WEAK SIGNAL RECEPTION USING SOFTWARE DEFINED RADIOS AND A 
TWO-ELEMENT PHASED ANTENNA ARRAY 
 
Except where reference is made to the work of others, the work described in this thesis is 
my own or was done in collaboration with my advisory committee. This thesis does not 
include proprietary or classified information. 
 
 
 
_______________________________ 
Victor Frederic Rundquist 
 
 
 
_______________________________ 
Stuart M. Wentworth 
Associate Professor 
Electrical and Computer Engineering 
 
 
_______________________________ 
Lloyd S. Riggs 
Professor 
Electrical and Computer Engineering 
 
 
_______________________________ 
Richard C. Jaeger, Chairman 
Distinguished University Professor 
Electrical and Computer Engineering 
 
 
_______________________________ 
Thaddeus A. Roppel 
Associate Professor 
Electrical and Computer Engineering 
 
 
 _______________________________ 
 Stephen L. McFarland 
 Acting Dean 
 Graduate School 
WEAK SIGNAL RECEPTION USING SOFTWARE DEFINED RADIOS AND A 
TWO-ELEMENT PHASED ANTENNA ARRAY 
 
Victor Frederic Rundquist 
 
A Thesis 
Submitted to 
the Graduate Faculty of 
Auburn University 
in Partial Fulfillment of the 
Requirements for the 
Degree of 
Master of Science 
 
Auburn, Alabama 
December 15, 2006 
WEAK SIGNAL RECEPTION USING SOFTWARE DEFINED RADIOS AND A 
TWO-ELEMENT PHASED ANTENNA ARRAY 
 
Victor Frederic Rundquist 
 
Permission is granted to Auburn University to make copies of this thesis at its discretion, 
upon request of individuals or institutions and at their expense.  The author reserves all 
publication rights. 
 
 
 
 
 
 
_____________________ 
Signature of Author 
 
 
_____________________ 
Date of Graduation 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
iii 
VITA 
Victor Frederic Rundquist was born May 15, 1976, in Tucson, Arizona, to Eric 
and Beverly (Turner) Rundquist.  He graduated from North Canyon High School in 1994.  
He attended DeAnza College in Cupertino, California, while working as an Engineering 
Intern at NASA Ames Research Center.  After his internship was finished, Victor 
transferred to Auburn University where he graduated Magna Cum Laude with a degree in 
Wireless Engineering in 2005.  Immediately upon graduation Victor entered graduate 
school where he also worked as a teaching assistant.  Victor married Amber Suzette 
Harmon, daughter of Jerry and Susan (Hilliard) Harmon, on December 31, 2005. 
 
 
 
 
 
 
 
 
 
 
 
iv 
THESIS ABSTRACT 
WEAK SIGNAL RECEPTION USING SOFTWARE DEFINED RADIOS AND A 
TWO-ELEMENT PHASED ANTENNA ARRAY 
Victor Rundquist 
Master of Science, December 15th, 2006 
(B.W.E., Auburn University, 2005) 
 
 
78 Typed Pages 
Directed by Richard C. Jaeger 
 
Software Defined Radio (SDR) is a quickly emerging technology.  SDR removes 
the signal processing task from the analog hardware portion of a radio and places it into 
the Digital Signal Processing (DSP) domain.  Many algorithms exist for removing noise 
from a signal and recovering the small signals inside.  This thesis will explore the use of a 
two-element antenna array in conjunction with adaptive signal processing algorithms to 
not only recover small signals but reject strong interfering ones. 
This project is implemented using a standard desktop PC with a high performance 
Analog-to-Digital (A/D) card in conjunction with MATLAB software from The 
Mathworks, Inc.  This thesis will describe the hardware used to acquire the signals, the 
theory of a two-element antenna array, details of the mathematical theory of 
v 
the DSP process, details of the software code used to decode the signals and performance 
metrics of each component.  Finally, the performance of the entire system will be 
reported as well as any future improvements that are needed. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
vi
ACKNOWLEDGEMENTS 
The author would like to thank the Flex Radio community for their help in 
understanding some of the hardware needed to complete the project as well as advice on 
how to implement DSP code.  Thanks are also due to family members Archie, Gatti, Mr. 
Bo Jangles, Tiger, and Calli for their loyalty and support.  A special thanks to Amber for 
being supportive and loving. 
Also the Author would like to thank Dr. Jaeger and the rest of the Auburn 
University, Electrical and Computer Engineering Faculty for their insight into this 
project.  Thanks to Linda Barresi, Joe Haggerty and Dr. J. Lowry for their support in 
installing the antennas on Broun Hall. 
 
 
 
 
 
 
 
 
 
 
vii 
Format of Body: Auburn University Graduate School: Guide to preparation and 
submission of theses and dissertations. 
 
Computer Software Used: Microsoft Office Professional 2003 
 MATLAB Release 14  
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
viii
TABLE OF CONTENTS 
LIST OF FIGURES xi
 
LIST OF TABLES xii
 
CHAPTER 1: INTRODUCTION........................................................................................1
 
CHAPTER 2:  HARDWARE............................................................................................ ..4
2.1: Antennas with Active Matching Networks.................................................... ..4
2.2: SDR 1000 Down-converter............................................................................ ..5
2.3: Analog to Digital Card................................................................................... ..7
 
CHAPTER 3: THE TWO-ELEMENT ANTENNA ARRAY.............................................8
3.1: Geometry........................................................................................................ ..8
3.2: Theoretical Equations..................................................................................... ..9
3.3: Project Measurements and Equations.............................................................12
 
CHAPTER 4: DSP ALGORITHMS................................................................................. 14
4.1: Noise and Interfering Signal Cancellation With a Two-Element  
Antenna Array....................................................................................................... 14
4.2: Beam Steering via Phase Shift....................................................................... 17
4.3: Quadrature Demodulation.............................................................................. 23
4.4: Automatic Notch Filter................................................................................... 26
 
CHAPTER 5: MATLAB IMPLEMENTATION.............................................................. 31
5.1: MATLAB Introduction and Toolboxes Used.................................................31
5.2: A/D Hardware Setup and Memory Management........................................... 33
5.3: Phase Shifter and Noise + Interferer Cancellation......................................... 36
5.4: Demodulation and Output.............................................................................. 38
5.5: Signal Analyzer and Radiation Pattern Simulator Used 
 in  Development....................................................................................................
40
5.6 Notch Filter...................................................................................................... 42
 
ix 
CHAPTER 6: PERFORMANCE, RESULTS, AND IMPROVEMENTS........................ 44
6.1: Conversion Gain............................................................................................. 44
6.2: Qualitative Results..........................................................................................45
6.3: Future Improvements......................................................................................51
 
REFERENCES.................................................................................................................. 54
 
APPENDIX 
A.1: Full MATLAB Software Code...................................................................... 55
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
x 
LIST OF FIGURES 
 
FIGURE 1.  System Block Diagram....................................................................................3
FIGURE 2.  Active Matching Network for Antenna System............................................ ..5
FIGURE 3.  SDR 1000 Down-converter and Block Diagram.............................................6
FIGURE 4.  A/D Card....................................................................................................... ..7
FIGURE 5.  Antenna Geometry...........................................................................................9
FIGURE 6.  Antenna/Signal Geometry............................................................................. 10
FIGURE 7.  Beam Solid Angle Representation................................................................ 13
FIGURE 8.  DSP Noise Cancelling Block Diagram......................................................... 14
FIGURE 9.  Correlation Value Plot and Time Domain Representation............................15
FIGURE 10.  Magnitude Response of 4 kHz Low Pass Filter.......................................... 16
FIGURE 11.  Isotropic Radiation Pattern..........................................................................18
FIGURE 12.  Radiation Pattern for Antenna Array N=0.................................................. 20
FIGURE 13.  N=20............................................................................................................20
FIGURE 14.  N=40............................................................................................................21
FIGURE 15.  N=60............................................................................................................21
FIGURE 16.  N=80............................................................................................................22
FIGURE 17.  N=100..........................................................................................................22
FIGURE 18. Block Diagram of Quadrature Demodulation.............................................. 23
FIGURE 19.  FFT Plot of Auburn?s Fight Song................................................................27
FIGURE 20.  FFT Plot of Auburn?s Fight Song with 2 kHz Interference.........................27
FIGURE 21.  Magnitude Response of 2 kHz Notch Filter................................................28
FIGURE 22.  FFT Plot of Auburn?s Fight Song after Notch Filter...................................28
FIGURE 23.  Output of Signal Analyzer FFT Plot........................................................... 40
FIGURE 24. WBIL Radiation Pattern...............................................................................47
FIGURE 25. WHBQ Radiation Pattern.............................................................................48
FIGURE 26. WBBM Radiation Pattern.............................................................................49
FIGURE 27. WBAP Radiation Pattern..............................................................................50
FIGURE 28. Radiation pattern of 150m Antenna Spacing vs. 55 Meter Spacing.............51
 
 
 
 
 
 
 
 
 
 
xi 
LIST OF TABLES 
 
TABLE 1.  Summary of Results........................................................................................46 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
xii 
 1
CHAPTER 1 
INTRODUCTION
Software Defined Radios (SDR) have been around for a long time in military 
applications.  It has only been in the last decade that a need for the SDR has been 
identified in the civilian market.  In today?s crowded spectrum, governments have been 
reducing the amount of spectrum available to individuals and broadcasters.  This has the 
effect of compressing the guard bands and allowing for multiple interfering signals to be 
combined with the user?s desired signal. 
Traditionally, in cellular systems, channel separation has been achieved by 
discrete filter banks and voltage controlled oscillators.  This approach is not completely 
accurate and requires a lot of hardware.  The end result is a very inefficient use of the 
spectrum.  In recent years the cellular industry has gone to digital transmission of voice 
signals.  Several new standards have emerged from this trend.  All of these standards 
have one thing in common; try to add more users to the same amount of available 
bandwidth.  The actual detail of these systems is not the topic of this thesis, rather the fact 
that some of the signal processing is done in software by specially designed Digital 
Signal Processing (DSP) microchips. 
This paper introduces a method for cancelling noise and interfering signals using 
DSP code in MATLAB.  MATLAB is a simulation and mathematical software suite from 
The Mathworks Inc.  The project described in this thesis does not operate at the cellular 
 2
frequencies, nor does it operate on cellular type frequencies.  The techniques and theories 
presented herein can easily be converted for use in cellular, radar, broadcast, or any other 
domain currently used in communications. 
The project uses a dual antenna array designed to receive signals from 0 to 30 
MHz.  The dual antennas provide two signals to the software that can then use statistical 
analysis to cancel the unwanted signals while simultaneously enhancing the desired ones.  
To keep costs down, an inexpensive Analog-to-Digital (A/D) card from Measurement 
Computing is used with two down-converters (SDR 1K) from Flex-Radio Systems.  The 
down-converter filters the antennas and down-converts the incoming signal to a 
frequency that the A/D card can easily acquire for use in MATLAB. 
The frequency band chosen for proof of concept is the AM Broadcast band, 540 
KHz to 1700 KHz.  The down-converter will take the signal from the antennas and 
reduce it to an Intermediate Frequency (IF) of 11025 Hz.  This is then digitized by the 
A/D card for processing in MATLAB.  Finally, the signal is output to the computer?s 
speaker via the soundcard. 
This project will make use of Quadrature signals from the down-converter as well 
as DSP algorithms to accomplish the assigned tasks.  DSP code will be written in 
MATLAB using functions designed by the author as well as pre-defined functions in the 
MATLAB toolboxes.  The signal enhancement/cancellation will be accomplished by a 
phase delay analog filter and the audio demodulation will be done by Quadrature 
Demodulation.  All of the system components can be seen in the block diagram of Fig. 1. 
 3
After the strongest signal is cancelled the remaining information is amplified and smaller 
signals can be recovered. 
 
 
Figure 1. System Block Diagram 
Finally the results of the project are measured by the system?s ability to either 
enhance or cancel the desired signal. Audio files of some of the final output can be 
obtained by e-mailing the author at victor@rundquistfamily.net. 
 
A/D 
SDR 1K-1  
MATLAB 
DSP 
 
Sound 
Card 
SDR 1K-2 
 4
CHAPTER 2 
HARDWARE 
 
This chapter will briefly detail the hardware used in the project.  The main 
purpose of the project is not to evaluate hardware, rather the software and DSP 
algorithms used in the radio.  This chapter is included for completeness.  The main 
hardware elements are the two-element antenna array, down-converters, and the A/D 
card.  The computer is a standard desktop 2.4 GHz Pentium machine with a standard 
soundcard and options from Dell Computer Corporation. 
 
2.1 Antennas with Active Matching Networks 
The antennas used are 102 inch whip style monopole antennas.  They are 
connected to an active matching network (DXE-ARAV-1P) by DX Engineering, 
http://www.dxengineering.com [1].  These antennas provide good reception from 100 
kHz to 30 MHz.  The matching network is fed from the receiver by 12V loaded onto the 
coax line.  The antennas have low spurious signal interference, which is ideal for small 
signal reception.  Fig. 2 is a photo of the active matching network of the antenna system.  
More information on this antenna can be found on DX Engineering?s website given 
earlier. 
 
 5
 
Figure 2.  Active Matching Network for Antenna System 
2.2  SDR 1000 Down-converter 
The signals coming from the antenna cannot be directly converted to digital 
signals for a number of reasons.  These reasons will be discussed in Chapter 4: DSP 
Algorithms.  The down-converter is from Flex Radio Systems, http://www.flex-
radio.com[2]. Flex radio uses this down-converter for their software defined radio, a 
general coverage receiver.  Fig. 3 shows the down-converter and a simplified block 
diagram.  The block diagram is for the original hardware which does not have a RF pre-
amp.  The SDR 1000 down-converter consists of band pass filters and an RF pre amp at 
the antenna input.  Then the signals are mixed with a local oscillator produced by an 
Analog Devices direct digital synthesis (DDS) microchip.  The local oscillator is 
comprised of a reference signal and a 90 degree shifted version.  By mixing the antenna 
signal with these two signals an in-phase (I) and quadrature (Q) component of the IF is 
produced.  The final signal is then filtered, scaled to +5 and -5 volts and sent to the 
 6
computer.  The IF used in this setup is 11025 Hz.  Since we are only dealing with signals 
that have a maximum bandwidth of 5 kHz, this choice of IF is appropriate. 
The ADS DDS chip is clocked using a 200 MHz precision crystal oscillator.  
Since two down-converters are used, it is essential that both chips produce the same local 
oscillator signal.  This is achieved in the SDR 1000 software.  A 20 MHz reference signal 
is supplied to the down-converters, and the resulting IF frequency is read.  The tuning 
command to the DDS chip is adjusted until the IF is exactly 11025 Hz on each unit.  The 
value for the clock offset is recorded and used to ensure both local oscillators are 
identical.  This procedure will set the frequency of the two local oscillators to be the 
same, but will have no effect on their phase.  In Chapter 4, it will be shown that the phase 
of the local oscillators does not matter because of the I (in-phase) and Q (Quadrature) 
output of the down-converter. 
 
Figure 3.  SDR 1000 Down-converter and Block Diagram [3] 
 
 
 
 7
2.3 Analog to Digital Card 
The I and Q channels coming from the two down-converters are fed into the 4 
channels of an analog-to-digital PCI card (PCI-DAS 4020/12) from Measurement 
Computing Corporation, http://www.measurementcomputing.com [4] as shown in Fig. 4.  
This card was selected because it has 4 input channels, a 20 MHz sampling rate, and 12 
bits of resolution.  The card works seamlessly with MATLAB and LabView 
programming environments.  The card has two programmable input ranges of +/- 1 volt 
and +/- 5 volts.  For this project the +/- 5 volts is used because of the auto scaling done by 
the SDR 1000 down-converter.  The card is installed into the aforementioned desktop 
computer and is configured to use direct memory addressing (DMA) and 50% of the 
computer?s physical RAM. 
 
Figure 4.  A/D Card 
 8
CHAPTER 3 
THE TWO-ELEMENT ANTENNA ARRAY 
 
The two-element antenna array is used throughout industry today.  This 
configuration provides both diversity in reception and with the right signal processing a 
reduction in noise and increase in directivity.  The antenna array consists of two antennas 
spaced some distance apart.  The antennas must be the same to use the simple form of the 
pattern multiplication and uniform linear array theories. 
 
3.1 Geometry 
The geometry of a two-element array is very simple.  The two antennas are placed 
at the same vertical height.  The line connecting the two antennas is referred to as the axis 
of the array.  Signals that are entering the array perpendicular to the side of the axis are 
considered to be broad side.  Signals coming from the end of the array are said to be 
entering axially.  The distance between the two antenna elements is d, and the angle 
which the signal is approaching is ?.  This geometry is detailed in Fig. 5. 
 9
 
Figure 5.  Antenna Geometry 
 
This configuration can be extended to as many elements as are desired.  The only 
restrictions are that each element has equal spacing from the other elements to conform 
with the uniform linear array theory.  This makes the mathematics simple when 
implementing the DSP code.  It should be noted that in an array that has more than two 
elements, the elements do not have to be arranged in a straight line.  Any geometry may 
be used as long as it has sufficient symmetry. 
 
3.2 Theoretical Equations 
The mathematics for the antenna array will now be introduced.  The antennas 
must be considered to be far from the source of the signals so that the incoming waves 
are planar. 
 
 
d
Signa
? 
Antenna 
Antenna 
 10
First, the transmitted signal is defined as: 
 
tj
c
etstr
?
)()( =
 
(3.2.1) 
?
c 
is the carrier frequency and s(t) is the envelope or the message signal. 
 
Figure 6.  Antenna/Signal Geometry 
The amount of time needed for the wave front to move from antenna 1 to antenna 2 is, 
 
?
?
?
?
?
?
?
=?
c
d
t
cos
   (3.2.2) 
where c is the speed of light [4].  At time t the signal at antenna 1 will be, 
                                                
()
tj
A
c
etsts
?
=)(
1
 (3.2.3) 
 
At the same time instant the signal at antenna 2 will be, 
 
()
()ttj
B
c
ettsts
?+
?+=
?
)(
2
 (3.2.4) 
 
Now assuming that the frequency of the message, ?
m 
is much less than the frequency of 
the carrier ?
c, 
 11
 cm
?? <<<
 (3.2.5) 
the information will be the same at both antennas at every instant in time.  In the context 
of this thesis, the information is a voice signal that is modulated onto the carrier.  The 
envelope signal at antenna 2 is, 
 
() )(tstts
AB
??+
 (3.2.6) 
Plugging (3.2.2) into (3.2.4) the signal at antenna 2 becomes, 
 
()
?
?
?
?
?
?
?
?
?
+=
??
?
?
c
j
A
d
tetsts
c
cos2
)(
2
  (3.2.7) 
Rearranging (3.2.7) yields the following, 
 
()
?
=
cos
2
2
)(
dj
j
eetsts
c ?
?
?
 (3.2.8) 
where ? is the wavelength of the incoming signal. 
Equation (3.2.8) shows us that the signal at antenna 2 is simply the phase shifted 
version of the antenna at signal 1.  The value of the phase shift is a function of the 
wavelength of the carrier, the distance between the antennas and the angle at which the 
signal approaches the array.  This value is, 
 
?
??
?
=
cos
2
d
 (3.2.9) 
 12
Angle ?  is referred to as the electrical angle, and is expressed in radians from 0 to 
2? .  In the DSP domain, this is easily realized as a shift of the samples from antenna 2 
relative to antenna 1.  This will be discussed in more detail in Chapter 4.  The signals 
from the two antennas can be linearly combined to either cancel out unwanted signals or 
enhance desired ones. 
 
3.3 Project Specific Equations and Measurements 
The spacing of the antennas installed on Broun Hall is 55 meters.  This will be 
inserted into equation (3.2.9) along with the wavelength of the carrier of interest and the 
electrical angle derived by the software.  Then the angle ?  at which the approaching 
signal is coming from can be determined by, 
 
?
?
?
?
?
?
=?
?
d?
??
2
cos
1
   (3.3.1) 
This angle is then used for either cancelling or enhancing purposes as determined 
by the user.  This equation can also be used as a direction finding device.  All that has to 
be done is to convert the electrical angle computed by software into the actual angle and 
output it to the user using an angle offset correction factor for the orientation of the array. 
 The two-element phased array provides a theoretical Signal-to-Noise (SNR) 
improvement over a single element.  By applying the actual distance and optimal phase 
shift of the two signals the following is obtained from (4.2.2), which is introduced in 
Chapter 4. 
 13
 
()()
()
()???
???
???
?
?
?
?
dd
d
d
p
??
==
?
?
?
?
?
?
+
+
=?
2/
0
3
2
0
2
2
sin
2
cos
sin
cossin
4
1
 (3.3.2) 
(3.3.2) is referred to the Beam Solid Angle.  This expression is numerically evaluated 
using MATLAB for values of ?  from 0 to ?2 .  Fig. 7 is a graphical representation of 
the beam solid angle.  The directivity of the array is
p
?
?4
.  The Gain of the antenna array 
is simply the efficiency of the antenna times its directivity.  For these calculations the 
antenna array elements are assumed to be 100% efficient.  Furthermore it is assumed that 
the incoming signal is aligned with the antenna array so that maximum gain is obtained. 
 
Figure 7. Beam Solid Angle Representation 
From MATLAB the optimum phase shift is 180
0
 and the array gain is 7.9 dB when the 
signal is entering the array along the array?s axis.  The program that calculates these 
values is included in the appendix. 
 14
 
CHAPTER 4 
DSP ALGORITHMS
 
Digital Signal Processing (DSP) is the heart of the radio.  The DSP must reduce 
the frequency of the signal from the 11025 Hz IF to the original baseband signal.  The 
original baseband signal is from 0 Hz to 5 kHz.  Also, the DSP must remove any 
unwanted signals as well as linearly combine the two separate signals from the antennas. 
 
4.1 Noise and Interfering Signal Cancellation with a Two-Element Antenna Array 
Given two measurements of the same signal, s
1
(t) and s
2
(t). These two 
measurements are correlated in time by the delay between the two antennas and 
uncorrelated in noise.  That is, the noise component of each signal, n
1
(t) and n
2
(t) are 
uncorrelated.  To remove this noise a correlation is performed between the two signals 
and the resulting filter is designed and run on one signal, then the two signals are 
combined.  The block diagram of this arrangement is detailed in Fig. 8. 
 
Figure 8.  DSP Noise Cancelling Block Diagram 
 
 15
Cross Correlation Definition [5]. 
 
][][s  [n] s(2)} )1({][
2
0  m
1
msmnsnz
M
?
=
+=?=
 (4.1.1) 
From this definition we can get the delay in samples from the subscript that gives the 
highest correlation.  Fig. 9 shows that the correlation of the two incoming signals follows 
a sinusoidal pattern as is to be expected. 
-100 -80 -60 -40 -20 0 20 40 60 80 10
-1.5
-1
-0.5
0
0.5
1
1.5
2
2.5
Correlation value vs. # of samples of shift
samples of shift
c
o
r
r
el
a
t
i
on v
a
l
u
e
 
0 0.005 0.01 0.015 0.02 0.025 0.03 0.035
-4
-3
-2
-1
0
1
2
3
4
 
Figure 9.  Correlation Value Plot and Time Domain Representation 
In practice this is done by taking both inputs and shifting one before multiplying both 
together.  This cross-correlation only needs to be done once during the initialization step 
 16
of the radio.  Once the program knows the delay from s
1
(t) to s
2
(t) it can use this 
information to construct the delay filter that filters s
2
(t).  To further remove any unwanted 
high frequency noise a 10
th
 order low-pass filter is implemented with a 4 kHz cutoff.  The 
frequency-magnitude response is plotted in Fig. 10. 
 
Figure 10. Magnitude Response of 4 kHz Low Pass Filter 
After the two signals are filtered and appropriately delayed, they are added 
together.  Since the noise components of the signals from antenna 1 and antenna 2 are 
uncorrelated, the process of filtering and delaying one of the signals will cancel the noise 
component.  With the noise cancelled and the two signals now in phase, weak signals can 
be recovered from the noise floor. 
 
 
 
 17
4.2 Beam Steering via Phase Shift 
The fact that the delay filter in the previous section shifts one of the signals in the 
time domain effectively changes the antenna array?s radiation pattern.  It was shown in 
Chapter 3 that the signals generated by one antenna relative to the other are simply offset 
by a phase,? : 
 
?
??
?
=
cos
2
d
 (4.2.1) 
From antenna theory it is helpful to introduce the array factor AF.  This is used to 
describe the radiation pattern of the antenna array.  All of the equations presented here 
are for the dual-element monopole array used in this project.  It is assumed that each 
individual element is isotropic in the horizontal plane, therefore only the radiation 
patterns in the horizontal plane will be discussed.  Furthermore this assumption is 
applicable due to the fact that all of the desired signals are approaching in the horizontal 
and not from the vertical direction. 
 
The array factor for the two-element array in this project is [6]; 
 
?
?
?
?
?
?
?
?
?
?
?
?
?
?
=
2
sin
2
2
sin
2
1
2
2
2
normalized
AF
, 
() ??? +=? cosd
 (4.2.2) 
 
 18
From this equation we can control the array factor by varying? , the phase 
difference between the antennas.  The final radiation pattern of the array is obtained by 
multiplying the pattern of one of the elements (Fig. 9) by the array factor.  Since the 
pattern of one element, shown in Fig. 11, is unity in all directions, then the array factor is 
simply the radiation pattern of the entire array. 
 
Figure 11. Isotropic Radiation Pattern 
By making the array factor a function of the phase offset, and ?  a function of the number 
of samples offset, the following results are obtained. 
For a 2 MHz sample rate, the sample period is: 
 
.sec105
1
7?
== x
F
T
s
S  (4.2.3) 
Defining the IF period as, 
 
IF
IF
F
T
1
=  (4.2.4) 
T
s
 and T
IF
 can be related as follows: 
 
 19
 
==
S
IF
s
T
T
N
 Samples per IF cycle. (4.2.5) 
Converting the number of samples per cycle to radians, 
 
IF
S
s
T
T
N
*22 ??
=  (4.2.6) 
With a 2 MHz sample rate and a 11025 Hz IF each shift of one sample will correspond to 
.0346 radians of shift. ?  can therefore be written as; 
 
S
IF
F
F
N
*2
*
?
? =
 (4.2.7) 
and substituted into the following; 
   
() ??? +=? cosd
     with     
30055
2 ?
?
?
? =d
 (4.2.8) 
In Figs. 12 through 17, (4.2.2) has been plotted for various values of the phase 
shift N.  The sampling frequency is 2 MHz, the desired signal is 1MHz and the distance 
between the antennas is computed as a fraction of one wavelength of the carrier based on 
antenna spacing of 55 meters.  The axis of the array is along the horizontal center line of 
the polar plots. As can be seen from the radiation plots, the pattern will flip over and 
radiate in the opposite direction once the phase shift 180 degrees or more. 
 
 
 
 20
 
Figure 12. N = 0 
 
Figure 13.  N = 20 
 21
 
Figure 14.  N = 40 
 
Figure 15.  N = 60 
 22
 
Figure 16.  N = 80 
 
Figure 17.  N = 100 
 
 
 
 23
4.3 Quadrature Demodulation 
The theory of Quadrature Demodulation is used principally so that the receiver 
does not need to have knowledge of the phase of the incoming signal.  The process also 
has the effect of removing image frequencies that get past the IF and audio filters.  Fig. 
18 is the block diagram for the Quadrature Demodulation process. 
 
Figure 18.  Block Diagram of Quadrature Demodulation 
Define the incoming signal as: 
 
)sin(* ?? += tAMS
c  (4.3.1) 
AM is the envelope or the message signal, 
c
?  is the carrier frequency and ?  is the phase 
of the incoming signal.  This is set to an arbitrary value because it will be shown that the 
receiver does not need to know this value.  In the project this signal will be 
 
)sin(*
111 LOCIF
tAMS ??? ++=
 (4.3.2) 
11 LOC
?? +  is the phase of the IF signal which is comprised of the linear combination of 
the phase of the carrier on antenna 1 with the phase of the local oscillator in down-
converter 1.  
 24
Likewise, 
 
)sin(*
222 LOCIF
tAMS ??? ++=
 (4.3.3) 
is the signal coming from down-converter 2.  In reality the signals from the two down-
converters are already split into the I and Q components by the Tayloe detector, but for 
simplicity we will describe them as above. 
Next the signal is beat with a local oscillator at 0 degrees and another at 90 degrees. 
 
)cos()sin( ttAMV
IFIFI
??? +=
 (4.3.4) 
and 
 
)sin()sin( ttAMV
IFIFQ
??? +=
 (4.3.5) 
Using trigonometric identities 
 
[])sin()2sin(
2
??? ++= t
AM
V
IFI
 (4.3.6) 
and 
 
[])2cos()cos(
2
??? +?=
IFQ
AM
V
 (4.3.7) 
 
 
Passing V
I
 and V
Q
 through a low pass filter yields the following, by eliminating the 
IF
?2  
term. 
 
 25
 
)sin(
2
?
AM
I =
 (4.3.8) 
and 
 
)cos(
2
?
AM
Q =
 (4.3.9) 
Next I and Q are squared, added and rearranged, 
 
[])(cos)(sin
2
22
2
22
?? +
?
?
?
?
?
?
=+
AM
QI
 (4.3.10) 
using a trigonometric identity, 
 
1)(cos)(sin
22
=+ ??
 
and taking the square root. 
 
2
1*
2
2
AMAM
=
?
?
?
?
?
?
 (4.3.11) 
Phase ?  has been removed from the signal, and just the message signal is left.  
Even if ?  is linearly comprised of phases of antenna 1 and 2 and LO 1 and 2, this method 
of demodulation removes the phase component.  Adding in the phase (time lag) of the 
signal from antenna 1 to antenna 2 the two resulting signals are 
 
?
?
=
?
=
1
1
1
2
)*
1
*(
n
s
t
f
nAM
S  (4.3.12) 
and 
 26
 
?
?
=
?
=
1
2
2
2
)*
1
*(
n
s
t
f
nAM
S  (4.3.13) 
1
t?  is set to 0 as the reference from antenna 1.  
2
t?  is the time lag for the signal to travel 
from antenna 1 to antenna 2.  It is easy to remove 
1
t?  and 
2
t?  from the two signals by 
shifting one signal in time and adding it to the other.  This will be discussed in detail in 
Chapter 5. 
 
4.4 Automatic Notch Filter 
An automatic notch filter is used to remove any unwanted interference from the 
audio signal.  The source of the interference is carriers near the desired signal.  The 
interference is typically heard as a loud tone superimposed onto the audio.  This filter is 
not intended to remove wide band noise.  In an FFT plot of an audio signal with 
interference tone, the interference can be seen as a sharp spike at the interference 
frequency. 
 27
 
Figure 19.  FFT Plot of Auburn?s Fight Song 
The plot in Fig. 19 reveals that most of the frequency magnitudes have a linear 
relationship from 0 Hz to 15 kHz.  This is true for most all high quality audio signals. 
 
Figure 20.  FFT Plot of Auburn?s Fight Song with 2 kHz Interference 
 28
In Fig. 20, a 2 kHz noise source has been added to the desired signal.  The desired 
response of the notch filter is in Fig. 21 and the resulting filtered signal is plotted in Fig. 
22. 
 
Figure 21.  Magnitude Response of a 200 Hz wide Notch Filter centered at  
2 kHz 
 
Figure 22.  FFT Plot of Auburn?s Fight Song After Notch Filter 
 29
To implement an Automatic Notch Filter, three design parameters must be 
considered.  First, is the threshold at which the highest frequency component needs to be 
at, to be considered interference.  This will be a level relative to the average level of the 
signal.  A reasonable value for the threshold parameter is 10 dB, or 10 times more power 
than the average value.  Second, is the range in which the notch filter is to operate. The 
notch filter will only consider data after the mean has been removed, i.e. the DC value of 
the data is removed.    The third parameter is the width of the notch filter.  A good value 
for this is 200 Hz since most of the interference will be at higher frequencies and losing 
200 Hz worth of data is not bad.  This notch filter can only notch one frequency, and thus 
the strongest signal will be deleted.  The data can be run through the notch filter to 
remove as many frequency spikes as desired. 
To implement the filter the following algorithm will be used: 
1. Take the FFT of the final audio signal. 
2. Average the FFT data to get the average signal level. 
3. Search for frequencies with amplitudes above this level. 
4. Choose the frequency with the highest amplitude above the threshold. 
5. Design the filter. 
6. Filter the data. 
7. Repeat if necessary. 
 
 
 30
This procedure will be performed on each sample of data.  In this way the filter 
will be an adaptive notch filter.  If the interference signal changes or a signal is 
intermittent, the Notch Filter can adapt to it quickly.  Finally, the notch filter will not 
have to act on each piece of data if none of the frequencies are 10 dB above the average 
value. 
 31
CHAPTER 5 
MATLAB IMPLEMENTATION 
 
In this chapter, the MATLAB [8] programming environment is introduced along 
with the code used to program the radio.  The MATLAB Data Acquisition (DAQ) 
Toolbox, Signal Processing Toolbox and general math functions will be introduced.  The 
programming method for the A/D hardware is also discussed.  Finally, in the last section, 
a MATLAB based signal analyzer was used during the development process and its detail 
is discussed.  Reference [8] and [9] are the sources of all the MATLAB code and 
functions used. 
MATLAB code will be used in this chapter and will be denoted in italics.  Only 
small samples of the code will be shown for reference.  The entire MATLAB code is 
included in the Appendix. 
 
5.1 MATLAB Introduction and Toolboxes Used 
MATLAB is a powerful programming and simulation environment.  It has 
command line, scripting, modular, and graphical programming modes.  In this project 
scripting/modular programming is employed.  To add functionality to the MATLAB 
environment, toolboxes are purchased from the Mathworks. The main toolboxes used in 
the development of this project are the DAQ Toolbox, Signal Processing Toolbox, Filter 
Design Toolbox, and the Communications Toolbox. 
 32
The DAQ toolbox is the primary interface to the analog-to-digital card.  This toolbox 
takes care of the communication with the A/D card?s software.  It also manages the 
memory of the DAQ session and the flow of data. 
The Signal Processing Toolbox is a collection of commonly used DSP functions.  
This toolbox provides the user with the ability to filter, correlate, and phase shift the 
signals in the program.  The main functions used in the project are the filtering and the 
phase shifting.  This toolbox also was used during the shift from a high to low sample 
rate.  Signal processing is the heart of this project and this toolbox proved to be 
invaluable. 
The Filter Design Toolbox is used to design filters for use in the Signal 
Processing functions.  This was used to design the infinite impulse response Butterworth 
filters used in the project.  The toolbox has command line functions so that filters can be 
designed by the software.  These allow you to adaptively change the response of the filter 
while the program is running.  This proved most useful for the operation of the Automatic 
Notch Filter.  Second, is the Filter Design and Analysis tool.  This is a Graphical User 
Interface (GUI) that allows the user to define all of the filter parameters like sample rate, 
cutoff frequency and format.  All the user has to do is then press the design button and 
the resulting filter is designed.  This filter is then exported into a file on the disk that the 
program accesses when needed.  The GUI also provides for analysis of filters that the 
user has designed elsewhere in MATLAB. 
The Communications Toolbox was not used in the final version of the radio.  The 
functions contained within it are too slow for real time operation.  During development 
 33
the toolbox was used to demodulate simple AM stations.  This proved most useful while 
trying to get the correct program structure.  In future versions this toolbox might be of 
use to demodulate digital signals.  This toolbox was used in the Signal Analyzer portion 
for displaying and interpreting the signals from the antennas and the down-converters. 
 
5.2 A/D Hardware Setup and Memory Management 
The A/D card needs very specific setup instructions to work properly.  It needs to 
know where to send its data once it is acquired, at what rate to acquire the data, and 
within what range to acquire the data. 
Before using any software with the A/D card, the computer must set aside 
contiguous memory in which the data will be placed in.  This is essential for high speed 
operation.  Having contiguous memory allocated allows the card to dump large amounts 
of data into memory without worrying about overwriting other important information.  
This allocation is performed during the boot up sequence of the computer and is 
controlled by the software provided by the A/D card manufacturer. 
In MATLAB the DAQ toolbox will control all of the functions of the A/D card.  
To invoke the toolbox and create a Data Acquisition object the following command is 
issued. 
AI = analoginput('mcc',2); 
This will create a Data Input object called AI that will communicate with the #2 
card from ?mcc?.  ?.mcc? is the hardware vendor that MATLAB has assigned for this type 
of board.  Through this variable AI, all of the boards features can be accessed. 
 34
Next a channel has to be added to the object AI. 
addchannel(AI,0); 
This command will add the #0 channel on the board to the object AI.  From this point 
forward the #0 channel will be referred to as the #1 channel because it was the first 
channel added.  All subsequent channels will be added in this manner and numbered in 
order. 
The set command is used to program in the user options into the card. 
set(AI,'SampleRate',samplerate); 
set(AI,'TransferMode','DMA'); 
The two above commands will program the sample rate of the card and set the 
card to DMA transfer mode.  Direct Memory Access (DMA) transfer mode is very 
important in memory management.  This allows the A/D card to use the memory directly 
without using the system processor to transfer the information for it.  By using the DMA 
controller to handle data transfer from the card to the memory of the computer, allows the 
processor to focus on the signal processing tasks. 
Finally, the range of the A/D card needs to be set.  This is very hardware specific.  
The card used in this project has two programmable ranges.  It can use +/- 5V and +/- 1V.  
Due to the level coming from the down-converter the +/- 5V is used. 
set(AI.channel(1),'UnitsRange',[-5.0 5.0]); 
Each channel must be programmed alike.  There are many more parameters that 
must be set before the A/D session can be started, such as the trigger method and the 
 35
number of samples to acquire.  Once the card has been programmed it will retain this 
information in its memory and will not need to be programmed again. 
After all of the hardware is set up, the card can be started and triggered to start 
acquiring data and logging it to memory. 
start(AI); 
trigger(AI); 
The start command will allocate all of the memory needed for the operation and 
inform the card to get ready to acquire data.  This will start the card?s internal clock.  The 
trigger command will start the acquisition process of reading the data and logging it to 
memory. 
Once the data has been logged to memory the DAQ toolbox must retrieve it for 
processing.  This is accomplished as follows: 
[data_in t] = getdata(AI,buffer_size); 
This statement will retrieve the data from memory allowing it to be processed.  
Along with the data is the absolute time each sample was taken.  This is referenced to 
zero seconds, the time the first sample is read.  The data comes into MATLAB in a 
matrix format.  Each column is a channel and each row is a sample corresponding to the 
same row in t, the time vector.  By using this continuous time vector generated by the 
card a continuous phase can be achieved.  Without this continuous phase the audio output 
has a very loud hum in it. 
 
 
 36
5.3 Phase Shifter and Noise + Interferer Cancellation 
The Phase Shifter and resulting interference cancellation consists of two parts.  
The first is the adaptive method to find the desired phase shift and then the design of the 
filter to do the shift.  Included in the filtering process is a low-pass filter to remove any 
unwanted high frequency noise.  This is all done within a function called get_init_shift(), 
which has no input arguments and only an output argument. 
First, the A/D card is set up, and a series of 0.5 second long samples are taken.  
Since each 0.5 second piece of audio is statistically the same as the next, it is fine to say 
that each section is correlated in audio but not in phase or carrier.  Each 0.5 second piece 
of audio is created with a different amount of phase shift.  This is accomplished with the 
following statement. 
 
 
if(m<=0) 
            out_normal1 = downsample(out_normal1,21); 
            out_normal2 = downsample(out_normal2,21,abs(m)); 
        else 
            out_normal1 = downsample(out_normal1,21,m); 
            out_normal2 = downsample(out_normal2,21); 
        end 
The shift amount is denoted by the variable m while the if else statements take 
care of the shift either being positive or negative.  If the shift is positive then antenna 2 is 
 37
shifted relative to antenna 1.  If the shift is negative, then antenna 1 is shifted relative to 
antenna 2.  The actual shifting is done in conjunction with the downsampling of the 
signal.  When downsampling a sampled signal, the software does is to pick out every n
th
 
sample, with n corresponding to the ratio: 
 
)(
)(
newratef
oldratef
s
s
 (5.3.1) 
The shifting is accomplished by starting the downsampling process with the m
th
 
sample, where m corresponds to the number of samples to shift.  The function, 
downsample(), is included with the MATLAB Signal Processing Toolbox. 
Once each 0.5 second of audio is shifted, it is low pass filtered and the signals 
from antenna 1 and 2 are correlated to each other using the following equation and 
MATLAB code. 
 ][][s  [n] s(2)} )1({][
2
-  m
1
msmnsmz
?
?
?=
+=?=  (4.1.1) 
for n=1:length(out_normal1) 
           CORR_VEC(m+21) = CORR_VEC(m+21)+(out_normal1(n)*out_normal2(n)); 
       end 
The correlation code is contained within the loop that changes the shift by one 
sample for each 0.5 seconds worth of audio.  This statement will build a vector of 
correlation coefficients.  At the end of the program the shift with the highest correlation is 
chosen and returned to the main radio program. 
 38
It must be noted that the original sampling frequency must be chosen high enough 
to give good resolution in phase shift.  If Nyquist?s criterion for A/D sampling is adhered 
to then only 2 samples of shift would be available before the signals repeat in time.  
Nyquist says that a continuous time signal needs to be sampled at least twice its highest 
frequency component in order to be reconstructed.  If this is adhered to then only 2 points 
would be sampled for each period of the sampled signal.  Therefore a much higher 
sampling rate must be chosen.  Also the audio sampling rate has an effect on the amount 
of shift available to the user.  The amount of shift is given by the following equation. 
 
10 ??? NShift
 (5.3.2) 
Where, 
 
)(
)(
newratef
oldratef
N
s
s
=
 (5.3.3) 
rounded to the nearest integer. 
 
5.4 Demodulation and Output 
The demodulation step is relatively easy.  Once the signals from antenna 1 and 2 
are added together the demodulation takes place.  There are still two separate I & Q 
streams available.  The following statement will eliminate any images, reduce the noise, 
and recover the original audio. 
 
out1 = sqrt(i1_down_filt.^2+q1_down_filt.^2); 
 39
 
This step can be performed before or after the mixing and adding of the signals if 
needed.  If this step is done before the downsampling and shifting then it must be done on 
two antennas.  If this step is done after the downsampling and shifting then the 
downsampling and shifting is done on 4 data streams. 
The final output is normalized and built up into a sound buffer.  By normalizing 
the data, the sound will be played as loud as possible by the sound card. 
out = out./max(out); 
       sound_buffer = cat(1,sound_buffer,out); 
The preceding statements are in the while loop that records sound for the 
specified amount of time.  The data is then sent to the sound card using an analog output 
object.  This object is created with the DAQ toolbox similar to the analog input object. 
AO = analogoutput('winsound'); 
addchannel(AO,1); 
. 
. 
. 
putdata(AO,sound_buffer) 
start(AO); 
trigger(AO); 
 
 40
The ?winsound? object uses the windows interface to the soundcard.  This way all 
of the windows elements are available like volume control and mixing.  The data is 
placed into the sound card?s memory, then started and triggered just like the input 
devices. 
 
5.5 Signal Analyzer and Radiation Pattern Simulator Used in Development 
During the development of the project the need was realized for a signal analyzer.  
Rather than spend a lot of money on a high end analyzer from HP, a simple one was 
developed in MATLAB.  Essentially a signal analyzer consists of an A/D converter and 
some DSP code.  Wideband analyzers achieve results by down-converting the incoming 
signal and sweeping the local oscillator within the desired frequency band.  All of this 
can be done with MATLAB and the Flex-Radio down-converters.  MATLAB has built in 
FFT capabilities, as well as power and phase analysis functions. 
The program read data from channels 1 and 2, and then produced the time and 
frequency domain information graphically in plots, as seen in Fig. 23. 
0 0.005 0.01 0.015 0.02 0.025 0.03 0.035
-4
-3
-2
-1
0
1
2
3
4
0 1 2 3 4 5 6 7 8 9 10
x 10
5
-20
-10
0
10
20
30
40
50
 
Figure 23.  Output of Signal Analyzer FFT Plot 
 41
The following statements were written into a function and performed the 
Frequency Domain translation of the data. 
xFFT = fft(data_in,samples_trigger); 
xfft = abs(xFFT); 
%% 
% Avoid taking the log of 0. 
index = find(xfft == 0); 
xfft(index) = 1e-17; 
 
mag = 20*log10(xfft); 
mag = mag(1:samples_trigger/2); 
 
f = (0:length(mag)-1)*samplerate/samples_trigger; 
f = f(:);  
 
The subsequent FFT data and frequency vector are plotted using MATLAB?s plot 
function.  The raw data is plotted versus time and is used in power and voltage level 
calculations.  This MATLAB signal analyzer aided in the determination of the IF and the 
settings of the A/D card, or more specifically the input voltage range. 
A program was written to simulate the antenna array radiation patterns.  This 
program relied on the antenna array theory presented in Chapter 3.  The results of the 
program are presented in Chapter 3.  The real importance of this program is its ability to 
 42
generate output for the user, while the radio is running, the direction in which the antenna 
array is receiving. 
beta_d = (2*pi/lamda)*(.1833*lamda); 
theta = 0:2*pi/360:2*pi; 
alpha = n*(2*pi*fif/fs); 
psi = beta_d*cos(theta+alpha); 
rho = (1/2^2)*((sin(psi)).^2)./((sin(psi./2)).^2); 
This code implements the Array Factor equation from Chapter 4. 
 
?
?
?
?
?
?
?
?
?
?
?
?
?
?
=
2
sin
2
2
sin
2
1
2
2
2
normalized
AF
 (5.5.1) 
 
 
5.6 Notch Filter 
 
 The notch filter is implemented in two different versions.  The first version runs 
only on the highest frequency component in the signal and then quits.  The second 
version automatically removes all of the frequency spikes above a user determined value.  
The first version is discussed here. 
 
[f mag] = vic_fft(data,length(data),fs); 
load HP_250; 
filtered = filter(HP_250,data); 
 43
This will compute the FFT data from the input and then high pass filter it to get rid of any 
frequency components near DC. 
 
Next the highest frequency is computed. 
 
[val i]=max(mag_filtered); 
max_freq = f(i); 
 
 A bandstop Butterworth filter is designed using the same toolbox that was used to 
design the radio?s IF filters. 
 
hs = fdesign.bandstop('N,Fc1,Fc2', 10, lower, upper,96000); 
H = butter(hs); 
 
The width of the notch filter is set at 200 hertz and lower and upper are computed from 
this.  Finally, the data is returned to the calling function.  The second version of the notch 
filter simply repeats this process in a ?while? loop until all of the frequency spikes above 
a user selected level are removed. 
 44
CHAPTER 6 
PERFORMANCE, RESULTS, AND IMPROVEMENTS 
 
The results of the project will be presented in this chapter.  The conversion gain of 
the entire system is computed, the qualitative results from the trials are presented as well 
as a discussion of future improvements to the radio.  For a baseline reference on all 
measurements, a Ten-Tec RX340 DSP HF Receiver was used as a measurement device. 
 
6.1 Conversion Gain 
Conversion gain is the ratio of the output power to the input signal level.  For this 
project there is no way to measure the power level at the input to the down-converter, so 
the power indicator on the RX340 receiver will be used as the baseline value.  
Considering AM 1230 in Auburn, the input power level to the down-converter is -40 
dBm.  The system has the ability to raise this to 0 dBm with no signal processing.  This 
would suggest the conversion gain to be at least 40 dB.  In reality, the conversion gain is 
much higher.  The output power level of the system is dependent on the software as well 
as the computer?s sound hardware.  The sound hardware is ignored and just the values 
produced by the software are observed. 
 During night time data collection, the lowest signal recovered by the radio was -
90 dBm on the RX340?s display.  The radio was tuned to 710 KHz and a barely 
intelligible station could be heard.  The announcer was speaking in Spanish.  The 
 45
RX340?s output was just noise.  From this observation the overall conversion gain of the 
radio was 
determined to be approximately 90 dB.  Once again this does not take into account the 
sound card?s ability to amplify the audio to the speakers. 
 
6.2 Qualitative Results 
 The end result of the project is to reproduce audio signals from radio 
transmissions.  The best way to describe the results is to listen to them.  Included with the 
printed version of this work is a CD that contains the digital .wav recordings of the radio.  
The CD is organized by station.  Each station that was recorded has three files.  The first 
is the audio from the RX340, which is usually noisy.  The second is the processed signal 
from the SDR.  The third is the processed audio (notch filtered) from the SDR.  If you are 
reading the electronic version of this thesis, e-mail the author to receive the files.  Table 1 
summarizes the results of the testing.  All of the data in the table and the CD was 
acquired after the sun went down.    Following Table 1 there are radiation patterns of the 
stations that were received and miscellaneous station data.  The last column in the table 
makes note to whether the signal itself was enhanced or the background noise was 
cancelled. 
 46
Summary of Results from Testing on July 10, 2006 
Frequency 
(MHz) 
Signal Level 
from RX340 
RX 340 
Audio 
Description 
SDR Audio 
Description 
Station ID Cancelled or 
Enhanced. 
0.580 -60 dBm Noise Only Gospel 
Music, low 
quality 
WBIL, 
Tuskegee, 
AL 
Enhanced 
0.560 -72 dBm Noise + 
Small 
Garbled 
Audio 
Fuzzy News 
Radio 
WHBQ 
Memphis, 
TN 
Cancelled,  
When 
enhanced, 
got 
bleedthrough 
from 0.580 
0.710 -80 dBm Spanish and 
Background 
music + lots 
of noise 
Spanish 
only, 
background 
music gone 
? Enhanced 
0.780 -60 dBm Noise and 
Garbled 
Audio 
Sports talk 
radio 
WBBM 
Chicago, IL 
Enhanced 
0.820 -68 dBm 2 Stations + 
noise 
News Talk 
radio + 
Music 
WBAP 
Ft. Worth, 
TX 
Enhanced 
Table 1.  Results Summary 
 47
The following information is from http://www.radio-locator.com. 
WBIL AM 580 kHz 
Tuskegee, AL 
500 Watts in the day time 
139 Watts in the Night time 
 
Figure 24. WBIL Radiation Pattern
 48
WHBQ AM 560 kHz 
Memphis, TN 
5000 Watts Day time 
1000 Watts Night time 
 
Figure 25. WHBQ Night time Radiation Pattern 
 49
WBBM AM 780 kHz 
Chicago, IL 
50k Watts Unlimited 
 
Figure 26. WBBM Radiation Pattern 
 50
WBAP AM 820 kHz 
Fort Worth, TX 
50k Watts Unlimited 
 
Figure 27. WBAP Radiation Pattern 
 51
6.3 Future Improvements 
 In the future the project needs to take a different path.  Although this project 
works well, there is plenty of room for improvement.  In no way was this project 
designed to be a complete product at the end.  As an ongoing work in progress, the three 
main areas of improvement are the antenna array, the downconversion process, and the 
DSP implementation. 
 The antennas could be placed further apart.  If the antennas were placed 150 
meters apart the radiation pattern of the array would be the plot in Figure 28.  
 
Figure 28.  Radiation pattern for 150m antenna spacing vs. 55 Meter Spacing 
  
 
 52
As can be seen there is a very noticeable null along the axis of the array.  This 
pattern can be rotated just like Figure 10 through Figure 15.  To do this, one of the 
antennas would have to be placed on another building on Auburn?s campus.  The deep 
null will provide better noise and strong signal rejection. 
 The downconversion process currently uses two Flex SDR 1000 boxes.  Each of 
these is controlled from a separate laptop computer.  There are a total of 3 computers 
needed to run the project.  The two local oscillators are synchronized in frequency but not 
in phase.  This means that the DSP software must account for this phase difference.  To 
alleviate this problem one local oscillator needs to be connected to two I/Q mixers.  
Minicircuits, Inc. [10] manufactures modular RF components and would have the perfect 
components for this modification.  The Level 7 Family of mixers along with an Analog 
Devices Direct Digital Conversion chip acting as the LO would make a good 
combination.  This would also need to be augmented with a RF pre-amp and an IF filter, 
all of which are available from Minicircuits.  This would reduce the number of computers 
to only one and greatly increase the accuracy of the conversions. 
 MATLAB must parse the text file of the program every time it runs.  MATLAB 
also must interface to the ADC through another software layer. To better increase the 
speed of the DSP code, the software should be written in C or C++.  MATLAB allows for 
quick development, but is not fast enough to run this project in real time.  As it stands the 
data has to be collected, processed, and recorded to the disk before the user can listen to 
it.  MATLAB does allow for GUIs to be created, but this would slow the process down 
even more.  The real solution is to use a Microsoft Windows GUI library with C++ and 
 53
write the DSP code in C.  This will remove one software layer from the project, thus 
speeding up the data processing.  Also to improve the response of the filters and the delay 
filter some shaping of the incoming signal needs to be done.  DSP literature [11] 
recommends that this shaping be done to coincide with the data.  Experiments will need 
to be performed to determine the best shaping to use. 
 54
REFERENCES 
[1] DX Engineering Inc., http://www.dxengineering.com, PO Box 1491, Akron, OH 
44309 
[2] Flex Radio Corporation, http://www.flex-radio.com, 12100 Technology Blvd, Austin, 
TX 78727 
[3] Gerald Youngblood, A Software Defined Radio for the Masses, Part 1; QEX, 
July/August 2002 
[4] Measurement Computing Corporation, http://www.measurementcomputing.com, 10 
Commerce Way, Norton, MA 02766 
[5] Ali H. Sayed, Fundamentals of Adaptive Filtering, Wiley, 2003 
[6] Stuart M. Wentworth, Fundamentals of Electromagnetics with Engineering 
Applications, Wiley, 2005 
[7] Warren L. Stutzman, Gary A. Thiele, Antenna Theory and Design Second Edition, 
Wiley, 1998 
[8] The Mathworks, Data Acquisition Toolbox For Use With MATLAB User?s Guide 
Version 2, The Mathworks Inc., 2001 
[9] The Mathworks Corporation, 
http://www.mathworks.com/access/helpdesk/help/techdoc/, MATLAB documentation 
[10] Minicircuits Corporation, http://www.minicircuits.com, P.O. Box 350166, Brooklyn, 
NY 11235  
[11] Doug Smith, KF6DX, Digital Signal Processing Technology, ARRL, 2003 
 55
APPENDIX 
 
A.1 FULL MATLAB SOFTWARE CODE  
 
This file is the main file for the radio.  As input, the user needs to tell the program 
whether to use the antennas for constructive or destructive purposes on the 
strongest signal. 
 
function final_radio1(can_keep) 
clc; 
 
daqreset; 
seconds_to_record = 10; 
 
%used for program control 
stop_running = 1; 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 
filling = 1; 
%calculate the needed values for setup% 
samplerate = 2e6; 
sound_samplerate = 96000; 
buffer_size = 65536; 
IF = 11025; 
sound_buffer_size = buffer_size; 
sound_buffer = zeros(1,1); 
 
%Run Initiatilization routine 
shift = get_init_shift(); 
 
first_time = 0; 
 
%setting up the input and output 
AI = analoginput('mcc',2); 
AO = analogoutput('winsound'); 
addchannel(AO,1); 
addchannel(AI,0); 
addchannel(AI,1); 
addchannel(AI,2); 
addchannel(AI,3); 
 56
set(AI,'SampleRate',samplerate); 
set(AO,'StandardSampleRates','off'); 
set(AO,'SampleRate',sound_samplerate);%setting the soundcard to 96000 out 
set(AI,'SamplesPerTrigger',inf); 
set([AI AO],'TriggerType','Manual'); 
set(AI,'ManualTriggerHwOn','Trigger') 
set(AI,'TransferMode','DMA'); 
set(AI.channel(1),'UnitsRange',[-5.0 5.0]); 
set(AI.channel(1),'SensorRange',[-5.0 5.0]); 
set(AI.channel(1),'InputRange',[-5.0 5.0]); 
set(AI.channel(2),'UnitsRange',[-5.0 5.0]); 
set(AI.channel(2),'SensorRange',[-5.0 5.0]); 
set(AI.channel(2),'InputRange',[-5.0 5.0]); 
set(AI.channel(3),'UnitsRange',[-5.0 5.0]); 
set(AI.channel(3),'SensorRange',[-5.0 5.0]); 
set(AI.channel(3),'InputRange',[-5.0 5.0]); 
set(AI.channel(4),'UnitsRange',[-5.0 5.0]); 
set(AI.channel(4),'SensorRange',[-5.0 5.0]); 
set(AI.channel(4),'InputRange',[-5.0 5.0]); 
 
 
%load the Low Pass Filter from the disk 
load LP_4KH; 
 
%initiate the data recording 
start(AI); 
trigger(AI); 
t = zeros(1,buffer_size); 
while(t(buffer_size) < seconds_to_record) 
     
    %retrieve data from memory 
    [data_in t] = getdata(AI,buffer_size); 
        LO = sin(2*pi*IF.*t); 
        I1 = data_in(1:buffer_size,1); 
        Q1 = data_in(1:buffer_size,2); 
        I2 = data_in(1:buffer_size,3); 
        Q2 = data_in(1:buffer_size,4); 
         
         
        %shift the data down in frequency 
 57
        i1_down = I1 .* LO; 
        q1_down = Q1 .* LO; 
        i2_down = I2 .* LO; 
        q2_down = Q2 .* LO; 
         
        %low pass filter the data 
        i1_down_filt = filter(LP_4KH,i1_down); 
        q1_down_filt = filter(LP_4KH,q1_down); 
        i2_down_filt = filter(LP_4KH,i2_down); 
        q2_down_filt = filter(LP_4KH,q2_down); 
         
        %demodulate each channel to remove noise etc. 
        out1 = sqrt(i1_down_filt.^2+q1_down_filt.^2); 
        out2 = sqrt(i2_down_filt.^2+q2_down_filt.^2); 
         
        
        %downsample and phase shift signal 
        if(shift<=0) 
            out_normal1 = downsample(out1,21); 
            out_normal2 = downsample(out2,21,abs(shift)); 
        else 
            out_normal1 = downsample(out1,21,shift); 
            out_normal2 = downsample(out2,21); 
        end 
        
       if(length(out_normal1) ~= length(out_normal2)) 
           sz1 = length(out_normal1); 
           sz2 = length(out_normal2); 
           if (sz1 < sz2) 
               out_normal1 = cat(1,out_normal1,out_normal1(sz1)); 
           else 
               out_normal2 = cat(1,out_normal2,out_normal2(sz2)); 
           end 
       end 
        
       %decide if the antennas are to add or subtract from on another 
       if(can_keep == 1) 
           out = out_normal1+out_normal2; 
       else 
           out = out_normal1-out_normal2; 
 58
       end 
        
       %normalize the output and add it to the sound buffer 
       out = out./max(out); 
       sound_buffer = cat(1,sound_buffer,out); 
       
      %clear the display and display the current time 
      clc; 
      disp(t(buffer_size)); 
     
     
end 
%output the data to the sound card 
putdata(AO,sound_buffer) 
start(AO); 
trigger(AO); 
 
 
 
 
This program will compute the offset needed for the desired signal.  It takes no 
input and outputs the desired shift value. 
 
function init_shift = get_init_shift() 
clear; 
daqreset; 
seconds_to_record = .1; 
 
 
 
%calculate the needed values for setup% 
 
samplerate = 2e6; 
sound_samplerate = 96000; 
buffer_size = 4096*2; 
IF = 11025; 
sound_buffer_size = buffer_size; 
sound_buffer = zeros(sound_buffer_size,1); 
 
%setting up the input and output 
 59
AI = analoginput('mcc',2); 
AO = analogoutput('winsound'); 
addchannel(AO,1); 
addchannel(AI,0); 
addchannel(AI,1); 
addchannel(AI,2); 
addchannel(AI,3); 
set(AI,'SampleRate',samplerate); 
set(AO,'StandardSampleRates','off'); 
set(AO,'SampleRate',sound_samplerate);%setting the soundcard to 96000 out 
set(AI,'SamplesPerTrigger',inf); 
set([AI AO],'TriggerType','Manual'); 
set(AI,'ManualTriggerHwOn','Trigger') 
set(AI,'TransferMode','DMA'); 
set(AI.channel(1),'UnitsRange',[-5.0 5.0]); 
set(AI.channel(1),'SensorRange',[-5.0 5.0]); 
set(AI.channel(1),'InputRange',[-5.0 5.0]); 
set(AI.channel(2),'UnitsRange',[-5.0 5.0]); 
set(AI.channel(2),'SensorRange',[-5.0 5.0]); 
set(AI.channel(2),'InputRange',[-5.0 5.0]); 
set(AI.channel(3),'UnitsRange',[-5.0 5.0]); 
set(AI.channel(3),'SensorRange',[-5.0 5.0]); 
set(AI.channel(3),'InputRange',[-5.0 5.0]); 
set(AI.channel(4),'UnitsRange',[-5.0 5.0]); 
set(AI.channel(4),'SensorRange',[-5.0 5.0]); 
set(AI.channel(4),'InputRange',[-5.0 5.0]); 
 
 
RMS = zeros(4,1); 
CORR_VEC = zeros(41,1); 
load LP_7KH; 
 
 
for m=-20:1:20 
    clc; 
    disp('acquiring initialization data'); 
    disp(m); 
    start(AI); 
    trigger(AI); 
    out_normal2_prev = zeros(ceil(buffer_size/23),1); 
 60
 
 
    while(AI.SamplesAcquired < seconds_to_record/(1/samplerate)) 
        [data_in t] = getdata(AI,buffer_size); 
        LO = sin(2*pi*IF.*t); 
        I1 = data_in(1:buffer_size,1); 
        Q1 = data_in(1:buffer_size,2); 
        I2 = data_in(1:buffer_size,3); 
        Q2 = data_in(1:buffer_size,4); 
        I1 = remove_mean(I1); 
        Q1 = remove_mean(Q1); 
        I2 = remove_mean(I2); 
        Q2 = remove_mean(Q2); 
        
        i1_down = I1 .* LO; 
        q1_down = Q1 .* LO; 
        i2_down = I2 .* LO; 
        q2_down = Q2 .* LO; 
         
        i1_down_filt = filter(LP_7KH,i1_down); 
        q1_down_filt = filter(LP_7KH,q1_down); 
        i2_down_filt = filter(LP_7KH,i2_down); 
        q2_down_filt = filter(LP_7KH,q2_down); 
         
        out1 = sqrt(i1_down_filt.^2+q1_down_filt.^2); 
        out2 = sqrt(i2_down_filt.^2+q2_down_filt.^2); 
        out1_no_mean = out1-mean(out1); 
        out2_no_mean = out2-mean(out2); 
         
        out_normal1 = out1_no_mean./(max(out1_no_mean)); 
        out_normal2 = out2_no_mean./(max(out2_no_mean)); 
        
        %downsample and phase shift signal 1 or two depending on sign of m 
        if(m<=0) 
            out_normal1 = downsample(out_normal1,21); 
            out_normal2 = downsample(out_normal2,21,abs(m)); 
        else 
            out_normal1 = downsample(out_normal1,21,m); 
            out_normal2 = downsample(out_normal2,21); 
        end 
 61
        
       if(length(out_normal1) ~= length(out_normal2)) 
           sz1 = length(out_normal1); 
           sz2 = length(out_normal2); 
           if (sz1 < sz2) 
               out_normal1 = cat(1,out_normal1,out_normal1(sz1)); 
           else 
               out_normal2 = cat(1,out_normal2,out_normal2(sz2)); 
           end 
       end 
       out = out_normal1+out_normal2; 
        
       %Compute the correlation of the vectors 
       for n=1:length(out_normal1) 
           CORR_VEC(m+21) = CORR_VEC(m+21)+(out_normal1(n)*out_normal2(n)); 
       end 
                
        sound_buffer = cat(1,sound_buffer,out); 
    end 
    stop(AI); 
    %Compute RMS of output 
    RMS(m+21) = norm(out)/sqrt(length(out)); 
 
end 
[y i] = max(CORR_VEC); 
disp('Done'); 
init_shift = i-21; 
disp(init_shift); 
daqreset; 
 
This Program will compute the FFT magnitude and the frequency vector for use by 
other programs. 
 
%This function computes the fft data and returns the frequency vector in 
%f and the magnatude vector in mag 
%[f mag] = vic_fft(data_in,number_of_samples,samplerate); 
function [f mag] = vic_fft(data_in,samples_trigger,samplerate) 
xFFT = fft(data_in,samples_trigger); 
xfft = abs(xFFT); 
 
 62
%% 
% Avoid taking the log of 0. 
index = find(xfft == 0); 
xfft(index) = 1e-17; 
 
mag = 20*log10(xfft); 
mag = mag(1:round(samples_trigger/2)); 
 
f = (0:length(mag)-1)*samplerate/samples_trigger; 
f = f(:); 
 
This program is used to automatically notch out frequency components above a user 
defined threshold. 
 
function output = notch2(data,fs,threshold) 
%w = input('Enter width of notch >>'); 
w=200; 
[f mag] = vic_fft(data,length(data),fs); 
load HP_250; 
filtered = filter(HP_250,data); 
 
[f mag_filtered] = vic_fft(filtered,length(data),fs); 
[val i]=max(mag_filtered); 
max_freq = f(i); 
mean_mag = mean(mag); 
output = filtered; 
 
while(mag(i) > mean_mag + threshold) 
     
    upper = max_freq+(w/2); 
    lower = max_freq-(w/2); 
    hs = fdesign.bandstop('N,Fc1,Fc2', 10, lower, upper,96000); 
    H = butter(hs); 
    %butter(hs); 
    disp('NOTCHING'); 
    output = filter(H,output); 
    %length = 2048; 
    [f mag] = vic_fft(output,round(length(output))/4,fs); 
    %mag(i) = 0; 
    [val i]=max(mag); 
 63
    max_freq = f(i); 
     
     
     
    mean_mag = mean(mag); 
 
end 
%[f2 mag_filtered] = vic_fft(filtered,length(filtered),fs); 
[f3 mag_output] = vic_fft(output,length(output),fs); 
 
 
%subplot(3,1,1),plot(f,mag); 
%subplot(3,1,2),plot(f2,mag_filtered); 
plot(f3,mag_output); 
 
This program is the signal analyzer main program. 
 
function sig_analyzer(); 
 
clear; 
daqreset; 
global T; 
global AI; 
AI = analoginput('mcc',2); 
addchannel(AI,0); 
 
global samples_trigger; 
samples_trigger = 4096; 
 
global samplerate; 
samplerate = 44100; 
 
period = 1/samplerate; 
sample_period = samples_trigger*period; 
 
set(AI,'SampleRate',samplerate); 
set(AI,'SamplesPerTrigger',samples_trigger); 
set(AI,'TriggerType','immediate'); 
set(AI.channel(1),'UnitsRange',[-5.0 5.0]); 
set(AI.channel(1),'SensorRange',[-5.0 5.0]); 
 64
set(AI.channel(1),'InputRange',[-5.0 5.0]); 
 
global hFig; 
hFig = figure(); 
htoggle = uicontrol(... 
   'Parent'          , hFig,... 
   'Style'           , 'pushbutton',... 
   'Units'           , 'normalized',... 
   'Position'        , [0.0150 0.0111 0.1 0.0556],... 
   'Value'           , 1,... 
   'String'          , 'Stop',... 
   'Callback'        , @stop_exec); 
 
T = timer('TimerFcn',@get_the_data,'Period',0.1,'ExecutionMode','FixedDelay'); 
 
start(T); 
 
function get_the_data(obj,event_time); 
global AI; 
global samplerate; 
global samples_trigger; 
start(AI); 
[input time] = getdata(AI); 
subplot(2,1,1),plot(time,input); 
 
xFFT = fft(input,samples_trigger); 
xfft = abs(xFFT); 
 
%% 
% Avoid taking the log of 0. 
index = find(xfft == 0); 
xfft(index) = 1e-17; 
%mag = xfft.* conj(xfft) / samples_trigger; 
 
mag = 10*log10(xfft); 
mag = mag(1:samples_trigger/2); 
 
f = (0:length(mag)-1)*samplerate/samples_trigger; 
f = f(:); 
subplot(2,1,2),plot(f,mag),axis([0 samplerate/4 -20 50]); 
 65
 
function stop_exec(obj,event_time) 
global T; 
stop(T); 
 
This program is used to plot the antenna radiation pattern for the desired sample 
shift amount. 
 
clear; 
clc; 
 
%this program generates a series of plots for the dual antenna array 
 
 
n = input('Enter # of samples to shift >> '); 
fs = input('Enter Sampling frequency in Hz >> '); 
fif = input('Enter IF Frequency in Hz >> '); 
 
lamda = 3e8/1e6; 
beta_d = (2*pi/lamda)*(.1833*lamda); 
theta = 0:2*pi/360:2*pi; 
alpha = n*(2*pi*fif/fs); 
psi = beta_d*cos(theta+alpha); 
rho = (1/2^2)*((sin(psi)).^2)./((sin(psi./2)).^2); 
 
figure; 
polar(theta,rho); 
str_for_title = strcat('Radiation Pattern for: ',num2str(n),' Samples of Shift'); 
title(str_for_title); 
text(1.25,0,'Array Axis'); 
line([-1.20 1.20],[0 0]); 
 
The following program calculates the directivity and Gain of the Two-Element 
Antenna Array. 
 
%This program will calculate the beam solid angle of the antenna array at 
%many values of alpha the phase offset.  The maximum directivity is then 
%found. 
clear; 
clc; 
 66
 
%We know the maximum directivity occurs at a 180 degree phase shift, or pi 
%in radians 
 
theta = 0:pi/180:(pi/2)-(pi/180); 
phi = 0:2*pi/360:2*pi-(2*pi/360); 
 
d_phi = 2*pi/360; 
d_theta = pi/180; 
 
betad = 2*pi/(300/55); 
psi = betad*cos(phi)+pi; 
 
%now we will compute the phi integral, first with the numerator, then the 
%denominator, create the fraction, and then integrate it. 
 
num = (sin(psi)).^2; 
den = (sin(psi./2)).^2; 
 
fraction =  num./den; 
 
polar(phi,.25*fraction); 
phi_integral = d_phi*sum(fraction); 
 
%now we calculate the theta integral 
 
theta_integral = d_theta*sum((sin(theta)).^3); 
 
%calculating the Beam Solid Angle 
omega_p = (1/4)*(phi_integral*theta_integral); 
 
%calculating directivity 
D = (4*pi)/omega_p; 
G = D*1; 
%converting to dB 
G_in_dB = 10*log10(G);