Resolution Enhancement Techniques for
Antenna Pattern Measurements
by
Minh Thanh Thii
Submitted to the Department of Electrical Engineering and Computer Science
in Partial Fulfillment of the Requirements for the Degree of
Master of Engineering in Electrical Engineering and Computer Science
at the Massachusetts Institute of Technology
January 28, 2000
Copyright 2000 Minh Thanh Thii. All rights reserved.
MASSACHUSETTS INSTITUTE
OF TECHNOLOGY
The author hereby grants to M.I.T permission to reproduce and
distribute publicly paper and electronic copies of this thesis
and to grant others the right to do so.
JUL 2 7 2000
LIBRARIES
Author
Department of Electrical Engineering and Computer Science
January 28, 2000
Certified by
David H. Staelin
Professor of Electrical Engineering
Thesis Supervisor
Certified by_
Senior
eibeT'of Technical.Staff,
com
Ozlem Kilic
COMSAT Laboratories
'esis Supervisor
Accepted by
Chairman, Department Committee
Ar ur C. Smith
raduate Theses
Resolution Enhancement Techniques for
Antenna Pattern Measurements
by
Minh Thanh Thii
Submitted to the
Department of Electrical Engineering and Computer Science
January 28, 2000
In Partial Fulfillment of the Requirements for the Degree of
Master of Engineering in Electrical Engineering and Computer Science
ABSTRACT
Two noise reduction methods using data processing techniques were studied to improve
the dynamic range and the noise variance of antenna pattern measurements. The first is
the averaging method which involves dividing the pattern into a number of small
segments and computing the arithmetic mean in each segment. While no improvement in
the dynamic range is achieved, the noise variance decreases by a factor of N, which is the
number of samples averaged in the segment. The second method improves the averaging
method by utilizing the pulse modulation of the test signal amplitude and synchronous
detection. The noise floor in the pattern is reduced by a factor of vN / 4 (assuming a
fifty-percent duty cycle of a power-limited transmitter). In addition, randomly
fluctuating local mean in the receiver output is reduced due to the benefits of
synchronous detection. These results have been verified by software simulations.
Experimental results from tests conducted on an implementation of this system show
improvements of as much as 25dB in the noise variance and over 11dB in the dynamic
range of the antenna pattern. Since many transmitters can provide fifty-percent duty
cycle modulated test signals, the cost of implementing this technique is minimal. In
addition, a computerized data collection method was developed to provide sufficient
input samples for data processing.
Thesis Supervisor: David H. Staelin
Title: Professor of Electrical Engineering
Company Supervisor: Ozlem Kilic, Dr.
Title: Senior Member of Technical Staff, COMSAT Laboratories
2
Acknowledgments
First and foremost, I would like to thank my supervisor, Professor David Staelin for the
three wonderful years that I worked with him. He has always been available to answer
questions and to give advice, guiding me through all the challenges an academic research
project could present.
I would like to express my appreciation to the R.F. & Satellite Technologies
Group of COMSAT Laboratories for providing me the topic of my research, as well as
the technical guidance and the necessary support regarding facilities and equipment.
Special thanks to Dr. Ernest Ekelman for providing the effective guidance and
supervision throughout the thesis work. Having the opportunity to work with him on a
daily basis, I have learned a great deal from his expertise and experience. Many thanks
to Dr. Ozlem Kilic for devoting her time and effort to help me completing of this
document. Thanks also to other members of COMSAT Laboratories for all the support
that made this project a success: Dr. Amir Zaghloul, Dr. Ramesh Gupta, Michael Onufry,
Robert Kroll, Tony Chambers, Matt Sherman and many others.
Finally, I am deeply indebted to my family for providing me with the opportunity
to pursue my education. Emotionally, they have always been there to help me through all
the struggles I faced in this long journey.
3
Contents
1 Introduction
7
2 Background
9
2.1
Definition of the Antenna Radiation Pattern
12
2.2 Characterization of the Antenna Pattern
2.3
9
The Conventional Measurement Method
14
21
2.4 Characteristics of the Additive Noise
3 Computerized Data Collection
23
4 Noise Reduction by Averaging
28
4.1
Characteristics of the Estimation by Averaging
30
4.1.1
Zero-Mean Noise
30
4.1.2
Constant-Mean Noise
31
4.1.3
Variable-Mean Noise
32
4.1.4
Dynamic versus Static Measurement
32
34
4.2 Simulation
4.2.1
Objectives
34
4.2.2
Implementation and Results
34
41
4.3 Implementation
42
5 Noise Reduction with Pulse Modulation
5.1 Motivation
42
5.2 Pulse Modulation Technique
45
5.3
48
Simulation
5.3.1
Objectives
48
5.3.2
Implementation and Results.
48
53
5.4 Implementation
5.5
56
Other Modulation Schemes
4
6 Experimental Results
57
6.1
Objectives
57
6.2
Implementation and Results
58
7 Conclusion
70
Bibliography
72
List of Figures
Figure 2-1 Coordinates in antenna measurement
10
Figure 2-2 The antenna pattern measurement system
15
Figure 2-3 Receiver setup with GPIB bus
16
Figure 2-4 Conventional method for data collection
17
Figure 3-1 Data collection by Computer
25
Figure 3-2 Gaps in the collected data
26
Figure 4-1 Communication over an additive Gaussian noise channel
28
Figure 4-2 Over-smoothing problem
33
Figure 4-3 Bessel function as simulated antenna pattern
35
Figure 4-4 Input signal with zero-mean noise
36
Figure 4-5 Input signal with non-zero mean noise
36
Figure 4-6 Simulation for noise reduction by averaging for zero-mean noise
38
Figure 4-7 Averaging zero-mean noise simulation
39
Figure 4-8 Averaging non-zero-mean noise simulation
39
Figure 5-1 Effects of averaging on the noise floor
43
Figure 5-2 Noise reduction with amplitude modulation
45
Figure 5-3 Modulation in the received power
46
Figure 5-4 Input signal with 20ms pulse
49
Figure 5-5 Simulation for pulse modulation with non-zero mean noise
49
Figure 5-6 Additive Gaussian noise with variable mean
50
Figure 5-7 Effect of different pulse periods with variable-mean noise
51
Figure 5-8 Generating modulated signal
53
5
Figure 5-9 Detecting pulses in a segment
55
Figure 6-1 Equipment setup at the transmit site
58
Figure 6-2 Equipment setup at the receive site
59
Figure 6-3 Low noise, high resolution benchmark pattern
60
Figure 6-4 Unprocessed pattern with full power signal
61
Figure 6-5 Pattern recovered by averaging with full power signal
62
Figure 6-6 Pattern recovered by modulation with full power signal
62
Figure 6-7 Unprocessed pattern with --10dB attenuated signal
63
Figure 6-8 Pattern recovered by averaging with -10dB attenuated signal
64
Figure 6-9 Pattern recovered by modulation with -10dB attenuated signal
64
Figure 6-10 Unprocessed pattern with -20dB attenuated signal
65
Figure 6-11 Pattern recovered by averaging with -20dB attenuated signal
66
Figure 6-12 Pattern recovered by modulation with -20dB attenuated signal
66
Figure 6-13 Unprocessed pattern with -30dB attenuated signal
68
Figure 6-14 Pattern recovered by averaging with -30dB attenuated signal
68
Figure 6-15 Pattern recovered by modulation with -30dB attenuated signal
69
6
Chapter 1
Introduction
The measurement of an antenna pattern is an important step in the development and
implementation of a wireless communication system. The success or failure of such a
system often depends on the performance of the antenna. It is, therefore, of great interest
for engineers in the field to develop a measurement technique that best characterizes the
operational behavior of the antenna, in the condition for which it has been designed. This
project joins the quest by looking for a way to utilize the great potential brought by the
advent of the computers. The goal is to improve the resolution of the antenna pattern
measurement.
This research focuses on measurement procedures applicable to earth-station
antennas in a satellite communication system. These antennas are often too large to be
tested on a ground test range; hence, they must be tested at their installation sites via a
satellite link. This type of setup introduces several challenges for the measurement.
First, there is a limit on the power of the satellite link, resulting in a limited dynamic
range in the signal. Second, the equipment setup for the measurement should be
available at the ground station. Additional instruments can be used, but to a limited
extent. Third, the signal path between the satellite and the antenna can be interfered by
the environment. The goal of this research is to investigate different methods to improve
the measurement; to determine whether a method is feasible for this application; and if
modifications to the ground station setup are needed, which new setup will provide the
best improvement.
7
The conventional method for measuring an antenna pattern is the starting point for
this research. However, ideas for solutions from various fields, not restricted to antenna
development, are taken into consideration. Through an assessment process at the
beginning of the project, only a few ideas were kept for further consideration. The work
presented in this document originated from those ideas.
Chapter 2 will discuss the background material and introduce the definitions of
the terminology that will be used throughout the text. Chapter 3 will describe the
computerized data collection method. Chapter 4 and 5 present the two noise reduction
methods studied. Chapter 6 will present the experimental results collected in this project.
Chapter 7 presents the final discussion and the conclusion of the project.
8
Chapter 2
Background
Radiation pattern is a very important measurement for characterizing an antenna. This
chapter will present the definitions relating to the antenna pattern measurement used in
this work. Some of the critical parameters in the antenna pattern measurement are also
identified in this section. The characterization of the antenna pattern and the noise are
key elements for this work and are discussed in detail in this section. In addition, the
conventional method used for antenna pattern measurement is also described.
2.1
Definition of the Antenna Radiation Pattern
A radiation pattern is defined in this work as the directive gain of the antenna,
G(f,6, p) . At a certain frequency
f
, the gain is a function of elevation angle 0 and
azimuth angle (p at which the signal is received or transmitted (see Figure 2-1). For an
aperture antenna, the direction that gives the maximum gain is called the boresight of the
antenna. The elevation and azimuth angles are often defined relative to this direction, i.e.
elevation angle of the boresight is 00. If the directive gain is uniform in the azimuth
plane, the pattern is said to have a rotational symmetry along the boresight. The function
of the gain is then reduced to G(f, 0). Antennas with circular aperture usually have this
feature.
The directive gain of an antenna can be related to the effective area of the aperture
A(f,0,(p) as follows
9
G(f,0,(p)=
4ff
2
A(f,0,T),
where A is the wavelength. The effective area of an antenna depends on the geometry of
the reflectors, feed characteristics and the efficiency of the antenna. Hence in theory, the
pattern of an antenna can be calculated from the design specification of the antenna.
However, several aspects like complicated surfaces, overhanging mounts for the antenna
feeds and sub-reflectors, and manufacturing imperfections usually make this calculation
extremely difficult. Direct measurement of the radiation pattern is therefore the only
reliable means to determine the performance of an antenna.
0
r
Figure 2-1 Coordinates in antenna measurement
The receive pattern of an antenna is identical to its radiation pattern. This is a
direct consequence of the Lorentz reciprocity theorem [Kong 1990]. Consequently, an
antenna can be configured as a receiver or a transmitter in the measurement setup. This
introduces flexibility for the tester as he sets up a measurement that gives the best
performance.
In this research, the antennas of interest usually have circular symmetry. These
antennas are designed to operate at certain frequency bands. Therefore, only the
measurements, which involve in measuring gain as a function of elevation angle have
10
been investigated in this study. However, the techniques proposed in this work are not
limited to symmetric antennas and the measurements using the proposed technique can be
carried out in any type of antenna.
The elevation angle 6 is defined with respect to the boresight, and will be
referred to as "off-axis angle" from now on, to avoid the confusion with the elevation
angle between the antenna boresight and the horizon. An on-axis signal will refer to the
signal that arrives to the antenna along its boresight direction. The pattern measurement
referred to in this work is the plot of the antenna gain as a function of the off-axis angle.
This measurement is repeated at several different frequencies, covering the whole
frequency band that the antenna is designed to operate at. The range of the off-axis angle
is usually wide enough to determine the antenna beamwidth, as well as its sidelobe levels
for full characterization of the antenna. Antennas with large apertures do not typically
require a large range because sidelobe levels drop quickly as the off-axis angle increases.
For these antennas, the ability to identify peaks and nulls at a small angle resolution is
very important. On the other hand, electrically smaller antennas require a much broader
angular range due to their broader beamwidth. In these cases, the first few sidelobe
levels can cause significant interference with nearby communication systems and should
be well characterized. With this diversity in the measurement requirements, a
measurement system needs to have flexible options to handle different antenna types.
As mentioned earlier, the ground station antennas studied in this project are part
of a satellite communication system. With high density of the existing communication
satellites, interference analysis for these antennas is extremely important. Ground station
antennas need low sidelobe levels to meet the spatial isolation requirement. In addition,
the beamwidth of the antenna has to meet the specification on the on-axis gain necessary
for its communication link. Antenna pattern measurement for such applications requires
both high angular resolution for the beamwidth measurement, and large dynamic range
for the sidelobe gain measurements.
11
2.2
Characterization of the Antenna Pattern
The determination of an antenna pattern involves two measurements: the off-axis angle
and the antenna gain at that angle. The quality of the off-axis angle measurement
depends on the mounting platform of the antenna and the position controller. Each
equipment has different precision. This research does not try to improve the reliability of
the off-axis angle readings, but rather focuses on utilizing the equipment to its best
performance. For example, if the readings of the angle from the position controller are
not very reliable, and the speed at which the platform rotates can be determined with
great precision, then the off-axis angle will be calculated by timing the rotation. The
measurement of the pointing angle of the antenna is sometimes compromised by the
vibration of the platform, or by movement of the antenna in the wind. Some position
controllers cannot rotate the antenna at a linear rate, and corrections for the angle are
needed in the measurement.
The resolution of peaks and nulls depend on the angular separation between
readings in a pattern measurement. If the readings are placed too far apart, there are just
not enough points to construct a peak or a null. On the other hand, if the readings are
placed too closed together, there will be too many readings to handle in a pattern. Even if
the angular separations are small enough, the fluctuations on the angle readings may
make it impossible to resolve peaks and nulls. So the angular resolution of the pattern is
a very important aspect of the measurement.
The characterization of the antenna pattern is limited when noise is present in the
received signal. In the absence of noise, a change in the power level readings is
contributed to the behavior of the antenna gain at different receiving angles. Fluctuations
caused by the noise make it difficult to reliably identify peaks and nulls in the pattern,
especially as the off-axis angle increases. It becomes harder to construct a pattern as the
noise levels increase in a measurement. The dynamic range of a pattern measurement is
the lowest power level measurable with the antenna gain normalized to OdB at the
boresight. Since gain is determined from the power level of the received signal, the
12
dynamic range can be defined as the difference between the maximum power received
and the noise floor, which is the power level measured in the absence of the signal. The
presence of signal below this power level is not readily detectable. The dynamic range
could be increased if the power level of the test signal can be increased. The stronger the
test signal the better the dynamic range is. In other words, the dynamic range strongly
relates to the signal-to-noise ratio of the test signal.
A large dynamic range is very desirable in an antenna pattern measurement. As
off-axis angle increases, the gain of the antenna decreases rapidly. If the signal is not
strong enough, the gain at these angles can be so low that the peaks and nulls in the
pattern just blend into the noise floor. In this case, the range of the off-axis angles for the
pattern measurement is limited by the dynamic range of the system. The angular range of
a measurement depends on the size of the antenna, while dynamic range only depends on
the signal-to-noise ratio of the signal. As a result, the dynamic range may completely
characterize the performance of the antenna gain measurement.
13
2.3
The Conventional Measurement Method
In this section, the conventional method for measuring the pattern for earth-station
antenna is reviewed. Since the radiation pattern of an antenna is identical to its receiving
pattern, an antenna can be set up as either a transmitting or a receiving antenna. Methods
that measure the receive pattern of an antenna often involve in setting up the antennaunder-test (AUT) to receive a signal with known characteristics. On the other hand,
methods that determine the transmitting pattern have the AUT set up to transmit a predetermined signal to well-characterized receiving antenna. The system, which has
provided the starting point for this research, is set up to measure the antenna's receiving
pattern.
The setup consists of two ground-station antennas: one transmits, one receives
with the AUT acting as the receiver (see [COMSAT93]). The two ground stations
communicate via a relay satellite. Using the relay satellite allows more accurate far-field
patterns that can only be obtained when the transmit-receive pair of antennas is placed far
enough apart. In addition, the satellite translates the signal from the frequency of the
transmitting ground station to the frequency of the receiving ground station. This feature
allows measurement with antennas operating on different frequency bands. The two
antennas can be located at the same ground station physically, or at two different parts of
the world, permitting flexible allocations for testing antennas.
14
Noise floor
Transmitted
signal
Received
signal
Figure 2-2 The antenna pattern measurement system
The diagram of this setup is shown in Figure 2-2. The path of the signal extends
from the transmitter antenna to the satellite, which includes a receiving antenna, a low
noise amplifier, and a transmitting antenna. Signal is retransmitted from the satellite to
the AUT on the ground station. During the course of an antenna pattern measurement,
the settings for all components on the signal path except the AUT are kept unchanged.
The transmitting antenna is positioned to point its boresight directly to satellite, allowing
the signal transmission at the maximum directive gain. The communication system
aboard the satellite is also configured to operate at its best signal-to-noise ratio. As the
measurement progresses, the AUT is positioned to receive at various different off-axis
angles. Readouts of the received signal at these angles are stored in a computer to
construct the antenna's receiving pattern after the measurement is over.
With this setup, the signal received at the AUT will be a continuous sinusoidal
wave (CW). If all of the unwanted fluctuations in the signal path were eliminated, the
incoming wave would have a constant flux of energy. As the off-axis angle of the AUT
varies, the fluctuations in the readouts from the antenna will solely be due to the variation
in the antenna gain at different receiving angles off the boresight. The relationship
between the antenna gain and the pointing angle, hence the receiving pattern, can be
15
constructed by recording the off-axis angles of the antenna and the strength of the
received signal.
RF
GPIB
SpectrumComputer
Analyzer
GPIB
Position Controller
~-~
-
Figure 2-3 Receiver setup with GPIB bus
The receiver setup is shown in Figure 2-3. The pointing angle of the AUT is
varied using a programmable position controller. Some controllers can be connected to a
computer via a GPIB bus for automated scans. The azimuth and elevation angles from
the boresight of the antenna can be set separately. In addition, the angles can be swept in
a continuous motion at a constant predetermined speed. This allows for precise
determination of off-axis angles. The sweep speed varies in a big range depending on the
models of different controllers, as well as the different sizes of the antennas. The range
of the scanning angles also depends on various setups; not all position controllers can
scan the off-axis angle from -180 degrees to +180 degrees. As a result, the radiation
pattern constructed has the range of angle limited by the setup.
Besides the AUT and its position controller, the setup in the ground station
consists of a low noise amplifier (LNA or LNB) with appropriate variable attenuator, a
spectrum analyzer, and a computer that controls the analyzer. This setup provides the
ability to alter the pointing direction of the AUT, and monitor the received signal changes
as this happens. The LNA and the attenuator bring the signal from the antenna to the
power level that is within operational input range to the spectrum analyzer. The spectrum
analyzer measures and records the power level of the received signal. The computer is
16
used to download the recorded signal from the analyzer and to match it with the sweeping
speed from the position controller to construct the desired radiation pattern. These two
devices communicate via a GPIB bus.
Setup the Spec Analyzer
Start Sweeping the Antenna
Spec. Analyzer Records
Power Levels
Antenna Sweeping Stops
I'l
Transfe Data to PC
Display pattern on PC
Figure 2-4 Conventional method for data collection
Figure 2-4 shows the flowchart of the conventional method for measuring the
antenna radiation pattern. All the steps in this procedure are initiated by the operator.
First, the spectrum analyzer is used to locate the precise carrier frequency of the received
signal. Next the analyzer is set to zero-span mode. In this mode, the input signal is
monitored and recorded at a single frequency, and this is set to the above-determined
carrier frequency. After the preparation step, the measurement will be started when the
position controller begins to scan the antenna across its off-axis angle at a constant speed.
As soon as the off-axis angle enters the range of interest, the spectrum analyzer is started
to record the power received. The sweep time of the trace in the analyzer is set such that
the recording finishes once the antenna leaves the desired angular range. After that, the
data stored in the spectrum analyzer is transferred to the computer, along with various
17
settings of the analyzer. This data represents a series of power levels of the received
signal at consecutive antenna pointing angles. The angular position of these data points
can be determined with the knowledge of the scanning speed from the position controller
and the time intervals between data points. The scanning speed indicates how fast the
antenna rotates, and its unit is degrees per second. The computer carries out the
necessary calculations and displays the obtained pattern.
In this measurement, the spectrum analyzer plays a major role; hence, the settings
of this instrument have a great influence on the resulting antenna pattern. During the
course of the data collection, the zero-span mode in which the analyzer is used requires
that the center frequency match the carrier frequency of the received signal. Even though
the rough estimate of the carrier frequency is available, it is necessary to determine a
more accurate frequency location of this test signal. To utilize the spectrum analyzer to
find the signal, the frequency spectrum for a narrow span in the vicinity of the known
rough estimate of the carrier frequency is obtained. In this spectrum, the test signal will
show up as an easily distinguishable peak. The display marker can be locked to this peak
and the marker's frequency is the desired carrier frequency.
Another important setting on the spectrum analyzer is the sweep time of the trace.
This is the amount of time in which the input power level is monitored and stored.
However, the analyzer has a fixed number of data points that its memory can store. As a
result, the time interval between two data points expands as the sweep time increases. In
addition, since the trace only sweeps once for the whole pattern measurement, in the
duration of the sweep time, the antenna should scan across the entire desired range of offaxis angle. The sweep speed of the antenna depends on position controller, as well as the
physical specifications of the antenna. The analyzer sweep time is calculated from this
antenna sweep speed. If the pattern covers a wide range of off-axis angle, there is a large
angular distance between two data points on the pattern.
Even though, the measurement is taken with the spectrum analyzer on zero-span
mode, the power level obtained is not at the exact center frequency with zero bandwidth,
but rather the power of the signal with a finite bandwidth at the center frequency. This is
the resolution bandwidth of the spectrum analyzer, which is a narrow band-pass filter
18
around the center frequency. The narrower the resolution bandwidth, the less noise
passes through, yielding a better signal-to-noise ratio. However, if the bandwidth is too
narrow, the signal component will be filtered out as well. Therefore, this resolution
bandwidth is set based on the characteristics of the test signal, i.e. how narrow the signal
bandwidth is, or how stable the carrier frequency is.
Once the antenna finishes scanning, the spectrum analyzer should have the
measured pattern stored in memory. This pattern can be verified visually on the analyzer
display. The pattern will then be transferred to the computer in the form of a series of
power level readouts. Using the antenna sweep speed (o, the trace sweep time T , and
the number of data points N, the angular distance between two data points 6 can be
obtained as follows
(OT
N -I
The unit of the transferred power levels is decibels (dB). These levels will be normalized
with respect to the highest peak in the pattern. This peak usually corresponds to the
boresight of the antenna for a co-polarization pattern. The off-axis angle for each point is
constructed using the reference of this peak. The radiation pattern is plotted with the offaxis angle in degrees on the horizontal axis and the power level in decibels on the vertical
axis.
This system for antenna radiation pattern measurement has several limitations.
This research project aims to identify and overcome these limitations. The first limitation
is the fixed maximum number of points on the radiation pattern. This is because the
whole pattern is constructed from a single sweep on the spectrum analyzer, and the
analyzer can store only a limited number of points on every sweep. As mentioned earlier,
this limit on the number of data points will result in a larger angular distance between two
consecutive points, as the total off-axis angle range that the pattern covers increases.
With narrow beam antennas, the angular distances between peaks on the sidelobs are
small enough that there are not enough points on the plot to identify these peaks clearly.
As a result, the existing system is capable of measuring a pattern with a wide angular
range for such antennas. In other words, the system has to make a trade off between
19
angular range and angular resolution. Clearly, this limitation exists because of the
spectrum analyzer and by the method it is used.
Next limitation comes from the system's lack of noise reduction feature. The
presence of noise along with signal in the input, as discussed in the previous section,
reduces the usable dynamic range of the system. As the off-axis angle increases, the
power level of the received signal decreases. If the difference between this off-axis level
and maximum power level detected at the boresight of the antenna exceeds the dynamic
range of the system, any variation in the input will not be detected; the pattern will hit a
plateau. For narrow beam antennas, the sidelobs decrease much more rapidly with offaxis angle. This results in a maximum angular range in the pattern before it flattens out.
The noisier the input signal is the smaller the range gets. The spectrum analyzer provides
some noise reduction capability by the means of a band-pass filter. However, this will
not help eliminate the noise portion that has the same frequency bandwidth as the signal.
Even though a computer is used in this system, it provides no pattern improvement. Most
of its computing power is not utilized, since the computer only does simple translation
from time to off-axis angle for the horizontal axis and displays the resulting pattern.
In summary, the conventional method for measuring the antenna pattern is simple.
The operator is given great control over the measurement. Nevertheless, the number of
data points is very limited. The computer, which controls the measurement, is not fully
utilized in this setup. Finally, other than the filters in the spectrum analyzer, no noise
reducing feature is available.
20
2.4
Characteristics of the Additive Noise
To effectively remove noise in the measurement, it is important to identify and
characterize the noise sources that the signal is subjected to. There are several noise
sources that are additive to the transmitted signal. Since the generation of noise by these
sources is statistically independent of the mechanism of generation of the signal, the
noise is statistically independent of the signal. The most important contributions are due
to thermal and shot noise from measurement equipment, as well as the atmospheric noise
that enters the satellite links. Other noise sources include extraterrestrial noise and
interference.
First and foremost, various instruments in the signal path from the transmitter site
through the relay satellite, to the receiver site can contribute to the thermal and shot
noise. These types of noise are Gaussian and white in the receiver band. [Raemer69]
summarizes the effect of this noise as a summation of three terms
Total noise= -10 log 0 Bz
-101og
10
Tab,
- (F,)d,.
The first term is associated with the receiver bandwidth, which is typically set to the
smallest value which still allows clean reception of the test signal. If the test signal has a
very narrow bandwidth, most of this component of the noise can be blocked out. The
second term in the expression above is related to the absolute temperature of the receiver.
This term can be reduced by cooling the receiver. For applications of antenna pattern
measurement, no cooling is used so Ta can be assumed to be about 300K, yielding a
noise amount of approximately -25dB (= -10loglo Tb,). In the last term in this
expression, the noise figure F, is actually the total noise figure of the cascade of
instruments along the signal path from the transmitter to the receiver.
A typical pattern measurement as described in the previous section takes a few
minutes to finish collecting data. The amount of time is small enough to assume the
operating condition of the instruments is stable, and the characteristics of the thermal and
21
shot noise generated remain unchanged. Thus, the noise power can be modeled as a
Gaussian distribution with constant mean.
In addition to the internal noise, there is atmospheric noise that enters the signal
on the uplink and downlink from the satellite. It arises partly from electrical discharges
in the atmosphere. This atmospheric noise level is nearly negligible at VHF and above,
and can be considered as white noise for the band-limited receiver used in the antenna
pattern measurement. Except for the highly impulsive noise due to nearby or overhead
thunderstorms, most atmospheric noise is Gaussian, and arises from thermal emission by
oxygen and water vapor molecules or clouds. Thus, it can be regarded as statistically
equivalent to internal noise (band-limited white, Gaussian, additive) within the receiver
bandpass. Unlike internal noise, however, atmospheric noise has variable mean as
electrical discharges can change quite rapidly during the course of data collection.
Another noise source in consideration is the fluctuation of the atmospheric
attenuation. The atmospheric attenuation may be due to natural constituents of the
atmosphere, irregularities along the transmission path, or weather conditions. This
includes oxygen absorption with a resonant peak at about 60GHz, water vapor absorption
with a resonant peak at about 22.4GHz, fog and cloud droplets and raindrops above
10GHz (where the drop radius becomes comparable to wavelength). The attenuation has
no direct contribution to the noise received. Nevertheless, the fluctuation in the
atmospheric attenuation causes the power level of the received signal to change even
when the antenna gain stays constant. This results in defected antenna gain
measurement. This type of fluctuation can be considered as noise with variable mean.
In summary, additive noise in the system is band-limited white noise with
Gaussian distribution. The noise sources can be divided into two groups: noise with
constant mean, and noise with variable mean. A noise reduction method that can filter
out variable-mean noise will also filter out noise with constant mean. However, utilizing
constant-mean noise reduction method alone, when the additive noise has variable mean,
will result in a distorted pattern.
22
Chapter 3
Computerized Data Collection
In the previous section the conventional system and its limitation on the size of a pattern
have been addressed. The spectrum analyzer is the bottleneck in this setup. However,
this research suggests a method to overcome this limitation without changing the required
equipment. Since the number of points stored in the trace for every sweep of the analyzer
cannot be improved directly, the only solution around this is to take more than one sweep
for each pattern measurement. In other words, each sweep of the analyzer will only
measure a segment of the pattern. Concatenating these segments will construct the
pattern with the full angular range.
As we recall, an antenna pattern is constructed from its directive gain values
measured at various off-axis angles. These angles need to be close enough together to
maintain the angular resolution. There are two ways to carry out a pattern measurement.
In the first way, the controller stops the antenna at different pointing angles of interest,
then the gain measurement will be taken at these stops. In the second way, the antenna
scans through the angular range of interest in a continuous motion, the gain will be
measured after fixed intervals. The former method is simple and can apply even for
antennas without motorized mount. This method is, however, very time-consuming. The
task of measuring the pointing angles at each stop is difficult and tedious, considering the
number of stops needed to maintain the necessary angular resolution. The latter method
is widely used, as most position controllers are capable of maintaining the scan of the
antenna at a constant rate.
23
The conventional data acquisition method makes use of the continuous scan of the
antenna. Since the spectrum analyzer only takes one sweep per antenna scan, the number
of gain measurements equals to the number data points in one trace of the analyzer. The
proposed data collection method overcomes this limitation by taking many sweeps for
each antenna scan. The more data is needed, the more sweeps will be taken by the
spectrum analyzer. Every time a new sweep is taken, the trace data in the analyzer's
memory is overwritten with new data. So the old trace data needs to be saved before the
new sweep is taken. The computer control allows the data to be downloaded
automatically from the spectrum analyzer between sweeps in a time saving manner.
Figure 3-1 shows the flowchart of the proposed data collection method. In this
figure, the shaded blocks represent the steps initiated by the operator. Compared to the
conventional system, the computer is given major control over the whole process. With
the conventional method, the measurement is done in three major steps: sweep-transferplot. The operator controls the spectrum analyzer to sweep the entire pattern. The
collected pattern is previewed on the analyzer display screen; and if the pattern is
satisfactory, it is downloaded and stored in the computer. In the proposed method, the
data collection is carried out in a measurement loop which involves the analyzer and the
computer. The computer controls the whole process. During each iteration, the computer
starts the sweep then downloads the trace data from the analyzer after each sweep
finishes. All this happens while the antenna continuously scans through the whole
desired angular range. A data processing step is also added in this scheme. In this step
the computing power is utilized to effectively reduce noise, improving the dynamic range
of the measurement. This step will be discussed in more detail in the following sections.
24
Start Sweeping
the Antenna
Enter Setup
Parameters in PC
__
__ _
._
..
yStart Data
PC Commands Spec.
PrAnalyzer to Record
Collection
on PC
PC Setups
Spec. Analyzer
Data Transferred to PC
Done
No
Sweeping?
Yes
Data Procesed
Pattern Displayed
Figure 3-1 Data collection by Computer
The proposed measurement technique has a potential problem associated with the
transfer of data over the GPIB bus. Having to transfer data from the spectrum analyzer to
the computer during a scan creates some gaps in the data collected. As soon as the data
transfer starts, the spectrum analyzer halts its data collection. These gaps correspond to
some off-axis angles at which no measurement is taken. Figure 3-2 shows the amount of
data collected over the whole angular range. The solid segments indicate the angles with
measurements. Typically each segment like this consists of 600 to 700 measurements,
depending on the spectrum analyzer model. The crossed-out sections are the pointing
angles that the antenna scans through during the data transfers. The length of these gaps
is proportional to the amount of time it takes to transfer the whole trace memory over the
GPIB bus that connects computer to the spectrum analyzer. This may take anywhere
25
between 50ms to 10OOms, depending on the transfer modes. Most modern spectrum
analyzers support text and binary transfer modes. While convenient, text mode is
typically slow. Binary mode allows faster data transfer, as readouts are stored in a more
compact form. In order to obtain evenly spaced measurements, the data processing needs
to be in such a way that, in this diagram, every solid segment results in one point on the
pattern. In order to maintain the angular resolution, the crossed-out segments are small
enough so that these points are close together in terms of off-axis angles. As a result, the
transfer time needs to be minimized. For the Hewlett-Package spectrum analyzer of the
856XE series available for the project, the shortest transfer time is approximately 60ms
when using binary transfer mode with 601 data points in a trace. The analyzer is also
controlled to alternate immediately between data measurement and data transfer. The
minimum sweep time for spectrum analyzer of this series is 50ms. Adding these two
amounts, the minimal distance between every two points in the pattern is 1 Oims. In other
words, roughly a 500-point plot for the pattern can be collected if it takes a minute to
scan the antenna across the angular range of interest.
Gaps
I ~
ZAA
/
IAAA
tVVV'
4
/vvvv
:V
\AA/
V\
Angle
I "Collected
Data
'V
AZ
Data Segments
Figure 3-2 Gaps in the collected data
26
The lengths of the gaps in the data collection are not all the same due to the
interaction between the computer and the GPIB bus. The transfer time is lengthened if
the bus is busy, or the computer cannot keep up with the bus speed momentarily. It is,
therefore, necessary to keep a record of the time of all the data transfers. This record will
be used to construct the plot of off-axis angle versus antenna gain, from the series of
antenna gain measurement over time. The computer puts timestamps on the collected
data at the start of every sweep. Transfer time can be calculated from the time difference
between two timestamps and the sweep time. Timestamps use the reference from the
computer internal clock, which has the precision of 1 ms.
The computerized data collection method incorporates significant improvement
over the conventional method. Over the similar scan of the antenna, the number of data
points collected is now over 600 times that using the conventional method. This method
provides the necessary data sample size for noise reduction processing. The
measurement procedure in the proposed method is quite similar to the conventional
method in its simplicity and time efficiency.
27
Chapter 4
Noise Reduction by Averaging
This project presents a very unique communication problem. Just like any
communication system, a message is delivered from one point to the other. The message
is, however, not contained in the test signal. In the simplest form, the test signal is just a
constant-amplitude sinusoidal wave with known frequency and phase. The unknown
message is transformed to the signal amplitude once the signal arrives at the receiving
antenna. This is not a problem of detection, but a problem of estimation. Estimation is
inherently the harder problem of the two. In a detection problem, there is a finite set of
possibilities for the results; and the performance can be measured by the ratio between
faulty detection and correct detection. In an estimation problem, all estimations are
incorrect; the question is just how much error is associated with the estimation.
Noise n[i]
RF Generator,
El
s]
Transmitter
Spectrum
Analyzer
Antenna Gain g[i]
Figure 4-1 Communication over an additive Gaussian noise channel
28
Figure 4-1 shows a diagram of the communication system in the antenna pattern
measurement. Let's assume a constant-amplitude continuous-wave signal is used for the
measurement. The output signal of the receiving antenna (also the antenna-under-test)
can be represented by a series of samples as followed
y[i]= Acos(co
with A, co and
e
i+e)+
w[i], i =0,,...,N-1
being the amplitude, carrier frequency and the phase of the signal
respectively; and w[i] being the additive noise. The amplitude A is the quantity of
interest and it will be estimated by the statistical mean of the input y[i].
29
4.1
Characteristics of the Estimation by Averaging
As mentioned in previous section, this signal is fed into the spectrum analyzer which, in
this case, acts like a total power radiometer. The readings produced by the analyzer
correspond to the power levels of the received signal. These power levels consist of the
power of the signal and the power of unwanted noise, presented as
i = 0,1,..., N -l
x[i]= s +n[i],
where the signal component s is assumed to stay constant when these N measurements
were taken for each segment in the pattern. The amplitude of the signal component s is
the power of the received signal, multiplied by the antenna gain. The noise component
n[i] are independent identically-distributed random variables with zero-mean Gaussian
distribution with an2 variance, N(m. , an 2).
As discussed in detail in section 2.4, the
additive noise can be separated into two components with constant mean and variable
mean. The following sections will investigate these components. In addition, the effect
of applying a static measurement model on a dynamic signal will be discussed. In the
static measurement model, the antenna is stopped for each reading. If the antenna is in a
constant motion, the measured signal is dynamic signal.
4.1.1 Zero-Mean Noise
This is the simplest case and a special case of the constant-mean noise when the mean is
zero. The maximum likelihood estimator for this problem is simply the arithmetic mean
of the inputs [Raemer69]
~() 1
S()= -
N-i
1x,[i] = s(O)
N i-o
where s(O) and S(O) are the desired signal and its estimator in the data segment
corresponding to the off-axis angle 0 ; and x, [i] is the input data in that segment. The
signal is assumed to stay constant within each segment.
30
The variance of the estimator is calculated as follows
a
2
=((x_s)2)=Kx2) s
2
N2 1:((s + n[i])(s + n[j])) - s
N 1 N-1
iwjO
2
nan]
N
where the noise samples n[i] and n[j] are assumed to be statistically independent and
have zero mean. This assumption results in the term (n[i]n[j]) to vanish for i #
j.
The
variance of the estimation is smaller than the input variance by a factor of N, which is the
number of readings. This estimator is also consistent, as the noise can be completely
removed given the long enough data sample, i.e.
2
2
C
__2
" -+0 as N -- >oo.
=
N
If enough samples are averaged the noise variance will always vanish, and the exact
signal can be recovered from the measurement.
4.1.2 Constant-Mean Noise
In the case of a noise with non-zero constant mean, the noise in every sample can be
decomposed into a zero-mean noise and a constant value as
n[i] = m + n, [i].
If the noise has a constant mean through out the measurement, the estimation for
each segment is now biased by an amount m, ,which is constant throughout the pattern
1 N-1
S(O)= -x6[ 1
N j=o
]= S(O)+ M.
31
This bias, however, results in no error in the measurement if all measured data can be
shifted down together by an amount of m, 2 .
4.1.3 Variable-Mean Noise
If the mean of the noise varies during the measurement, the estimation can be carried out
in the same fashion as in the case with constant-mean noise, except the estimation will be
biased by a varying amount m, (0)
)=
x
[i] = s(O) + Mr (0).
The estimation can no longer be made unbiased by a simple shift of measured values;
instead, each segment has a different mean noise. This will result in a non-repeatable,
defective antenna pattern.
4.1.4 Dynamic versus Static Measurement
In this data processing method for noise reduction, the antenna pattern measurement
consists of a series of data segment measurements. The signal received in each segment
is assumed to be constant for that entire segment. These are static measurements. This is
a very important assumption, because the signal, or the antenna gain in this case, always
changes as the antenna is scanned in its off-axis angle. This assumption of constant
signal is acceptable for this application because the antenna pattern is a slowly varying
function compared to the angular range that each segment covers.
In the case that the signal is not a slowly varying function, or a dynamic
measurement, the problem has to be addressed differently. The effect of using a noise
reduction method for a constant signal on a varying signal will be investigated in this
section. The input can be decomposed to the signal and noise as before but the signal is
now a function
i = 0,1,...,N ,
x[i] = s[i] + n[i],
32
where the additive noise has Gaussian distribution with zero mean. The arithmetic mean
of the input is the mean of the signal
s= -
N
x[i]= -
N
s[i].
This estimated signal is a smoothened version of the original signal. The longer the
averaged sample, the smoother the signal becomes. If the sample is too long, it exhibits
the over-smoothing problem as demonstrated in Figure 4-2. The estimated signal no
longer follows the original signal closely in amplitude. All sharp edges in the signal have
been removed. In order for the dynamic measurement to produce meaningful results, the
segments within which data is averaged to a single point need to be sized small enough so
that the signal does not vary in each segment. The measurement can then be
approximated by a static measurement, by replacing the varying signal with the averaged
values. It is a challenging task to achieve this when the pattern is going through peaks, or
nulls. This effect is most severe at the peaks and especially the nulls of the pattern.
1.6
1.4
1.2
1
0.8
E
0.6
0.4
0.2
n
0
5
10
20
15
Off-axis angle (degree)
25
Figure 4-2 Over-smoothing problem
33
30
35
Therefore, in order to improve the performance of the noise reduction method, the
signal should change as little as possible. In this implementation, that would require to
minimize the time it takes to collect the data in a segment. This duration is determined
by the sweep time of the spectrum analyzer, which should be configured at the smallest
setting possible.
4.2
Simulation
A simulation of the antenna pattern measurement has been implemented in the MatLab
environment to investigate the characteristics of the noise reduction method by averaging
4.2.1 Objectives
In this simulation, the data processing subsystem is tested for its noise reducing capability
by using the averaging technique. The data input to this subsystem is simulated based on
the characteristics of the signal in the actual measurement. The noise reduction method
by averaging is implemented with the same algorithm used in the real system. The
simulation produces outputs comparable to the measured antenna patterns.
In the first test, the effect of the number of samples on the variance of the noise is
investigated. In the second test, two different noise sources have been used to
contaminate the signal, and the ability to recover an antenna pattern from this signal is
evaluated. One source has Gaussian noise with zero mean; while the other is Gaussian
noise with non-zero mean.
4.2.2 Implementation and Results
First, the program creates the input data to the data processing subsystem of the antenna
pattern measurement. This input is the power level of the received signal with the
addition of noise. This power level is varied in amplitude following the antenna gain at
different off-axis angles as the antenna is rotated. The simulation generates this input
signal by adding a Gaussian noise into the sampled antenna pattern. This pattern will be
34
compared to the antenna patterns that the noise reduction methods recover from the noisy
input. The antenna pattern is simulated by a zero-ordered Bessel function of the first
type, J, (p) (see Figure 4-3). An input signal with zero-mean Gaussian noise with -10dB
variance is shown in Figure 4-4. Figure 4-5 shows the signal with the same noise
variance, but mean noise is -10dB off the signal peak.
The input signal has a total of 100,000 data samples covering the off-axis angle
from 00 to 450. The data transferred from the spectrum analyzer in the proposed data
collection procedure is simulated by a series of 100-point segments. The gaps between
two segments are 100 points long. There are 500 data segments, which will produce an
antenna pattern with 500 points, after processing.
0
-5 --
S-10-
~0
Z
-20-
-25-
-30
1ppp
0
5
10
15
20
25
30
35
40
Off-axis angle (degree)
Figure 4-3 Bessel function as simulated antenna pattern
35
45
5
1
1
1
1
1
1
I
0
-5
-10
-15
ca)
0
0
-20
-251
-30 1-
-35'1
0
5
11
15
10
20
25
Off-axis angle (degree)
30
35
40
45
Figure 4-4 Input signal with zero-mean noise
5
0
-510-10c
> -15 N
= -200
Z -25-
-30-35-
-40
0
5
10
15
30
20
25
Off-axis angle (degree)
35
Figure 4-5 Input signal with non-zero mean noise
36
40
45
Figure 4-6 shows the estimated patterns in the first part of the simulation overlaid
on the actual pattern. The sizes of the averaged samples are 10 points, 50 points, and 100
points corresponding to an improvement in the noise variance of 10dB, 17dB, and 20dB.
The additive noise has zero mean and a signal-to-noise ratio of 10dB. These results
verify the predicted relationship between the noise variance and the number of samples
averaged. As the size of the sample increases, the output pattern gets smoother. This is
the indication that the noise variance has been reduced. The recovered patterns closely
resemble the original pattern in Figure 4-3.
The effect of averaging on the noise floor is also verified. While averaging
improves the noise variance significantly, the noise floor at -10dB has no visible
improvement. The produced patterns rarely have a value below the noise floor,
regardless of the sample size. This behavior strongly agrees with the conclusion in the
previous chapter about this method's ineffectiveness on enhancing the dynamic range.
37
10 samples averaged
0
101
c,)
(1)
N
-20
E -30
0
z
.
-
-40
0
5
10
15
Recovered
Original
I
40
45
30
35
I
I
I
30
35
40
45
30
20
25
Off-axis angle (degree)
35
40
45
20
25
50 samples aweraged
0
0
101-
M
Co
a)
-20
L
E -30 0
z
-40 I
0
I
I
I
I
I
5
10
15
20
25
100 samples averaged
r
M
-10
-20
_0
E -30 -
0
-40
0
5
10
15
Figure 4-6 Simulation for noise reduction by averaging for zero-mean noise
38
0
-5-10
-15-0
0)
N
0
-20-25-
z
-30-35- - --
-4C
0
5
10
15
25
20
30
Recovred
Original
35
40
45
Off-axis angle (degree)
Figure 4-7 Averaging zero-mean noise simulation
0
-o-
20-
E- -250
-30-35Recovered
-40
I
p
0
5
10
15
20
25
30
Off-axis angle (degree)
Original
.
35
Figure 4-8 Averaging non-zero-mean noise simulation
39
40
45
In the second part of the simulation, the effects of different noise sources on the
performance of this noise reduction method are studied. The unwanted fluctuation in the
input signal is the power of the additive noise; hence, the noise source in the antenna
pattern measurement always has a positive mean. This is, therefore, very important to
characterize the inconsistency between the original pattern and the pattern recovered by
the averaging method. Figure 4-7 and Figure 4-8 show the recovered patterns compared
to the original pattern when the noise source has zero mean and when the noise source
has -10dB mean, respectively. When noise has zero mean, the noise reduction method
can reproduce the original pattern very well, except for the limited dynamic range
observed at the nulls. However, when the mean power of the noise is non-zero, the
estimated pattern is slightly higher than the original pattern. The averaging calculation
has been done in linear scale of power (Watts), then plotted in logarithmic scale of
normalized gain (dB). As a result, the shifted amount is higher at larger angles, as the
signal gets weaker at these angles. The pattern is leveling out as off-axis angle increases,
consistent with lack of dynamic range in the measurement.
40
4.3
Implementation
An antenna pattern measurement system has been implemented based on the
computerized data collection method. The data processing subsystem utilizes the
described noise reduction method. The computer software has been written using
Microsoft Visual Basic under Microsoft Windows 98 environment. The computer is
equipped with a National Instrument's GPIB controller card. A Hewlett-Packard 856XE
series spectrum analyzer is used in the setup. The software can handle the GPIB
command set for spectrum analyzer of this series, even though support for other analyzers
can be implemented with ease.
In this system, the input data samples to be processed are taken in a series of data
segments. Each segment consists of the whole trace data memory. For the spectrum
analyzer in this implementation, each segment has 601 data points. The sweep time on
the analyzer is set to its minimal value of 50ms. The data transfer is at binary mode, the
fastest mode with transfer time of about 60ms. This timing setup provides the highest
angular resolution at each antenna scan speed.
After the data collection finishes, the stored data samples are processed to reduce
noise. Data is processed segment by segment. Each point on the pattern is the average of
all the samples of a segment. So a data set of 500 segments would produce a 500-point
plot of the antenna pattern. According to calculation presented above, the signal-to-noise
ratio would be improved by 601 times, or roughly 27.8dB. The calculations are carried
out on power levels measured in linear scale (Watts).
41
Chapter 5
Noise Reduction with Pulse Modulation
5.1
Motivation
Even though the noise reduction method presented in the previous section can provide
very good results in reducing noisy fluctuations, this method has its limitations in the
application of antenna pattern measurement. First, the additive noise in the received
signal does not always have a constant mean. This method may produce faulty patterns
with variable-mean noise. Secondly and more importantly, this method does not change
the noise floor in the measured pattern; hence, the dynamic range of the measurement is
not improved. A noise reduction method involving a modulated test signal is proposed to
address these problems. In each case, the test signal is modulated in amplitude with a
square wave at a much lower frequency than the carrier frequency.
When the additive noise has constant mean, the entire pattern is shifted up by the
amount due to the noise. Normalizing the pattern can get the relative gain corrected.
However, when the mean of the noise power varies a considerable amount during the
measurement, this noise fluctuation cannot be distinguished from the variations of the
antenna gain. The measurement via this method is not reliable, as the resulting pattern is
not repeatable. The proposed method is able to determine the mean value of the
fluctuations in the noise power, and can compensate for the gain measurement
accordingly.
42
As discussed in section 4.3, the noise reduction method by averaging the input
samples can improve the noise variance in the signal by over 27dB. This improvement in
the noise variance; however, has little effect on the dynamic range of the measurement.
This is because averaging out the noise component in the signal does not lower the noise
floor. Since the noise floor is the noise power in the absence of the signal, averaging just
makes the noise floor approach its mean value and a constant line on the pattern. In other
words, averaging makes the measurement of the noise power more accurate, but it does
not remove that unwanted power from the measurement of the signal. Hence this line
representing the noise floor masks out all antenna gain fluctuation that is smaller than the
noise power in magnitude.
0
-- - -- - - - - -.- - - - - - - - -.......
- - - - - -........................
1................
-20 - - - - - -.- - - - -.
-10
N
-
z -40 ----
- --
00
-601-
-5
0
5
10
30
25
20
15
Off-axis angle (degree)
35
40
45
50
Figure 5-1 Effects of averaging on the noise floor
Figure 5-1 shows the effects of noise reduction by averaging on the noise floor of
the pattern. The two plots in this figure are the antenna pattern from the same
measurement. The top line is the unprocessed pattern. Starting from 5* off-axis, the data
43
get extremely noisy and no pattern can be determined at this noise level. The noise floor
for this pattern is the upper edge of the noisy part, around -28dB. The bottom line shows
the processed pattern. Each point in this pattern is the average of 601 points from the
unprocessed pattern. The noisy line becomes a smooth solid line at around -30dB for the
off-axis greater than 150. The antenna pattern simply does not level out at -30dB. This
is the limitation of the noise floor. There is an improvement of 2dB in the noise floor and
an improvement of 100 in angular range due to averaging. However this improvement is
nowhere near the calculated improvement presented in section 4.3 as 27.8dB. The small
improvement of 2dB observed is due to the fact that the initial noise floor is based on the
upper values of the fluctuation. When the fluctuation is smoothened out, the noise floor
is at the averaged values, which are lower than the upper bound of the fluctuation.
The variance of the power measurement has been improved significantly by the
averaging method. However as long as the noise level is not subtracted out from the
readings, the noise floor will still limit the dynamic range of the measurement. A
proposed method should take advantage of the fact that the noise floor can be measured
quite accurately by averaging the input when no signal is present, and compensate for the
measurement of both signal and noise. If this is achieved, a fluctuation in the antenna
gain that is smaller than the noise can now be detected.
44
5.2
Pulse Modulation Technique
The pulse modulation of the test signal is introduced as an improvement to the averaging
method discussed earlier in order to enhance the performance for variable-mean noise,
and extend the dynamic range of the measurement. The signal is demodulated during the
data processing stage by the computer. The modulation allows the program to distinguish
and measure the power levels of the input with and without the wanted signal. The noise
component can then be eliminated from the noisy signal samples by simply subtracting
the mean of the noise from the measurement.
Noise n[i]
kli]
RF Generator,
Transmitter
FI
ReevrComputer
ReevrDemodulator
TL
Antenna Gain g[i]
Wave Gnerator
Figure 5-2 Noise reduction with amplitude modulation
Figure 5-2 shows the measurement setup with a modulated signal. The test signal
is modulated in amplitude with a series of on-off pulses. When the pulse is on the signal
generator outputs the sinusoidal test signal at its full amplitude. When the pulse is off, no
test signal is transmitted. The receiver setup remains the same as with the continuous
wave signal. The pulse frequency is significantly smaller than the carrier frequency, so
that the duration of the on pulse is sufficiently long for the receiver to measure the power
level. The power of the received signal will alternate between two levels due to the pulse
modulation. The program will detect these switches in the received power and determine
the presence of the signal in the input.
45
-45
- - - ---- -- --
-50
-.-..-.- ....-.
-
---------- -- . - - - - . - - - -------------- - - - - - - - - - -
-55
-.
- -.
- -.
- -.
- -.
- -.
-
V
-60
0)
0
0~ -65
*0
-.-. .-. .-. .-.--.--.---- - -- -- ---- -
-70
0
0)
- - - - - -- - - -
-75
-80
-.
-.-.
-.
.----.
.-.
-
-85
90
0
5
10
15
20
25
Time (ms)
30
35
40
45
50
Figure 5-3 Modulation in the received power
Figure 5-3 shows a sample of the modulated signal when received at the antenna
under test over a 50ms period. This signal corresponds to the power levels measured in a
segment; hence, the signal power remains relatively constant. There are two power levels
observed. The higher level at -50dB corresponds to the input when the signal is on;
while the lower level at -75dB is received when the signal is off. Let xo [i], xff [i] be the
sample of the received power when the pulse is on and off
xo [i]
n[i] = m n+ n[i]
1
xon[i]= s + n[i]=s + m, +n0 [i],
In the expression above, i denotes the index of the sample in a segment, n[i] is the
additive noise power which can be decomposed to a zero-mean noise n0 [i] and the mean
power mn as a constant. The average of the samples when the pulse is on is the total
power of both signal and noise; and the average of the samples when the pulse is off is
just the noise power:
S
S o=
=
xoff[i] =mn
Xo
U] = S+
46
M.
The difference between the averages corresponding to the on and off states of the
pulse is the desired signal power
on
M
=
off -S
This estimation is valid as long as the noise behavior is unchanged during the time
the pulse switches from one state to the other. This is a more realistic assumption than
having the noise behavior remain unchanged for the whole pattern measurement, since
the pulse period is much smaller than the time it takes to measure the entire pattern. In
this implementation the maximum pulse period is 50ms, while the typical pattern takes
over a minute for data collection.
The improvement in the dynamic range of the measurement can be calculated
from the size of the averaged sample. Since, the estimation
s
of the signal is obtained by
subtracting the noise power measured, the noise floor in this estimation is the r.m.s. error
of the noise power measurement multiplied by
J
By averaging, the noise variance is
improved by N, the sample size, the standard deviation is improved by
-\NI .
As a result,
the noise floor is lowered by IN /2 . However, as the test signal is transmitted with a
fifty-percent cycle, the effective noise floor improvement decreases by a factor of -F
Amn =10og1 0
N
/4 (dB).
This is an 11 dB improvement in the dynamic range.
The addition of pulse modulation on the amplitude of the test signal can solve the
two problems that the noise reduction method by averaging cannot. First, in each data
segment the mean noise power is calculated and subtracted out from the output. Even if
the noise has its mean value varying from one segment to another, the mean fluctuation
will no longer perturb the output. Secondly, the dynamic range of the measurement is
improved as the noise floor is significantly lowered, if not completely removed. In the
previous noise reduction method, the dynamic range is limited by the noise floor mn. In
this method, the mean noise power is removed from the output
47
si].
In theory, the noise
floor can be completely removed in an ideal case where the number of samples N -> oo
and signal and noise mean power stay constant forever.
5.3
Simulation
A simulation was implemented to demonstrate the improvement in the noise reduction
performance by the pulse modulation method.
5.3.1 Objectives
The noise reduction method presented in this chapter originated from the averaging
method. As a result, this method has very similar performance to the previous method in
many aspects. The noise variance improvement is equivalent between the two methods,
except for the -3dB loss due to the smaller effective averaged sample size when the
modulation is introduced. This simulation will explore two areas where the averaging
method cannot provide satisfactory results: i) in the case of a variable-mean noise; ii)
improving the dynamic range of the pattern. In addition, the pulse rate of the amplitude
modulation is varied, and the change in the noise reducing capability is observed.
5.3.2 Implementation and Results.
The signal and noise model implemented in this test is similar to the simulation described
in 4.2.2. Modifications in the setup include the pulse modulation in the amplitude of the
test signal. A sample of the received power is shown in Figure 5-4 over a 120ms period
where the pulse period is 20ms. For each segment, the phase of the pulse is fixed so that
the first data point in the segment is always the rising edge of the pulse. As a result, no
pulse detection scheme is needed.
48
5
0
-5
V
U)
0
a
-10-
V
U)
C.)
U)
-15-
-20-
-25-
-30
0
40
20
60
Time (ms)
120
100
80
Figure 5-4 Input signal with 20ms pulse
0
-5-10-
c
-15-
-20
N*-
E
"-25-30-35-
Recovered
-----
-40
'
0
5
10
15
30
25
20
Off-axis angle (degree)
Original
35
40
45
Figure 5-5 Simulation for pulse modulation with non-zero mean noise
49
I
-N
-
Figure 5-5 shows the recovered pattern when the pulse modulation method is
applied on the signal with constant-mean noise. The additive noise is generated with a
signal-to-noise ratio of 10dB and a constant mean power of -10dB less than the signal
power. The pulse that modulates the signal in this test has a period which is equal to the
length of a data segment. Compared to the simulation results for the averaging method
shown in Figure 4-8, the recovered signal no longer deviates from the original signal.
In the next test, a Gaussian noise with a mean varying linearly from -10dB
relative to the signal power at the boresight to -3dB at 450 angle is added to the signal
(see Figure 5-6). The highest signal-to-noise ratio is 10dB at the boresight. The
simulation is repeated twice with two pulse rates. In the first run, the pulse period is 100
data points, or one pulse per segment. In the second run, the pulse period is 50 data
points, equivalent to two pulses per segment. The antenna patterns recovered by the
modulation method are shown in Figure 5-7. Regardless of the pulse rate, the effective
number of data sample to be averaged is still one half the size of the data segment, 50 in
this case.
0
-5
10
co
15
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
..
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
...
.
.
.
.
.
.
.
.
.
.
. .
N
20
0
Z
-25-
.....
......
............
......
......... ...... .......
.............. . . . . . . . . . . . . . . ..
-35
0
5
10
20
25
30
15
Off-axis angle (degree)
35
40
Figure 5-6 Additive Gaussian noise with variable mean
50
45
In the presence of the variable-mean noise, the averaging method will not be able
to correctly recover the original pattern. On the other hand, the patterns produced by the
modulation method closely follow the original pattern. This proves that this method can
not only handle non-zero mean noise, but also variable-mean noise, both of which the
averaging method cannot handle effectively.
One pulse per segment
0
-5
-10
-15
_0
N
-20
-25
0
z -30
-35
-40
Recowered
Original
-
35
40
45
I
I
35
40
-
5
0
10
15
25
20
30
Off-axis angle (degree)
Two pulses per segment
0
-5
E -10
-15
-20
I
SI
I
I
I
N
-25
0
Z -30
-35
-40
0
5
10
15
30
25
20
(degree)
Off-axis angle
Figure 5-7 Effect of different pulse periods with variable-mean noise
51
45
The dynamic range is determined by the difference between the maximum gain
and the lowest measured gain that is not due to noise. These above patterns show a
dynamic range of as much as 20dB, corresponding to an improvement of almost 10dB in
the noise floor. For the data segments with 100 points, the modulation method promises
8.5dB improvement. These results demonstrated the dynamic range improvement
introduced by the pulse modulated test signal.
Under variable-mean noise, the pulse period of 50 may outperform the larger
pulse period. Shorter period means the measurement alternates between the signal and
the noise more frequently; hence the change in the noise behavior when switching
between measurement would be less. The simulation results, however, do not show
much difference in the performance with two pulse periods. This can be explained by the
small size of the segment compared to the total data sample. A movement of the mean of
the noise can be significant in the overall pattern, but at the same time insignificant
within a data segment. Both modulation setups produce excellent recovery of the original
antenna pattern.
52
5.4
Implementation
An antenna pattern measuring system has been implemented based on this method of
noise reduction. The instrument setup for this system is very similar to the
implementation of the system that utilizes averaging method for noise reduction,
described in Section 4.3. Additional equipment may be needed on the transmitting site to
generate modulated test signal. An RF signal generator is usually used to provide a
continuous sinusoidal signal to be transmitted. Signal generators similar to the HewlettPackard 8672A can modulate the output signal in amplitude using an external source.
For this setup, a waveform synthesizer was used to create the square wave that drives the
signal generator as shown in Figure 5-8.
RF Signal
Generator
RF
LNA/LNB,
Attenuator
---
Waveform
Synthesizer
Figure 5-8 Generating modulated signal
More advanced RF signal generators, like the Hewlett-Packard 83620A, may be
available at the test site. Signal generators of this type have an internal waveform
synthesizer capable of standard waveforms like square wave, saw-tooth wave, triangle
wave, and sinusoidal wave. These waveforms can be used to drive the signal modulation.
The waveform generator, whether internal or external, is set to produce square wave with
the desired pulse width and pulse period. The RF signal generator will operate at the
modulated mode with 100% amplitude modulation. This creates the "on-off' pulse in the
53
RF signal. The generated signal is then amplified or attenuated appropriately before fed
into the transmitting antenna.
On the receiving site the signal is demodulated at the post-detection stage. The
data processing program will detect the pulses after all the data is collected. No reference
signal is transmitted between the two sites for the purpose of synchronizing to the pulse.
With the knowledge of the pulse characteristics, the program will search through the data
samples in each segment to locate the start and stop of the "on" and "off" pulses. At the
position where the pulse switches states, the input jumps abruptly from one level to
another level, called the rising edge. The positive rising edge corresponds to the switch
from the "off' state to the "on" state, and the negative rising edge to switch from the "on"
to the "off' state. When the signal is strong these rising edges can be easily detected.
The search algorithm does not actually try to detect the positive or negative rise of the
pulse as this task is impossible in the extremely noisy signal at large off-axis angles. In
each segment, the program, instead, locates the position of the pulses by searching for the
one that give the largest detection response. At this position the difference between the
averaged power levels of the "on" pulses and the "off' pulses is maximized.
While this method is more computationally intensive than the rising edge
detection method, the resulting pulse detection is more reliable. The averaged power
levels of the "on" and "off' pulses at all possible positions are calculated and compared,
and the largest response is most likely due to the square-wave modulation, rather than
random noise. Even when the input is extremely noisy, and the positive or negative rise
edges of the pulse is perturbed by the noise, this method still works, as it exploits the
overall effect of the amplitude modulation on the received signal.
54
-40
-60
o
-2-- 1-- ---
-70
0 -..
-5
-50
~-80
0
9
.
.
..
-.- - .
.
--
..
-. - -
..
..4----0..
.. . - -. . ..
- ..-. . .
-
.
.
.
.
.
-
CCun
-1101
0
100
200
300
400
500
600
Count
Figure 5-9 Detecting pulses in a segment
Figure 5-9 shows an example of pulse detection in a data segment in the vicinity
of the boresight of the antenna. The segment has 601 data samples. The pulse rate is set
so that the segment is only two pulse periods long, equivalent to 300 samples per period.
The pulse width is also set to half of the period, or 150 samples. As a result, there is at
least one positive or negative rising edge of the pulse in the first 150 samples of the
segment. In the example shown above, a negative rising edge can be found at the 4 3th
data sample of the segment. The program will only have to search for the starting
position of the first pulse in the first quarter of the data segment, reducing the search time
by four times. The starting positions of the following pulses can be calculated using the
pulse period. This search range of 150 samples will change as the pulse rate changes.
The size of the data segment in this implementation is 601. This is due to the size
of the trace memory of the Hewlett-Packard 8563E spectrum analyzer used in the
receiver setup. However, the waveform of the pulse modulation does not have to be
exactly the same as in the example presented above. A waveform that provides the best
performance in noise reduction is selected. As long as there is an integer number of pulse
fit in the data segment, the effective data sample size will be half the size of the segment,
55
or 300. This is because all samples in the "on" pulses are calculated separately from the
samples in the "off' pulses.
The effect of the different pulse rates lies on the ability to remove noise with
variable mean. As the pulse rate increases, the time between an "on" pulse measurement
and an "off" pulse measurement decreases. As a result, the change in the input power
due to the variable mean of the noise is reduced. The error of the measurement is
improved.
Nevertheless, the pulse rate cannot be too high. If the pulse period is too small,
the timing resolution problem in the spectrum analyzer will arise. The analyzer makes
601 measurement over the duration of a segment, which is 50ms on the fastest mode.
50
Each measurement will take roughly ns. When the pulse half-period is in this order
601
of magnitude, the pulses may keep switching in the middle of a measurement. "On"
pulses and "off' pulses can no longer be distinguished.
5.5
Other Modulation Schemes
The amplitude modulation on the test signal in the noise reduction method presents itself
to be an effective way to lower the noise floor; hence increase the dynamic range.
However the total signal power is lost by -3dB as the signal is transmitted with fiftypercent duty cycle. Frequency modulation and phase modulation, as well as more
complex source coding methods will increase the duty cycle to one-hundred percent.
These modulation schemes have not been studied further in the scope of this project, as
the equipment required in their implementation is not typically available at antenna
ground stations.
56
Chapter 6
Experimental Results
The two noise reduction methods presented have been tested successfully by software
simulations. However, these simulations do not provide conclusive evidence that these
methods will work in a real communication system. This is because the test data is
simulated based on the same mathematical models for signal and noise that these
methods use. In a real system, the input signal and noise will not conform completely to
these models, so the results from the proposed noise reduction methods might not be as
predicted. The performance of such system can only be truly tested experimentally.
6.1
Objectives
An experiment was set up to evaluate the improvement in the antenna measurement of
the proposed system. Using the theoretical prediction and the simulation results, the
system is configured to give the best performance out of each noise reduction method.
The computerized data collection method has been implemented and grouped with the
data processing subsystem into a software package for antenna pattern measurement.
The improvement in the dynamic range of the measurement is the main objective
of this experiment. An antenna pattern measurement is repeated several times as the
equipment setup is changed. This allows the two noise reduction methods to be tested
with different signal levels. The noise variance and the resolution of the pattern are also
analyzed in this experiment. The experiment setup includes equipment that is typically
available at antenna ground stations.
57
6.2
Implementation and Results
The experiment has been carried on an outdoor antenna test range. Similar setup that
involved a relay satellite can be arranged; but the test range was chosen as it provided a
very well controlled environment. The distance between the signal source and the
receiving site is 1760ft, sufficiently long for the antenna under test.
HP 8672A
RFGenerator
-30dB
Switch
Attenuator
HP 83620A
RF Generator
Figure 6-1 Equipment setup at the transmit site
Figure 6-1 shows the equipment setup at the signal source. Two signal generators
are used along with a remotely controlled switch to provide easy access to continuous
wave signal and modulated signal. The Hewlett-Packard 8672A generates a sinusoidal
signal at Ku band, 11.7GHz. The Hewlett-Packard 83620A provides an RF signal at the
same frequency, but this signal is modulated in amplitude by an internally synthesized
"on/off" pulse. The two generators output the power level, and this level can be
controlled remotely. The transmitting antenna has a diameter of 6ft, with an efficiency of
approximately 65%, providing a gain of about 45dBi. An attenuator of -30dB is used to
bring the total power down, creating a noisier-than-normal test signal.
58
RF
HP 8563E
Spectrum
Analyzer
GPIB
Computer
Position Controller
Figure 6-2 Equipment setup at the receive site
Figure 6-2 shows the receiver setup. The antenna under test is an offset single
reflector antenna. The reflector is made from wire mesh and has the dimension of 25in
wide by 27in tall. The antenna output is amplified by an LNB that brings the carrier
frequency down to 1.95GHz. The antenna is mounted on a universal platform controlled
by a position controller model 4139 by Scientific-Atlanta. In this setup, the antenna can
be positioned in a wide range of azimuth and elevation angles. In addition, this position
controller is capable of scanning the antenna in a wide range of speed. The HewlettPackard 8563E spectrum analyzer takes input directly from the antenna. A computer
running software developed for data collection and processing is connected to the
analyzer via GPIB bus.
For this experiment, the antenna was scanned in the azimuth direction from the
boresight. A very low noise measurement of the antenna pattern was taken. This was
achieved by having the source output a continuous wave signal at the maximum power.
In addition, the pre-detection resolution bandwidth was configured at 10kHz, the smallest
bandwidth that still allows a strong detection of the test signal. The post-detection video
bandwidth is configured the same as the resolution bandwidth. This setup effectively
disabled the video smoothing feature, since this feature may interfere with the detection
of the pulse position in a segment. 1000 data segments were collected over the azimuth
angle ranging from -8' to +660. The antenna scan speed is set at half the full speed, or
59
0.682deg/sec for high angular resolution. The measured pattern is shown in Figure 6-3.
This pattern is used as the benchmark for other processed patterns.
0
-10 -
- - - - - - --
-----
- - - - - - - -- - - - - - - - -- - - - - - - --- - -
I
40
cu-30 -- - - - - - - - - -6
4..........................
5-1.............
-..
- - -- - - -
-
..
-.
- -- - - - - -- - ..............................
ng...........................
-70
0
10
20
30
40
50
Off-axis angle (degree)
Figure 6-3 Low noise, high resolution benchmark pattern
First, the improvement on the dynamic range is observed for different signal
levels. Second, the improvement on the noise variance is verified by the ability to
reconstruct the antenna pattern from the noisy signal at large off-axis angles. All setup
parameters are kept unchanged throughout this part of the experiment. The higher scan
speed at 75% of the maximum speed, or 1.023deg/sec, is used as only 500 data segments
are collected for each pattern. Due to the limitation of the Hewlett-Packard 8563E
spectrum analyzer, each segment in the measurement has 601 data points. At this scan
speed, the azimuth angle range is roughly from -5
to +55". The resolution bandwidth is
opened wider at 30kHz, allowing a noisier input signal. The output power of the signal
source is decreased in the steps of 10dB after each run, down to -30dB off the maximum
power. The objectives of this experiment was to observe and compare the performance
of the two noise reduction methods, namely the averaging method and the pulse
modulated averaging method.
60
Both signal generators are used to provide a continuous-wave test signal and a
pulse modulated test signal. The pulse rate is 40Hz, equivalent to two pulse periods over
a 50ms data segment.
0
-10.
. .
..
. .
. .
. .
. .
-20
-40
- - - - -- -- - - - - - - - - - - - -
------------------- -
0)
E
70
0
10
30
20
Off-axis angle (degree)
40
50
Figure 6-4 Unprocessed pattern with full power signal
Figure 6-4 shows the pattern when the source is at its full power. Before
processing, this pattern has the noise floor at about -60dB. A comparison to the low
noise pattern shown in Figure 6-3 demonstrates that the information content in this
measurement is reliable to only 20' off the boresight. Beyond this angle, the noise
fluctuation is too much to identify the antenna gain.
Figure 6-5 and Figure 6-6 show the same pattern after data processing. The
averaging method still has the noise floor at -60dB, while the modulation method down
to below -70dB. The angular range of the pattern is extended to about +400 with the
averaging method and about +50' with the modulation method.
61
0
- - --
101
- -
-
- -
-
-
- -
-
- - .
- - .
- .
- - .
- .
- - .
- .
- - .
- .
- - .
- .
--..
-20
0
-- -
- - -
-
--- - -
-
- - -- -- -
-
- -
- - - - -
- - -
-
- -
---
- -- -
-
- - -
- -
- - -
-30
- - --- - - - - ----- - - - N
-
. .....
- ---
--
-40
-- -
0
z
-
---- - -- -
- - - - - - - - - --. . . . . - - - - - - --
- --- -- - -
- - -
--- -
- - - -
-50
--- - --------- - - - - - - - -- - - - - - - - - - - - - -- - ----
-60
-70
0
20
30
Off-axis angle (degree)
10
40
50
Figure 6-5 Pattern recovered by averaging with full power signal
0
-1 0
-
-2 0 - - --
--
-
-
-
- - - .--.--
-- -- - -
-3 0 --------- - - - - - - - - - -
a>
N
-4 0 - - -- -
-- - -- - - -
-
-
-
--
- -
-
- -
-
- - - --
--
- -. - - - - - - - - - --.-
- - - - - -.-- - - - - -
. ...- - - - - -.--
- - - - - - - - - - - - . - - - - - - - - - - - - - - .- - - --
70
0
10
20
30
Off-axis angle (degree)
40
50
Figure 6-6 Pattern recovered by modulation with full power signal
62
--
0
-30 - -
C
- - .- . .-.
-
-- - - - -
- - - - - - -
- - - - - - - - - - - --- - - - - - - - - --
70
N
-20 - 0
-- - - - - - -
-20
z
.-.-.-.-.
.-.-.-.
-.
. .-.2
3
4-5
20
30
40
.-.
-.-
-70'
0
10
50
Off-axis angle (degree)
Figure 6-7 Unprocessed pattern with -10dB attenuated signal
The antenna pattern measured when the test signal is attenuated down -10dB is
shown in Figure 6-7. As signal power is lowered, the noise floor is raised to -50dB as
expected. The noisy measurement makes it impossible to resolve the pattern at more than
+10' angle. At this angle the antenna gain measured still maintains the general shape of
the antenna pattern, but the pattern is no longer smooth.
Figure 6-8 and Figure 6-9 show the two processed patterns. Compared to the
measurement at the full power signal, similar improvement in the dynamic range is
observed. The averaging method has recovered the shape of the antenna pattern at large
angles very well. However, due the limited dynamic range, the gain values measured at
these angles are shifted up. On the other hand, the modulation method performs well in
both power levels and the pattern shape.
63
0
-101
-20
m
- - - -J ---- -
- - - ----
- - -- - - - -- -
- - - - - ------ - - - - ----- - --
-30
- - - - --- - --- ---- - - - - - ---- - - - - - - - - - - - - - a)
N
- -
- - -
- -
- -
-40
0
z
-50
- - - -- -----
- - --- - - ---- - --- - - - - - - - - ---
---
--
-
-60
-70
0
10
20
30
Off-axis angle (degree)
40
50
Figure 6-8 Pattern recovered by averaging with --10dB attenuated signal
0
- - - --- - - - - - - --- - - --
-10 -- - -
-2 0 -
- -. - - - - - -
-
-- - - -- - - - - - -
- - - - - - - - - - - - - - - - - - - --.
CO
N
70
0
10
20
30
Off-axis angle (degree)
40
50
Figure 6-9 Pattern recovered by modulation with -10dB attenuated signal
64
A
-10 - - - -
-20 -- -
--
0----40
-- -- --
-
-
-
- -
--
- -- - -- - - - - - - -
-
-- -
-- - - - ----
.
--..
- - - - .
- - - -- - - - - -- - - - -- - - -- - - -- - -- -
N
E
--
-~0
z
-50 -------- -- ----
-60
-70
--
0
-- - -. .
- -- - - -
10
-. - -.-
-.
30
20
Off-axis angle (degree)
-.--
-.
40
- - - ..--
50
Figure 6-10 Unprocessed pattern with -20dB attenuated signal
Figure 6-10, Figure 6-11, and Figure 6-12 show the measured and processed
patterns when the signal power is lowered by -20dB. Figure 6-13, Figure 6-14, and
Figure 6-15 show similar patterns with -30dB attenuated signal. Improvement in the
dynamic range of over 10dB can be seen through out for the noise reduction method by
amplitude modulation. With the 601-point segments, an improvement of as much as
11dB is expected for this method. In this same setup, the averaging method promises a
28dB improvement in the noise variance. No real improvement in the dynamic range is
expected, as the noise power is not subtracted out from the output. Experiment results
show no change in the noise floor as the pattern being processed with the noise reduction
method by averaging.
65
0
-10
-20 - - - - -..
..
.-- - - -
..
- - - - - - - -- - - - - - - - - - - - - - - - - - --..
-30
N
-40
=O
0
z
-50
.-
-
-.
.
--- - -
.
J.
.
......
-
-
-
-
- -
-. -
.
0......
-
-
.
-
.
- ..
.
-
-.
.
.
.
-
-
.
.
- .
--.
- .
- .
- - .
- .
- - .
- .
- .
- - .
- .
- .
- - .
- .
- - .
-60
-70
0
20
30
Off-axis angle (degree)
10
40
50
Figure 6-11 Pattern recovered by averaging with -20dB attenuated signal
0
-1 0- - - - - - - - - - - - - - -2 0
- -3 0 -
--
-
-
--
-
-
. - - - - - - -- - - - - - - - - - - - --..
-- - - - - - - -
-
-- - - -- - - -- - - -- - - - --- - - -- - - -- - - -- - - -- - .
~0)..
N
-40
-
.......------
0
z
-70
0
10
30
20
Off-axis angle (degree)
40
50
Figure 6-12 Pattern recovered by modulation with -20dB attenuated signal
66
. .
The angular range of the pattern is increased as both the noise variance and the
dynamic range are improved. The averaging method tends to give smoother pattern with
limited dynamic range, while the modulation method provides pattern with more
fluctuation and more dynamic range. The noise variance is expected to be 3dB better
with the averaging method, since the effective data sample size of the modulation method
is only half that of the averaging method. In noisier condition, the modulation method
can do better than the averaging method, since the dynamic range is now very limited,
and becomes a deciding factor. In this situation, the pattern recovered by modulation is
not very smooth, but the shape and the amplitude of the antenna pattern are still
acceptable results.
Using the modulation method, the features of all the recovered antenna patterns
are very similar as shown in Figure 6-6, Figure 6-9, Figure 6-12 and Figure 6-15. In
addition, these patterns are consistent with the high resolution, low noise antenna pattern
in Figure 6-3. These results are repeatable; therefore, the nulls and peaks in these
patterns are not due to the noise, but rather to true antenna directive gain. As the noise
component becomes more comparable to the signal component, it is more difficult to
detect the position of the pulse in each segment. If the wrong position is assumed, the
calculation of the gain will be invalid. In other words, the resulting output is just noise.
This effect was observed in Figure 6-15, where the pattern levels out with noisy readings
for off-axis angles which are greater than 150.
67
IImE-uIEhII
q-~-*-
I
-.------*-
.i ~-
0
.. ..................
.-..............
-....
---..
--
-- - - - -- - -
- - - - ----
-
-20
C
C
-
-
-10-
-
-30 .......
N
-- ..............
-40
0
z
-60
- - -----
- -- -----
-------------
----
---.. . . .
-fU
0
10
20
30
Off-axis angle (degree)
40
50
Figure 6-13 Unprocessed pattern with -30dB attenuated signal
0
-10 --
- -
-
--
-20 - - -
0)
3
-
- - -
-
- -
-
- -
- -
- -
- -
- -
- -
-.-- - - - - - - - - - - - - - - - - - .-- - - - - - - - - - - - - - - - - - --
1.
. ..
4...
2.
N
0
z
-50-
.....................................
-70
0
10
30
20
40
50
Off-axis angle (degree)
Figure 6-14 Pattern recovered by averaging with -30dB attenuated signal
68
- -~ -
~- -
-
-
~- -
-
0
- --
-10-
--
-20 - -
- - -- - - -- - - -- - - -- - - - - - - - - - - - - - - - - - - --
- -- - -
N
-70
I
0
10
30
20
Off-axis angle (degree)
40
50
Figure 6-15 Pattern recovered by modulation with -30dB attenuated signal
69
Chapter 7
Conclusion
Extensive research has been done to determine the data processing methods that improve
the performance of the antenna radiation pattern measurement. The study has focused on
reducing noise in the measurement in order to enhance the resolution and the dynamic
range of the measurement. The noise reduction method by arithmetic averaging of the
input data was investigated and found good results in reducing the noise variance in the
signal. The pulse modulation of the signal amplitude was introduced to handle noise with
variable-mean and to lower the noise floor in the antenna pattern. In these tests, the
averaging method showed over 25dB improvement in the noise variance and no
improvement in the dynamic range. The modulation method provided over 20dB
improvement in the noise variance and about 11dB improvement in the dynamic range.
This improvement will be higher with a bigger data sample size. This can be achieved by
using spectrum analyzer with larger trace memory, increasing the number of samples in
each data segment. An alternative solution is to slow down the scan of the antenna to
collect more segments over the same angular. In this case, data from more than one
segment will be used to calculate one point in the resulting pattern.
In the pulse modulation method, demodulation of the test signal in the receiver is
done by the software in the data processing stage. For each segment of 600 data samples,
all possible square-wave phases are tested to find the one which gives the largest
synchronous detection response. Subsequence averaging calculation is based on this
detected phase. As the signal sinks into the noise, the average largest response
approaches a very small nominal value. Under this condition, the phase synchronization
70
is lost, the measured amplitude is random noise. This effect is best demonstrated in the
experiment when the signal source is attenuated by 30dB. The measured antenna pattern
is shown in Figure 6-15. The measured antenna levels out at approximately -40dB when
the off-axis angle is more than 140. At this angle, the phase of the pulsed test signal is no
longer detected correctly and the pattern consists of the fluctuations due to the noise
power.
Further study is required to determine the performance of the pulse detection
scheme which was implemented in the software. In the presented simulation of the pulse
modulation method, this phase detection strategy was not included, as the square-wave
pulse phase was assumed known. It is unclear whether this pulse detection scheme
affects the overall performance of the antenna pattern measurement. Future work may
include a simulation with phase detection and compare the results to the existing
simulation where the phase is known. If similar results are obtained, then the
performance of this pulse detection scheme is sufficient for the antenna pattern
measurement.
A new method for data collection was also introduced to provide the sufficient
input sample size for data processing. In this method, the computer controls the
measurement process, allowing rapid data transaction between the spectrum analyzer and
the computer. The two methods of data processing were tested and their performance
verified using software simulation of the antenna pattern measurement, along with
experimental results from tests done in the controlled environment of the antenna range.
71
Bibliography
[COMSAT93] "COMSAT Antenna Verification Program, User's Manual", COMSA T
Labs., Ant. Sys. Dept. Pub. (1993).
[Davenport58] W. B. Davenport, W. L. Root. "An Introduction to the Theory of Random
Signal and Noise", McGraw-Hill (1958).
[Ekelman92]
E. P. Ekelman, S. M. Frimel. "On-Site Earth Station Antenna
Verification", IEEE APS Int. Symp. Proc. Vol. 4 (1992).
[Kong90]
J. A. Kong. "Electromagnetic Wave Theory", Wiley Interscience (1990).
[Papoulis65]
A. Papoulis. "Probability,Random Variables, and Stochastic Processes",
McGraw-Hill (1965).
[Papoulis77]
A. Papoulis. "Signal Analysis", McGraw-Hill (1977).
[Raemer69]
H. R. Raemer. "Statistical Communication Theory andApplications",
Prentice-Hall(1969).
[Rowe65]
H. E. Rowe. "Signal and Noise in Communication System ", D. Van
Nostrand Company (1965).
[Wozen67]
J. M. Wozencraft, I. M. Jacobs. "Principlesof Communication
Engineering",John Wiley & Sons (1967).
72