IMPLEMENTATION OF NULL STEERING ALGORITHMS IN A COMPACT
ANALOG ARRAY
by
Hugo Orlando Condori Quispe
A thesis submitted in partial fulfillment
of the requirements for the degree
of
Master of Science
in
Electrical Engineering
MONTANA STATE UNIVERSITY
Bozeman, Montana
April, 2014
c© COPYRIGHT
by
Hugo Orlando Condori Quispe
2014
All Rights Reserved
ii
ACKNOWLEDGEMENTS
This stage of my life as a graduate student at Montana State University has been
one of the most memorable in my life. I would like to thank many people that have
contributed in many ways in this journey.
I want to give thanks to my adviser Prof. Richard Wolff. I am grateful for all
his help and for giving me the freedom to pursue my ideas in research and providing
unconditional support during my stage at Montana State University. My gratitude
goes to my thesis committee: Prof. Yikun Huang and Prof. Ross Snider. Prof.
Huang has been constant source of support during the development of this work.
Uncountable hours of technical discussions were given to discuss the status of the
project and future directions.
I would like to gratefully acknowledge the support of the Fulbright Scholarship
which made this work possible.
Every result described in this thesis was accomplished with the help and support
of fellow lab mates. I am especially grateful to a great friend Aditya Angampally. I
have had the great pleasure to work with him on this project, through all the ups
and downs of the countless hours that we spent together in the communications lab
trying to make our experiments work (some of them did actually). I would like to
acknowledge Raymond Weber for his assistance and contributions on this project.
iii
TABLE OF CONTENTS
1. INTRODUCTION ........................................................................................1
Motivation....................................................................................................1
Null Steering ................................................................................................1
Project Definition .........................................................................................4
Overview ......................................................................................................5
2. SYSTEM OVERVIEW..................................................................................6
Antenna Array..............................................................................................6
Analog Beamformer Board ............................................................................7
3. NULL STEERING ALGORITHMS ...............................................................9
Data Model ..................................................................................................9
Null Steering Algorithms ............................................................................. 11
Open-loop Null Steering .......................................................................... 12
Optimal Null Steering Algorithm .......................................................... 12
Waveform Modification ........................................................................ 13
Closed-loop Null Steering......................................................................... 14
4. SIMULATION STUDY ............................................................................... 17
Null Steering Performance Analysis.............................................................. 17
Null Patterns .......................................................................................... 17
Cumulative Distribution Function Analysis ............................................... 18
Case I: Null Inside the Main Beam ....................................................... 19
Case II: Null Outside the Main Beam ................................................... 24
Phase and Magnitude Errors........................................................................ 27
Phase Error Analysis ............................................................................... 27
Magnitude Analysis ................................................................................. 29
Quantization Error and Phase Perturbation.................................................. 33
Multiple Nulls............................................................................................. 38
5. LAB TESTS .............................................................................................. 40
Lab Setup .................................................................................................. 40
Lab Test Results ......................................................................................... 44
iv
TABLE OF CONTENTS – CONTINUED
6. CONCLUSION AND FUTURE WORK....................................................... 47
Conclusions ................................................................................................ 47
Future Work ............................................................................................... 48
REFERENCES CITED.................................................................................... 48
vLIST OF TABLES
Table Page
4.1 Uniform Circular Antenna Array Characteristics ................................... 18
4.2 Simulation Null Steering Results ......................................................... 18
4.3 CDF Values Summary for Case I.......................................................... 23
4.4 CDF Values Summary for Case II ........................................................ 26
4.5 Multi-null Steering Results for the Optimal Null Steering Algorithm ...... 38
5.1 Experimental Null Steering Results ..................................................... 45
vi
LIST OF FIGURES
Figure Page
1.1 Null steering to the interference signal ....................................................3
2.1 Circular antenna array...........................................................................6
2.2 Beamformer board with the UCA...........................................................7
2.3 Beamformer board block diagram...........................................................8
3.1 Diagram of the antenna array .............................................................. 10
3.2 System output interference to signal ratio E(OISR).............................. 13
3.3 Illustration of the waveform modification algorithm ............................... 14
3.4 Diagram of closed-loop adaptive null steering algorithm......................... 15
4.1 Beam pattern for the optimal null steering algorithm............................. 19
4.2 Beam pattern for the waveform modification null steering algorithm....... 20
4.3 Beam pattern for the adaptive null steering algorithm ........................... 20
4.4 Beam pattern for case I ....................................................................... 21
4.5 CDF for case I using the optimal null steering algorithm........................ 22
4.6 CDF for case I using the waveform modification algorithm..................... 22
4.7 CDF for case I using the LMS algorithm............................................... 23
4.8 Beam pattern for case II ..................................................................... 24
4.9 CDF for case II using the optimal null steering algorithm ...................... 25
4.10 CDF for case II using the waveform modification algorithm ................... 25
4.11 CDF for case II using LMS null steering algorithm ................................ 26
4.12 Effect of the phase errors on the power pattern ..................................... 28
4.13 Effect of the phase error for the optimal null steering algorithm ............. 29
4.14 Effect of the phase error for the waveform modification algorithm .......... 30
4.15 Effect of the phase error for the LMS null steering algorithm ................. 30
4.16 Effect of the magnitude error for the optimal null steering algorithm ...... 31
vii
LIST OF FIGURES – CONTINUED
Figure Page
4.17 Effect of the magnitude error for the waveform modification algorithm ... 31
4.18 Effect of the magnitude error for the LMS null steering algorithm .......... 32
4.19 Effect of 10% magnitude error on the power pattern .............................. 33
4.20 Effect of 20% magnitude error on the power pattern .............................. 34
4.21 Effect of the magnitude error for the optimal null steering algorithm ...... 34
4.22 Effect of the magnitude error for the waveform modification algorithm ... 35
4.23 Effect of the magnitude error for the LMS null steering algorithm .......... 35
4.24 Beam pattern without phase perturbation............................................. 36
4.25 Beam pattern with phase perturbation ................................................. 37
4.26 Beam pattern for the optimal multi-null steering algorithm.................... 39
5.1 Block diagram of the lab test set up for receiving null steering .............. 41
5.2 Anechoic chamber ............................................................................... 42
5.3 Instruments ....................................................................................... 42
5.4 Beam pattern for the optimal null steering algorithm............................. 44
5.5 Beam pattern for the waveform modification null steering algorithm....... 45
5.6 Beam pattern for the LMS adaptive null steering algorithm ................... 46
viii
ABSTRACT
In this thesis, the implementation of null steering algorithms in a compact analog
array is demonstrated and validated. The performance of the null steering algorithms
is validated through extensive simulation and hardware implementation. The results
of the techniques of null steering, including controlling the complex weights, usually
have to rely on simulations to study system performances, design trade-offs, and
system optimization, which by itself can be quite complex and a time-consuming
task. Even after extensive simulations, it is not easy to get insights as to what
parameters determine system performance in different system parameters, and the
interactions on system parameters. Therefore, experimentation and deployment on a
real system is required. Few studies have proposed null steering algorithms studies
using real implementations. With this motivation, this work presents comprehensive
performance comparison of some of the available null steering techniques using an
analog array. The contributions of this thesis are: optimize the performance of null
steering algorithms taking into account realistic considerations in the simulations and
demonstrating the benefits through extensive simulations; and verify the performance
of the null steering system through experimental implementation using a simple,
compact, lightweight, low cost, high gain, high throughput analog antenna array.
1INTRODUCTION
Motivation
One of the major problems of security in military radars and wireless communica-
tions is jamming. Due to their open and ubiquitous nature, wireless communication
systems are extremely vulnerable to attack. Jamming, defined as the use of active
signals to prevent data distribution, has emerged as an attractive attack method [1].
In this attack, the adversary tries to prevent or interfere with the reception of signals
at the nodes in the network. Most current data communication standards, such as
IEEE802.16 and Bluetooth [2], are not designed to resist malicious interference; a
small number of jammers with limited energy resources can disrupt operation of an
entire network. In addition, jamming is a common method of attack in military
networks where transmissions are often performed in the presence of an adversary
whose goal is to disrupt the communication to a maximum degree [3].
Different security mechanisms and countermeasures against jamming for defending
the attacks have been proposed in literature. A survey describing the anti-jamming
countermeasures can be found in [4].
Null Steering
Null steering is one of the efficient methods to counter jamming attacks. The
techniques of placing nulls in the antenna array pattern to suppress jamming signals
and maximize its gain toward the direction of the desired signal has received consid-
erable attention in the past and it is still of great interest [5]. Implementation of a
null steering algorithm in an antenna array implies that the antenna array can be
2used to steer nulls in the direction of known interference signals while maintaining
the main beam toward a desired direction [6]. This improves the performance of the
antenna system enhancing the Signal to Interference Ratio (SIR) by suppressing the
interference signal [5]. However, null steering methods have seen limited use due to
the cost and size of the array system. If null steering is available in the analog Radio
Frequency (RF) stage of antenna arrays, it can provide drastic improvement in both
Direct Current (DC) power dissipation and fabrication costs, an improvement that is
proportional to the number of array elements [6].
Null steering algorithms rely on controlling the weights of the antenna array. Since
the parameters of the null steering weights follow a complex form, null steering can
be controlled by changing only the amplitude, only the phase of the weights or both.
Null steering methods that change only the phase of the null steering weights
have been extensively considered in the literature [7, 8, 9, 10] . In [7], the null steer-
ing method proposed is based on the adaptive Sequential Quadratic Programming
(SQP) algorithm that transforms the nonlinear minimization problem to a sequence
of quadratic sub-problems. This method works efficiently when multiple users are tar-
geted while simultaneously nulling the interference. Another technique was proposed
by Zhu et al. [8], where the phases of the null steering weights are calculated using
genetic algorithms. The method modeled and targeted linear arrays. By using this
technique, it was possible to steer the null toward the interference angular location
and simultaneously minimize the maximum sidelobe level. Another method for phase-
only null steering is proposed by Ananasso [9]. In this method the performance of
the null-steering system, using digital phase-only weights, is analyzed numerically
by a computer simulation. Another genetic algorithm approach has been proposed
by Haupt and Haupt [10]. The authors demonstrate that it is possible to control
the phases only of the null steering weights following a genetic algorithm, and place
3Antenna Array
Standard beamforming to the user
Null steering to interference
User
Interference
Figure 1.1: Null steering to the interference signal
multiple deep nulls in the directions of the interferences. This genetic algorithm takes
into account the quantization errors of the weights introduced when the algorithms
are implemented in hardware. The authors demonstrate that it is possible to achieve
deep nulls at the direction of the interferences while having a low side lobe level. One
disadvantage of this method is that it relies on the utilization of a high number of
elements to easily converge to the solution of the null steering weights.
Null steering methods that rely on the changes of the magnitude-only have also
been studied and different approaches can be found in the literature [11, 12]. The
author in [11] proposes a method of null steering controlling only the magnitude of the
weights; therefore excluding the phase shifters when performing null steering. The
author demonstrates the functionality of the algorithm, using an 8 element linear
array, by forcing the nulls in such a way that the zeros of the power pattern of the
antenna array occurs in conjugate pairs. Genetic algorithms have been proposed to
4calculate the null steering weights by controlling only the magnitude. Yallaparagada
et al. [12] reported a genetic algorithm for null steering in a circular antenna array.
One of the major drawbacks in this algorithm is the number of convergence cycles
necessary to arrive at a final solution.
Another approach for calculating the null steering weights relies on changes of the
phase as well as the magnitude [5, 13, 14, 15, 16]. In this thesis, a comprehensive per-
formance comparison of some of the available null steering techniques was performed.
The parameters taken into account for comparison were null depth, side lobe level,
and SIR.
Project Definition
The goal of this thesis is to provide a realistic evaluation of the performance of null
steering techniques targeting the implementation in a simple, compact, lightweight,
low cost, high gain, high throughput, analog antenna array with efficient null steering
performance. The performance of the algorithms is validated through extensive sim-
ulations and hardware implementation. This thesis consolidates the work presented
in [17, 18, 19, 20, 5].
The results of the techniques of null steering, including controlling the complex
weights, usually have to rely on simulations to study system performances, design
trade-offs, and system optimization, which by itself can be quite complex and a time-
consuming task. Even after extensive simulations, it is not easy to get insights as to
what parameters determine system performance in different system parameters, and
the interactions on system parameters. Therefore, experimentation and deployment
on a real system is required. Few studies have proposed null steering algorithms
studies using real implementations. With this motivation, this work presents com-
5prehensive performance comparison of some of the available null steering techniques
using an analog array.
The contributions of this thesis are two fold:
• optimizing the performance of null steering algorithms taking into account real-
istic considerations in the simulations and demonstrating the benefits through
extensive simulations;
• verifying the performance of the null steering system through extensive simu-
lations and experimental implementation using a simple, compact, lightweight,
low cost, high gain, high throughput analog antenna array.
Overview
The thesis is divided into six chapters. Chapter 2 describes the hardware sys-
tem utilized to prove and evaluate the performance of the null steering algorithms.
Chapter 3 describes the rationale behind the null steering algorithms studied and
implemented. Chapter 4 contains the results of the simulation of the null steering
algorithms. Chapter 5 presents the experimental results obtained after implement-
ing the null steering algorithms in an analog antenna array. The conclusions and
discussion of future work are presented in the last chapter.
6SYSTEM OVERVIEW
Antenna Array
The uniform circular antenna array (UCA) developed at Montana State Univer-
sity (MSU) is an 8 element UCA, composed of two functional blocks: the thin-wire
monopole apertures and the ground plane with ground skirt as shown in Figure 2.1.
The ground plane and skirt provide a virtual infinite ground plane and mechanical
rigidity [21, 22]. The array has an operating center frequency of 5.8 GHz and spatially
covers 360◦ in the azimuth plane. The array electrical size is βρ = 3.05, where β is
the wave number, ρ is the array radius, 2.54 cm. The inter-element spacing is 0.375λ
and the antenna element length is 0.23λ. The array gain is 12− 15 dBi depending on
the algorithm used in weighting the beamformer channels. The operating bandwidth
of 200 MHz centered about 5.8 GHz has relatively flat gain [23, 24].
The beam patterns of the array were measured in the anechoic chamber at the
Communications Lab at MSU. The chamber size is 41.74′′×79.5′′×51.5′′ (W×L×H).
The frequency range of the chamber is 2GHz−30GHz and the microwave absorber
thickness is: 5 inches (−42dB) and 8 inches (−52dB). A 5.8 GHz resonant horn
antenna (WR159 f = 4.9− 7.05 GHz) is located at one end of the chamber [25]. The
Figure 2.1: Circular antenna array
7Figure 2.2: Beamformer board with the UCA
other end of the chamber has a rotating pedestal with a stepper motor attached. The
antenna array is mounted on the rotating pedestal, controlled by the step motor with
a personal computer (PC) through a Data AcQuisition card (DAQ), which allows it
to collect a full 360◦ power spectrum [17]. The pedestal is built to hold the complete
antenna array system.
Analog Beamformer Board
The purpose of the RF beamformer board is to apply the PC generated beam-
forming weights to the RF signal coming from the array so that the directional beam
is formed.
A photo of the beamformer board is shown in Figure 2.2 and a block diagram
can be seen in Figure 2.3. The beamformer board is an 8 channel digitally controlled
analog beamforming system that controls phase and amplitude of each channel to
form a beam in the desired direction. The beamforming system consists of five
functional blocks: controller, analog beamforming circuitry, radio interface, power
detection, and power regulation [25]. The controlling unit provides digital control via
8An
ten
na
arr
ay
Tx
/Rx
 
sw
itch
es
. . .
Tx
/Rx
 
sw
itch
es
PA LN
A PA LN
A
Tx
/Rx
Am
plif
ier
s
Ph
ase
 
Sh
ifte
rs
PS PS
  MB DIV CO Po
we
r 
div
ide
r
/co
mb
ine
r
VA
TT
Va
ria
ble
Att
en
ua
tor
s
VA
TT
y(t
)
PCFP
GA
Figure 2.3: Beamformer board block diagram
an Field-Programmable Gate Array (FPGA) (Xilinx Spartan-3). The FPGA delivers
96 parallel control lines to eight 6−bit phase shifters (MAPCGM0002) and eight
6−bit attenuators (HMC425LP3) [18, 26]. The 6−bit phase shifters can produce
phase changes between −180◦ and +180◦ in 5.6◦ increments. The attenuation range
is 0 to −31.5 dB in increments of 0.5 dB [18].
The beamformer board contains power amplifiers (SZA−5033) and low noise am-
plifiers (HMC320MS8G) as well as switches that toggle the channels between trans-
mission and receiving modes. Another component of this board is a Xilinx CoolRun-
nerII Complex Programmable Logic Device (CPLD). The CPLD receives the control
information from the PC and uses it to directly control the phase shifters and attenu-
ators. The device was programmed to implement a shift register which acquires serial
data from the PC and latches it out to the individual channels in parallel [27, 28, 29].
9NULL STEERING ALGORITHMS
In this chapter, the data model and the null steering algorithms implemented in
an analog antenna array, are described.
Data Model
An m element array with an arbitrary geometry is considered. The array can
receive signals from K different sources located in different angular locations. The
signal arriving to the antenna array, x(t) can be expressed as:
x(t) =
K∑
k=1
a (ϕk) sk(t) + n(t) (3.1)
where
sk(t) is the kth impinging signal.
a(ϕk) is the spatial signature of the signal sk from ϕk.
ϕk is the direction of arrival of the kth signal.
n(t) is the noise at the receiver site.
K is the number of signals received by the smart antenna array.
In this thesis, the simulations study and the implementation of the algorithms
consider the characteristics of a UCA. The circular antenna array configuration was
chosen because of access of pre-existing UCA hardware developed at MSU, see [30, 25].
10
w2
w1
w3
wm
...
...
A
n
te
n
n
a
A
rr
ay
+
y(t)
Figure 3.1: Diagram of the antenna array
The spatial signature of the uniform circular antenna array at relevant angles, θ and
ϕ, is defined as the following [31]:
a (ϕ, θ) =
[
1, ejβρ sin(θ) cos(ϕ−
2pi
m ), ejβρ sin(θ) cos(ϕ−
2·2pi
m ), ..., ejβρ sin(θ) cos(ϕ−
(m−1)·2pi
m )
]
(3.2)
where
ϕ is the azimuthal angle.
θ is the elevation angle.
β is the wavenumber defined as: β = 2piλ .
βρ is the electrical size of the array.
As shown in Figure 3.1, the m channels of the antenna data are scaled and shifted
by the weight values, and the linear combination is the output of the beamformer,
y(t), defined as:
y(t) = wH · x (t)
= wH ·
K∑
k=1
a (ϕk) sk(t) + wH · n(t)
(3.3)
where
11
w is the null-steering weight vector for the antenna array.
H is the complex conjugate transpose.
Assuming that the direction of arrival (DOA) of one user signal is ϕd; and the
DOA of one interference signal is ϕint; equation 3.3 takes the form:
y(t) = wH · a (ϕd) sd(t) + wH · a (ϕint) sint(t) + wH · n(t) (3.4)
The Signal to Interference Ratio (SIR) allows evaluation of the performance of
the algorithms in the presence of Kn interference signals; in this thesis, the SIR is
calculated as shown in equation 3.5 [32] :
SIR =
S
I
=
S
Kn∑
k=1
Ik
(3.5)
Null Steering Algorithms
Interference cancellation can be achieved by suppressing the power density at the
angle of the interference signal. This is achieved by properly scaling and phase shifting
the UCA element currents, such that the power received at the interference angular
direction is minimized. The constraints for the null steering weights are:
• Minimize wH · a (ϕint)
• Maximize wH · a (ϕd)
• Mantain wH ·w constant
The algorithms studied in this thesis can be categorized into two groups. The
first group corresponds to open-loop null steering methods; these algorithms rely on
12
the previous estimation of the DOA of the interference and the user signal sources.
The second group corresponds to closed-loop adaptive null steering methods where
the nulls are formed adaptively and no previous knowledge of the DOAs is required
in advance.
Open-loop Null Steering
Open-loop null steering algorithms involve a two-step solution. The first step con-
sists of estimating the directions of arrival of all wavefronts impinging on an antenna
array. The second step consists of forming nulls in the estimated directions of the
interference signal, while maximizing the received signals [13].
Two different open-loop null steering algorithms were analyzed and implemented
in the UCA and are described below.
Optimal Null Steering Algorithm: This algorithm was first proposed by Fried-
lander and Porat [13]. The null steering weights were defined using matrix subspace
algebra to separate the signal space from the interference space and uses a vector null
space to achieve the maximum signal minimum noise criteria.
The null steering weights are calculated as follows:
w =
[
I− a(ϕint)
(
a(ϕint)H · a(ϕint)
)−1
· a(ϕint)H
]
a(ϕd) (3.6)
where I is the identity matrix.
An analytical study of the expectation of the system output interference to signal
ratio E(OSIR) versus the angular space between DOA of the interference signal ϕint
and the desired signal ϕd was proposed and studied in [13, 33]. The optimal weight
defined in Equation 3.6 was used. In Figure 3.2, the DOA of the desired signal is
13
DOA interference Angle(deg)
O
u
tp
u
t
in
te
rf
er
en
ce
to
si
g
n
a
l
ra
ti
o
O
IS
R
0 50 100 150 200 250 300 350
-450
-400
-350
-300
-250
-200
-150
-100
-50
0
Figure 3.2: System output interference to signal ratio E(OISR)
ϕd = 180◦ and the DOA of the interference signal takes values in the range from
[0◦−360◦]. Note that in Figure 3.2 we have OISR = PintPd = 0 dB at ϕd = ϕint = 180
◦
as expected.
Waveform Modification: The second method is based on waveform modification
proposed by Y. Huang and M. Panique [33].
This method makes use of element current phase and magnitude perturbation.
The algorithm starts with independent beamforming weights for both the desired
signal and interference as shown in Figure 3.3. The weights for null steering are
calculated by taking the linear difference of the two sets of weights.
w = a(ϕd) − c · a(ϕint) (3.7)
14
ࢇఝ೏
ࢇఝ೔೙೟
࢝
߮௜௡௧
߮ௗ
Figure 3.3: Illustration of the waveform modification algorithm
The constant c is defined as the linear difference in power between the beams
formed by a(ϕd), the angular location of the user signal, and a(ϕint) at the angular
location of the interference, ϕint.
Closed-loop Null Steering
Closed-loop adaptive null steering algorithms are more robust than open-loop
algorithms since they can adjust to uncertainties in the phase-gain characteristics of
the array elements and do not require array calibration. Moreover, these algorithms do
not require the knowledge of the DOAs of the sources in advance. The adaptive null
steering methods utilize sophisticated signal processing algorithms to continuously
distinguish between the desired signal and interferences without knowing the DOAs
of the desired signal and interference in advance. It can form an unlimited number of
beam patterns to optimally improve signal strength and suppress interference signals.
15
Beamformer
w2
w1
w3
wm
...
...
Maximize
Signal to Interference
Ratio
y(t)
Antenna Array
Figure 3.4: Diagram of closed-loop adaptive null steering algorithm
These algorithms are fairly simple to implement; they rely on an iterative process,
the final set of weights may not be a truly optimal setting [6]. Although mathemati-
cally elegant and efficient, the solution given by this method might not be the optimal,
giving as a solution the local minima around the vicinity of the starting point [34].
The adaptive weight w can be obtained using any suitable adaptive algorithms as
shown in Figure 3.4. Here, we use Least Mean Square (LMS) algorithm for proof of
concept, assuming the reference signal s(t) is known
min

∣
∣wHadaptive · x(t) − s(t)
∣
∣2 (3.8)
The output of the beamformer is
y(t) = wHadaptive · x(t) (3.9)
16
The advantages of adaptive null steering algorithms are its superior flexibility and
efficient adjustment to uncertainties in the phase and amplitude oscillations of the
null steering weights.
17
SIMULATION STUDY
In this chapter, the performance of the algorithms is validated. The simulations
were constructed to demonstrate the performance of the algorithms described in chap-
ter 3. The UCA consists of 8 elements as described in Chapter 2. A summary table
with its dimensions is shown in table 4.1.
Simulation data collection and statistical processing were carried out using a com-
bination of scripts and functions in MATLAB. Custom functions were written to
model the antenna array.
Null Steering Performance Analysis
Some simulation results are discussed to verify the functionality of the algorithms
presented in Chapter 3. The main parameters that were used to evaluate the perfor-
mance of the null steering algorithms were the SIR and the pointing angle. The SIR
is obtained by taking the ratio between the energy at the angular location of the user
and the energy at the angular location of the interference as defined in equation 3.5.
For the results presented, the interference signal DOA is assumed to be at 300 ◦;
the desired signal DOA is assumed to be at 180 ◦. The signal to noise ratio is assumed
to be 20 dB The power plots were normalized, unless noted otherwise.
Null Patterns
Figure 4.1 shows the null steering beam pattern using the optimal null steering
algorithm. Note that the main beam is pointing to the user signal angular location;
there is a null at the angular location of the interference signal. The SIR in this case
is 64.43 dB. Similar analysis was performed for the waveform modification algorithm,
18
Table 4.1: Uniform Circular Antenna Array Characteristics
Number of elements 8
Operating frequency (GHz) 5.8
Bandwidth (MHz) 200
Array radious ρ(cm) 2.54
Array electrical size βρ 3.05
Inter-element Spacing 0.375λ
Element length 0.23λ
Table 4.2: Simulation Null Steering Results
Method ϕd [◦] ϕint [◦] SIR[dB]
Optimal null steering 180 300 64.43
Waveform modification 180 300 59.33
LMS null steering 180 300 59.33
Figure 4.2. A maximum was observed at the angular location of the user signal and
a deep null at the location of the interference. The SIR obtained is 59 dB.
The results for the LMS algorithm is shown in Figure 4.3. There is a deep null at
the angular location of the interference signal and the SIR is 59 dB.
The summary of the results obtained after setting up this scenario for the three
algorithms described in Chapter 3 are shown in Table 4.2.
Cumulative Distribution Function Analysis
A key point of the analysis of these algorithms is the resolution of the phase
shifters and the attenuators. This aspect is specifically taken into account to better
understand the implementation in a real antenna array.
19
Angle(deg)
P
ow
er
(d
B
)
SIR:-64.43
0 50 100 150 200 250 300 350
-60
-50
-40
-30
-20
-10
0
ES Power
SOI DOA
Interference DOA
Figure 4.1: Beam pattern for the optimal null steering algorithm
In this section, the performance of the algorithm in general is discussed. For
simulation purposes, the user signal is located at 180 degrees while the interferer
takes integer values in the range 1-360 degrees. The effect of the relative position of
the interferer with respect to the user is analyzed in two different cases.
Case I: Null Inside the Main Beam: When the interference signal’s DOA is lo-
cated close to the user signal’s DOA, the null steering algorithms, studied in Chapter
3, do not perform as expected. The null depth starts to degrade in value and the null
pointing angle error increases as the interference signal is close in angle to the user
signal, as presented in the following example, Figure 4.4.
Figure 4.4 shows the beam pattern of the optimal null steering algorithm when
the interference signal is located at 200◦ and the user signal is located at 180◦. The
20
Angle(deg)
P
ow
er
(d
B
)
SIR:-59.33
0 50 100 150 200 250 300 350
-60
-50
-40
-30
-20
-10
0
ES Power
SOI DOA
Interference DOA
Figure 4.2: Beam pattern for the waveform modification null steering algorithm
Angle(deg)
P
ow
er
(d
B
)
SIR:-59.33
0 50 100 150 200 250 300 350
-60
-50
-40
-30
-20
-10
0
ES Power
SOI DOA
Interference DOA
Figure 4.3: Beam pattern for the adaptive null steering algorithm
21
Angle(deg)
P
ow
er
(d
B
)
SIR:-32.02
0 50 100 150 200 250 300 350
-70
-60
-50
-40
-30
-20
-10
0
ES Power
SOI DOA
Interference DOA
Figure 4.4: Beam pattern for case I
measured SIR in this case is 32 dB. Note that in this case the main beam is pointing
towards 160◦.
Monte Carlo simulations, with 1000 samples and 100 runs were performed to
extract the statistics of the null steering algorithms in the case that the interference
signal is located inside the main beam of the user’s signal. The user’s signal is fixed at
180◦ and the interference signal direction ranges from 130◦ to 230◦, which represents
the bound angle values for the main beam of the user’s signal at 180◦. From the
statistics extracted, two parameters were of importance. Find the probability that
SIR is higher than 40 dB and the performance of the algorithms, i.e. the value of the
SIR, for a probability of 75 %.
Figure 4.5 shows the results of this simulation for the optimal null steering al-
gorithm. The cumulative distribution function shows that the SIR will be higher
than 40 dB with a probability of 33%; and 75% of the time the SIR will be higher
22
Null depth Inside Main Beam
C
u
m
u
la
ti
v
e
p
ro
b
a
b
il
it
y
SIR = 28.05
p = 0.76
SIR = 40.41
p = 0.33
-90 -80 -70 -60 -50 -40 -30 -20 -10 0 10
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Null depth CDF
95% confidence bounds
CDF Null depth fit
Figure 4.5: CDF for case I using the optimal null steering algorithm
Null depth Inside Main Beam
C
u
m
u
la
ti
v
e
p
ro
b
a
b
il
it
y
SIR = 28.87
p = 0.75
SIR = 40.41
p = 0.34
-90 -80 -70 -60 -50 -40 -30 -20 -10 0 10
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Null depth CDF
95% confidence bounds
CDF Null depth fit
Figure 4.6: CDF for case I using the waveform modification algorithm
23
Null depth Inside Main Beam
C
u
m
u
la
ti
v
e
p
ro
b
a
b
il
it
y
SIR = 21.45
p = 0.75
SIR = 40.41
p = 0.32
-90 -80 -70 -60 -50 -40 -30 -20 -10 0 10
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Null depth CDF
95% confidence bounds
CDF Null depth fit
Figure 4.7: CDF for case I using the LMS algorithm
Table 4.3: CDF Values Summary for Case I
Method SIR [dB] (p ≥ 0.75) p (SIR ≥ 30dB)
Optimal null steering 28.05 0.65
Waveform modification 28.05 0.64
LMS null steering 21.45 0.63
24
Angle(deg)
P
ow
er
(d
B
)
SIR:-51.1
0 50 100 150 200 250 300 350
-60
-50
-40
-30
-20
-10
0
ES Power
SOI DOA
Interference DOA
Figure 4.8: Beam pattern for case II
than 28 dB. Similar analysis was performed for the LMS null steering algorithm and
the waveform modification algorithm. The resulting CDFs for these algorithms are
presented in Figures 4.6 and 4.7. The results are summarized in Table 4.3.
Case II: Null Outside the Main Beam: In this section, the performance of the
null steering algorithms is explored when the interference signal’s DOA is located
outside the main beam of the user’s signal.
Figure 4.8 shows the results of the null steering algorithm when the interference
signal is located at 90◦ and the user signal is located at 180◦. The measured SIR in
this case is 51 dB. Note that in this case the main beam is pointing towards 180◦ and
there is no error in the null pointing angle.
Monte Carlo simulations described in the previous section were performed. The
user’s signal is fixed at 180◦ and the interference signal ranges from 1◦ to 130◦, and
25
Null depth Outside the Main Beam
C
u
m
u
la
ti
v
e
p
ro
b
a
b
il
it
y
SIR = 35.17
p = 0.75
SIR = 40.94
p = 0.49
-100 -90 -80 -70 -60 -50 -40 -30 -20 -10
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Null depth CDF
95% confidence bounds
CDF Null depth fit
Figure 4.9: CDF for case II using the optimal null steering algorithm
Null depth Outside the Main Beam
C
u
m
u
la
ti
v
e
p
ro
b
a
b
il
it
y
SIR = 35.17
p = 0.74
SIR = 40.94
p = 0.48
-100 -90 -80 -70 -60 -50 -40 -30 -20 -10
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Null depth CDF
95% confidence bounds
CDF Null depth fit
Figure 4.10: CDF for case II using the waveform modification algorithm
26
Null depth Outside the Main Beam
C
u
m
u
la
ti
v
e
p
ro
b
a
b
il
it
y
SIR = 34.45
p = 0.75
SIR = 40.94
p = 0.45
-100 -90 -80 -70 -60 -50 -40 -30 -20 -10
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Null depth CDF
95% confidence bounds
CDF Null depth fit
Figure 4.11: CDF for case II using LMS null steering algorithm
230◦ to 360◦. From the statistics extracted, two parameters were of importance: the
probability that SIR is higher than 40 dB and the performance of the algorithms, i.e.
the value of the SIR, for a probability of 75 %.
Figure 4.9 shows the results of this simulation for the optimal null steering al-
gorithm. The cumulative distribution function shows that the SIR will be higher
than 40 dB with a probability of 33%; and 75% of the time the SIR will be higher
than 28 dB. Similar analysis was performed for the LMS null steering algorithm and
Table 4.4: CDF Values Summary for Case II
Method SIR [dB] (p ≥ 0.75) p (SIR ≥ 30dB)
Optimal null steering 35.17 0.96
Waveform modification 35.75 0.98
LMS null steering 34.45 0.95
27
the waveform modification algorithm. The resulting CDFs for these algorithms are
presented in Figures 4.10 and 4.11. The results are summarized in Table 4.4.
Phase and Magnitude Errors
Phase and magnitude errors on the null steering weights are not possible to avoid
during hardware implementation. This section analyzes the effect of those errors in
the performance of the null steering algorithms described in Chapter 3.
The quantization errors have an effect on the output of the algorithms: they affect
null depth as well as the null direction. This effect has been studied through a Monte
Carlo simulation for each algorithm as described below.
Phase Error Analysis
Consider the scenario where the user signal DOA is 180◦ and the interference signal
DOA is 45◦. In this scenario, phase errors on the weights are introduced to analyze
the effect on the performance of the algorithms. Figure 4.12 shows the resulting beam
pattern for different sets of phase-errors introduced into the phase of the null steering
weights. The phase values of the null steering weights, after the introduction of the
errors, oscillate ±10% their initial values. The error follows an arctangent distribution
due to the nature of the phases of the weights of the antenna.
Note that the main beam pointing angle still points toward the direction of the
signal user. However, the null pointing angle, as well as the null depth, is changed
with the introduction of the phase errors.
A Monte Carlo simulation, with 1000 samples and 100 runs, was set up to study
the performance of the null steering algorithms in terms of the null depth, the SIR,
and the null pointing angle.
28
Figure 4.12: Effect of the phase errors on the power pattern
The results of the effect are presented in Figures 4.13, 4.14, and 4.15. These
results shows the effects of errors in the phase in the performance of the null steering
in terms of the SIR, defined in equation 3.5.
From these figures, it is possible to note interesting effects of the errors in the
performance of the algorithms. The plots in Figures 4.13 - 4.15 show that the best
performance of the algorithms, i.e. higher SIR, is obtained when the error tends to
zero or is less than 4 %. When the phase error reaches values higher than 6 %, the
SIR, on average, drops to 30 dB. Errors above 8 % have a negative effect on the SIR.
For phase-errors higher than 8% the SIR drops below 20 dB.
However, it is interesting to note that at some specific angles, the errors have
no effect in performance of the algorithms or even improve the performance of the
algorithms. For example, in Figure 4.13, note that for the optimal null steering the
effects of the errors at 150 ◦ have minimum incidence on the SIR. In this case the SIR
29
Figure 4.13: Effect of the phase error for the optimal null steering algorithm
remains constant between 40 dB and 60 dB, even with a 10 % error introduced to
the phase.
Another interesting example is given at 300◦. The null-depth with no error im-
proves when the phases of the weights are introduced with an error of −4% as shown
in Figure 4.14 for the waveform modification: the SIR improves from 40 dB up to 60
dB. This behavior is also present in the other two algorithms at different directions,
shown in Figures 4.13 and 4.15.
The 3-dimensional (3D) power plots in function of the phase errors are shown in
Figure 4.16, 4.17, 4.18.
Magnitude Analysis
Consider the scenario where the user signal DOA is 180◦ and the interference
signal DOA is 45◦. In this scenario, magnitude errors on the weights are introduced
to see the effect on the performance of the algorithms. Figure 4.19 shows the resulting
30
Figure 4.14: Effect of the phase error for the waveform modification algorithm
Figure 4.15: Effect of the phase error for the LMS null steering algorithm
31
Figure 4.16: Effect of the magnitude error for the optimal null steering algorithm
Figure 4.17: Effect of the magnitude error for the waveform modification algorithm
32
Figure 4.18: Effect of the magnitude error for the LMS null steering algorithm
power plot for different sets of magnitude-errors introduced into the magnitude of the
null steering weights. Note that the main beam pointing angle still points toward
the direction of the signal user. The null pointing angle, as well as the null depth,
are changed with the introduction of the magnitude errors. However, as can be seen
on Figure 4.19, the performance of the algorithms, with the addition of magnitude
errors, is not as sensitive as in the case of phase errors. The magnitude values after
the introduction of the errors oscillate ±10% their initial values. To better visualize
the effect of the errors, the limits of the magnitude errors were increased up to 20%;
even in this case the effect is minimum, as seen in Figure 4.20.
A Monte Carlo simulation was set up to study the performance of the null steering
algorithms in terms of the null depth, the SIR, and the null pointing angle.
A magnitude error was introduced to the null steering weights. The error followed
a Gaussian distribution due to the nature of the magnitude of the weights. The
33
Figure 4.19: Effect of 10% magnitude error on the power pattern
results of the effect, in the performance of the null steering in terms of the SIR, as
defined in equation 3.5, are presented in Figures 4.21, 4.22 and 4.23.
From these figures, it is possible to note the effect of the magnitude errors com-
pared to the phase errors in the SIR, shown in Figures 4.21, 4.22 and 4.23. Note
that the null depth remains almost constant for error changes in the magnitude of
the weights.
Quantization Error and Phase Perturbation
In the previous sections, the uncertainties and quantization errors of the phase
shifters and attenuators were taken into account for simulation purposes. The final
goal of taking this approach is to best simulate the conditions in the real implemen-
tation.
34
Figure 4.20: Effect of 20% magnitude error on the power pattern
Figure 4.21: Effect of the magnitude error for the optimal null steering algorithm
35
Figure 4.22: Effect of the magnitude error for the waveform modification algorithm
Figure 4.23: Effect of the magnitude error for the LMS null steering algorithm
36
Angle(deg)
P
o
w
er
(d
B
)
SIR:-32.9
0 50 100 150 200 250 300 350
-50
-40
-30
-20
-10
0
User Power
User DOA
Interference DOA
Figure 4.24: Beam pattern without phase perturbation
The quantized settings of the phase shifters and attenuators, i.e. the weights of
the antenna array, limits the accuracy of the SIR and the null pointing angle. The
next example illustrates this issue.
Figure 4.24 shows the null steering results using the optimal null steering algorithm
presented in Chapter 3. The user signal is arriving from 180◦ and the interference
signal is arriving from 45◦. Note that the null pointing angle is shifted and it does
not accurately point toward the interference signal. The obtained SIR in this case is
32 dB.
Figure 4.12 shows the behavior of the beam pattern when phase errors are present
on the null steering weights. There are two main aspects worth noting. First, the
main beam that is pointing in the direction of the user does not change and remains
constant even though phase errors are introduced. Second, the null pointing angle,
37
Angle(deg)
P
o
w
er
(d
B
)
SIR:-55.89
0 50 100 150 200 250 300 350
-60
-50
-40
-30
-20
-10
0
ES Power
SOI DOA
Interference DOA
Figure 4.25: Beam pattern with phase perturbation
as opposed to the main beam pointing angle, moves along the interference direction
for the same phase error. Therefore, it is possible to correct the null pointing angle,
i.e. the SIR, by introducing controlled phase perturbations into the calculated null
steering weights. The phase perturbations must follow the characteristics of the
quantized steps of the phase shifters for practical purposes. This means that the
phase perturbations must be discrete, i.e. in steps of 5.6◦. The simulation results for
the previous scenario, after adding the phase perturbation, are shown in Figure 4.25.
The main beam points toward the desired direction: 180◦ in each simulation and
does not change. However, the null pointing direction changes and improves the
performance of the null steering system. The SIR obtained after the measurements is
55 dB. This represents an improvement of 23 dB on the SIR, reaching a true optimum
in the null steering algorithms.
38
Table 4.5: Multi-null Steering Results for the Optimal Null Steering Algorithm
ϕint [◦] SIR [dB] Null angle [◦] Null depth [dB] Pointing angle [◦]
Null #1 30 -73.7 30 -73.7 138
Null #2 210 -36.2 213 -51.1 138
Null #3 280 -31.6 289 -38.6 138
Null #4 320 -39.2 318 -63.0 138
It is possible to perform equal analysis on the magnitude of the antenna array
weights. However, as can be seen in Figures 4.21, 4.22, and 4.23, the effect of
the magnitude errors in the weights sent to the beamformer is not considerable, as
discussed in previous sections.
Multiple Nulls
Assume that the user is located at 135 ◦ and the interference signals are arriving
at 30◦, 210◦, 280◦ and 320◦. Figure 4.26 shows the beam pattern of the simulation
results for multi-null steering using the optimal null steering algorithm. Table 4.5
shows the summary of the results obtained using this algorithm. The nulls are widely
separated and the simulation result verifies the theory predicted by the algorithms.
The results show that there are nulls located at the interference angles summarized
in Table 4.5.
39
:-73.7 :-36.24 :-31.57 :-39.23
Angle(deg)
P
o
w
er
(d
B
)
0 50 100 150 200 250 300 350
-70
-60
-50
-40
-30
-20
-10
0
ES Power
SOI DOA
Interference DOA
Figure 4.26: Beam pattern for the optimal multi-null steering algorithm
40
LAB TESTS
Experiments presented in this chapter are proof of concept. This chapter summa-
rizes the experiment performed. Numerous tests have been performed to validate the
simulations presented in Chapter 4.
The hardware implementation of the null steering system was achieved using the
communications lab at Montana State University. This includes:
• implementation of algorithms, including hardware and software platforms;
• the test environment.
The hardware interface with the analog array and the lab test diagram is shown
in Figure 5.1.
Lab Setup
The experiments were conducted in an anechoic chamber. The user and the
interference signal were generated by continuous wave (CW) signal sources with a
Signal to Noise Ratio (SNR) higher than 30 dB. The transmitter antenna was a horn
antenna capable of transmitting RF signals from 4.9 to 7.05 GHz.
The receiver consisted of an 8-element circular antenna array. The attenuation
and the phase shift for the elements were controlled by a beamformer that is part of
the smart antenna system [25].
In order to capture the power pattern of the receiving antenna at different angles,
the circular antenna array was placed on turntable equipped with a high resolution
0.1 degrees, stepper motor.
41
Antenna Array
Beamformer
board
DAQ
PC
Transmitter antenna
Signal Generator
Spectrum
Analizer
Anechoic chamber
Figure 5.1: Block diagram of the lab test set up for receiving null steering
42
Figure 5.2: Anechoic chamber
Figure 5.3: Instruments
Various MATLAB and LabVIEW scripts were used to control the hardware in the
anechoic chamber.
A 68369 A/NV Anritsu signal generator used to send a CW signal at 5.8 GHz to
the transmitter. A R3273 Advantest Spectrum Analyzer was placed to measure the
power received by the circular antenna array. A National Instruments DAQ card (PCI
6013) was used to provide an interface between the computer and the beamformer.
Using this card and a LabVIEW script, it was possible to send the weights to the
antenna to perform null steering and beamforming.
43
The system setup is shown in Figure 5.3 and refanant Initial work on the imple-
mentation is described in Weber [30], Panique [6], Tidd [25].
In order to obtain the power pattern for the null steering system, the weights are
first calculated and then sent to the beamformer board. The null steering weights are
calculated using the null steering algorithms described in Chapter 2. The beamformer
board is an eight channel system, each channel equipped with a 6−bit phase shifter
and a 6−bit attenuator. Therefore, the complex weights have to be transformed into
6−bit form, before being sent to the beamformer board. A custom MATLAB script
was designed to perform this transformation. After the null steering weights are sent
to the beamformer board, the antenna array is placed inside the anechoic chamber
with all necessary connections. Then, the Anritsu signal generator sends an RF CW
signal at 5.8 GHz to the transmitter antenna.
The signal coming from the horn antenna is then received by the UCA; processed
by the eight channel beamformer board; and after processing, the signal is sent to the
spectrum analyzer to measure the energy from the signal received. The null steering
weights are calculated using the null steering algorithms described in Chapter 2. At
this point, the assumption is that the antenna main lobe is located at 0◦ with respect
to the main user signal. To measure the power spectrum with a resolution of 1 degree,
the circular antenna array is rotated and the energy of the signal is measured. The
rotation process is automated by the turntable, which is controlled by a personal
computer. The signal arriving at the antenna array is measured at every angle of
arrival, i.e. from 1 to 360 degrees. A MATLAB script was written for post-processing
purposes. After the measurements were finished, it was possible to obtain the SIR as
well as the pointing angle to verify the performance of the Null Steering system.
44
Angle(deg)
P
o
w
er
(d
B
)
SIR: 32.52
0 50 100 150 200 250 300 350
-40
-35
-30
-25
-20
-15
-10
-5
0
5
ES Power
SOI DOA
Interference DOA
Figure 5.4: Beam pattern for the optimal null steering algorithm
Lab Test Results
The three algorithms described in Chapter 3 were implemented on a personal
computer that calculates the weights. For the first algorithm, the perturbed patterns
of imposing one null at 300 degrees is shown in Figure 5.4.
Note that for the optimal null steering algorithm, the obtained SIR reaches up to
32 dB. The null pointing angle for this measurement does not present error. There,
the null imposed at the interference DOA (300◦) can be clearly observed.
Similar measurements were performed for the waveform modification null steering
algorithm. The results is presented in Figure 5.5. The weights sent to the beamformer
are summarized in Table 5.1. In this case, the SIR obtained using this method is 36
dB. There is no error in the null pointing angle in this case.
45
Table 5.1: Experimental Null Steering Results
Method ϕd [◦] ϕint [◦] SIR[dB]
Optimal null steering 180 300 32.52
Waveform modification 180 300 36.00
LMS null steering 180 300 34.18
Angle(deg)
P
o
w
er
(d
B
)
SIR: 36
0 50 100 150 200 250 300 350
-45
-40
-35
-30
-25
-20
-15
-10
-5
0
5
ES Power
SOI DOA
Interference DOA
Figure 5.5: Beam pattern for the waveform modification null steering algorithm
46
Angle(deg)
P
o
w
er
(d
B
)
SIR: 34.18
0 50 100 150 200 250 300 350
-40
-35
-30
-25
-20
-15
-10
-5
0
5
ES Power
SOI DOA
Interference DOA
Figure 5.6: Beam pattern for the LMS adaptive null steering algorithm
Finally, the results for the measurements using the LMS adaptive null steering
algorithm is presented in Figure 5.6. Note that, in this case, the SIR obtained is 34
dB.
All the measured results presented have reached SIR values higher than 30 dB for
the described setup.
47
CONCLUSION AND FUTURE WORK
Conclusions
Null steering algorithms for a compact analog array were successfully imple-
mented.
• A simulation study was carried out to validate the performance of the null steer-
ing algorithms, and all achieve deep nulls at the interference angular location.
• Three algorithms were implemented. Two of the algorithms calculated the
weights analytically allowing a fast null steering operation with prior knowledge
of the direction of arrival of the signals. The third algorithm calculated the null
steering weights adaptively, allowing a simple implementation without prior
estimation of the direction of arrival.
• Realistic considerations were taken into account to accurately model the null
steering algorithms when implemented in hardware.
• The effect of the phase and amplitude oscillations of the null steering weights
on the performance of the algorithms was analyzed.
• The effect of the weight quantization error on the null placement was analyzed.
The quantization errors in the phase were proven to have more impact than
quantization errors in amplitude on the performance of the null steering algo-
rithms.
• By introducing discrete phase perturbations, the performance of the null steer-
ing algorithms was improved in terms of the SIR. The performance improvement
on the SIR was up to 20 dB.
48
• Real implementation of the null steering algorithms was performed using an 8
element uniform circular array.
• By measuring the power pattern of the antenna array, the SIR was obtained.
A SIR up to 36 dB was measured in a real scenario.
• The measured results proved the validity of the null steering algorithms. In
spite of the unpredictable fluctuation on the actual implementation, the analog
array performs extremely well for interference cancellation, considering the SIR
obtained.
Future Work
The algorithms analyzed have been optimized from a general perspective with-
out considering a particular application. Additional work is needed to implement
null steering algorithms, taking into account application specific properties of real
scenarios.
In this thesis, the null steering algorithms considered changes in the amplitude and
phase mainly due to the hardware availability. Phase-only null steering algorithms
should be implemented to simplify the hardware implementation.
49
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