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Integrated Systems & Solutions – S & R Systems
Introduction to
Synthetic Aperture
Radar (SAR)
Floyd Millet
August 2005
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Work was done under US Government contract.
Radar Applications
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Air Traffic Control
Remote Sensing the Earth
Air traffic and weather
Ground Control approach landing
Flood monitoring
Crop and forest assessment
Location of archeological ruins
Aircraft Navigation
Altimeter
Doppler navigation
Weather avoidance
Remote Sensing the Solar System
Planetary rotation rates
Range to the moon and planets
Meteor tracking
Law Enforcement
Police speedometers
Intrusion alarms
Ship Safety
Collision avoidance
Piloting in restricted waters
Military
Surveillance and reconnaissance
Weapon guidance and control
Proximity fuzes for weapons
Bomb damage assessment
Space
Rendezvousing of spacecraft
Spacecraft docking and landing
Satellite tracking
RaDAR is an acronym for Radio Detection And Ranging
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Radar Imaging
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Problem
Form a terrain image using a radar in
a moving airborne vehicle
Simplest approach:
Real-Beam Imaging Radar
Example:
Plan Position Indicator (PPI)
Range
Azimuth
Individual image points (pixels) must
be discriminated in two dimensions,
range and azimuth
PPI Display
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Target Not Identified When
Coarse Resolution Used
Cell Size: 1/5 Major Dimension
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Corresponding Map
Target Identified When
Fine Resolution Used
Cell Size: 1/20 Major Dimension
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Corresponding Map
Resolution Required for Various
Mapping Applications
da
Resolution
Cell
dr
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Features to be resolved
Cell Size
Coast lines, large cities,
outlines of mountains
150m
Major highways, variations in
fields
20-35 m
“roadmap” details: city streets,
large buildings, small air fields
10-20 m
Vehicles, houses, small
buildings
1-3 m
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High-Resolution Mapping
Synthetic Aperture Radar (SAR)
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What is High Resolution
Radar Mapping?
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• HRM involves breaking up
real antenna beam into fine
resolution cells
Footprint of
mainlobe on
ground
• The map is made by forming cells and
measuring signal intensity in each cell
dAZ
dr
dAZ = Azimuth Resolution
dr
8
= Range Resolution
Resolution Cell
What Does a Radar Measure?
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 Amplitude versus Time
All other SAR parameters are derived:
 Range (known time relationship)
 Phase - coherent transmission plus demodulation
 Doppler frequency
 Range resolution (pulse compression)
 Azimuth Resolution
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Range Discrimination
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The transmitted pulse travels at the speed of light
300,000 km/second
3.3 nanoseconds/meter
Round-trip “radar time”
6.7 nanoseconds/meter
(²d = 2 meters
² = 13.3 nanoseconds)
But target returns overlap if targets are separated by less than
c/2
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Short Pulse Range Resolution
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R2 = R1 + ΔR
R1
Transmitted
Pulse
O 
Time


Received Pulses
2(R1 + ΔR/c)
2R1/c
2ΔR/c
Pulses Just
Resolvable

ΔR = c/2
2ΔR/c
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Shorter Pulses
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So for better resolution, just make the transmitted pulse SHORTER
However, the shorter pulses must somehow transmit the
SAME ENERGY to the target
As the pulse gets SHORTER, the peak power gets HIGHER
Problem
Peak power gets MUCH to high before pulse
length even approaches high resolution
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Coded Pulses
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Solution
Transmit a long coded pulse that can be decoded (compressed) after
reception into a much shorter pulse
f1
f2

Linear Frequency Modulation (FM)
Linear Swept Frequency
“Chirp”
Note: A typical 200 microsecond pulse extends over
60 km resulting in a range resolution of 30 km
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Pulse Compression
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Frequency
f2
Transmitted/Received Pulse
Resolution = c/2
Δf
f1
1
f2
Variable Delay Line
“Compression” Filter
Decoded/”Compressed” Output
Resolution = c/2Δf = (/2)(fo/ Δf)
F number = fo/ 2Δf

2
Time

Delay
Time
Δf
f1
f2
Δf
1/Δf
f1
Time
Resolution varies as 1/ Δf , that is, it varies with transmitted bandwidth
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Linear FM (Chirp) Waveform
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o Swept frequency having bandwidth BWt across the pulse length
S x ( n,t ) = A cos(2p f t + pαt2 )
0
ft ( n,t )
fc + BWt
2
A

f0 = fc - BWt
2
-A
Tran smit w aveform
o Transmit bandw idth given by:

f (n, t ) = 2 p f0 t + pαt2
1 d f (n, t )
ft ( n,t ) =
2p
dt
= fo + αt
,0  t  
,0  t  
BW t = ατ
o Linear FM has desirable properties over other w aveform types :
• Easy to generate
• "Stretch mode"demodulation
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t
Frequ ency mod ulation of p ulse
o Phase function given by:
o Transmit frequency given by:
fÝ
fc
t
Pulse Compression
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2
Sr ( n,t ) = C (n , t ) cos [ 2 p f0 ( t - TR ) + pα ( t - TR ) ]
o Received S ign al Given By:
Sx (0, t )
S r (0 , t )
Puls e n=0
A

-A
2 R tgt
c
2 Rtgt + 
c
R tgt = Range-to-Target
o Com plex S ign al (after dem od u lation an d/or
sideb an d removal)* G iven By:
Sv ( n,t ) = Sr (n,t ) e - jw 0 t = [C(n,t ) e - jw0 TR ]  exp{ jpα (t - T R ) } = D(n,t )  exp{ jpα(t - T R ) }
2
2
o G oal of Pu lse Comp res sion :
• Produ ce finest possib le resolution,
w hich is analogous to:
• Maximizin g the signal-to-noise ratio
BUT:
We h ave th e ad ditional req uirem ent th at we min im ize artifacts in th e image
( G ood s id elob e con trol on th e im pu ls e respon se (IPR) )
* d oes no t apply to "Stretch Mo de"s ig nals after the IF m ixer s tag e--w e w i ll co ver thi s sho rtly
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Fine Range Resolution Requires
Large Radar Bandwidth
Fourier
Transform Pair

Time
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1/
Frequency
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Pulse Compression Advantages
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 Range resolution independent of transmit pulse length
• Transmit long pulses
• Keep peak power comfortably low
 Set range resolution with transmitted bandwidth
• Resolution inversely proportional to bandwidth
– 150 MHz
1 meter resolution
– 300 MHz
0.5 meter resolution
• Resolution independent of slant range
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Azimuth Resolution
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Ability to Resolve Closely Spaced
Targets is Beamwidth Dependent
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A
B
The half-power (3dB) beamwidth is a measure of angular resolution of radar
AB
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(1/2)3dB
A B
3dB
A
B
(3/2)3dB
Azimuth Considerations
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SAR
Synthetic-Aperture Radar
Antenna beamwidth is inversely proportional to the
number of wavelengths in its length (aperture)
= /L radians
L
= C/f
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R
R
Azimuth Discrimination
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Flight Path
R/L
L
Δd
R/L
L
R
Real-beam imaging radar
 As the collection vehicle moves along the flight path, targets are
detected as they move in and out of the antenna pattern
 But target returns overlap if the targets are separated in azimuth by
less than the antenna beamwidth
• So achievable azimuth resolution degrades with range
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Azimuth Discrimination
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 So for better azimuth resolution, just make the antenna beam
NARROWER!
• Generate more wavelengths in the antenna aperture by
lengthening the antenna or by shorting the wavelength
(increasing the frequency)
 However, very LONG antennas are difficult to carry and position
and very HIGH frequencies limit performance in weather and at
long ranges
Problem
Antennas get MUCH too long and frequencies
MUCH to high before the beamwidth even
approaches high resolution
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Synthetic-Aperture
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Solution
Synthesize a long antenna aperture using a physically short antenna
SAR
Synthetic-Aperture Radar
Store the data collected sequentially and coherently
across a long aperture and then process the data to
synthesize a full aperture collection
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Design Options for Improving
Resolution Before SAR
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Range Resolution
•Decrease pulsewidth, at expense of power and range
•Operate at short range/decrease power
Azimuth Resolution
•Increase operating frequency to Ku and Ka-bands or
higher, with increased atmospheric and weather
attenuation, lower available power sources
•Increase antenna aperture, with attendant installation
and stabilization problems
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The Resolution Breakthrough
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Range Pulse Compression - Increased range resolution without loss
of power
Azimuth Synthetic Aperture - Increased azimuth resolution without large
antenna installation
Note: 1. Both use special waveforms
2. Both use signal processing techniques
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Synthetic Aperture Radar
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Phase History of a Scatterer
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From Hovanessian, “Introduction to Synthetic Array and Imaging Radars”
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Anamorphic Hologram
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SAR Collection Geometry
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Resolution Limitation on
Sidelooking SAR
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Maximum Synthetic
Aperture Length Lmax
Ro
Beamwidth beam
Range
Resolution
R
Minimum Resolution =  o
2 L max
Azimuth
Beam Coverage
L max =  beam R o   R o
d
d
Minimum Resolution  2
where d is the antenna length
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Synthetic Aperture
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Tgt 1
"Integration Angle"
 INT 
Ls
Ro
=
0.886k A
2WAZ
INT
Ro
Ls
-Resolution limitation on sidelooking SAR:
Maximum θINT is limited by azimuth antenna beamwidth
 az 
Waz 

, Lant is length of linear array
Lant

2 IN T
Wazmin 

2  az

( )=
 Lant
2

Lant
2
-This limitation does not apply to spotlight collection
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Point-Target Phase History
Compressed in Both Range and Azimuth
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First SAR Imagery
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ADTS Advanced Detection
Technology Sensor
Ft. Devens, MA
35 GHZ
HH Polarization
± 20 Deg Depression Angle
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Where Do You Fit in?
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Future Topics
Implementation of Theory
September 6
Algorithm Architecture for SAR Ground
Processing
Creating an Image
September 20 Concepts in Image Processing
From Idealization to Realization
October 11
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PACE: An Autofocus Algorithm for SAR
Texts and Software
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Texts
Curlander, John and McDonough, Robert
Synthetic-Aperture Radar - Systems
and Signal Processing
Skolnik, Merrill
Introduction to Radar Systems
Nathanson, Fred
Radar Design Principles
Carrara, Walter et al
Spotlight Synthetic-Aperture Radar
Oppenheim, Alan and Schafer, Ron
Discrete Time Signal Processing
Skolnik, Merrill
Radar Handbook
Software
Mathcad V6
Matlab
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