THESE ENVIRONMENTS
4ARGET 2ESOLUTION )N AUTOMATIC DETECTION SYSTEMS A SINGLE LARGE TARGET WILL PROB
ABLY BE DETECTED IE CROSS A DETECTION THRESHOLD MANY TIMES EG IN ADJACENT RANGE
CELLS AZIMUTH BEAMS AND ELEVATION BEAMS 4HEREFORE AUTOMATIC DETECTION SYSTEMS
HAVE ALGORITHMS FOR MERGING THE INDIVIDUAL DETECTIONS INTO A SINGLE CENTROIDED DETEC
TION -OST ALGORITHMS HAVE BEEN DESIGNED SO THAT THEY WILL RARELY SPLIT A SINGLE TARGET
INTO TWO TARGETS 4HIS PROCEDURE RESULTS IN POOR RANGE RESOLUTION CAPABILITY ! MERG
ING ALGORITHM OFTEN USED IS THE ADJACENT DETECTION MERGING ALGORITHM WHICH DECIDES
WHETHER A NEW DETECTION IS ADJACENT TO ANY OF THE PREVIOUSLY DETERMINED SETS OF ADJACENT
DETECTIONS )F THE NEW DETECTION IS ADJACENT TO ANY DETECTION IN THE SET OF ADJACENT DETEC
TIONS IT IS ADDED TO THE SET 4WO DETECTIONS ARE ADJACENT IF TWO OF THEIR THREE PARAMETERS
RANGE AZIMUTH AND ELEVATION ARE THE SAME AND THE OTHER PARAMETER DIFFERS BY THE
RESOLUTION ELEMENT RANGE CELL $2 AZIMUTH BEAMWIDTH P OR ELEVATION BEAMWIDTH F
! STUDY COMPARED THE RESOLVING CAPABILITY OF THREE COMMON DETECTION PROCE
DURES LINEAR DETECTOR WITH 4 M} !S} LINEAR DETECTOR WITH 4 "M} AND LOG DETECTOR
WITH 4 # M} WHERE THE CONSTANTS ! " AND # ARE USED TO OBTAIN THE SAME 0FA FOR
ALL DETECTORS 4HE ESTIMATES M} AND S} OF L AND R WERE OBTAINED FROM EITHER ALL THE
REFERENCE CELLS OR THE LEADING OR LAGGING HALF OF THE REFERENCE CELLS CHOOSING THE
Ç°Óä
2!$!2 (!.$"//+
4!",% 0ROBABILITY OF $ETECTING "OTH 4ARGETS WITH ,OG 6IDEO 7HEN THE 4WO 4ARGETS !RE
3EPARATED BY OR 2ANGE #ELLS 3. OF TARGET IS D" AND 3. OF TARGET IS OR D"
4HRESHOLDING
4ECHNIQUE
!LL REFERENCE CELLS
2EFERENCE CELLS WITH
MINIMUM MEAN VALUE
4ARGET
3EPARATION
3. OF 4ARGET NO AFTER ' 6 4RUNK Ú )%%% HALF WITH THE LOWER MEAN VALUE 4HE FIRST SIMULATION INVOLVED TWO TARGETS SEPARATED BY
OR RANGE CELLS AND A THIRD TARGET RANGE CELLS FROM THE FIRST TARGET
7HEN THE TWO CLOSELY SPACED TARGETS WERE WELL SEPARATED EITHER OR RANGE CELLS
APART THE PROBABILITY OF DETECTING BOTH TARGETS 0$ WAS FOR THE LINEAR DETECTOR
WITH 4 M} !S} 0$ FOR THE LINEAR DETECTOR WITH 4 "M} AND 0$ FOR THE LOG DETECTOR ! SECOND SIMULATION INVOLVING ONLY TWO TARGETS INVESTIGATED THE
EFFECT OF TARGET SUPPRESSION ON LOG VIDEO AND THE RESULTS ARE SUMMARIZED IN 4ABLE 4HE MAXIMUM VALUE OF 0$ IS OBTAINED WHEN BOTH TARGETS HAVE AN 3. OF D" )F ONE
OF THE TARGETS HAS A LARGER 3. THAN THE OTHER TARGET SUPPRESSION OCCURSˆEITHER TARGET SUPPRESSES TARGET OR VICE VERSA !LSO ONE NOTES AN IMPROVED PERFORMANCE FOR A SMALL
3. TO D" WHEN CALCULATING THE THRESHOLD USING ONLY THE HALF OF THE REFERENCE
CELLS WITH THE LOWER MEAN VALUE 4HE RESOLUTION CAPABILITY OF THE LOG DETECTOR THAT USES
ONLY THE HALF OF THE REFERENCE CELLS WITH THE LOWER MEAN IS SHOWN IN &IGURE 4HE
PROBABILITY OF RESOLVING TWO EQUAL AMPLITUDE TARGETS DOES NOT RISE ABOVE UNTIL THEY
ARE SEPARATED IN RANGE BY PULSE WIDTHS
"Y ASSUMING THAT THE TARGET IS SMALL WITH RESPECT TO THE PULSE WIDTH AND THAT THE PULSE
SHAPE IS KNOWN THE RESOLUTION CAPABILITY CAN BE IMPROVED BY FITTING THE KNOWN PULSE
SHAPE TO THE RECEIVED DATA AND COMPARING THE RESIDUE SQUARE ERROR WITH A THRESHOLD
)F ONLY ONE TARGET IS PRESENT THE RESIDUE SHOULD BE ONLY NOISE AND HENCE SHOULD BE
SMALL )F TWO OR MORE TARGETS ARE PRESENT THE RESIDUE WILL CONTAIN SIGNAL FROM THE
REMAINING TARGETS AND SHOULD BE LARGE 4HE RESULTS OF RESOLVING TWO TARGETS WITH
3. D" ARE SHOWN IN &IGURE 4HESE TARGETS CAN BE RESOLVED AT A RESOLU
TION PROBABILITY OF WITH A FALSE ALARM PROBABILITY OF AT SEPARATIONS VARYING
BETWEEN ONE FOURTH AND THREE FOURTHS OF A PULSE WIDTH DEPENDING ON THE RELATIVE PHASE
DIFFERENCE BETWEEN THE TWO TARGETS -OREOVER THIS RESULT CAN BE IMPROVED FURTHER BY
PROCESSING MULTIPLE PULSES
!UTOMATIC $ETECTION 3UMMARY 7HEN ONLY TO SAMPLES PULSES ARE AVAIL
ABLE A BINARY INTEGRATOR SHOULD BE USED TO AVOID FALSE ALARMS DUE TO INTERFERENCE 7HEN
A MODERATE NUMBER OF PULSES TO ARE AVAILABLE A BINARY INTEGRATOR OR A MOV
ING WINDOW INTEGRATOR SHOULD BE USED )F THE NUMBER OF PULSES IS LARGE GREATER THAN
A BATCH PROCESSOR SHOULD BE USED )F THE SAMPLES ARE INDEPENDENT A ONE PARAM
ETER MEAN THRESHOLD CAN BE USED )F THE SAMPLES ARE DEPENDENT ONE CAN EITHER USE
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&)'52% 2ESOLUTION CAPABILITY OF A LOG DETECTOR THAT USED HALF OF THE REFERENCES CELLS WITH
LOWER MEAN AFTER ' 6 4RUNK Ú )%%% A TWO PARAMETER MEAN AND VARIANCE THRESHOLD OR ADAPT A ONE PARAMETER THRESHOLD
ON A SECTOR BASIS (OWEVER THESE RULES SHOULD SERVE ONLY AS A GENERAL GUIDELINE )T IS
HIGHLY RECOMMENDED THAT BEFORE A DETECTOR IS CHOSEN THE RADAR VIDEO FROM THE ENVI
RONMENT OF INTEREST BE COLLECTED AND ANALYZED AND THAT VARIOUS DETECTION PROCESSES BE
SIMULATED ON A COMPUTER AND TESTED AGAINST THE RECORDED DATA
&)'52% 0ROBABILITY OF RESOLUTION AS A FUNCTION OF RANGE SEPARATION PROBABILITY OF FALSE ALARM
IS SAMPLING RATE $2 SAMPLES PER PULSE WIDTH TARGET STRENGTHS NONFLUCTUATING ! ! D" PHASE DIFFERENCES — — — — AND — AFTER ' 6 4RUNK Ú )%%% Ç°ÓÓ
2!$!2 (!.$"//+
-ANY MODERN RADARS USE COHERENT PROCESSING TO REMOVE CLUTTER &OR THE PURPOSE OF
APPLYING THE PREVIOUS DISCUSSIONS ON NONCOHERENT PROCESSING TO COHERENT PROCESSING
THE INTEGRATED OUTPUT IN A RANGE DOPPLER CELL OF THE DOPPLER PROCESSOR FOR A SINGLE COHER
ENT PROCESSING INTERVAL #0) CAN BE TREATED AS A SINGLE NONCOHERENT PULSE "ECAUSE
THREE AMBIGUOUS MEASUREMENTS IE DETECTIONS ARE USUALLY REQUIRED TO REMOVE THE
RANGE AND DOPPLER AMBIGUITIES TO #0)S MAY BE TRANSMITTED AND HENCE THERE
ARE USUALLY TO NONCOHERENT PULSES AVAILABLE FOR PROCESSING
Ç°ÎÊ 1/"/ Ê/, ! TRACK REPRESENTS THE BELIEF THAT A PHYSICAL OBJECT OR hTARGETv IS PRESENT AND HAS ACTU
ALLY BEEN DETECTED BY THE RADAR !N AUTOMATIC RADAR TRACKING SYSTEM FORMS A TRACK WHEN
ENOUGH RADAR DETECTIONS ARE MADE IN A BELIEVABLE ENOUGH PATTERN TO INDICATE A TARGET IS
ACTUALLY PRESENT AS OPPOSED TO A SUCCESSION OF FALSE ALARMS AND WHEN ENOUGH TIME HAS
PASSED TO ALLOW ACCURATE CALCULATION OF THE TARGETS KINEMATIC STATEˆUSUALLY POSITION
AND VELOCITY 4HUS THE GOAL OF TRACKING IS TO TRANSFORM A TIME LAPSE DETECTION PICTURE
SHOWN IN &IGURE A CONSISTING OF TARGET DETECTIONS FALSE ALARMS AND CLUTTER INTO
A TRACK PICTURE SHOWN IN &IGURE B CONSISTING OF TRACKS ON REAL TARGETS OCCASIONAL
FALSE TRACKS AND OCCASIONAL DEVIATIONS OF TRACK POSITION FROM TRUE TARGET POSITIONS
&IGURES A AND B ALSO ILLUSTRATE SOME OF THE CHALLENGES OF AUTOMATIC TRACK
ING $ETECTIONS ARE MADE ON TARGETS BUT SOME DETECTIONS ARE MISSING BECAUSE OF TARGET
FADES OR MULTIPLE TARGETS IN THE SAME RESOLUTION CELL WHEREAS ADDITIONAL DETECTIONS ARE
PRESENT DUE TO CLUTTER OR NOISE
&)'52% A 4HIRTY MINUTE TIME LAPSE OF !.&0. , BAND AIR TRAFFIC
CONTROL RADAR DETECTIONS OVER A Ò KM SQUARE AREA AFTER ( ,EUNG ET AL
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&)'52% B 4HIRTY MINUTE TIME LAPSE OF TRACKS FORMED FROM DATA
IN &IGURE A USING 'LOBAL .EAREST .EIGHBOR '.. 4ECHNIQUE AFTER
( ,EUNG ET AL Ú )%%% !UTOMATIC TRACKING CAN GENERALLY BE DIVIDED INTO THE FIVE STEPS SHOWN IN &IGURE AND DETAILED HERE
2ADAR DETECTION ACCEPTANCE ACCEPTING OR REJECTING DETECTIONS FOR INSERTION INTO THE
TRACKING PROCESS 4HE PURPOSE OF THIS STEP IS TO CONTROL FALSE TRACK RATES
!SSOCIATION OF ACCEPTED DETECTIONS WITH EXISTING TRACKS
5PDATING EXISTING TRACKS WITH ASSOCIATED DETECTIONS
.EW TRACK FORMATION USING UNASSOCIATED DETECTIONS
2ADAR SCHEDULING AND CONTROL
4HE RESULT OF THE AUTOMATIC TRACKING PROCESS IS A TRACK FILE THAT CONTAINS A TRACK STATE
FOR EACH TARGET DETECTED BY THE RADAR
!S SHOWN IN &IGURE THERE IS A FEEDBACK LOOP BETWEEN ALL THESE FUNCTIONS SO THE
ABILITY TO UPDATE EXISTING TRACKS ACCURATELY NATURALLY AFFECTS THE ABILITY TO ASSOCIATE DETEC
TIONS WITH EXISTING TRACKS !LSO THE ABILITY TO CORRECTLY ASSOCIATE DETECTIONS WITH EXISTING
TRACKS AFFECTS THE TRACKS ACCURACY AND THE ABILITY TO CORRECTLY DISTINGUISH BETWEEN AN EXIST
ING TRACK AND A NEW ONE 4HE DETECTION ACCEPTREJECT STEP MAKES USE OF FEEDBACK FROM THE
ASSOCIATION FUNCTION THAT MEASURES THE DETECTION ACTIVITY IN DIFFERENT REGIONS OF THE RADAR
COVERAGE -ORE STRINGENT ACCEPTANCE CRITERIA ARE APPLIED IN MORE ACTIVE REGIONS
4RACK &ILE 7HEN A TRACK IS ESTABLISHED IN THE COMPUTER IT IS ASSIGNED A TRACK NUM
BER !LL PARAMETERS ASSOCIATED WITH A GIVEN TRACK ARE REFERRED TO BY THIS TRACK NUMBER
4YPICAL TRACK PARAMETERS ARE THE FILTERED AND PREDICTED POSITION VELOCITY ACCELERATION
WHEN APPLICABLE TIME OF LAST UPDATE TRACK QUALITY SIGNAL TO NOISE RATIO COVARIANCE
MATRICES THE COVARIANCE CONTAINS THE ACCURACY OF ALL THE TRACK COORDINATES AND ALL THE
STATISTICAL CROSS CORRELATIONS BETWEEN THEM IF A +ALMAN TYPE FILTER IS BEING USED AND
&)'52% 3TRUCTURE OF AUTOMATIC TRACKING PROCESS
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TRACK HISTORY IE THE LAST N DETECTIONS 4RACKS AND DETECTIONS CAN BE ACCESSED IN VARI
OUS SECTORED LINKED LIST AND OTHER DATA STRUCTURES SO THAT THE ASSOCIATION PROCESS CAN
BE PERFORMED EFFICIENTLY )N ADDITION TO THE TRACK FILE A CLUTTER FILE IS MAINTAINED !
CLUTTER NUMBER IS ASSIGNED TO EACH STATIONARY OR VERY SLOWLY MOVING ECHO !LL PARAM
ETERS ASSOCIATED WITH A CLUTTER POINT ARE REFERRED TO BY THIS CLUTTER NUMBER !GAIN EACH
CLUTTER NUMBER IS ASSIGNED TO A SECTOR IN AZIMUTH FOR EFFICIENT ASSOCIATION
2ADAR $ETECTION !CCEPTANCE 7HEN THE RADAR SYSTEM HAS EITHER NO OR LIMITED
COHERENT PROCESSING NOT ALL THE DETECTIONS DECLARED BY THE AUTOMATIC DETECTOR ARE USED
IN THE TRACKING PROCESS 2ATHER MANY OF THE DETECTIONS CONTACTS ARE FILTERED OUT IN
SOFTWARE USING A PROCESS CALLED ACTIVITY CONTROL 4HE BASIC IDEA IS TO USE DETECTION
SIGNAL CHARACTERISTICS IN CONNECTION WITH A MAP OF THE DETECTION ACTIVITY TO REDUCE THE
RATE OF DETECTIONS TO ONE THAT IS ACCEPTABLE FOR FORMING TRACKS 4HE MAP IS CONSTRUCTED
BY COUNTING THE UNASSOCIATED DETECTIONS THOSE THAT DO NOT ASSOCIATE WITH EXISTING
TRACKS AT THE POINT IN THE TRACK PROCESSING SHOWN IN &IGURE #OUNTS ARE AVERAGED OVER MANY REVISITS OF THE RADAR TO ACHIEVE STATISTICAL SIGNIFI
CANCE 4HE DETECTION SIGNAL CHARACTERISTICS SUCH AS AMPLITUDE OR SIGNAL TO NOISE ARE
THEN RE THRESHOLDED TO REDUCE SENSITIVITY IN REGIONS OF UNACCEPTABLY HIGH ACTIVITY )N
NO CIRCUMSTANCES ARE DETECTIONS ELIMINATED IF THEY FALL WITHIN A TRACK GATE IE A GATE
CENTERED ON THE PREDICTED POSITION OF A FIRM TRACK &IGURE ILLUSTRATES AN EXAMPLE
&)'52% (ISTOGRAM OF DETECTION SIGNAL TO NOISE RATIO DETECTION
ILLUSTRATING THE EFFECTIVENESS OF THE ACTIVITY CONTROL USING THE SIGNAL TO NOISE
TEST IN RAIN CLUTTER 5NGATED CONTACTS GENERALLY REPRESENT CLUTTER 'ATED CON
TACTS GENERALLY REPRESENT TARGETS 2E THRESHOLDING IN THIS CASE SUCCESSFULLY
ELIMINATES LARGE NUMBERS OF CLUTTER DETECTIONS WHILE PRESERVING MOST TARGET
DETECTIONS AFTER 7 ' "ATH ET AL
Ç°ÓÈ
2!$!2 (!.$"//+
OF THIS PROCESS WHEN LARGE NUMBERS OF RAIN CLUTTER DETECTIONS ARE POTENTIALLY OVERLOAD
ING THE TRACKING PROCESS )N THIS CASE ACTIVITY CONTROL EFFECTIVELY ELIMINATES MOST OF THE
CLUTTER DETECTIONS WITHOUT ELIMINATING MANY OF THE ACTUAL TARGET DETECTIONS (OWEVER
BECAUSE THIS PROCESS ESSENTIALLY CONSTITUTES CONTROLLED DESENSITIZATION OF THE RADAR IT
MUST BE USED WITH CARE 4HE MAPPING OF THE DETECTION ACTIVITY MUST BE PRECISE SO THAT
DESENSITIZATION OCCURS ONLY IN THOSE REGIONS REQUIRING IT
5PDATING %XISTING 4RACKS WITH !SSOCIATED $ETECTIONS
OF UPDATING A TRACK STATE IS THE @ A FILTER DESCRIBED BY
XSK XP K
VSK VSK
XPK
4HE SIMPLEST METHOD
@ ;XMK
XPK =
A ;XMK
XPK =4
XSK
VSK 4
WHERE XSK IS THE FILTERED POSITION VSK IS THE FILTERED VELOCITY XPK IS THE PREDICTED
POSITION XMK IS THE MEASURED POSITION 4 IS THE TIME BETWEEN DETECTIONS AND @ A
ARE THE POSITION AND VELOCITY GAINS RESPECTIVELY 4HE SELECTION OF @ A IS A DESIGN
TRADEOFF 3MALL GAINS MAKE A SMALL CORRECTION IN THE DIRECTION OF EACH DETECTION !S A
RESULT THE TRACKING FILTER IS LESS SENSITIVE TO NOISE BUT IS MORE SLUGGISH TO RESPOND TO
MANEUVERSˆDEVIATION FROM THE ASSUMED TARGET MODEL #ONVERSELY LARGE GAINS PRO
DUCE MORE TRACKING NOISE BUT QUICKER RESPONSE TO MANEUVERS 4HESE ERRORS ARE READILY
CALCULATED AS A FUNCTION OF @ AND A USING THE FORMULAS SHOWN IN 4ABLE 4O TUNE THE @ A FILTER FOR RADAR TRACKING ONE USES THE RADAR PARAMETERS TO CALCULATE
THE TRACKING ERRORS LISTED IN 4ABLE AS A FUNCTION OF THE TRACKING GAINS @ AND A
4HEN ONE SELECTS THE GAINS THAT BEST MEET THE NEEDS OF THE APPLICATION &OR EXAMPLE
CONSIDER A RADAR THAT HAS METER RANGE MEASUREMENT ACCURACY AND A TWO SECOND
CONSTANT UPDATE INTERVAL 4HE APPLICATION OF THIS RADAR SYSTEM IS TO TRACK A TARGET THAT
MOVES LINEARLY BUT WITH OCCASIONAL UNPREDICTABLE MANEUVERS OF UP TO G MS 4!",% #HARACTERIZATION OF 4RACKING %RRORS AS A &UNCTION OF 4RACKING 'AINS @ AND A
%RROR 3OURCE
2ADAR DETECTION
NOISE STANDARD
DEVIATION R
2ADAR DETECTION
NOISE STANDARD
DEVIATION R
#ONSTANT
MANEUVERˆA
UNITS OF GS
#ONSTANT
MANEUVERˆA
UNITS OF GS
3TEADY STATE
4RACK %RROR
3TANDARD
DEVIATION OF
FILTERED TRACKING
STATE
3TANDARD
DEVIATION
OF PREDICTED
TRACKING STATE
,AG BIAS IN
FILTERED TRACK
STATE
,AG BIAS IN
PREDICTED TRACK
STATE
)N 0OSITION
)N 6ELOCITY
§ A B A ¶
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&OR SIMPLICITY ASSUME THE "ENEDICT "ORDNER CONSTANT RELATIONSHIP ;A @ @ =
BETWEEN @ AND A
4HE POSITION ACCURACY OF THE FILTER CAN THEN BE CALCULATED USING THE FORMULAS IN
4ABLE AND IS SHOWN IN &IGURE 7HEN THE TARGET IS NONMANEUVERING ACCURACY
AS MEASURED BY THE STANDARD DEVIATION OF THE PREDICTED TRACKING STATE IMPROVES MONO
TONICALLY AS THE TRACKING GAIN @ DECREASES TO #ONVERSELY WHEN THE TARGET IS PER
FORMING THE G MANEUVER ACCURACY AS MEASURED BY THE LAG OR BIAS IN THE PREDICTED
TRACKING STATE IMPROVES MONOTONICALLY AS THE TRACKING GAIN INCREASES TO 4HE TOTAL
TRACKING ERROR CAN BE DEFINED AS THE ERROR THAT IS EXCEEDED ONLY OF THE TIME DUE TO
THE SUM OF RANDOM ERRORS AND BIAS 4HE TOTAL RANGE TRACKING ERROR IS BEST IN THE REGION
@ WITH A MINIMUM AROUND )F ACCURACY FOR MANEUVERS IS THE DOMINANT
CONCERN THEN ONE WOULD PROBABLY TUNE THIS FILTER TO TO ACHIEVE THE LOWEST TOTAL
ERROR FOR A G ACCELERATION 4HIS SAME TECHNIQUE CAN BE APPLIED TO MANY DIFFERENT
RADAR TRACKING PROBLEMS USING THE EQUATIONS IN 4ABLE TO CALCULATE A GRAPH SUCH AS
THE ONE SHOWN IN &IGURE &OR SIMPLE TRACKING PROBLEMS THE @ A FILTER WITH CONSTANT GAINS SELECTED FOR THE APPLI
CATION WILL OFTEN BE ADEQUATE (OWEVER MORE COMPLEX TRACKING PROBLEMS REQUIRE VARI
ABLE TRACKING GAINS EG LARGER GAINS AT THE BEGINNING OF THE TRACK AND LARGER GAINS AFTER
MISSED DETECTIONS OR WHEN THE RANGE TO THE TRACK DECREASES MAKING ANGLE NOISE LESS OF
AN ISSUE ! SYSTEMATIC METHOD FOR CALCULATING THE GAINS DEPENDING ON THE SITUATION IS THE
&)'52% %XAMPLE OF THE TUNING OF AN @ A RADAR RANGE TRACKING FILTER BY SELECTING THE GAIN THAT MINI
MIZES TOTAL ERROR RADAR PARAMETERS RANGE ACCURACY METERS UPDATE INTERVAL SECONDS TARGET PARAMETER
G UNKNOWN ACCELERATION GAIN RELATION ;A @ @ =
Ç°Ón
2!$!2 (!.$"//+
+ALMAN FILTER 4HE +ALMAN FILTER MINIMIZES THE MEAN SQUARE PREDICTION ERROR WHEN
THE RANDOM PROCESSES ARE GAUSSIAN 4HE +ALMAN FILTER CAN BE FORMULATED FOR TARGET MOTION
IN ONE TWO OR THREE DIMENSIONS IN POLAR #ARTESIAN OR %ARTH CENTERED COORDINATES AND
FOR THREE DIMENSIONAL TWO DIMENSIONAL OR ONE DIMENSIONAL RADAR MEASUREMENTS &OR
SIMPLICITY A THREE DIMENSIONAL TRACKING PROBLEM IN #ARTESIAN SPACE WITH THREE MEASURED
RADAR DIMENSIONS IS CONSIDERED HERE 4ARGET MOTION IS DESCRIBED BY
8TK ETK 8TK
!TK
!PTK
WHERE 8TK IS THE TARGET STATE AT TIME TK CONSISTING OF POSITION AND VELOCITY COMPONENTS
ETK IS A TRANSITION MATRIX THAT MOVES THE TARGET LINEARLY OVER AN ELAPSED TIME 4K TK TK
FROM TIME TK TO TIME TK !TK IS THE TARGET STATE CHANGE DUE TO AN UNKNOWN ACCELERATION
CAUSED BY A MANEUVER OR ATMOSPHERIC DRAG AND !PTK IS TARGET STATE CHANGE DUE TO A KNOWN
ACCELERATION THAT CAN BE CORRECTED SUCH AS GRAVITY FOR A FALLING OBJECT OR #ORIOLLIS ACCELERA
TION 4HE COMPONENTS OF THE STATE VECTOR AND TRANSITION MATRIX FOR THIS PROBLEM ARE
X T K
u
X T K
Y T K
8 T K u
Y T K
Z T K
u
Z T K
F T K
4K
4K
4K
4HE UNKNOWN ACCELERATION !TK IS ZERO MEAN AND IS CHARACTERIZED BY ITS COVARIANCE
MATRIX 1TK )F ONE VIEWS THE UNKNOWN MANEUVER AS A WHITE NOISE PROCESS WITH SPEC
TRAL DENSITY Q G(Z THEN THE ACCELERATION IS SAMPLED BY EACH RADAR DETECTION PRODUCING
A DISCRETE COVARIANCE MATRIX
4K 4K 4K 4K
4K 4K 1 T K Q
4K 4K
4K 4K 4K 4K
4HE OBSERVATION EQUATION RELATES THE ACTUAL RADAR MEASUREMENTS 9K AT TIME TK TO THE
TARGET STATE
9K H8TK
NK
WHERE NK IS THE RADAR MEASUREMENT NOISE HAVING A COVARIANCE MATRIX
S R S Q €K S J S $
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COMPOSED OF THE RADAR MEASUREMENT ACCURACIES IN RANGE AZIMUTH ELEVATION AND DOP
PLER 4HE FUNCTION H IS THE COORDINATE TRANSFORM THAT RELATES THE MEASUREMENTS TO THE
STATE AT TIME TK ACCORDING TO THE COORDINATE FRAME DESIGN CHOICES SEE 4ABLE LATER IN
THE CHAPTER )N ORDER TO USE THE +ALMAN FILTER H IS APPROXIMATED AS A LINEAR FUNCTION
IN THE VICINITY OF THE PREDICTED TRACK STATE
—
H 8 H 8 T K \ T K
—
(;8
—
8 T K \ T K = r 8
8 T K \ T K
WHERE ( IS THE GRADIENT OF H %ACH COORDINATE FRAME HAS ITS OWN APPROXIMATION FOR ( &OR
EXAMPLE IF THE STATE COORDINATE SYSTEM IS COMPOSED OF THREE DIMENSIONAL #ARTESIAN COOR
DINATES CENTERED AT THE RADAR THEN MULTIPLICATION BY ( TRANSFORMS #ARTESIAN COORDINATES
X Y Z INTO POLAR MEASUREMENT COORDINATES RANGE AZIMUTH ELEVATION DOPPLER AND
X
§
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R
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Y
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XZ
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¨ XR
XR
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Y
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X
X
Y
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YR
YR
R
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X
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X Y
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ZR
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R
¶
·
·
·
·
·
·
·
Z·
·
R¸
WHERE R X Y Z IS RANGE
4HE +ALMAN FILTER EQUATIONS FOR RADAR TRACKING ARE THEN SIMPLY GENERALIZATIONS
OF THE @ A FILTER EQUATIONS WHERE @ AND A VARY WITH TIME 4HE +ALMAN FILTER UPDATE
PROCEDURE CONTINUES AS FOLLOWS
—
&IRST PREDICT A NEW TARGET STATE ESTIMATE 8 TK \ TK OF THE STATE 8TK AT TIME TK GIVEN ALL MEASUREMENTS UP TO TIME TK
—
8 T K \ T K F T K 8 T K
!P T K
ALONG WITH ITS COVARIANCE
0K \ K E¼
TK 0K \ K E¼
TK 4
4HEN UPDATE THE TARGET STATE USING THE K
—
—
8 T K \ T K 8 T K \ T K
1TK
ST RADAR MEASUREMENT
+ K ;9K —
( T K 8 T K \ T K =
AND ITS COVARIANCE
0K \ K ;(
*K (TK =0K
\K
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USING THE +ALMAN GAINS
*K 0K \ K (4TK ;(TK 0K \ K (4TK €K= "ECAUSE THE GAINS ARE CALCULATED USING THE HISTORY OF ALL PAST UPDATE TIMES AND
ACCURACIES THE GAINS AUTOMATICALLY INCREASE AFTER MISSED DETECTIONS AND AUTOMATICALLY
INCREASE TO GIVE GREATER WEIGHT TO A DETECTION WHEN IT IS KNOWN TO BE MORE ACCURATE
AND THEY AUTOMATICALLY DECREASE AS THE TRACK AGES REFLECTING THE VALUE OF THE DETECTIONS
ALREADY FILTERED &OR EXAMPLE FOR A ZERO RANDOM ACCELERATION 1K AND A CONSTANT
DETECTION COVARIANCE MATRIX €K THE @ n A FILTER CAN BE MADE EQUIVALENT TO THE +ALMAN
FILTER BY SETTING
A
K K K B
K K AND
ON THE KTH SCAN 4HUS AS TIME PASSES @ AND A APPROACH ZERO APPLYING HEAVY FILTERING
TO THE NEW SAMPLES )N PRACTICAL RADAR APPLICATIONS 1K AND SO THE TRACKING GAINS
EVENTUALLY SETTLE TO A NON ZERO VALUE TERMED THE STEADY STATE TRACKING GAINS
4HE TRADEOFFS FOR EMPLOYING A +ALMAN FILTER FOR RADAR TRACKING GENERALLY ARE TUNING
THE FILTER FOR THE DESIRED DEGREE OF FILTERING SELECTING THE TRACKING COORDINATES AND
ADAPTING THE FILTER TO DEAL WITH CHANGES IN THE TARGET MOTION EG MANEUVERS DIFFERENT
PHASES OF BALLISTIC FLIGHT AND SO ON 4UNING THE +ALMAN &ILTER 4HE GREATEST ADVANTAGE OF THE +ALMAN FILTER FOR RADAR
TRACKING IS THAT IT PROVIDES A SYSTEMATIC WAY OF CALCULATING GAINS (OWEVER A DISADVAN
TAGE IS THAT THIS GAIN CALCULATION ASSUMES LINEAR TARGET MOTION WITH RANDOM PERTURBA
TIONS %Q -OST PRACTICAL RADAR TRACKING PROBLEMS INVOLVE TARGETS THAT DEVIATE
FROM LINEAR MOTION IN MORE COMPLEX WAYS EG COURSE CORRECTIONS TERRAIN FOLLOWING
EVASIVE MANEUVERS AND ATMOSPHERIC DRAG 4HE +ALMAN FILTER IS TUNED TO A PRACTICAL
RADAR TRACKING PROBLEM THROUGH THE SELECTION OF THE COVARIANCE MATRIX 1TK OF THE
UNKNOWN RANDOM MANEUVER 4HE GOAL OF THIS SELECTION IS TO OBTAIN THE BEST POSSIBLE
TRACKING PERFORMANCE FOR THE MORE COMPLEX CASES OF INTEREST WHILE STILL USING THE SIM
PLE +ALMAN RANDOM PERTURBATION MODEL &OR EXAMPLE IN THE SIMPLIFIED CASE OF A SINGLE
DIMENSION AND CONSTANT TRACKING CONDITIONS THE MEASUREMENT COVARIANCE MATRIX IS
SIMPLY A SINGLE CONSTANT MEASUREMENT VARIANCE €K R¼
M AND THE TIME BETWEEN DETEC
TIONS IS A CONSTANT 2K 4 )N THIS CASE THE +ALMAN FILTER DESCRIBED IN %QS TO HAS GAINS THAT ARE A FUNCTION OF THE DIMENSIONLESS TRACK FILTERING PARAMETER FTRACK
G TRACK Q4 S M
"ECAUSE THE RADAR MEASUREMENT ACCURACY AS REPRESENTED BY THE COVARIANCE MATRIX
€ AND THE TIME BETWEEN DETECTION OPPORTUNITIES 4 ARE PARAMETERS OF THE RADAR DESIGN
ITSELF THE SELECTION OF 1TK IS THE DEGREE OF FREEDOM AVAILABLE TO THE TRACKING FILTER
DESIGN 4ABLE SUMMARIZES THE METHODS FOR TUNING THE +ALMAN FILTER
-ODEL NO 2ANDOM
CHANGE IN VELOCITY AT EACH
MEASUREMENT INTERVAL
S V
S A
4K
4K 4K 4K
4 4K
Q K 4K
4K
-ODEL NO 7HITE NOISE
SPECTRAL DENSITY Q G(Z
ACCELERATION SAMPLED BY RADAR
MEASUREMENT
-ODEL NO 2ANDOM
CHANGE IN ACCELERATION AT
EACH MEASUREMENT INTERVAL
3TANDARD DEVIATION OF
ACCELERATION CHANGE IS RA 1 SUBMATRIX
-ANEUVER -ODEL
Q4 S M
A S A4 S M
S V4 S M
A
A
G TRACK AND
B
G TRACK B A
G TRACK A
B
A
A
AND
AND
3TEADY STATE 'AIN 2ELATION AND
4RACKING )NDEX
4!",% #OMPARISON OF -ETHODS OF 4UNING +ALMAN &ILTER FOR 0RACTICAL 2ADAR 4RACKING 0ROBLEMS
6ARY RV TO INCREASE
DECREASE GAINS
AND OBTAIN DESIRED
PERFORMANCE USING
EQUATIONS IN 4ABLE 6ARY RA TO INCREASE
DECREASE GAINS
AND OBTAIN DESIRED
PERFORMANCE USING
EQUATIONS IN 4ABLE 6ARY Q TO INCREASE
DECREASE GAINS
AND OBTAIN DESIRED
PERFORMANCE USING
EQUATIONS IN 4ABLE 4UNING -ETHOD
2ESPONDS VERY WELL TO
MANEUVERS BUT OPERATES AT
THE EDGE OF FILTER STABILITY
(IGHER RADAR MEASUREMENT
RATE CAN ACTUALLY RESULT IN LESS
ACCURATE TRACK
6ERY CONSERVATIVE WITH
RESPECT TO FILTER STABILITY
!CCOMMODATES VARIABLE
MEASUREMENT RATES WELL
2ESPONDS TO MANEUVERS
BUT NOT AT THE EDGE OF FILTER
STABILITY
#HARACTERISTICS
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1 SUBMATRIX NOT
APPLICABLE )NSTEAD
ASSUME CONSTANT
PARABOLIC MOTION AT -ODEL NO #ONSTANT
DETERMINISTIC ACCELERATION
A G &ILTER OBJECTIVE IS TO
MINIMIZE LAG PLUS C STANDARD
DEVIATIONS 4K
4K
4K
4K
4K
J
4K
-ODEL NO #ONSTANTLY
ACCELERATING TARGET WITH
A WHITE NOISE JERK
J ;GS (Z= SAMPLED BY RADAR
MEASUREMENT *ERK IS THE RATE
OF CHANGE OF ACCELERATION 4K
4K
4K
1 SUBMATRIX
-ANEUVER -ODEL
J4 S M
G TRACK AND
A 4 C S M
B A
G TRACK AND
A
3TEADY STATE GAIN CALCULATIONS
DESCRIBED IN &ITZGERALD
3TEADY STATE 'AIN 2ELATION AND
4RACKING )NDEX
6ARY A TO INCREASE
DECREASE GAINS
AND OBTAIN DESIRED
PERFORMANCE USING
EQUATIONS IN 4ABLE 3ELECT THIS MODEL WHEN
TARGET IS KNOWN
EXPECTED TO BE
ACCELERATING
4UNING -ETHOD
4!",% #OMPARISON OF -ETHODS OF 4UNING +ALMAN &ILTER FOR 0RACTICAL 2ADAR 4RACKING 0ROBLEMS #ONTINUED
&ILTER MINIMIZES ERROR FOR
A WORST CASE DETERMINISTIC
MANEUVER VICE A RANDOM ONE
:ERO LAGS TO CONSTANT
ACCELERATION HOWEVER NOISE
ERRORS ARE MUCH GREATER
#HARACTERISTICS
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!S SEEN IN &IGURE THE SELECTION OF 1TK AND THUS FTRACK ALLOWS ONE TO UNIQUELY
DETERMINE THE STEADY STATE TRACKING GAINS AS A FUNCTION OF FTRACK /NE CAN SEE THAT
LARGE ASSUMED MANEUVERS LARGE Q @A OR A LARGER TIME BETWEEN UPDATES 4 OR VERY
ACCURATE RADAR MEASUREMENTS SMALL € WILL RESULT IN LARGE TRACKING GAINS 4HE POSI
TION GAIN @ IS NEARLY IDENTICAL FOR THE 1TK MODELS NO AND IN 4ABLE (OWEVER THE VELOCITY GAIN A DIFFERS CONSIDERABLY &OR RANDOM CHANGES IN ACCEL
ERATION AT EACH MEASUREMENT INTERVAL MODEL NO THE GAINS INCREASE TO @ A ¼
¼
WHICH IS THE LIMIT OF FILTER STABILITY 4HUS THIS MODEL PRODUCES FILTER GAINS THAT
ARE THE MOST AGGRESSIVE AT MINIMIZING LAGS TO MANEUVERSˆAT THE EXPENSE OF LARGER
%"(% '! $ $(
%"%
%"(% %"% '! $$-
$*')'(*'#$) *')'(*'#$)
%,$*+'')
$*+'')
%')&)$)'+"
%$&)$)'+"
&)'52% 4HE RELATIONSHIP BETWEEN THE STEADY STATE TRACKING GAINS @ AND A IS SHOWN FOR DIFFERENT
1TK S CORRESPONDING TO DIFFERENT ASSUMPTIONS ABOUT THE UNKNOWN TARGET MANEUVER -ODEL NO WHITE
NOISE ACCELERATION SAMPLED AT EACH MEASUREMENT INTERVAL MODEL NO RANDOM CHANGE IN ACCELERATION AT
EACH MEASUREMENT INTERVAL MODEL NO RANDOM CHANGE IN VELOCITY AT EACH MEASUREMENT INTERVAL AND
MODEL NO CONSTANT DETERMINISTIC ACCELERATION -ODEL NO NOT SHOWN AS IT IS A GAIN MODEL
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TRACKING ERRORS DUE TO RADAR MEASUREMENT NOISE &OR RANDOM CHANGES IN VELOCITY AT
EACH MEASUREMENT INTERVAL MODEL NO THE GAINS INCREASE TO @ A WHICH
IS VERY CONSERVATIVE FROM A FILTER STABILITY POINT OF VIEW &OR WHITE NOISE ACCELERATION
SAMPLED BY RADAR MEASUREMENTS MODEL NO THE GAINS ARE A COMPROMISE INCREASING
"ECAUSE THIS MODEL IS A SAMPLED CONTINUOUS TIME ACCELERATION
TO A B IT IS PREFERRED WHEN UPDATE TIMES ARE VARIABLE BECAUSE THE TARGET DOES NOT MANEUVER
MORE OR LESS WHEN THE UPDATE INTERVAL CHANGES
4HE EQUATIONS IN 4ABLE CAN THEN BE USED TO CALCULATE THE FILTER PERFORMANCE IN
TERMS OF VARIANCE REDUCTION RATIOS AND TRACKING LAGS !DJUSTMENTS TO PARAMETERS OF FTRACK
CAN BE MADE TO OBTAIN THE DESIRED NOISE AND LAG TRADEOFF
3ELECTION OF 4RACKING #OORDINATES 4HE +ALMAN FILTER ASSUMES LINEAR TARGET
MOTION AND A LINEAR RELATION BETWEEN THE RADAR DETECTIONS AND THE TARGET COORDINATES
(OWEVER RADARS MAKE DETECTIONS IN POLAR COORDINATES RANGE ANGLE DOPPLER WHILE
TARGET MOTION IS MOST LIKELY LINEAR IN #ARTESIAN COORDINATES X Y Z 4HEREFORE SOME
COMPROMISES MUST GENERALLY BE MADE IN SELECTING A COORDINATE SYSTEM FOR FILTERING
4ABLE DESCRIBES THE DESIGN TRADEOFFS FOR DIFFERENT SELECTIONS
4HE POLAR +ALMAN FILTER IS RARELY USED BECAUSE OF THE PSEUDO ACCELERATIONS INTRO
DUCED BY PROPAGATING THE STATE IN POLAR COORDINATES 4HE #ARTESIAN%ARTH CENTERED
+ALMAN FILTER CAN WORK WELL BUT MAY HAVE DIFFICULTY ACCOMMODATING RADAR MEASURE
MENTS OF LESS THAN THREE DIMENSIONS 4HE EXTENDEDDUAL COORDINATE SYSTEM +ALMAN
FILTER PREVENTS PSEUDO ACCELERATIONS AND ACCOMMODATES MEASUREMENTS OF ANY DIMEN
SIONALITY "OTH THE #ARTESIAN%ARTH CENTERED +ALMAN FILTERS INVOLVE NONLINEAR TRANSFOR
MATIONS RESULTING IN AN IMPERFECT CALCULATION OF THE TRACKING ACCURACY 7HEN PREDICTION
TIMES ARE LONG ANDOR WHEN VERY ACCURATE RESULTS ARE NEEDED THESE IMPERFECTIONS IN
THE +ALMAN FILTER COVARIANCE CALCULATION CAN BE SIGNIFICANT AND THE TRACKING ERRORS CAN
BE QUITE NON GAUSSIAN 0ARTICLE FILTERS TYPICALLY PROPAGATE A LARGE NUMBER OF RANDOM
SAMPLES PARTICLES FROM A STATE TRANSITION PRIOR DISTRIBUTION TO ESTIMATE POSTERIOR DIS
TRIBUTIONS THAT ARE NOT REQUIRED TO BE GAUSSIAN IN FORM 4HUS IN A PARTICLE FILTER EVEN
MULTI MODAL DISTRIBUTIONS CAN BE USED AS PRIOR AND REALIZED AS POSTERIOR DISTRIBUTIONS
(OWEVER PARTICLE FILTERS REQUIRE QUITE A BIT OF COMPUTATION
4HE UNSCENTED +ALMAN FILTER MORE EFFICIENTLY CALCULATES THE TRACKING ACCURACY BY
PROPAGATING SELECTED CARDINAL POINTS THROUGH THE FILTER 4HE UNSCENTED +ALMAN &ILTER
APPROXIMATES THE COVARIANCE MATRIX WITH A SET OF , SAMPLE POINTS WHERE , IS THE
NUMBER OF STATE DIMENSIONS 4HE SAMPLE POINTS ARE PROPAGATED THROUGH AN ARBITRARY
TRANSFORM FUNCTION AND THEN USED TO RECONSTRUCT A GAUSSIAN COVARIANCE MATRIX 4HIS
TECHNIQUE HAS THE ADVANTAGE OF REPRESENTING THE COVARIANCE ACCURATELY TO THE THIRD
ORDER OF A 4AYLOR SERIES EXPANSION !S A RESULT THE CALCULATED TRACKING ACCURACY IS AT
LEAST TO THIRD ORDER UNCONTAMINATED OR hUNSCENTEDv BY THE NONLINEARITY
!DAPTING &ILTER TO $EAL WITH #HANGES IN 4ARGET -OTION 4HE +ALMAN FILTER
ASSUMES LINEAR TARGET MOTION PERTURBED BY A RANDOM MANEUVER MODEL AS A MATHEMATI
CAL CONVENIENCE IN CALCULATING TRACKING GAINS (OWEVER MOST RADAR TARGETS DO NOT
MOVE IN A RANDOM MANEUVER BUT INSTEAD MOVE LINEARLY AT TIMES AND THEN MANEUVER
UNPREDICTABLY AT TIMES 4HE CHALLENGE IN ADAPTING THE FILTER TO DEAL WITH CHANGES IN THE
TARGET MOTION EG MANEUVERS BALLISTIC RE ENTRY IS TO ADAPT THE TARGET MOTION MODEL
FOR THE +ALMAN FILTER OVER TIME SO THAT MORE ACCURATE TRACKING OCCURS THAN WITH A SINGLE
MODEL 4HE SIMPLEST FORM OF ADAPTATION IS A MANEUVER DETECTOR TO MONITOR THE TRACKING
FILTER RESIDUALS DIFFERENCES BETWEEN MEASURED AND PREDICTED POSITION ,ARGE CORRELATED
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4!",% !DVANTAGES AND $ISADVANTAGES OF %MPLOYING THE +ALMAN &ILTER IN $IFFERENT
#OORDINATE &RAMES
+ALMAN &ILTER
#OORDINATE
&RAME
6ARIANTS
#OORDINATES FOR
'AIN #ALCULATION
%QS AND STATE UPDATE
%Q #OORDINATES FOR
3TATE 0REDICTION
%QS -ETHOD OF
#OVARIANCE
0ROPAGATION
!DVANTAGES
$ISADVANTAGES
0OLAR +ALMAN
FILTER
0OLAR
0OLAR
%QS TO
IN POLAR
COORDINATES
&ILTER COVARIANCES
ARE CALCULATED
EXACTLY AND STATE
ERRORS GAUSSIAN
DISTRIBUTED 2ADAR
DETECTIONS OF
LESS THAN THREE
DIMENSIONS CAN
BE USED
0SEUDO
ACCELERATIONS
INTRODUCED
IN STATE
PROPAGATION
#ARTESIAN
%ARTH
#ENTERED
+ALMAN
FILTER
#ARTESIAN
%ARTH CENTERED
#ARTESIAN
%ARTH CENTERED
%QS TO IN #ARTESIAN
%ARTH CENTERED
COORDINATES
3TATE PROPAGATION
IS LINEAR
NO PSEUDO
ACCELERATIONS &ILTER
COVARIANCES ARE
NOT EXACT DUE
TO NONLINEAR
TRANSFORMATION
%XTENDED
DUAL
COORDINATE
+ALMAN
FILTER
0OLAR
#ARTESIAN
%ARTH CENTERED
%QS TO
IN POLAR
COORDINATES
2EQUIRES
FREQUENT
COORDINATE
TRANSFORMS
5NSCENTED
+ALMAN
FILTER
0OLAR OR
#ARTESIAN
%ARTH CENTERED
#ARTESIAN
%ARTH CENTERED
#OVARIANCE
INFERRED BY
PROPAGATING
MULTIPLE STATES
3TATE PROPAGATION
IS LINEAR
NO PSEUDO
ACCELERATIONS 2ADAR DETECTIONS
OF LESS THAN THREE
DIMENSIONS
CAN BE EASILY
ACCOMMODATED
3TATE PROPAGATION
IS LINEAR
NO PSEUDO
ACCELERATIONS &ILTER COVARIANCE
MORE EXACT
THAN TRADITIONAL
METHODSˆ
PARTICULARLY FOR
LONG EXTRAPOLATION
TIMES
-ORE COMPLEX
BUT NOT
NECESSARILY
MORE
COMPUTATION
RESIDUALS GENERALLY INDICATE A MANEUVER A DEVIATION FROM THE FILTER MODEL 5PON
MANEUVER DETECTION THE MANEUVER SPECTRAL DENSITY Q IS INCREASED IN THE +ALMAN FILTER
MODEL RESULTING IN HIGHER TRACKING GAINS AND BETTER FOLLOWING OF THE MANEUVER
! MORE COMPLEX APPROACH IS TO USE MULTIPLE +ALMAN FILTERS RUNNING SIMULTANEOUSLY
WITH DIFFERENT TARGET MOTION MODELSˆGENERALLY DIFFERENT Q VALUES OR DIFFERENT EQUA
TIONS FOR TARGET MOTION EG CONSTANT ACCELERATION OR CONSTANT VELOCITY &IGURE SHOWS A BANK OF MULTIPLE PARALLEL FILTERS ALL FED BY THE SAME STREAM OF ASSOCIATED MEA
SUREMENTS !T EACH DETECTION TIME TK ONE OF THE SEVERAL FILTER OUTPUTS MUST BE SELECTED
TO BE THE TRACK STATE USED FOR DETECTION TO TRACK ASSOCIATION
! SYSTEMATIC WAY OF EMPLOYING MULTIPLE TARGET MOTION MODELS IS THE )NTERACTING
-ULTIPLE -ODEL )-- APPROACH DIAGRAMMED IN &IGURE -ULTIPLE MODELS RUN
SIMULTANEOUSLY HOWEVER THEY DO NOT RUN INDEPENDENTLY )NSTEAD THERE IS MIXING OF
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AFTER 3 "LACKMAN AND 2 0OPOLI Ú !RTECH (OUSE &)'52% &LOWCHART OF INTERACTING MULTIPLE MODELS AFTER 3 "LACKMAN AND 2 0OPOLI
Ú !RTECH (OUSE !54/-!4)# $%4%#4)/. 42!#+).' !.$ 3%.3/2 ).4%'2!4)/.
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THE MODEL STATES 4HE UPDATE EQUATION FOR THE ITH MODEL DEPENDS NOT ONLY ON THE ITH
MODEL STATE BUT ALSO ON THE STATES OF ALL OTHER MODELS 4HESE STATES ARE MIXED USING
INFERRED PROBABILITIES OF THE TARGET TRANSITIONING FROM ONE MOTION MODEL TO ANOTHER
!S AN EXAMPLE CONSIDER RADAR TRACKING OF A BALLISTIC MISSILE THAT UNDERGOES DISTINCT
PHASES OF FLIGHT BOOST EXO ATMOSPHERIC FLIGHT AND ENDO ATMOSPHERIC RE ENTRY %ACH OF
THESE PHASES OF FLIGHT HAS A DISTINCT TARGET MODEL $URING BOOST THE TARGET IS CONTINUALLY
ACCELERATING AND INCREASING SPEED 4HIS ACCELERATION IS UNKNOWN AND MUST BE ESTIMATED
$URING EXO ATMOSPHERIC FLIGHT THE OBJECT IS FALLING WITH THE KNOWN ACCELERATION OF
GRAVITY $URING ENDO ATMOSPHERIC RE ENTRY THE TARGET CONTINUES TO FALL BUT EXPERIENCES A
DRAG ACCELERATION DUE TO ITS BALLISTIC COEFFICIENT AN UNKNOWN TARGET PARAMETER RELATED TO
THE SHAPE AND MASS OF THE TARGET !N )-- FILTER CAN BE USED TO SYSTEMATICALLY TRANSITION
BETWEEN THESE DIFFERENT PHASES OF FLIGHT PROVIDING A SINGLE FILTER OUTPUT &IGURE SHOWS THE MODEL PROBABILITIES FOR SUCH AN )-- FILTER APPLICATION
"$
#"
"$
" $
"
"!
!
&)'52% -ODEL PROBABILITIES RESULTING FROM THE APPLICATION OF AN )-- FILTER TO A BALLISTIC
MISSILE TRACKING PROBLEM A PROBABILITY THAT TARGET MOTION IS hBOOST PHASE v B PROBABILITY THAT TARGET
MOTION IS hEXO ATMOSPHERICv FLIGHT C PROBABILITY THAT TARGET MOTION IS hENDO ATMOSPHERICv RE ENTRY
AFTER 2 #OOPERMANR Ú &IFTH )NTERNATIONAL #ONFERENCE ON )NFORMATION &USION VOL Ç°În
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!SSOCIATION OF !CCEPTED $ETECTION WITH %XISTING 4RACKS 4HE GOAL OF DETECTION
TO TRACK ASSOCIATION IS TO CORRECTLY ASSIGN RADAR DETECTIONS TO EXISTING TRACKS SO THE TRACK
STATES IN THE TRACK FILE CAN BE CORRECTLY UPDATED 4HE BASIS FOR ASSIGNMENT IS A MEASURE OF
HOW CLOSE TOGETHER THE DETECTION AND TRACK ARE IN TERMS OF MEASURABLE PARAMETERS SUCH
AS RANGE ANGLE DOPPLER AND WHEN AVAILABLE TARGET SIGNATURE 4HE STATISTICAL DISTANCE
IS CALCULATED AS A WEIGHTED COMBINATION OF THE AVAILABLE DETECTION TO TRACK COORDINATE
DIFFERENCES )N THE MOST GENERAL CASE THIS IS A COMPLEX QUADRATIC FORM
$ 9K —
H 8 T K \ T K ; ( T K 0 K \ K ( 4 T K 2K = 9K —
H 8 T K \ T K
4
&OR MOST SINGLE RADAR TRACKING PROBLEMS IT REDUCES TO A SIMPLE WEIGHTED SUM
$ RM RP S R S PR
Q M Q P S Q S PQ
J M J P S J S PJ
$M $ P S $ S P$
WHERE RM PM IM $M ARE THE MEASURED RANGE AZIMUTH ELEVATION AND DOPPLER WITH
ACCURACIES RR RP RI R$ RP PP IP $P ARE THE RANGE AZIMUTH ELEVATION AND DOP
PLER PREDICTED BY THE AUTOMATIC TRACKER WITH ACCURACIES RPR RPP RPI RP$ 4HE PRE
DICTED ACCURACIES ARE A BYPRODUCT OF THE RADAR TRACKING FILTER 3TATISTICAL DISTANCE RATHER
THAN %UCLIDEAN DISTANCE MUST BE USED BECAUSE THE RANGE ACCURACY IS USUALLY MUCH
BETTER THAN THE AZIMUTH ACCURACY
7HEN TARGETS ARE WIDELY SPACED AND IN A CLEAR ENVIRONMENT ONLY ONE TARGET DETECTION
PAIR HAS A SMALL $ MAKING THESE ASSIGNMENTS OBVIOUS 4HUS THE DESIGN OF DETECTION TO
TRACK ASSOCIATION IS USUALLY DOMINATED BY THE MORE DIFFICULT CONDITIONS OF CLOSELY SPACED
TARGETS OR CLOSELY SPACED TARGETS AND CLUTTER &IGURE SHOWS A COMMON SITUATION FOR
CLOSELY SPACED TARGETS ANDOR CLUTTER 4HREE ASSOCIATION GATES ARE CONSTRUCTED AROUND THE
PREDICTED POSITIONS OF THREE EXISTING TRACKS 4HREE DETECTIONS ARE MADE BUT ASSIGNMENT OF
THE DETECTIONS TO THE TRACKS IS NOT OBVIOUS TWO DETECTIONS ARE WITHIN GATE THREE DETEC
TIONS ARE WITHIN GATE AND ONE DETECTION IS WITHIN GATE 4ABLE LISTS ALL DETECTIONS
&)'52% %XAMPLES OF THE PROBLEMS CAUSED BY MULTIPLE DETECTIONS AND
TRACKS IN CLOSE VICINITY FROM ' 6 4RUNK
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$ETECTION .O c
c
FROM ' 6 4RUNK
WITHIN THE TRACKING GATES AND THE STATISTICAL DISTANCE BETWEEN THE DETECTION AND TRACK )F
THE DETECTION IS OUTSIDE THE TRACK GATE THE STATISTICAL DISTANCE IS SET TO INFINITY
.EAREST NEIGHBOR ASSIGNMENT IS THE MOST COMMON SOLUTION TO THIS PROBLEM 4HE
SIMPLEST FORM OF NEAREST NEIGHBOR WORKS SEQUENTIALLY ON INCOMING DATA !S EACH NEW
DETECTION IS MADE IT IS ASSIGNED TO THE TRACK WITH WHICH IT HAS THE SMALLEST STATISTICAL
DISTANCE (ENCE IF DETECTION NO WAS RECEIVED FIRST IT WOULD BE ASSIGNED TO TRACK NO
(OWEVER IT IS BETTER TO DELAY THE ASSOCIATION PROCESS SLIGHTLY SO THAT ALL DETECTIONS IN
A LOCAL NEIGHBORHOOD ARE RECEIVED AND STORED AND AN ASSOCIATION TABLE SUCH AS 4ABLE GENERATED 4HIS HAS IMPLICATIONS ABOUT HOW SECTORS ARE SCANNED WITH A PHASED ARRAY
.EAREST NEIGHBOR ASSIGNMENT CAN NOW BE APPLIED TO THE ASSOCIATION TABLE BY FINDING
THE SMALLEST STATISTICAL DISTANCE BETWEEN A DETECTION AND A TRACK MAKING THAT ASSOCIA
TION AND ELIMINATING THAT DETECTION AND TRACK ROW AND COLUMN FROM THE TABLE 4HIS
PROCESS IS REPEATED UNTIL THERE ARE EITHER NO TRACKS OR NO DETECTIONS LEFT !PPLYING THIS
ALGORITHM TO 4ABLE RESULTS IN DETECTION NO UPDATING TRACK NO DETECTION NO UPDATING TRACK NO AND TRACK NO NOT BEING UPDATED "ETTER ASSIGNMENTS ARE POSSIBLE
WITH MORE SOPHISTICATED PROCESSING ALGORITHMS 4HE THREE TYPES OF MORE SOPHISTICATED
ALGORITHMS MOST FREQUENTLY USED ARE
'LOBAL .EAREST .EIGHBOR '.. #ONSIDER THE WHOLE MATRIX OF STATISTICAL DIS
TANCES SIMULTANEOUSLY AND MINIMIZE A METRIC SUCH AS THE SUM OF ALL STATISTICAL
DISTANCES FOR A COMPLETE ASSIGNMENT SOLUTION 0ERFORMING THIS OPTIMIZATION CAN
BE DONE USING -UNKRES ALGORITHM -UNKRES ALGORITHM IS AN EXACT SOLUTION OF
THE MINIMIZATION PROBLEM BUT IS RARELY USED BECAUSE IT IS COMPUTATIONALLY SLOW !
MORE COMPUTATIONALLY EFFICIENT EXACT SOLUTION IS THE *ONKER 6OLGENANT #ASTANON
*6# ALGORITHM 4HE *6# IS MUCH MORE EFFICIENT FOR SPARSE ASSIGNMENT MATRICES
WHICH ARE LIKELY FOR PRACTICAL RADAR TRACKING PROBLEMS 3PEED IMPROVEMENTS OF
TO TIMES HAVE BEEN REPORTED !N EFFECTIVE SUBOPTIMAL SOLUTION IS THE !UCTION
ALGORITHM WHICH VIEWS THE TRACKS AS BEING hAUCTIONED OFFv TO THE DETECTIONSˆ
ITERATIVELY ASSIGNING HIGHER COSTS TO TRACKS COMPETED FOR BY MORE DETECTIONS
&IGURE PROVIDES A COMPARISON OF THE -UNKRES *6# AND !UCTION ALGORITHMS
OPTIMIZED FOR SPARSE DATA 4HE *6# AND !UCTION ALGORITHMS PROVIDE A SIGNIFICANT
INCREASE IN COMPUTATIONAL SPEED !LTHOUGH THE !UCTION ALGORITHM IS SIMPLER REQUIR
ING LESS LINES OF CODE THE *6# ALGORITHM GENERALLY REQUIRES LESS COMPUTATION TIME
0ROBABILISTIC $ATA !SSOCIATION 0$! !NOTHER ALTERNATIVE IS THE PROBABILISTIC
DATA ASSOCIATION 0$! ALGORITHM WHERE NO ATTEMPT IS MADE TO ASSIGN TRACKS
TO DETECTIONS BUT INSTEAD TRACKS ARE UPDATED WITH ALL THE NEARBY DETECTIONSˆ
WEIGHTED BY THE PERCEIVED PROBABILITY OF THE TRACK BEING THE CORRECT ASSOCIATION
"ECAUSE 0$! RELIES ON ERRONEOUS ASSOCIATIONS ESSENTIALLY hAVERAGING OUT v IT IS
MOST EFFECTIVE WHEN TRACKS ARE FAR ENOUGH APART THAT NEARBY DETECTIONS ORIGINATE
FROM SPATIALLY RANDOM NOISE OR CLUTTER EXCLUSIVELY AND WHEN THE TRACKING GAINS
ARE SMALL IE WHEN THE TRACKING INDEX FTRACK IS SMALL 4HE *OINT 0ROBABILISTIC $ATA
Ç°{ä
2!$!2 (!.$"//+
&)'52% ! COMPARISON OF THE EXECUTION TIME FOR
THE -UNKRES OPTIMUM *6# OPTIMUM AND !UCTION
SUBOPTIMUM ALGORITHMS SHOWS THE RAPID INCREASE IN
COMPUTATION REQUIRED FOR -UNKRES AS THE NUMBER OF
ROWS IN THE ASSIGNMENT MATRIX INCREASES 4HE *6# AND
AUCTION ALGORITHMS SHOW MUCH MORE GRADUAL GROWTH
AFTER ) +ADAR ET AL Ú 30)%
!SSOCIATION *0$! IS AN EXTENSION OF 0$! THAT HANDLES MORE CLOSELY SPACED
TARGETS )N *0$! DETECTIONS ARE WEIGHTED LESS WHEN THEY ARE NEAR ANOTHER TRACK
-ULTIPLE (YPOTHESIS !LGORITHMS 4HE MOST SOPHISTICATED ALGORITHMS ARE MULTIPLE
HYPOTHESIS ALGORITHMS IN WHICH ALL OR MANY POSSIBLE TRACKS ARE FORMED AND UPDATED
WITH EACH POSSIBLE DETECTION )N 4ABLE TRACK NO WOULD BECOME THREE
TRACKS OR HYPOTHESES CORRESPONDING TO UPDATING WITH DETECTION NO DETECTION
NO AND NO DETECTION %ACH OF THESE TRACKS WOULD UNDERGO A +ALMAN FILTER UPDATE
AND BE ELIGIBLE FOR ASSOCIATION WITH THE NEXT SET OF DETECTIONS 4RACKS ARE PRUNED
AWAY IN A SYSTEMATIC MANNER LEAVING ONLY THE MOST PROBABLE &IGURE ILLUS
TRATES THE TRACKING OF A SINGLE TARGET USING MULTIPLE HYPOTHESIS TECHNIQUES )N THIS
EXAMPLE MANY HYPOTHESES ARE FORMED AND OVER SUCCESSIVE MEASUREMENT INTERVALS
SUCCESSFULLY PRUNED AWAY LEAVING ONLY ONE CORRECT TRACK
4HE REGION OF APPLICABILITY FOR THE MORE SOPHISTICATED ALGORITHMS IS DETERMINED BY TWO
PARAMETERS THE DENSITY OF EXTRANEOUS DETECTIONS K DETECTIONS PER UNIT AREA OR VOLUME
&)'52% %XAMPLE OF THE USE OF MULTIPLE HYPOTHESIS TRACKING ON SCANS OF SIMULATED RADAR DATA
CONTAINING A SINGLE TARGET AND MANY FALSE ALARMS A SHOWS ALL HYPOTHESES FORMS AND B SHOWS THE SINGLE
HYPOTHESIS SELECTED 0RUNED HYPOTHESES ARE GRAYED OUT AFTER 7 +OCH Ú )%%% !54/-!4)# $%4%#4)/. 42!#+).' !.$ 3%.3/2 ).4%'2!4)/.
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&)'52% 4HE APPLICABILITY OF DIFFERENT DETECTION TO TRACK ASSOCIATION ALGORITHMS
IS DETERMINED BY THE DENSITY OF FALSE ALARMS AND THE DIMENSIONLESS TRACKING PARAMETER
FTRACK AFTER $ * 3ALMOND Ú 30)% AND THE DIMENSIONLESS TRACK FILTERING PARAMETER FTRACK &IGURE BOUNDS THIS REGION
OF APPLICABILITY 7HEN K AND FTRACK ARE SMALL THEN THERE IS NO NEED FOR ANY MORE THAN
SIMPLE NEAREST NEIGHBOR TRACKING AND INDEED MOST TRACKING SYSTEMS STILL USE THIS
APPROACH !S K INCREASES THERE IS GREATER RISK OF FALSE ASSOCIATION DECISIONS HOWEVER
THE EFFECT OF THIS IS REDUCED IF FTRACK IS SMALL !T THE OTHER EXTREME WHEN K AND FTRACK ARE
LARGE THE TRACKING PROBLEM IS ESSENTIALLY UNSOLVABLE WITHOUT BASIC CHANGES TO THE RADAR
DESIGN PARAMETERS TO REDUCE THEM 4HERE IS AN INTERMEDIATE REGION WHERE SOPHISTICATED
ASSOCIATION HAS VALUE 4HE WIDTH OF THIS REGION IS VERY SPECIFIC TO THE PARTICULAR PROB
LEM 7HEN FTRACK IS LARGE AND VERY LITTLE DELAY IN THE OUTPUT CAN BE TOLERATED THEN THE
REGION OF APPLICABILITY IS FAIRLY SMALL AND VERY SIMPLE MULTIPLE HYPOTHESIS APPROACHES
SPLITTING TRACKS INTO AT MOST ONE OR TWO HYPOTHESES ARE THEN THE BEST ANSWER
7HEN FTRACK IS SMALL THEN 0$!*0$! CAN BE USED TO OPERATE AT SIGNIFICANTLY HIGHER
FALSE ALARM DENSITIES 7HEN SIGNIFICANT DELAY CAN BE TOLERATED IN THE OUTPUT THEN MANY
HYPOTHESES CAN BE FORMED AS IN &IGURE AND ORDERS OF MAGNITUDE MORE DETECTIONS
HANDLED "LACKMAN AND 0OPOLI PROVIDE A GOOD SURVEY OF COMPARATIVE STUDIES IN THIS
AREA /NE STUDY USING DATA RECORDED FROM FLIGHTS OF CLOSELY SPACED AIRCRAFT SHOWED
VERY LITTLE DIFFERENCE BETWEEN '.. *0$! AND -(4 (OWEVER THEORETICAL PREDIC
TIONS CAN SHOW DIFFERENCES OF ORDERS OF MAGNITUDE IN THE DENSITY OF CLUTTER DETECTIONS
THAT CAN BE HANDLED
.EW 4RACK &ORMATION 4HERE ARE TWO CLASSES OF TRACK FORMATION ALGORITHMS
&ORWARD TRACKING ALGORITHMS BASICALLY PROPAGATE ONE HYPOTHESIS FORWARD IN TIME
RECURSIVELY CHECKING FOR hTARGET LIKEv MOTION $ETECTIONS THAT DO NOT CORRELATE WITH
CLUTTER POINTS OR TRACKS ARE USED TO INITIATE NEW TRACKS )F THE DETECTION DOES NOT
CONTAIN DOPPLER INFORMATION THE NEW DETECTION IS USUALLY USED AS THE PREDICTED
POSITION IN SOME MILITARY SYSTEMS ONE ASSUMES A RADIALLY INBOUND VELOCITY AND
A LARGE CORRELATION REGION MUST BE USED FOR THE NEXT OBSERVATION 4HE CORRELATION
REGION MUST BE LARGE ENOUGH TO CAPTURE THE NEXT DETECTION OF THE TARGET ASSUMING
THAT IT COULD HAVE THE MAXIMUM VELOCITY OF INTEREST ! COMMON TRACK INITIATION
Ç°{Ó
2!$!2 (!.$"//+
CRITERION IS FOUR OUT OF FIVE ALTHOUGH ONE MAY REQUIRE ONLY THREE DETECTIONS OUT OF
FIVE OPPORTUNITIES IN REGIONS WITH A LOW FALSE ALARM RATE AND A LOW TARGET DENSITY
(OWEVER ONE MAY REQUIRE A MUCH LARGER NUMBER OF DETECTIONS WHEN THE RADAR HAS
THE FLEXIBILITY OF AN ELECTRONIC SCAN THAT CAN PLACE MANY DETECTION OPPORTUNITIES IN
A SHORT TIME INTERVAL
"ACKWARD TRACKING OR hBATCHv ALGORITHMS CONSIDER ALL THE DETECTIONS SIMULTANE
OUSLY ATTEMPTING TO MATCH THE DETECTIONS TO A hTARGET LIKEv PATTERN 4HIS CAN BE DONE
BY ACTUALLY CONSTRUCTING A LARGE NUMBER OF MATCHED FILTERS AS IN RETROSPECTIVE PRO
CESSING SEE &IGURE OR BY USING A FORWARD TRACKING PROCESS WITH MULTIPLE
HYPOTHESIS FORMED AND PROPAGATED
*UST AS AUTOMATIC RADAR DETECTION IS A TRADEOFF BETWEEN PROBABILITY OF DETECTION
AND PROBABILITY OF FALSE ALARM NEW TRACK FORMATION IS A TRADEOFF BETWEEN THE SPEED AT
WHICH A TRACK IS FORMED AND THE PROBABILITY OF ERRONEOUSLY FORMING A FALSE TRACK THAT
DOES NOT REPRESENT A PHYSICAL OBJECT OF INTEREST 4HERE ARE TWO TYPES OF FALSE TRACKS
4RACKS ON REAL OBJECTS THAT ARE SIMPLY NOT OF INTEREST &OR EXAMPLE IF THE TARGETS OF
INTEREST ARE AIRPLANES THEN A FALSE TRACK COULD BE A TRACK ON A BIRD 4RACKS COMPOSED
OF UNRELATED DETECTIONS FROM DIFFERENT OBJECTS THAT THE AUTOMATIC TRACKING PROCESS HAS
MISTAKENLY ASSOCIATED TOGETHER &OR EXAMPLE A FALSE TRACK COULD BE COMPOSED OF DETEC
TIONS FROM SEVERAL DIFFERENT STATIONARY CLUTTER POINTS THAT HAVE BEEN ASSOCIATED TOGETHER
OVER TIME TO CREATE A FALSE MOVING TRACK
4HE APPROACH FOR PREVENTING FALSE TRACKS ON OBJECTS NOT OF INTEREST IS TO ACTUALLY
DEVELOP TRACKS ON ALL OF THEM BUT THEN OBSERVE THEM LONG ENOUGH TO CLASSIFY THEM AS
UNWANTED )N THE CASE OF THE BIRD ONE WOULD GATHER ENOUGH DETECTIONS TO IMPROVE THE
VELOCITY ACCURACY OF THE TRACK SO THAT IT IS CLEAR WHETHER THE TRACK IS OF INTEREST OR NOT
4HUS ONE DESIRES TO DELAY THE DISCLOSURE OF A TRACK UNTIL ENOUGH TIME HAS PASSED TO
CLASSIFY IT ACCURATELY 4HIS ACCURACY CAN BE DETERMINED BY 4OBS THE AMOUNT OF TIME OVER
WHICH THE OBJECT IS OBSERVED AND BY BASIC PARAMETERS OF THE RADAR
4 THE TIME BETWEEN SUCCESSIVE DETECTIONS
R THE ACCURACY IN A PARTICULAR DIMENSION OF INTEREST
- THE NUMBER OF DETECTIONS USED IN FORMING THE TRACK
. 4OBS 4
WHICH IS THE NUMBER OF DETECTION OPPORTUNITIES
4HE VELOCITY ACCURACY IS GIVEN BY THE FOLLOWING EQUATION
SV S
§ . ¶
r
4OBS ¨© . . ·¸
4HE DOMINANT DESIGN PARAMETERS IN THE EQUATION ARE THE ACCURACY OF THE RADAR AND
THE OBSERVATION TIME "ETTER ACCURACY OR LONGER OBSERVATION TIME ALLOWS MORE ACCURATE
MEASUREMENT OF VELOCITY -AKING MORE DETECTIONS IN THE OBSERVATION TIME IMPROVES
THE ACCURACY BUT ONLY IN A SQUARE ROOT SENSE
4HE APPROACH TO PREVENTING FALSELY COMPOSED TRACKS FROM DIFFERENT OBJECTS IN A
CLUTTER REGION ' IS TO REQUIRE ENOUGH DETECTIONS IN A TIGHT ENOUGH PATTERN TO MAKE
%;.&4= THE EXPECTED NUMBER OF FALSE TRACKS SMALL 7HEN THERE IS AN AVERAGE OF .#
DETECTIONS IN A $ DIMENSIONAL REGION ' THEN
- %;.&4= K& r K¼
r . #- r F¼
$ . P
!54/-!4)# $%4%#4)/. 42!#+).' !.$ 3%.3/2 ).4%'2!4)/.
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&)'52% 4HE RETROSPECTIVE PROCESS A A SINGLE SCAN OF DATA B EIGHT SCANS OF DATA AND C EIGHT
SCANS OF DATA WITH TRAJECTORY FILTERS APPLIED AFTER 0RENGAMAN ET AL Ú )%%% Ç°{{
2!$!2 (!.$"//+
WHERE K& IS THE RATIO OF THE SIZE OF THE POSSIBLE SPACE A TARGET CAN TRAVEL IN ONE DETECTION
INTERVAL TO THE SIZE OF ENTIRE CLUTTER REGION '
L& 6-!8 $
'
AND K0 IS THE RATIO OF THE SIZE OF A RADAR RESOLUTION CELL TO THE SIZE OF THE ENTIRE CLUTTER
REGION '
L0 T • • • T $
'
$ . - BEING THE COM
SI BEING THE RESOLUTION hDISTANCEv IN THE ITH DIMENSION AND F¼
BINATORIAL TERM
¤ . ³ $ - G $ . - . $ ¥
¦ - ´µ
&IGURE GIVES AN EXAMPLE OF THE APPLICATION OF %QS TO TO A RADAR
WITH K0 AND K0 )NCREASING THE NUMBER OF DETECTIONS REQUIRED TO FORM
&)'52% 6ARIATION OF THE EXPECTED NUMBER OF FALSE TRACKS WITH THE TRACK FORMATION - OUT OF . CRITE
RION AFTER 7 ' "ATH ET AL
!54/-!4)# $%4%#4)/. 42!#+).' !.$ 3%.3/2 ).4%'2!4)/.
Ç°{x
A TRACK FROM THREE OUT OF FIVE TO FIVE OUT OF EIGHT INCREASES THE DENSITY OF FALSE
ALARMS THAT CAN BE TOLERATED BY MORE THAN AN ORDER OF MAGNITUDE &ORWARD AND
BACKWARD TRACKING ALGORITHMS PRODUCE SIMILAR NUMBERS OF FALSE TRACKS (OWEVER
THE BACKWARD TRACKING ALGORITHMS CAN OPERATE IN MORE AMBIGUOUS SITUATIONS WHERE
THE DENSITY OF FALSE ALARMS K IS COMPARABLE TO OR GREATER THAN K& OR K0 5NDER THESE
AMBIGUOUS CIRCUMSTANCES THE FORWARD TRACKER WILL HAVE MULTIPLE DETECTIONS IN A
TRACK FORMATION OR PROMOTION GATE AND WILL REQUIRE MULTIPLE HYPOTHESIS TO RELIABLY
FORM TRACKS
4HE DESIGN OF THE TRACK FORMATION PROCESS AND THE AUTOMATIC DETECTION PROCESS
SHOULD BE CONSIDERED TOGETHER ! LONGER TIME ALLOWED FOR TRACK FORMATION HIGHER
-. ALLOWS THE RADAR DETECTION PROCESS TO USE LOWER DETECTION THRESHOLDS RESULT
ING IN BETTER RADAR SENSITIVITY &OR ANY GIVEN SET OF RADAR PARAMETERS -. TRACK
FORMATION CRITERION AND PROBABILITY DISTRIBUTION OF CLUTTER AMPLITUDES THERE EXISTS
AN OPTIMUM FALSE ALARM RATE THAT MINIMIZES THE SIGNAL TO NOISE RATIO REQUIRED TO
DETECT TARGETS &IGURE ILLUSTRATES THIS OPTIMIZATION FOR AN EIGHT SCAN TRACK FOR
MATION PROCESS
&)'52% /VERALL SENSITIVITY OF AN AUTOMATIC DETECTION AND AUTOMATIC
TRACKING PROCESS WORKING TOGETHER 4HE SINGLE SCAN FALSE ALARM PROBABILITY
CAN BE OPTIMIZED TO PROVIDE THE LOWEST REQUIRED SIGNAL TO NOISE RATIO FOR VARI
OUS PROBABILITY DISTRIBUTIONS OF CLUTTER AMPLITUDE AFTER 0RENGAMAN ET AL
Ú )%%% Ç°{È
2!$!2 (!.$"//+
6ERY LOW SINGLE SCAN FALSE ALARM PROBABILITIES ALLOW TRACKS TO BE FORMED QUICKLY
(OWEVER IF A LONGER DELAY IS TOLERABLE THEN DETECTION THRESHOLDS CAN BE LOWER RESULT
ING IN BETTER SENSITIVITY IN NON GAUSSIAN CLUTTER
2ADAR 3CHEDULING AND #ONTROL 4HE INTERACTION OF THE RADAR TRACKING SYSTEM
WITH THE SCHEDULING AND CONTROL FUNCTION OF THE RADAR IS MINOR FOR MECHANICAL ROTATING
RADARS BUT MAJOR FOR PHASED ARRAY RADARS &OR MECHANICALLY ROTATING RADARS ALL THAT IS
USUALLY DONE IS THAT THE TRACKING GATES ARE FED BACK TO THE SIGNAL PROCESSOR 4HE TRACKING
GATES ARE ALWAYS USED TO FACILITATE THE ASSOCIATION PROCESS AND MAY BE USED TO LOWER
THE DETECTION THRESHOLD WITHIN THE GATE ANDOR MODIFY THE CONTACT ENTRY LOGIC WITHIN THE
GATE EG MODIFY RULES GOVERNING CLUTTER MAPS 4HE INTERACTION OF THE TRACKING SYSTEM WITH A PHASED ARRAY RADAR IS MUCH MORE SIG
NIFICANT 4HE MAJOR BENEFIT OF A PHASED ARRAY WITH RESPECT TO TRACKING IS IN THE AREA OF
TRACK INITIATION 0HASED ARRAYS USE A CONFIRMATION STRATEGY TO INITIATE TRACKS RAPIDLY
4HAT IS AFTER THE ASSOCIATION PROCESS ALL UNASSOCIATED DETECTIONS GENERATE CONFIRMATION
DWELLS TO CONFIRM THE EXISTENCE OF A NEW TRACK 4HE INITIAL CONFIRMATION DWELL USES THE
SAME WAVEFORM FREQUENCY AND 02& IF A PULSE DOPPLER WAVEFORM BUT MAY INCREASE THE
ENERGY !NALYSIS HAS SHOWN THAT A D" INCREASE IN THE TRANSMITTED CONFIRMATION ENERGY
ADDITIONAL ENERGY IS ALSO AVAILABLE BY PLACING THE TARGET IN THE CENTER OF THE CONFIRMA
TION BEAM CAN SIGNIFICANTLY INCREASE THE PROBABILITY OF CONFIRMATION &URTHERMORE
THE CONFIRMATION DWELL SHOULD BE TRANSMITTED AS SOON AS POSSIBLE TO MAINTAIN A 3WERLING
) FLUCTUATION MODEL 4HAT IS IF THE TARGET WAS ORIGINALLY DETECTED WHEN THE TARGET FLUC
TUATION PRODUCED A LARGE RETURN THE CONFIRMATION DWELL WILL SEE THIS SAME LARGE RETURN
!FTER CONFIRMATION A SERIES OF INITIAL TRACK MAINTENANCE DWELLS OVER SEVERAL SECONDS IS
USED TO DEVELOP AN ACCURATE STATE VECTOR ! COMPLETE DISCUSSION OF PRIORITY ASSOCIATED
WITH TRACKING WITHIN THE SCHEDULER OF A PHASED ARRAY IS BEYOND THE SCOPE OF THIS BRIEF
DISCUSSION (OWEVER IT IS WORTHWHILE NOTING THESE GENERAL RULES #ONFIRMATION DWELLS
SHOULD HAVE A PRIORITY HIGHER THAN ALL OTHER FUNCTIONS EXCEPT THOSE ASSOCIATED WITH WEAPON
CONTROL LOW PRIORITY TRACKS EG TRACKS AT LONG RANGE CAN BE UPDATED USING SEARCH
DETECTIONS AND HIGH PRIORITY TRACKS SHOULD HAVE A PRIORITY HIGHER THAN VOLUME SURVEIL
LANCE 4HE UPDATE RATE FOR HIGH PRIORITY TRACKS SHOULD BE SUCH THAT A SINGLE TRACKING DWELL IS
SUFFICIENT TO UPDATE THE TRACK 4HE ACTUAL UPDATE RATE WILL DEPEND ON MANY FACTORS INCLUD
ING A MAXIMUM TARGET SPEED AND MANEUVER CAPABILITY B RADAR BEAMWIDTH BEAM COULD
BE SPOILED C RANGE OF THE RADAR TRACK AND D ACCURACY OF PREDICTED POSITION )F A PULSE
DOPPLER DWELL IS REQUIRED TO UPDATE THE TRACK IN CLUTTER THE WAVEFORM SHOULD BE SELECTED TO
PLACE THE TARGET NEAR THE CENTER OF THE AMBIGUOUS RANGE DOPPLER DETECTION SPACE &INALLY
THE TRACK CAN BE UPDATED WITH THE AMBIGUOUS RANGE DOPPLER DETECTION BECAUSE THE TRACK
STATE VECTOR CAN BE USED TO REMOVE THE AMBIGUITY
Ç°{Ê
/7",
Ê, ,-
)DEALLY A SINGLE RADAR CAN RELIABLY DETECT AND TRACK ALL TARGETS OF INTEREST (OWEVER THE
ENVIRONMENT AND THE LAWS OF PHYSICS OFTEN WILL NOT PERMIT THIS )N GENERAL NO SINGLE
RADAR CAN PROVIDE A COMPLETE SURVEILLANCE AND TRACKING PICTURE 2ADAR NETWORKING CAN
BE A GOOD SOLUTION TO THIS PROBLEM AND IN SOME CASES MAY BE MORE COST EFFECTIVE THAN
SOLVING THE PROBLEM THROUGH ONE VERY HIGH PERFORMANCE RADAR 2ADAR NETWORKING SYSTEMS
ARE GENERALLY CHARACTERIZED BY WHAT RADAR DATA ARE SHARED AND HOW THEY ARE CORRELATED
AND FUSED 4HE TWO MOST COMMON WAYS OF COMBINING RADAR DATA ARE AS FOLLOWS
!54/-!4)# $%4%#4)/. 42!#+).' !.$ 3%.3/2 ).4%'2!4)/.
Ç°{Ç
$ETECTION TO TRACK FUSION SEE &IGURE UPPER HALF ASSOCIATES EACH DETECTION TO
THE NETWORKED TRACK CALCULATED POTENTIALLY USING DETECTIONS FROM ALL RADARS 4HUS
THE ENTIRE STREAM OF DETECTIONS UP TO THE PRESENT IS POTENTIALLY AVAILABLE TO CALCU
LATE THE TRACK STATE USED FOR THE ASSOCIATION DECISION ON THE MOST RECENT DETECTION
4RACK TO TRACK FUSION SEE &IGURE LOWER HALF ASSOCIATES EACH DETECTION TO A
SINGLE RADAR TRACK STATE CALCULATED USING ONLY DETECTIONS FROM THAT RADAR 4HE SINGLE
RADAR TRACK STATES ARE THEN GROUPED WITH EACH OTHER TO PRODUCE A NETTED TRACK STATE
4HE DESIGN DECISION AS TO WHICH APPROACH IS BETTER FOR GROUPING DATA DEPENDS ON THE
RADARS AND TARGETS INVOLVED /NE CASE WHERE DETECTION TO TRACK ASSOCIATION IS CLEARLY BET
TER IS WHEN THE RADARS HAVE A REDUCED PROBABILITY OF DETECTION SO THERE ARE POTENTIAL GAPS
IN THE DATA STREAM OR PERIODS WHERE THE DATA STREAM IS SPARSE )N THESE CASES A MUCH MORE
ACCURATE TRACK STATE CAN BE CALCULATED USING MULTIPLE DATA STREAMS THAN USING ONLY ONE
BECAUSE MULTIPLE STREAMS WILL TEND TO FILL IN THE GAPS IN DETECTION AND RESTORE A HIGH CON
SISTENT DATA RATE DURING PERIODS OF REDUCED PROBABILITY OF DETECTION &IGURE ILLUSTRATES
THE SENSITIVITY TO TARGET FADES BY PLOTTING THE TRACK REGION OF UNCERTAINTY 2/5 VERSUS THE
PROBABILITY OF DETECTION FOR SINGLE RADAR TRACKING AND MULTIPLE RADAR TRACKING 4HE 2/5 IS
DEFINED AS THE DISTANCE THAT CONTAINS THE ERROR WITH PERCENT PROBABILITY AND IS
2/5 TRACKING ERROR DUE TO DETECTION NOISE
TRACKING ERROR DUE TO MANEUVER
4HIS CAN BE CALCULATED FOR ANY CASE OF INTEREST USING THE FORMULAS IN 4ABLE &)'52% 4HERE ARE TWO COMMON METHODS OF FUSION DATA IN RADAR NETWORKING DETECTION TO TRACK AND
TRACK TO TRACK AFTER 7 "ATH Ú )%% Ç°{n
2!$!2 (!.$"//+
&)'52% #OMPARISON OF DETECTION TO TRACK AND TRACK TO TRACK ASSOCIATION &OR FAD
ING TARGETS 0D DETECTION TO TRACK IS PREFERRED &OR LARGE SENSOR BIASES AND NON FADING
TARGETS TRACK TO TRACK IS PREFERRED AFTER 7"ATH Ú )%% 7HEN THE PROBABILITY OF DETECTION IS MUCH LESS THAN UNITY THE MEASUREMENT TO TRACK
FUSION IS CONSIDERABLY MORE ACCURATE 4HIS IS EASILY EXPLAINED BY THE FACT THAT THE PROB
ABILITY OF A SIGNIFICANT OUTAGE OF DATA IS MUCH REDUCED IF TWO SOURCES ARE AVAILABLE 7ITH
A MORE ACCURATE TRACK TIGHTER ASSOCIATION CRITERIA CAN BE USED FOR DETECTIONS
)F THE BIASES CANNOT BE EFFECTIVELY REMOVED THEN THERE MAY BE AN ADVANTAGE TO ASSO
CIATING TO A SINGLE RADAR TRACKˆWHICH BY DEFINITION IS UNBIASED WITH RESPECT TO ITSELF
)F BIASES CANNOT BE KEPT SMALLER THAN THE 2/5 THEN AT HIGH PROBABILITIES OF DETECTION
ONE PREFERS SINGLE RADAR ASSOCIATION FOLLOWED BY TRACK TO TRACK ASSOCIATION
)T IS POSSIBLE TO MAKE SIMPLE COMPARISONS BETWEEN THE ACCURACY OF DETECTION FUSION
AS OPPOSED TO TRACK FUSION FOR EQUIVALENT USE OF DATA BANDWIDTH TO EXCHANGE RADAR DATA
7HEN 2/5 IS PLOTTED AS A FUNCTION OF THE POSITION GAIN @ IT HAS THE hBATHTUBv SHAPE
SHOWN BY THE SINGLE RADAR CURVE IN &IGURE 4HE LEFT HAND SIDE OF THE hBATHTUBv IS
DOMINATED BY THE LAG COMPONENT WHILE THE RIGHT HAND SIDE IS DOMINATED BY THE RADAR
MEASUREMENT NOISE COMPONENT "ECAUSE THE GAINS HORIZONTAL AXIS ARE THE DESIGNERS
CHOICE THE SINGLE RADAR 2/5 IS THE MINIMUM OF THE hBATHTUBv CURVE
.OW CONSIDER THE FUSION OF TWO RADARS IN A PARTICULAR DIMENSION )F ONE RADAR HAS ONE
TENTH THE 2/5 OF THE OTHER IN THIS DIMENSION THEN THE MORE ACCURATE RADAR IN THIS DIMENSION
WILL DOMINATE AND ESSENTIALLY DETERMINE THE RESULT !T LEAST IN STEADY STATE IT IS RELATIVELY
EASY TO PRODUCE THIS DOMINANCE BY ANY OF THE FUSION METHODS /F MORE INTEREST IS THE CASE
WHERE THE RADARS ARE COMPARABLE IN TERMS OF ACCURACY AND UPDATE RATE PRODUCING COMPA
RABLE 2/5S 4HIS CASE MORE CLEARLY SHOWS THE DIFFERENCE IN THE FUSION METHODS
&OR EXAMPLE WHEN TWO IDENTICAL RADARS ARE COMBINED BY DETECTION FUSION THEN
THE UPDATE RATE IS ESSENTIALLY DOUBLED 4HIS REDUCES THE LAG BY A FACTOR OF ALLOWING A
SMALLER GAIN TO BE SELECTED OPTIMIZATION MORE TO THE LEFT OF THE hBATHTUBv REDUCING
THE TRACKING ERRORS DUE TO MEASUREMENT NOISE 4HE NET RESULT IS THE MOVEMENT FROM THE
SINGLE RADAR CURVE TO THE DETECTION FUSION CURVE IN &IGURE !54/-!4)# $%4%#4)/. 42!#+).' !.$ 3%.3/2 ).4%'2!4)/.
Ç°{™
&)'52% #OMPARISON OF DETECTION FUSION AND TRACK FUSION APPROACHES &OR AIR BREATHING TARGETS
DETECTION FUSION PRODUCES THE MOST ACCURATE TRACK SMALLEST 2/5 AFTER 7"ATH Ú )%% 7HEN TWO IDENTICAL RADARS ARE COMBINED BY TRACK FUSION THE UPDATE RATE FOR EACH
TRACKING PROCESS DOES NOT CHANGE AND SO THE LAG DOES NOT CHANGE (OWEVER THE STAN
DARD DEVIATION OF THE TRACKING ERRORS DUE TO MEASUREMENT NOISE IS REDUCED BY THE SQUARE
ROOT OF ALLOWING A LARGER GAIN TO BE SELECTED OPTIMIZATION MORE TO THE RIGHT OF THE
BATHTUB REDUCING THE LAG 4HE NET RESULT IS THE MOVEMENT FROM THE SINGLE RADAR CURVE
TO THE TRACK FUSION CURVE IN &IGURE )F THERE IS ANY SIGNIFICANT MANEUVER POSSIBLE THE FACTOR OF IN LAG WILL HAVE A MORE
SIGNIFICANT EFFECT THAN THE FACTOR OF THE SQUARE ROOT OF IN THE SQUARE ROOT OF THE TRACKING
ERRORS DUE TO MEASUREMENT NOISE 4HUS ONE CAN SEE THE DETECTION FUSION CURVE ACHIEVES
A SIGNIFICANTLY LOWER MINIMUM THAN THE TRACK FUSION CURVE
4O COMBINE DATA FROM MULTIPLE RADARS THE DATA MUST BE PLACED IN A COMMON COOR
DINATE SYSTEM 4HIS PROCESS IS CALLED GRID LOCKING AND INVOLVES SPECIFYING THE LOCATION
OF THE RADARS AND ESTIMATING RADAR BIASES IN RANGE AND ANGLE 4HE PREVIOUS DIFFICULT
PROBLEM OF RADAR LOCATION IS SOLVED TRIVIALLY BY THE GLOBAL POSITIONING SYSTEM !N ESTI
MATE OF RADAR BIASES BETWEEN TWO RADARS CAN BE OBTAINED FROM A LONG TERM AVERAGE OF
THE DIFFERENCE BETWEEN PREDICTED AND MEASURED COORDINATES ON ALL TRACKS THAT HAVE A
SUBSTANTIAL NUMBER OF DETECTIONS FROM BOTH RADARS
Ç°xÊ 1 ‡-
-",Ê / ,/"
! NUMBER OF SENSORS CAN BE INTEGRATED RADAR IDENTIFICATION FRIEND OR FOE )&& THE
AIR TRAFFIC CONTROL RADAR BEACON SYSTEM !4#2"3 INFRARED OPTICAL AND ACOUSTIC 4HE
SENSORS THAT ARE MOST EASILY INTEGRATED ARE THE ELECTROMAGNETIC SENSORS IE RADAR )&&
AND STROBE EXTRACTORS OF NOISE SOURCES OR EMITTERS
Ç°xä
2!$!2 (!.$"//+
)&& )NTEGRATION 4HE PROBLEM OF INTEGRATING RADAR AND MILITARY )&& DATA IS LESS
DIFFICULT THAN THAT OF INTEGRATING TWO RADARS 4HE QUESTION OF WHETHER DETECTIONS OR
TRACKS SHOULD BE INTEGRATED IS A FUNCTION OF THE APPLICATION )N A MILITARY SITUATION BY
INTEGRATING DETECTIONS ONE COULD INTERROGATE THE TARGET ONLY A FEW TIMES IDENTIFY IT
AND THEN ASSOCIATE IT WITH A RADAR TRACK &ROM THEN ON THERE WOULD BE LITTLE NEED FOR
RE INTERROGATING THE TARGET (OWEVER IN AN AIR TRAFFIC CONTROL SITUATION USING !4#2"3
TARGETS WOULD BE INTERROGATED AT EVERY SCAN AND CONSEQUENTLY EITHER DETECTIONS OR
TRACKS COULD BE INTEGRATED
2ADARn$& "EARING 3TROBE )NTEGRATION #ORRELATING RADAR TRACKS WITH $&
DIRECTION FINDING BEARING STROBES ON EMITTERS HAS BEEN CONSIDERED BY #OLEMAN AND
LATER BY 4RUNK AND 7ILSON 4RUNK AND 7ILSON CONSIDERED THE PROBLEM OF ASSOCI
ATING EACH $& TRACK WITH EITHER NO RADAR TRACK OR ONE OF M RADAR TRACKS )N THEIR FOR
MULATION THERE WERE + $& ANGLE TRACKS EACH SPECIFIED BY A DIFFERENT NUMBER OF $&
DETECTIONS AND SIMILARLY M RADAR TRACKS EACH SPECIFIED BY A DIFFERENT NUMBER OF RADAR
DETECTIONS "ECAUSE EACH TARGET CAN CARRY MULTIPLE EMITTERS IE MULTIPLE $& TRACKS
CAN BE ASSOCIATED WITH EACH RADAR TRACK EACH $& TRACK ASSOCIATION CAN BE CONSIDERED
BY ITSELF RESULTING IN + DISJOINT ASSOCIATION PROBLEMS #ONSEQUENTLY AN EQUIVALENT
PROBLEM IS GIVEN A $& TRACK SPECIFIED BY N $& BEARING DETECTIONS ONE CAN ASSOCIATE
THE $& TRACK WITH NO RADAR TRACK OR WITH ONE OF M RADAR TRACKS THE JTH RADAR TRACK BEING
SPECIFIED BY MJ RADAR DETECTIONS 5SING A COMBINATION OF "AYES AND .EYMAN 0EARSON
PROCEDURES AND ASSUMING THAT THE $& DETECTION ERRORS ARE USUALLY INDEPENDENT AND
GAUSSIAN DISTRIBUTED WITH ZERO MEAN AND CONSTANT VARIANCE R BUT WITH OCCASIONAL OUT
LIERS IE LARGE ERRORS NOT DESCRIBED BY THE GAUSSIAN DENSITY 4RUNK AND 7ILSON ARGUED
THAT THE DECISION SHOULD BE BASED ON THE PROBABILITY
0J PROBABILITY : q DJ
WHERE : HAS A CHI SQUARE DENSITY WITH NJ DEGREES OF FREEDOM AND DJ IS GIVEN BY
NJ
D J £ MIN[ ;Q E TI
Q J TI = S ]
J M
I WHERE NJ IS THE NUMBER OF $& DETECTIONS OVERLAPPING THE TIME INTERVAL FOR WHICH THE
JTH RADAR TRACK EXISTS PETI IS THE $& DETECTION AT TIME TI PJTI IS THE PREDICTED AZIMUTH
OF RADAR TRACK J FOR TIME TI AND THE FACTOR LIMITS THE SQUARE ERROR TO R TO ACCOUNT FOR
$& OUTLIERS "Y USING THE TWO LARGEST 0JS DESIGNATED 0MAX AND 0NEXT AND THRESHOLDS
4, 4( 4- AND 2 THE FOLLOWING DECISIONS AND DECISION RULES WERE GENERATED
&IRM CORRELATION $& SIGNAL GOES WITH RADAR TRACK HAVING LARGEST 0J IE 0MAX
WHEN 0MAX q 4( AND 0MAX q 0NEXT 2
4ENTATIVE CORRELATION $& SIGNAL PROBABLY GOES WITH RADAR TRACK HAVING LARGEST 0J
IE 0MAX WHEN 4( 0MAX q 4- AND 0MAX q 0NEXT 2
4ENTATIVE CORRELATION WITH SOME TRACK $& SIGNAL PROBABLY GOES WITH SOME RADAR
TRACK BUT CANNOT DETERMINE WHICH WHEN 0MAX q 4- BUT 0MAX 0NEXT 2
4ENTATIVELY UNCORRELATED $& SIGNAL PROBABLY DOES NOT GO WITH ANY RADAR TRACK
WHEN 4- 0MAX 4,
&IRMLY UNCORRELATED $& SIGNAL DOES NOT GO WITH ANY RADAR TRACK WHEN 4, q 0MAX
!54/-!4)# $%4%#4)/. 42!#+).' !.$ 3%.3/2 ).4%'2!4)/.
Ç°x£
4HE LOWER THRESHOLD 4, DETERMINES THE PROBABILITY THAT THE CORRECT RADAR TRACK IE
THE ONE ASSOCIATED WITH THE $& SIGNAL WILL BE INCORRECTLY REJECTED FROM FURTHER CONSID
ERATION )F THE DESIRED REJECTION RATE FOR THE CORRECT TRACK IS 02 ONE CAN OBTAIN THIS BY
SETTING 4, 02 4HE THRESHOLD 4( IS SET EQUAL TO 0FA DEFINED AS THE PROBABILITY OF FALSELY
ASSOCIATING A RADAR TRACK WITH A $& SIGNAL WHEN THE $& SIGNAL DOES NOT BELONG WITH
THE RADAR TRACK 4HE THRESHOLD 4( IS A FUNCTION OF THE AZIMUTH DIFFERENCE L BETWEEN THE
TRUE $& POSITION AND THE RADAR TRACK UNDER CONSIDERATION 4HE THRESHOLD 4( WAS FOUND
FOR L R AND L R BY SIMULATION TECHNIQUES AND THE RESULTS FOR 0FA ARE
SHOWN IN &IGURE "ETWEEN THE HIGH AND LOW THRESHOLDS THERE IS A TENTATIVE REGION
4HE MIDDLE THRESHOLD DIVIDES THE hTENTATIVEv REGION INTO A TENTATIVELY CORRELATED REGION
AND A TENTATIVELY UNCORRELATED REGION 4HE RATIONALE IN SETTING THE THRESHOLD IS TO SET THE
TWO ASSOCIATED ERROR PROBABILITIES EQUAL FOR A PARTICULAR SEPARATION 4HE THRESHOLD 4WAS FOUND BY USING SIMULATION TECHNIQUES AND IS ALSO SHOWN IN &IGURE 4HE PROBABILITY MARGIN 2 ENSURES THE SELECTION OF THE PROPER $& RADAR ASSOCIATION
AVOIDING RAPIDLY CHANGING DECISIONS WHEN THERE ARE TWO OR MORE RADAR TRACKS CLOSE
TO ONE ANOTHER 4HE CORRECT SELECTION IS REACHED BY POSTPONING A DECISION UNTIL THE TWO
HIGHEST ASSOCIATION PROBABILITIES DIFFER BY 2 4HE VALUE FOR 2 IS FOUND BY SPECIFYING A
PROBABILITY OF AN ASSOCIATION ERROR 0E ACCORDING TO 0E 0 0MAX q 0NEXT 2 WHERE
0MAX CORRESPONDS TO AN INCORRECT ASSOCIATION AND 0NEXT CORRESPONDS TO THE CORRECT
ASSOCIATION 4HE PROBABILITY MARGIN 2 IS A FUNCTION OF 0E AND THE SEPARATION L OF THE
RADAR TRACKS 4HE PROBABILITY MARGIN 2 WAS FOUND FOR L R R AND R BY
USING SIMULATION TECHNIQUES AND THE RESULTS FOR 0E ARE SHOWN IN &IGURE &)'52% (IGH THRESHOLD SOLID LINES AND MIDDLE THRESHOLD DASHED LINES
VERSUS NUMBER OF SAMPLES FOR TWO DIFFERENT SEPARATIONS AFTER '6 4RUNK AND *$
7ILSON Ú )%%% Ç°xÓ
2!$!2 (!.$"//+
&)'52% 0ROBABILITY MARGIN VERSUS NUMBER OF $& DETECTIONS FOR
THREE DIFFERENT TARGET SEPARATIONS 4HE OS XS AND $S ARE THE SIMULATION
RESULTS FOR L L AND L RESPECTIVELY AFTER '6 4RUNK AND
*$ 7ILSON Ú )%%% "ECAUSE THE CURVES CROSS ONE ANOTHER ONE CAN ENSURE THAT 0E a FOR ANY L BY SETTING
2 EQUAL TO THE MAXIMUM VALUE OF ANY CURVE FOR EACH VALUE OF N
4HE ALGORITHM WAS EVALUATED BY USING SIMULATIONS AND RECORDED DATA 7HEN THE
RADAR TRACKS ARE SEPARATED BY SEVERAL STANDARD DEVIATIONS OF THE DETECTION ERROR COR
RECT DECISIONS ARE MADE RAPIDLY (OWEVER IF THE RADAR TRACKS ARE CLOSE TO ONE ANOTHER
ERRORS ARE AVOIDED BY POSTPONING THE DECISION UNTIL SUFFICIENT DATA ARE ACCUMULATED !N
INTERESTING EXAMPLE WITH RECORDED DATA IS SHOWN IN &IGURES AND &IGURE SHOWS THE RADAR AZIMUTH DETECTIONS OF THE CONTROL AIRCRAFT THE RADAR DETECTIONS OF FOUR
AIRCRAFT OF OPPORTUNITY IN THE VICINITY OF THE CONTROL AIRCRAFT AND THE $& DETECTIONS ON
THE RADAR ON THE CONTROL AIRCRAFT 4HE ASSOCIATION PROBABILITIES WITH AND WITHOUT LIMIT
ING IN %Q ARE SHOWN IN &IGURE )NITIALLY AN AIRCRAFT OF OPPORTUNITY HAS THE
HIGHEST ASSOCIATION PROBABILITY HOWEVER A FIRM DECISION IS NOT MADE BECAUSE 0MAX
DOES NOT EXCEED 0NEXT BY THE PROBABILITY MARGIN !FTER THE TH $& DETECTION THE
EMITTER IS FIRMLY CORRELATED WITH THE CONTROL AIRCRAFT (OWEVER AT THE TH $& DETEC
TION A VERY BAD DETECTION OUTLIER IS MADE AND THE FIRM CORRELATION IS DOWNGRADED
TO A TENTATIVE CORRELATION IF LIMITING IS NOT USED )F LIMITING IS EMPLOYED HOWEVER THE
CORRECT DECISION REMAINS FIRM
)N A COMPLEX ENVIRONMENT WHERE THERE ARE MANY RADAR TRACKS AND $& SIGNAL SOURCES
IT IS QUITE POSSIBLE THAT MANY $& SIGNALS WILL BE ASSIGNED THE CATEGORY THAT THE $&
SIGNAL PROBABLY GOES WITH SOME RADAR TRACK 4O REMOVE MANY OF THESE AMBIGUITIES
MULTISITE $& OPERATION CAN BE CONSIDERED 4HE EXTENSION OF THE PREVIOUS PROCEDURES
!54/-!4)# $%4%#4)/. 42!#+).' !.$ 3%.3/2 ).4%'2!4)/.
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&)'52% 2ADAR DETECTIONS O AND $& DETECTIONS COLLECTED ON THE CONTROL AIRCRAFT 4HE OS
$S S AND XS ARE RADAR DETECTIONS ON FOUR AIRCRAFT OF OPPORTUNITY IN THE VICINITY OF THE CONTROL
AIRCRAFT AFTER '6 4RUNK AND *$ 7ILSON Ú )%%% &)'52% !SSOCIATION PROBABILITIES FOR EXPERIMENTAL DATA 4HE BOLD LINES ARE PROBABILITIES FOR
THE CONTROL AIRCRAFT THE SOLID LINE FOR LIMITING THE DASHED LINE FOR NO LIMITING THE THIN LINE THE ASSO
CIATION PROBABILITY FOR THE AIRCRAFT OF OPPORTUNITY AND THE THIN DASHED LINES THE THRESHOLDS 4- AND 4(
AFTER '6 4RUNK AND *$ 7ILSON Ú )%%% Ç°x{
2!$!2 (!.$"//+
TO MULTISITE OPERATION IS STRAIGHTFORWARD 3PECIFICALLY IF PETI AND PETK ARE THE $&
ANGLE DETECTIONS WITH RESPECT TO SITES AND AND IF PJTI AND PJTK ARE THE ESTI
MATED ANGULAR POSITIONS OF RADAR TRACK J WITH RESPECT TO SITES AND THEN THE MULTISITE
SQUARED ERROR IS SIMPLY
N J
[
D J £ MIN ;Q E TI
I N J
] £ MIN [ ;Q T
Q J TI = S E
K K
]
Q J TK = S 4HE PREVIOUSLY DESCRIBED PROCEDURE CAN THEN BE USED WITH DJ BEING DEFINED BY
%Q INSTEAD OF %Q , ,
-
* ) -ARCUM h! STATISTICAL THEORY OF TARGET DETECTION BY PULSED RADAR v )2% 4RANS VOL )4 PP n !PRIL 0 3WERLING h0ROBABILITY OF DETECTION FOR FLUCTUATING TARGETS v )2% 4RANS VOL )4 PP n
!PRIL * .EYMAN AND % 3 0EARSON h/N THE PROBLEMS OF THE MOST EFFICIENT TESTS OF STATISTICAL HYPOTH
ESES v 0HILOS 4RANS 2 3OC ,ONDON VOL SER ! P , 6 "LAKE h4HE EFFECTIVE NUMBER OF PULSES PER BEAMWIDTH FOR A SCANNING RADAR v 0ROC )2%
VOL PP n *UNE ' 6 4RUNK h#OMPARISON OF THE COLLAPSING LOSSES IN LINEAR AND SQUARE LAW DETECTORS v 0ROC
)%%% VOL PP n *UNE 0 3WERLING h-AXIMUM ANGULAR ACCURACY OF A PULSED SEARCH RADAR v 0ROC )2% VOL PP n
3EPTEMBER ' 6 4RUNK h3URVEY OF RADAR !$4 v .AVAL 2ES ,AB 2EPT *UNE ' 6 4RUNK h#OMPARISON OF TWO SCANNING RADAR DETECTORS 4HE MOVING WINDOW AND THE FEEDBACK
INTEGRATOR v )%%% 4RANS VOL !%3 PP n -ARCH ' 6 4RUNK h$ETECTION RESULTS FOR SCANNING RADARS EMPLOYING FEEDBACK INTEGRATION v )%%% 4RANS
VOL !%3 PP n *ULY ' 6 4RUNK AND " ( #ANTRELL h!NGULAR ACCURACY OF A SCANNING RADAR EMPLOYING A POLE INTEGRA
TOR v )%%% 4RANS VOL !%3 PP n 3EPTEMBER " ( #ANTRELL AND ' 6 4RUNK h#ORRECTIONS TO @ANGULAR ACCURACY OF A SCANNING RADAR EMPLOYING
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VOL PP n -AY 6 ' (ANSEN h0ERFORMANCE OF THE ANALOG MOVING WINDOW DETECTION v )%%% 4RANS VOL !%3 PP n -ARCH 0 3WERLING h4HE @DOUBLE THRESHOLD METHOD OF DETECTION v 0ROJECT 2AND 2ES -EM 2- $ECEMBER * 6 (ARRINGTON h!N ANALYSIS OF THE DETECTION OF REPEATED SIGNALS IN NOISE BY BINARY INTEGRATION v
)2% 4RANS VOL )4 PP n -ARCH - 3CHWARTZ h! COINCIDENCE PROCEDURE FOR SIGNAL DETECTION v )2% 4RANS VOL )T PP n
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$# PP n
h2ADAR PROCESSING SUBSYSTEM EVALUATION v VOL *OHNS (OPKINS 5NIVERSITY !PPL 0HYS ,AB
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SPACIALLY SAMPLED CLUTTER LEVEL ESTIMATES v 2#! 2EV VOL PP n 3EPTEMBER 2 , -ITCHELL AND * & 7ALKER h2ECURSIVE METHODS FOR COMPUTING DETECTION PROBABILITIES v )%%%
4RANS VOL !%3 PP n *ULY ' 6 4RUNK AND * $ 7ILSON h!UTOMATIC DETECTOR FOR SUPPRESSION OF SIDELOBE INTERFERENCE v IN
)%%% #ONF $ECISION #ONTROL $ECEMBER n PP n
' 6 4RUNK AND 0 + (UGHES )) h!UTOMATIC DETECTORS FOR FREQUENCY AGILE RADAR v IN )%% )NT
2ADAR #ONF ,ONDON PP n
' 6 4RUNK " ( #ANTRELL AND & $ 1UEEN h-ODIFIED GENERALIZED SIGN TEST PROCESSOR FOR $
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PP n -ARCH " ! 'REEN h2ADAR DETECTION PROBABILITY WITH LOGARITHMIC DETECTORS v )2% 4RANS VOL )4 -ARCH 6 ' (ANSEN AND * 2 7ARD h$ETECTION PERFORMANCE OF THE CELL AVERAGE LOG#&!2 RECEIVER v
)%%% 4RANS VOL !%3 PP n 3EPTEMBER ' - $ILLARD AND # % !NTONIAK h! PRACTICAL DISTRIBUTION FREE DETECTION PROCEDURE FOR MULTIPLE
RANGE BIN RADARS v )%%% 4RANS VOL !%3 PP n 3EPTEMBER 6 ' (ANSEN AND " ! /LSEN h.ONPARAMETRIC RADAR EXTRACTION USING A GENERALIZED SIGN TEST v
)%%% 4RANS VOL !%3 3EPTEMBER 7 ' "ATH , ! "IDDISON 3 & (AASE AND % # 7ETZLAR h&ALSE ALARM CONTROL IN AUTOMATED
RADAR SURVEILLANCE SYSTEMS v IN )%% )NT 2ADAR #ONF ,ONDON PP n
# % -UEHE , #ARTLEDGE 7 ( $RURY % - (OFSTETTER - ,ABITT 0 " -C#ORISON AND 6 *
3FERRINO h.EW TECHNIQUES APPLIED TO AIR TRAFFIC CONTROL RADARS v 0ROC )%%% VOL PP n
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'6 4RUNK AND 3 - "ROCKETT h2ANGE AND VELOCITY AMBIGUITY RESOLUTION v IN )%%% .ATIONAL
2ADAR #ONF "OSTON PP n
'6 4RUNK AND - +IM h!MBIGUITY RESOLUTION OF MULTIPLE TARGETS USING PULSE DOPPLER WAVE
FORMS v )%%% 4RANS VOL !%3 PP /CTOBER ( ,EUNG : (U AND - "LANCHETTE h%VALUATION OF MULTIPLE RADAR TARGET TRACKERS IN STRESSFUL
ENVIRONMENTS v )%%% 4RANS !EROSPACE AND %LECTRONIC 3YSTEMS VOL NO PP n
" ( #ANTRELL ' 6 4RUNK AND * $ 7ILSON h4RACKING SYSTEM FOR TWO ASYNCHRONOUSLY SCANNING
RADARS v .AVAL 2ES ,AB 2EPT 7 $ 3TUCKEY h!CTIVITY CONTROL PRINCIPLES FOR AUTOMATIC TRACKING ALGORITHMS v IN )%%% 2ADAR #ONFERENCE PP n
4 2 "ENEDICT AND ' 7 "ORDNER h3YNTHESIS OF AN OPTIMAL SET OF RADAR TRACK WHILE SCAN FILTERING
EQUATIONS v )2% 4RANS VOL !# PP n 2 % +ALMAN h! NEW APPROACH TO LINEAR FILTERING AND PREDICTION PROBLEMS v * "ASIC %NG !3-%
4RANS SER $ VOL PP n 2 % +ALMAN AND 2 3 "UCY h.EW RESULTS IN LINEAR FILTERING AND PREDICTION THEORY v * "ASIC %NG
!3-% 4RANS SER $ VOL PP n Ç°xÈ
2!$!2 (!.$"//+
3 "LACKMAN AND 2 0OPOLI $ESIGN AND !NALYSIS OF -ODERN 4RACKING 3YSTEMS "OSTON !RTECH
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)%%% 4RANS VOL !%3 PP n " &RIEDLAND h/PTIMUM STEADY STATE POSITION AND VELOCITY ESTIMATION USING NOISY SAMPLED POSI
TION DATA v )%%% 4RANS VOL !%3 P 0 +ALATA h4HE TRACKING INDEX ! GENERALIZED PARAMETER FOR @ A AND @ A F TARGET TRACKERS v
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DATA ALWAYS MEAN BETTER ESTIMATESv )%%% 4RANS !EROSPACE AND %LECTRONIC 3YSTEMS VOL PP & 2#ASTELLA h!NALYTICAL RESULTS FOR THE X Y +ALMAN TRACKING FILTER v )%%% 4RANS !EROSPACE AND
%LECTRONIC 3YSTEMS .OVEMBER VOL PP 2 & &ITZGERALD h3IMPLE TRACKING FILTERS 3TEADY STATE FILTERING AND SMOOTHING PERFORMANCE v
)%%% 4RANS !EROSPACE AND %LECTRONIC 3YSTEMS VOL !%3 PP n ' * 0ORTMANN * -OORE AND 7 ' "ATH h3EPARATED COVARIANCE FILTERING v IN 2EC )%%% )NTERNATIONAL 2ADAR #ONFERENCE PP n
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4RANS !EROSPACE AND %LECTRONIC 3YSTEMS VOL NO PP n ! 3 'ELB !PPLIED /PTIMAL %STIMATION #AMBRIDGE -! -)4 0RESS & 2 #ASTELLA h-ULTISENSOR MULTISITE TRACKING FILTER v )%% 0ROC 2ADAR 3ONAR .AVIGATION
VOL ISSUE PP n % ! 7AN 2 VAN DER -ERWE AND ! 4 .ELSON h$UAL ESTIMATION AND THE UNSCENTED TRANSFORMA
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ALGORITHM v IN 0ROC &IFTH )NTERNATIONAL #ONFERENCE ON )NFORMATION &USION VOL PP n
# , -OREFIELD h!PPLICATION OF n INTEGER PROGRAMMING TO MULTI TARGET TRACKING PROBLEMS v
)%%% 4RANS VOL !# PP n 2 *ONKER AND ! 6OLGENANT h! SHORTEST AUGMENTING PATH ALGORITHM FOR DENSE AND SPARSE LINEAR
ASSIGNMENT PROBLEMS v #OMPUTING VOL NO PP n $ "ERTSEKAS h4HE AUCTION ALGORITHM FOR ASSIGNMENT AND OTHER NETWORK FLOW PROBLEMS ! TUTO
RIAL v )NTERFACES VOL PP n ) +ADAR % %ADAN AND 2 'ASSNER h#OMPARISON OF ROBUSTIZED ASSIGNMENT ALGORITHMS v 30)%
VOL PP n 9 "AR 3HALOM AND % 4SE h4RACKING IN A CLUTTERED ENVIRONMENT WITH PROBABILISTIC DATA ASSOCIA
TION v !UTOMATICA VOL PP n 3 " #OLEGROVE AND * + !YLIFFE h!N EXTENSION OF PROBABILISTIC DATA ASSOCIATION TO INCLUDE
TRACK INITIATION AND TERMINATION v IN TH )2%% )NT #ONV $IG -ELBOURNE !USTRAILIA PP n
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0ROC )%%% )NTERNATIONAL 2ADAR #ONFERENCE PP n
$ * 3ALMOND h-IXTURE REDUCTION ALGORITHMS FOR TARGET TRACKING IN CLUTTER v 30)% 3IGNAL AND
$ATA 0ROCESSING OF 3MALL 4ARGETS VOL PP n 2 * 0RENGAMAN 2 % 4HURBER AND 7 ' "ATH h! RETROSPECTIVE DETECTION ALGORITHM FOR EXTRAC
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PP n
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CONTACT ENVIRONMENTS v IN 0ROC 2!$!2 PP n
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TION OF WEAK TARGETS IN CLUTTER AND INTERFERENCE ENVIRONMENTS v IN )%%% )NT 2ADAR #ONF ,ONDON
PP n
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/CTOBER PP n
' 6 4RUNK * $ 7ILSON AND 0 + (UGHES )) h0HASED ARRAY PARAMETER OPTIMIZATION FOR LOW
ALTITUDE TARGETS v IN )%%% )NTERNATIONAL 2ADAR #ONFERENCE -AY PP n
7 "ATH h4RADEOFFS IN RADAR NETWORKING v IN 0ROC )%% 2!$!2 PP n
* 2 -OORE AND 7 $ "LAIR h0RACTICAL ASPECTS OF MULTISENSOR TRACKING v IN -ULTITARGET -ULTISENSOR
4RACKING !PPLICATIONS AND !DVANCES 6OL ))) "OSTON !RTECH (OUSE * / #OLEMAN h$ISCRIMINANTS FOR ASSIGNING PASSIVE BEARING OBSERVATIONS TO RADAR TARGETS v IN
)%%% )NT 2ADAR #ONF 7ASHINGTON $# PP n
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4RANS VOL !%3 PP n
' 6 4RUNK AND * $ 7ILSON h#ORRELATION OF $& BEARING MEASUREMENTS WITH RADAR TRACKS v IN
)%%% )NT 2ADAR #ONF ,ONDON PP n
#HAPTER *ՏÃiÊ œ“«ÀiÃȜ˜Ê,>`>À
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n°£Ê /," 1 /"
! PULSE COMPRESSION RADAR TRANSMITS A LONG PULSE WITH PULSEWIDTH 4 AND PEAK POWER
0T WHICH IS CODED USING FREQUENCY OR PHASE MODULATION TO ACHIEVE A BANDWIDTH
" THAT IS LARGE COMPARED TO THAT OF AN UNCODED PULSE WITH THE SAME DURATION 4HE
TRANSMIT PULSEWIDTH IS CHOSEN TO ACHIEVE THE SINGLE PULSE TRANSMIT ENERGY GIVEN
BY %T 0T4 THAT IS REQUIRED FOR TARGET DETECTION OR TRACKING 4HE RECEIVED ECHO
IS PROCESSED USING A PULSE COMPRESSION FILTER TO YIELD A NARROW COMPRESSED PULSE
RESPONSE WITH A MAINLOBE WIDTH OF APPROXIMATELY " THAT DOES NOT DEPEND ON THE
DURATION OF THE TRANSMITTED PULSE
&IGURE SHOWS A BLOCK DIAGRAM OF A BASIC PULSE COMPRESSION RADAR 4HE CODED
PULSE IS GENERATED AT A LOW POWER LEVEL IN THE WAVEFORM GENERATOR AND AMPLIFIED TO THE
REQUIRED PEAK TRANSMIT POWER USING A POWER AMPLIFIER TRANSMITTER 4HE RECEIVED SIGNAL
IS MIXED TO AN INTERMEDIATE FREQUENCY )& AND AMPLIFIED BY THE )& AMPLIFIER 4HE SIG
NAL IS THEN PROCESSED USING A PULSE COMPRESSION FILTER THAT CONSISTS OF A MATCHED FILTER
TO ACHIEVE MAXIMUM SIGNAL TO NOISE RATIO 3.2 !S DISCUSSED BELOW THE MATCHED
FILTER IS FOLLOWED BY A WEIGHTING FILTER IF REQUIRED FOR REDUCTION OF TIME SIDELOBES 4HE
OUTPUT OF THE PULSE COMPRESSION FILTER IS APPLIED TO AN ENVELOPE DETECTOR AMPLIFIED BY
THE VIDEO AMPLIFIER AND DISPLAYED TO AN OPERATOR
4HE RATIO OF THE TRANSMIT PULSEWIDTH TO THE COMPRESSED PULSE MAINLOBE WIDTH IS
DEFINED AS THE PULSE COMPRESSION RATIO 4HE PULSE COMPRESSION RATIO IS APPROXIMATELY
4" OR 4" WHERE 4" IS DEFINED AS THE TIME BANDWIDTH PRODUCT OF THE WAVEFORM
4YPICALLY THE PULSE COMPRESSION RATIO AND TIME BANDWIDTH PRODUCT ARE LARGE COMPARED
TO UNITY
4HE USE OF PULSE COMPRESSION PROVIDES SEVERAL PERFORMANCE ADVANTAGES 4HE
INCREASED DETECTION RANGE CAPABILITY OF A LONG PULSE RADAR SYSTEM IS ACHIEVED WITH
PULSE COMPRESSION WHILE RETAINING THE RANGE RESOLUTION CAPABILITY OF A RADAR THAT
USES A NARROW UNCODED PULSE 4HE REQUIRED TRANSMITTED ENERGY CAN BE ESTABLISHED BY
4HE AUTHORS WOULD LIKE TO ACKNOWLEDGE THE USE OF MATERIAL PREVIOUSLY PREPARED BY %DWARD # &ARNETT AND
'EORGE ( 3TEVENS FOR THE h0ULSE #OMPRESSION 2ADARv CHAPTER IN THE SECOND EDITION OF THE 2ADAR (ANDBOOK
EDITED BY -ERRILL ) 3KOLNIK
n°£
n°Ó
2!$!2 (!.$"//+
!
"#
!
&)'52% "
"LOCK DIAGRAM OF A BASIC PULSE COMPRESSION RADAR
INCREASING THE WAVEFORM PULSEWIDTH WITHOUT EXCEEDING CONSTRAINTS ON TRANSMITTER PEAK
POWER 4HE AVERAGE POWER OF THE RADAR MAY BE INCREASED WITHOUT INCREASING THE PULSE
REPETITION FREQUENCY 02& AND HENCE DECREASING THE RADARS UNAMBIGUOUS RANGE )N
ADDITION THE RADAR IS LESS VULNERABLE TO INTERFERING SIGNALS THAT DIFFER FROM THE CODED
TRANSMITTED SIGNAL
4HE MAINLOBE OF THE COMPRESSED PULSE AT THE OUTPUT OF THE MATCHED FILTER HAS TIME
OR RANGE SIDELOBES THAT OCCUR WITHIN TIME INTERVALS OF DURATION 4 BEFORE AND AFTER THE
PEAK OF THE PEAK OF THE COMPRESSED PULSE 4HE TIME SIDELOBES CAN CONCEAL TARGETS
WHICH WOULD OTHERWISE BE RESOLVED USING A NARROW UNCODED PULSE )N SOME CASES SUCH
AS PHASE CODED WAVEFORMS OR NONLINEAR FREQUENCY MODULATION WAVEFORMS MATCHED
FILTER PROCESSING ALONE ACHIEVES ACCEPTABLE TIME SIDELOBE LEVELS (OWEVER FOR THE CASE
OF A LINEAR FREQUENCY MODULATION WAVEFORM THE MATCHED FILTER IS GENERALLY FOLLOWED
BY A WEIGHTING FILTER TO PROVIDE A REDUCTION IN TIME SIDELOBE LEVELS )N THIS CASE THE
WEIGHTING FILTER RESULTS IN A SIGNAL TO NOISE RATIO LOSS COMPARED TO THAT OF MATCHED FILTER
PROCESSING ALONE
n°ÓÊ *1- Ê "*, --" Ê76 ",Ê/9* 4HE FOLLOWING SECTIONS DESCRIBE THE CHARACTERISTICS OF THE LINEAR AND NONLINEAR FRE
QUENCY MODULATION WAVEFORMS PHASE CODED WAVEFORMS AND TIME FREQUENCY CODED
WAVEFORMS 4HE APPLICATION OF SURFACE ACOUSTIC WAVE 3!7 DEVICES FOR LINEAR FRE
QUENCY MODULATION ,&- WAVEFORM PULSE COMPRESSION IS DISCUSSED 7AVEFORM
SIGNAL ANALYSIS TECHNIQUES MATCHED FILTER PROPERTIES AND THE WAVEFORM AUTOCOR
RELATION AND AMBIGUITY FUNCTION DEFINITIONS USED ARE SUMMARIZED IN THE !PPENDIX
AT THE END OF THIS CHAPTER
05,3% #/-02%33)/. 2!$!2
n°Î
,INEAR &REQUENCY -ODULATION 4HE LINEAR FREQUENCY MODULATION OR CHIRP
WAVEFORM HAS A RECTANGULAR AMPLITUDE MODULATION WITH PULSEWIDTH 4 AND A LINEAR
FREQUENCY MODULATION WITH A SWEPT BANDWIDTH " APPLIED OVER THE PULSE 4HE TIME
BANDWIDTH PRODUCT OF THE ,&- WAVEFORM IS EQUAL TO 4" WHERE 4" IS THE PRODUCT OF
PULSEWIDTH AND SWEPT BANDWIDTH 4HE D" WIDTH OF THE COMPRESSED PULSE AT THE OUT
PUT OF THE MATCHED FILTER IS S " FOR LARGE VALUES OF TIME BANDWIDTH PRODUCT
4HE PEAK TIME SIDELOBE LEVEL OF THE COMPRESSED PULSE IS n D"
!S DISCUSSED IN 3ECTION A FREQUENCY DOMAIN WEIGHTING FILTER IS GENERALLY
REQUIRED FOLLOWING THE MATCHED FILTER TO PROVIDE REDUCED TIME SIDELOBE LEVELS AT THE
COST OF REDUCED 3.2 AND AN INCREASE IN THE WIDTH OF THE COMPRESSED PULSE !S AN
EXAMPLE THE USE OF D" 4AYLOR WEIGHTING REDUCES THE PEAK TIME SIDELOBE LEVEL FROM
n D" TO n D" AND INTRODUCES A D" LOSS IN 3.2 4HE D" WIDTH OF THE COM
PRESSED PULSE WITH WEIGHTING INCREASES FROM S " TO S "
4HE ,&- WAVEFORM HAS A KNIFE EDGE AMBIGUITY FUNCTION WITH CONTOURS THAT ARE
APPROXIMATELY ELLIPTICAL WITH A MAJOR AXIS DEFINED BY THE LINE V @S WHERE @ o "4
IS THE ,&- SLOPE 4HIS PROPERTY INTRODUCES RANGE DOPPLER COUPLING AT THE MATCHED FILTER
OUTPUT CAUSING THE MATCHED FILTER OUTPUT PEAK TO OCCUR EARLIER IN TIME FOR A TARGET WITH A
POSITIVE DOPPLER FREQUENCY COMPARED TO A STATIONARY TARGET AT THE SAME RANGE ASSUMING
A POSITIVE LINEAR FREQUENCY MODULATION SLOPE AND LATER IN TIME FOR A NEGATIVE SLOPE
4HE COMPRESSED PULSE SHAPE AND 3.2 ARE TOLERANT TO DOPPLER SHIFT FOR THE ,&WAVEFORM !S A RESULT IT IS NOT NECESSARY TO IMPLEMENT MULTIPLE MATCHED FILTERS TO
COVER THE RANGE OF EXPECTED TARGET DOPPLER SHIFTS
,&- 7AVEFORM $EFINITION
DEFINED AS
4HE ,&- WAVEFORM IS A SINGLE PULSE BANDPASS SIGNAL
XT ! RECT T4 COS ;O F T
O@ T=
WHERE 4 IS THE PULSEWIDTH F IS THE CARRIER FREQUENCY @ IS THE ,&- SLOPE AND THE RECT
FUNCTION IS DEFINED AS
ª­ \ X \ RECTX «
¬­ \ X \ 4HE ,&- SLOPE IS GIVEN BY @ o "4 WHERE THE PLUS SIGN APPLIES FOR A POSITIVE
,&- SLOPE TERMED AN UP CHIRP AND THE MINUS SIGN FOR A NEGATIVE ,&- SLOPE A DOWN
CHIRP 4HE AMPLITUDE MODULATION IS AT ! RECT T4 AND THE PHASE MODULATION IS A
QUADRATIC FUNCTION OF TIME
E T O@ T
4HE FREQUENCY MODULATION DEFINED AS THE INSTANTANEOUS FREQUENCY DEVIATION FROM
THE CARRIER FREQUENCY F IS EXPRESSED IN TERMS OF THE PHASE MODULATION BY
FI T DF
P DT
4HE FREQUENCY MODULATION FOR AN ,&- WAVEFORM IS LINEAR WITH SLOPE EQUAL TO @
FI T A T o " 4 T \ T \ a 4 n°{
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WHERE THE PLUS SIGN APPLIES FOR A POSITIVE ,&- SLOPE AND THE MINUS SIGN FOR A NEGATIVE
SLOPE 4HE COMPLEX ENVELOPE OF THE ,&- WAVEFORM IS EXPRESSED IN TERMS OF THE
AMPLITUDE AND PHASE MODULATION FUNCTIONS AS
UT ! RECTT4 EJO @ T
&IGURE SHOWS AN EXAMPLE OF AN ,&- BANDPASS SIGNAL WITH A PULSEWIDTH 4 §S
SWEPT BANDWIDTH " -(Z AND TIME BANDWIDTH PRODUCT EQUAL TO 4" 4HE ,&SLOPE IS "4 -(Z§S 4HE INSTANTANEOUS FREQUENCY OF THE ,&- WAVEFORM VARIES
BETWEEN AND -(Z OVER THE PULSE DURATION AS INDICATED BY THE REDUCTION IN THE
SPACING OF SUCCESSIVE POSITIVE GOING ZERO CROSSINGS OF THE SIGNALo
,&- 7AVEFORM 3PECTRUM 4HE SPECTRUM OF THE ,&- WAVEFORM HAS A SIGNIFI
CANT AMPLITUDE VARIATION VERSUS FREQUENCY FOR SMALL TIME BANDWIDTH PRODUCTS &OR LARGE
VALUES OF TIME BANDWIDTH PRODUCT THE MAGNITUDE OF THE SPECTRUM APPROACHES RECT F"
UT RECTT 4 E JPA T
4
\ 5 F \ y RECT F " FOR 4" 4HE ,&- SPECTRUM IS EXPRESSED IN TERMS OF THE COMPLEX &RESNEL INTEGRAL AND THE
AMPLITUDE VARIATION PRESENT FOR LOW VALUES OF 4" IS TERMED THE &RESNEL RIPPLE
,&- 7AVEFORM !MBIGUITY &UNCTION 4HE WAVEFORM AUTOCORRELATION FUNCTION AND
AMBIGUITY FUNCTION FOR AN ,&- WAVEFORM ARE GIVEN BY
C U T FD ; \ T 4 \= SINC; FD AT 4 \ T 4 \ = REECT T 4 E JP FDT
9U T FD ; \ T 4 \= SINC ; FD
AT 4 \ T 4 \ = RECTT 4
WHERE THE SINC FUNCTION IS DEFINED AS
SINCX SINOX OX
4HE MATCHED FILTER TIME RESPONSE FOR A TARGET WITH DOPPLER SHIFT FD IS OBTAINED BY THE
SUBSTITUTION T nT IN THE AUTOCORRELATION FUNCTION
YT C U T FD ; \ T 4 \= SINC; FD
A T 4 \ T 4 \ = RECTT 4 E JP FD T
,&- 2ANGE DOPPLER #OUPLING 4HE ,&- WAVEFORM EXHIBITS RANGE DOPPLER COU
PLING WHICH CAUSES THE PEAK OF THE COMPRESSED PULSE TO SHIFT IN TIME BY AN AMOUNT
PROPORTIONAL TO THE DOPPLER FREQUENCY 4HE PEAK OCCURS EARLIER IN TIME AT T nFD4" FOR
A POSITIVE ,&- SLOPE COMPARED TO PEAK RESPONSE FOR A STATIONARY TARGET 4HE PEAK OF
THE AMBIGUITY FUNCTION IS SHIFTED TO S FD4" FOR A POSITIVE ,&- SLOPE
4IME $ELAY AND 2ANGE 2ESOLUTION 7IDTHS 4HE TIME DELAY RESOLUTION WIDTH IS EQUAL
TO THE WIDTH OF THE AMBIGUITY FUNCTION AT A SPECIFIED LEVEL RELATIVE TO THE PEAK VALUE
o ,OW VALUES OF CARRIER FREQUENCY AND TIME BANDWIDTH PRODUCT HAVE BEEN USED TO ILLUSTRATE THE VARIATION OF INSTANTA
NEOUS FREQUENCY OVER THE PULSE IN &IGURE 05,3% #/-02%33)/. 2!$!2
&)'52% F -(Z
n°x
,&- BANDPASS SIGNAL EXAMPLE SHOWN FOR 4 §S " -(Z
&OR THE CASE OF A LARGE TIME BANDWIDTH THE MAGNITUDE OF THE AUTOCORRELATION FUNCTION
MEASURED ALONG THE RELATIVE TIME DELAY AXIS IS GIVEN BY
\ C U T \ y \SINC"T \ \T \ 4
4HE X D" TIME DELAY RESOLUTION IS MEASURED BETWEEN THE VALUES OF T FOR WHICH
LOG \ SINC"S \ X D"
4HE RANGE RESOLUTION IS EQUAL TO C TIMES THE CORRESPONDING TIME DELAY RESOLUTION
WHERE C IS THE SPEED OF LIGHT 4ABLE CONTAINS A SUMMARY OF THE RESOLUTION WIDTHS
FOR THE ,&- WAVEFORM
,&- 7AVEFORM %XAMPLES &IGURE SHOWS THE MAGNITUDE OF THE AUTOCORRELA
TION FUNCTION AS A FUNCTION OF RELATIVE TIME DELAY T FOR DOPPLER SHIFTSp OF n -(Z
AND -(Z PULSEWIDTH 4 §S SWEPT BANDWIDTH " -(Z AND ,&- SLOPE
@ "4 -(Z§S ! DOPPLER SHIFT OF FD " -(Z CAUSES THE PEAK OF THE
CORRELATION FUNCTION TO MOVE TO S FD4" §S &IGURE SHOWS THE RESULT WHEN
THE PULSEWIDTH IS INCREASED TO §S TO YIELD A WAVEFORM WITH AN ,&- SLOPE EQUAL
4!",% ,&- 7AVEFORM 4IME $ELAY AND 2ANGE 2ESOLUTION 7IDTHS
-AINLOBE 7IDTH
D"
D"
D"
D"
4IME $ELAY 2ESOLUTION S
S "
S "
S "
S "
2ANGE 2ESOLUTION M
$2 C"
$2 C"
$2 C"
$2 C"
p 4HESE VALUES OF DOPPLER SHIFT ARE LARGE FOR MICROWAVE RADARS AND WERE SELECTED TO SHOW THE EFFECT OF RANGE DOPPLER
COUPLING
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&)'52% 4" ,&- WAVEFORM AUTOCORRELATION FUNCTION 4 §S " -(Z
TO -(Z§S )N THIS CASE A DOPPLER SHIFT OF -(Z SHIFTS THE PEAK OF AUTOCOR
RELATION FUNCTION TO S §S AN INCREASE OF A FACTOR OF TEN COMPARED TO THE RESULT
FOR A §S PULSEWIDTH
&)'52% 4" ,&- WAVEFORM AUTOCORRELATION FUNCTION 4 §S " -(Z
05,3% #/-02%33)/. 2!$!2
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&REQUENCY $OMAIN 7EIGHTING FOR ,&- 4IME 3IDELOBE 2EDUCTION ! FREQUENCY
DOMAIN WEIGHTING FILTER IS USED FOLLOWING THE MATCHED FILTER FOR TIME SIDELOBE REDUCTION
4AYLOR WEIGHTING PROVIDES A REALIZABLE APPROXIMATION TO THE IDEAL $OLPH #HEBYSHEV
WEIGHTING WHICH ACHIEVES THE MINIMUM MAINLOBE WIDTH FOR A GIVEN VALUE OF PEAK
TIME SIDELOBE LEVEL 4HE FREQUENCY RESPONSE OF THE EQUIVALENT LOW PASS FILTER FOR THE
4AYLOR WEIGHING FILTER IS
N ¤ MF ³
7 F £ &M COS ¥ P ´
"µ
¦
M WHERE &M IS THE 4AYLOR COEFFICIENT AND N IS THE NUMBER OF TERMS IN THE WEIGHTING FUNC
TION 4HE COMPRESSED PULSE RESPONSE AT THE OUTPUT OF THE WEIGHTING FILTER IS GIVEN BY
N YO T SINC"T
£ &M ;SINC"T M
SINC"T M =
M !S DISCUSSED BELOW THE COMPRESSED PULSE RESPONSE %Q IS BASED ON THE ASSUMP
TION THAT THE TIME BANDWIDTH PRODUCT OF THE ,&- WAVEFORM IS MUCH GREATER THAN UNITY
4" 4HE FILTER MATCHING LOSS FOR 4AYLOR WEIGHTING IS GIVEN BY +LAUDER ET AL AS
N ,M £ &M M &IGURE SHOWS A COMPARISON OF THE COMPRESSED PULSE RESPONSE FOR THREE FRE
QUENCY DOMAIN WEIGHTING TYPES #URVE ! IS FOR UNIFORM WEIGHTING WHERE 7 F &)'52% #OMPARISON OF COMPRESSED PULSE SHAPES FOR THREE FREQUENCY DOMAIN
WEIGHTING FUNCTIONS
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MATCHED FILTER PROCESSING #URVE # IS FOR 4AYLOR WEIGHTING WITH n D" PEAK TIME
SIDELOBE LEVEL N AND #URVE " IS FOR (AMMING WEIGHTING WHERE
¤ MF ³
7 F & COS ¥ P ´
"µ
¦
& 4HE 4AYLOR COEFFICIENTS FOR n D" 4AYLOR WEIGHTING N ARE LISTED HERE
& & –
& & –
& 4ABLE SHOWS THE PEAK TIME SIDELOBE LEVEL D" AND D" COMPRESSED PULSE
WIDTHS AND FILTER MATCHING LOSS FOR THE THREE WEIGHTING FUNCTION TYPES 4HE APPLICATION
OF n D" 4AYLOR WEIGHTING REDUCES THE PEAK TIME SIDELOBE LEVEL FROM n D" TO
n D" AND INCREASES THE FILTER MATCHING LOSS FROM D" TO D" 4HE D" COM
PRESSED PULSE MAINLOBE WIDTH INCREASES FROM " TO " WHEN n D" 4AYLOR
WEIGHTING IS USED 4HE D" AND D" MAINLOBE WIDTHS AND FILTER MATCHING LOSS FOR
(AMMING WEIGHTING ARE APPROXIMATELY THE SAME AS FOR n D" 4AYLOR WEIGHTING
4HESE RESULTS ASSUME THAT THE TIME BANDWIDTH PRODUCT OF THE ,&- WAVEFORM IS
MUCH GREATER THAN UNITY SO THAT THE TIME SIDELOBE PERFORMANCE IS NOT LIMITED BY THE
&RESNEL AMPLITUDE RIPPLE IN THE SPECTRUM OF THE ,&- WAVEFORM #OOK AND 0AOLILLO
AND #OOK AND "ERNFELD HAVE ANALYZED THE EFFECT OF THE &RESNEL AMPLITUDE RIPPLE AND
PULSE RISE TIME AND FALL TIME ON TIME SIDELOBE LEVELS ! PHASE PREDISTORTION TECHNIQUE
IS DESCRIBED BY #OOK AND 0AOLILLO WHICH REDUCES THE &RESNEL AMPLITUDE RIPPLE TO
ALLOW LOW TIME SIDELOBES TO BE ACHIEVED FOR ,&- WAVEFORMS WITH RELATIVELY SMALL
TIME BANDWIDTH PRODUCTS
2ADAR EQUIPMENT DISTORTION SOURCES ALSO ESTABLISH LIMITATIONS ON ACHIEVABLE TIME
SIDELOBE LEVELS AND ARE DISCUSSED BY +LAUDER ET AL AND #OOK AND "ERNFELD 4HE
METHOD OF PAIRED ECHO ANALYSIS IS USED TO EVALUATE THE EFFECT OF AMPLITUDE AND PHASE
DISTORTION ON THE TIME SIDELOBE LEVELS &REQUENCY DOMAIN AMPLITUDE AND PHASE DIS
TORTION IS TYPICALLY CAUSED BY FILTERS AND TRANSMISSION LINE REFLECTIONS 4IME DOMAIN
AMPLITUDE AND PHASE DISTORTION TERMED MODULATION DISTORTION BY #OOK AND "ERNFELD
CAN RESULT FROM POWER SUPPLY RIPPLE IN HIGH POWER TRANSMITTER AMPLIFIERS
4!",% #OMPARISON OF ,&- 7EIGHTING &ILTERS
7EIGHTING
&UNCTION
0EAK 4IME 3IDELOBE
,EVEL D"
D" -AINLOBE
7IDTH S
D" -AINLOBE
7IDTH S
&ILTER -ATCHING
,OSS D"
5NIFORM
4AYLOR
D" N (AMMING
"
"
"
"
"
"
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4AYLOR 6ERSUS #OSINE 3QUARED 0LUS 0EDESTAL 7EIGHTING &IGURE A PLOTS THE
TAPER COEFFICIENT & AND PEDESTAL HEIGHT ( VERSUS THE PEAK TIME SIDELOBE LEVEL FOR
COSINE SQUARED PLUS PEDESTAL WEIGHTING &OR A GIVEN PEAK TIME SIDELOBE LEVEL 4AYLOR
WEIGHTING OFFERS THEORETICAL ADVANTAGES IN RANGE RESOLUTION AND 3.2 PERFORMANCE AS
ILLUSTRATED IN &IGURE B AND &IGURE C
&)'52% A 4APER COEFFICIENT AND PEDESTAL HEIGHT VERSUS PEAK TIME SIDELOBE
LEVEL B #OMPRESSED PULSE WIDTH VERSUS PEAK TIME SIDELOBE LEVEL C 3.2 LOSS
VERSUS PEAK TIME SIDELOBE LEVEL
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3!7 $EVICES FOR ,&- 0ULSE #OMPRESSION ! 3URFACE !COUSTIC 7AVE 3!7
DEVICE CONSISTS OF AN INPUT TRANSDUCER AND AN OUTPUT TRANSDUCER MOUNTED ON A PIEZO
ELECTRIC SUBSTRATE 4HESE TRANSDUCERS ARE USUALLY IMPLEMENTED AS INTERDIGITAL DEVICES
THAT CONSIST OF A METAL FILM DEPOSITED ON THE SURFACE OF THE ACOUSTIC MEDIUM 4HIS METAL
FILM IS MADE OF FINGERS SEE &IGURE THAT DICTATE THE FREQUENCY CHARACTERISTIC OF THE
UNIT 4HE INPUT TRANSDUCER CONVERTS AN ELECTRICAL SIGNAL INTO A SOUND WAVE WITH OVER
OF THE ENERGY TRAVELING ALONG THE SURFACE OF THE MEDIUM 4HE OUTPUT TRANSDUCER
TAPS A PORTION OF THIS SURFACE SOUND WAVE AND CONVERTS IT BACK INTO AN ELECTRIC SIGNAL
4HE 3!7 DEVICE HAS UNIQUE FEATURES THAT DICTATE ITS USEFULNESS FOR A GIVEN RADAR
APPLICATION )T REPRESENTS ONE OF THE FEW ANALOG PROCESSING DEVICES USED IN MODERN
RADAR 4HE ADVANTAGES OF THE 3!7 DEVICE ARE ITS COMPACT SIZE THE WIDE BANDWIDTHS
THAT CAN BE ATTAINED THE ABILITY TO TAILOR THE TRANSDUCERS TO A PARTICULAR WAVEFORM THE
ALL RANGE COVERAGE OF THE DEVICE AND THE LOW COST OF REPRODUCING A GIVEN DESIGN 4HE
MAJOR SHORTCOMINGS OF THE 3!7 APPROACH ARE THAT THE WAVEFORM LENGTH IS RESTRICTED
3INCE SOUND TRAVELS ABOUT TO MM§S ON THE SURFACE OF A 3!7 DEVICE A MM
QUARTZ DEVICE ABOUT THE LARGEST AVAILABLE HAS A USABLE DELAY OF ABOUT §S FOR A
SINGLE PASS !LSO BECAUSE EACH 3!7 DEVICE IS WAVEFORM SPECIFIC EACH WAVEFORM
REQUIRES A DIFFERENT DESIGN
3!7 PULSE COMPRESSION DEVICES DEPEND ON THE INTERDIGITAL TRANSDUCER FINGER LOCA
TIONS OR THE SURFACE ETCHED GRATING TO DETERMINE ITS BANDPASS CHARACTERISTICS &IGURE SHOWS THREE TYPES OF FILTER DETERMINATION APPROACHES ! WIDEBAND INPUT TRANSDUCER AND
A FREQUENCY SELECTIVE DISPERSIVE OUTPUT TRANSDUCER ARE USED IN &IGURE A 7HEN AN
IMPULSE IS APPLIED TO THE INPUT THE OUTPUT SIGNAL IS INITIALLY A LOW FREQUENCY THAT INCREASES
BASED ON THE OUTPUT TRANSDUCER FINGER SPACINGS AT LATER PORTIONS OF THE PULSE 4HIS RESULTS
&)'52% 3!7 TRANSDUCER TYPES A DISPERSIVE OUTPUT B BOTH INPUT AND OUTPUT DISPERSIVE AND
C DISPERSIVE REFLECTIONS
05,3% #/-02%33)/. 2!$!2
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IN AN UP CHIRP WAVEFORM THAT WOULD BE A MATCHED FILTER FOR A DOWN CHIRP TRANSMITTED
WAVEFORM )N &IGURE B BOTH THE INPUT TRANSDUCER AND THE OUTPUT TRANSDUCER ARE DIS
PERSIVE WHICH WOULD RESULT IN THE SAME IMPULSE RESPONSE AS THAT SHOWN IN &IGURE A
&OR A GIVEN CRYSTAL LENGTH AND MATERIAL THE WAVEFORM DURATION FOR THE APPROACHES IN
&IGURE A AND &IGURE B WOULD BE THE SAME AND IS LIMITED TO THE TIME THAT IT TAKES
AN ACOUSTIC WAVE TO TRAVERSE THE CRYSTAL LENGTH &IGURE C SHOWS A REFLECTION ARRAY
COMPRESSION 2!# APPROACH THAT ESSENTIALLY DOUBLES THE ACHIEVABLE PULSE LENGTH FOR
THE SAME CRYSTAL LENGTH )N AN 2!# THE INPUT AND OUTPUT TRANSDUCERS HAVE A BROAD BAND
WIDTH ! FREQUENCY SENSITIVE GRATING IS ETCHED ON THE CRYSTAL SURFACE TO REFLECT A PORTION
OF THE SURFACE WAVE SIGNAL TO THE OUTPUT TRANSDUCER 4HIS GRATING COUPLING DOES NOT HAVE A
SIGNIFICANT IMPACT ON THE SURFACE WAVE ENERGY %XCEPT FOR A INCREASE IN THE WAVEFORM
DURATION THE IMPULSE RESPONSE OF THE 2!# IS THE SAME AS FOR THE APPROACHES SHOWN IN
&IGURE A AND B 4HUS THESE THREE APPROACHES YIELD A SIMILAR IMPULSE RESPONSE
&IGURE SHOWS A SKETCH OF A 3!7 PULSE COMPRESSION DEVICE WITH DISPERSIVE
INPUT AND OUTPUT TRANSDUCERS !S THE ENERGY IN A 3!7 DEVICE IS CONCENTRATED IN ITS SUR
FACE WAVE THE 3!7 APPROACH IS MUCH MORE EFFICIENT THAN BULK WAVE DEVICES WHERE
THE WAVE TRAVELS THROUGH THE CRYSTAL 4HE PROPAGATION VELOCITY OF THE SURFACE WAVE IS
IN THE RANGE OF TO MS DEPENDING ON THE CRYSTAL MATERIAL AND ALLOWS A LARGE
DELAY IN A COMPACT DEVICE !COUSTIC ABSORBER MATERIAL IS REQUIRED AT THE CRYSTAL EDGES
TO REDUCE THE REFLECTIONS AND HENCE THE SPURIOUS RESPONSES 4HE UPPER FREQUENCY
LIMIT DEPENDS ON THE ACCURACY THAT CAN BE ACHIEVED IN THE FABRICATION OF THE INTERDIGITAL
TRANSDUCER 4HE 3!7 DEVICE MUST PROVIDE A RESPONSE THAT IS CENTERED ON A CARRIER
AS THE LOWEST FREQUENCY OF OPERATION IS ABOUT -(Z AND IS LIMITED BY THE CRYSTAL
! MATCHED FILTER 3!7 PULSE COMPRESSION DEVICE CAN USE VARIABLE FINGER LENGTHS TO
ACHIEVE FREQUENCY WEIGHTING AND THIS INTERNAL WEIGHTING CAN CORRECT FOR THE &RESNEL
AMPLITUDE RIPPLES IN THE &- SPECTRUM 7ITH THIS CORRECTION n D" TIME SIDELOBE
LEVELS CAN BE ACHIEVED FOR A LINEAR &- WAVEFORM WITH 4" AS LOW AS 4HE LEVEL OF
SIDELOBE SUPPRESSION DEPENDS UPON THE TIME BANDWIDTH PRODUCT THE WEIGHTING FUNC
TION APPLIED AND FABRICATION ERRORS IN THE 3!7 DEVICE 4IME SIDELOBE LEVELS OF n D"
HAVE BEEN ACHIEVED FOR 4" BETWEEN AND 4" PRODUCTS OF UP TO HAVE BEEN
ACHIEVED WITH TIME SIDELOBES BETTER THAN n D" $YNAMIC RANGE IS LIMITED BY NON
LINEARITIES IN THE CRYSTAL MATERIAL BUT DYNAMIC RANGES OVER D" HAVE BEEN ACHIEVED
4HE MOST COMMON 3!7 MATERIALS ARE QUARTZ LITHIUM NIOBATE AND LITHIUM TANTALITE
&)'52% 3URFACE WAVE DELAY LINE
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.ONLINEAR &REQUENCY -ODULATION 7AVEFORMS 4HE NONLINEAR &- WAVE
FORM HAS SEVERAL DISTINCT ADVANTAGES OVER ,&- )T REQUIRES NO FREQUENCY DOMAIN
WEIGHTING FOR TIME SIDELOBE REDUCTION BECAUSE THE &- MODULATION OF THE WAVEFORM IS
DESIGNED TO PROVIDE THE DESIRED SPECTRUM SHAPE THAT YIELDS THE REQUIRED TIME SIDELOBE
LEVEL 4HIS SHAPING IS ACCOMPLISHED BY INCREASING THE RATE OF CHANGE OF FREQUENCY
MODULATION NEAR THE ENDS OF THE PULSE AND DECREASING IT NEAR THE CENTER 4HIS SERVES
TO TAPER THE WAVEFORM SPECTRUM SO THAT THE MATCHED FILTER RESPONSE HAS REDUCED TIME
SIDELOBES 4HUS THE LOSS IN SIGNAL TO NOISE RATIO ASSOCIATED WITH FREQUENCY DOMAIN
WEIGHTING AS FOR THE ,&- WAVEFORM IS ELIMINATED
)F A SYMMETRICAL &- MODULATION IS USED &IGURE A WITH TIME DOMAIN AMPLITUDE
WEIGHTING TO REDUCE THE FREQUENCY SIDELOBES THE NONLINEAR &- WAVEFORM WILL HAVE A
THUMBTACK LIKE AMBIGUITY FUNCTION &IGURE ! SYMMETRICAL WAVEFORM TYPICALLY
HAS A FREQUENCY THAT INCREASES OR DECREASES WITH TIME DURING THE FIRST HALF OF THE
PULSE AND DECREASES OR INCREASES DURING THE LAST HALF OF THE PULSE ! NONSYMMETRICAL
WAVEFORM IS OBTAINED BY USING ONE HALF OF A SYMMETRICAL WAVEFORM &IGURE B (OWEVER THE NONSYMMETRICAL WAVEFORM RETAINS SOME OF THE RANGE DOPPLER COUPLING
OF THE LINEAR &- WAVEFORM
/NE OF THE PRIMARY DISADVANTAGES OF THE NONLINEAR &- WAVEFORM IS THAT IT IS LESS
DOPPLER TOLERANT THAN THE ,&- )N THE PRESENCE OF DOPPLER SHIFT THE TIME SIDELOBES
OF THE PULSE COMPRESSED .,&- TEND TO INCREASE COMPARED TO THOSE OF THE ,&-
&IGURE SHOWN LATER IN THIS SECTION AND 4ABLE ILLUSTRATE THIS BEHAVIOR FOR A TYPICAL
.,&- PULSE
4HIS CHARACTERISTIC OF THE .,&- WAVEFORM SOMETIMES NECESSITATES PROCESSING USING
MULTIPLE MATCHED FILTERS OFFSET IN DOPPLER SHIFT TO ACHIEVE THE REQUIRED TIME SIDELOBE
LEVEL "ECAUSE OF THE DOPPLER SENSITIVITY OF THE AMBIGUITY FUNCTION THE NONLINEAR FRE
QUENCY MODULATION WAVEFORM IS USEFUL IN A TRACKING SYSTEM WHERE RANGE AND DOPPLER
FREQUENCY ARE APPROXIMATELY KNOWN AND THE TARGET DOPPLER SHIFT CAN BE COMPENSATED IN
THE MATCHED FILTER 4HE NONSYMMETRICAL .,&- WAVEFORM IS USED IN THE --2 SYSTEM
FOR EXAMPLE WHICH DETECTS AND TRACKS ORDNANCE SUCH AS MORTARS ARTILLERY AND ROCKETS
4O ACHIEVE A n D" 4AYLOR COMPRESSED PULSE RESPONSE FOR EXAMPLE THE FRE
QUENCY VERSUS TIME FREQUENCY MODULATION FUNCTION OF A NONSYMMETRICAL .,&WAVEFORM OF BANDWIDTH " IS
¤T
F T " ¥
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&)'52% P NT ³
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N 3YMMETRICAL AND NONSYMMETRICAL NONLINEAR &- WAVEFORMS
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&)'52% !MBIGUITY FUNCTION OF AN ,&- WAVEFORM COMPARED TO A SYMMETRICAL .,&- WAVEFORM
WHERE THE COEFFICIENTS ARE
+ + + + + + + /THER .,&- WAVEFORMS THAT HAVE BEEN UTILIZED IN RADAR INCLUDE THE NONSYM
METRICAL SINE BASED AND TANGENT BASED WAVEFORMSe &OR THE SINE BASED WAVEFORM THE
RELATIONSHIP BETWEEN TIME AND FREQUENCY MODULATION IS GIVEN AS
T
F
4 "
K
SIN P F "
P
FOR
" a F a" WHERE 4 IS THE PULSEWIDTH " IS THE SWEPT BANDWIDTH AND K IS A TIME SIDELOBE LEVEL
CONTROL FACTOR
4YPICAL K VALUES ARE AND WHICH YIELD TIME SIDELOBE LEVELS OF n D" AND
n D" RESPECTIVELY &IGURE IS A PLOT OF PEAK TIME SIDELOBE LEVEL AS A FUNCTION OF THE
TIME SIDELOBE CONTROL FACTOR K FOR VARIOUS 4" PRODUCTS FOR THIS .,&- WAVEFORM
e #OURTESY OF %DWIN - 7ATERSCHOOT ,OCKHEED -ARTIN -ARITIME AND 3ENSOR 3YSTEMS 3YRACUSE .9
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&)'52% 0EAK TIME SIDELOBE LEVEL FOR A SINE BASED .,&- WAVEFORM AS
A FUNCTION OF K FACTOR #OURTESY OF $R 0ETER ( 3TOCKMANN ,OCKHEED -ARTIN
-ARITIME AND 3ENSOR 3YSTEMS 3YRACUSE .9
4HE FREQUENCY MODULATION VERSUS TIME FUNCTION FOR A TANGENT BASED WAVEFORM IS
GIVEN AS
F T " TAN B T 4 TAN B
FOR
4 aTa4 WHERE 4 IS THE PULSEWIDTH " IS THE SWEPT BANDWIDTH AND A IS DEFINED AS
B TAN A a A c
WHERE @ IS A TIME SIDELOBE LEVEL CONTROL FACTOR
7HEN @ IS ZERO THE TANGENT BASED .,&- WAVEFORM REDUCES TO AN ,&- WAVE
FORM (OWEVER @ CANNOT BE MADE ARBITRARILY LARGE BECAUSE THE COMPRESSED PULSE
TENDS TO DISTORT #OLLINS AND !TKINS DISCUSS AN EXTENSION OF THE TANGENT BASED .,&FOR WHICH THE FREQUENCY MODULATION FUNCTION IS A WEIGHTED SUM OF TANGENT BASED AND
LINEAR FREQUENCY MODULATION TERMS
&IGURE SHOWS THE FREQUENCY MODULATION VERSUS TIME FUNCTIONS FOR A SINE
BASED .,&- WAVEFORM WITH K A TANGENT BASED .,&- WAVEFORM WITH @ AND AN ,&- WAVEFORM
4HE SENSITIVITY OF A .,&- WAVEFORM TO DOPPLER SHIFT CAN BE SEEN IN &IGURE WHICH SHOWS THE MATCHED FILTER OUTPUT FOR A SINE BASED .,&- WAVEFORM IN THE PRES
ENCE OF DOPPLER SHIFT
4HE AMBIGUITY FUNCTION OF A .,&- SINE BASED WAVEFORM IS SHOWN IN &IGURE )T CAN BE NOTED THAT THIS AMBIGUITY FUNCTION IS MORE THUMBTACK LIKE IN NATURE THAN FOR
AN ,&- WAVEFORM INDICATING THAT THIS WAVEFORM IS MORE DOPPLER SENSITIVE THAN THE
,&- WAVEFORM
4ABLE PROVIDES A COMPARISON OF .,&- WAVEFORMS WITH WEIGHTED AND
UNWEIGHTED ,&- FOR DIFFERENT VALUES OF THE TARGET RADIAL VELOCITY IN TERMS OF PEAK
AND AVERAGE TIME SIDELOBE LEVELS AND 3.2 LOSS 4HE .,&- WAVEFORM SHOWS BETTER
n°£x
05,3% #/-02%33)/. 2!$!2
&)'52% &REQUENCY MODULATION VERSUS TIME FOR SINE BASED .,&- TANGENT BASED
.,&- AND ,&- WAVEFORMS
PERFORMANCE IN TERMS OF 3.2 LOSS AND PEAK TIME SIDELOBE LEVEL 43, THAN THE ,&WAVEFORM 4HE 43, LEVEL DOES NOT DEGRADE APPRECIABLY FOR THE ,&- WAVEFORM FOR
HIGHER RADIAL VELOCITIES DEMONSTRATING THE HIGHER DOPPLER TOLERANCE OF ,&-
&)'52% -ATCHED FILTER OUTPUT OF 3 BAND §S PULSEWIDTH -(Z BAND
WIDTH .,&- SINE BASED WAVEFORM WITH MS RADIAL VELOCITY #OURTESY OF %DWIN -
7ATERSCHOOT ,OCKHEED -ARTIN -ARITIME AND 3ENSOR 3YSTEMS 3YRACUSE .9
n°£È
2!$!2 (!.$"//+
&)'52% !MBIGUITY FUNCTION OF A SINE BASED SYMMETRICAL .,&- WAVEFORM
0HASE #ODED 7AVEFORMS )N PHASE CODED WAVEFORMS THE PULSE IS SUBDIVIDED
INTO A NUMBER OF SUBPULSES EACH OF DURATION C 4. WHERE 4 IS THE PULSEWIDTH AND .
IS THE NUMBER OF SUBPULSES 0HASE CODED WAVEFORMS ARE CHARACTERIZED BY THE PHASE
MODULATION APPLIED TO EACH SUBPULSE
"INARY 0HASE #ODES ! PHASE CODED WAVEFORM THAT EMPLOYS TWO PHASES IS
CALLED BINARY OR BIPHASE CODING ! BINARY PHASE CODED WAVEFORM IS CONSTANT
IN MAGNITUDE WITH TWO PHASE VALUES n OR n 4HE BINARY CODE CONSISTS OF A
SEQUENCE OF EITHER S AND S OR S AND S 4HE PHASE OF THE SIGNAL ALTERNATES
4!",% #OMPARISON OF ,INEAR &- AND .ONLINEAR &- 7AVEFORM 0ERFORMANCE
7EIGHTING
,&- UNWEIGHTED
,&- UNWEIGHTED
,&- WITH n D"
4AYLOR WEIGHTING
,&- WITH n D"
4AYLOR WEIGHTING
3INE BASED .,&WITH K 3INE BASED .,&WITH K 4ARGET 2ADIAL
6ELOCITY MS
0EAK 43, D"
!VERAGE
43, D"
&ILTER -ATCHING
,OSS D"
o
o
o
!N 3 BAND RADAR WITH §S TRANSMIT PULSEWIDTH AND -(Z BANDWIDTH WAS USED IN THIS COMPARISON
4HE DOPPLER SHIFT EXPRESSED IN (Z IS FD K 6R 6R WHERE 6R IS THE RADIAL VELOCITY EXPRESSED IN
MS 6R FOR AN OUT BOUND TARGET !VERAGE OF 43, POWER RATIO
05,3% #/-02%33)/. 2!$!2
n°£Ç
BETWEEN n AND n IN ACCORDANCE
WITH THE SEQUENCE OF ELEMENTS S AND
S OR S AND S IN THE PHASE CODE
AS SHOWN IN &IGURE "ECAUSE THE
FREQUENCY IS NOT USUALLY A MULTIPLE OF
THE RECIPROCAL OF THE SUBPULSE WIDTH
THE CODED SIGNAL IS GENERALLY DISCON
TINUOUS AT THE PHASE REVERSAL POINTS
4HIS DOES NOT IMPACT ITS TIME SIDE
LOBES BUT DOES CAUSE SOME INCREASE &)'52% "INARY PHASE CODED SIGNAL
IN THE SPECTRUM SIDELOBE LEVELS
5PON RECEPTION THE COMPRESSED PULSE IS OBTAINED BY MATCHED FILTER PROCESSING
4HE WIDTH OF THE COMPRESSED PULSE AT THE HALF AMPLITUDE POINT IS NOMINALLY EQUAL TO
THE SUBPULSE WIDTH 4HE RANGE RESOLUTION IS HENCE PROPORTIONAL TO THE TIME DURATION OF
ONE ELEMENT OF THE CODE ONE SUBPULSE 4HE TIME BANDWIDTH PRODUCT AND PULSE COM
PRESSION RATIO ARE EQUAL TO THE NUMBER OF SUBPULSES IN THE WAVEFORM IE THE NUMBER
OF ELEMENTS IN THE CODE
/PTIMAL "INARY #ODES /PTIMAL BINARY CODES ARE BINARY SEQUENCES WHOSE PEAK
SIDELOBE OF THE APERIODIC AUTOCORRELATION FUNCTION IS THE MINIMUM POSSIBLE FOR A GIVEN
CODE LENGTH #ODES WHOSE AUTOCORRELATION FUNCTION OR ZERO DOPPLER RESPONSE EXHIBIT
LOW SIDELOBES ARE DESIRABLE FOR PULSE COMPRESSION RADARS 2ESPONSES DUE TO MOVING
TARGETS WILL DIFFER FROM THE ZERO DOPPLER RESPONSE )F THE MATCHED FILTER IS BASED ONLY
ON THE ZERO DOPPLER RESPONSE AN INCREASE IN THE TIME SIDELOBES WILL RESULT 5LTIMATELY
IF THE DOPPLER SHIFT BECOMES VERY LARGE THE MATCHED FILTER RESPONSE WILL DEGRADE 4HIS
CAN BE ALLEVIATED BY UTILIZING A BANK OF MATCHED FILTERS COVERING THE EXPECTED RANGE OF
DOPPLER SHIFTS "ECAUSE THIS IS MORE COMPUTATIONALLY INTENSIVE THAN A SINGLE MATCHED
FILTER OLDER RADAR SYSTEMS TEND NOT TO EMPLOY BANKS OF FILTERS 4HE INCREASE IN COMPU
TATIONAL CAPACITY OF MODERN RADAR SYSTEMS HOWEVER CAN MAKE THIS MORE ATTRACTIVE
"ARKER #ODES ! SPECIAL CLASS OF BINARY CODES IS THE "ARKER CODES "ARKER CODES
ARE BINARY CODES WITH PEAK TIME SIDELOBE LEVELS EQUAL TO nLOG. WHERE . IS THE
LENGTH OF THE CODE 4HE ENERGY IN THE SIDELOBE REGION IS MINIMUM AND UNIFORMLY DIS
TRIBUTED 4HE "ARKER CODE IS THE ONLY UNIFORM PHASE CODE THAT REACHES THIS LEVEL
!LL THE KNOWN BINARY "ARKER CODES ARE LISTED IN 4ABLE /NLY BINARY "ARKER CODES
OF LENGTHS AND HAVE BEEN FOUNDn
! PULSE COMPRESSION RADAR USING "ARKER CODES WOULD BE LIMITED TO A MAXIMUM
TIME BANDWIDTH PRODUCT OF &IGURE SHOWS THE AUTOCORRELATION FUNCTION OF
4!",% +NOWN "INARY "ARKER #ODES
,ENGTH
#ODE
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2!$!2 (!.$"//+
&)'52% 3UPERPOSITION OF THE AUTOCORRELATION FUNCTIONS FOR ALL
POSSIBLE BIT CODE SEQUENCES WITH THE "ARKER #ODE HIGHLIGHTED DARK
SHOWN FOR ZERO DOPPLER SHIFT
A LENGTH "ARKER CODE FOR ZERO DOPPLER SHIFT SUPERIMPOSED UPON ALL POSSIBLE AUTO
CORRELATION FUNCTIONS OF BIT BINARY SEQUENCES )T CAN BE SEEN THAT THE "ARKER CODE
PROVIDES THE LOWEST TIME SIDELOBE LEVELS OF ALL POSSIBLE CODES
!LLOMORPHIC &ORMS ! BINARY CODE MAY BE REPRESENTED IN ANY ONE OF FOUR ALLO
MORPHIC FORMS ALL OF WHICH HAVE THE SAME CORRELATION CHARACTERISTICS 4HESE FORMS ARE
THE CODE ITSELF THE INVERTED CODE THE CODE WRITTEN IN REVERSE ORDER THE COMPLEMENTED
CODE S CHANGED TO S AND S TO S AND THE INVERTED COMPLEMENTED CODE &OR SYM
METRICAL CODES THE CODE AND ITS INVERSE ARE IDENTICAL
-AXIMAL ,ENGTH 3EQUENCES -AXIMAL LENGTH SEQUENCES HAVE A STRUCTURE SIMI
LAR TO RANDOM SEQUENCES AND THEREFORE POSSESS DESIRABLE AUTOCORRELATION FUNCTIONS
4HEY ARE OFTEN CALLED PSEUDORANDOM NOISE 02. SEQUENCES (ISTORICALLY THESE
SEQUENCES WERE GENERATED USING N STAGES OF SHIFT REGISTERS WITH SELECTED OUTPUT TAPS
USED FOR FEEDBACK SEE &IGURE 7HEN THE FEEDBACK CONNECTIONS ARE PROPERLY
CHOSEN THE OUTPUT IS A SEQUENCE OF MAXIMAL LENGTH WHICH IS THE MAXIMUM LENGTH
OF A SEQUENCE OF S AND S THAT CAN BE FORMED BEFORE THE SEQUENCE IS REPEATED 4HE
LENGTH OF THE MAXIMAL SEQUENCE IS . N WHERE N IS THE NUMBER OF STAGES IN THE
SHIFT REGISTER GENERATOR
4HE FEEDBACK CONNECTIONS THAT PROVIDE THE MAXIMAL LENGTH SEQUENCES MAY BE
DETERMINED FROM A STUDY OF PRIMITIVE AND IRREDUCIBLE POLYNOMIALS !N EXTENSIVE LIST OF
THESE POLYNOMIALS IS GIVEN BY 0ETERSON AND 7ELDON
!LTHOUGH MAXIMAL LENGTH SEQUENCES HAVE SOME DESIRABLE AUTOCORRELATION CHAR
ACTERISTICS A MAXIMUM LENGTH SEQUENCE DOES NOT GUARANTEE LOWEST TIME SIDELOBES
WHEN COMPARED TO OTHER BINARY CODES !N EXAMPLE OF THIS IS PROVIDED FOR A BIT
SEQUENCE &IGURE A IS A HISTOGRAM OF THE PEAK TIME SIDELOBE LEVEL FOR THE AUTO
CORRELATION OF EVERY POSSIBLE COMBINATION OF A BIT CODE &IGURE B IS THE SAME
BUT FOR ONLY MAXIMAL LENGTH SEQUENCES OF
LENGTH CODE A SUBSET OF &IGURE A &IGURE A SHOWS A LOWEST TIME SIDELOBE
LEVEL OF n D" 4HE LOWEST SIDELOBE FOR
THE MAXIMAL LENGTH SEQUENCE IS SEEN FROM
&IGURE B TO BE ONLY n D"
&)'52% 3HIFT REGISTER GENERATOR
05,3% #/-02%33)/. 2!$!2
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#+!-)(,%/
"!$!#&-#*
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!+.!$#%+ (,%*
&)'52% (ISTOGRAM OF PEAK TIME SIDELOBE LEVELS FOR BIT SEQUENCES A ALL POSSIBLE BIT
SEQUENCES AND B BIT MAXIMAL LENGTH SEQUENCES
-INIMUM 0EAK 3IDELOBE #ODES "INARY CODES THAT PROVIDE MINIMUM PEAK TIME SIDE
LOBE LEVELS BUT EXCEED THE TIME SIDELOBE LEVELS ACHIEVED BY "ARKER CODES n LOG . ARE
TERMED MINIMUM PEAK SIDELOBE CODES 4HESE CODES ARE USUALLY FOUND USING COMPUTER
SEARCH TECHNIQUES 3KOLNIK AND ,EVANON AND -OZESON PROVIDE THESE CODES FOR VARIOUS
SEQUENCE LENGTHS ALONG WITH THE RESULTING TIME SIDELOBE LEVELS
#OMPLEMENTARY 3EQUENCES #OMPLEMENTARY SEQUENCES CONSIST OF TWO SEQUENCES
OF THE SAME LENGTH . WHOSE APERIODIC AUTOCORRELATION FUNCTIONS HAVE SIDELOBES EQUAL
IN MAGNITUDE BUT OPPOSITE IN SIGN 4HE SUM OF THE TWO AUTOCORRELATION FUNCTIONS HAS
A PEAK OF . AND A SIDELOBE LEVEL OF )N A PRACTICAL APPLICATION THE TWO SEQUENCES
MUST BE SEPARATED IN TIME FREQUENCY OR POLARIZATION WHICH RESULTS IN DECORRELATION OF
RADAR RETURNS SO THAT COMPLETE SIDELOBE CANCELLATION MAY NOT OCCUR (ENCE THEY HAVE
NOT BEEN WIDELY USED IN PULSE COMPRESSION RADARS
0OLYPHASE #ODES 7AVEFORMS CONSISTING OF MORE THAN TWO PHASES MAY ALSO BE
USED 0OLYPHASE CODES CAN BE CONSIDERED AS COMPLEX SEQUENCES WHOSE ELEMENTS HAVE
A MAGNITUDE OF ONE BUT WITH VARIABLE PHASE 4HE PHASES OF THE SUBPULSES ALTERNATE
AMONG MULTIPLE VALUES RATHER THAN JUST THE n AND n OF BINARY PHASE CODES 4HESE
CODES TEND TO BE DISCRETE APPROXIMATIONS TO ,&- WAVEFORMS AND HENCE POSSESS SIMI
LAR AMBIGUITY FUNCTIONS AND DOPPLER SHIFT CHARACTERISTICS 4HE AUTOCORRELATION FUNCTIONS
ARE SIMILAR WITH A PEAK TO SIDELOBE RATIO OF ABOUT . &RANK #ODES 4HE &RANK CODE CORRESPONDS TO A STEPPED PHASE APPROXIMATION OF
AN ,&- WAVEFORM (ERE THE PULSE IS BROKEN UP INTO - GROUPS EACH OF WHICH IS
FURTHER BROKEN UP INTO - SUBPULSES (ENCE THE TOTAL LENGTH OF THE &RANK CODE IS -
WITH A CORRESPONDING COMPRESSION RATIO OF - 4HE &RANK POLYPHASE CODES DERIVE THE
SEQUENCE OF PHASES FOR THE SUBPULSES BY USING A MATRIX TECHNIQUE AS FOLLOWS
§
¨
¨
¨
"
¨"
¨ - ©
"
- !
¶
! - ·
·
! - ·
"
"
·
! - ·¸
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2!$!2 (!.$"//+
4HE MATRIX ELEMENTS REPRESENT THE MULTIPLYING COEFFICIENTS OF A BASIC PHASE SHIFT
O - WHERE - IS AN INTEGER 4HE PHASE SHIFT CORRESPONDING TO THE ELEMENT M N OF THE
MATRIX CAN BE WRITTEN AS
FM N P
M N M -
- N -
!N EXAMPLE OF A &RANK #ODE MATRIX FOR - IS GIVEN HERE
§
P ¨
¨
¨
©¨
¶
§
· P ¨
· ¨
· ¨
¸·
©¨
¶
¶ §
C
C
¨
·
C·
·
·¨
· ¨ C
C ·
¸· ¨© C C C ·¸
#ONCATENATING THE ROWS OF THIS MATRIX YIELDS THE PHASE FOR EACH OF THE SUBPULSES
&IGURE SHOWS THE PHASE MODULATION CHARACTERISTIC OF THE &RANK #ODE FOR THE ABOVE
EXAMPLE .OTE HOW THE PHASE STEP BETWEEN SUBPULSES INCREASES BETWEEN SUBPULSE
GROUPS WITH A LENGTH EQUAL TO FOUR 4HIS CHARACTERISTIC CAN BE REGARDED AS A STEPPED
PHASE APPROXIMATION TO QUADRATIC PHASE MODULATION
!S - INCREASES THE PEAK SIDELOBEnVOLTAGE RATIO APPROACHES O - 4HIS COR
RESPONDS TO APPROXIMATELY A D" IMPROVEMENT OVER PSEUDORANDOM SEQUENCES
OF SIMILAR LENGTH 4HE AMBIGUITY FUNCTION GROSSLY RESEMBLES THE KNIFE EDGE RIDGE
CHARACTERISTIC ASSOCIATED WITH ,&- WAVEFORMS AS CONTRASTED WITH THE THUMBTACK
CHARACTERISTIC OF PSEUDORANDOM SEQUENCES &IGURE (OWEVER FOR SMALL RATIOS OF
DOPPLER SHIFT TO WAVEFORM BANDWIDTH A GOOD DOPPLER RESPONSE CAN BE OBTAINED FOR
REASONABLE TARGET VELOCITIES
,EWIS AND +RETSCHMER #ODES 0 0 0 0 ,EWIS AND +RETSCHMER HAVE STUD
IED THE 0 0 0 AND 0 POLYPHASE CODES 4HESE CODES ARE STEP APPROXIMATIONS
TO THE ,&- PULSE COMPRESSION WAVEFORMS HAVE LOW RANGE SIDELOBES AND HAVE THE
&)'52% 0HASE VERSUS TIME RELATIONSHIP FOR &RANK CODE OF
LENGTH - n°Ó£
05,3% #/-02%33)/. 2!$!2
&)'52% !MBIGUITY FUNCTION OF A &RANK CODE OF LENGTH - DOPPLER TOLERANCE OF THE ,&- CODES 4HE 0 AND 0 CODES ARE MODIFIED VERSIONS OF
THE &RANK CODE WITH THE $# FREQUENCY TERM AT THE CENTER OF THE PULSE INSTEAD OF AT THE
BEGINNING 4HEY ARE MORE TOLERANT OF RECEIVER BAND LIMITING PRIOR TO PULSE COMPRESSION
ENCOUNTERED IN DIGITAL RADAR SYSTEMS 4HE 0 CODES CONTAINS - ELEMENTS AS DOES THE
&RANK CODE BUT THE RELATIONSHIP OF THE ITH ELEMENT TO THE JTH GROUP IS EXPRESSED AS
FI J P - ; - J =; J - I =
WHERE I AND J ARE INTEGERS RANGING FROM TO -
0 CODES ARE SIMILAR BUT THE PHASE IS SYMMETRIC WITH THE FOLLOWING CHARACTERISTIC
FI J [P ; - - = P - I
J ]; - J=
4HE 0 AND 0 CODES ARE DERIVED BY ESSENTIALLY CONVERTING AN ,&- WAVEFORM TO
BASEBAND 4HESE TEND TO BE MORE DOPPLER TOLERANT THAN THE &RANK 0 OR 0 CODES
AND ARE ALSO MORE TOLERANT OF PRECOMPRESSION BANDWIDTH LIMITATIONS THAT APPEAR IN
RADAR SYSTEMS 4HE PHASE OF THE 0 CODE IS GIVEN AS
JN P N
.
Nx.n
4HE 0 CODE PHASE RELATIONSHIP IS SIMILAR
FN P N
.
PK
aNa.
4ABLE SUMMARIZES THE PHASE AND AUTOCORRELATION CHARACTERISTICS OF THE &RANK
CODE AND THE ,EWIS AND +RETSCHMER 0 THROUGH 0 POLYPHASE CODES
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4!",% 3UMMARY OF 0HASE AND !UTOCORRELATION #HARACTERISTICS OF &RANK AND ,EWIS AND
+RETSCHMER 0OLYPHASE #ODES
0OLYPHASE
#ODE
0HASE
&RANK
P
I J .
0
0
0
0HASE VS 4IME #HARACTERISTIC !UTOCORRELATION D"
. %XAMPLE
. %XAMPLE
I x.
J x.
P
; - J =
s ;J - I =
FOR ITH ELEMENT IN
THE JTH GROUP
[P ; - - =
P - I J ]
; ; - J=
FOR ITH ELEMENT IN
THE JTH GROUP
P N
.
N x . n 0
P N
.
PK
aNa.
0N K 0OLYPHASE #ODES 7HEREAS THE PREVIOUSLY DISCUSSED POLYPHASE CODES ARE
DERIVED FROM ,&- WAVEFORMS 0N K CODES ARE DERIVED FROM STEP APPROXIMATIONS OF
THE PHASE CHARACTERISTIC OF THE WEIGHTING FUNCTION OF .,&- WAVEFORMS 4HE WEIGHT
ING FUNCTION IS GIVEN BY
¤P F ³
7 F K K COSN ¥ ´
¦ "µ
WHERE K AND N ARE PARAMETERS OF THE WEIGHTING FUNCTION " IS THE SWEPT BANDWIDTH OF
THE WAVEFORM AND n" a F a " 4HIS IS A COSN WEIGHTING ON A PEDESTAL OF HEIGHT K
&IGURE (AMMING WEIGHTING IS ACHIEVED FOR N AND K n°ÓÎ
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N
&)'52% COS ON PEDESTAL WEIGHTING FUNCTION SHOWN FOR N &OR THE CASE WHERE N THE WEIGHTING FUNCTION CAN BE INTEGRATED TO OBTAIN THE FOLLOWING
RELATIONSHIP BETWEEN TIME AND FREQUENCY
T
F
4 "
A SIN P F "
WHERE A n K K
WHICH IS SIMILAR TO THE SINE BASED .,&- DISCUSSED EARLIER 4HIS PARTICULAR CODE IS
CALLED 0HASE FROM .ONLINEAR &REQUENCY 0., AND ITS AUTOCORRELATION FUNCTION IS
SHOWN IN &IGURE FOR A §S PULSEWIDTH -(Z BANDWIDTH WAVEFORM WITH
A AND FD 4HE TIME SIDELOBE LEVELS ARE SEEN TO BE BELOW n D"
4HE AMBIGUITY FUNCTION IS SIMILAR TO THAT PROVIDED IN THE DISCUSSION OF .,&WHICH IS EXPANDED IN &IGURE TO SHOW IN MORE DETAIL THE IMPACT OF DOPPLER SHIFT ON
THE PULSE COMPRESSED WAVEFORM FOR PRACTICAL VALUES OF DOPPLER SHIFTS
&)'52% §S 0., PULSE AUTOCORRELATION FUNCTION FOR 4" A AND FD n°Ó{
2!$!2 (!.$"//+
&)'52% " -(Z
%XPANDED VIEW OF 0., AMBIGUITY DIAGRAM FOR §S PULSE A AND
!S THE DOPPLER SHIFT MOVES AWAY FROM ZERO THE PEAK DECREASES AND THE CLOSE IN
TIME SIDELOBE LEVELS ON ONE SIDE OR THE OTHER BEGIN TO INCREASE .OTE THAT AN F" RATIO
OF CORRESPONDS TO A DOPPLER SHIFT ASSOCIATED WITH APPROXIMATELY A -ACH TARGET
AT A 3 BAND CARRIER FREQUENCY
)N GENERAL FOR 0N K WAVEFORMS THE INTEGRAL OF THE WEIGHTING FUNCTION PROVIDES
THE RELATIONSHIP BETWEEN TIME AND FREQUENCY MODULATION AS SHOWN IN %Q PF
T
"
;K K COSN X = DX
4 P ¯ P
3INCE FREQUENCY MODULATION IS PROPORTIONAL TO THE TIME DERIVATIVE OF PHASE PHASE
IS OBTAINED BY INTEGRATING THE FREQUENCY WITH RESPECT TO TIME 4HE EXPRESSION FOR FRE
QUENCY HOWEVER IS NOT STRAIGHTFORWARD AND IS USUALLY OBTAINED THROUGH NUMERICAL
EVALUATION
1UADRIPHASE #ODES 1UADRIPHASE CODES ARE AN EXAMPLE OF A PHASE CODED WAVE
FORM WITHOUT PHASE DISCONTINUITIES 1UADRIPHASE CODES ARE BASED ON THE USE OF
SUBPULSES WITH A HALF COSINE SHAPE AND PHASE CHANGES BETWEEN ADJACENT SUBPULSES
OF MULTIPLES OF on 4HE COSINE WEIGHTING PROVIDES FASTER SPECTRUM ROLL OFF LOWER
FILTER MATCHING LOSS AND SMALLER RANGE SAMPLING LOSS WHEN COMPARED TO RECTANGULAR
SUBPULSE PHASE CODED WAVEFORMS 4ABLE 4!",% 1UADRIPHASE 7AVEFORM 0ERFORMANCE 3UMMARY
2ADIATED 3PECTRUM D" 7IDTH
&ALLOFF C SUBPULSE DURATION
2ANGE 3AMPLING ,OSS
&ILTER -ATCHING ,OSS
1UADRIPHASE #ODE
2ECTANGULAR
3UBPULSE #ODE
C
D" /CTAVE
D"
D"
C
D" /CTAVE
D"
D"
05,3% #/-02%33)/. 2!$!2
&)'52% n°Óx
4IME FREQUENCY CODED WAVEFORM
4IME &REQUENCY #ODED 7AVEFORMS ! TIME FREQUENCY CODED WAVEFORM
&IGURE CONSISTS OF A TRAIN OF . PULSES WITH EACH PULSE AT A DIFFERENT FREQUENCY
'ENERALLY THE FREQUENCIES ARE EQUALLY SPACED AND THE PULSES ARE OF THE SAME AMPLI
TUDE 4HE AMBIGUITY FUNCTION FOR A PERIODIC WAVEFORM OF THIS TYPE CONSISTS OF A CENTRAL
SPIKE PLUS MULTIPLE SPIKES OR RIDGES DISPLACED IN TIME AND FREQUENCY !LTHOUGH IT IS
UNACHIEVABLE IN PRACTICE THE OBJECTIVE IS TO CREATE A HIGH RESOLUTION THUMBTACK LIKE
CENTRAL SPIKE WITH A CLEAR AREA AROUND IT -EASUREMENT IS THEN PERFORMED ON THE HIGH
RESOLUTION CENTRAL SPIKE 4HE RANGE RESOLUTION OR COMPRESSED PULSE WIDTH IS DETERMINED
BY THE TOTAL BANDWIDTH OF ALL THE PULSES AND THE DOPPLER RESOLUTION IS DETERMINED BY THE
RECIPROCAL OF THE WAVEFORM DURATION 4 &OR EXAMPLE A TYPICAL WAVEFORM IN THIS CLASS
HAS . CONTIGUOUS PULSES OF WIDTH T WHOSE SPECTRA OF WIDTH S ARE PLACED SIDE BY SIDE
IN FREQUENCY TO ELIMINATE GAPS IN THE COMPOSITE SPECTRUM 3INCE THE WAVEFORM BAND
WIDTH IS NOW .S THE NOMINAL COMPRESSED PULSE WIDTH IS S . 4HESE RELATIONSHIPS ARE
SUMMARIZED IN 4ABLE 3HAPING OF THE HIGH RESOLUTION CENTRAL SPIKE AREA AS WELL AS THE GROSS STRUCTURE OF THE
AMBIGUITY SURFACE CAN BE ACCOMPLISHED BY VARIATIONS OF THE BASIC WAVEFORM PARAM
ETERS SUCH AS AMPLITUDE WEIGHTING OF THE PULSE TRAIN STAGGERING OF THE PULSE REPETITION
INTERVAL AND FREQUENCY OR PHASE CODING OF THE INDIVIDUAL PULSES
#OSTAS #ODES #OSTAS CODES ARE A CLASS OF FREQUENCY CODED WAVEFORMS THAT
HAVE NEAR IDEAL RANGE AND DOPPLER SIDELOBE BEHAVIOR )N OTHER WORDS THEIR AMBI
GUITY FUNCTION APPROACHES THE IDEAL THUMBTACK PROVIDING BOTH DOPPLER AND RANGE
INFORMATION &IGURE !LL SIDELOBES EXCEPT FOR A FEW NEAR THE ORIGIN HAVE
AN AMPLITUDE OF - ! FEW SIDELOBES CLOSE TO THE ORIGIN ARE ABOUT TWICE AS LARGE
OR ABOUT - WHICH IS CHARACTERISTIC OF #OSTAS CODES 4HE COMPRESSION RATIO OF A
#OSTAS CODE IS ABOUT -
4HE #OSTAS CODE IS A BURST OF - CONTIGUOUS UNCODED PULSE WAVEFORMS EACH WITH A
DIFFERENT FREQUENCY SELECTED FROM A FINITE SET OF - EQUALLY SPACED FREQUENCIES THAT ARE
4!",% . 0ULSES #ONTIGUOUS IN 4IME AND &REQUENCY
7AVEFORM DURATION 4
7AVEFORM BANDWIDTH "
4IME BANDWIDTH PRODUCT 4"
#OMPRESSED PULSE WIDTH "
$OPPLER RESOLUTION 4
.S
.S
.
S . S .
.S
n°ÓÈ
2!$!2 (!.$"//+
&)'52% #OMPARISON OF AMBIGUITY FUNCTIONS FOR . STEPPED LINEAR AND #OSTAS SEQUENCE SHOWING
THE IMPACT OF FREQUENCY ORDER
PROCESSED COHERENTLY 4HE ORDER IN WHICH THE FREQUENCIES ARE GENERATED GREATLY INFLU
ENCES THE NATURE OF THE AMBIGUITY FUNCTION OF THE BURST )F THE FREQUENCIES ARE MONOTONI
CALLY INCREASING OR DECREASING THE WAVEFORM IS SIMPLY A STEPPED APPROXIMATION TO AN
,&- WHICH HAS A RIDGE IN ITS AMBIGUITY FUNCTION &IGURE )N ORDER TO APPROACH A
THUMBTACK LIKE AMBIGUITY FUNCTION THE ORDER OF THE FREQUENCIES NEEDS TO BE MORE RAN
DOM IN NATURE 4HE ORDER OF FREQUENCIES IS THE CODE AND IT IS GENERATED VIA A SPECIAL CLASS
OF - ¾ - #OSTAS ARRAYS #OSTAS SUGGESTED A TECHNIQUE FOR SELECTING THE ORDER OF THESE
FREQUENCIES TO PROVIDE MORE CONTROLLED RANGE AND DOPPLER SIDELOBES !N EXAMPLE OF A
#OSTAS CODE OF LENGTH IS SHOWN IN &IGURE AS IT COMPARES TO THE STEPPED ,&-
4ABLES SHOWING THE SEQUENCE ORDER FOR EACH WAVEFORM ARE ALSO PROVIDED
n°ÎÊ /",-Ê / Ê " Ê"ÊÊ
*1- Ê "*, --" Ê-9-/ 4HE CHOICE OF A PULSE COMPRESSION SYSTEM INVOLVES THE SELECTION OF THE TYPE OF WAVE
FORM AND THE METHOD OF GENERATION AND PROCESSING -ETHODS OF GENERATING AND PROCESS
ING PULSE COMPRESSION WAVEFORMS ARE DISCUSSED IN THE SECTION ON PULSE COMPRESSION
IMPLEMENTATION IN THIS CHAPTER $ISCUSSIONS HERE WILL CONCENTRATE ON THE WAVEFORM
ITSELF 4HE PRIMARY FACTORS INFLUENCING THE SELECTION OF A PARTICULAR WAVEFORM ARE USU
ALLY THE RADAR REQUIREMENTS OF DOPPLER TOLERANCE AND TIME SIDELOBE LEVELS
4ABLE SUMMARIZES THESE FACTORS FOR THREE &- TYPES ,&- .,&- AND PHASE CODED
WAVEFORMS 4HE SYSTEMS ARE COMPARED ON THE ASSUMPTION THAT INFORMATION IS EXTRACTED BY
PROCESSING A SINGLE WAVEFORM AS OPPOSED TO MULTIPLE PULSE PROCESSING 4HE SYMBOLS "
AND 4 DENOTE THE BANDWIDTH AND THE PULSEWIDTH OF THE WAVEFORM RESPECTIVELY
)N CASES WHERE AN INSUFFICIENT DOPPLER SHIFT OCCURS SUCH AS WITH A STATIONARY OR
TANGENTIAL TARGET RANGE RESOLUTION IS THE CHIEF MEANS FOR SEEING A TARGET IN CLUTTER
05,3% #/-02%33)/. 2!$!2
4!",% n°ÓÇ
#OMPARISONS OF 0ERFORMANCE #HARACTERISTICS FOR ,&- .,&- AND 0HASE #ODED
7AVEFORMS
&ACTOR
,INEAR &-
$OPPLER
TOLERANCE
3UPPORTS DOPPLER !DEQUATE INSENSITIVITY (IGHER SENSITIVITY TO (IGHEST SENSITIVITY
SHIFTS UP TO o " TO DOPPLER TO ALLOW USE DOPPLER SHIFT 4IME TO DOPPLER SHIFT
4IME SHIFT OF FD4" GENERALLY UP TO -ACH SIDELOBES INCREASE 4IME SIDELOBES
INCREASE WHILE
WHILE MAINLOBE
4IME SHIFT OF FD4" IS
IS INTRODUCED BY
RESPONSE DECREASES MAINLOBE RESPONSE
RANGE DOPPLER
INTRODUCED BY RANGE
COUPLING
DOPPLER COUPLING FOR A FOR HIGHER DOPPLER DECREASES FOR
HIGHER DOPPLER
4IME SIDELOBE
NONSYMMETRICAL .,&- CHARACTERISTIC
CHARACTERISTIC OF
OF A THUMBTACK
PERFORMANCE
WAVEFORM #OMMON
A THUMBTACK LIKE
LIKE AMBIGUITY
REMAINS EXCELLENT THEREFORE IN !4#
AMBIGUITY FUNCTION FOR LARGE DOPPLER RADARS -ULTIPLE TUNED FUNCTION 5SED
5SED THEREFORE FOR
THEREFORE FOR
SHIFTS
PULSE COMPRESSORS
LOW SPEED TARGET
REQUIRED FOR HIGH SPEED LOW SPEED TARGET
APPLICATIONS AND
APPLICATIONS AND
TARGETS
WITH SMALL 4"
WITH SMALL 4"
PRODUCTS ,ONGER
PRODUCTS
PHASE CODED
WAVEFORMS ARE MORE
SENSITIVE TO DOPPLER
SHIFTS THAN THE
SHORTER ONES
"ETTER TIME SIDELOBES
'OOD TIME
&OR NONSYMMETRICAL
!DEQUATE
THAN BINARY PHASE
SIDELOBES THAT ARE
.,&- EXCELLENT
WEIGHTING HIGH
CODED WAVEFORMS
DETERMINED BY
TIME SIDELOBES IF
4" PRODUCT AND
CODING
THERE IS ADEQUATE
LOW AMPLITUDE
.,&- PHASE CODING
AND PHASE ERRORS
A HIGH 4" PRODUCT
ARE NECESSARY TO
ACHIEVE GOOD TIME AND SUFFICIENTLY LOW
AMPLITUDE AND PHASE
SIDELOBES
ERRORS )NCREASING
.,&- PHASE CODE
WEIGHTING INTRODUCES
INCREASED RADIAL
VELOCITY SENSITIVITY
4IME
SIDELOBE
LEVEL
'ENERAL
/FTEN USED FOR
HIGH SPEED
TARGET CAPABILITY
-ACH %XTREMELY WIDE
BANDWIDTHS
ACHIEVABLE
.ONLINEAR &-
"INARY 0HASE #ODED 0OLYPHASE #ODED
'ENERALLY FOUND IN 'ENERALLY FOUND IN
5SE IS GENERALLY
LOW DOPPLER SHIFT
RESTRICTED TO APPLICATIONS LOW DOPPLER SHIFT
APPLICATIONS
APPLICATIONS
WHERE PRIMARY
TARGET RADIAL VELOCITIES
-ACH -ULTIPLE
TUNED MATCHED FILTERS
ARE GENERALLY NOT
COMPUTATIONALLY
PRACTICAL
#LUTTER REJECTION WITH PULSE COMPRESSION WAVEFORMS IS DUE TO THE GREATER RANGE RESO
LUTION ACHIEVABLE OVER UNCODED WAVEFORMS "ECAUSE THE RANGE RESOLUTION IS PRO
PORTIONAL TO THE RECIPROCAL OF THE BANDWIDTH WIDER BANDWIDTH PULSE COMPRESSION
WAVEFORMS CAN OFFER GREATER CLUTTER REJECTION
n°Ón
2!$!2 (!.$"//+
n°{Ê *1- Ê "*, --" Ê* Ê, ,Ê-9-/ Ê 8* -
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4HIS SECTION DESCRIBES THE GENERATION AND PROCESSING OF PULSE COMPRESSION WAVEFORMS
AND PROVIDES EXAMPLES OF RADAR SYSTEMS THAT UTILIZE THESE PROCESSING TECHNIQUES -AJOR
ADVANCES ARE CONTINUALLY BEING MADE IN THE DEVICES AND TECHNIQUES USED IN PULSE COM
PRESSION RADARS 3IGNIFICANT ADVANCES ARE EVIDENT IN THE DIGITAL AND 3!7 TECHNIQUES
THAT ALLOW THE IMPLEMENTATION OF A VARIETY OF PULSE COMPRESSION WAVEFORM TYPES 4HE
DIGITAL APPROACH HAS BLOSSOMED BECAUSE OF THE MANIFOLD INCREASE IN COMPUTATIONAL
SPEED AND ALSO BECAUSE OF THE SIZE REDUCTION AND THE SPEED INCREASE OF THE MEMORY
UNITS 3!7 TECHNOLOGY HAS EXPANDED BECAUSE OF THE INVENTION OF THE INTERDIGITAL TRANS
DUCER WHICH PROVIDES EFFICIENT TRANSFORMATION OF AN ELECTRICAL SIGNAL INTO ACOUSTIC
ENERGY AND VICE VERSA
$IGITAL 7AVEFORM 'ENERATION &IGURE SHOWS A DIGITAL APPROACH FOR GEN
ERATING THE RADAR WAVEFORM 4HE PHASE CONTROL ELEMENT SUPPLIES DIGITAL SAMPLES OF THE
IN PHASE COMPONENT ) AND THE QUADRATURE COMPONENT 1 WHICH ARE CONVERTED TO THEIR
ANALOG EQUIVALENTS 4HESE PHASE SAMPLES MAY DEFINE THE BASEBAND COMPONENTS OF THE
DESIRED WAVEFORM OR THEY MAY DEFINE THE WAVEFORM COMPONENTS ON A LOW FREQUENCY
CARRIER )F THE WAVEFORM IS ON A CARRIER THE BALANCED MODULATOR IS NOT REQUIRED AND THE
FILTERED COMPONENTS WOULD BE ADDED DIRECTLY 4HE SAMPLE AND HOLD CIRCUIT REMOVES
THE TRANSIENTS DUE TO THE NONZERO TRANSITION TIME OF THE DIGITAL TO ANALOG $! CON
VERTER 4HE LOW PASS FILTER SMOOTHES OR INTERPOLATES THE ANALOG SIGNAL COMPONENTS
BETWEEN WAVEFORM SAMPLES TO PROVIDE THE EQUIVALENT OF A MUCH HIGHER WAVEFORM
SAMPLING RATE 4HE )T COMPONENT MODULATES A n CARRIER SIGNAL AND THE 1T COMPO
NENT MODULATES A n PHASE SHIFTED CARRIER SIGNAL 4HE DESIRED WAVEFORM IS THE SUM OF
THE n MODULATED CARRIER AND THE n MODULATED CARRIER !S MENTIONED EARLIER WHEN
THE DIGITAL PHASE SAMPLES INCLUDE THE CARRIER COMPONENTS THE ) AND 1 COMPONENTS ARE
CENTERED ON THIS CARRIER FREQUENCY AND THE LOW PASS FILTER CAN BE REPLACED WITH A BAND
PASS FILTER CENTERED ON THE )& CARRIER
7HEN A LINEAR &- WAVEFORM IS DESIRED THE PHASE SAMPLES FOLLOW A QUADRATIC PAT
TERN AND CAN BE GENERATED BY TWO CASCADED DIGITAL INTEGRATORS 4HE INPUT DIGITAL COM
MAND TO THE FIRST INTEGRATOR DEFINES THIS QUADRATIC PHASE FUNCTION 4HE DIGITAL COMMAND
TO THE SECOND INTEGRATOR IS THE OUTPUT OF THE FIRST INTEGRATOR PLUS THE DESIRED CARRIER
FREQUENCY 4HIS CARRIER MAY BE DEFINED BY THE INITIAL VALUE OF THE FIRST INTEGRATOR 4HE
DESIRED INITIAL PHASE OF THE WAVEFORM IS THE INITIAL VALUE OF THE SECOND INTEGRATOR OR ELSE
MAY BE ADDED TO THE SECOND INTEGRATOR OUTPUT
7ITH ADVANCES IN DIGITAL TECHNOLOGY IT HAS BECOME POSSIBLE AND PRACTICAL TO GENERATE
WAVEFORMS DIRECTLY AT )& OR 2& CARRIER FREQUENCIES ON A SINGLE INTEGRATED CIRCUIT CHIP 4HIS
TECHNIQUE IS CALLED $IRECT $IGITAL 3YNTHESIS OR $$3 AND INVOLVES GENERATING WAVEFORMS AT
&)'52% $IGITAL WAVEFORM GENERATION BLOCK DIAGRAM
n°Ó™
05,3% #/-02%33)/. 2!$!2
HIGH SAMPLING RATES AND FILTERING THE OUTPUT 4HESE DEVICES GENERATE THE WAVEFORM BY ACCU
MULATING PHASE INFORMATION WHICH IS THEN USED TO LOOK UP VALUES OF THE WAVEFORM USUALLY
A SINE WAVE 4HIS IS CONVERTED TO AN ANALOG SIGNAL WITH A DIGITAL TO ANALOG CONVERTER $!#
OR $! CONVERTER AND FILTERED ! VARIETY OF WAVEFORM TYPES EG ,&- .,&- AND #7
WAVEFORMS CAN BE GENERATED IN THIS WAY BY USING THE APPROPRIATE PHASE MODULATION CHAR
ACTERISTIC !S AN EXAMPLE THE !NALOG $EVICES !$ $IRECT $IGITAL 3YNTHESIZER USES A
BIT $!# OPERATING AT UP TO A '(Z INTERNAL CLOCK SPEED $!# UPDATE RATE $IGITAL 0ULSE #OMPRESSION n $IGITAL PULSE COMPRESSION TECHNIQUES ARE
ROUTINELY USED FOR MATCHED FILTERING OF RADAR WAVEFORMS 4HE MATCHED FILTER MAY BE
IMPLEMENTED BY USING A DIGITAL CONVOLUTION FOR ANY WAVEFORM OR ELSE BY USE OF STRETCH
PROCESSING FOR A LINEAR &- WAVEFORM
$IGITAL PULSE COMPRESSION HAS DISTINCT FEATURES THAT DETERMINE ITS ACCEPTABILITY
FOR A PARTICULAR RADAR APPLICATION $IGITAL MATCHED FILTERING USUALLY REQUIRES MULTIPLE
OVERLAPPED PROCESSING UNITS FOR EXTENDED RANGE COVERAGE 4HE ADVANTAGES OF THE DIGI
TAL APPROACH ARE THAT LONG DURATION WAVEFORMS PRESENT NO PROBLEM THE RESULTS ARE
EXTREMELY STABLE UNDER A WIDE VARIETY OF OPERATING CONDITIONS AND THE SAME IMPLEMEN
TATION COULD BE USED TO HANDLE MULTIPLE WAVEFORM TYPES
!NALOG PRODUCT DETECTORS USED TO EXTRACT ) AND 1 BASEBAND COMPONENTS HAVE BEEN
REPLACED IN MANY SYSTEMS BY DIGITAL DOWN CONVERSION TECHNIQUES )N THIS APPROACH THE
COMPLEX ENVELOPE SEQUENCE IS EVALUATED BY DIGITAL SIGNAL PROCESSING OF !$ CONVERTER
SAMPLES AT THE FINAL )& OUTPUT OF THE RECEIVER RATHER THAN BY SEPARATE !$ CONVERSION OF
BASEBAND ANALOG ) AND 1 COMPONENTSn $IGITAL DOWN CONVERSION IS ADVANTAGEOUS
BECAUSE PERFORMANCE IS NOT LIMITED BY AMPLITUDE AND PHASE IMBALANCES THAT EXIST IN
ANALOG PRODUCT DETECTION HARDWARE
&IGURE ILLUSTRATES TWO DIGITAL SIGNAL PROCESSING APPROACHES TO PROVIDING THE
MATCHED FILTER FOR A PULSE COMPRESSION WAVEFORM )N BOTH CASES THE INPUT SIGNAL IS THE
COMPLEX ENVELOPE SEQUENCE AS FORMED USING EITHER DIGITAL DOWN CONVERSION OR ANALOG
#!
! !
!
$
#!
!
"
%
&)'52% A 4IME DOMAIN DIGITAL PULSE COMPRESSION PROCESSOR AND B FREQUENCY DOMAIN DIGITAL
PULSE COMPRESSION PROCESSOR
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2!$!2 (!.$"//+
PRODUCT DETECTION FOLLOWED BY !$ CONVERSION IN EACH BASEBAND CHANNEL &IGURE A
SHOWS A DIGITAL IMPLEMENTATION OF A TIME DOMAIN CONVOLUTION PROCESSOR THAT WILL PRO
VIDE MATCHED FILTER PERFORMANCE FOR ANY RADAR WAVEFORM )N THIS CASE DISCRETE TIME
CONVOLUTION IS DONE IN THE TIME DOMAIN BY CONVOLUTION OF THE COMPLEX ENVELOPE INPUT
SEQUENCE FOLLOWING DIGITAL DOWN CONVERSION WITH THE MATCHED FILTER IMPULSE RESPONSE
SEQUENCE "ECAUSE TIME DOMAIN CONVOLUTION CAN BE COMPUTATIONALLY INTENSIVE A MORE
ECONOMICAL APPROACH FROM A COMPUTATIONAL STANDPOINT IS SHOWN IN &IGURE B IN
WHICH FREQUENCY DOMAIN PROCESSING IS USED TO IMPLEMENT THE CONVOLUTION
4HE FREQUENCY DOMAIN DIGITAL PULSE COMPRESSION PROCESSOR OPERATES ON THE PRINCI
PLE THAT THE DISCRETE &OURIER TRANSFORM $&4 OF THE TIME CONVOLUTION OF TWO SEQUENCES
IS EQUAL TO THE PRODUCT OF THE DISCRETE &OURIER TRANSFORMS OF EACH OF THE SEQUENCES )F
- RANGE SAMPLES ARE TO BE PROVIDED BY ONE PROCESSOR THE LENGTH OF THE $&4 MUST
EXCEED - PLUS THE NUMBER OF SAMPLES IN THE REFERENCE WAVEFORM MINUS ONE TO ACHIEVE
AN APERIODIC CONVOLUTION 4HESE ADDED - SAMPLES ARE FILLED WITH ZEROS IN THE REFER
ENCE WAVEFORM $&4 &OR EXTENDED RANGE COVERAGE REPEATED PROCESSING OPERATIONS ARE
REQUIRED WITH RANGE DELAYS OF - SAMPLES BETWEEN ADJACENT OPERATIONS USING THE OVER
LAP SAVE CONVOLUTION TECHNIQUE 4HIS PROCESSOR CAN BE USED WITH ANY WAVEFORM
AND THE REFERENCE WAVEFORM CAN BE OFFSET IN DOPPLER FREQUENCY TO ACHIEVE A MATCHED
FILTER AT THIS DOPPLER FREQUENCY
0ULSE #OMPRESSION 2ADAR %XAMPLES 4HERE ARE MANY RADARS UNDER DEVELOP
MENT OR DEPLOYED THAT UTILIZE SOME OF THE PULSE COMPRESSION WAVEFORMS PREVIOUSLY DIS
CUSSED !DVANCES IN DIGITAL SIGNAL PROCESSING TECHNOLOGY HAVE ENABLED A WIDER VARIETY
OF WAVEFORM IMPLEMENTATIONS &OR EXAMPLE RADAR SYSTEMS ARE NO LONGER LIMITED TO THE
,&- WAVEFORM INSTEAD RADAR SYSTEM CAPABILITIES CAN BE EXTENDED TO TAKE ADVANTAGE
OF THE MORE COMPLEX PROCESSING ASSOCIATED WITH THE NONLINEAR &- WAVEFORM
!.403 AND !.&03 3URVEILLANCE 2ADARS 4HE !.403 AND !.
&03 ARE A FAMILY OF , BAND LONG RANGE SURVEILLANCE RADARS THAT EMPLOY ,&WAVEFORMS 4HE ANTENNA IS MECHANICALLY ROTATED IN AZIMUTH AND ELECTRONIC PENCIL
BEAM SCANNING IS PERFORMED IN ELEVATION 4HE TRANSMISSION UTILIZES TWO TIME SEQUENCED
,&- PULSES OF DIFFERENT FREQUENCIES IN ORDER TO CREATE 3WERLING #ASE TARGET STATISTICS
"OTH RADARS EMPLOY FREQUENCY DOMAIN DIGITAL PULSE COMPRESSION PROCESSING
!IR 3URVEILLANCE AND 0RECISION !PPROACH 2ADAR 3YSTEM 4HE !IR 3URVEILLANCE
AND 0RECISION !PPROACH 2ADAR 3YSTEM !30!2#3 IS INTENDED TO PROVIDE THE NEXT
GENERATION AIR TRAFFIC CONTROL !4# RADAR AS PART OF THE -ULTI -ISSION 3URVEILLANCE
2ADAR --32 FAMILY OF !4# RADARS BUILT BY ,OCKHEED -ARTIN #O .ONLINEAR &WAVEFORMS ARE USED BECAUSE THE TARGETS OF INTEREST HAVE RELATIVELY LOW DOPPLER SHIFTS
LESS THAN -ACH ,IKE THE !.&03 RADAR THIS SYSTEM IMPLEMENTS FREQUENCY
DOMAIN DIGITAL PULSE COMPRESSION PROCESSING
-ULTI -ISSION 2ADAR 4HE -ULTI -ISSION 2ADAR --2 IS DESIGNED TO DETECT AND
TRACK MORTARS ARTILLERY AND ROCKETS 4HIS RADAR USES A NONLINEAR &- SINE BASED WAVE
FORM $IGITAL FREQUENCY DOMAIN PULSE COMPRESSION PROCESSING IS PERFORMED
!32 .EXT 'ENERATION 3OLID 3TATE !IR 4RAFFIC #ONTROL 2ADAR 4HE !32 TER
MINAL AIRPORT SURVEILLANCE RADAR TRANSMITS A §S PULSE WITH PEAK POWER OF K7 TO
PROVIDE A SINGLE PULSE TRANSMIT ENERGY OF * .ONLINEAR FREQUENCY MODULATION IS
USED WITH A PULSE COMPRESSION RATIO OF TO ACHIEVE RANGE RESOLUTION EQUIVALENT TO
AN UNCODED §S PULSE 4HE FILTER MATCHING LOSS IS LESS THAN D" AND TYPICAL TIME
05,3% #/-02%33)/. 2!$!2
n°Î£
SIDELOBE LEVELS MEASURED ON PRODUCTION HARDWARE ARE n D" $IGITAL PULSE COMPRES
SION IS USED !N UNCODED §S PULSE IS USED TO PROVIDE COVERAGE FOR TARGETS WITHIN
THE RANGE INTERVAL FROM TO NMI
3TRETCH 0ULSE #OMPRESSIONn 3TRETCH PULSE COMPRESSION IS A TECHNIQUE FOR
PERFORMING ,&- PULSE COMPRESSION OF WIDEBAND WAVEFORMS USING A SIGNAL PROCESSOR
WITH BANDWIDTH THAT IS MUCH SMALLER THAN THE WAVEFORM BANDWIDTH WITHOUT LOSS OF
SIGNAL TO NOISE RATIO OR RANGE RESOLUTION 3TRETCH PULSE COMPRESSION IS USED FOR A SINGLE
TARGET OR FOR MULTIPLE TARGETS THAT ARE LOCATED WITHIN A RELATIVELY SMALL RANGE WINDOW
CENTERED AT A SELECTED RANGE
&IGURE SHOWS A BLOCK DIAGRAM OF A STRETCH PULSE COMPRESSION SYSTEM 4HE
,&- WAVEFORM HAS A SWEPT BANDWIDTH " PULSEWIDTH 4 AND ,&- SLOPE A 4HE REFER
ENCE WAVEFORM IS GENERATED WITH TIME DELAY S2 SWEPT BANDWIDTH "2 PULSEWIDTH 42
AND ,&- SLOPE @2 4HE REFERENCE WAVEFORM TIME DELAY IS TYPICALLY DERIVED BY RANGE
TRACKING OF A SELECTED TARGET WITHIN THE RANGE WINDOW 4HE CORRELATION MIXER #IN &IGURE PERFORMS A BANDPASS MULTIPLICATION OF THE RECEIVED SIGNAL BY THE OUTPUT
OF THE REFERENCE WAVEFORM GENERATOR 4HE LOWER SIDEBAND AT THE #- OUTPUT IS SELECTED
BY A BANDPASS FILTER "0& 3PECTRUM ANALYSIS IS PERFORMED WHEN THE ,&- SLOPES OF THE TRANSMIT AND REFERENCE
WAVEFORMS ARE EQUAL @ @2 2EDUCED BANDWIDTH PULSE COMPRESSION PROCESSING IS
PERFORMED IF THE REFERENCE WAVEFORM ,&- SLOPE IS LESS THAN THE TRANSMIT WAVEFORM
,&- SLOPE @2 @ )N BOTH CASES THE REQUIRED PROCESSING BANDWIDTH "P IS MUCH
SMALLER THAN THE WAVEFORM BANDWIDTH
&IGURE SHOWS THE PRINCIPLE OF STRETCH PULSE COMPRESSION FOR THE CASE WHERE THE
,&- SLOPES OF THE TRANSMIT AND REFERENCE WAVEFORMS ARE EQUAL 4HE INSTANTANEOUS FRE
QUENCY IS PLOTTED AS A FUNCTION OF TIME AT THREE POINTS IN THE STRETCH PULSE COMPRESSION
SYSTEM BLOCK DIAGRAM CORRELATION MIXER INPUT CORRELATION MIXER ,/ REFERENCE
WAVEFORM GENERATOR OUTPUT AND CORRELATION MIXER OUTPUT OUTPUT OF BANDPASS
FILTER 4HREE ,&- TARGET SIGNALS ARE SHOWN AT THE CORRELATION MIXER INPUT TARGET IS AT
ZERO TIME OFFSET RELATIVE TO THE REFERENCE WAVEFORM TARGET IS EARLIER IN TIME THAN THE
REFERENCE WAVEFORM AND TARGET IS LATER IN TIME )N EACH CASE THE ,&- SLOPE FOR THE
TARGET SIGNALS IS "4 4HE REFERENCE WAVEFORM APPLIED TO THE ,/ PORT OF THE #- HAS
,&- SLOPE EQUAL TO "242 "4
4HE INSTANTANEOUS FREQUENCY AT THE CORRELATION MIXER OUTPUT IS THE DIFFERENCE
BETWEEN THE INSTANTANEOUS FREQUENCIES AT THE #- INPUT AND ,/ PORTS !S A RESULT THE
#- OUTPUT SIGNALS FOR THE THREE TARGET SIGNALS ARE UNCODED PULSES PULSED #7 SIGNALS
WITH FREQUENCY OFFSET FROM THE MIXER )& OUTPUT F)& GIVEN BY
¤ "³
D F ¥ ´ TD
¦4µ
!
$ $
$ $ !%
!# !
"
&)'52% 3TRETCH PULSE COMPRESSION SYSTEM BLOCK DIAGRAM
!
! !
n°ÎÓ
2!$!2 (!.$"//+
"# $#
!
%!
! $&
#
#
"# $#$#
&)'52% #ORRELATION MIXER SIGNALS IN STRETCH PULSE COMPRESSION AFTER 2OTH ET AL
WHERE TD IS THE TIME DELAY OF THE MIDPOINT OF THE SIGNAL MEASURED RELATIVE TO THE MID
POINT OF THE REFERENCE WAVEFORM &OR THE CASE SHOWN WHERE THE 2& CARRIER FREQUENCY
IS ABOVE THE CARRIER FREQUENCY OF THE REFERENCE WAVEFORM A POSITIVE TIME DELAY RESULTS
IN A NEGATIVE FREQUENCY OFFSET 4HE SIGNALS AT THE CORRELATION MIXER OUTPUT ARE THEN
RESOLVED IN THE FREQUENCY DOMAIN BY SPECTRAL ANALYSIS PROCESSING
! TYPICAL IMPLEMENTATION FOR THE SPECTRAL ANALYSIS PROCESSING INCLUDES A SECOND
FREQUENCY CONVERSION FOLLOWING THE #- TO A FINAL INTERMEDIATE FREQUENCY )& ANTI
ALIASING FILTERING DIRECT SAMPLING AT THE FINAL )& USING AN ANALOG TO DIGITAL CONVERTER
!$# DIGITAL DOWN CONVERSION $$# TO A COMPLEX ENVELOPE SEQUENCE TIME DOMAIN
WEIGHTING AND SPECTRAL ANALYSIS USING AN &&4 PADDED WITH ZEROS 0REVIOUS IMPLE
MENTATIONS USED ANALOG PRODUCT DETECTORS TO EXTRACT ) AND 1 BASEBAND SIGNALS WITH
SEPARATE !$#S IN THE ) AND 1 BASEBAND CHANNELS
#ORRELATION -IXER /UTPUT 3IGNAL !NALYSIS 4HE RECEIVED SIGNAL AT THE #- INPUT
PORT FROM A POINT TARGET IS
¤T T³
XIN T ! RECT ¥
COS;P F
¦ 4 ´µ
FD T T
PA T T =
WHERE ! IS THE AMPLITUDE 4 IS THE TRANSMIT PULSEWIDTH F IS THE CARRIER FREQUENCY FD
IS THE DOPPLER FREQUENCY S IS THE SIGNAL TIME DELAY AND @ IS THE ,&- SLOPE FOR THE
TRANSMIT WAVEFORM 4HE REFERENCE WAVEFORM APPLIED TO THE ,/ PORT IS
¤T T2³
X 2 T RECT ¥
COS;P F2 T T 2
¦ 42 ´µ
PA 2 T T 2 =
WHERE 42 IS THE PULSEWIDTH F2 IS THE CARRIER FREQUENCY S2 IS THE REFERENCE WAVEFORM
TIME DELAY AND @2 IS THE ,&- SLOPE FOR THE REFERENCE WAVEFORM @2 a @ n°ÎÎ
05,3% #/-02%33)/. 2!$!2
4HE CORRELATION MIXER ACTS AS A BANDPASS MULTIPLIER WITH OUTPUT XINT X2T 4HE )&
OUTPUT OF THE CORRELATION MIXER IS EVALUATED USING THE IDENTITY
COS X COS Y COSX
Y
COS X
Y
WHERE THE FIRST TERM ON THE RIGHT HAND SIDE OF THE EQUATION CORRESPONDS TO THE UPPER
SIDEBAND AND THE SECOND TO THE LOWER SIDEBAND AT THE MIXER OUTPUT 4HE UPPER SIDEBAND
IS REJECTED BY THE BANDPASS FILTER TO YIELD
¤T T2³
¤T T³
X)& T ! RECT ¥
RECT ¥
¦ 4 ´µ
¦ 42 ´µ
• COS;P F)& T T
P FD T T
PA 2 T 2
T T T
P A A 2 T T F=
WHERE F)& F
SHIFT IS
F2 IS THE )& CARRIER FREQUENCY F F2 IS ASSUMED AND THE CARRIER PHASE
F P F2 T
T2
PA 2 T
T2 4HE )& SIGNAL IS AN ,&- WAVEFORM WITH REDUCED SLOPE @ @2 THE FACTOR THAT MULTI
PLIES THE QUADRATIC TERM IN THE ARGUMENT OF THE COSINE AND A FREQUENCY OFFSET RELATIVE
TO THE )& CARRIER FREQUENCY F)& GIVEN BY
D F FD
A 2 T 2
T
4HE DURATION OF THE REFERENCE WAVEFORM IS REQUIRED TO EXCEED THE TRANSMIT PULSE
WIDTH TO AVOID A LOSS IN 3.2 CAUSED BY TARGET ECHOES THAT ARE NOT CONTAINED WITHIN THE
REFERENCE WAVEFORM
%QUAL 4RANSMIT AND 2EFERENCE 7AVEFORM ,&- 3LOPES &OR THE CASE WHERE THE
TRANSMIT AND REFERENCE WAVEFORM ,&- SLOPES ARE EQUAL @ @ 2 THE )& SIGNAL IS AN
UNCODED PULSE WITH FREQUENCY OFFSET GIVEN BY
D F FD A T 2 T
4HE FREQUENCY OFFSET IS MEASURED USING SPECTRUM ANALYSIS AND CONVERTED TO TARGET
TIME DELAY AND RANGE RELATIVE TO THE REFERENCE WAVEFORM BY
$T T
T2 $R 2 2 DF
A
C
$T
WHERE 2 CS2 IS THE RANGE CORRESPONDING TO THE TIME DELAY OF THE REFERENCE WAVEFORM
+ELLOG DESCRIBES ADDITIONAL CONSIDERATIONS FOR APPLICATION OF TIME DOMAIN
WEIGHTING IN STRETCH PROCESSING AND PROVIDES DETAILS ON COMPENSATION TECHNIQUES FOR
HARDWARE ERRORS 4HE EFFECT OF TIME MISMATCH BETWEEN THE SIGNAL AND THE WEIGHTING
FUNCTION IS ANALYZED BY 4EMES
n°Î{
2!$!2 (!.$"//+
5NEQUAL 4RANSMIT AND 2EFERENCE 7AVEFORM 3LOPES ! STRETCH PROCESSOR WITH
UNEQUAL FREQUENCY SLOPE WAVEFORMS REQUIRES PULSE COMPRESSION OF THE RESIDUAL LINEAR
&- AT THE OUTPUT OF THE CORRELATION MIXER ! LINEAR &- SIGNAL WITH A SLOPE OF @ IN @ 2
OCCURS AT THE TARGET RANGE WHICH IS OFFSET IN FREQUENCY FROM THE )& CARRIER FREQUENCY
BY @ 2S2 S 7ITH THE RANGE DOPPLER COUPLING OF THE ,&- WAVEFORM THE APPARENT
TIME DELAY OF THIS TARGET WILL BE
SAPP @2 S2 S @ @2
4HIS RESULT CAN BE INTERPRETED AS YIELDING A TIME EXPANSION FACTOR OF @ 2@ – @ 2
FOR THE COMPRESSED PULSE !S FOR THE CASE OF EQUAL ,&- SLOPES THE RANGE WINDOW
WIDTH DEPENDS ON THE ACHIEVABLE PROCESSING BANDWIDTH
3TRETCH 0ROCESSING 2ANGE 2ESOLUTION 7IDTH 4HE D" FREQUENCY RESOLUTION WIDTH
FOR SPECTRAL ANALYSIS USING A RECTANGULAR WINDOW OF TIME DURATION EQUAL TO THE TRANSMIT
PULSEWIDTH IS
$F 4
4HE D" TIME DELAY RESOLUTION WIDTH OBTAINED BY STRETCH PROCESSING IS OBTAINED BY
DIVIDING $F BY \@ \ TO CONVERT TO UNITS OF TIME DELAY
T $F
" 4
"
#ONSEQUENTLY THE D" RESOLUTION WIDTH ACHIEVED BY STRETCH PROCESSING IS THE SAME
AS THAT ACHIEVED BY THE MATCHED FILTER FOR THE ,&- WAVEFORM 4HE D" RANGE RESOLU
TION WIDTH IS
$2 C
"
4IME DOMAIN WEIGHTING IS UTILIZED IN THE SPECTRAL ANALYSIS PROCESSING TO REDUCE
THE TIME SIDELOBES OF THE COMPRESSED PULSE AND IMPROVE THE RESOLUTION PERFORMANCE
WHEN MULTIPLE TARGETS ARE PRESENT WITHIN THE RANGE WINDOW !S AN EXAMPLE THE USE OF
(AMMING TIME DOMAIN WEIGHTING REDUCES THE PEAK TIME SIDELOBE LEVEL FROM n D"
TO n D" WITH AN INCREASE IN THE D" FREQUENCY RESOLUTION WIDTH TO $F 4
4HE D" RANGE RESOLUTION WIDTH FOR (AMMING WEIGHTING IS
$2 C
(AMMING 7EIGHTING
"
2ANGE 7INDOW 7IDTH 4HE WIDTH OF THE RANGE WINDOW IS ESTABLISHED BY THE BAND
WIDTH OF THE SPECTRAL ANALYSIS AND THE ,&- SLOPE OF THE TRANSMIT WAVEFORM !SSUME A TIME
WINDOW OF WIDTH $T AND A STRETCH PROCESSING BANDWIDTH "P ! TARGET AT THE EDGE OF THE TIME
WINDOW YIELDS A FREQUENCY OFFSET EQUAL TO ONE HALF OF THE PROCESSING BANDWIDTH
OR
" $T " P
4 $T 4
"P
"P
" " 4
05,3% #/-02%33)/. 2!$!2
n°Îx
4HE RANGE WINDOW WIDTH IS
$R C4 " P C "P
" " 4
3TRETCH 0ULSE #OMPRESSION 2ADAR %XAMPLES 4HIS SECTION DESCRIBES THREE
EXAMPLES OF RADARS THAT EMPLOY STRETCH PULSE COMPRESSION SYSTEMS
,ONG 2ANGE )MAGING 2ADAR 4HE ,ONG 2ANGE )MAGING 2ADAR ,2)2 IS AN
8 BAND RADAR WITH STRETCH PROCESSING BANDWIDTHS OF -(Z AND -(Z 4HE
WIDEBAND WAVEFORM HAS A SWEPT BANDWIDTH OF -(Z TO A PULSEWIDTH OF APPROXI
MATELY §S AND A ,&- SLOPE "4 y -(Z §S -(Z§S 4HE RANGE
WINDOW WIDTH FOR THE -(Z PROCESSING BANDWIDTH IS
$R M MS r -(Z
C "P
M
" 4
-(Z MS
-ILLIMETER 7AVE 2ADAR 4HE STRETCH PROCESSING IMPLEMENTATION FOR THE -ILLIMETER
7AVE RADAR --7 LOCATED AT +WAJALEIN !TOLL IS DESCRIBED BY !BOUZAHARA AND
!VENT 4HE --7 RADAR OPERATES AT A CARRIER FREQUENCY OF '(Z USING WAVEFORMS
WITH A MAXIMUM SWEPT BANDWIDTH OF -(Z AND PULSEWIDTH OF §S 4HE ,&SLOPE FOR THE TRANSMIT WAVEFORM IS
A
" -(Z
-(ZMS
4
MS
4HE STRETCH PROCESSING BANDWIDTH IS "P -(Z 4HE WIDTH OF THE STRETCH PROCESSING
TIME WINDOW IS
$T -(Z
MS
-(Z MS
4HE REFERENCE WAVEFORM PULSEWIDTH IS 42 §S TO AVOID A LOSS IN 3.2
FOR TARGETS AT THE EDGES OF THE RANGE WINDOW 4HE SWEPT BANDWIDTH OF THE REFERENCE
WAVEFORM AND THE RANGE WINDOW WIDTH ARE
"2 -(ZMS r MS -(Z
C
$R $T M MS r MS M
4HE D" RANGE RESOLUTION WIDTH WITH (AMMING WEIGHTING APPLIED OVER THE §S
PULSEWIDTH IN THE SPECTRAL ANALYSIS PROCESSING IS
$2 C
M MS
M
"
-(Z
#OBRA $ANE 7IDEBAND 0ULSE #OMPRESSION 3YSTEM 4HE CHARACTERISTICS OF THE
WIDEBAND PULSE COMPRESSION SYSTEM DEVELOPED FOR THE #OBRA $ANE RADAR ARE SUM
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2EFERENCE ,&- BANDWIDTH
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2EFERENCE WAVEFORM SWEPT BANDWIDTH "REF
4RANSMIT PULSEWIDTH 4
2EFERENCE PULSEWIDTH 4REF
4RANSMIT WAVEFORM ,&- SLOPE
#OMPRESSED PULSEWIDTH n D" S
4IME BANDWIDTH PRODUCT 4"
4IME SIDELOBE LEVEL
4ARGET RANGE WINDOW
.UMBER OF RANGE SAMPLES
2ANGE SAMPLE SPACING
&IRST )& AT OUTPUT OF CORRELATION MIXER
3ECOND )&
3TRETCH PROCESSING BANDWIDTH "P
!$ CONVERTER SAMPLING FREQUENCY
TO -(Z
TO -(Z
-(Z
-(Z
§S
§S
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FT
n D"
FT
FT
-(Z
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K(Z
-(Z IN ) AND 1 BASEBAND CHANNELS
%XCLUDES PULSEWIDTH AND SWEPT BANDWIDTH EXTENSION DUE TO FT RANGE WINDOW
**
8
3IGNAL !NALYSIS 3UMMARYn 4ABLE IS A SUMMARY OF SIGNAL ANALYSIS DEFI
NITIONS AND RELATIONSHIPS 4ABLE SHOWS 7OODWARDS &OURIER TRANSFORM RULES AND
PAIRS 4HESE RELATIONSHIPS SIMPLIFY THE APPLICATION OF SIGNAL ANALYSIS TECHNIQUES )N
MOST CASES IT WILL NOT BE NECESSARY TO EXPLICITLY PERFORM AN INTEGRATION TO EVALUATE THE
&OURIER TRANSFORM OR INVERSE &OURIER TRANSFORM
4!",% 3IGNAL !NALYSIS $EFINITIONS AND 2ELATIONSHIPS
&OURIER TRANSFORM SPECTRUM OF
SIGNAL XT
c
8 F ¯ XT E J P FT DT
c
)NVERSE &OURIER TRANSFORM OF
SPECTRUM 8 F
c
XT ¯ 8 F E J P FT DF
c
#ONVOLUTION OF SIGNALS XT AND YT
Y T X T
HT
c
c
¯ XT HT T DT ¯ XT T HT DT
c
&ILTER FREQUENCY RESPONSE
%ULERS IDENTITY
c
( F 9 F 8 F
E JQ COS Q
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#OSINE AND SINE FUNCTIONS EXPRESSED
IN TERMS OF COMPLEX EXPONENTIALS
0ARSEVALS THEOREM
SUPERSCRIPT ASTERISK INDICATES
COMPLEX CONJUGATE
COS Q E JQ
E JQ SIN Q E JQ
E JQ
c
J
c
¯ XT Y T DT ¯ 8 F 9 F DF
c
c
c
c
¯ \ XT \ DT ¯ \ 8 F \ DF
c
c
RECT FUNCTION
ª­ \ T \ RECTT «
­¬ \ T \ SINC FUNCTION
SINC F SINP F P F
2EPETITION OPERATOR
c
REP4 ; XT = £ XT N4
N c
#OMB OPERATOR
c
COMB & ; 8 F = £ 8 N& D F
N&
N c
3AMPLING PROPERTY OF DELTA FUNCTION
c
¯ XT D T T DT XT
c
#AUCHY 3CHWARZ INEQUALITY
c
c
c
¯ F X G X DX a ¯ \ F X \ DX ¯ \ G X \ DX
c
c
c
WITH EQUALITY IF AND ONLY IF F X KG X
2ADAR 4RANSMIT 7AVEFORMS n 4HE TRANSMITTED WAVEFORMS USED IN RADAR
ARE BANDPASS SIGNALS THAT CAN BE EXPRESSED IN THE FORM
XT AT COS;P FT F T =
WHERE AT IS THE AMPLITUDE MODULATION 6 ET IS THE PHASE MODULATION RAD AND
F IS THE CARRIER FREQUENCY (Z 4HE AMPLITUDE AND PHASE MODULATION FUNCTIONS VARY
SLOWLY COMPARED TO THE PERIOD OF THE CARRIER F #ONSEQUENTLY XT IS A NARROWBAND
WAVEFORM WITH A BANDWIDTH THAT IS SMALL COMPARED TO THE CARRIER FREQUENCY
#OMPLEX %NVELOPE
4HE COMPLEX ENVELOPE OF XT IS GIVEN BY
UT AT E JF T
A
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#OMMENTS
&OURIER TRANSFORM PAIR
,INEARITY
3IGNAL TIME REVERSAL
#ONJUGATE OF SIGNAL
4IME DOMAIN DIFFERENTIATION
&REQUENCY DOMAIN DIFFERENTIATION
3IGNAL TIME SHIFT
3IGNAL FREQUENCY SHIFT
4IME SCALING
4IME DOMAIN CONVOLUTION
4IME DOMAIN MULTIPLICATION
8 F 9 F
\ 4 \ COMB 4 ; 8 F = 7OODWARDS REPETITION OPERATOR
COMB4 ; XT =
\ 4 \ REP 4 ; 8 F =
7OODWARDS COMB OPERATOR
8T
C T
RECTT
SINCT
EXPnPT
XnF
C F
SINC F
RECT F
EXPnP F
4IME FREQUENCY INTERCHANGE DUALITY
$ELTA FUNCTION IN TIME
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'AUSSIAN TIME FUNCTION
3IGNAL
XT
!XT "UT
X T
X T
DXDT
JPTXT
XT S
XT EXPJPFT
XT4
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3PECTRUM
8 F
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"5 F
8 F
8 F
JPF8 F
D8DF
8 F EXP JPFS
8 F F
\4\8 F4
8 F 9 F
Y T
4HE BANDPASS SIGNAL IS EXPRESSED IN TERMS OF THE COMPLEX ENVELOPE BY
B
UT 2E; XT E J P FT =
#OMPLEX %NVELOPE 2EPRESENTATION OF 2ADAR %CHOES 4HE RADAR ECHO SIGNAL
FROM A POINT TARGET IS
SR T !R AT
TD COS;P F
FD T
TD
F T
TD =
WHERE !R IS A DIMENSIONLESS AMPLITUDE SCALE FACTOR TD IS THE TARGET TIME DELAY S FD IS
THE TARGET DOPPLER SHIFT (Z AT IS THE AMPLITUDE MODULATION 6 E T IS THE PHASE
MODULATION RAD AND F IS THE TRANSMIT CARRIER FREQUENCY (Z 4HE COMPLEX ENVELOPE
OF SRT IS
UR T !R E J P FTD UT
T D E J P FD T T D
4HE TERM UT n TD IS THE COMPLEX ENVELOPE OF THE TRANSMIT WAVEFORM DELAYED IN TIME
BY TD 4HE COMPLEX EXPONENTIAL EXP;JO FDT n TD = REPRESENTS A LINEAR PHASE MODULATION
VERSUS TIME THAT IS IMPRESSED ON THE RECEIVED ECHO SIGNAL BY THE DOPPLER SHIFT FD 4HE
CARRIER PHASE SHIFT IS PC nO FTD
4HE TIME DELAY AND DOPPLER SHIFT ARE EXPRESSED IN TERMS OF TARGET RANGE AND RANGE
RATE BY TD 2C S AND FD nK 6R (Z WHERE 2 IS THE TARGET RANGE M 6R D2DT
05,3% #/-02%33)/. 2!$!2
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IS THE RANGE RATE NEGATIVE FOR AN INCOMING TARGET C IS THE SPEED OF LIGHT AND K CF
M IS THE CARRIER WAVELENGTH
-ATCHED &ILTERS ! MATCHED FILTER ACHIEVES MAXIMUM OUTPUT SIGNAL TO NOISE
RATIO FOR A SIGNAL RECEIVED IN WHITE NOISE 4HE MATCHED FILTER FREQUENCY RESPONSE FOR
A SIGNAL UT IS
( MF F K5 F E J P FT
WHERE K IS AN ARBITRARY COMPLEX CONSTANT AND 5 F IS THE SPECTRUM OF UT 4HE TIME
DELAY T IS REQUIRED TO EXCEED THE DURATION OF UT TO ACHIEVE A CAUSAL IMPULSE RESPONSE
THAT IS ZERO FOR NEGATIVE TIME 4HE MATCHED FILTER IMPULSE RESPONSE IS
HMF T KU T
T
4HE PEAK SIGNAL TO NOISE TO MEAN NOISE POWER RATIO AT THE OUTPUT OF A FILTER WITH
FREQUENCY RESPONSE ( F IS DEFINED AS
3 . O !
S NO
WHERE !O IS THE MATCHED FILTER OUTPUT SIGNAL AMPLITUDE AT THE PEAK OF THE SIGNAL AND R NO
IS THE MATCHED FILTER OUTPUT NOISE POWER 4HE MATCHED FILTER OUTPUT 3.2 IS GIVEN BY
%
3 . MF .
WHERE % IS THE ENERGY OF THE RECEIVED BANDPASS SIGNAL AT THE MATCHED FILTER INPUT *
AND . IS THE ONE SIDED NOISE POWER SPECTRUM AT THE MATCHED FILTER INPUT 7(Z &ILTER -ATCHING ,OSS &ILTER MATCHING LOSS ,M IS THE LOSS IN 3.2 THAT RESULTS WHEN
A SIGNAL IS NOT PROCESSED USING A MATCHED FILTER 4HE FILTER MATCHING LOSS IS DEFINED AS
,M 3 . MF
3 . O
WHERE 3. O IS THE 3.2 AT THE OUTPUT OF A FILTER WITH FREQUENCY RESPONSE ( F AND
3. MF IS THE MATCHED FILTER 3.2 4HE FILTER MATCHING LOSS CAN ALSO BE EXPRESSED AS
,M % . 3 . O
WHERE THE MATCHED FILTER 3.2 IS GIVEN BY 3. MF %. 4HE FILTER MATCHING LOSS IS
q WHERE ,M FOR THE MATCHED FILTER 4HE FILTER MATCHING LOSS EXPRESSED IN DECIBELS
IS ,MD" LOG,M AND EQUALS D" FOR THE MATCHED FILTER
!N ALTERNATE DEFINITION OF SIGNAL TO NOISE RATIO IS ALSO USED IN THE LITERATURE IN WHICH THE SIGNAL POWER AT THE PEAK OF
THE WAVEFORM IS AVERAGED OVER ONE CYCLE OF THE CARRIER )N THIS CASE THE AVERAGE SIGNAL POWER IS ONE HALF OF THE
PEAK SIGNAL POWER AND THE MATCHED FILTER OUTPUT 3.2 IS %.
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!MBIGUITY &UNCTIONS n 4HE AUTOCORRELATIONo FUNCTION FOR A TRANSMIT
WAVEFORM WITH COMPLEX ENVELOPE UT IS DEFINED AS
c
C U T FD ¯ UT U T T E J P FD T DT
c
WHERE S IS THE RELATIVE TIME DELAY AND FD IS DOPPLER SHIFT 4HE RELATIVE TIME DELAY IS
POSITIVE FOR A TARGET FURTHER IN RANGE THAN A REFERENCE TARGET AND DOPPLER FREQUENCY IS
POSITIVE FOR AN INCOMING TARGET NEGATIVE RANGE RATE 4HE COMPLEX ENVELOPE UT
IS NORMALIZED TO UNIT ENERGY
c
¯ \ UT \ DT c
4HE AMBIGUITY FUNCTION OF UT IS DEFINED AS THE SQUARE MAGNITUDE OF THE AUTOCORRELATION
FUNCTION
9U T FD \ C U T FD \
4HE AMBIGUITY FUNCTION IS INTERPRETED AS A SURFACE ABOVE THE DELAY DOPPLER S n FD
PLANE 4HE MAXIMUM VALUE OF THE AMBIGUITY FUNCTION IS UNITY AT THE ORIGIN S FD 9 U T FD a 9 U 4HE VOLUME UNDER THE AMBIGUITY SURFACE IS UNITY FOR ANY WAVEFORM UT c
c
¯ ¯ 9 U T FD DT DFD c
c
)N THE GENERAL CASE WHERE THE ENERGY OF THE COMPLEX ENVELOPE IS NOT NORMALIZED
TO UNITY THE VALUE OF THE AMBIGUITY FUNCTION AT THE ORIGIN IS EQUAL TO % WHERE %
IS THE ENERGY OF THE BANDPASS SIGNAL CORRESPONDING TO UT AND THE VOLUME UNDER THE
AMBIGUITY FUNCTION IS ALSO EQUAL TO % 4HE NORMALIZATION CONDITION IS EQUIVALENT TO
THE ASSUMPTION THAT THE ENERGY OF THE BANDPASS TRANSMIT WAVEFORM EQUALS *
-ATCHED &ILTER 4IME 2ESPONSE 4HE MATCHED FILTER TIME RESPONSE TO A TARGET
WITH DOPPLER SHIFT FD CAN BE EXPRESSED IN TERMS OF THE AUTOCORRELATION FUNCTION 4HE
MATCHED FILTER IMPULSE RESPONSE WITH K AND T IS
HMF T U T
4HE MATCHED FILTER INPUT SIGNAL IS ASSUMED TO HAVE ZERO TIME DELAY AND A DOPPLER
SHIFT FD
ST UT E J P FD T
o 4HE TERMINOLOGY FOR THIS FUNCTION IS NOT STANDARDIZED IN THE LITERATURE 7OODWARD USES THE TERM CORRELATION FUNC
TION 4HE TERM TIME FREQUENCY AUTOCORRELATION FUNCTION IS USED BY 3PAFFORD 4HE SIGNS ASSOCIATED WITH S AND FD
WITHIN THE INTEGRAND ALSO DIFFER IN THE LITERATURE 4HE STANDARDIZED DEFINITION PROPOSED BY 3INSKY AND 7ANG IS
USED IN THIS CHAPTER
05,3% #/-02%33)/. 2!$!2
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4HE MATCHED FILTER OUTPUT SIGNAL YT IS FOUND BY CONVOLUTION OF ST WITH THE
MATCHED FILTER IMPULSE RESPONSE HMFT c
YT ¯ UT ` U T `
T E J P FD T ` DT `
c
#OMPARISON OF THIS RESULT WITH THE DEFINITION OF THE AUTOCORRELATION FUNCTION SHOWS
THAT THE MATCHED FILTER RESPONSE CAN BE EXPRESSED AS
YT 8U T FD
!S A RESULT THE MATCHED FILTER TIME RESPONSE FOR A TARGET WITH DOPPLER FREQUENCY FD
IS A TIME REVERSED VERSION OF THE AUTOCORRELATION FUNCTION
#ONDITIONS FOR 4ARGET 2ESOLUTION IN 4IME $ELAY AND $OPPLER &REQUENCY !SSUME THAT TWO TARGETS WITH EQUAL RADAR CROSS SECTIONS ARE PRESENT AT THE SAME ANGULAR
POSITION 4HE FIRST TARGET TERMED THE REFERENCE TARGET IS LOCATED AT THE ORIGIN OF THE
DELAY DOPPLER PLANE WITH ZERO RELATIVE TIME DELAY AND ZERO DOPPLER FREQUENCY AND THE
SECOND TARGET IS AT RELATIVE TIME DELAY S AND DOPPLER FREQUENCY FD 4HE RELATIVE TIME DELAY
IS POSITIVE WHEN THE SECOND TARGET IS FARTHER IN RANGE THAN THE REFERENCE TARGET AND THE
DOPPLER FREQUENCY IS POSITIVE FOR AN INCOMING TARGET 4HE MATCHED FILTER OUTPUT POWER
FOR THE REFERENCE TARGET IS PROPORTIONAL TO THE AMBIGUITY FUNCTION AND IS GIVEN BY
0REF 9U 4HE MATCHED FILTER OUTPUT POWER FOR THE SECOND TARGET EVALUATED AT THE PEAK OF THE
REFERENCE TARGET IS
0 9U S FD
4HE SECOND TARGET IS UNRESOLVED FROM THE REFERENCE TARGET AT LOCATIONS IN THE DELAY
DOPPLER PLANE WHERE 9US FD y , ,
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4YPICAL TRACKING RADARS HAVE A PENCIL BEAM TO RECEIVE ECHOES FROM A SINGLE TARGET AND
TRACK THE TARGET IN ANGLE RANGE ANDOR DOPPLER )TS RESOLUTION CELLˆDEFINED BY ITS
ANTENNA BEAMWIDTH TRANSMITTER PULSE LENGTH EFFECTIVE PULSE LENGTH MAY BE SHORTER
WITH PULSE COMPRESSION ANDOR DOPPLER BANDWIDTHˆIS USUALLY SMALL COMPARED WITH
THAT OF A SEARCH RADAR AND IS USED TO EXCLUDE UNDESIRED ECHOES OR SIGNALS FROM OTHER
TARGETS CLUTTER AND COUNTERMEASURES %LECTRONIC BEAM SCANNING PHASED ARRAY RADARS
MAY TRACK MULTIPLE TARGETS BY SEQUENTIALLY DWELLING UPON AND MEASURING EACH TARGET
WHILE EXCLUDING OTHER ECHO OR SIGNAL SOURCES
"ECAUSE OF ITS NARROW BEAMWIDTH TYPICALLY FROM A FRACTION OF n TO OR n TRACKING
RADARS USUALLY DEPEND UPON INFORMATION FROM A SURVEILLANCE RADAR OR OTHER SOURCE OF
TARGET LOCATION TO ACQUIRE THE TARGET IE TO PLACE ITS BEAM ON OR IN THE VICINITY OF THE
TARGET BEFORE INITIATING A TRACK 3CANNING OF THE BEAM WITHIN A LIMITED ANGLE SECTOR MAY
BE NEEDED TO ACQUIRE THE TARGET WITHIN ITS BEAM AND CENTER THE RANGE TRACKING GATES ON
THE ECHO PULSE PRIOR TO LOCKING ON THE TARGET OR CLOSING THE TRACKING LOOPS 4HE GATE ACTS
LIKE A FAST ACTING ON OFF SWITCH THAT TURNS THE RECEIVER hONv AT THE LEADING EDGE OF THE
TARGET ECHO PULSE AND hOFFv AT THE END OF THE TARGET ECHO PULSE TO ELIMINATE UNDESIRED
ECHOES 4HE RANGE TRACKING SYSTEM PERFORMS THE TASK OF KEEPING THE GATE CENTERED ON
THE TARGET ECHO AS DESCRIBED IN 3ECTION 4HE PRIMARY OUTPUT OF TRACKING RADAR IS THE TARGET LOCATION DETERMINED FROM THE
POINTING ANGLES OF THE BEAM AND POSITION OF ITS RANGE TRACKING GATES 4HE ANGLE LOCA
TION IS THE DATA OBTAINED FROM SYNCHROS AND ENCODERS ON THE ANTENNA TRACKING AXES
OR DATA FROM A BEAM POSITIONING COMPUTER ON AN ELECTRONIC SCAN PHASED ARRAY RADAR )N SOME CASES TRACKING LAG IS MEASURED BY CONVERTING TRACKING LAG ERROR VOLTAGES FROM
THE TRACKING LOOPS TO UNITS OF ANGLE 4HIS DATA IS USED TO ADD TO OR SUBTRACT FROM THE
ANGLE SHAFT POSITION DATA FOR REAL TIME CORRECTION OF TRACKING LAG
4HERE ARE A LARGE VARIETY OF TRACKING RADAR SYSTEMS INCLUDING SOME THAT ACHIEVE
SIMULTANEOUSLY BOTH SURVEILLANCE AND TRACKING FUNCTIONS ! WIDELY USED TYPE OF
TRACKING RADAR AND THE ONE DISCUSSED IN DETAIL IN THIS CHAPTER IS A GROUND BASED SYS
TEM CONSISTING OF A PENCIL BEAM ANTENNA MOUNTED ON A ROTATABLE PLATFORM WITH SERVO
MOTOR DRIVE OF ITS AZIMUTH AND ELEVATION POSITION TO FOLLOW A TARGET &IGURE A %RRORS IN POINTING DIRECTION ARE DETERMINED BY SENSING THE ANGLE OF ARRIVAL OF THE
ECHO WAVEFRONT AND CORRECTED BY POSITIONING THE ANTENNA TO KEEP THE TARGET CENTERED
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IN THE BEAM -ODERN REQUIREMENTS FOR SIMULTANEOUS PRECISION TRACKING OF MULTIPLE
TARGETS HAS DRIVEN THE DEVELOPMENT OF THE ELECTRONIC SCAN ARRAY MONOPULSE RADAR
WITH THE CAPABILITY TO SWITCH ITS BEAM PULSE TO PULSE AMONG MULTIPLE TARGETS 4HE
!.-03 SHOWN IN &IGURE B IS AN EXAMPLE OF A HIGHLY VERSATILE ELECTRONIC SCAN
MONOPULSE MISSILE RANGE INSTRUMENTATION RADAR
4HE PRINCIPAL APPLICATIONS OF PRECISION TRACKING RADAR ARE WEAPON CONTROL AND
MISSILE RANGE INSTRUMENTATION )N BOTH APPLICATIONS A HIGH DEGREE OF PRECISION AND AN
ACCURATE PREDICTION OF FUTURE POSITION OF THE TARGET ARE GENERALLY REQUIRED 4HE EARLIEST
USE OF TRACKING RADAR WAS GUNFIRE CONTROL 4HE AZIMUTH ANGLE ELEVATION ANGLE AND THE
RANGE TO THE TARGET WERE MEASURED AND FROM THE RATE OF CHANGE OF THESE PARAMETERS THE
VELOCITY VECTOR OF THE TARGET SPEED AND DIRECTION WAS COMPUTED AND ITS FUTURE POSITION
PREDICTED 4HIS INFORMATION WAS USED TO MOVE THE GUN TO LEAD THE TARGET AND SET THE FUZE
DELAY 4HE TRACKING RADAR PERFORMS A SIMILAR ROLE IN PROVIDING GUIDANCE INFORMATION
AND STEERING COMMANDS FOR MISSILE CONTROL
)N MISSILE RANGE INSTRUMENTATION THE TRACKING RADAR OUTPUT IS USED TO MEASURE THE
TRAJECTORY OF THE MISSILE AND TO PREDICT FUTURE POSITION 4RACKING RADARS ARE USED TO COM
PUTE THE IMPACT POINT OF A LAUNCHED MISSILE CONTINUOUSLY DURING THE LAUNCH PHASE IN CASE
OF MISSILE FAILURE FOR RANGE SAFETY )F THE IMPACT POINT APPROACHES A POPULATED OR OTHER
CRITICAL AREA THE MISSILE IS DESTROYED -ISSILE RANGE INSTRUMENTATION RADARS ARE NORMALLY
USED WITH A BEACON PULSE REPEATER TO PROVIDE A POINT SOURCE ECHOˆUSUALLY ITS PULSE
IS DELAYED TO SEPARATE IT FROM THE TARGET ECHOˆAND WITH HIGH SIGNAL TO NOISE RATIO TO
ACHIEVE PRECISION TRACKING ON THE ORDER OF MIL IN ANGLE AND M IN RANGE
A
B
&)'52% A !.&01 # BAND MONOPULSE PRECISION TRACKING RADAR INSTALLATION AT THE .!3!
7ALLOPS )SLAND 3TATION 6! )T HAS A FT DIAMETER DISH AND A SPECIFIED TRACKING PRECISION OF MRAD RMS
B !.-03 # BAND ELECTRONIC SCAN PHASED ARRAY -ULTI /BJECT 4RACKING 2ADAR -/42 INSTALLED AT
THE 7HITE 3ANDS -ISSILE 2ANGE 0HOTO OF THE !.-03 COURTESY OF THE 7HITE 3ANDS -ISSILE 2ANGE AND
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4HIS CHAPTER DESCRIBES THE MONOPULSE SIMULTANEOUS LOBING WITH EITHER PHASE COM
PARISON OR AMPLITUDE COMPARISON CONICAL SCAN AND SEQUENTIAL LOBING TRACKING RADAR
TECHNIQUES WITH THE MAIN EMPHASIS ON THE AMPLITUDE COMPARISON MONOPULSE SIMUL
TANEOUS LOBING RADAR
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4HE SUSCEPTIBILITY OF CONICAL SCANNING AND SEQUENTIAL LOBING TRACKING TECHNIQUES TO
ECHO AMPLITUDE FLUCTUATIONS AND AMPLITUDE JAMMING AS DESCRIBED IN 3ECTION WAS THE MAJOR REASON FOR THE DEVELOPMENT OF TRACKING RADAR THAT PROVIDES SIMULTANE
OUSLY ALL THE NECESSARY LOBES FOR ANGLE ERROR SENSING 4HIS REQUIRED THAT THE OUTPUT
FROM THE LOBES BE COMPARED SIMULTANEOUSLY ON A SINGLE PULSE ELIMINATING THE EFFECTS
OF ECHO AMPLITUDE CHANGE WITH TIME 4HE TECHNIQUE TO ACCOMPLISH THIS WAS INITIALLY
CALLED SIMULTANEOUS LOBING WHICH WAS DESCRIPTIVE OF THE TECHNIQUE ,ATER THE TERM
MONOPULSE WAS COINED REFERRING TO THE ABILITY TO OBTAIN ANGLE ERROR INFORMATION ON
A SINGLE PULSE )T HAS BECOME THE COMMONLY USED NAME FOR THIS TRACKING TECHNIQUE
EVEN THOUGH THE LOBES ARE GENERATED SIMULTANEOUSLY AND MONOPULSE TRACKING CAN BE
PERFORMED WITH #7 RADAR
4HE ORIGINAL MONOPULSE TRACKING RADARS SUFFERED IN ANTENNA EFFICIENCY AND COM
PLEXITY OF MICROWAVE CIRCUITRY BECAUSE WAVEGUIDE SIGNAL COMBINING CIRCUITRY WAS A
RELATIVELY NEW ART 4HESE PROBLEMS WERE OVERCOME AND MONOPULSE RADAR WITH MOD
ERN COMPACT OFF THE SHELF PROCESSING CIRCUITRY CAN READILY OUTPERFORM SCANNING AND
LOBING SYSTEMS 4HE MONOPULSE TECHNIQUE ALSO HAS AN INHERENT CAPABILITY FOR HIGH
PRECISION ANGLE MEASUREMENT BECAUSE ITS FEED STRUCTURE IS COMPACT WITH SHORT SIGNAL
PATHS AND RIGIDLY MOUNTED WITH NO MOVING PARTS 4HIS HAS MADE POSSIBLE THE DEVEL
OPMENT OF PENCIL BEAM TRACKING RADARS THAT MEET MISSILE RANGE INSTRUMENTATION RADAR
REQUIREMENTS OF n ANGLE TRACKING PRECISION
4HIS CHAPTER IS DEVOTED TO TRACKING RADAR BUT MONOPULSE TECHNIQUES ARE USED IN
OTHER SYSTEMS INCLUDING HOMING DEVICES DIRECTION FINDERS AND SOME SEARCH RADARS
(OWEVER MOST OF THE BASIC PRINCIPLES AND LIMITATIONS OF MONOPULSE APPLY FOR ALL APPLI
CATIONS -ORE GENERAL COVERAGE IS FOUND IN 3HERMAN AND ,EONOV AND &ORMICHEV
!MPLITUDE #OMPARISON -ONOPULSE ! METHOD FOR VISUALIZING THE OPERATION OF
AN AMPLITUDE COMPARISON RECEIVER IS TO CONSIDER THE ECHO SIGNAL AT THE FOCAL PLANE OF
AN ANTENNA 4HE ECHO IS FOCUSED TO A FINITE SIZE hSPOTv 4HE hSPOTv IS CENTERED ON THE
FOCAL PLANE WHEN THE TARGET IS ON THE ANTENNA AXIS AND MOVES OFF CENTER WHEN THE TAR
GET MOVES OFF AXIS 4HE ANTENNA FEED IS LOCATED AT THE FOCAL POINT TO RECEIVE MAXIMUM
ENERGY FROM A TARGET ON AXIS
4HE AMPLITUDE COMPARISON FEED IS DESIGNED TO SENSE ANY FEED PLANE DISPLACEMENT
OF THE SPOT FROM THE CENTER OF THE FOCAL PLANE ! MONOPULSE FEED USING THE FOUR HORN
SQUARE FOR EXAMPLE WOULD BE CENTERED AT THE FOCAL PLANE )T PROVIDES SYMMETRY
SO THAT WHEN THE SPOT IS CENTERED EQUAL ENERGY FALLS ON EACH OF THE FOUR HORNS 4HE
RADAR SENSES TARGET DISPLACEMENT FROM THE ANTENNA AXIS THAT SHIFTS THE SPOT OFF OF THE
CENTER OF THE FOCAL PLANE BY MEASURING THE RESULTANT UNBALANCE OF ENERGY RECEIVED
IN THE FOUR HORNS 4HIS IS ACCOMPLISHED BY USE OF MICROWAVE WAVEGUIDE HYBRIDS TO
SUBTRACT OUTPUTS OF PAIRS OF HORNS PROVIDING A SENSITIVE DEVICE THAT GIVES SIGNAL OUT
PUT WHEN THERE IS AN UNBALANCE CAUSED BY THE TARGET BEING OFF AXIS 4HE 2& CIRCUITRY
FOR A CONVENTIONAL FOUR HORN SQUARE FEED SEE &IGURE SUBTRACTS THE OUTPUT OF
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&)'52% -ICROWAVE COMPARATOR CIRCUITRY USED WITH A FOUR HORN
MONOPULSE FEED
THE LEFT PAIR FROM THE OUTPUT OF THE RIGHT PAIR TO SENSE ANY UNBALANCE IN THE AZIMUTH
DIRECTION )T ALSO SUBTRACTS THE OUTPUT OF THE TOP PAIR FROM THE OUTPUT OF THE BOTTOM
PAIR TO SENSE ANY UNBALANCE IN THE ELEVATION DIRECTION )N ADDITION THE CIRCUITRY ADDS
THE OUTPUT OF ALL FOUR HORNS FOR A SUM SIGNAL FOR DETECTION MONOPULSE PROCESSING
AND RANGE TRACKING
4HE COMPARATOR SHOWN IN &IGURE IS THE CIRCUITRY THAT PERFORMS THE ADDITION AND
SUBTRACTION OF THE FEED HORN OUTPUTS TO OBTAIN MONOPULSE SUM AND DIFFERENCE SIGNALS )T
IS ILLUSTRATED WITH HYBRID 4 OR MAGIC 4 WAVEGUIDE COMPONENTS 4HESE ARE FOUR PORT
DEVICES THAT IN BASIC FORM HAVE THE INPUTS AND OUTPUTS LOCATED AT RIGHT ANGLES TO EACH
OTHER (OWEVER THE MAGIC 4S HAVE BEEN DEVELOPED IN CONVENIENT hFOLDEDv CONFIGU
RATIONS FOR A VERY COMPACT COMPARATOR 4HE PERFORMANCE OF THESE AND OTHER SIMILAR
FOUR PORT DEVICES IS DESCRIBED IN #HAPTER OF 3HERMAN
4HE SUBTRACTOR OUTPUTS ARE CALLED DIFFERENCE SIGNALS WHICH ARE ZERO WHEN THE TARGET
IS ON AXIS INCREASING IN AMPLITUDE WITH INCREASING DISPLACEMENT OF THE TARGET FROM THE
ANTENNA AXIS 4HE DIFFERENCE SIGNALS ALSO CHANGE n IN PHASE FROM ONE SIDE OF CENTER
TO THE OTHER 4HE SUM OF ALL FOUR HORN OUTPUTS PROVIDES A REFERENCE SIGNAL TO CONTROL
ANGLE TRACKING SENSITIVITY VOLTS PER DEGREE OF ERROR TO REMAIN CONSTANT EVEN THOUGH
THE TARGET ECHO SIGNAL MAY VARY OVER A LARGE DYNAMIC RANGE 4HIS IS ACCOMPLISHED BY
AUTOMATIC GAIN CONTROL !'# TO KEEP THE SUM SIGNAL OUTPUT AND ANGLE TRACKING LOOP
GAINS CONSTANT FOR STABLE AUTOMATIC ANGLE TRACKING
&IGURE IS A BLOCK DIAGRAM OF TYPICAL MONOPULSE RADARS 4HE SUM SIGNAL ELEVA
TION DIFFERENCE SIGNAL AND AZIMUTH DIFFERENCE SIGNAL ARE EACH CONVERTED TO INTERMEDI
ATE FREQUENCY )& USING A COMMON LOCAL OSCILLATOR TO MAINTAIN RELATIVE PHASE AT )&
4HE )& SUM SIGNAL OUTPUT IS DETECTED AND PROVIDES THE VIDEO INPUT TO THE RANGE TRACKER
4HE RANGE TRACKER MEASURES AND TRACKS THE TIME OF ARRIVAL OF THE DESIRED TARGET ECHO
AND PROVIDES GATE PULSES THAT TURN ON THE RADAR RECEIVER CHANNELS ONLY DURING THE BRIEF
PERIOD WHEN THE DESIRED ECHO IS EXPECTED 4HE GATED VIDEO IS USED TO GENERATE THE DC
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&)'52% "LOCK DIAGRAM OF A CONVENTIONAL MONOPULSE TRACKING RADAR
VOLTAGE PROPORTIONAL TO THE MAGNITUDE OF THE 3 SIGNAL OR ¨3 ¨FOR THE !'# OF ALL THREE )&
AMPLIFIER CHANNELS 4HE !'# MAINTAINS CONSTANT ANGLE TRACKING SENSITIVITY VOLTS PER
DEGREE ERROR EVEN THOUGH THE TARGET ECHO SIGNAL VARIES OVER A LARGE DYNAMIC RANGE BY
CONTROLLING GAIN OR DIVIDING BY ¨3 ¨ !'# IS NECESSARY TO KEEP THE GAIN OF THE ANGLE
TRACKING LOOPS CONSTANT FOR STABLE AUTOMATIC ANGLE TRACKING 3OME MONOPULSE SYSTEMS
SUCH AS THE TWO CHANNEL MONOPULSE CAN PROVIDE INSTANTANEOUS !'# OR NORMALIZING
BY USE OF LOG DETECTORS AS DESCRIBED LATER IN THIS SECTION
4HE SUM SIGNAL AT THE )& OUTPUT ALSO PROVIDES A REFERENCE SIGNAL TO PHASE DETECTORS
THAT DERIVE ANGLE TRACKING ERROR VOLTAGES FROM THE DIFFERENCE SIGNALS 4HE PHASE DETEC
TORS ARE ESSENTIALLY DOT PRODUCT DEVICES PRODUCING THE OUTPUT VOLTAGE
E
\3\ \$\
COS Q
\ 3 \ \ $\
OR
E
$
COS Q
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WHERE E ANGLE ERROR DETECTOR OUTPUT VOLTAGE
¨3 ¨ MAGNITUDE OF SUM SIGNAL
¨$ ¨ MAGNITUDE OF DIFFERENCE SIGNAL
P PHASE ANGLE BETWEEN SUM AND DIFFERENCE SIGNALS
4HE DOT PRODUCT ERROR DETECTOR IS ONLY ONE OF A WIDE VARIETY OF MONOPULSE ANGLE ERROR
DETECTORS DESCRIBED IN #HAPTER OF 3HERMAN
.ORMALLY P IS EITHER n OR n WHEN THE RADAR IS PROPERLY ADJUSTED AND THE ONLY
PURPOSE OF THE PHASE SENSITIVE CHARACTERISTIC IS TO PROVIDE A PLUS OR MINUS POLARITY COR
RESPONDING TO P n AND P n RESPECTIVELY GIVING A OR n POLARITY TO THE ANGLE
ERROR DETECTOR OUTPUT TO INDICATE TO THE SERVO WHICH DIRECTION TO DRIVE THE PEDESTAL
)N A PULSED TRACKING RADAR THE ANGLE ERROR DETECTOR OUTPUT IS BIPOLAR VIDEO THAT
IS IT IS A VIDEO PULSE WITH AN AMPLITUDE PROPORTIONAL TO THE ANGLE ERROR AND WHOSE
POLARITY POSITIVE OR NEGATIVE CORRESPONDS TO THE DIRECTION OF THE ERROR 4HIS VIDEO
IS TYPICALLY PROCESSED BY A SAMPLE AND HOLD CIRCUIT THAT CHARGES A CAPACITOR TO THE
PEAK VIDEO PULSE VOLTAGE AND HOLDS THE CHARGE UNTIL THE NEXT PULSE AT WHICH TIME THE
CAPACITOR IS DISCHARGED AND RECHARGED TO THE NEW PULSE LEVEL 7ITH MODERATE LOW PASS
FILTERING THIS GIVES THE DC ERROR VOLTAGE OUTPUT TO THE SERVO AMPLIFIER TO CORRECT THE
ANTENNA POSITION
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4HE THREE CHANNEL AMPLITUDE COMPARISON MONOPULSE TRACKING RADAR IS THE MOST
COMMONLY USED MONOPULSE SYSTEM (OWEVER THE THREE SIGNALS MAY SOMETIMES BE
COMBINED IN OTHER WAYS TO PERFORM WITH A TWO CHANNEL RECEIVER SYSTEM AS DESCRIBED
LATER IN THIS SECTION USED IN SOME CURRENT SURFACE TO AIR MISSILE 3!- SYSTEMS
-ONOPULSE !NTENNA &EED 4ECHNIQUES -ONOPULSE RADAR FEEDS MAY HAVE ANY OF
A VARIETY OF CONFIGURATIONS 3INGLE APERTURES ARE ALSO EMPLOYED BY USE OF HIGHER ORDER
WAVEGUIDE MODES TO EXTRACT ANGLE ERROR SENSING DIFFERENCE SIGNALS 4HERE ARE MANY
TRADEOFFS IN FEED DESIGN BECAUSE OPTIMUM SUM AND DIFFERENCE SIGNALS LOW SIDELOBE
LEVELS SELECTABLE POLARIZATION CAPABILITY AND SIMPLICITY CANNOT ALL BE FULLY SATISFIED
SIMULTANEOUSLY 4HE TERM SIMPLICITY REFERS NOT ONLY TO COST SAVINGS BUT ALSO TO THE USE
OF NONCOMPLEX CIRCUITRY WHICH IS NECESSARY TO PROVIDE A BROADBAND SYSTEM WITH GOOD
BORESIGHT STABILITY TO MEET PRECISION TRACKING REQUIREMENTS "ORESIGHT IS THE ELECTRICAL
AXIS OF THE ANTENNA OR THE ANGULAR LOCATION OF A SIGNAL SOURCE WITHIN THE ANTENNA BEAM
AT WHICH THE ANGLE ERROR DETECTOR OUTPUTS GO TO ZERO
3OME OF THE TYPICAL MONOPULSE FEEDS ARE DESCRIBED TO SHOW THE BASIC RELATIONS AND
TRADEOFFS INVOLVED IN THE VARIOUS PERFORMANCE FACTORS AND HOW THE MORE IMPORTANT
FACTORS CAN BE OPTIMIZED BY A FEED CONFIGURATION BUT AT THE PRICE OF LOWER PERFORMANCE
IN OTHER AREAS -ANY NEW TECHNIQUES HAVE BEEN ADDED SINCE THE ORIGINAL FOUR HORN
SQUARE FEED IN ORDER TO PROVIDE GOOD OR EXCELLENT PERFORMANCE IN ALL DESIRED FEED CHAR
ACTERISTICS IN A WELL DESIGNED MONOPULSE RADAR
4HE ORIGINAL FOUR HORN SQUARE MONOPULSE FEED IS INEFFICIENT BECAUSE THE OPTIMUM
FEED SIZE APERTURE FOR THE DIFFERENCE SIGNALS IS APPROXIMATELY TWICE THE OPTIMUM SIZE
FOR THE SUM SIGNAL #ONSEQUENTLY AN INTERMEDIATE SIZE IS TYPICALLY USED WITH A SIGNIFI
CANT COMPROMISE FOR BOTH SUM AND DIFFERENCE SIGNALS 4HE OPTIMUM FOUR HORN SQUARE
FEED WHICH IS SUBJECT TO THIS COMPROMISE DESCRIBED IN 3HERMAN IS BASED ON MINI
MIZING THE ANGLE ERROR CAUSED BY RECEIVER THERMAL NOISE (OWEVER IF SIDELOBES ARE A
PRIME CONSIDERATION A SOMEWHAT DIFFERENT FEED SIZE MAY BE DESIRED
4HE LIMITATION OF THE FOUR HORN SQUARED FEED IS THAT THE SUM AND DIFFERENCE SIGNAL
% FIELDS CANNOT BE CONTROLLED INDEPENDENTLY )F INDEPENDENT CONTROL COULD BE PROVIDED
THE IDEAL WOULD BE APPROXIMATELY AS DESCRIBED IN &IGURE WITH TWICE THE DIMENSION
FOR THE DIFFERENCE SIGNALS IN THE PLANE OF ERROR SENSING THAN FOR THE SUM SIGNAL
! TECHNIQUE USED BY THE -)4 ,INCOLN ,ABORATORY TO APPROACH THE IDEAL IS A HORN
FEED &IGURE 4HE OVERALL FEED AS ILLUSTRATED IS DIVIDED INTO SMALL PARTS AND THE
MICROWAVE CIRCUITRY SELECTS THE PORTIONS NECESSARY FOR THE SUM AND DIFFERENCE SIGNALS TO
APPROACH THE IDEAL /NE DISADVANTAGE IS THAT THIS FEED REQUIRES A VERY COMPLEX MICROWAVE
CIRCUIT !LSO THE DIVIDED FOUR HORN PORTIONS OF THE FEED ARE EACH FOUR ELEMENT ARRAYS THAT
GENERATE LARGE FEED SIDELOBES IN THE ( PLANE
BECAUSE OF THE DOUBLE PEAK % FIELD !NOTHER
CONSIDERATION IS THAT THE HORN FEED IS NOT
PRACTICAL FOR FOCAL POINT FED PARABOLAS OR
REFLECTARRAYS BECAUSE OF ITS SIZE ! FOCAL
POINT FEED IS USUALLY SMALL TO PRODUCE A
BROAD PATTERN AND MUST BE COMPACT TO AVOID
BLOCKAGE OF THE ANTENNA APERTURE )N SOME
CASES THE SMALL OPTIMUM SIZE REQUIRED IS
BELOW WAVEGUIDE CUTOFF AND DIELECTRIC
LOADING OF THE HORN APERTURES BECOMES NEC
&)'52% !PPROXIMATELY IDEAL FEED APERTURE
ESSARY TO AVOID CUTOFF
% FIELD DISTRIBUTION FOR SUM AND DIFFERENCE SIGNALS
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4WELVE HORN FEED
! PRACTICAL APPROACH TO MONOPULSE FEED DESIGN USES HIGHER ORDER WAVEGUIDE MODES
RATHER THAN MULTIPLE HORNS FOR INDEPENDENT CONTROL OF SUM AND DIFFERENCE SIGNAL
% FIELDS 4HIS ALLOWS MUCH GREATER SIMPLICITY AND FLEXIBILITY ! TRIPLE MODE TWO HORN
FEED USED BY 2#! RETRACTS THE % PLANE SEPTA TO ALLOW BOTH THE 4% AND 4% MODES
TO BE EXCITED AND PROPAGATE IN THE DOUBLE WIDTH SEPTUMLESS REGION AS ILLUSTRATED IN
&IGURE !T THE SEPTUM THE DOUBLE HUMPED % FIELD IS REPRESENTED BY THE COMBINED
4% AND 4% MODES SUBTRACTING AT THE CENTER AND ADDING AT THE 4% MODE OUTER
PEAKS (OWEVER BECAUSE THE TWO MODES PROPAGATE AT DIFFERENT VELOCITIES A POINT IS
REACHED FARTHER DOWN THE DOUBLE WIDTH GUIDE WHERE THE TWO MODES ADD IN THE CENTER
AND SUBTRACT AT THE OUTER HUMPS OF THE 4% MODE 4HE RESULT IS A SUM SIGNAL % FIELD
CONCENTRATED AS DESIRED TOWARD THE CENTER OF THE FEED APERTURE
4HIS SHAPING OF THE SUM SIGNAL % FIELD IS ACCOMPLISHED INDEPENDENTLY OF THE
DIFFERENCE SIGNAL % FIELD 4HE DIFFERENCE SIGNAL IS TWO 4% MODE SIGNALS SIDE BY SIDE
ARRIVING AT THE SEPTUM OF &IGURE OUT OF PHASE !T THE SEPTUM IT BECOMES THE 4%
MODE WHICH PROPAGATES TO THE HORN APERTURE AND USES THE FULL WIDTH OF THE HORN AS
DESIRED 4HE 4% MODE HAS ZERO % FIELD IN THE CENTER OF THE WAVEGUIDE WHERE THE
SEPTUM IS LOCATED AND IS UNAFFECTED BY THE SEPTUM
! FURTHER STEP IN FEED DEVELOPMENT IS THE FOUR HORN TRIPLE MODE FEED ILLUSTRATED IN
&IGURE 4HIS FEED USES THE SAME APPROACH AS DESCRIBED ABOVE BUT WITH THE ADDI
TION OF A TOP AND BOTTOM HORN 4HIS ALLOWS THE % PLANE DIFFERENCE SIGNAL TO COUPLE TO
ALL FOUR HORNS AND USES THE FULL HEIGHT OF THE FEED 4HE SUM SIGNAL USES ONLY THE CENTER
TWO HORNS TO LIMIT ITS % FIELD IN THE % PLANE AS DESIRED FOR THE IDEAL FIELD SHAPING
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&)'52% 5SE OF RETRACTED SEPTUM TO SHAPE THE SUM SIGNAL % FIELD
4HE USE OF SMALLER TOP AND BOTTOM HORNS IS A SIMPLER METHOD OF CONCENTRATING THE
% FIELD TOWARD THE CENTER OF THE FEED WHERE THE FULL HORN WIDTH IS NOT NEEDED
4HE FEEDS DESCRIBED THUS FAR ARE FOR LINEAR POLARIZATION OPERATION 7HEN CIRCULAR
POLARIZATION IS NEEDED IN A PARABOLOID TYPE ANTENNA SQUARE OR CIRCULAR CROSS SECTION
HORN THROATS ARE USED 4HE VERTICAL AND HORIZONTAL COMPONENTS FROM EACH HORN ARE
&)'52% &OUR HORN TRIPLE MODE FEED AFTER 0 7 (ANNAN Ú )%%% 42!#+).' 2!$!2
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SEPARATED AND COMPARATORS PROVIDED FOR EACH POLARIZATION 4HE SUM AND DIFFERENCE
SIGNALS FROM THE COMPARATORS ARE COMBINED WITH — RELATIVE PHASE TO OBTAIN CIRCULAR
POLARIZATION 5SE OF THE PREVIOUSLY DESCRIBED FEEDS FOR CIRCULAR POLARIZATION WOULD
REQUIRE THE WAVEGUIDE CIRCUITRY TO BE PROHIBITIVELY COMPLEX #ONSEQUENTLY A FIVE HORN
FEED HAS BEEN USED AS ILLUSTRATED IN &IGURE 4HE FIVE HORN FEED IS SELECTED BECAUSE OF THE SIMPLICITY OF THE COMPARATOR THAT
REQUIRES ONLY TWO MAGIC OR HYBRID 4S FOR EACH POLARIZATION 4HE SUM AND DIFFER
ENCE SIGNALS ARE PROVIDED FOR THE TWO LINEAR POLARIZATION COMPONENTS AND IN AN
!.&01 RADAR ARE COMBINED IN A WAVEGUIDE SWITCH FOR SELECTING POLARIZATION
4HE SWITCH SELECTS EITHER THE VERTICAL OR THE HORIZONTAL INPUT COMPONENT OR COMBINES
THEM WITH A — RELATIVE PHASE FOR CIRCULAR POLARIZATION 4HIS FEED DOES NOT PROVIDE
OPTIMUM SUM AND DIFFERENCE SIGNAL % FIELDS BECAUSE THE SUM HORN OCCUPIES SPACE
DESIRED FOR THE DIFFERENCE SIGNALS 'ENERALLY AN UNDERSIZED SUM SIGNAL HORN IS USED
AS A COMPROMISE (OWEVER THE FIVE HORN FEED IS A PRACTICAL CHOICE BETWEEN COM
PLEXITY AND EFFICIENCY )T HAS BEEN USED IN SEVERAL INSTRUMENTATION RADARS INCLUDING
THE !.&01 !.&01 !.401 AND!.-03 AND IN THE !.401 TACTICAL PRECISION TRACKING RADAR
4HE MULTIMODE FEED TECHNIQUE CAN BE EXPANDED TO OTHER HIGHER ORDER MODES FOR
ERROR SENSING AND % FIELD SHAPING 4HE DIFFERENCE SIGNALS ARE CONTAINED IN UNSYM
METRICAL MODES SUCH AS THE 4% MODE FOR ( PLANE ERROR SENSING AND COMBINED 4%
AND 4- MODES FOR % PLANE ERROR SENSING 4HESE MODES PROVIDE THE DIFFERENCE SIG
NALS AND NO COMPARATORS ARE USED 'ENERALLY MODE COUPLING DEVICES CAN GIVE GOOD
PERFORMANCE IN SEPARATING THE SYMMETRICAL AND UNSYMMETRICAL MODES WITHOUT SIGNIFI
CANT CROSS COUPLING PROBLEMS
&)'52% &IVE HORN FEED WITH COUPLING TO BOTH LINEAR POLARIZATION COMPONENTS WHICH ARE
COMBINED BY THE SWITCH MATRIX TO SELECT HORIZONTAL VERTICAL OR CIRCULAR POLARIZATION
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-ULTIBAND MONOPULSE FEED CONFIGURATIONS ARE PRACTICAL AND IN USE IN SEVERAL SYS
TEMS ! SIMPLE EXAMPLE IS A COMBINED 8 BAND AND +A BAND MONOPULSE PARABOLOID
ANTENNA RADAR 3EPARATE CONVENTIONAL FEEDS ARE USED FOR EACH BAND WITH THE +A BAND
FEED AS A #ASSEGRAIN FEED AND THE 8 BAND FEED AT THE FOCAL POINT 4HE #ASSEGRAIN SUB
DISH IS A HYPERBOLIC SHAPED HIGHLY EFFICIENT GRID OF WIRES REFLECTIVE TO PARALLEL POLARIZA
TION AND TRANSPARENT TO ORTHOGONAL POLARIZATION )T IS ORIENTED TO BE TRANSPARENT TO THE
8 BAND FOCAL POINT FEED BEHIND IT AND REFLECTIVE TO THE ORTHOGONALLY POLARIZED +A BAND
FEED EXTENDING FROM THE VERTEX OF THE PARABOLOID
-ONOPULSE FEED HORNS AT DIFFERENT MICROWAVE FREQUENCIES CAN ALSO BE COMBINED
WITH CONCENTRIC FEED HORNS 4HE MULTIBAND FEED CLUSTERS WILL SACRIFICE EFFICIENCY BUT
CAN SATISFY MULTIBAND REQUIREMENTS IN A SINGLE ANTENNA
!'# !UTOMATIC 'AIN #ONTROL 4O MAINTAIN A STABLE CLOSED LOOP SERVOSYSTEM FOR
ANGLE TRACKING THE RADAR MUST MAINTAIN ESSENTIALLY CONSTANT LOOP GAIN INDEPENDENT OF
TARGET ECHO SIZE AND RANGE 4HE PROBLEM IS THAT MONOPULSE DIFFERENCE SIGNALS FROM THE
ANTENNA ARE PROPORTIONAL TO BOTH THE ANGLE DISPLACEMENT OF THE TARGET FROM THE ANTENNA AXIS
AND THE ECHO SIGNAL AMPLITUDE &OR A GIVEN TRACKING ERROR THE ERROR VOLTAGE WOULD CHANGE
WITH ECHO AMPLITUDE AND TARGET RANGE CAUSING A CORRESPONDING CHANGE IN LOOP GAIN
!'# IS USED TO REMOVE THE ANGLE ERROR DETECTOR OUTPUT DEPENDENCE ON ECHO AMPLI
TUDE AND RETAIN CONSTANT TRACKING LOOP GAIN ! TYPICAL !'# TECHNIQUE IS ILLUSTRATED IN
&IGURE FOR A ONE ANGLE COORDINATE TRACKING SYSTEM 4HE !'# SYSTEM DETECTS THE
PEAK VOLTAGE OF THE SUM SIGNAL AND PROVIDES A NEGATIVE DC VOLTAGE PROPORTIONAL TO THE
PEAK SIGNAL VOLTAGE 4HE NEGATIVE VOLTAGE IS FED TO THE )& AMPLIFIER STAGE WHERE IT IS
USED TO DECREASE GAIN AS THE SIGNAL INCREASES ! HIGH GAIN IN THE !'# LOOP IS EQUIVALENT
TO DIVIDING THE )& OUTPUT BY A FACTOR PROPORTIONAL TO ITS AMPLITUDE
)N A THREE CHANNEL MONOPULSE RADAR ALL THREE CHANNELS ARE CONTROLLED BY THE !'#
VOLTAGE WHICH EFFECTIVELY PERFORMS A DIVISION BY THE MAGNITUDE OF THE SUM SIGNAL OR
ECHO AMPLITUDE #ONVENTIONAL !'# ESSENTIALLY HOLDS CONSTANT GAIN DURING THE PULSE
REPETITION INTERVAL !LSO THE !'# OF THE SUM CHANNEL NORMALIZES THE SUM ECHO PULSE
AMPLITUDE TO SIMILARLY MAINTAIN A STABLE RANGE TRACKING SERVO LOOP
4HE ANGLE ERROR DETECTOR ASSUMED TO BE A PRODUCE DETECTOR HAS AN OUTPUT
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— OR — ON A POINT SOURCE TARGET 4HE RESULTANT IS
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#OMPLEX TARGETS CAN CAUSE OTHER PHASE RELATIONS AS A PART OF THE ANGLE SCINTILLATION
PHENOMENON 4HE ABOVE ERROR VOLTAGE PROPORTIONAL TO THE RATIO OF THE DIFFERENCE
SIGNAL DIVIDED BY THE SUM SIGNAL IS THE DESIRED ANGLE ERROR DETECTOR OUTPUT GIVING A
CONSTANT ANGLE ERROR SENSITIVITY
7ITH LIMITED !'# BANDWIDTH SOME RAPID SIGNAL FLUCTUATIONS MODULATE ¨E ¨BUT THE
LONG TIME AVERAGE ANGLE SENSITIVITY IS CONSTANT 4HESE FLUCTUATIONS ARE LARGELY FROM
RAPID CHANGES IN TARGET REFLECTIVITY R T THAT ARE FROM TARGET AMPLITUDE SCINTILLATION
4HE RANDOM MODULATION OF ¨E ¨CAUSES AN ADDITIONAL ANGLE NOISE COMPONENT THAT AFFECTS
THE CHOICE OF !'# BANDWIDTH
4HE !'# PERFORMANCE IN CONICAL SCAN RADARS PROVIDES SIMILAR CONSTANT ANGLE ERROR
SENSITIVITY /NE MAJOR LIMITATION IN CONICAL SCAN RADARS IS THAT THE !'# BANDWIDTH
MUST BE SUFFICIENTLY LOWER THAN THE SCAN FREQUENCY TO PREVENT THE !'# FROM REMOVING
THE MODULATION CONTAINING THE ANGLE ERROR INFORMATION
0HASE #OMPARISON -ONOPULSE ! SECOND MONOPULSE TECHNIQUE IS THE USE OF MUL
TIPLE ANTENNAS WITH OVERLAPPING NONSQUINTED BEAMS POINTED AT THE TARGET )NTERPOLATING
TARGET ANGLES WITHIN THE BEAM IS ACCOMPLISHED AS SHOWN IN &IGURE BY COMPARING
THE PHASE OF THE SIGNALS FROM THE ANTENNAS FOR SIMPLICITY A SINGLE COORDINATE TRACKER
IS DESCRIBED )F THE TARGET WERE ON THE ANTENNA BORESIGHT AXIS THE OUTPUTS OF EACH
&)'52% A 7AVEFRONT PHASE RELATIONSHIPS IN A PHASE COMPARISON MONOPULSE RADAR AND B BLOCK
DIAGRAM OF A PHASE COMPARISON MONOPULSE RADAR ONE ANGLE COORDINATE
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INDIVIDUAL APERTURE WOULD BE IN PHASE !S
THE TARGET MOVES OFF AXIS IN EITHER DIREC
TION THERE IS A CHANGE IN RELATIVE PHASE
4HE AMPLITUDES OF THE SIGNALS IN EACH APER
TURE ARE THE SAME SO THAT THE OUTPUT OF THE
ANGLE ERROR PHASE DETECTOR IS DETERMINED
BY THE RELATIVE PHASE SEE &IGURE 4HE
PHASE DETECTOR CIRCUIT IS ADJUSTED WITH A
— PHASE SHIFT ON ONE CHANNEL TO GIVE ZERO
OUTPUT WHEN THE TARGET IS ON AXIS AND AN
OUTPUT INCREASING WITH INCREASING ANGULAR
DISPLACEMENT OF THE TARGET WITH A POLARITY
CORRESPONDING TO THE DIRECTION OF ERROR
4YPICAL FLAT FACE CORPORATE FED PHASED
ARRAYS COMPARE THE OUTPUT OF HALVES OF THE
APERTURE AND FALL INTO THE CLASS OF PHASE
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COMPARISON MONOPULSE (OWEVER THE PULSE SYSTEM WITH SUM AND DIFFERENCE OUTPUTS AND
BASIC SIGNAL PROCESSING OF AMPLITUDE AND B VECTOR DIAGRAM OF THE SUM AND DIFFERENCE SIGNALS
PHASE COMPARISON MONOPULSE IS SIMILAR
BUT THE CONTROL OF AMPLITUDE DISTRIBUTION ACROSS AN ARRAY APERTURE FOR THE SUM AND
DIFFERENCE SIGNALS MAINTAINS EFFICIENCY AND LOWER SIDELOBES
&IGURE SHOWS THE ANTENNA AND RECEIVER FOR ONE ANGULAR COORDINATE TRACKING BY
PHASE COMPARISON MONOPULSE !NY PHASE SHIFTS OCCURRING IN THE MIXER AND )& AMPLI
FIER STAGES CAUSES A SHIFT IN THE BORESIGHT OF THE SYSTEM 4HE DISADVANTAGES OF PHASE
COMPARISON MONOPULSE WITH SEPARATE APERTURES COMPARED WITH AMPLITUDE COMPARISON
MONOPULSE ARE THE RELATIVE DIFFICULTY IN MAINTAINING A HIGHLY STABLE BORESIGHT AND THE
DIFFICULTY IN PROVIDING THE DESIRED ANTENNA ILLUMINATION TAPER FOR BOTH SUM AND DIF
FERENCE SIGNALS 4HE LONGER PATHS FROM THE ANTENNA OUTPUTS TO THE COMPARATOR CIR
CUITRY MAKE THE PHASE COMPARISON SYSTEM MORE SUSCEPTIBLE TO BORESIGHT CHANGE DUE
TO MECHANICAL LOADING SAG DIFFERENTIAL HEATING ETC
! TECHNIQUE GIVING GREATER BORESIGHT STABILITY COMBINES THE TWO ANTENNA OUT
PUTS AT 2& WITH PASSIVE CIRCUITRY TO YIELD SUM AND DIFFERENCE SIGNALS AS SHOWN IN
&IGURE 4HESE SIGNALS MAY THEN BE PROCESSED LIKE A CONVENTIONAL AMPLITUDE
COMPARISON MONOPULSE RECEIVER 4HE SYSTEM SHOWN IN &IGURE WOULD PROVIDE
A RELATIVELY GOOD DIFFERENCE CHANNEL TAPER HAVING SMOOTHLY TAPERED % FIELDS ON
EACH ANTENNA (OWEVER A SUM SIGNAL EXCITATION WITH THE TWO ANTENNAS PROVIDES A
TWO HUMPED IN PHASE % FIELD DISTRIBUTION THAT CAUSES HIGH SIDELOBES SINCE IT LOOKS
LIKE A TWO ELEMENT ARRAY 4HIS PROBLEM MAY BE REDUCED BY ALLOWING SOME APERTURE
OVERLAP BUT AT THE PRICE OF LOSS OF ANGLE SENSITIVITY AND ANTENNA GAIN
%LECTRONIC 3CAN 0HASED !RRAY -ONOPULSE 4RACKING RADARS DEDICATED TO SINGLE
TARGET TRACKING CAN PROVIDE VERY HIGH PRECISION LONG RANGE PERFORMANCE SUCH AS THE
!.&01 &IGURE A WITH A SPECIFIED PRECISION OF MILLIRADIAN 7ITH
HIGH POWER AND A HIGH GAIN ANTENNA D" AND SPECIAL TRACKING TECHNIQUES THEY ARE
THE WORKHORSE FOR PRECISION TRACKING OF SATELLITES AND SIMILAR TASKS (OWEVER MOST
MODERN TASKS REQUIRE PRECISION SIMULTANEOUS TRACKING OF MULTIPLE SIMULTANEOUS TARGETS
WHERE USE OF MULTIPLE SINGLE TARGET TRACKING RADARS ARE NOT COST EFFECTIVE 4HE DEVELOP
MENT OF ELECTRONIC SCAN PHASED ARRAY TECHNOLOGY HAS RESULTED IN VERSATILE HIGH PRECI
SION MONOPULSE TRACKING WITH THE CAPABILITY OF SIMULTANEOUS MULTITARGET TRACKING BY
SWITCHING ITS BEAM TO EACH OF SEVERAL TARGETS ON A PULSE TO PULSE BASIS OR BY GROUPS
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OF PULSES -ONOPULSE TRACKING IS NECESSARY TO OBTAIN ANGLE DATA ON EACH PULSE TO
MAINTAIN ADEQUATE DATA RATES WHEN SHARING PULSES AND POWER AMONG SEVERAL TARGETS !
DETAILED DISCUSSION OF ELECTRONIC SCAN PHASED ARRAYS IS GIVEN IN #HAPTER HOWEVER
SOME CHARACTERISTICS OF THE ARRAYS REQUIRE SPECIAL CONSIDERATION FOR THE ANGLE TRACKING
PERFORMANCE OF TRACKING RADARS USING MONOPULSE PHASED ARRAY ANTENNAS
/PTICAL FEED -ONOPULSE %LECTRONIC 3CAN !RRAYS /PTICAL FEED MONOPULSE ARRAYS
INCLUDE THE LENS ARRAY AND REFLECTARRAY #HAPTER THAT ARE OPTICALLY FED BY A CONVEN
TIONAL MONOPULSE FEED 4HE !.-01 &IGURE B IS AN EXAMPLE OF AN OPTICALLY
FED ARRAY LENS WITH THE ANTENNA MOUNTED ON A TWO AXIS PEDESTAL 4YPICAL INSTANTANEOUS
ELECTRONIC ANGLE COVERAGE IS o— TO AN ALMOST o— CONE FIELD OF VIEW THAT MAY BE
MOVED BY PEDESTAL DRIVE TO CENTER ON A MULTITARGET EVENT OR FOLLOW AN EVENT PROGRESS
ING TO A DIFFERENT AREA 3OME MILITARY SYSTEMS SUCH AS THE 0ATRIOT WITH THE o— CONE
OF INSTANTANEOUS VIEW IS FIXED ON ITS VEHICLE WITHOUT A PEDESTAL AND IS DEPENDENT ON
MOVEMENT OF ITS VEHICLE TO CHANGE THE REGION OF ANGULAR COVERAGE AS NEEDED 4HE
ADVANTAGES OF SPACE FED ARRAYS ARE
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#ONVENTIONAL MONOPULSE MICROWAVE HORN FEEDS ARE USED
!RRAY ELEMENTS ARE AVAILABLE WITH SELECTABLE POLARIZATION OF THE RADIATED ENERGY WHEN
FED BY AN OPTIMIZED LINEAR POLARIZED MONOPULSE FEED SUCH AS IN &IGURE AND SELECT
ABLE RECEIVE POLARIZATION AS WELL 4HIS AVOIDS THE TYPICAL COMPROMISE AND GREATER COM
PLEXITY OF A POLARIZATION CONTROLLED MONOPULSE FEED AS DESCRIBED IN &IGURE %LECTRONIC SCAN ARRAY LENSES CAN ALSO REFOCUS FROM A TRANSMIT FEED HORN TO AN ADJACENT
RECEIVE FEED HORN ON RECEPTION TO ALLOW HIGH POWER TRANSMISSION THROUGH A SIMPLE
SINGLE HORN FEED TO SIMPLIFY ISOLATION OF THE RECEIVER FROM THE TRANSMIT POWER
!RRAYS ALLOW GREATER FLEXIBILITY TO OPTIMIZE AMPLITUDE DISTRIBUTION OF THE RADIATED
ENERGY ACROSS THE ARRAY TO REDUCE SIDELOBES
-OST OF THE ELECTRONIC SCAN PHASED ARRAY DISADVANTAGES ARE DESCRIBED IN #HAPTER AND INCLUDE LOSSES IN THE ARRAY PHASE SHIFTING ELEMENTS LIMITATION OF INSTANTANEOUS
BANDWIDTH WITH CONVENTIONAL PHASE CONTROL ELEMENTS IMPROVED WITH SPECIAL TRUE
TIME DELAY PHASE SHIFTING PHASE QUANTIZATION ERRORS #HAPTER RESULTING FROM
PHASE SHIFTING IN STEPS RESTRICTION TO A SINGLE RF BAND MULTIBAND ARRAYS REQUIRE SPECIAL
TECHNIQUES WITH MAJOR COMPROMISES AND GRADUAL DEGRADATION OF PERFORMANCE AS THE
BEAM IS SCANNED FROM THE NORMAL TO THE ARRAY 4HE QUANTIZATION ERRORS FROM PHASE
SHIFTING IN STEPS ARE OF CONCERN TO MONOPULSE RADAR BECAUSE IT RESULTS IN CORRESPONDING
RANDOM ERROR STEPS IN THE ELECTRONIC AXIS OF THE ARRAY !S DESCRIBED IN #HAPTER THE
QUANTIZATION ERRORS ARE INVERSELY PROPORTIONAL TO THE NUMBER OF PHASE SHIFTING ELEMENTS
AND 0 WHERE 0 IS THE NUMBER OF BITS OF PHASE CONTROL IN EACH ELEMENT #ONSEQUENTLY
THE HIGH PRECISION TRACKING RADARS WITH TYPICALLY TO PHASE SHIFTERS AND FOUR
OR MORE PHASE SHIFT BITS HAVE SMALL RESULTANT ELECTRICAL AXIS ERROR STEPS ON THE ORDER OF
MILLIRADIANS OR LESS 4HE ELECTRICAL AXIS ERRORS ARE ESSENTIALLY RANDOM AND CAN BE
FURTHER REDUCED BY AVERAGING )NTENTIONAL DITHER OF PHASE STEPS MAY BE INTRODUCED TO
AID IN AVERAGING
4HE OPTICALLY FED TECHNIQUE RESULTS IN FEED ENERGY SPILLOVER AROUND THE APERTURE
HOWEVER THESE RESULTANT SPILLOVER SIDELOBES CAN BE ELIMINATED BY AN ABSORBING CONE
BETWEEN THE FEED AND THE ARRAY APERTURE 4HE ABSORBING CONE IS OBSERVED IN THE !.
-01 &IGURE B (OWEVER COOLING IS ALSO NECESSARY AND PROVIDED AS OBSERVED
BY THE COOLING COILS AROUND THE ABSORBING CONE
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/F FURTHER CONCERN TO HIGH PRECISION MONOPULSE APPLICATIONS IS DRIFT OF THE ELEC
TRONIC AXIS THAT CAUSES VARIATIONS IN PHASE AND TEMPERATURE VARIATION ACROSS THE ARRAY
SURFACE THAT CAUSES DISTORTION OF THE LENS 3IGNIFICANT VARIATION OF HEAT DISTRIBUTION
ACROSS THE ARRAY FACE CAN RESULT FROM HIGH POWER TRANSMITTED THROUGH THE PHASE SHIFTING
ELEMENTS AS WELL AS THE ELECTRONIC PHASE CONTROL #ONSEQUENTLY WHERE HIGH PRECISION
TRACKING IS REQUIRED SPECIAL COOLING TECHNIQUES MAY BE NECESSARY TO MAINTAIN CONSTANT
TEMPERATURE ACROSS THE APERTURE
#ORPORATE &EED -ONOPULSE %LECTRONIC 3CAN 0HASED !RRAY 4HE CORPORATE FEED
ARRAY IS FED BY DIVIDING AND SUBDIVIDING THE TRANSMIT SIGNAL THROUGH TRANSMISSION LINES
TYPICALLY TO SUBARRAYS OF MULTIPLE ARRAY RADIATING ELEMENTS 4HIS TECHNIQUE ALTHOUGH
TYPICALLY RESULTING IN HEAVIER AND HIGHER COST IMPLEMENTATION OFFERS THE ADVANTAGE
OF FLEXIBILITY OF CONTROL OF THE SIGNAL PATHS THROUGH THE ARRAY STRUCTURE AS DESCRIBED
IN #HAPTER !NOTHER ADVANTAGE IS THE CAPABILITY TO TRANSMIT VERY HIGH PEAK POWER
WITHOUT THE LIMITATIONS OF FULL PEAK POWER PROPAGATING THROUGH A SINGLE TRANSMISSION
LINE 4HIS IS ACCOMPLISHED IN THE CORPORATE FEED ARRAY BY PLACING HIGH POWER AMPLIFIERS
WHERE THE POWER DIVIDES TO THE SUBARRAYS ALLOWING THE SUM OF THE HIGH PEAK POWER
AMPLIFIER OUTPUTS TO ADD IN SPACE TO MEET REQUIREMENTS FOR LONG RANGE TRACKING AND
POWER SHARING BETWEEN MULTIPLE SIMULTANEOUS TARGETS
4HE PARALLEL POWER AMPLIFIER CONFIGURATION ALSO PROVIDES A PRACTICAL MEANS FOR
OVERCOMING THE NARROW INSTANTANEOUS BANDWIDTH OF TYPICAL PHASED ARRAYS AT WIDE
SCAN ANGLES &ULL ARRAY INSTANTANEOUS BANDWIDTH REQUIRES EQUAL PATH LENGTHS BETWEEN
EACH ARRAY ELEMENT AND THE TARGET REQUIRING MANY WAVELENGTHS OF PHASE CONTROL OR THE
EQUIVALENT TIME DELAY IN ARRAY ELEMENTS AT WIDE ANGLE SCANS (OWEVER THIS CONTROL HAS
PROHIBITIVELY HIGH LOSS FOR TYPICAL PHASED ARRAY RADIATING ELEMENTS CONSEQUENTLY TYPI
CAL PHASED ARRAY ELEMENTS PROVIDE ONLY SUFFICIENT PHASE CONTROL OF UP TO — OR TO ONE
WAVELENGTH LIMITED TO TOLERABLE LOSS TO CAUSE THE SIGNAL FROM EACH ELEMENT TO ARRIVE
APPROXIMATELY IN PHASE AT THE TARGET 5NFORTUNATELY THIS SHORTCUT IS ADEQUATE FOR ONLY
A NARROW INSTANTANEOUS BANDWIDTH 4HE PARALLEL POWER AMPLIFIERS AS DESCRIBED ABOVE
PROVIDE A LOW POWER AMPLIFIER DRIVE STAGE WHERE THE HIGH LOSS OF THE DESIRED TIME
DELAY CONTROL CAN BE TOLERATED TO GAIN WIDE INSTANTANEOUS BANDWIDTH AS DESCRIBED IN
#HAPTER 4HE TIME DELAY MAY BE CONTROLLED SIMILAR TO THE DIODE PHASE SHIFTERS USED
IN RADIATING ELEMENTS THAT SWITCH BETWEEN DIFFERENT LINE LENGTHS TO ADJUST PHASE ,ONGER
TIME DELAY TRANSMISSION LINE COULD BE SIMILARLY CONTROLLED BY DIODE SWITCHING TO PRO
VIDE THE WIDE INSTANTANEOUS BANDWIDTH TO ALLOW FOR EXAMPLE USE OF WIDEBAND NARROW
PULSES TO PROVIDE THE RANGE RESOLUTION REQUIREMENTS FOR TRACKING RADAR APPLICATIONS
4WO #HANNEL -ONOPULSE -ONOPULSE RADARS MAY BE DESIGNED WITH FEWER THAN THE
CONVENTIONAL THREE )& CHANNELS 4HIS IS ACCOMPLISHED FOR EXAMPLE BY COMBINING THE SUM
AND DIFFERENCE SIGNALS IN TWO )& CHANNELS AND THE SUM AND TWO DIFFERENCE SIGNAL OUTPUTS
ARE THEN INDIVIDUALLY RETRIEVED AT THE OUTPUT 4HESE TECHNIQUES PROVIDE SOME ADVANTAGES
IN !'# OR OTHER PROCESSING TECHNIQUES BUT AT THE COST OF REDUCED 3.2 REDUCED ANGLE
DATA RATE AND POTENTIAL FOR CROSS COUPLING BETWEEN AZIMUTH AND ELEVATION INFORMATION
! TWO CHANNEL MONOPULSE RECEIVER COMBINES THE SUM AND DIFFERENCE SIGNALS
AT 2& AS SHOWN IN &IGURE 4HE MICROWAVE RESOLVER IS A MECHANICALLY ROTATED
2& COUPLING LOOP IN CYLINDRICAL WAVEGUIDE 4HE AZIMUTH AND ELEVATION DIFFERENCE
SIGNALS ARE EXCITED IN THIS GUIDE WITH % FIELD POLARIZATION ORIENTED AT O 4HE
ENERGY IN THE COUPLER CONTAINS BOTH DIFFERENCE SIGNALS COUPLED AS THE COSINE
AND SINE OF THE ANGULAR POSITION OF THE COUPLER VST WHERE VS IS THE ANGULAR RATE
OF ROTATION 4HE HYBRID ADDS THE COMBINED DIFFERENCE SIGNALS $ AT THE ANGULAR
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"LOCK DIAGRAM OF A TWO CHANNEL MONOPULSE RADAR SYSTEM FROM 2 3 .OBLIT
RATE OF ROTATION 4HE 3 $ AND 3 n $ OUTPUTS EACH LOOK LIKE THE OUTPUT OF A CONICAL
SCAN TRACKER EXCEPT THAT THEIR MODULATION FUNCTION DIFFERS BY — )N CASE ONE
CHANNEL FAILS THE RADAR CAN BE OPERATED AS A SCAN ON RECEIVE ONLY CONICAL SCAN RADAR
WITH ESSENTIALLY THE SAME PERFORMANCE AS A CONICAL SCAN RADAR 4HE ADVANTAGE OF TWO
CHANNELS WITH OPPOSITE SENSE ANGLE ERROR INFORMATION ON ONE CHANNEL WITH RESPECT TO
THE OTHER IS THAT SIGNAL AMPLITUDE FLUCTUATIONS IN THE RECEIVED SIGNAL ARE CANCELED IN THE
POST DETECTION SUBTRACTION AT THE )& OUTPUT THAT RETRIEVES THE ANGLE ERROR INFORMATION
4HE LOG )& PERFORMS ESSENTIALLY AS AN INSTANTANEOUS !'# GIVING THE DESIRED CONSTANT
ANGLE ERROR SENSITIVITY OF THE DIFFERENCE SIGNALS NORMALIZED BY THE SUM SIGNAL 4HE
DETECTED $ INFORMATION IS A BIPOLAR VIDEO WHERE THE ERROR INFORMATION IS CONTAINED IN
THE SINUSOIDAL ENVELOPE 4HIS SIGNAL IS SEPARATED INTO ITS TWO COMPONENTS AZIMUTH
AND ELEVATION ERROR INFORMATION BY AN ANGLE DEMODULATION 4HE DEMODULATOR USING
A REFERENCE FROM THE DRIVE ON THE ROTATING COUPLER EXTRACTS THE SINE AND COSINE
COMPONENTS FROM $ TO GIVE THE AZIMUTH AND ELEVATION ERROR SIGNALS 4HE MODULATION
CAUSED BY THE MICROWAVE RESOLVER IS OF CONCERN IN INSTRUMENTATION RADAR APPLICATIONS
BECAUSE IT ADDS SPECTRAL COMPONENTS IN THE SIGNAL COMPLICATING THE POSSIBLE ADDITION
OF PULSE DOPPLER TRACKING CAPABILITY TO THE RADAR
4HIS SYSTEM PROVIDES INSTANTANEOUS !'# OPERATION WITH ONLY TWO )& CHANNELS AND
OPERATION WITH REDUCED PERFORMANCE IN CASE OF FAILURE OF EITHER CHANNEL (OWEVER
THERE IS A LOSS OF D" 3.2 AT THE RECEIVER INPUTS ALTHOUGH THIS LOSS IS PARTLY REGAINED
BY COHERENT ADDITION OF THE 3 SIGNAL INFORMATION 4HE DESIGN OF THE MICROWAVE RESOLVER
MUST MINIMIZE LOSS THROUGH THE DEVICE AND PRECISELY MATCHED )& CHANNELS ARE REQUIRED
TO MINIMIZE CROSS COUPLING BETWEEN THE AZIMUTH AND ELEVATION CHANNELS )N SOME MOD
ERN SYSTEMS THE RESOLVER PERFORMANCE IS IMPROVED BY USE OF FERRITE SWITCHING DEVICES
TO REPLACE THE MECHANICAL ROTATING COUPLER
#ONOPULSE #ONOPULSE ALSO CALLED SCAN WITH COMPENSATION IS A RADAR TRACKING
TECHNIQUE THAT IS A COMBINATION OF MONOPULSE AND CONICAL SCAN ! PAIR OF ANTENNA
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BEAMS IS SQUINTED IN OPPOSITE DIRECTIONS FROM THE ANTENNA AXIS AND ROTATED LIKE A PAIR
OF CONICAL SCAN RADAR BEAMS 3INCE THEY EXIST SIMULTANEOUSLY MONOPULSE INFORMATION
CAN BE OBTAINED FROM THE PAIR OF BEAMS 4HE PLANE IN WHICH MONOPULSE INFORMATION
IS MEASURED ROTATES #ONSEQUENTLY ELEVATION AND AZIMUTH INFORMATION IS SEQUENTIAL
AND MUST BE SEPARATED FOR USE IN EACH TRACKING COORDINATE #ONOPULSE PROVIDES THE
MONOPULSE ADVANTAGE OF AVOIDING ERRORS CAUSED BY AMPLITUDE SCINTILLATION AND IT
REQUIRES ONLY TWO RECEIVERS (OWEVER IT HAS THE DISADVANTAGE OF LOWER ANGLE DATA
RATES AND THE MECHANICAL COMPLEXITY OF PROVIDING AND COUPLING TO A PAIR OF ROTATING
ANTENNA FEEDHORNS
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Ê" 4HE FIRST TECHNIQUE USED FOR RADAR ANGLE TRACKING WAS TO DISPLACE THE ANTENNA BEAM
ABOVE AND BELOW THE TARGET IN ELEVATION AND SIDE TO SIDE OF THE TARGET IN AZIMUTH TO
COMPARE BEAM AMPLITUDES SIMILAR TO MONOPULSE RADAR SIMULTANEOUS LOBING BUT DIFFER
ING BY BEING IN A TIME SEQUENCE 4HIS WAS PERFORMED BY A CONTINUOUS CONICAL BEAM
SCAN AS ILLUSTRATED IN &IGURE OR BY SEQUENTIALLY LOBING UPDOWN AND RIGHTLEFT
AND OBSERVING THE DIFFERENCE BETWEEN AMPLITUDES AS A MEASURE OF DISPLACEMENT OF THE
ANTENNA AXIS FROM THE TARGET 4HE SIGNAL OUTPUT FOR A CONICAL SCAN RADAR ILLUSTRATED IN
&IGURE IS TYPICALLY A SINUSOID AMPLITUDE MODULATION OF THE RECEIVED TARGET ECHO
PULSES 4HE AMPLITUDE OF THE MODULATION IS A MEASURE OF THE MAGNITUDE OF THE ANGLE
ERROR AND THE PHASE RELATIVE TO THE SCANNING BEAM ROTATION ANGLE INDICATES THE PORTION
OF THE ERROR CAUSED BY EACH TRACKING AXIS
4HE PERFORMANCE OF SCANNING AND LOBING RADAR RELATIVE TO THE BEAM OFFSET ANGLE IS
DESCRIBED IN "ARTON !N OPTIMUM BEAM OFFSET IS DESCRIBED AS A COMPROMISE BETWEEN
THE LOSS OF ANTENNA GAIN AND THE INCREASE IN SENSITIVITY TO TARGET ANGLE DISPLACEMENT
FROM THE ANTENNA AXIS AS BEAM OFFSET IS INCREASED 4HE OPTIMUM OFFSET IS TYPICALLY
CHOSEN TO PROVIDE THE MINIMUM RMS ANGLE TRACKING ERROR AS AFFECTED BY THE SIGNAL TO
NOISE RATIO AND TRACKING SENSITIVITY 3PECIAL TRACKING RADAR APPLICATIONS WITH NONTYPICAL
REQUIREMENTS COULD ARRIVE AT A DIFFERENT OPTIMUM BEAM OFFSET
! MAJOR LIMITATION OF SCANNING AND LOBING RADAR IS THE SUSCEPTIBILITY TO TARGET AMPLI
TUDE FLUCTUATIONS THAT OCCUR DURING THE TIME THE BEAM IS MOVED FROM SIDE TO SIDE OR UP
AND DOWN )T IS ALSO SUSCEPTIBLE TO FALSE MODULATION ON SIGNALS FROM COUNTERMEASURES
4HE ECHO FLUCTUATIONS NOT RELATED TO ANTENNA BEAM POSITION CAUSE FALSE TARGET ANGLE
TRACKING ERRORS
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&)'52% A !NGLE ERROR INFORMATION CONTAINED IN THE ENVELOPE
OF THE RECEIVED PULSES IN A CONICAL SCAN RADAR AND B REFERENCE SIGNAL
DERIVED FROM THE DRIVE OF THE CONICAL SCAN FEED
-ONOPULSE RADAR WAS DEVELOPED TO PROVIDE SIMULTANEOUS OFFSET ANTENNA BEAMS FOR
COMPARISON OF TARGET ECHO AMPLITUDES ON A SINGLE PULSE INDEPENDENT OF ECHO SIGNAL
AMPLITUDE FLUCTUATIONS (OWEVER FEW MICROWAVE DEVICES AND COMPONENTS WERE INI
TIALLY AVAILABLE AND THE FIRST MONOPULSE SYSTEMS WERE COMPLEX AND RESULTED IN CUM
BERSOME AND INEFFICIENT ANTENNAS !T PRESENT MODERN MONOPULSE RADARS AS DESCRIBED
IN 3ECTION PROVIDE HIGHLY STABLE AND EFFICIENT ANTENNAS WITH HIGH PRECISION PERFOR
MANCE AND HAVE GENERALLY DISPLACED SCANNING AND LOBING TRACKING RADARS FOR MEETING
THE INCREASING DEMANDS FOR HIGH PRECISION AND HIGH DATA RATE OF ANGLE INFORMATION ON
EACH PULSE (OWEVER SPECIAL RADAR TRACKING REQUIREMENTS MAY EXIST WHERE A PRACTICAL
IMPLEMENTATION OF CONICAL SCAN OR LOBING TRACKING RADAR MAY MORE EFFECTIVELY PROVIDE
ADEQUATE PERFORMANCE
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4HE SERVOSYSTEM OF A TRACKING RADAR IS THE SUBSYSTEM OF THE RADAR THAT RECEIVES AS ITS
INPUT THE TRACKING ERROR VOLTAGE AND PERFORMS THE TASK OF MOVING THE ANTENNA BEAM IN A
DIRECTION THAT WILL REDUCE TO ZERO THE ALIGNMENT ERROR BETWEEN THE ANTENNA AXIS AND THE
TARGET &OR TWO AXIS TRACKING WITH A MECHANICAL TYPE ANTENNA PEDESTAL THERE ARE TYPI
CALLY SEPARATE AXES OF ROTATION FOR AZIMUTH AND ELEVATION AND SEPARATE SERVOSYSTEMS TO
MOVE THE ANTENNA ABOUT EACH AXIS ! CONVENTIONAL SERVOSYSTEM IS COMPOSED OF AMPLI
FIERS FILTERS AND A MOTOR THAT MOVES THE ANTENNA IN A DIRECTION TO MAINTAIN THE ANTENNA
AXIS ON THE TARGET 2ANGE TRACKING IS ACCOMPLISHED BY A SIMILAR SYSTEM TO MAINTAIN
RANGE GATES CENTERED ON THE RECEIVED ECHO PULSES 4HIS MAY BE ACCOMPLISHED BY ANALOG
TECHNIQUES OR BY DIGITAL COUNTER REGISTERS THAT RETAIN NUMBERS CORRESPONDING TO TARGET
RANGE TO PROVIDE A CLOSED RANGE TRACKING LOOP DIGITALLY
3ERVOSYSTEMS MAY USE HYDRAULIC DRIVE MOTORS CONVENTIONAL ELECTRIC MOTORS
GEARED DOWN TO DRIVE THE ANTENNA OR DIRECT DRIVE ELECTRIC MOTORS WHERE THE ANTENNA
MECHANICAL AXIS SHAFT IS PART OF THE ARMATURE AND THE MOTOR FIELD IS BUILT INTO
THE SUPPORT CASE 4HE DIRECT DRIVE IS HEAVIER FOR A GIVEN HORSEPOWER BUT ELIMINATES
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GEAR BACKLASH "ACKLASH MAY ALSO BE REDUCED WITH CONVENTIONAL MOTORS BY DUPLICATE
PARALLEL DRIVES WITH A SMALL RESIDUAL OPPOSING TORQUE WHEN NEAR ZERO ANGLE RATE
!MPLIFIER GAIN AND FILTER CHARACTERISTICS AS WELL AS MOTOR TORQUE AND INERTIA DETER
MINE THE VELOCITY AND ACCELERATION CAPABILITY OR THE ABILITY TO FOLLOW THE HIGHER ORDER
MOTION OF THE TARGET
)T IS DESIRED THAT THE ANTENNA BEAM FOLLOW THE CENTER OF THE TARGET AS CLOSELY AS POS
SIBLE WHICH IMPLIES THAT THE SERVOSYSTEM SHOULD BE CAPABLE OF MOVING THE ANTENNA
QUICKLY 4HE COMBINED VELOCITY AND ACCELERATION CHARACTERISTICS OF A SERVOSYSTEM CAN
BE DESCRIBED BY THE FREQUENCY RESPONSE OF THE TRACKING LOOP WHICH ACTS ESSENTIALLY LIKE
A LOW PASS FILTER )NCREASING THE BANDWIDTH INCREASES THE QUICKNESS OF THE SERVOSYS
TEM AND ITS ABILITY TO FOLLOW A STRONG STEADY SIGNAL CLOSELY (OWEVER A TYPICAL TARGET
CAUSES SCINTILLATION OF THE ECHO SIGNAL GIVING ERRONEOUS ERROR DETECTOR OUTPUTS AND AT
LONG RANGE THE ECHO IS WEAK ALLOWING RECEIVER NOISE TO CAUSE ADDITIONAL RANDOM FLUC
TUATIONS ON THE ERROR DETECTOR OUTPUT #ONSEQUENTLY A WIDE SERVO BANDWIDTH WHICH
REDUCES LAG ERRORS ALLOWS THE NOISE TO CAUSE GREATER ERRONEOUS MOTIONS OF THE TRACKING
SYSTEM 4HEREFORE FOR BEST OVERALL PERFORMANCE IT IS NECESSARY TO LIMIT THE SERVO BAND
WIDTH TO THE MINIMUM NECESSARY TO MAINTAIN A REASONABLY SMALL TRACKING LAG ERROR
4HERE IS AN OPTIMUM BANDWIDTH THAT MAY BE CHOSEN TO MINIMIZE THE AMPLITUDE OF
THE TOTAL ERRONEOUS OUTPUTS INCLUDING BOTH TRACKING LAG AND RANDOM NOISE DEPENDING
UPON THE TARGET ITS TRAJECTORY AND OTHER RADAR PARAMETERS
4HE OPTIMUM BANDWIDTH FOR ANGLE TRACKING IS RANGE DEPENDENT ! TARGET WITH TYPICAL
VELOCITY AT LONG RANGE HAS LOW ANGLE RATES AND A LOW 3.2 AND A NARROWER SERVO PASSBAND
WILL FOLLOW THE TARGET WITH REASONABLY SMALL TRACKING LAG WHILE MINIMIZING THE RESPONSE
TO RECEIVER THERMAL NOISE !T CLOSE RANGE THE SIGNAL IS STRONG OVERRIDING RECEIVER NOISE
BUT TARGET ANGLE SCINTILLATION ERRORS PROPORTIONAL TO THE ANGULAR SPAN OF THE TARGET ARE LARGE
! WIDER SERVO BANDWIDTH IS NEEDED AT CLOSE RANGE TO KEEP TRACKING LAG WITHIN REASONABLE
VALUES BUT IT MUST NOT BE WIDER THAN NECESSARY OR THE TARGET ANGLE SCINTILLATION ERRORS
WHICH INCREASE INVERSELY PROPORTIONAL TO TARGET RANGE MAY BECOME EXCESSIVE
4HE LOW PASS CLOSED LOOP CHARACTERISTIC OF A SERVOSYSTEM IS UNITY AT ZERO FREQUENCY
TYPICALLY REMAINING NEAR THIS VALUE UP TO A FREQUENCY NEAR THE LOW PASS CUTOFF WHERE
IT MAY PEAK UP TO HIGHER GAIN AS SHOWN IN &IGURE A 4HE PEAKING IS AN INDICATION
OF SYSTEM INSTABILITY BUT IS ALLOWED TO BE AS HIGH AS TOLERABLE TYPICALLY TO ABOUT D"
ABOVE UNITY GAIN TO OBTAIN MAXIMUM BANDWIDTH FOR A GIVEN SERVOMOTOR DRIVE SYSTEM
3YSTEM ! IN &IGURE A IS A CASE OF EXCESSIVE PEAKING OF ABOUT D" 4HE EFFECT OF
THE PEAKING IS OBSERVED BY APPLYING A STEP ERROR INPUT TO THE SERVOSYSTEM 4HE PEAKING
OF THE LOW PASS CHARACTERISTIC RESULTS IN AN OVERSHOOT WHEN THE ANTENNA AXIS MOVES TO
ALIGN WITH THE TARGET (IGH PEAKING CAUSES A LARGE OVERSHOOT AND A RETURN TO THE TARGET
WITH ADDITIONAL OVERSHOOT )N THE EXTREME AS IN SYSTEM ! SHOWN IN &IGURE B
THE ANTENNA ZEROS IN ON THE TARGET WITH A DAMPED OSCILLATION !N OPTIMUM SYSTEM
COMPROMISE BETWEEN SPEED OF RESPONSE AND OVERSHOOT AS IN SYSTEM " ALLOWS THE
ANTENNA TO MAKE A SMALL OVERSHOOT WITH REASONABLY RAPID EXPONENTIAL MOVEMENT BACK
TO THE TARGET 4HIS CORRESPONDS TO ABOUT D" PEAKING OF THE CLOSED LOOP LOW PASS
CHARACTERISTIC
4HE RESONANT FREQUENCY OF THE ANTENNA AND SERVOSYSTEM STRUCTURE INCLUDING THE
STRUCTURE FOUNDATION WHICH IS A CRITICAL ITEM MUST BE KEPT WELL ABOVE THE BANDWIDTH
OF THE SERVOSYSTEM OTHERWISE THE SYSTEM CAN OSCILLATE AT THE RESONANT FREQUENCY
! FACTOR OF AT LEAST IS DESIRABLE FOR THE RATIO OF SYSTEM RESONANCE FREQUENCY TO SERVO
BANDWIDTH (IGH RESONANT FREQUENCY IS DIFFICULT TO OBTAIN WITH A LARGE ANTENNA SUCH
AS THE !.&01 RADAR WITH A FT DISH BECAUSE OF THE LARGE MASS OF THE SYSTEM
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&)'52% A #LOSED LOOP FREQUENCY RESPONSE CHARACTERISTICS OF TWO
SERVOSYSTEMS AND B THEIR CORRESPONDING TIME RESPONSE TO A STEP INPUT
4HE RATIO WAS PUSHED TO A VERY MINIMUM OF ABOUT TO OBTAIN SERVOSYSTEM BANDWIDTH
OF THE SPECIFIED (Z ! SMALLER RADAR WITH A FT DISH FOR EXAMPLE CAN PROVIDE A
SERVOSYSTEM BANDWIDTH UP TO OR (Z WITH CONVENTIONAL DESIGN
,OCKE DESCRIBES METHODS FOR CALCULATING ANGLE TRACKING LAG FOR A GIVEN TARGET
TRAJECTORY VERSUS TIME AND SET OF SERVOSYSTEM CHARACTERISTICS 2ANGE TRACKING LAGS
MAY BE SIMILARLY CALCULATED BUT WITH TYPICAL INERTIALESS ELECTRONIC TRACKING SYSTEMS
TRACKING LAGS ARE USUALLY NEGLIGIBLE
%LECTRONICALLY STEERABLE ARRAYS PROVIDE A MEANS FOR INERTIALESS ANGLE TRACKING
(OWEVER BECAUSE OF THIS CAPABILITY THE SYSTEM CAN TRACK MULTIPLE TARGETS BY RAPIDLY
SWITCHING FROM ONE TO ANOTHER RATHER THAN CONTINUOUSLY TRACKING A SINGLE TARGET
4HE TRACKER SIMPLY PLACES ITS BEAM AT THE LOCATION WHERE THE TARGET IS EXPECTED
CORRECTS FOR THE POINTING ERROR BY CONVERTING ERROR VOLTAGES WITH KNOWN ANGLE ERROR
SENSITIVITY TO UNITS OF ANGLE AND MOVES TO THE NEXT TARGET 4HE SYSTEM DETERMINES
WHERE THE TARGET WAS AND FROM CALCULATIONS OF TARGET VELOCITY AND ACCELERATION PRE
DICTS WHERE IT SHOULD BE THE NEXT TIME THE BEAM LOOKS AT THE TARGET 4HE LAG ERROR IN
THIS CASE IS DEPENDENT ON MANY FACTORS INCLUDING THE ACCURACY OF THE VALUE OF ANGLE
SENSITIVITY USED TO CONVERT ERROR VOLTAGES TO ANGULAR ERROR THE SIZE OF THE PREVIOUS
TRACKING ERROR AND THE TIME INTERVAL BETWEEN LOOKS
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Ê, Ê/, 2ANGE TRACKING IS ACCOMPLISHED BY CONTINUOUSLY MEASURING THE TIME DELAY BETWEEN
THE TRANSMISSION OF AN 2& PULSE AND THE ECHO SIGNAL RETURNED FROM THE TARGET AND CON
VERTING THE ROUNDTRIP DELAY TO UNITS OF DISTANCE 4HE RANGE MEASUREMENT IS THE MOST
PRECISE POSITION COORDINATE MEASUREMENT OF THE RADAR TYPICALLY WITH HIGH 3.2 IT CAN
BE WITHIN A FEW METERS AT HUNDREDS OF MILES RANGE 2ANGE TRACKING USUALLY PROVIDES
THE MAJOR MEANS FOR DISCRIMINATING THE DESIRED TARGET FROM OTHER TARGETS ALTHOUGH
DOPPLER FREQUENCY AND ANGLE DISCRIMINATION ARE ALSO USED BY PERFORMING RANGE GAT
ING TIME GATING TO ELIMINATE THE ECHO OF OTHER TARGETS AT DIFFERENT RANGES FROM THE
ERROR DETECTOR OUTPUTS 4HE RANGE TRACKING CIRCUITRY IS ALSO USED FOR ACQUIRING A DESIRED
TARGET 2ANGE TRACKING REQUIRES NOT ONLY THAT THE TIME OF TRAVEL OF THE PULSE TO AND FROM
THE TARGET BE MEASURED BUT ALSO THAT THE RETURN IS IDENTIFIED AS A TARGET RATHER THAN NOISE
AND A RANGE TIME HISTORY OF THE TARGET BE MAINTAINED
!LTHOUGH THIS DISCUSSION IS FOR TYPICAL PULSE TYPE TRACKING RADARS RANGE MEASURE
MENT MAY ALSO BE PERFORMED WITH #7 RADARS USING &- #7 A FREQUENCY MODULATED
#7 THAT IS TYPICALLY A LINEAR RAMP &- 4HE TARGET RANGE IS DETERMINED BY THE RANGE
RELATED FREQUENCY DIFFERENCE BETWEEN THE ECHO FREQUENCY RAMP AND THE FREQUENCY OF
THE RAMP BEING TRANSMITTED 4HE PERFORMANCE OF &- #7 SYSTEMS WITH CONSIDERATION
OF THE DOPPLER EFFECT IS DESCRIBED IN 3HERMAN
!CQUISITION 4HE FIRST FUNCTION OF THE RANGE TRACKER IS ACQUISITION OF A DESIRED
TARGET !LTHOUGH THIS IS NOT A TRACKING OPERATION IT IS A NECESSARY FIRST STEP BEFORE RANGE
TRACKING OR ANGLE TRACKING MAY TAKE PLACE IN A TYPICAL RADAR 3OME KNOWLEDGE OF TARGET
ANGULAR LOCATION IS NECESSARY FOR PENCIL BEAM TRACKING RADARS TO POINT THEIR TYPICALLY
NARROW ANTENNA BEAMS IN THE DIRECTION OF THE TARGET 4HIS INFORMATION CALLED DESIGNA
TION DATA MAY BE PROVIDED BY SURVEILLANCE RADAR OR SOME OTHER SOURCE )T MAY BE SUF
FICIENTLY ACCURATE TO PLACE THE PENCIL BEAM ON THE TARGET OR IT MAY REQUIRE THE TRACKER
TO SCAN A LARGER REGION OF UNCERTAINTY 4HE RANGE TRACKING PORTION OF THE RADAR HAS THE
ADVANTAGE OF SEEING ALL TARGETS WITHIN THE BEAM FROM CLOSE RANGE OUT TO THE MAXIMUM
RANGE OF THE RADAR )T TYPICALLY BREAKS THIS RANGE INTO SMALL INCREMENTS EACH OF WHICH
MAY BE SIMULTANEOUSLY EXAMINED FOR THE PRESENCE OF A TARGET 7HEN BEAM SCANNING IS
NECESSARY THE RANGE TRACKER EXAMINES THE INCREMENTS SIMULTANEOUSLY FOR SHORT PERIODS
SUCH AS S MAKES ITS DECISION ABOUT THE PRESENCE OF A TARGET AND ALLOWS THE BEAM TO
MOVE TO A NEW LOCATION IF NO TARGET IS PRESENT 4HIS PROCESS IS TYPICALLY CONTINUOUS FOR
MECHANICAL TYPE TRACKERS THAT MOVE THE BEAM SLOWLY ENOUGH THAT A TARGET WILL REMAIN
WELL WITHIN THE BEAM FOR THE SHORT EXAMINATION PERIOD OF THE RANGE INCREMENTS
4ARGET ACQUISITION INVOLVES CONSIDERATION OF THE 3. THRESHOLD AND INTEGRATION TIME
NEEDED TO ACCOMPLISH A GIVEN PROBABILITY OF DETECTION WITH A GIVEN FALSE ALARM RATE
SIMILAR TO SURVEILLANCE RADAR (OWEVER HIGH FALSE ALARM RATES AS COMPARED WITH VALUES
USED FOR SURVEILLANCE RADARS ARE USED BECAUSE THE OPERATOR KNOWS THAT THE TARGET IS PRES
ENT AND OPERATOR FATIGUE FROM FALSE ALARMS WHEN WAITING FOR A TARGET IS NOT INVOLVED
/PTIMUM FALSE ALARM RATES ARE SELECTED ON THE BASIS OF PERFORMANCE OF ELECTRONIC CIR
CUITS THAT OBSERVE EACH RANGE INTERVAL TO DETERMINE WHICH INTERVAL HAS THE TARGET ECHO
! TYPICAL TECHNIQUE IS TO SET A VOLTAGE THRESHOLD SUFFICIENTLY HIGH TO PREVENT MOST
NOISE PEAKS FROM CROSSING THE THRESHOLD BUT SUFFICIENTLY LOW THAT A WEAK SIGNAL MAY
CROSS !N OBSERVATION IS MADE AFTER EACH TRANSMITTER PULSE AS TO WHETHER IN THE RANGE
INTERVAL BEING EXAMINED THE THRESHOLD HAS BEEN CROSSED 4HE INTEGRATION TIME ALLOWS THE
RADAR TO MAKE THIS OBSERVATION SEVERAL TIMES BEFORE DECIDING IF THERE IS A TARGET PRESENT
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4HE MAJOR DIFFERENCE BETWEEN NOISE AND A TARGET ECHO IS THAT NOISE SPIKES EXCEEDING THE
THRESHOLD ARE RANDOM BUT IF A TARGET IS PRESENT THE THRESHOLD CROSSINGS ARE MORE REGULAR
/NE TYPICAL SYSTEM SIMPLY COUNTS THE NUMBER OF THRESHOLD CROSSINGS OVER THE INTEGRATION
PERIOD AND IF CROSSINGS OCCUR FOR MORE THAN HALF THE NUMBER OF TIMES THAT THE RADAR HAS
TRANSMITTED A TARGET IS INDICATED AS BEING PRESENT )F THE RADAR PULSE REPETITION FREQUENCY
IS (Z AND THE INTEGRATION TIME IS S THE RADAR WILL OBSERVE THRESHOLD CROSSINGS
IF THERE IS A STRONG AND STEADY TARGET (OWEVER BECAUSE THE ECHO FROM A WEAK TARGET
COMBINED WITH NOISE MAY NOT ALWAYS CROSS THE THRESHOLD A LIMIT MAY BE SET SUCH AS
CROSSINGS THAT MUST OCCUR DURING THE INTEGRATION PERIOD FOR A DECISION THAT A TARGET IS
PRESENT &OR EXAMPLE PERFORMANCE ON A NON SCINTILLATING TARGET HAS A PROBABILITY
OF DETECTION AT A D" PER PULSE 3.2 AND A FALSE ALARM PROBABILITY OF n 4HE !.
&03 AND !.&01 INSTRUMENTATION RADARS USE THESE DETECTION PARAMETERS WITH CONTIGUOUS RANGE GATES OF YD EACH FOR ACQUISITION 4HE GATES GIVE COVERAGE OF A
NMI RANGE INTERVAL AT THE RANGE WHERE THE TARGET IS EXPECTED POSSIBLY FROM COARSE RANGE
DESIGNATION FROM SEARCH RADAR
2ANGE 4RACKING /NCE A TARGET IS ACQUIRED IN RANGE IT IS DESIRABLE TO FOLLOW THE
TARGET IN THE RANGE COORDINATE TO PROVIDE DISTANCE INFORMATION OR SLANT RANGE TO THE TAR
GET !PPROPRIATE TIMING PULSES PROVIDE RANGE GATING SO THE ANGLE TRACKING CIRCUITS AND
!'# CIRCUITS LOOK AT ONLY THE SHORT RANGE INTERVAL OR TIME INTERVAL WHEN THE DESIRED
ECHO PULSE IS EXPECTED 4HE RANGE TRACKING OPERATION IS PERFORMED BY CLOSED LOOP
TRACKING SIMILAR TO THE ANGLE TRACKER %RROR IN CENTERING THE RANGE GATE ON THE TARGET
ECHO PULSE IS SENSED ERROR VOLTAGES ARE GENERATED AND CIRCUITRY IS PROVIDED TO RESPOND
TO THE ERROR VOLTAGE BY CAUSING THE GATE TO MOVE IN A DIRECTION TO RECENTER ON THE TARGET
ECHO PULSE
4HE RANGE TRACKING ERROR MAY BE SENSED IN MANY WAYS 4HE MOST COMMONLY USED
METHOD IS THE EARLY AND LATE GATE TECHNIQUE SEE &IGURE 4HESE GATES ARE TIMED
SO THAT THE EARLY GATE OPENS AT THE BEGINNING OF THE MAIN RANGE GATE AND CLOSES AT THE
CENTER OF THE MAIN GATE 4HE LATE GATE OPENS AT THE CENTER AND CLOSES AT THE END OF
THE MAIN RANGE GATE 4HE EARLY AND LATE GATES EACH ALLOW THE TARGET VIDEO TO CHARGE
CAPACITORS DURING THE TIME WHEN THE GATES ARE OPEN 4HE CAPACITORS ACT AS INTEGRATORS
4HE EARLY GATE CAPACITOR CHARGES TO A VOLTAGE PROPORTIONAL TO THE AREA OF THE FIRST HALF
OF THE TARGET VIDEO PULSE AND THE LATE GATE CAPACITOR CHARGES NEGATIVELY PROPORTION
ALLY TO THE LATE HALF OF THE TARGET VIDEO 7HEN THE GATES ARE PROPERLY CENTERED ABOUT A
SYMMETRICAL VIDEO PULSE THE CAPACITORS ARE EQUALLY CHARGED 3UMMING THEIR CHARGE
VOLTAGES YIELDS A ZERO OUTPUT
7HEN THE GATES ARE NOT CENTERED ABOUT THE TARGET VIDEO SO THAT THE EARLY GATE
EXTENDS PAST THE CENTER OF THE TARGET VIDEO THE EARLY GATE CAPACITOR CHARGED POSI
TIVELY RECEIVES A GREATER CHARGE 4HE LATE GATE SEES ONLY A SMALL PORTION OF THE PULSE
RESULTING IN A SMALLER NEGATIVE CHARGE 3UMMING THE CAPACITOR VOLTAGES RESULTS IN A
NEGATIVE OUTPUT /VER A RANGE OF ERRORS OF APPROXIMATELY o OF THE TARGET VIDEO
PULSE WIDTH THE VOLTAGE OUTPUT IS ESSENTIALLY A LINEAR FUNCTION OF TIMING ERROR AND
OF A POLARITY CORRESPONDING TO THE DIRECTION OF ERROR $URING ACQUISITION THE TARGET
IS CENTERED IN THE YD ACQUISITION GATE BY RANGE TRACKING TECHNIQUES DESCRIBED
AS FOLLOWS AND THE GATE IS REDUCED TO APPROXIMATELY THE WIDTH OF THE RADAR TRANSMIT
PULSE FOR NORMAL TRACKING
-ANY RADAR RANGE TRACKING SYSTEMS USE HIGH SPEED SAMPLING CIRCUITRY TO TAKE THREE
TO FIVE SAMPLES IN THE VICINITY OF THE ECHO VIDEO PULSE 4HE AMPLITUDES OF THE SAMPLES
ON THE LEADING AND LAGGING HALVES OF THE PULSE ARE COMPARED FOR RANGE ERROR SENSING
SIMILAR TO THE COMPARISON OF AMPLITUDES IN THE EARLY LATE GATES RANGE TRACKER
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&)'52% %ARLY AND LATE GATE RANGE ERROR SENSING CIRCUIT
)N SOME CASES LEADING OR LAGGING EDGE RANGE TRACKING IS DESIRED 4HIS HAS BEEN
ACCOMPLISHED IN SOME APPLICATIONS BY SIMPLY ADDING A BIAS TO MOVE THE ERROR SENSING
GATES EITHER TO LEAD OR LAG THE CENTER OF THE TARGET 4HIS PROVIDES SOME REJECTION BY THE
GATES OF UNDESIRED RETURNS THAT MIGHT OCCUR NEAR THE TARGET SUCH AS THE ECHOES FROM
OTHER NEARBY TARGETS 4HRESHOLD DEVICES ARE ALSO USED AS LEADING OR LAGGING EDGE
TRACKERS BY OBSERVING WHEN THE TARGET VIDEO EXCEEDS A GIVEN THRESHOLD LEVEL 4HE
POINT OF CROSSING THE THRESHOLD IS USED TO TRIGGER GATING CIRCUITS TO READ OUT A TARGET
RANGE FROM TIMING DEVICES OR TO GENERATE A SYNTHETIC TARGET PULSE
4HE RANGE TRACKING LOOP IS CLOSED BY USING THE RANGE ERROR DETECTOR OUTPUT TO REPO
SITION RANGE GATES AND CORRECT RANGE READOUT /NE TECHNIQUE USES A HIGH SPEED DIGITAL
COUNTER DRIVEN BY A STABLE OSCILLATOR 4HE COUNTER IS RESET TO ZERO AT THE TIME OF THE
TRANSMIT PULSE 4ARGET RANGE IS REPRESENTED BY A NUMBER STORED IN A DIGITAL REGISTER AS
SHOWN IN &IGURE ! COINCIDENCE CIRCUIT SENSES WHEN THE DIGITAL COUNTER REACHES THE
NUMBER IN THE RANGE REGISTER AND GENERATES THE RANGE GATE AS INDICATED IN THE BLOCK DIA
GRAM SHOWN IN &IGURE ! RANGE ERROR SENSED BY THE RANGE ERROR DETECTOR RESULTS IN AN
ERROR VOLTAGE THAT DRIVES A VOLTAGE CONTROLLED VARIABLE FREQUENCY OSCILLATOR TO INCREASE
OR DECREASE THE COUNT IN THE RANGE REGISTER DEPENDING ON THE POLARITY OF THE ERROR VOLT
AGE 4HIS CHANGES THE NUMBER IN THE RANGE REGISTER TOWARD THE VALUE CORRESPONDING TO
THE RANGE OF THE TARGET 2ANGE READOUT IS ACCOMPLISHED BY READING THE NUMBER IN THE
REGISTER WHERE FOR EXAMPLE EACH BIT MAY CORRESPOND TO A YD RANGE STEP
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&)'52% $IGITAL RANGE TRACKER OPERATION
!NOTHER TECHNIQUE IS TO USE A PAIR OF OSCILLATORSˆONE CONTROLLING THE TRANSMITTER
TRIGGER AND THE OTHER CONTROLLING THE RANGE GATE 4HE RANGE RATE IS CONTROLLED BY THE
BEAT FREQUENCY BETWEEN THE OSCILLATORS WHERE ONE IS FREQUENCY CONTROLLED BY THE RANGE
&)'52% "LOCK DIAGRAM OF A DIGITAL RANGE TRACKER
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ERROR DETECTOR OUTPUT VOLTAGE 4HE BEAT FREQUENCY IS A SMALL FRACTION OF ONE (Z AND IS
BETTER VISUALIZED AS A PHASE RATE BETWEEN THE TRANSMIT PULSE CYCLE AND CYCLE OF THE RANGE
GATE 4HE CHANGING PHASE CAUSES THE RANGE GATE TO FOLLOW A MOVING TARGET
4HE ELECTRONIC RANGE TRACKER IS INERTIALESS ALLOWING ANY DESIRED SLEW SPEED AND PRO
VIDES FLEXIBILITY FOR CONVENIENTLY GENERATING ACQUISITION GATES FOR AUTOMATIC DETECTION
CIRCUITRY AS WELL AS TRANSMITTER TRIGGER AND PRE TRIGGER PULSES 4RACKING BANDWIDTH IS USU
ALLY LIMITED TO THAT NECESSARY FOR TRACKING TO MINIMIZE LOSS OF TRACK TO FALSE TARGETS AND
COUNTERMEASURES -ANY OTHER ELECTRONIC RANGE TRACKING TECHNIQUES ALSO OFFERING MOST OF
THESE ADVANTAGES ARE USED
NTH 4IME !ROUND 4RACKING 4O EXTEND UNAMBIGUOUS RANGE BY REDUCING THE
02& INCREASES THE ACQUISITION TIME AND REDUCES THE DATA RATE ! SOLUTION TO THIS PROB
LEM IS CALLED NTH TIME AROUND TRACKING WHICH AVOIDS TRANSMITTING AT THE TIME THAT AN
ECHO IS EXPECTED TO ARRIVE AND CAN RESOLVE THE RANGE AMBIGUITY 4HIS ALLOWS THE RADAR
TO OPERATE AT HIGH 02& AND TRACK UNAMBIGUOUSLY TO LONG RANGES WHERE SEVERAL PULSES
MAY BE PROPAGATING IN SPACE TO AND FROM THE TARGET 4HE TECHNIQUE IS USEFUL ONLY WHEN
A TARGET IS BEING TRACKED $URING ACQUISITION THE RADAR MUST LOOK AT THE REGION BETWEEN
TRANSMITTER PULSES AND UPON INITIAL ACQUISITION IT CLOSES THE RANGE AND ANGLE TRACK
ING LOOPS WITHOUT RESOLVING THE RANGE AMBIGUITY 4HE NEXT STEP IS TO FIND WHICH RANGE
INTERVAL OR BETWEEN WHICH PAIR OF TRANSMIT PULSES THE TARGET IS LOCATED 4HE ZONE N IS
DETERMINED BY CODING A TRANSMIT PULSE AND COUNTING HOW MANY PULSES RETURN BEFORE
THE CODED PULSE RETURNS
)NSTRUMENTATION RADARS PROVIDE NTH TIME AROUND TRACKING CAPABILITY BECAUSE BEA
CONS ARE USED ON ROCKETS AND SPACE VEHICLES TO PROVIDE SUFFICIENT SIGNAL LEVEL AT VERY
LONG RANGES
4O PREVENT THE TARGET ECHO FROM BEING BLANKED BY A TRANSMIT PULSE IT IS NECESSARY
TO SENSE WHEN THE TARGET IS APPROACHING AN INTERFERENCE REGION AND SHIFT THE REGION
4HIS IS ACCOMPLISHED BY CHANGING THE 02& OR ALTERNATELY DELAYING GROUPS OF PULSES
EQUAL TO THE NUMBER OF PULSES IN PROPAGATION 4HIS CAN BE PERFORMED AUTOMATICALLY
TO PROVIDE AN OPTIMUM 02& SHIFT OR TO ALTERNATELY DELAY PULSE GROUPS OF THE CORRECT
NUMBER OF PULSES
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$UAL "AND -ONOPULSE $UAL BAND MONOPULSE CAN BE EFFICIENTLY ACCOMMO
DATED ON A SINGLE ANTENNA TO COMBINE THE COMPLEMENTARY FEATURES OF TWO 2& BANDS ! USEFUL COMBINATION OF BANDS IS 8 BAND '(Z AND +A BAND '(Z 4HE
8 BAND OPERATION PROVIDES THE EXPECTED MICROWAVE PERFORMANCE OF GOOD RADAR RANGE
AND PRECISE TRACKING )TS WEAKNESS IS THE LOW ANGLE MULTIPATH REGION AND THE AVAILABIL
ITY OF ELECTRONIC COUNTERMEASURES IN THE BAND 4HE +A BAND ALTHOUGH ATMOSPHERIC AND
RAIN ATTENUATION LIMITED PROVIDES MUCH GREATER TRACKING PRECISION IN THE LOW ANGLE
MULTIPATH REGION AND A SECOND AND MORE DIFFICULT BAND THAT THE ELECTRONIC COUNTERMEA
SURES TECHNIQUES MUST COVER
! .AVAL 2ESEARCH ,ABORATORY SYSTEM CALLED 42!+8 4RACKING 2ADAR !T +A AND
8 BANDS WAS DESIGNED FOR INSTRUMENTATION RADAR APPLICATIONS FOR MISSILE AND TRAINING
RANGES )TS PURPOSE WAS TO ADD PRECISION TRACKING ON TARGETS ESSENTIALLY TO hSPLASHv
AND PROVIDE PRECISION TRACKING AT +A BAND IN AN ENVIRONMENT OF 8 BAND COUNTERMEA
SURE EXPERIMENTS
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! SIMILAR 8 AND +A BAND SYSTEM WAS DEVELOPED BY (OLLANDSE 3IGNAALAPPARATEN OF
THE .ETHERLANDS FOR TACTICAL APPLICATION 4HE LAND BASED VERSION CALLED &,9 #!4#(%2
IS PART OF A MOBILE ANTI AIR WARFARE SYSTEM !NOTHER VERSION '/!, +%%0%2 IS FOR
A SHIPBOARD ANTI AIR WARFARE APPLICATION FOR THE FIRE CONTROL OF 'ATLING GUNS "OTH
SYSTEMS TAKE FULL ADVANTAGE OF THE TWO BANDS TO PROVIDE PRECISION TRACKING IN MULTIPATH
AND ELECTRONIC COUNTERMEASURES ENVIRONMENTS
-IRROR 3CANNED !NTENNA )NVERSE #ASSEGRAIN !N ANTENNA TECHNIQUE THAT
USES A MOVABLE 2& MIRROR FOR SCANNING THE BEAM CALLED A MIRROR SCANNED ANTENNA OR
INVERSE #ASSEGRAIN PROVIDES USEFUL APPLICATIONS TO MONOPULSE RADAR 4HE TECHNIQUE
USES A RADOME SUPPORTED WIRE GRID PARABOLOID THAT REFLECTS PARALLEL POLARIZED FEED
ENERGY 4HE BEAM POLARIZED PARALLEL TO THE GRID IS COLLIMATED BY THE PARABOLOID AND
IS REFLECTED BY A FLAT MOVEABLE POLARIZATION ROTATING MIRROR 4HE BASIC POLARIZATION
ROTATING MIRROR IS A FLAT METAL SURFACE WITH A GRID OF WIRES LOCATED A QUARTER WAVE
LENGTH ABOVE THE METAL SURFACE AND ORIENTED AT — RELATIVE TO THE 2& ENERGY REFLECTED
FROM THE PARABOLOID 4HE 2& ENERGY MAY BE VISUALIZED AS BEING COMPOSED OF A
COMPONENT PARALLEL TO AND REFLECTING FROM THE GRID AND A COMPONENT PERPENDICULAR
TO AND PASSING THROUGH THE GRID TO REFLECT FROM THE METAL MIRROR SURFACE BELOW "Y
TRAVELING THE QUARTER WAVESPACE TWICE THIS COMPONENT IS SHIFTED BY — IN PHASE
7HEN ADDED TO THE REFLECTION FROM THE GRID IT RESULTS IN A — CHANGE IN POLARIZA
TION 4HE TOTAL REFLECTED ENERGY FROM THE MIRROR ROTATED BY — WILL EFFICIENTLY PASS
THROUGH THE WIRE GRID PARABOLOID 4HE ADVANTAGES ARE AS FOLLOWS 4HE MIRROR AND
ITS DRIVE MECHANISM ARE THE ONLY MOVING PARTS FOR BEAM MOVEMENT 4HE FEED AND
RADOME SUPPORTED PARABOLOID REMAIN FIXED 4HE BEAM MOVEMENT IS BY SPECULAR
REFLECTION TWICE THE ANGLE OF THE MIRROR TILT 4HIS PROVIDES A COMPACT STRUCTURE FOR
A GIVEN ANGLE COVERAGE REQUIREMENT 4HE NORMALLY LIGHTWEIGHT MIRROR AND THE
BEAM DISPLACEMENT VERSUS MIRROR TILT ALLOW REDUCED SIZE AND VERY RAPID BEAM
SCAN WITH LOW SERVO DRIVE POWER
4HE COMPACTNESS AND LIGHTNESS ARE PARTICULARLY ATTRACTIVE FOR AIRBORNE APPLICATIONS
SUCH AS THE 4HOMPSON #3& !GAVE RADAR IN THE 3UPER %NTENDARDS WHICH DETERMINES
TARGET RANGE AND DESIGNATION DATA FOR THE %XOCET MISSILE )T IS A COMPACT MONOPULSE
ROLL AND PITCH STABILIZED RADAR WITH — AZIMUTH AND — ELEVATION SCAN 4HE )SRAELI
%LTA SUBSIDIARY OF )SRAELI !IRCRAFT )NDUSTRIES ALSO DEVELOPED AN AIRBORNE TRACKING RADAR
USING THIS ANTENNA TECHNOLOGY FOR AIR TO AIR COMBAT AND GROUND WEAPON DELIVERY
! GROUND OR SHIPBOARD BASED EXPERIMENTAL MIRROR ANTENNA SYSTEM CONCEPT WAS
DEVELOPED WITH DUAL BAND MONOPULSE CAPABILITY '(Z AND '(Z BANDS 4HE
OBJECTIVE INCLUDED HIGH SPEED BEAM MOVEMENT FOR HIGH DATA RATE $ SURVEILLANCE
AND MULTITARGET PRECISION TRACKING $UAL BAND POLARIZATION TWIST MIRROR DESIGN WAS
ACCOMPLISHED WITH A TWO LAYER MIRROR GRID CONFIGURATION
/N !XIS 4RACKING 4HE BEST RADAR TRACKING PERFORMANCE IS USUALLY ACCOMPLISHED
WHEN THE TARGET IS ESSENTIALLY ON THE RADAR ANTENNA AXIS 4HEREFORE FOR MAXIMUM
PRECISION TRACKING IT IS DESIRABLE TO MINIMIZE LAG AND OTHER ERROR SOURCES AFFECTING
THE BEAM POINTING ! TECHNIQUE CALLED ON AXIS TRACKING WAS DEVELOPED TO MINIMIZE
RADAR AXIS DEVIATION FROM THE TARGET BY PREDICTION AND OPTIMUM FILTERING WITHIN THE
TRACKING LOOP 4HE TECHNIQUE IS PARTICULARLY EFFECTIVE WHEN THE TARGET TRAJECTORY IS
KNOWN APPROXIMATELY SUCH AS WHEN TRACKING SATELLITES IN ORBIT OR A BALLISTIC TARGET !
COMPUTER IN THE TRACKING LOOP CAN CAUSE THE RADAR TO FOLLOW AN ESTIMATED SET OF ORBITAL
PARAMETERS FOR EXAMPLE )T ALSO PERFORMS OPTIMUM FILTERING OF RADAR ANGLE ERROR
DETECTOR OUTPUT TO GENERATE AN ERROR TREND FROM WHICH IT CAN UPDATE THE ASSUMED SET
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OF ORBITAL PARAMETERS TO CORRECT THE RADAR BEAM MOVEMENT TO UPDATE THE ORIGINAL
SET OF ORBITAL PARAMETERS AND BY THIS MEANS THE RADAR ANTENNA AXIS CAN BE HELD ON
TARGET WITH MINIMUM ERROR
)MPROVED TRACKING CAN ALSO BE PROVIDED ON OTHER TARGETS WHERE THE APPROXIMATE
TRAJECTORY CAN BE ANTICIPATED (OWEVER PERFORMANCE OF ON AXIS TRACKING IS LIMITED
WHEN TRACKING TARGETS WITH UNANTICIPATED MANEUVERS
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4HERE ARE MANY SOURCES OF ERROR IN RADAR TRACKING PERFORMANCE &ORTUNATELY MOST ARE
INSIGNIFICANT EXCEPT FOR VERY HIGH PRECISION TRACKING RADAR APPLICATIONS SUCH AS RANGE
INSTRUMENTATION WHERE THE ANGLE PRECISION REQUIRED MAY BE OF THE ORDER OF MRAD
MRAD OR MILLIRADIAN IS ONE THOUSANDTH OF A RADIAL OR THE ANGLE SUBTENDED BY M
CROSS RANGE AT M RANGE -ANY SOURCES OF ERROR CAN BE AVOIDED OR REDUCED BY
RADAR DESIGN OR MODIFICATION OF THE TRACKING GEOMETRY #OST IS A MAJOR FACTOR IN PROVID
ING HIGH PRECISION TRACKING CAPABILITY 4HEREFORE IT IS IMPORTANT TO KNOW HOW MUCH
ERROR CAN BE TOLERATED WHICH SOURCES OF ERROR AFFECT THE APPLICATION AND WHAT IS THE
MOST COST EFFECTIVE MEANS TO SATISFY THE ACCURACY REQUIREMENTS
"ECAUSE TRACKING RADARS TRACK TARGETS NOT ONLY IN ANGLE BUT ALSO IN RANGE AND SOME
TIMES IN DOPPLER THE ERRORS IN EACH OF THESE TARGET PARAMETERS MUST BE CONSIDERED ON
MOST ERROR BUDGETS 4HE REST OF THIS CHAPTER WILL PROVIDE A GUIDE FOR DETERMINING THE
SIGNIFICANT ERROR SOURCES AND THEIR MAGNITUDES
)T IS IMPORTANT TO RECOGNIZE WHAT THE ACTUAL RADAR INFORMATION OUTPUT IS &OR A
MECHANICALLY MOVED ANTENNA THE ANGLE TRACKING OUTPUT IS USUALLY OBTAINED FROM THE
SHAFT POSITION OF THE ELEVATION AND AZIMUTH ANTENNA AXES !BSOLUTE TARGET LOCATION
RELATIVE TO EARTH COORDINATES WILL INCLUDE THE ACCURACY OF THE SURVEY OF THE ANTENNA
PEDESTAL SITE
0HASED ARRAY INSTRUMENTATION RADAR SUCH AS THE -ULTI OBJECT 4RACKING 2ADAR
-/42 PROVIDE ELECTRONIC BEAM MOVEMENT OVER A LIMITED SECTOR OF ABOUT o O TO
APPROXIMATELY o O PLUS MECHANICAL MOVEMENT OF THE ANTENNA TO MOVE THE COVERAGE
SECTORn 4HE OUTPUT WILL BE MECHANICAL SHAFT POSITIONS LOCATING THE NORMAL TO THE
ARRAY PLUS DIGITAL ANGLE INFORMATION FROM THE ELECTRONIC BEAM SCAN FOR EACH TARGET
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2ADAR TRACKING OF TARGETS IS PERFORMED BY USE OF THE ECHO SIGNAL REFLECTED FROM A TARGET
ILLUMINATED BY THE RADAR TRANSMIT PULSE 4HIS IS CALLED SKIN TRACKING TO DIFFERENTIATE
IT FROM BEACON TRACKING WHERE A BEACON OR A TRANSPONDER TRANSMITS ITS SIGNAL TO THE
RADAR AND USUALLY PROVIDES A STRONGER POINT SOURCE SIGNAL "ECAUSE MOST TARGETS SUCH
AS AIRCRAFT ARE COMPLEX IN SHAPE THE TOTAL ECHO SIGNAL IS COMPOSED OF THE VECTOR SUM
OF A GROUP OF SUPERIMPOSED ECHO SIGNALS FROM THE INDIVIDUAL PARTS OF THE TARGET SUCH AS
THE ENGINES PROPELLERS FUSELAGE AND WING EDGES 4HE MOTIONS OF A TARGET WITH RESPECT
TO THE RADAR CAUSES THE TOTAL ECHO SIGNAL TO CHANGE WITH TIME RESULTING IN RANDOM
FLUCTUATIONS IN THE RADAR MEASUREMENTS OF THE PARAMETERS OF THE TARGET 4HESE FLUCTUA
TIONS CAUSED BY THE TARGET ONLY EXCLUDING ATMOSPHERIC EFFECTS AND RADAR RECEIVER NOISE
CONTRIBUTIONS ARE CALLED TARGET NOISE
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4HIS DISCUSSION OF TARGET NOISE IS BASED LARGELY ON AIRCRAFT BUT IT IS GENERALLY APPLI
CABLE TO ANY TARGET INCLUDING LAND TARGETS OF COMPLEX SHAPE THAT ARE LARGE WITH RESPECT
TO A WAVELENGTH 4HE MAJOR DIFFERENCE IS IN THE TARGET MOTION BUT THE DISCUSSIONS ARE
SUFFICIENTLY GENERAL TO APPLY TO ANY TARGET SITUATION
4HE ECHO RETURN FROM A COMPLEX TARGET DIFFERS FROM THAT OF A POINT SOURCE BY THE
MODULATIONS THAT ARE PRODUCED BY THE CHANGE IN AMPLITUDE AND RELATIVE PHASE OF THE
RETURNS FROM THE INDIVIDUAL ELEMENTS 4HE WORD MODULATIONS IS USED IN PLURAL FORM
BECAUSE FIVE TYPES OF MODULATION OF THE ECHO SIGNAL THAT ARE CAUSED BY A COMPLEX TARGET
AFFECT RADARS 4HESE ARE AMPLITUDE MODULATION PHASE FRONT MODULATION GLINT POLAR
IZATION MODULATION DOPPLER MODULATION AND PULSE TIME MODULATION RANGE GLINT 4HE
BASIC MECHANISM BY WHICH THE MODULATIONS ARE PRODUCED IS THE MOTION OF THE TARGET
INCLUDING YAW PITCH AND ROLL WHICH CAUSES THE CHANGE IN RELATIVE RANGE OF THE VARIOUS
INDIVIDUAL ELEMENTS WITH RESPECT TO THE RADAR
!LTHOUGH THE TARGET MOTIONS MAY APPEAR SMALL A CHANGE IN RELATIVE RANGE OF THE
PARTS OF A TARGET OF ONLY ONE HALF WAVELENGTH BECAUSE OF THE TWO WAY RADAR SIGNAL
PATH CAUSES A FULL — CHANGE IN RELATIVE PHASE !T 8 BAND THIS IS ABOUT CM WHICH
IS SMALL EVEN COMPARED WITH THE FLEXURE BETWEEN PARTS OF AN AIRCRAFT
4HE FIVE TYPES OF MODULATION CAUSED BY A COMPLEX TARGET ARE DISCUSSED NEXT
!MPLITUDE .OISE !MPLITUDE NOISE IS THE CHANGE IN ECHO SIGNAL AMPLITUDE CAUSED
BY A COMPLEX SHAPED TARGET EXCLUDING THE EFFECTS OF CHANGING TARGET RANGE )T IS THE
MOST OBVIOUS OF THE VARIOUS TYPES OF ECHO SIGNAL MODULATION BY A COMPLEX SHAPED
TARGET AND IS READILY VISUALIZED AS THE FLUCTUATING SUM OF MANY SMALL VECTORS CHANGING
RANDOMLY IN RELATIVE PHASE !LTHOUGH IT IS CALLED NOISE IT MAY INCLUDE PERIODIC COMPO
NENTS !MPLITUDE NOISE TYPICALLY FALLS INTO A LOW FREQUENCY AND HIGH FREQUENCY REGION
OF INTEREST 4HESE CATEGORIES OVERLAP IN SOME RESPECTS BUT IT IS CONVENIENT TO SEPARATE
THE NOISE IN THESE TWO FREQUENCY RANGES BECAUSE THEY ARE GENERATED BY DIFFERENT PHE
NOMENA AND THEY ARE EACH SIGNIFICANT TO DIFFERENT FUNCTIONS OF THE RADAR
,OW &REQUENCY !MPLITUDE .OISE 4HE LOW FREQUENCY AMPLITUDE NOISE IS THE TIME
VARIATION OF THE VECTOR SUM OF THE ECHOES FROM ALL THE REFLECTING SURFACES OF THE TARGET
4HE TIME VARIATION IS VISUALIZED BY CONSIDERING THE TARGET AS A RELATIVELY RIGID BODY
WITH NORMAL YAW PITCH AND ROLL MOTIONS 4HE SMALL CHANGES IN RELATIVE RANGE OF THE
REFLECTORS CAUSED BY THIS MOTION RESULT IN CORRESPONDING hRANDOMv CHANGE IN THE RELA
TIVE PHASES #ONSEQUENTLY THE VECTOR SUM FLUCTUATES RANDOMLY 4YPICALLY TARGET RAN
DOM MOTION IS LIMITED TO SMALL ASPECT CHANGES SUCH THAT THE AMPLITUDES OF THE ECHOES
FROM THE INDIVIDUAL REFLECTORS VARY LITTLE OVER A PERIOD OF A FEW SECONDS AND CHANGE IN
RELATIVE PHASE IS THE MAJOR CONTRIBUTOR %XCEPTIONS ARE LARGE FLAT SURFACES WITH NARROW
REFLECTION PATTERNS
!N EXAMPLE OF A TARGET CONFIGURATION IS A DISTRIBUTION OF REFLECTING SURFACES THAT
CHANGE IN RELATIVE RANGE WITH TARGET MOTION ! TYPICAL PULSE AMPLITUDE TIME FUNCTION IS
A SLOWLY VARYING ECHO AMPLITUDE 4HE LOW FREQUENCY AMPLITUDE NOISE CONTRIBUTES THE
LARGEST PORTION OF THE NOISE MODULATION DENSITY AND IS CONCENTRATED MAINLY BELOW ABOUT
(Z AT 8 BAND 4HE AMPLITUDE NOISE SPECTRUM IS SIMILAR FOR BOTH LARGE AND SMALL
TARGETS 4HIS IS BECAUSE THE RATE OF RELATIVE RANGE CHANGE IS A FUNCTION OF BOTH ANGULAR
YAW AND DISTANCE FROM THE CENTER OF GRAVITY OF THE AIRCRAFT 4HUS A LARGER AIRCRAFT WITH
SLOW YAW RATES BUT GREATER WINGSPAN GENERATES A LOW FREQUENCY NOISE SPECTRUM SIMI
LAR TO THAT OF A SMALL AIRCRAFT WITH HIGH YAW RATES BUT SMALLER WINGSPAN (OWEVER THE
LARGER AIRCRAFT TYPICALLY HAS THE BROADER NOISE SPECTRUM BECAUSE OF THE DIFFERENCE IN
DISTRIBUTION OF DOMINANT REFLECTORS
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4HE RADAR FREQUENCY AFFECTS THE LOW FREQUENCY AMPLITUDE NOISE SPECTRUM SHAPE
WHERE THE SPECTRUM WIDTH IS CLOSELY PROPORTIONAL TO THE RADAR FREQUENCY IF THE TARGET
SPAN IS ASSUMED TO BE AT LEAST SEVERAL WAVELENGTHS 4HE REASON FOR THIS DEPENDENCE
IS THAT THE RELATIVE PHASE OF THE INDIVIDUAL ECHO SIGNALS IS A FUNCTION OF THE NUMBER OF
WAVELENGTHS OF CHANGE IN RELATIVE RANGE CAUSED BY THE TARGETS RANDOM MOTION 4HUS
WITH SHORTER WAVELENGTHS A GIVEN RELATIVE RANGE CHANGE WILL SUBTEND MORE WAVE
LENGTHS CAUSING HIGHER PHASE RATE RESULTING IN HIGHER FREQUENCY NOISE COMPONENTS
4HE RATE OF AMPLITUDE FLUCTUATIONS OF THE ENVELOPE OF THE ECHO PULSES IS APPROXIMATELY
PROPORTIONAL TO THE RADAR FREQUENCY
! MATHEMATICAL MODEL OF LOW FREQUENCY AMPLITUDE NOISE OF A TYPICAL AIRCRAFT IS
GIVEN BY
! F "
" F WHERE ! F FRACTIONAL MODULATION (Z
" HALF POWER BANDWIDTH (Z
F FREQUENCY (Z
4HE VALUE OF " FALLS TYPICALLY BETWEEN (Z AND (Z AT 8 BAND WITH THE LARGER
AIRCRAFT AT THE HIGHER VALUES BECAUSE OF THE LARGER REFLECTORS SUCH AS ENGINES SPREAD
OUT ALONG THE WINGS 4HESE REFLECTORS WITH THE GREATER SEPARATION CONTRIBUTE TO THE
HIGHER FREQUENCIES BECAUSE THEIR RELATIVE RANGE CHANGE IS LARGE FOR A GIVEN ANGULAR
MOVEMENT OF THE TARGET ! F IS THE MODULATION POWER DENSITY SUCH THAT THE SPECTRUM
MAY BE INTEGRATED OVER ANY FREQUENCY RANGE TO FIND THE TOTAL NOISE POWER WITHIN A
FREQUENCY BAND OF INTEREST 4AKING THE SQUARE ROOT OF THE VALUE OF THE INTEGRAL GIVES
THE RMS MODULATION
(IGH &REQUENCY !MPLITUDE .OISE (IGH FREQUENCY AMPLITUDE NOISE CONSISTS OF
BOTH RANDOM NOISE AND PERIODIC MODULATION 4HE RANDOM NOISE IS LARGELY A RESULT OF
THE VIBRATION AND MOVING PARTS OF THE AIRCRAFT PRODUCING A RELATIVELY FLAT NOISE SPEC
TRUM SPREAD OUT TO A FEW HUNDRED (Z DEPENDING ON THE TYPE OF AIRCRAFT 4HE RMS NOISE
DENSITY IS TYPICALLY A FEW PERCENT OF MODULATION PER (Z 4HE PERIODIC MODULATION APPEARING AS SPIKES IN THE &IGURE SPECTRUM ARE
CAUSED BY RAPIDLY ROTATING PARTS OF AN AIRCRAFT SUCH AS THE PROPELLERS !S THE ECHO
FROM A PROPELLER BLADE CHANGES WITH ASPECT WHEN IT ROTATES A PERIODIC MODULATION
&)'52% 4YPICAL AMPLITUDE SPECTRAL VOLTAGE DISTRIBUTION SHOWING THE PROPELLER MODULATION MEASURED
ON A PROPELLER DRIVEN AIRCRAFT IN FLIGHT &IGURE FROM $UNN (OWARD AND +ING ¡ )2% 42!#+).' 2!$!2
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IS PRODUCED 4HE BACKGROUND NOISE FROM THE AIRFRAME IS ALSO OBSERVED 4HE SPIKES
IN THE SPECTRUM RESULT FROM A FUNDAMENTAL MODULATION FREQUENCY RELATED TO THE PRO
PELLER REVMIN AND NUMBER OF BLADES 3INCE IT IS NOT USUALLY SINUSOIDAL THERE ARE
HARMONIC FREQUENCIES SPREAD THROUGHOUT THE SPECTRUM AS SHOWN IN &IGURE FOR
THE 3." A SMALL AIRCRAFT WITH TWO PROPELLER ENGINES 4HE LOCATION OF THESE SPIKES
IS NOT DEPENDENT ON 2& FREQUENCY AS IN THE CASE OF LOW FREQUENCY AMPLITUDE NOISE
BECAUSE THE TARGET CONTROLS THE PERIODICITY OF THE MODULATION WHICH IS DEPENDENT
ONLY ON THE AIRCRAFT PROPELLER ROTATION RATE AND NUMBER OF BLADES *ET AIRCRAFT MAY ALSO
CAUSE ECHO AMPLITUDE MODULATION OF RADAR SIGNALS REFLECTED FROM ROTATING FAN BLADES
FROM WITHIN THE JET ENGINES 4HE JET ENGINE CAUSED MODULATION IS CALLED *ET %NGINE
-ODULATION *%- SPECTRAL MODULATION LINES 4HE HIGH FREQUENCY NOISE MODULATION
AFFECTS SCAN TYPE TRACKING RADARS AS DESCRIBED LATER AND GIVES SOME INFORMATION AS
TO THE TYPE OF AIRCRAFT
%FFECTS OF !MPLITUDE 3CINTILLATION ON 2ADAR 0ERFORMANCE !MPLITUDE NOISE TO
SOME EXTENT AFFECTS ALL TYPES OF RADARS IN PROBABILITY OF DETECTION AND TRACKING RADAR
ACCURACYn /NE EFFECT ON ALL TYPES OF TRACKING RADARS IS THE INTERRELATION BETWEEN THE
LOW FREQUENCY SPECTRUM OF AMPLITUDE NOISE THE !'# CHARACTERISTICS WHICH DETERMINE
TO WHAT EXTENT THE SLOW FLUCTUATIONS ARE SMOOTHED AND THE ANGLE NOISE 4HE EFFECTS ON
ANGLE NOISE ARE DESCRIBED LATER IN THIS SECTION WHERE IT IS DESCRIBED WHY A FAST ACTING
!'# IS GENERALLY THE PREFERRED CHOICE FOR MAXIMIZING OVERALL TRACKING ACCURACY
(IGH FREQUENCY AMPLITUDE NOISE CAUSES ERRORS ONLY IN CONICAL SCAN OR SEQUENTIAL LOB
ING TRACKING RADARS BECAUSE THE EFFECTS ARE ELIMINATED BY THE MONOPULSE TECHNIQUES
#ONICAL SCAN OR SEQUENTIAL LOBING TO SENSE TARGET DIRECTION DEPEND UPON MEASURING THE
AMPLITUDE OF THE SIGNAL FOR AT LEAST TWO DIFFERENT ANTENNA BEAM POSITIONS FOR EACH TRACKING
AXIS )N AZIMUTH TRACKING FOR EXAMPLE THE ANTENNA BEAM IS DISPLACED TO THE LEFT OF THE
TARGET AND THEN TO THE RIGHT )F THE TARGET WERE ON THE ANTENNA AXIS THE SIGNAL WOULD DROP
THE SAME AMOUNT WHEN THE BEAM ASSUMED TO BE SYMMETRICAL IS MOVED AN EQUAL AMOUNT
IN EITHER DIRECTION 4HE AMPLITUDES FOR EACH BEAM POSITION ARE SUBTRACTED IN AN ANGLE ERROR
DETECTOR HENCE THE OUTPUT IS ZERO IF THE TARGET IS ON THE ANTENNA AXIS AND BECOMES FINITE
INCREASING POSITIVELY OR NEGATIVELY AS THE TARGET MOVES OFF AXIS TO THE RIGHT OR LEFT
(IGH FREQUENCY NOISE CAN CAUSE THE AMPLITUDE TO CHANGE DURING THE TIME TAKEN TO
MOVE THE ANTENNA BEAM FROM ONE POSITION TO THE NEXT %VEN IF THE TARGET IS ON AXIS
HIGH FREQUENCY NOISE CAN CAUSE THE AMPLITUDE AT THE TWO BEAM POSITIONS TO DIFFER
THUS CAUSING AN ERRONEOUS INDICATION THAT THE TARGET IS OFF AXIS 4HIS EFFECT IS AVERAGED
OUT EXCEPT FOR THE NOISE SPECTRAL ENERGY NEAR THE SCAN RATE &OR EXAMPLE A PERIODIC
MODULATION SPIKE NEAR THE SCAN RATE WILL CAUSE THE TRACKING RADAR TO DRIVE ITS ANTENNA
IN A CIRCULAR MOTION AROUND THE TARGET AT A RATE EQUAL TO THE DIFFERENCE IN FREQUENCY
BETWEEN THE SCAN RATE AND THE FREQUENCY OF THE SPECTRAL LINE 4HE DIRECTION CLOCKWISE
OR COUNTERCLOCKWISE DEPENDS UPON WHETHER THE SPECTRAL LINE IS ABOVE OR BELOW THE
SCAN RATE AND WHETHER THE SCAN IS CLOCKWISE OR COUNTERCLOCKWISE 4HE SERVOSYSTEM
FILTERS OUT ALL FREQUENCIES OUTSIDE THE FREQUENCY RANGE BETWEEN THE SCAN RATE PLUS THE
SERVO BANDWIDTH AND THE SCAN RATE MINUS THE SERVO BANDWIDTH AND AN ANGLE SENSITIVITY
CONSTANT THAT CONVERTS RMS MODULATION TO RMS ANGLE ERROR
!N EQUATION USING THIS RELATION TO CALCULATE RMS NOISE IN SCANNING AND LOBING TYPE
TRACKING RADARS CAUSED BY HIGH FREQUENCY AMPLITUDE NOISE IS
SS Q"
KS
! FS B
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WHERE RS RMS ANGLE ERROR IN SAME ANGULAR UNITS AS P"
! FS RMS FRACTIONAL MODULATION NOISE DENSITY IN VICINITY OF SCAN RATE
KS CONICAL SCAN ERROR SLOPE KS FOR SYSTEM OPTIMUM
P" ONE WAY ANTENNA BEAMWIDTH
A SERVO BANDWIDTH (Z
! SAMPLE CALCULATION FOR AN FS OF (Z WHERE !FS FROM MEASURED DATA TAKEN ON A
LARGE JET AIRCRAFT IS APPROXIMATELY (Z P" IS MILS AND A IS (Z GIVES A RS
OF MIL RMS
)N THE CASE OF A PERIODIC MODULATION WHERE A SPECTRAL LINE FALLS WITHIN THE BAND
FS o A THE RMS NOISE IS RS P" ! FS WHERE ! FS IS THE RMS FRACTIONAL MODULATION
CAUSED BY THE SPECTRAL LINE 4HE RESULTANT RMS TRACKING ERROR RS WILL BE PERIODIC AT THE
FREQUENCY FS FT WHERE FT IS THE FREQUENCY OF THE SPECTRAL LINE
4HE EFFECTS OF AMPLITUDE NOISE ON TARGET DETECTION AND ACQUISITION ARE OF CONCERN IN
ALL TYPES OF RADARS PARTICULARLY AT LONG RANGES WHERE THE SIGNAL IS WEAK 4HE AMPLITUDE
FLUCTUATIONS CAN CAUSE THE SIGNAL TO DROP BELOW THE NOISE LEVEL FOR SHORT PERIODS OF TIME
THUS AFFECTING THE CHOICE OF THRESHOLDS ACQUISITION SCAN RATE AND DETECTION LOGICn
!NGLE .OISE 'LINT !NGLE NOISE CAUSES A CHANGE WITH TIME IN THE APPARENT
LOCATION OF THE TARGET WITH RESPECT TO A REFERENCE POINT ON THE TARGET 4HIS REFERENCE
POINT IS USUALLY CHOSEN AS THE CENTER OF hGRAVITYv OF THE REFLECTIVITY DISTRIBUTION ALONG
THE TARGET COORDINATE OF INTEREST 4HE CENTER OF GRAVITY IS THE LONG TIME AVERAGED TRACK
ING ANGLE ON A TARGET 4HE TERM GLINT IS SOMETIMES USED FOR ANGLE NOISE BUT IT GIVES
THE FALSE IMPRESSION THAT THE WANDER IN THE APPARENT POSITION OF A TARGET ALWAYS FALLS
WITHIN THE TARGET SPAN )T WAS ORIGINALLY EXPECTED THAT ANGLE FLUCTUATIONS CAUSED IN A
MONOPULSE RADAR BY A TARGET WOULD BE SIMPLE VARIATIONS IN THE CENTER OF GRAVITY OF
THE REFLECTING AREAS HOWEVER MUCH LARGER ANGLE ERRORS WERE OBSERVED 4HE APPARENT
ANGULAR LOCATION OF A TARGET CAN FALL AT A POINT COMPLETELY OUTSIDE THE EXTREMITIES OF
THE TARGET 4HIS CAN BE DEMONSTRATED BOTH EXPERIMENTALLY AND THEORETICALLY ! PAIR
OF SCATTERERS CAN BE APPROPRIATELY SPACED TO CAUSE A TRACKING RADAR WITH CLOSED LOOP
TRACKING TO ALIGN ITS ANTENNA AXIS AT A POINT MANY TIMES THE SCATTERER SPACING AWAY
FROM THE SCATTERERS )F THE SCATTERERS ARE STATIONARY THE RADAR ANTENNA WILL STAY POINTING
IN THE ERRONEOUS DIRECTION &IGURE SHOWS EXPERIMENTAL DATA DEMONSTRATING THIS
PHENOMENON WITH A TWO REFLECTOR TARGET
4HE ANGLE NOISE PHENOMENON AFFECTS ALL TYPES OF TRACKING RADARS BUT IS MAINLY OF
CONCERN FOR TRACKING RADARS WHERE PRECISION TARGET LOCATION IS NEEDED 4O AID IN VISU
ALIZING WHY ANGLE NOISE AFFECTS ANY RADAR TYPE ANGULAR DIRECTION SENSING DEVICE THE
ECHO SIGNAL PROPAGATING IN SPACE WAS ANALYZED SHOWING THAT THE ANGLE NOISE IS PRES
ENT IN THIS PROPAGATING ENERGY AS A DISTORTION OF THE PHASE FRONT 4HEORETICAL PLOTS OF
A DISTORTED PHASE FRONT FROM DUAL SOURCES COMPARE VERY CLOSELY WITH PHOTOGRAPHS OF
THE PHASE FRONT OF THE RADIATING SURFACE RIPPLES IN THE RIPPLE TANK EXPERIMENT WITH DUAL
VIBRATING PROBES !LL RADAR ANGLE SENSING DEVICES SENSE BY ONE MEANS OR ANOTHER THE
PHASE FRONT OF THE SIGNAL AND INDICATE THE TARGET TO BE IN A DIRECTION NORMAL TO THE PHASE
FRONT 4HUS THE PHASE FRONT DISTORTIONS AFFECT ALL TYPES OF ANGLE SENSING RADARS
-ANY MEASUREMENTS OF ANGLE NOISE HAVE BEEN MADE ON A VARIETY OF AIRCRAFT AND
THE RESULTS OF THEORETICAL STUDIES HAVE BEEN VERIFIED 4HE THEORY AND MEASUREMENTS
SHOW THAT ANGLE NOISE EXPRESSED IN LINEAR UNITS OF DISPLACEMENT SUCH AS METERS OF THE
APPARENT POSITION OF THE TARGET FROM THE CENTER OF GRAVITY OF THE TARGET IS INDEPENDENT
OF RANGE EXCEPT FOR VERY SHORT RANGES 4HEREFORE RMS ANGLE NOISE RANG IS EXPRESSED IN
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%
%
% !"#!!$
&)'52% !PPARENT LOCATION OF A DUAL SOURCE TARGET AS A FUNCTION OF RELATIVE PHASE E FOR DIFFERENT
VALUES OF RELATIVE AMPLITUDE A MEASURED WITH A TRACKING RADAR &IGURE FROM (OWARD
UNITS OF METERS OF ERROR MEASURED AT THE TARGET LOCATION 4HE RESULTS SHOW THAT THE RMS
VALUE OF ANGLE NOISE RANG IS EQUAL TO 2O WHERE 2O IS THE RADIUS OF GYRATION TAKEN
ALONG THE ANGULAR COORDIN