high resolution jamming detection in global …

HIGH RESOLUTION JAMMING DETECTION IN

GLOBAL NAVIGATION SATELLITE SYSTEMS

By

Mohamed Moussa

A thesis submitted to the Department of Electric and Computer Engineering

In conformity with the requirements for the

Degree of Doctor of Philosophy

Queen’s University

Kingston, Ontario, Canada

May, 2015

Copyright ©Mohamed Moussa, 2015

ii

Abstract

Global Positioning System (GPS) is increasingly threatened by interference and

especially jamming. They are substantial threats to the functions that rely on the GPS position

velocity and time solutions. The ultimate objective of this thesis is to enhance GPS receivers’

anti-jamming abilities. Particular focus is given to the detection of Continuous Wave (CW)

jamming signals that are close-by in frequency and in space. To tackle the challenge, two high

resolution signal processing methods are proposed for single antenna receivers and for antenna

array receivers. The first method operates in the frequency domain and targets accurate and

efficient detection and frequency estimation of single and multiple in-band CW jammers that lie

between two FFT frequency lines. This is achieved by utilizing high resolution spectral

estimation that is based on orthogonal search. On the other hand, the second method operates in

the space domain to estimate the Direction of Arrivals (DoA) of the jamming signals. Unlike

conventional DoA estimation methods that have a low resolution and fail to detect multiple

close-by jammers, the proposed method utilizes Fast Orthogonal Search (FOS) for nonlinear

modelling to accurately detect the presence of multiple neighboring jammers and estimate their

DoAs efficiently and accurately.

Investigation of the proposed methods’ performance is conducted on GPS signals

obtained using a Spirent GSS 6700 GPS simulator. The proposed frequency domain method

outperformed FFT in terms of number of jamming signals detected and the accuracy of their

frequencies’ estimation at up to a tenth of the required FFT window size. The proposed spatial

domain method was implemented on antenna array geometries such as Uniform Linear Array

(ULA), Uniform Circular Array (UCA) and optimized UCA. Performance was compared to

predominant DoA estimation methods such as the Classical method and Multiple Signal

iii

Classification (MUSIC). The proposed method yields higher accuracy jammer DoA estimates in

addition to accurately and correctly estimating jammer amplitudes due to the immunity to noise.

The research conducted in this thesis contributes to the enhancement of GPS anti-

jamming systems in both frequency and spatial domains. It increases the robustness of single

antenna receivers and improves theirs anti-jamming ability by providing accurate estimates of

multiple jammers whose frequencies are close-by. Additionally, for multi-antenna systems, the

accurate estimation of the number of multiple close-by jammers and their DoAs significantly

improves the anti-jamming process by limiting erroneous spatial attenuation of GPS signals

arriving from an angle close to the jammer.

iv

Acknowledgments

I would like to offer my sincerest gratitude to my family for their continuous support and

encouragement; for always having faith in me and for pushing me forwards in the hardest of

times throughout this difficult journey.

I would like to express my deepest thanks to my supervisor, Prof. Aboelmagd Noureldin, for his

continuous guidance, scientific, educational and financial support. I would also like to thank my

co-supervisor, Prof. Michael Korenberg for his support, insight and continuous encouragement.

The valuable knowledge and advice that my supervisors constantly provided guided me to reach

where I am today.

An acknowledgment has to be made to Dr. Abdalla Osman who worked closely with me and

offered me his valuable expertise and time in the field of array processing.

I would like to thank my sincerest friend Dr. Mohamed Tamazin to whom I owe an immense

amount of gratitude; he always put my best interests beforehand and was a brother to me.

My colleagues at the NavINST lab are to be thanked for their support, friendship and enjoyable

scientific debates.

From all my heart I thank my wife, who has always been patiently by my side, who was always

pushing me towards success, and offered endless support to our family and our son.

v

Table of Contents

Abstract ......................................................................................................................................................... ii

Acknowledgments ........................................................................................................................................ iv

Table of Contents .......................................................................................................................................... v

List of Figures ............................................................................................................................................ viii

List of Tables ............................................................................................................................................... xi

List of Abbreviations .................................................................................................................................. xii

List of Symbols ........................................................................................................................................... xv

List of Notations ...................................................................................................................................... xviii

Introduction .................................................................................................................................. 1 Chapter 1

1.1 Motivation ........................................................................................................................................... 1

1.2 Previous Work .................................................................................................................................... 3

1.3 Research Objectives ............................................................................................................................ 6

1.4 Research Contributions ....................................................................................................................... 8

1.5 Thesis Outline ................................................................................................................................... 10

GPS System Overview ............................................................................................................... 12 Chapter 2

2.1 Introduction ....................................................................................................................................... 12

2.2 GPS Segments ................................................................................................................................... 12

2.2.1 Space Segment ........................................................................................................................... 13

2.2.2 Control Segment ........................................................................................................................ 14

2.2.3 User Segment ............................................................................................................................. 15

2.3 GPS Signal ........................................................................................................................................ 15

2.4 GPS Observables .............................................................................................................................. 17

2.4.1 Pseudorange Measurements ....................................................................................................... 17

2.4.2 Carrier Phase and Doppler ......................................................................................................... 18

2.5 GPS Receiver .................................................................................................................................... 19

2.5.1 The GPS Antenna....................................................................................................................... 21

2.5.2 RF Front-End ............................................................................................................................. 22

2.6 GPS Errors ........................................................................................................................................ 24

2.6.1 Hardware Clock Error ................................................................................................................ 24

2.6.2 Unintentional Delays.................................................................................................................. 24

2.6.2.1 Ionospheric and Tropospheric Delays ................................................................................. 25

vi

2.6.3 Receiver Noise ........................................................................................................................... 25

2.6.4 Errors Caused by RF Signals in the Receiver’s Vicinity ........................................................... 26

2.6.4.1 Multipath Delay .................................................................................................................. 28

2.7 Interference and Jamming ................................................................................................................. 28

2.7.1 Jamming Attacks on GPS .......................................................................................................... 31

2.7.2 Jamming Effect on GPS ............................................................................................................. 32

2.8 Jamming Detection ........................................................................................................................... 35

2.9 Anti- Jamming Techniques ............................................................................................................... 36

2.9.1 Single Antenna Receiver-Based Solutions................................................................................. 37

2.9.1.1 Front-End-Based Solution ................................................................................................... 37

2.9.1.2 Adaptive Notch Filter (ANF) .............................................................................................. 38

2.9.1.3 Switching Between GNSS Constellations .......................................................................... 38

2.9.1.4 Integrating GNSS with Inertial Navigation Systems (INS) ................................................ 39

2.9.2 Antenna Array Based Solutions ................................................................................................. 39

2.9.2.1 Null Steering ....................................................................................................................... 40

2.9.2.2 Beamforming ...................................................................................................................... 41

2.10 DoA Estimation of Jamming Signals .............................................................................................. 43

2.10.1 Array Data Model .................................................................................................................... 44

2.10.2 Conventional Beamforming ..................................................................................................... 46

2.10.3 Capon’s Beamformer ............................................................................................................... 47

2.10.4 DoA Estimation Using Subspace Techniques .......................................................................... 48

2.10.5 Multiple Signal Classification (MUSIC) ................................................................................. 49

2.10.5.1 Spatial Smoothing ............................................................................................................. 50

2.10.6 Search-Free DoA Estimation Techniques ................................................................................ 51

2.10.7 Root MUSIC ............................................................................................................................ 51

2.10.8 Estimation of Signal Parameters via Rotational Invariance Technique (ESPRIT) .................. 52

Enhanced GPS Narrowband Jamming Detection Using High Resolution Spectral Estimation 56 Chapter 3

3.1 Introduction ....................................................................................................................................... 56

3.2 Continuous Wave Interference: ........................................................................................................ 57

3.2.1 Out -of -Band Signals ................................................................................................................ 57

3.2.2 Impacts of CW Interference ....................................................................................................... 59

3.2.3 Related Work ............................................................................................................................. 61

3.3 Proposed Method .............................................................................................................................. 63

3.4 Jammer Detection ............................................................................................................................. 64

vii

3.4.2 FOS-based Jamming Detection .................................................................................................. 70

3.4.3 Experimental Work .................................................................................................................... 71

3.4.4 Simulation Scenarios.................................................................................................................. 73

3.4.5 Results and Discussions ............................................................................................................. 74

3.5 Conclusion ........................................................................................................................................ 84

DoA Estimation of GPS Narrowband Interference .................................................................... 85 Chapter 4

4.1 Introduction ....................................................................................................................................... 85

4.2 DoA Estimation Using Nonlinear Signal Modeling ......................................................................... 87

4.2.1 Stopping Conditions for FOS Algorithm ................................................................................... 92

4.2.2 FOS complexity: ........................................................................................................................ 93

4.2.3 Candidate Function Selection for FOS Algorithm ..................................................................... 93

4.3 Antenna Array Design ...................................................................................................................... 94

4.3.1 Uniform Linear Array ................................................................................................................ 94

4.3.2 Two-Dimensional Arrays ........................................................................................................... 97

4.3.2.1 Rectangular Arrays ............................................................................................................. 98

4.3.2.2 Circular Array ................................................................................................................... 102

4.4 Array Geometry Optimization ........................................................................................................ 106

4.5 High resolution FOS-based DoA Estimation Using a 2D Circular Array with Central Element ... 112

4.6 Experimental Setup ......................................................................................................................... 114

4.7 Simulation and Results ................................................................................................................... 120

4.7.1 Results for ULA ....................................................................................................................... 121

4.7.1.1 Single Jammer ................................................................................................................... 121

4.7.1.2 Multiple Jamming Signals ................................................................................................ 123

4.7.2 Results for UCA ....................................................................................................................... 126

4.7.2.1 Single Jammer ................................................................................................................... 126


4.7.3 Results of Optimum Array ....................................................................................................... 135

4.7.3.1 Single Jammer ................................................................................................................... 136


4.8 Conclusion ...................................................................................................................................... 146

Conclusions and Recommendations ......................................................................................... 148 Chapter 5

5.1 Conclusions ..................................................................................................................................... 148

5.2 Recommendations and Future Work ............................................................................................... 151

viii

List of Figures

Figure 2-1: Different GPS segments ........................................................................................................... 13

Figure 2-2: GPS satellites in orbit [22] ....................................................................................................... 14

Figure 2-3: Locations of the different sections of the control segment around the world [25]................... 15

Figure 2-4 : GPS L1 signal structure .......................................................................................................... 16

Figure 2-5: Pseudorange measurements [21] .............................................................................................. 18

Figure 2-6: Block diagram of a GPS receiver ............................................................................................. 20

Figure 2-7: Receiver channels in the signal processing phase [29] ............................................................ 20

Figure 2-8: Typical RHCP and LHCP normalized radiation pattern of NovAtel antenna GPS-702 GG for

GPS L1 and L2 Signals [34] ....................................................................................................................... 21

Figure 2-9: Building blocks of the AGC signal conditioning stage ............................................................ 23

Figure 2-10: Distribution of 1 sec of real I and Q data sampled at 2.5 MHz .............................................. 23

Figure 2-11: LoS signal (red) and its reflection (green) in an urban canyon .............................................. 28

Figure 2-12: Absence of LoS component in an urban canyon .................................................................... 28

Figure 2-13: Common interference and jamming sources .......................................................................... 31

Figure 2-14: Different types of PPDs [47] .................................................................................................. 32

Figure 2-15: Tracking results of an experiment after applying swept CW and Gaussian noise jamming. . 34

Figure 2-16: Tracking results of an experiment without applying jamming............................................... 35

Figure 2-17: Classification of anti-jamming techniques ............................................................................. 37

Figure 2-18: A generic nulling antenna [56] ............................................................................................... 42

Figure 2-19: Multiple output beamformer [56] ........................................................................................... 43

Figure 2-20: Different arrival times of satellite signals impinging on ULA ............................................... 44

Figure 2-21: Comparison of Classical and MVDR Beamformers with an 8 degree separation ................. 48

Figure 2-22 : Eigen decomposition of antenna array signals for jamming detection and DoA estimation

[60] .............................................................................................................................................................. 49

Figure 2-23: Comparison between MUSIC, MVDR and the classical beamformer with closely spaced

sources ........................................................................................................................................................ 50

Figure 2-24: The doublets between the two subarrays X and Y, non-overlapping subarrays .................... 53

Figure 2-25: The doublets between the two subarrays X and Y, overlapping subarrays ............................ 53

Figure 3-1: Spectrum describing CW interference [36] .............................................................................. 57

Figure 3-2: Out of band signal being falsely considered as an in band signal [36]. ................................... 58

Figure 3-3: Effective range of a 4 Watt GPS jamming device [66] ............................................................ 59

ix

Figure 3-4: Distribution of a CW signal ..................................................................................................... 60

Figure 3-5 Histogram of a GPS L1 signal before and after being subjected to moderate and high power

CW jamming. .............................................................................................................................................. 60

Figure 3-6: Proposed jamming detection method applied in the pre-correlation stage of the receiver ...... 63

Figure 3-7 Estimated jammer frequency due to FFT (window size = 1 ms) .............................................. 64

Figure 3-8 FFT detection of multiple simultaneous CW jammers ............................................................. 65

Figure 3-9: The Novatel FireHose Frontend [83] ....................................................................................... 72

Figure 3-10: Simulation setup using the Spirent GSS 6700 in the NAVINST lab. .................................... 72

Figure 3-11: Demonstration of the procedure for conducting scenarios ..................................................... 73

Figure 3-12: Detection error of FOS vs FFT at JSR = 0 dB ....................................................................... 75

Figure 3-13: Detection error of the second jammer component. ................................................................ 76

Figure 3-14: Effect of jammer power on FOS detection of three jammers. ................................................ 78

Figure 3-15: Effect of JSR on correct detection ......................................................................................... 79

Figure 3-16: FOS vs FFT jammer detection at different JSR and a 2 ms window size .............................. 81

Figure 3-17: FOS vs FFT jammer detection at different window sizes for 3 jammers at different JSR (A)

.................................................................................................................................................................... 82

Figure 3-18: FOS vs FFT jammer detection at different window sizes for 3 jammers at different JSR (B)

.................................................................................................................................................................... 83

Figure 4-1:Uniform linear array .................................................................................................................. 95

Figure 4-2 Array factor for ULA ................................................................................................................ 97

Figure 4-3 Rectangular array geometry ...................................................................................................... 98

Figure 4-4 Array factor magnitude for rectangular array .......................................................................... 100

Figure 4-5 Array factor pattern for rectangular array ............................................................................... 101

Figure 4-6 XY-Plane view of array factor pattern for rectangular array .................................................. 101

Figure 4-7 Circular array geometry .......................................................................................................... 102

Figure 4-8 Array factor magnitude for circular array ............................................................................... 104

Figure 4-9 Array factor pattern for circular array ..................................................................................... 104

Figure 4-10 XY-plane view of array factor pattern for circular array ...................................................... 105

Figure 4-11 Circular array with central element ....................................................................................... 109

Figure 4-12 Array factor magnitude for circular array with central element ............................................ 110

Figure 4-13: Array factor pattern for circular array with central element ................................................ 111

Figure 4-14 XY-Plane view of array factor pattern for circular array with central element ..................... 112

Figure 4-15: Simulation sequence of an M-element array of GPS antennas ............................................ 115

Figure 4-16: Experimental setup and Skyplot of the experiment. ............................................................ 118

x

Figure 4-17: Acquisition results confirming the utilized satellites after the rest of the available satellites

have been switched off using SimReplay Plus ......................................................................................... 119

Figure 4-18 DoA estimation of one jammer at JSR=15 dB ...................................................................... 122

Figure 4-19: DoA estimation of one jammer at JSR=45 dB ..................................................................... 123

Figure 4-20 DoA estimation of 3 jammers at JSR=15 dB and frequencies of 100Hz, 200Hz and 300Hz 124

Figure 4-21 DoA estimation of 3 jammers arriving at JSR=45 dB and frequencies of 100Hz, 200Hz and

300Hz ........................................................................................................................................................ 125

Figure 4-22 DoA estimation of one jammer using Classical DoA at JSR=45 dB .................................... 126

Figure 4-23: DoA estimation of a single jammer using MUSIC at JSR = 45 dB ..................................... 127

Figure 4-24 DoA estimation of one jammer using FOS at JSR = 45 dB .................................................. 127

Figure 4-25: DoA estimation of 3 closely spaced jammers using MUSIC at JSR = 15 dB ...................... 128

Figure 4-26: DoA estimation of 3 closely spaced jammers using FOS at JSR = 15 dB ........................... 129

Figure 4-27: DoA Estimation of 3 closely spaced jammers using MUSIC at JSR = 45 dB ..................... 130






Figure 4-33: DoA estimation of one jammer using MUSIC at JSR=15 dB (optimum array) .................. 136

Figure 4-34: DoA estimation of one jammer using FOS at JSR=15 dB (optimum array) ........................ 137

Figure 4-35 DoA estimation of one jammer using MUSIC at JSR=45 dB (optimum array) .................. 137

Figure 4-36: DoA estimation of one jammer using FOS JSR=45 dB (optimum array) ........................... 138

Figure 4-37: DoA estimation of 3 jammers using MUSIC at JSR=15 dB (optimum array) ..................... 139

Figure 4-38: DoA estimation of 3 jammers using FOS at JSR=15 dB (optimum array) .......................... 139

Figure 4-39: DoA estimation of 3 jammers using MUSIC at JSR=45 dB (optimum array) ..................... 140

Figure 4-40: DoA estimation of 3 jammers using FOS at JSR=45 dB (optimum array) .......................... 141

Figure 4-41: DoA estimation of 2 closely spaced jammers using MUSIC at JSR=15 dB (optimum array)

.................................................................................................................................................................. 142

Figure 4-42 DoA estimation of 2 closely spaced jammers using FOS at JSR=15 dB (optimum array) ... 143

Figure 4-43: DoA estimation of 2 closely spaced jammers using MUSIC at JSR=45 dB (optimum array)

.................................................................................................................................................................. 144

Figure 4-44: DoA estimation of 2 closely spaced jammers using FOS at JSR=45 dB (optimum array) .. 144

xi

List of Tables

Table 2-1: Typical pseudo-range measurement errors for a single –frequency L1 receiver [20] ............... 26

Table 2-2: Classification of interferences based on spectral characteristics ............................................... 29

Table 2-3: Types of RF interference and their probable sources ................................................................ 30

Table 4-1: Settings adopted for data collection using FireHose frontend ................................................. 116

Table 4-2: Location of the array elements used in the experiment ........................................................... 117

Table 4-3: Experimental results for DoA estimation of 5 satellites. ......................................................... 120

Table 4-4: Simulation results of 3 closely spaced jammers at JSR=15dB ................................................ 129




Table 4-8: Simulation results of 3 closely spaced jammers using optimum array at JSR=15dB ............. 140

Table 4-9: Simulation results of 3 closely spaced jammers using optimum array at JSR=45dB ............. 141

Table 4-10: Simulation results of 2 closely spaced jammers using optimum array at JSR=15dB............ 143

Table 4-11: Simulation results of 2 closely spaced jammers using optimum array at JSR=45 dB........... 145

xii

List of Abbreviations

ADC Analog to Digital Converter

AF Array Factor

AGC Automatic Gain Control

AJ Anti-Jamming

AM Amplitude Modulation

ANF Adaptive Notch Filter

CBF Conventional Beamforming

CRPA Controlled Reception Pattern Antenna

CW Continuous Wave

CWI Continuous Wave Interference

DFT Discrete Fourier Transform

DGA Digital GNSS Antenna

DoA Direction Of Arrival

ESPRIT Estimation of Signal Parameters Via Rotational Invariance Technique

FFT Fast Fourier Transform

FIR Finite Impulse Response

FM Frequency Modulation

FOS Fast Orthogonal Search

GAJT GPS Anti-Jamming Technology

GNSS Global Navigation Satellite Systems

xiii

GPS Global Positioning System

GS Gram Schmidt

IF Intermediate Frequency

INS Inertial Navigation Systems

I & Q In-Phase and Quadrature

JSR Jamming to Signal Ratio

LO Local Oscillator

LoS Line of Sight

MCS Master Control Station

MMSE Minimum Mean Square Error

MSE Mean Squared Error

MVDR Minimum Variance Distortionless Response

MUSIC Multiple Signal Classification

NF Notch Filter

NGA National Geospatial-Intelligence Agency

NLoS Non Line of Sight

PLL Phase Locked Loop

PPD Personal Privacy Device

PPS Precise Positioning Service

PRN Pseudo-Random Noise

PVT Position, Velocity and Time

RFI Radio Frequency Interference

RHCP Right Hand Circularly Polarized

xiv

SLC Side Lobe Canceller

SNR Signal to Noise Ratio

SPS Standard Positioning Service

STFT Short Time Fourier Transform

SVN Space Vehicle Number

UCA Uniform Circular Array

ULA Uniform Linear Array

UWB Ultra-Wideband

VGA Variable Gain Amplifier

WGN White Gaussian Noise

xv

List of Symbols

𝑎 Element separation in rectangular array along the x-axis

𝑎𝑚 Weights of the functional expansion of FOS

𝐴𝑖 Amplitude of the 𝑖𝑡ℎ Useful signal

𝑨(𝜣) Steering matrix

𝑏 Element separation in rectangular array along the y-axis

𝐵𝐼𝐹 GPS signal’s bandwidth after the IF stage

𝐵𝑖𝑛𝑡 Bandwidth of interference signal

𝑐𝑖 Spreading code of the 𝑖𝑡ℎ Signal

𝑑 Inter-element spacing in the antenna array

𝑑𝑖 Navigation message

𝑒(𝑛) Modelling error

𝒆𝒏 Vector of spatially uncorrelated noise at antenna elements

𝜀(𝑛) Error term of orthogonal functional expansion of FOS

𝑓𝑐 GPS carrier frequency

𝑓𝑑𝑖 Doppler frequency affecting the 𝑖𝑡ℎ GPS signal

𝑓𝐼𝐹 GPS signal’s center frequency after the IF stage

𝑓𝑖𝑛𝑡 Carrier frequency of interference signal

f0 Fundamental GPS frequency

fL1 Frequency of GPS L1 signal


xvi


f𝑠 Sampling frequency

𝑔𝑚 Set of orthogonal weights of functional expansion of FOS

𝑀 Number of antenna elements in an antenna array

𝑁𝑠 Number of samples in the record

𝑝𝑚(𝑛) Arbitrary set of non-orthogonal candidate functions

𝑃 Number of candidate freqency pairs

𝑃𝑘 Complex amplitude of the 𝑘𝑡ℎ source

𝑃𝑀𝑈𝑆𝐼𝐶(𝜃) Spatial spectrum produced by MUSIC

𝑄𝑚 MSE reduction given by the 𝑚𝑡ℎ Candidate function

𝑸𝑛 Noise subspace

𝑹𝒚𝒚 Spatial covariance matrix of 𝒚

𝑠𝑘(𝑡) GPS signal transmitted from satellite 𝑘

𝐬𝒏 Transmitted GPS signals vector

𝑡 Time

𝑇 Sampling period

𝑤𝑚(𝑛) Set of orthogonal function

𝑦 Received signal

𝒚(𝑛) Functional expansion of the input signal constructed by FOS

𝒚𝒏 Received signal vector at sample 𝑛

xvii

𝜀2̅̅ ̅ Total MSE

𝛼𝑚𝑟 GS coefficients

λ Wavelength of the received signal

∆0 Magnitude of the displacement vector in ESPRIT

𝛥𝑡 The difference between the satellite and receiver times

𝜃𝑘 Direction of arrival of the 𝑘𝑡ℎ Source (elevation)

𝜏𝑙(𝜃𝑘) Propagation delay across the array associated with the 𝑘𝑡ℎ Source

and the 𝑙𝑡ℎ Antenna

𝜏𝑖 Delay introduced by the communication channel for the 𝑖𝑡ℎ gps

signal

𝑛 Noise encountered at the receiver forthe 𝑖𝑡ℎ gps signal

𝜑𝑖 Random phase of the 𝑖𝑡ℎ gps signal

𝜙𝑘 Direction of arrival of the 𝑘𝑡ℎ Source (azimuth)

𝜔𝑚 Digital frequency of the candidate pair

xviii

List of Notations

(. )𝑇 Transpose

(. )𝐻 Complex conjugate transpose

(. )−1 Inverse

(. )̅̅ ̅̅ Average

{. } Set of a certain quantity

(. )∗ Complex-conjugate transpose of quantity in the parenthesis

‖ . ‖ Norm of the quantity

𝑞1∗𝑞2 Correlation between quantity 𝑞1 and quantity 𝑞2

𝐸[ ] Statistical expectation

𝐶𝑚 Correlation between the input and a candidate function 𝑚

𝐶𝑛𝑘 Correlation between the candidate 𝑛 and the observations vector 𝑘

𝐷𝛽1𝛽2 Correlation between two candidate functions 𝛽1 And 𝛽2

1

Chapter 1

Introduction

1.1 Motivation

Nowadays, the world’s increasing dependence on the Global Positioning System (GPS) is

prevalent. GPS, which was once considered a military asset, is now an indispensable tool

upon which governments, industries and consumers depend; and will increasingly

continue to do so, as GPS integration deepens. An example of integration is in consumer

industries such as the mobile industry, where the majority of phones produced, house a

GPS chip. Smart watches are being introduced; they too have built in GPS chips.

GPS provides positioning, navigation and timing solutions for a multitude of applications

in a vast and growing variety of industries. Therefore, a GPS disruption would have a

stronger effect, given the increased dependability on GPS. Due to the distance GPS

signals travel, they are considered weak signals [1]. In addition to the uncontrollable

factors that deteriorate the GPS signal such as attenuation, fading, multipath and Earth’s

atmosphere, GPS is becoming more vulnerable to sabotage or disruption than ever. GPS

receivers are now confronted with jamming and several other interference sources. There

is a substantial outlawed market for personal privacy and GPS jamming devices, which

make them easily accessible. Recently, offenders have been using jammers to prevent

stolen vehicles from being tracked or simply to remain undetected. Equally, personal

privacy devices (PPDs) are becoming cheaper and easier to acquire leading to the

increased threat of GPS outages for the everyday consumer [2,3] thus posing a larger

threat [4,5].

2

As such, there is a crushing need for new and advanced methods to help preserve GPS

service availability and protect GPS signals from being overwhelmed by powerful

jamming signals that deteriorate accuracy and may lead to complete service denial. In

addition, since the majority of GPS receivers are equipped with one antenna, unlike smart

antenna anti-jamming receivers, they are deprived of the benefits of exploiting the spatial

domain in mitigating a jammer regardless of its type. Therefore, an anti-jamming

enhancement that targets this vast majority, and that operates in domains other than the

spatial domain is necessary. Furthermore, given that smart antenna anti-jamming

systems, that spatially mitigate jammers by electronically steering nulls towards them,

must have knowledge the DoAs of the jammers, the accuracy of those DoA estimation

methods is of paramount importance. Thus, erroneous or inaccurate null steering would

result in the attenuation of the GPS signals that are closest to the jammer and

consequently degrade the GPS solution.

The GPS signal is a direct sequence spread spectrum signal, which entails that the

received GPS signal’s power level is below noise levels and that a despreading process in

the receiver’s signal processing unit restores it to pre-spreading levels. Nonetheless, the

jamming signal can effortlessly overwhelm the GPS receiver’s front-end and prevent the

actual signal from being processed. Unfortunately, this is possible due to the fact that the

spreading gain (approximately 30 dB) is not yet applied to the signal. At that time, even

after the spreading gain is applied, the jamming signal is also amplified therefore

preventing further processing of GPS signals. The gain of the amplifier adjusts itself to

the jamming signal, which is more powerful. Consequently, the Analog to Digital

Converter (ADC) samples the jamming signal instead of the much weaker GPS signal

3

[6]. There are several types of interference and jamming signals that vary depending on

the spectral characteristics (whether the signal is narrowband or wideband), modulation

technique used, or if the signal is high power matched spectrum noise.

Jamming deteriorates the positioning solution accuracy, leads to the total loss of lock on

the satellite signals and therefore impairs the positioning availability. It affects different

parts of the receiver in different manners. Initially, the received GPS signal’s signal to

noise ratio (SNR) suffers severe degradation as the Jamming to Signal Ratio (JSR)

increases. The receiver’s front-end erroneously samples the jamming signals, eventually,

code and carrier phase are lost along with frequency lock and finally the navigation

solution. It is difficult for acquisition and tracking algorithms to recover lost GPS data

when jamming occurs [1].

1.2 Previous Work

The focus of this thesis is directed towards CW signals. CW Interference can obstruct and

hinder the operation of several blocks and parameters of a GPS receiver. This effect is

witnessed on synchronization and acquisition steps, pseudorange measurements and

positioning solutions [1,7,8]. The spectral location of the CW interference compared to

the GPS L1 center frequency is of importance; the closeness of the jammer’s carrier

frequency to the GPS L1 center frequency contributes directly to faster degradation in the

carrier to noise ratio (C/N0), largely because of the correlation conducted in the

acquisition module. It was found that a CW interferer whose center frequency was closest

to the L1 frequency recurrently caused false lock [9]. The notch filter (NF) is a frequently

used tool for the mitigation of CW signals in single antenna receivers. Unfortunately, the

excision of the undesired frequencies by the notch filter will also lead to the removal of

4

the GPS signal spectrum found in the excised bandwidth of the notch. The Automatic

Gain Control (AGC) input histogram was used to develop a notch frequency estimation

and interference signals discrimination detection algorithm [8]. Detection metrics that

were established when CW jamming was applied were acquired in the post-processing

stage of the receiver, for example correlator output power, carrier phase indecision and

the variation in correlator output power. Test statistics that observe the operational

reliability of the GPS receiver were recommended based on these metrics [8]. Moreover,

the least mean squares algorithm was used as a base for an adaptive Finite Impulse

Response (FIR) notch filter which was introduced and implemented to adaptively detect,

locate and mitigate narrowband interferences. Z. Jiang proposed an algorithm that

depends on spectral analysis to excise high power interference [10].

Fast Fourier Transform (FFT) is a predominant spectral analysis method that is widely

used in the detection of jammers in the spectral domain. FFT resolution depends on the

selected window size, which has an inversely proportional relation to processing time. If

a jammer’s frequency is located between frequency bins, it will be approximated to the

nearest bin thus generating an estimation error, and if multiple jammers are closely

spaced between two bins, FFT will neither be able to detect their number nor their

frequencies, as they will be detected as one jammer.

Spatial domain detection and mitigation is a mature field, therefore, many DoA

estimation methods have been proposed. Classical beamforming, also known as

conventional beamforming and the Bartlett method [11] is an earlier approach to DoA

estimation, it scans the spatial spectrum using predetermined angular steps in search of

the direction angle that corresponds to the highest power in the spectrum. Regrettably, the

5

spatial spectrum has a resolution threshold, the major limitation attributed to this method

is it inability to form neither narrow nor sharp peaks unless a large number of elements is

used in the array. Consequently, the method suffers from a limited ability to resolve

closely spaced sources [12].

Capon’s beamformer, also known as the Minimum Variance Distortionless Response

(MVDR), attempts to improve the drawbacks associated with the Classical method. It

results in a significant improvement [13]. The output power is minimized while

constraining the gain in the required direction to unity. The MVDR method demands an

additional matrix inversion compared to the classical method; fortunately, it outperforms

the classical method in the majority of the cases. The disadvantages of the MVDR

method are the necessary additional computations and its failure to estimate the DoAs of

highly correlated (coherent) signals [14].

Advances in the field of direction finding lead to the development of high resolution DoA

estimation methods that utilize the signal subspace. By performing Eigen analysis on the

spatial covariance matrix, the signal and noise subspaces are generated. Multiple Signal

Classification (MUSIC) is among the subspace techniques [15]. MUSIC showed that the

steering vectors associated to the received signals are found in the signal subspace. A

search throughout the possible steering vectors is conducted; the ones that are orthogonal

to the noise subspace are designated as desired signals. However, errors arise in real

scenarios since full orthogonality is difficult to achieve due to errors in the estimation of

the noise subspace. The MUSIC spectrum generates a large value when a match between

the generated steering vector and the actual DoA occurs. The disadvantage of MUSIC is

that it is not able to identify DOAs of correlated signals on its own; the received signal

6

must undergo a pre-processing technique called spatial smoothing [16]. In addition, it is

computationally expensive, sensitive to noise and must have prior knowledge of the

signals it is looking for. Several variants of the method have been proposed to improve its

performance [17].

The Estimation of Signal Parameters via Rotational Invariance Technique (ESPRIT)

algorithm was proposed by R. Roy et al. [18]. It is computationally efficient and more

robust if compared to MUSIC as it does not search the entire spectrum but a significant

drawback is the incompatibility with all array geometries, as it was designed for Uniform

Linear Arrays (ULA). The method has been extended to include multi-dimensional arrays

and many versions have been produced [18,19].

1.3 Research Objectives

The ultimate aim of the research is providing an uninterrupted service for GPS users by

limiting the effect that interference and jamming may have on a GPS receiver. Mitigating

these effects is obtained by improving GPS anti-jamming. By significantly improving

the jamming detection capabilities of current GPS receivers, enhanced jamming

mitigation performance is reached. To attain the desired goals, methods that provide high

resolution jamming detection to a multitude of platforms such as single antenna receivers

and multiple antenna array receivers are proposed. They employ different jamming

detection methods that operate in different domains depending on the structure of the

receiver. The proposed methods are pre-correlation methods; which means they detect the

presence of jamming signals prior to the GPS receiver’s acquisition and tracking

modules.

7

The proposed high resolution jamming detection method for single-antenna receivers is

chosen to operate in the frequency domain, where FFT is a predominant detection

method. On the other hand, the methods proposed for multi-antenna systems exploit the

spatial domain processing which provides, in addition to the frequency domain

processing, DoA estimation of jammers; therefore, benefiting the anti-jamming process

and increasing the resilience of the GPS receiver to jamming. High resolution spectral

estimation that is based on the Gramm-Schmidt orthogonalization procedure is utilized

for single antenna systems. As for multi-antenna systems, a high resolution DoA

estimation method is developed for both ULAs as well as planar arrays, (specifically

uniform circular arrays). The proposed methods address the drawbacks of conventional

DoA algorithms, such as the Classical method which is also known as the Bartlett

method, which cannot provide high resolution estimates.

Considering the above, the outlined research objectives are defined:

1. Developing a high-resolution frequency domain jamming detection method to

isolate jammer frequencies in the received GPS signal. The method aims to

achieve the accurate estimation of the frequencies of single in-band jammer

signals with a resolution higher than the predominant FFT, additionally, the

methods aspires to accurately detect the exact number of multiple in-band

jammers surrounding the receiver and accurately estimate their frequencies.

Exploring the benefits of FOS spectral estimation method will be adopted in this

research due to its very high-resolution capabilities.

2. Developing a high resolution DoA estimation method that is capable of accurately

detecting and differentiating between the DoAs of multiple jammers multiple

8

jammers that are located at close-by distances from each other (i.e. spatially close-

by). This method should be implemented to serve both one-dimensional arrays

such as ULA and two-dimensional planar arrays. The benefit of expanding and

applying the method to two-dimensional arrays is obtaining DoA estimates in

both azimuth and elevation. In addition, a study of array geometries is required so

as to choose the most suitable geometry for the application. In this thesis, UCA

and an optimized version of the UCA which is constructed by adding a center

element are studied.

3. This research will conduct a comparative study between the developed method

and other predominant DoA techniques (conventional and subspace based).

Conventional DoA estimation approaches are still being used in DoA estimation.

As of recently, researchers began to apply MUSIC and other subspace based

techniques. This research will develop these predominant methods and compare

their performance to FOS-based DoA.

1.4 Research Contributions

The aforementioned objectives necessitated extensive research, which when completed,

paved the way for several contributions. They are classified according to the above

mentioned objectives. Initially, the problem of jamming detection for the enhancement of

single antenna receivers was approached. The research contributes to the development of

a high resolution jamming detection method that is based on spectral estimation using a

nonlinear modelling method called Fast Orthogonal Search. The method accomplishes

the following:

9

a. accurate estimation of the frequencies of in-band jammer signals with a

resolution that is finer than that of the predominant FFT

b. accurate and efficient estimation of the number of multiple in-band CW

jammers whose frequency separation is lower than the FFT frequency

resolution

c. accurate estimation of the frequencies of multiple in-band CW jammers.

The next phase of the research required the simulation of multi-antenna systems. A

significant hurdle that prevented the commencement of testing and experimentation was

the lack of suitable hardware for this type of research. Therefore a method that allows for

multi antenna GPS simulations using only one Spirent 6700 GPS simulator and one

frontend (called FireHose and provided by Novatel Inc.) was devised, developed and

validated. The developed method paves the way for one-dimensional and two-

dimensional array simulations which in turn lead to the accomplishment of the desired

goals.

The final phase of the research was the study of array geometries, the selection of the

most suitable configurations and the implementation of the simulations using the Sprient

6700 GPS simulator, the FireHose and Matlab for post-processing and performance

analysis and comparison with predominant DoA estimation methods. The proposed high

resolution method contributes to higher accuracy DoA estimation of the multiple spatially

close-by jammers by employing ULA, UCA and optimum UCA. It also contributes to

more accurate determination of jammer amplitude which is useful to jammer localization

systems that utilize signal strength to determine location. The methods directly contribute

to the robustness enhancement of GPS receivers and especially receivers that are not only

10

developed to detect jammers but to mitigate them. Providing a more accurate DoA

estimate minimizes the GPS signal degradation incurred by the inaccuracy of anti-

jamming receivers that rely on less accurate DoA estimation methods.

1.5 Thesis Outline

The thesis presented is structured as follows: Initially in Chapter 2, an overview of the

GPS system components with particular attention to the receiver is given. The chapter

then introduces the different types of interference and jamming followed by a review of

anti-jamming techniques and finally moving onto the predominant DoA estimation

methods found in literature; thus providing sufficient background knowledge for readers

who will move onto Chapter 3. Special interest is given to CW interference and jamming

in Chapter 3 where the proposed spectral estimation based high resolution jamming

detection method is introduced. The jammers used in this chapter are CW jammers. The

signal processing required is explained along the chapter. The effects of JSR levels

variation, window size and the number of jammers are studied and the proposed method

is compared to the predominant FFT. Chapter 4 primarily reviews the necessary concepts

required in order to understand array processing, a review of the different arrays

geometries such as ULA, URA and UCA is given, and it is followed by an optimization

process that leads to the use of the optimized UCA. The chapter continues by

demonstrating the developed method for multi-dimensional GPS antenna array

simulation which is used throughout the chapter. Experimental results achieved by the

proposed DoA method and its comparison to the predominant DoA estimation methods

are presented and discussed when the method is applied to the aforementioned array

11

geometries. The conclusions, recommendations and future work relating to the research’s

outcomes are subsequently presented in Chapter 5.

12

Chapter 2

GPS System Overview

2.1 Introduction

The role of the Global Positioning System (GPS) has become indispensable in our lives.

Because of its significance, research is very active in this sector and obtaining higher

reliability and higher accuracy is essential to sustain the integrity of the position, velocity

and time (PVT) solutions. Initially a military satellite system that was later on provided

partially to the public, GPS has seen an explosive growth in the number of users. There

are also many industry sectors that rely on it such as precise timing, precise positioning

used in geodesy and structural engineering, aviation, land and maritime navigation...etc.

[20]. This chapter starts with a general introduction of the GPS system’s sectors followed

by the GPS observables, the generic structure of the receiver and finally a summary of the

GPS errors which will pave the way towards the main objectives of this research.

Interference and jamming are then overviewed; where their types, causes, sources, effects

and mitigation techniques are described. Additionally, one of the detection and mitigation

techniques; based on array processing, will be explained for its importance and relevance

to Chapter 4.

2.2 GPS Segments

GPS is made up of three segments as shown in Figure 2-1, the first is the space segment

explained briefly in section 1.3.1, the second is the control segment and the last is the

user segment [21].

13

Figure 2-1: Different GPS segments

2.2.1 Space Segment

GPS constellation as shown in Figure 2-2 consists of 24 operational satellites in six

orbital planes with four satellites in each plane. It has been recently upgraded to 27 by the

US air force [22]. The number of satellites can increase up to 30. The ascending nodes of

the orbital planes are separated by 60 degrees and the orbital planes are inclined 55

degrees. The orbit of each GPS satellite is nearly circular with a semi-major axis of

26578 km and a period of about twelve hours. The satellites continuously orient

themselves to ensure that their solar panels stay pointed towards the Sun, and their

antennas point toward the Earth. Each satellite carries four atomic clocks, is the size of a

car and weighs about 1000 kg [23].

14

Figure 2-2: GPS satellites in orbit [22]

2.2.2 Control Segment

The control segment of GPS is made up of a network of tracking stations positioned all

across the Earth as shown in Figure 2-3 with a master control station (MCS) located at

Colorado Springs, Colorado, USA. This MCS is staffed around the clock [24]. There are

16 monitoring stations located throughout the globe. Six of them are operated from Air

Force bases and 10 from the National Geospatial-Intelligence Agency (NGA) [25]. They

are located around the Earth and their positions are known very precisely. These stations

are equipped with very sophisticated GPS receivers and a cesium oscillator for tracking

all of the satellites in view. The MCS remotely operates these ground control stations.

Among the tasks of the control segment are: (a) monitoring and maintaining satellite

orbits and health by maneuvering and relocation, (b) maintaining GPS time, (c)

predicting satellite ephemerides and clock parameters and (d) updating satellite

navigation messages periodically [20].

15

Figure 2-3: Locations of the different sections of the control segment around the world [25]

2.2.3 User Segment

The user segment consists of users (individuals, commercial or military) with different

radio receivers that receive signals from GPS satellites and estimate their position,

velocity, and time. Users of GPS can be classified into civil and military. The user

segment is experiencing exponential growth since inauguration due to decreasing prices

of receiver and the increasing application of GPS in daily life. When a GPS receiver is

activated, it will acquire the GPS satellite signals [26]. The signal is processed, and the

receiver position is determined by the intersection of the spheres created by the satellite

pseudoranges. A minimum of four satellites with good geometry is required. Three

satellites are required for the position fix, while the fourth is required to account for the

receiver clock offset. An in depth look at the user segment can be found in [27] and [28].

2.3 GPS Signal

GPS signals are transmitted on two frequencies in the UHF band (which covers the

frequency band from 500 MHz to 3 GHz) [29]. The two frequencies are referred to as L1

and L2 and are derived from a common frequency, f0=10.23 MHz, there is a third

frequency that is not present in all satellites called the L5, it is only available on block IIF

16

satellites [30] and, till now, only four satellites from this block have been launched with

the operational L5 signal [31]. The GPS frequencies are generated as follows:

Each frequency is modulated by ranging codes called pseudo-random noise (PRN)

sequence which enable precise range measurements. A Coarse Acquisition (C/A) code is

associated with the Standard Positioning Service (SPS) set aside for civil use while a

Precise Code (P-code) is associated with Precise Positioning Service (PPS) (further

encrypted to P(Y)-code for security reasons) and meant for authorized military users. The

L1 frequency is modulated by both C/A and P-codes whereas L2 is modulated by P-code

only. Figure 2-4 depicts the structure of a L1 signal transmitted by the GPS satellite.

Figure 2-4 : GPS L1 signal structure

fL1 = 154 × f0 = 1575.42 MHz Eq. 2-1

fL2 = 120× f0 = 1227.60 MHz Eq. 2-2

fL5 = 115× f0= 1176.45 MHz Eq. 2-3

90° Phase Shift

Antenna

1.023 MHz C/A code

50 Hz Navigation Data

10.23 MHz P(Y) code

50 Hz Navigation

Data

17

It is necessary for the receiver to identify the position of the satellite in order to convert

range measurements into velocity and position by using the navigation message. This

message is superimposed on both L1 and L2 carriers along with PRN codes. The

navigation message is binary coded data consisting of information on the satellite’s

health, ephemeris (position and velocity), clock bias parameters and almanac (which is a

less precise version of ephemeris but concerning the rest of the constellation) [32]. The

GPS signal received from the 𝑖𝑡ℎ satellite is shown in Eq. 2-4

where

𝐴𝑖 is the amplitude of the 𝑖𝑡ℎ useful signal,

𝑓𝑑𝑖 is the Doppler frequency affecting the 𝑖𝑡ℎ GPS signal

𝜑𝑖is the random phase of the signal

𝑓𝑐 is the GPS carrier frequency

𝑐𝑖(𝑡) is the spreading code

𝑑𝑖(𝑡) is the navigation message

𝜏𝑖 is the delay introduced by the communication channel [7].

𝜂 is the noise encountered at the receiver.

2.4 GPS Observables

There are three essential observables which are pseudo-ranges measurements, Doppler

measurements and carrier phase measurements [32]. Carrier phase is more precise than

pseudo-range and is used for applications such as surveying.

2.4.1 Pseudorange Measurements

Pseudorange is the measurement of the distance between the GPS receiver’s antenna and

the GPS satellite’s antenna which is necessary for the calculation of position [21]. It can

𝑦𝑖(𝑡) = 𝐴𝑖𝑐𝑖(𝑡 − 𝜏𝑖)𝑑𝑖(𝑡 − 𝜏𝑖) cos[2𝜋(𝑓𝑐 + 𝑓𝑑𝑖)𝑡 + 𝜑𝑖] + 𝜂 Eq. 2-4

18

be computed from either the C/A code or the P code. The transit time is measured by the

correlation between the C/A-code, received from a GPS satellite, and its replica generated

at the receiver. Since the clocks, installed on the satellite and the receiver, are not

synchronized, the measured range is biased and called a pseudorange [33]. At least four

pseudorange observations are required to estimate the receiver’s three-dimensional

position and clock offset. The pseudo-range is calculated by computing the difference

between the satellite and receiver times and multiplying it with the speed of light [32] as

seen in Figure 2-5.

Figure 2-5: Pseudorange measurements [21]

2.4.2 Carrier Phase and Doppler

A more accurate technique to acquire the range to the satellites can be achieved using

carrier phase measurements. By adding the number of full carrier cycles to the total

number of fractional cycles at both the receiver and the satellite and then multiplying the

sum by the wavelength of the carrier, we get the range. According to [21] , the range of

the accuracy of the L1 signal is approximately 19 cm. The problem with carrier phase

measurements is that the GPS receiver is unable to obtain the number of complete cycles,

but is able to track the phase changes and thus keep the initial cycle ambiguity (initial

number of complete cycles is unknown) unchanged.

Δt

Satellite code

Receiver replica code

19

A GPS receiver can observe the carrier frequency of the received signal by generating a

replica carrier wave. Based on the Doppler effect, the observed frequency will be

different from the L1 signal or any other carrier frequency emitted from the satellites.

This frequency shift is due to the relative motion of the receiver and the satellite and it is

called Doppler measurement [7]. By providing Doppler measurements and knowing the

satellite velocity, the receiver’s velocity can be measured.

2.5 GPS Receiver

GPS receivers process signals transmitted by GPS satellites, estimate the user-to-satellite

ranges and range rates and compute a position, velocity and time solution .As shown in

Figure 2-6, the GPS receiver consists of four blocks: Antenna, Radio Frequency (RF)

front-end, local oscillator and signal processing block. The latter is illustrated in

Figure 2-7 where there are multiple receiver channels that function simultaneously; one

for each received satellite signal. Each receiver channel is responsible for acquiring a

visible satellite, and then the tracking loops track the code and carrier phase of the signal.

Once the tracking is established, the navigation data is extracted and processed to provide

the pseudorange of the specific receiver channel. The receiver channels pseudoranges are

further processed to compute the position of the receiver.

20

Figure 2-6: Block diagram of a GPS receiver

Figure 2-7: Receiver channels in the signal processing phase [29]

RF Front-end

Signal Processing

Local Oscillator

Antenna

Acquisition

Carrier Tracking

Code Tracking

Navigation Data

Extraction

Pseudorange Calculation

21

2.5.1 The GPS Antenna

The antenna is the first element of the receiver architecture. The transmitted signal is

Right Hand Circularly Polarized (RHCP), so the antenna must be designed to receive

RHCP signals. The antenna gain pattern is an important consideration that indicates how

well the antenna performs at different center frequencies, different polarizations and

different elevation angles. Figure 2-8 illustrates the typical gain patterns of the NovAtel

antenna GPS 702GG that can receive GPS L1 and L2 signals.

Figure 2-8: Typical RHCP and LHCP normalized radiation pattern of NovAtel antenna

GPS-702 GG for GPS L1 and L2 Signals [34]

The pre-amplifier is the first active component succeeding the antenna. It is often housed

in the same enclosure as the antenna element. The antenna may be capable of receiving

multiple frequency bands. Thus, there may be one pre-amplifier per frequency band of

interest, or a single pre-amplifier may cover multiple frequency bands. The primary

purpose of the preamplifier is to amplify the signal at the output of the antenna for further

processing [35]. However, it is vital that this amplifier has a very low noise figure; hence

the amplifier is usually referred to as a Low Noise Amplifier (LNA).

22

2.5.2 RF Front-End

RF front-end represents the second stage in the receiver architecture after the antenna and

LNA. RF front-end filters, down converts and digitizes the received signal. The front-end

conditions the narrowband signal in each GPS band and with the help of the local

oscillator and the low pass filters; down converts the signal to the Intermediate Frequency

(IF) .This process is followed by the digitization of the data using the ADC [35]. Initially,

the signal is amplified after which it is filtered such that unwanted out-of-band signals are

removed. The front-end utilizes a crystal along with a Phase Locked Loop (PLL) to

create the Local Oscillator (LO) signal [36]. Filtering in the front-end achieves a number

of objectives such as rejecting out-of-band signals, reducing the noise content in the

received signal and reducing the effect of aliasing. Wide bandwidth signals, if

appropriately processed, can provide higher resolution measurements in the time domain,

but come at the cost of requiring higher sampling rates, and hence result in larger power

consumption in the receiver [35]. Modern front-ends rely on multi-bit ADCs; therefore an

AGC unit is required to ensure that the power of the received signal is adjusted such that

it remains within the dynamic range of the ADC [36]. The AGC consists of three main

parts, the Variable Gain Amplifier (VGA), the gain controller and the ADC as shown in

Figure 2-9.

23

Figure 2-9: Building blocks of the AGC signal conditioning stage

The digital IF signal consists of quantized In-phase and Quadrature (I&Q) samples, they

follow the Gaussian distribution because the GPS signals are spread spectrum signals and

as previously mentioned in section 2.3 the modulating ranging codes are noise-like.

Figure 2-10 demonstrates the Gaussian distribution of one second of real unjammed GPS

I and Q data sampled at 2.5 MHz.

Figure 2-10: Distribution of 1 sec of real I and Q data sampled at 2.5 MHz

-100 -50 0 50 1000

0.5

1

1.5

2

2.5

3

3.5

4x 10

5

In-phase data

-100 -50 0 50 1000

0.5

1

1.5

2

2.5

3

3.5

4x 10

5

Quadrature-phase data

Gain Controller

ADC VGA Analog IF Signal

Digital IF Signal

24

2.6 GPS Errors

GPS receiver uses the trilateration principle to calculate its position by making range

measurement to at least four satellites. Unfortunately, these measurements contain lots of

errors arising from several sources. The effect of these errors must be mitigated so that an

accurate position is obtained.

2.6.1 Hardware Clock Error

Hardware clock errors originate from both the satellite and the receiver. Despite their

high accuracy, satellite clocks, with time, drift away from the GPS system time [21].

Based on the observed satellite clock data from monitoring stations, the control segment

estimates the correction parameters for satellite clocks and transmits them to the

satellites, which in turn broadcast these parameters in the navigation message every 30

minutes. These parameters enable the user to correct the satellite clock error in the

measured range [1]. The clocks in GPS receivers should be inexpensive for affordability.

Consequently they are far less accurate than the satellite clocks and thus contain a bias.

This clock bias error affects all measurements in same manner. Therefore if four pseudo-

range measurements are available, the clock bias can be estimated along with the three

components required to determine the position of the user [24].

2.6.2 Unintentional Delays

The surrounding environment causes another source of delay. In order to receive the

signal at the receiver’s end, the transmitted GPS signal must traverse the ionosphere and

the troposphere layers. These layers add inevitable delay to the signal. Another source of

delay is the reflection of the satellite signals off surfaces before reaching the receiver and

this is termed multipath delay.

25

2.6.2.1 Ionospheric and Tropospheric Delays

Delays caused by the Ionosphere and the Troposphere are introduced and added to other

delays that affect the transit time. They must be modeled and compensated for at the

receiver.

Ionospheric Delay

The ionosphere is the layer of the atmosphere containing ionized gases (free electrons

and ions). It is found approximately from 60 to 1,000 km above the Earth’s surface [28].

Solar activity changes the ionization level of this layer thus affecting the refractive

indices of the various layers of the ionosphere and, as a result, changing the transit time

of a GPS signal and introducing an extra delay that the receivers must remove.

Tropospheric Delay

The troposphere is the lower part of the atmosphere extending from 8 to 40km above the

earth’s surface. It is mainly composed of dry gases and water vapor. The troposphere is

non-dispersive for GPS frequencies, in comparison with the ionosphere, but it is

refractive and causes a decrease in speed relative to free space [28]. Tropospheric errors

are consistent between L1 and L2 carriers and the delay caused by the troposphere has a

dry and a wet component. The wet component is responsible for 10% of the tropospheric

delay and difficult to model as water vapor content varies locally. The dry component is

better modeled which accounts for 90% of the tropospheric delay.

2.6.3 Receiver Noise

Noise is always present in GPS measurements due to component nonlinearity and thermal

noise. Receiver noise cannot be entirely avoided, and its effect on location precision is a

function of the signal-to-noise ratio of the received signal. This error in receiver

26

technology is usually modeled as white noise [37]. A standard GPS receiver performs a

self-test when switched on. Tests for high precision receivers can be performed to

evaluate their noise performance; more on that topic is explained in [21] and [38].

Table 2-1 demonstrates the approximate errors attributed to different factors that affect

the GPS solution accuracy.

Table 2-1: Typical pseudo-range measurement errors for a single –frequency L1 receiver

[20]

Error Source RMS Range Error

Satellite Clock and Ephemeris Parameters 3 m

Atmospheric Propagation Modelling 5 m

Received Noise and Multipath 1 m

2.6.4 Errors Caused by RF Signals in the Receiver’s Vicinity

GPS signal can be classified as a weak signal, as such; it is vulnerable to unintentional

and intentional RF interference signals that limit the receiver’s ability to provide a PVT

solution. Some of the commonly mentioned terms (oriented towards GPS usage) are

defined below [39]:

Background or Thermal Noise. It is the characteristic noise of the system.

Thermal noise is produced mainly in the first amplifier of the receiver.

Interference Noise: is the noise that is present at the same frequency or

frequencies of the desired signal. It can contribute to partially or fully concealing

the GPS signal. Such properties are exploited in AWGN jammers.

Interference Source: it is any electric device which radiates electromagnetic

signals that interfere with the proper operation of the receiver.

27

Unintentional Interferences: is any interference received from a source that does

not have the specific intent of harming GPS operation but unfortunately does so.

Intentional Interferences: they are RF signals that are purposefully generated to

harm and impair the correct functionality of GPS receivers. They comprise

jamming, spoofing and meaconing.

Jamming: is sending certain RF signals in the GPS operating bandwidth, there

are narrowband and wideband jammer.

Spoofing: is transmitting RF signals that mimic GPS signals’ structure while

enclosing faulty navigation data, thus misleading the receiver and causing it to

produce an erroneous PVT solution. Connecting GPS receivers to GPS simulators

can be considered as a harmless type of spoofing.

Meaconing: is the rebroadcasting of intercepted GPS signals at higher power than

the original ones leading to confusion at the receiver. The received GPS signal is

is recorded for a certain time and later re-transmitted. It only needs to be slightly

stronger than the real GPS signal to have the receiver lock on the wrong signal.

The terms of interest throughout this thesis are interference and jamming; they will refer

to unintentional and intentional interference respectively. Interference and jamming are

two of the main degrading factors of the reliability of the GPS solution [40]. Interference

itself can either be caused by signals emitting from different communication systems or

by identical delayed copies of the GPS satellite signal such as multipath which is briefly

explained in the following section.

28

2.6.4.1 Multipath Delay

Multipath is a major contributor of error due to the delay it introduces. The GPS signal

reaches the receiver by one or more different delayed paths; in some cases the Line of

Sight (LoS) signal is not available. The received signal usually comprises direct LoS and

reflected signals from other objects around the receiving antenna named Non Line of

Sight (NLoS) signals. The multipath effect is more evident in urban environments and is

extremely service degrading in urban canyons as shown in Figure 2-11 where one LoS

component is visible and in Figure 2-12 where a LoS component is not available. The

signal that arrives indirectly is delayed and usually leads to a lower SNR. This can cause

a position error in excess of 10 m. Further details are found in [20,28,1]. The multipath

error is two orders of magnitude lower for carrier phase measurements than for pseudo-

range measurements.

Figure 2-11: LoS signal (red) and its

reflection (green) in an urban canyon

Figure 2-12: Absence of LoS component in an

urban canyon

2.7 Interference and Jamming

As mentioned earlier, interference and jamming signals prevent the RF front-end from

functioning correctly. It has been reported in [1] that no matter what tracking and

acquisition algorithms have been implemented in the digital part of the receiver, they will

29

be rendered useless. The latter condition is true if the GPS signals were totally corrupted

by the nonlinear behavior of the front-end. Spectral characteristics such as the carrier

frequency and bandwidth, 𝑓𝑖𝑛𝑡 and 𝐵𝑖𝑛𝑡 respectively, can lead to a broad classification of

interferences. A higher level classification would include in-band and out-of band

signals. The former would encompass any signal whose carrier frequency is close but

outside the GPS band while the latter would encompass signals found inside the GPS

band. A more specific classification for the in-band interferences would differentiate

between the bandwidths of different interference sources and categorize them into

narrowband and wideband interferences. The different classifications are demonstrated in

Table 2-2 where 𝐵𝐼𝐹 and 𝑓𝐼𝐹 correspond to the GPS signal’s bandwidth and center

frequency after the IF stage [41].

Table 2-2: Classification of interferences based on spectral characteristics

Class Spectral Characteristics

Out-of-band interference 𝑓𝑖𝑛𝑡 > 𝑓𝐼𝐹 + 𝐵𝐼𝐹/2 or 𝑓𝑖𝑛𝑡 < 𝑓𝐼𝐹 −

𝐵𝐼𝐹/2

In-band interference (𝑓𝐼𝐹 − 𝐵𝐼𝐹/2 < 𝑓𝑖𝑛𝑡 < 𝑓𝐼𝐹 + 𝐵𝐼𝐹/2)

Narrowband interference 𝐵𝑖𝑛𝑡 ≪ 𝐵𝐼𝐹

Wideband interference 𝐵𝑖𝑛𝑡 ≈ 𝐵𝐼𝐹

Most interference signals are generated by licensed emitters that do not transmit in the L1

band; nonetheless, harmonics of these signals find their way into the GPS L1 band [9]. A

summary of the different types of interference signals based on their modulation types as

30

well as their potential sources is shown in Table 2-3. Some of the most common

interference and jamming sources are demonstrated in Figure 2-13.

Table 2-3: Types of RF interference and their probable sources

Class Type Potential Sources

Narrowband Continuous Wave

(CW)

Intentional CW jammers or near-band

unmodulated transmitter’s carriers

Narrowband Swept CW Intentional swept CW jammers or frequency

modulation (FM) stations transmitters’

harmonics

Narrowband Phase/frequency

modulation

Intentional chirp jammers or harmonics from

an amplitude modulation (AM) radio station,

citizens band (CB) radio, or amateur radio

transmitter

Wideband Pulse Any type of burst transmitters such as radar or

ultra-wideband (UWB)

Wideband Wideband—matched

spectrum

Intentional matched-spectrum jammers,

spoofers, or nearby pseudolites

Wideband Wideband—

phase/frequency

modulation

Television transmitters’ harmonics or near-

band microwave link transmitters overcoming

the front-end filter of a GPS receiver

Wideband Wideband—band-

limited Gaussian

Intentional matched bandwidth noise jammers

31

Figure 2-13: Common interference and jamming sources

2.7.1 Jamming Attacks on GPS

GPS anti-jamming was always considered a priority of the military sector, unfortunately,

due to primarily, the growing demand of personal privacy devices (PPDs),

[5,42,4,43,44,45] jamming is being viewed as a threat to the public; especially with the

increasing dependence on the GPS system. Jamming attacks have a sole objective of

preventing the receiver from providing the desired solution. Although jamming is illegal

and therefore criminalized, it has been reported that offenders have been using jammers

to prevent stolen vehicles from being tracked or simply to remain undetected. Equally,

PPDs are becoming cheaper and easier to acquire leading to the increased threat of GPS

outages for the everyday consumer [2,3]. Therefore, the struggle against jamming has

been moved from the battlefield to the streets. Different types of PPDs are shown in

Figure 2-14 [46].

Spoofers

Broadcasting Stations’ Harmonics

Jammers

Multipath Propagation GPS

receiver

32

Figure 2-14: Different types of PPDs [47]

A GPS jamming signal is typically transmitted on or around the GPS L1 frequency,

which is 1575.42 MHz. It is not necessarily required to be very complex or powerful due

to the fact that the GPS signals are extremely weak. The signal power level of a received

GPS signal at earth’s surface is approximately -163 dBW, which is below the noise floor

of the receiver (estimated at -138 dB for a 20 MHz bandwidth signal located in the L

band). The jamming signal can effortlessly overwhelm the GPS receiver’s front-end and

prevent the actual signal from being processed. Unfortunately, this occurs due to the fact

that the spreading gain (approximately 30 dB) is not yet applied to the signal. At that

time, even after the spreading gain is applied, the jamming signal is also amplified

therefore preventing further processing of GPS signals. The gain of the amplifier adjusts

itself to the jamming signal, which is more powerful. Consequently, the ADC samples the

jamming signal instead of the much weaker GPS signal [6].

2.7.2 Jamming Effect on GPS

Several studies [44,46,5] have explored the effects of jamming and especially PPDs on

Global Navigation Satellite Systems (GNSS) performance. Jamming deteriorates the

positioning solution accuracy, leads to the total loss of lock on the satellite signals and

therefore impairs the positioning availability. It has been reported that the typical front-

end is saturated in case of broadband AWGN signals, high power narrowband and pulsed

33

signals. Contrarily, the front-end was not saturated when low power narrowband,

spoofing and meaconing signals were applied [39].

Several authors have studied the effects of jamming on acquisition and tracking [9,7,48].

Acquisition success is documented in [48]; where it has been identified that CW has the

most damaging effect compared to swept CW and broadband noise which come in

second place such that 10 and 15 dB Jamming to Signal Ratios (JSR) are required to

prevent acquisition respectively. Additionally, applying sufficiently high power jamming

signals will inflict loss of tracking to one or more channels; hence the receiver will go

into reacquisition mode; since tracking requires a carrier to noise ratio (C/N0) that is 10

dB lower than that for acquisition. When tracking loops are affected, the pseudorange

measurements will be erroneous. To understand the effects of jamming experimentally, a

simulation was conducted using the Spirent GSS 8000 in the TECTERRA geomatics lab

in Calgary. The GPS L1 C/A signal was jammed three times, two of which were swept

CW jamming at a jamming to signal ratio (JSR) of 50db. The final jamming incident was

caused by a Gaussian noise jammer of the same JSR (considered wideband) as shown in

Figure 2-15. The jamming effects are clearly shown in the tracking loops of the software

receiver. The results show loss of both carrier phase lock and code phase lock, thus

leading to service denial in the durations of the jamming which start at 4:00 mins, 9:00

mins and 15 mins. By comparing the navigation data bits in Figure 2-15 and Figure 2-16,

it is clear that during the jamming periods (marked by the red arrow); the navigation bits

cannot be distinguished or decoded thus preventing a navigation solution. Furthermore, in

the correlation results, the prompt correlation peaks (in green) should always be higher

than the early and the late correlation peaks. However, during the jamming period, they

34

are superimposed on the early and late peaks, which prohibit the computation of the code

delay. Moreover, both the phase locked loop and the delay locked loop are affected such

that keeping track of carrier phase and code phase becomes difficult. It is also observed

that when jamming signals were turned off, the receiver resumed normal operation.

Figure 2-16 shows the tracking results of a test conducted under normal operating

conditions that lasted for 29 seconds. Jamming signals were not added during this test.

The figure clearly shows navigation bits and the difference between early, late and

prompt correlation peaks.

Figure 2-15: Tracking results of an experiment after applying swept CW and Gaussian

noise jamming.

35

Figure 2-16: Tracking results of an experiment without applying jamming

2.8 Jamming Detection

The PVT solution is compromised when interference and jamming signals are transmitted

on GPS frequencies. Damage is incurred and performance is degraded whether or not it

was originally intended. Nevertheless, knowledge of such an incident is essential to

determine the reliability of the PVT solution. Detecting the presence of interference and

jamming alerts the user about the state of the receiver’s operating conditions. Detection

can either be achieved in the pre-correlation or the post correlation (also referred to as

baseband processing) stages. In the former, the front-end is relied upon to detect the

interference. The AGC is a commonly utilized tool in interference and jamming

detection. Since the signal power is lower than the noise floor, the AGC is accustomed to

the normal operating levels. Jamming signals’ power is regularly higher than the signal

and lead to a change in operating levels and to detection [39]. The gains observed from

the AGC control loop serve as test statistic for detection [49]. Additionally, the

36

distribution of the ADC bins is also used as a statistical measure for interference

detection. It is important to note that multipath and signals sharing GPS structural

characteristics such as spoofing and meaconing can’t be detected by the front-end [39].

An alternate method of detection is achieved by exploiting the transformation of the

received signal to the frequency domain. FFT is commonly utilized and thresholding is

employed to detect the presence of jammers, this topic is researched in detail in Chapter 3

where one of the contributions of this thesis is demonstrated. In the post correlation

methods; based on the studies of the effects of interference and jamming on base band

processing, measurements from the correlators, the PLL and the DLL along with

variations in C/N0 are exploited for RFI detection. A group of test statistics can also be

used as a measure of the presence of RFI such as the correlator’s output power, its

variance and the carrier phase vacillation, which are all unique to each receiver channel.

These test statistics are computed from I and Q sample values obtained after digitization

[49].

2.9 Anti- Jamming Techniques

Successive detection is followed by mitigation if the receivers are equipped for it. A

multitude of techniques have been proposed for anti-jamming and interference

suppression. They can be classified mainly into single antenna based techniques, which

perform jamming mitigation based on receiver processing, whether in pre-correlation or

post-correlation, and antenna array based techniques, which benefit from the presence of

the array to spatially mitigate the jamming signals by electronically controlling the

radiation pattern of the array. Since all the mitigation techniques used by single antenna

systems are present in the receiver, then it is appropriate to imply that they are all

37

applicable in multi-antenna systems. Figure 2-17 depicts a classification of different anti-

jamming approaches from a perspective that focuses on the utilized antenna system. The

classification is explored in the following section.

Figure 2-17: Classification of anti-jamming techniques

2.9.1 Single Antenna Receiver-Based Solutions

2.9.1.1 Front-End-Based Solution

Mitigation solutions in the front-end of the receiver are usually accomplished either by

means of spectral or temporal excision. Mitigation of certain types of interference such as

pulsed interference can be accomplished using a technique called pulse blanking. It is an

appropriate technique aimed at mitigating pulsed interference. Interference excision is

implemented in the time domain on the samples obtained from the ADC that are above a

certain threshold. Alternatively, frequency excision is implemented in the front-end; it is

based on determining the frequencies occupied by the interference signal. A common

method of spectral excision is the Adaptive Notch Filter (ANF) which is explained in the

following section [41].

Anti-jamming Mitigation

Single Antenna Receiver-Based

Front-end-based Adaptive Gain

Control

Adaptive Notch Filter

Spectral Excision

Switching GNSS Constellations

Integrating with INS

Antenna Array-Based

Beam Forming

Null Steering

38

2.9.1.2 Adaptive Notch Filter (ANF)

ANF is a band-stop filter that attenuates a band of frequencies that is very specific and

narrow, namely a notch, in the frequency spectrum. It is usually used for the extraction of

the jammer signal from the received signal. In the case of a continuous wave (CW)

jammer also known as CW interference (CWI), a high power single tone signal is used to

overwhelm the front-end. The filter will remove all frequency components located in the

notch bandwidth which means removing valuable GPS signal components as well; thus

leading to degradation of the signal [43,50]. Using ANF, the undesired signals can be

mitigated by clipping the frequency bins of the jamming signal and transforming the

signal back into the time domain [5]. A cascade of ANFs is studied in [50] for the

detection of multiple CWI signals using the power of the signal to exploit the statistic

value and internal state associated with the filter. The author also acknowledges the fact

that spatial domain mitigation is more effective but hard to implement in mobile devices.

Adaptive notch filtering is also studied and suggested as a countermeasure to jamming

chirp signals. The ability to track the frequency changes in the chirp signal is being

investigated in [42] and carrier-to-Noise density power ratio (C/ N0) degradation is used

as a measure of performance in this analysis.

2.9.1.3 Switching Between GNSS Constellations

Typically, a jammer is used to jam the signals of specific GNSSs and not all systems at

the same time, nevertheless such jammers can be acquired at an expensive cost. A

solution for this problem is to switch to another GNSS when service denial is sensed,

such as GPS, GLONASS, GALILEO and BEIDOU (which has limited coverage).

39

Switching from one GNSS to another, requires more advanced hardware such as multiple

frequency antennas and multi-constellation capable receivers.

2.9.1.4 Integrating GNSS with Inertial Navigation Systems (INS)

Among the proposed solutions that improve the anti-jamming capability [51] is the

integration of INS with GPS [32]. Since INS cannot be spoofed or jammed unlike GPS; it

can be used as a backup in the absence of GPS. Unfortunately, if the jamming continues

for a certain amount of time, the INS will start to drift. Weapon manufacturers are

producing solutions that combine combat grade INS with an anti-jamming unit, such an

example is the integrated GPS anti-jam system by Rockwell Collins [52].

2.9.2 Antenna Array Based Solutions

An antenna array is a group of antennas for which the outputs are combined to create an

overall radiation pattern that is different from that of each antenna element individually

[53]. These antennas are arranged in space depending on the array geometry. They are

processed such that the radiation pattern of the array increases the gain towards a selected

direction while rejecting signals emitted from other directions [54]. Thus, the interference

signal(s) are rejected in space, rather than in the frequency or time domain. Interference

mitigation is significantly enhanced by using an adaptive antenna array (also known as a

smart antenna) through the capabilities of spatial filtering techniques. These techniques

frequently attain high anti-jamming (AJ) margins. They are effective against both narrow

and especially broadband interference signals that single antenna systems cannot combat

[55]. Hence, adaptive arrays improve SNR in the presence of jamming which enables

signal tracking in environments that would otherwise lack code and carrier phase

40

observables. The most common techniques applied in adaptive spatial filtering are null

steering and beamforming.

2.9.2.1 Null Steering

Null steering, also known as side lobe canceller (SLC), is based on the fact that the GPS

signal power is lower than the noise floor. Null Steering considers any signal with a

power level higher than that of the satellite to be an interference signal. Accordingly the

antenna’s beam is steered away from that source and a null is directed towards it. The

objective is to decrease the output power subject to the constraint that one antenna

element is always on (bottom arm of the receiver in Figure 2-18) while trying to maintain

unit gain in all other directions. The rest of the channels have their output phase and

amplitude adjusted in order to block jammers. This is done during the summation process

shown in right side of Figure 2-18. The number of interference signals from different

directions that can be cancelled has a limit that is usually referred to as the degree of

freedom of the array. For example, if there are N antennas in the array, then only up to N-

1 spatially independent interference signals can be rejected [54]. According to [56] an N

element array can steer up to N-1 spatial nulls. Novatel’s GPS Anti-jamming Technology

(GAJT) [57] which is the commercial name of their null steering antenna is an example

of a null steering. It is a seven element controlled reception pattern antenna (CRPA) that

can create up to six nulls in case of jammers. Null steering has been implemented

commercially such as the GAJT [57] mainly due to its lower complexity compared with

beamforming. For example if an M channel L1 receiver ideally has an M beam adaptive

beamformer associated with it; M beams are required for L1. Contrastingly, a null

steering configuration would only require one output for L1.

41

2.9.2.2 Beamforming

Beamforming on the other hand, enhances signal reception by directing beams towards

desired signals. The desired antenna outputs are weighted using different sets of complex

beamforming coefficients. In the case of GPS, multiple beams are required; one for every

satellite. The presence of individual beams that are formed for each satellite as shown in

Figure 2-19, maximizes the SNR. A factor of N improvement is achieved compared to

the SNR that is gained in a non-interference environment when applying the null steering

approach, where N is the number of array elements [55]. Maximizing the power of the

beam achieved by beamforming will also utilize the available degrees of freedom to

shape the spatial null and minimize GPS signal cancellation. Therefore, the probability

that GPS signals will be preserved increases. It is a known disadvantage of null steering

that there will be a probable reduction in the received GPS signal’s energy level and

especially if the signal’s Direction of arrival (DoA) is close to the interferer’s DoA [58].

42

Figure 2-18: A generic nulling antenna [56]

It is desirable that the direction of the satellite be known either through DoA

estimation or from the receiver’s solution. It has been reported that null steering does not

require any prior knowledge of the DoA of the satellite signals [54], although knowledge

of the DoA of the interference source remains a requirement. The advantages gained from

beamforming come at the cost of a more complex receiver that is not yet mainstream and

available to the market. As reported by [59] it could be in the market soon given the

current advances in antenna minimization. A common disadvantage of both methods is

when the GPS signal direction is in line with the interference signal. Consequently,

rejecting such interference will also block the signal from that satellite.

RF Downconversion

A/D

Receiver channel conditionnning


RF Downconversion

Weight Computation

A/D Receiver channel conditionnning

RF Downconversion A/D

Output to receiver

“1”

43

Figure 2-19: Multiple output beamformer [56]

2.10 DoA Estimation of Jamming Signals

This section deals with the application of array processing for the DoA estimation

of the jamming signals. As previously mentioned, whether nullsteering or beamforming

are chosen, the DoA estimates are essential to complete the function of either one. As

such, light must be shed on array processing and DoA estimation techniques. A thorough

review of array processing data model can be found in [11,60,61,62,2] and a quick

summary is given in the following section.

RF Downconversion

A/D



RF Downconversion

Weight Computation

A/D Receiver channel conditionnning

RF Downconversion A/D

“1”

Beam 1

Beam 2

Beam M

Unique Weights For Each Beam

44

2.10.1 Array Data Model

The following data model is based on an example that assumes the presence of S

electromagnetic far-field sources (GPS satellites) of directions 𝚯 where 𝚯 =

[𝜃1, 𝜃2 … , 𝜃𝑆] and 𝜃𝑘 is the angle of arrival of the signal corresponding to 𝑘𝑡ℎ source

such that 𝑘 = 1,2, … , 𝑆 .The satellite signals impinge on an array of 𝑀 GPS antennas

equally separated by distance 𝑑 as shown in Figure 2-20, for simplicity of the diagram;

only the signal from one satellite is displayed.

Figure 2-20: Different arrival times of satellite signals impinging on ULA

The signal received by the 𝑙th antenna at time t, is expressed in the discrete time matrix

notation. Time is referred to by sample number (𝑛) where 𝑛 = 0 is the first sample and

= 0 ,1 … . 𝑇 , where 𝑇 is the entire sampling period. The sampled received signal is

modelled as shown in Eq. 2-5 and is simplified in Eq. 2-6 and Eq. 2-7

. . . .

45

[

𝑦0[𝑛]

𝑦1[𝑛]⋮

𝑦𝑀−1[𝑛]

] = [

𝑎0(𝜃0) 𝑎0(𝜃1) … 𝑎0(𝜃𝑆−1)

𝑎1(𝜃0) ⋱ 𝑎1(𝜃𝑆−1)⋮

𝑎𝑀−1(𝜃0)…

⋮𝑎𝑀−1(𝜃𝑆−1)

] [

𝑠0[𝑛]

𝑠1[𝑛]⋮

𝑠𝑀−1[𝑛]

] + [

𝑒0[𝑛]

𝑒1[𝑛]⋮

𝑒𝑁−1[𝑛]

] Eq. 2-5

𝑦𝑛 = [𝒂(𝜃0) 𝒂(𝜃1) . . . 𝒂(𝜃𝑆−1)] 𝐬𝒏 + 𝐞𝒏 = 𝐀𝐬𝒏 + 𝐞𝒏 Eq. 2-6

𝒚𝒏 = 𝐀(𝚯)𝒔𝒏 + 𝒆𝒏 Eq. 2-7

where 𝑙 = 0 … 𝑀 − 1, 𝑦𝑙[𝑛] is the discrete time received signal at sample 𝑛 for

antenna𝑙, the 𝑆 × 𝑀 matrix 𝐀(𝚯) is called the steering matrix (array response matrix)

where every column corresponds to the steering vector of the signal 𝑠𝑘(𝑡) (a GPS

satellite signal). The vector 𝒆𝒏 represents the uncorrelated noise present at each antenna

element. 𝒚𝒏 , 𝒔𝒏 and 𝒆𝒏 are 𝑀 × 1 vectors where 𝒆𝒏 is considered as zero mean

spatially white noise (i.e. the additive noise is uncorrelated in both time and space

domain) whose variance is σ2 present at the 𝑙𝑡ℎ antenna at time t. The propagation delay

across the array associated with the 𝑘𝑡ℎ source and the 𝑙𝑡ℎ antenna is τl(θk). No delay is

measured at the reference element (τ0(θk) = 0) and the measured delay is maximum at

the last element of the array as shown in Eq. 2-8.

Calculation of the spatial covariance matrix of the input 𝒚𝒏 is a necessary step for DoA

estimation. As per Eq. 2-9 , 𝑹𝒚𝒚 is the spatial covariance matrix where 𝐸[ ] represents the

expectation and 𝒚𝒏𝑯 is the Hermitian (complex conjugate) transpose of 𝒚𝒏.

τM−1(𝜃𝑘) = 𝑀 − 1 × τ1(θk) Eq. 2-8

𝑹𝒚𝒚 = 𝑬 [𝒚𝒏 𝒚𝒏𝑯] Eq. 2-9

46

DoA estimation is a very mature field that affects many communication systems,

as such, a lot of progress has been established. For this reason the following classification

of DoA estimation techniques will be made. The two different categories consist of

conventional DoA estimation and high resolution DoA estimation methods. The former

includes the classical beamforming method and Capon’s beamforming method while the

latter encompasses the Multiple Signal Classification (MUSIC) method along with its

many variants and the Estimation of Signal Parameters via Rotational Invariance

Technique (ESPRIT) which has also generated many variations.

2.10.2 Conventional Beamforming

The conventional beamforming method (CBF) is also known as the delay-and-

sum beamformer and also as the Bartlett method and the Classical method. It is based on

searching the region of interest (angle wise) usually in discrete steps. Once a certain

direction produces the largest output power, then it is estimated that the desired signal is

in that direction. As the direction 𝜃 is varied incrementally across the space of access, the

array response vector 𝐀(𝚯) is calculated and the output power of the beamformer is

measured as per Eq. 2-10

This quantity is also referred to as the spatial spectrum and the estimate of the true DoA

is the angle 𝜃 that corresponds to the peak value of the output power spectrum. The

method is also referred to as Fourier method since it is a natural extension of the classical

Fourier based spectral analysis with different window functions [11]. Unfortunately, the

𝑃𝐶𝑙𝑎𝑠𝑠𝑖𝑐𝑎𝑙(𝜃) =𝐀𝑯(𝚯)𝑅𝒚𝒚𝐀(𝚯)

𝐀𝑯(𝚯)𝐀(𝚯) Eq. 2-10

47

spatial spectrum has a resolution threshold, an array with only a few elements is not able

to form neither narrow nor sharp peaks and thus has a limited ability to resolve closely

spaced signals sources [12] as shown in the comparison in Figure 2-21.

2.10.3 Capon’s Beamformer

Capon’s Beamformer is also known as the Minimum Variance Distortionless

Response (MVDR). The Capon method is an attempt to solve the problem of the poor

resolution that comes with the delay-and-sum method and it results in a significant

improvement [13]. In this method, the output power is minimized with the constraint that

the gain in the desired direction remains unity. Solving this constraint optimization

problem for the weight vector [11] we obtain Eq. 2-11 which is used to obtain the

Capon’s Spatial Spectrum [63] in Eq. 2-12 :

where 𝑅𝒚𝒚−1 is the inverse of the spatial covariance matrix 𝑅𝒚𝒚. The MVDR method

requires an extra matrix inversion but if compared to the CBF, it shows greater resolution

in a majority of the cases. The disadvantages of the MVDR method are the expensive

computations of 𝑅𝒚𝒚 and its failure to locate highly correlated (coherent) source signals

[14]. Figure 2-21 shows a comparison between the Classical and the MVDR

beamformers, it is evident that MVDR confirms the claims that it has higher resolution.

This simulation was conducted with three sources situated at -13,-5, and 40 degrees

𝑤 =𝑅𝒚𝒚

−1𝐀(𝚯)

𝐀𝑯(𝚯)𝑅𝒚𝒚−1𝐀(𝚯)

Eq. 2-11

𝑃𝐶𝑎𝑝𝑜𝑛 = 𝑤𝐻𝑅𝒚𝒚𝑤 =1

𝐀𝑯(𝚯)𝑅𝒚𝒚−1𝐀(𝚯)

Eq. 2-12

48

respectively, noise variance is 1 and the antenna array is a 10 element ULA with

separation of λ/2 where λ is the wavelength of the received signal.

Figure 2-21: Comparison of Classical and MVDR Beamformers with an 8 degree separation

2.10.4 DoA Estimation Using Subspace Techniques

In this section DoA estimators that exploit the signal subspace are explained.

These DoA estimators possess high-resolution estimation capabilities and are also called

high resolution and super resolution DoA estimation techniques. Signal subspace

methods originated in spectral estimation research [64]; where they estimate the

autocovariance of a model that incorporates signal with additive noise. A matrix whose

Eigen structure gives rise to the signal and noise subspaces is generated from the model.

Similarly, this method can be used in DoA estimation of jammers by processing the

spatial covariance matrix as shown in Figure 2-22

49

Figure 2-22 : Eigen decomposition of antenna array signals for jamming detection and DoA

estimation [60]

2.10.5 Multiple Signal Classification (MUSIC)

MUSIC was developed by Schmidt in 1986 [15]. It was shown in details in [60]

that the signal subspace is where the steering vectors corresponding to the incoming

signals are. It was also shown that they are orthogonal to the noise subspace. So, in order

to estimate the DoAs, a search could be conducted through all the possible steering

vectors so that the ones that are orthogonal to the noise subspace are found. If 𝑎(𝜃) is the

steering vector corresponding to one of the incoming signals from the direction 𝜃 and

𝑎𝐻(𝜃) is its conjugate transpose, thus 𝑎𝐻(𝜃)𝑸𝑛 = 0, where 𝑸𝑛 is the noise subspace. In

real life scenarios, 𝑎(𝜃) will not be completely orthogonal to the noise subspace due to

errors in estimating 𝑸𝑛. Eq. 2-13 is referred to as the MUSIC spectrum.

Constructing the Covariance

Matrix

Eigen Decomposition and

Subspace Formation

w0

w1

wM-1

( − 1)

Weight update

Jamming Detection

DoA Estimation

𝑃𝑀𝑈𝑆𝐼𝐶(𝜃) =1

𝐀𝑯(𝚯)𝑸𝑛𝑸𝑛𝐻𝐀(𝚯)

Eq. 2-13

50

The MUSIC spectrum will produce a large value when θ is equal to the DoA of one of

the signals. The MUSIC method is known for outperforming conventional methods,

additionally, it can be used with a variety of array geometries. Figure 2-23 compares

MUSIC to the previously mentioned methods taking into consideration the same

simulation settings used in Figure 2-21.

Figure 2-23: Comparison between MUSIC, MVDR and the classical beamformer with

closely spaced sources

It is clear from Figure 2-23 that MUSIC is the only method that has estimated the

presence of three sources with exceptional DoA estimation for the closely spaced

sources, as the simulation shows that the two close sources are located at −13 and −5.1

degrees

2.10.5.1 Spatial Smoothing

Among the disadvantages of MUSIC is that it is not able to identify DoAs of

correlated signals and is computationally expensive as it requires a search over the

51

function PMUSIC for the peaks. A solution for this problem is found in [16]. It is a

technique named “Spatial Smoothing” it can be introduced to overcome this problem. In

fact, spatial smoothing is essential in a multipath propagation environment and to apply

this technique; the array must be divided up into smaller subarrays. The possibility of

overlapping the subarrays can be considered. By averaging the spatial covariance matrix

of each subarray, one single spatially smoothed covariance matrix can be formed, and is

subsequently introduced to the MUSIC algorithm.

2.10.6 Search-Free DoA Estimation Techniques

Other subspace-based DoA estimation methods that avoid any spectral search,

whose computational complexity is often lower than that of the spectral MUSIC

algorithm have been proposed, which provide a significantly improved performance as

compared to the traditional spectral MUSIC algorithm. Among the most popular

algorithms are root-MUSIC [17], [18] and ESPRIT. However, root-MUSIC and ESPRIT

can be applied only in the case of specific array geometries. In particular, root-MUSIC is

applicable only if the sensors are located on a uniform grid, whereas ESPRIT requires

that the array consists of two identical and identically oriented subarrays.

2.10.7 Root MUSIC

The root MUSIC algorithm was proposed by Barabell, unfortunately, it is only

applicable for Uniform Linear Arrays (ULA). He has shown in [17] that the root MUSIC

algorithm provides improved resolution relative to the ordinary MUSIC method

discussed in section 2.10.5 especially at low SNRs where MUSIC does not perform well.

In root MUSIC, by recalling 𝑃𝑀𝑈𝑆𝐼𝐶(𝜃) =1

𝑎𝐻(𝜃)𝑸𝑛𝑸𝑛𝐻𝑎(𝜃)

and computing 𝑃𝑀𝑈𝑆𝐼𝐶(𝜃)−1

52

and with a short mathematical derivation [60], the polynomial with is the equivalent to

𝑃𝑀𝑈𝑆𝐼𝐶(𝜃)−1 is evaluated on the unit circle. Since the MUSIC spectrum will have 𝑟

peaks, then 𝑃𝑀𝑈𝑆𝐼𝐶(𝜃)−1 will have 𝑟 valleys and thus the denominator will have 𝑟 zeros

on the unit circle. The remaining zeros of thus the denominator will be located away from

the unit circle. The authors of [12] showed that in the absence of noise, thus the

denominator will have roots that are located precisely on the unit circle, but unlike in the

presence of noise; the roots will be located close to the unit circle. The root MUSIC

algorithm reduces the complexity of the estimation process of the DoAs to finding the

roots of a (2𝑀 + 1) order polynomial where M is the number of array elements.

2.10.8 Estimation of Signal Parameters via Rotational Invariance Technique

(ESPRIT)

ESPRIT algorithm was proposed by [18], it is computationally efficient and more

robust if compared to MUSIC as it does not search the entire spectrum. ESPRIT is based

on separating the ULA of M sensors into two identical subarrays consisting of the same

number of sensors. Figure 2-24 shows what is defined as a doublet, it is a matched pair

of sensors with identical displacement ,it should be noted that the number of doublets 𝑚

has a varying range from M/2 in case of non-overlapping as shown in Figure 2-24 to

M-1 in case of fully overlapping as in Figure 2-25. The latter does not necessitate the

presence of two separate arrays. For instance, a ULA consisting of four identical

elements with constant inter-element spacing 𝑑 can be considered as two arrays of three

matched pairs, the first subarray would be made up of the first three elements and the

second would be made up of the last three elements in a manner that the first and the

second elements would form the first pair, the second and the third elements would form

53

the second pair; and the third and the fourth elements would form the third and final pair.

This would be a case of M-1 doublets where the two subarrays are displaced by the

distance d.

Figure 2-24: The doublets between the two subarrays X and Y, non-overlapping subarrays

Figure 2-25: The doublets between the two subarrays X and Y, overlapping subarrays

ESPRIT exploits that the two subarrays are rotationally invariant and employs the

configuration shown in in Figure 2-24 to model the output of the array [11]. Assuming

that the signals induced on the 𝑙𝑡ℎ pair due to a narrowband source in the direction 𝜃 be

denoted by 𝑥𝑚(𝑡) and 𝑦𝑚(𝑡) ; also assuming the phase difference between these two

signals depends on the time travelled by the plane wave from one element of the doublet

to the other given that the distance between the two elements is Δ0 (measured in

wavelengths), Eq. 2-14 is obtained as follows.

𝑦𝑙(𝑡) = 𝑥𝑙(𝑡)𝑒𝑗2𝜋∆0𝑐𝑜𝑠𝜃 Eq. 2-14

54

Note that Δ0 is the magnitude of the displacement vector that sets the reference direction;

and that all angles are measured with reference to this vector. 𝑥(𝑡) and 𝑦(𝑡) are the

signals received by the two 𝐾 element subarrays, as shown below in Eq. 2-15 and

Eq. 2-16

where A is a 𝐾 × 𝑀 matrix whose columns denote the M steering vectors corresponding

to M directional sources associated with the first subarray, 𝚽 is an 𝑀 × 𝑀 diagonal

matrix with its 𝑚𝑡ℎdiagonal element given by Eq. 2-17

and 𝑠(𝑡) denotes M satellite signals induced on a reference element, and 𝒏𝑥(𝑡) and 𝒏𝑦(𝑡)

denote the noise induced on the elements of the two subarrays. By Comparing both the

𝒙(𝑡) and 𝒚(𝑡) equations, the steering vectors corresponding to the M directional sources

associated with the second subarray are given by A𝚽. Let 𝑈𝑥 and 𝑈𝑦 denote two 𝐾 × 𝑀

matrices whose columns represent M eigenvectors corresponding to the largest

eigenvalues of the two array correlation matrices 𝑅𝑥𝑥 and 𝑅𝑦𝑦 respectively. As these two

sets of eigenvectors span the same M-dimensional signal space, as a consequence the two

matrices 𝑈𝑥 and 𝑈𝑦 are related by a unique nonsingular transformation matrix 𝜓, that

is 𝑈𝑥𝜓 = 𝑈𝑦. Similarly, 𝑈𝑥 and 𝑈𝑦 are related to the steering vector matrices 𝐴 and A𝚽

by another unique nonsingular transformation matrix T since the same signal subspace is

𝒙(𝑡) = 𝐴𝑠(𝑡) + 𝑛𝑥(𝑡) Eq. 2-15

𝒚(𝑡) = 𝐴Φ𝑠(𝑡) + 𝑛𝑦(𝑡) Eq. 2-16

𝚽𝑚,𝑚 = 𝑒𝑗2𝜋∆0𝑐𝑜𝑠𝜃𝑚 Eq. 2-17

55

spanned by 𝑈𝑥 = 𝐴𝑇 and 𝑈𝑦 = 𝐴𝚽𝑇. By substituting for 𝑈𝑥 and 𝑈𝑦 and given that 𝐴 is

a full rank matrix, we obtain Eq. 2-18 as shown below.

According to this equation, the eigenvalues of 𝜓 are equal to the diagonal elements of Φ,

and the columns of the matrix T are eigenvectors of 𝜓. This is the core relationship in the

development of the ESPRIT algorithm [18]. It requires an estimate of 𝜓 from the

measurement x(t) and y(t). Moreover, an Eigen decomposition of 𝜓 will provide its

eigenvalues, and by equating them to Φ we get the DoA estimates with 𝑙 = 1, … , 𝑀 as

shown in Eq. 2-19

Many versions of the ESPRIT algorithm were developed by relying on different means of

estimating 𝜓 from the array signal measurements [19] [18].

𝑇𝜓𝑇−1 = 𝚽 Eq. 2-18

𝜃𝑚 = cos−1 {𝐴𝑟𝑔(𝜆𝑚)

2𝜋Δ0} Eq. 2-19

56

Chapter 3

Enhanced GPS Narrowband Jamming Detection Using

High Resolution Spectral Estimation

3.1 Introduction

As discussed in the previous chapter, GPS interference and jamming have a damaging

effect on the proper operation of GPS receivers. Interference signals within the GPS C/A-

code bandwidth are named narrowband interference [40]. There exists a multitude of

solutions that were proposed in order to confront the challenge of accurate positioning in

the presence of RFI and jamming. The initial requirement that enables solving the

problem of jamming is to successfully and effectively detect the presence of the

malicious signal. Interference detection is essential to allow the receiver to activate the

suitable interference suppression methods. Unfortunately, the application of incorrect

interference suppression techniques will not provide anticipated enhancements. Once the

interference has been detected and characterized, an appropriate interference mitigation

algorithm could be applied by the receiver.

Not only does the detection of interferers determine which interference suppression

technique will be utilized; it can also be used to enhance the acquisition process by

making it more robust. The knowledge of the type of jammer, for example whether it is

fixed or swept, enables the improvement of the receiver operating characteristic (ROC)

results when determining a searching algorithm in system-level acquisition or in the cell-

level. [8]

57

3.2 Continuous Wave Interference:

Continuous Wave (CW) signals are one of the most common interference types; they can

be approximated as pure sinusoids. Undeniably, the majority of electronic devices and

communication systems generate CW signals that can be responsible for producing

harmonics in the GNSS bands. For example, CW signals are inadvertently transmitted by

television ground stations in the GPS L1 frequency band [7] causing unintentional

interference. Therefore, CWs constitute a very common type of interference. The spectral

and temporal characteristics of a CW can be summarized as follows. In the time domain,

they can be approximated as pure sinusoids, meanwhile, in the frequency domain; their

spectrum is concentrated around certain frequencies [7]. Consequently, the bandwidth

occupied by CWs is considered narrow, and the signals are narrowband, such as AM or

FM [65]. In Figure 3-1, a single frequency CW jammer is demonstrated.

Figure 3-1: Spectrum describing CW interference [36]

3.2.1 Out -of -Band Signals

In the conversion of an analog signal to the digital domain, the frequency content

becomes limited to between zero and half the sampling frequency (namely, the Nyquist

sampling criterion). Consequently, all signals located outside the sampling range will be

folded into the sampled signal, thus increasing the noise; this is demonstrated in

Figure 3-2. An ideal band-pass filter would have a pass-band before and after which all

Freq.

Band of

interest

Interference Amplitude

fc

58

frequencies are completely rejected, unfortunately, all filters have a certain amount of roll

off band in which considerable increases in attenuation are achieved. The presence of

powerful signals located outside the band of interest but very close to its edges can be

unsafe and cause these signals to creep into the desired band. If the utilized filters are not

sharp enough to block the unwanted signals; the effect of the out of band interference will

be the similar to that of an in band signal with an equivalent received power.

Out of band RFI can be generated by powerful transmitters such as television

broadcasting stations which transmit very high power signals. The creation of relatively

low power harmonics that act as out of band interferences is attributed to flaws in filter

design. Difficulties arise due to the fact that 60dB attenuation might be insufficient if the

transmitter broadcasts at power of 1MW. Therefore, the 60dB attenuation would cause a

transmission of a relatively powerful 1W interferer [36].

Figure 3-2: Out of band signal being falsely considered as an in band signal [36].

Amplitude

Amplitude

Freq. Freq.

Freq. Freq.

Amplitude

Sampling

59

3.2.2 Impacts of CW Interference

Due to its low power when received on earth, the GPS signal is susceptible to jamming

over long distances. Brown et al. examined the effects inflicted upon the GPS acquisition

in a GPS receiver due to a single CW jammer generating a 4-Watt signal [66]. As shown

in Figure 3-3, the results demonstrated that the jammer power was detected at more than

2 kilometers away, C/A-code acquisition was lost at 1.4 km from the jammer; and GPS

tracking was compromised when the jammer was within 1 km of the receiver. They

concluded that airborne users were more affected by a ground-based jammer than the

civilians who were on the ground because they had a direct line-of-sight (LOS) to the

jammer for distances of up to 145 km.

Figure 3-3: Effective range of a 4 Watt GPS jamming device [66]

Figure 3-4 and Figure 3-5 illustrate the distribution of a CW signal and depict how the

gradual increase of the CW jammer’s power affects the distribution of the combined GPS

1 km

1.4 km

2.1 km

Tracking is lost

Acquisition is lost

Jamming power is

detected

60

plus jamming signal and systematically transforms it until it is similar to that of the CW

jammer.

Figure 3-4: Distribution of a CW signal

Figure 3-5 Histogram of a GPS L1 signal before and after being subjected to moderate and

high power CW jamming.

-250 -200 -150 -100 -50 0 50 100 150 200 2500

2

4

6

8

10

12x 10

4

Amplitude of the signal x(t)

Distribution of a high power CW signalP

robabili

ty D

ensity F

untion

-100 -80 -60 -40 -20 0 20 40 60 80 1000

0.5

1

1.5

2

2.5x 10

4

-300 -200 -100 0 100 200 3000

0.5

1

1.5

2

2.5x 10

4

-80 -60 -40 -20 0 20 40 60 800

5

10

15x 10

4

No jamming JSR =5 dB JSR = 20dB

-250 -200 -150 -100 -50 0 50 100 150 200 2500

2

4

6

8

10

12x 10

4


Distribution of a high power CW signal

Pro

babili

ty D

ensity

Funtio

n

-250 -200 -150 -100 -50 0 50 100 150 200 2500

2

4

6

8

10

12x 10

4



Pro

babi

lity

Den

sity

Fun

tion

-250 -200 -150 -100 -50 0 50 100 150 200 2500

2

4

6

8

10

12x 10

4



Pro

babi

lity

Den

sity

Fun

tion

61

3.2.3 Related Work

CW Interference can harm the operation of several blocks and parameters of a GPS

receiver. This effect is witnessed on synchronization and acquisition steps, pseudorange

measurements and positioning solutions [1,7,8]

It has been proven that CW interference affects the GPS C/A code signal in a manner that

is mostly visible in the characteristics of the frequency spectrum of the signal [28].

Additionally, in [48] Deshapande has demonstrated that CW interference is responsible

for more impairment of the acquisition process unlike AM/FM interference sources. He

concluded that it distorts the signal spectrum and affects the carrier tracking loop. A

tracking loop will lock onto the frequency of a single tone interference signal given that

the CW power level is significantly high. Therefore, inaccurate carrier phase and Doppler

measurements will be generated. The location of the CW interference relative to the L1

center frequency is also important; if the jammer is sufficiently close to the L1 center

frequency, it is assumed that degradation in the carrier to noise ratio(C/ N0) is fast,

mainly due to the correlation process. A CW interferer whose center frequency was

closest to the L1 frequency repeatedly caused false lock [9]. A commonly used method

for the excision of CW signals is the notch filter (NF). In [65], Montloin demonstrated

that CW removal using NFs introduced an average position error of several tens of

centimeters; it was found that linear phase FIR notch filters were more accurate than

Infinite Impulse Response IIR filters.

A detection algorithm based on notch frequency estimation and interference signals

discrimination method based on AGC input histogram were proposed in [8]. Early efforts

to detect CW jamming for GPS applications were conducted in [49] . Detection metrics

62

have been tested when CW jamming was applied. Such metrics can be obtained in the

post-processing stage of the receiver, for instance correlator output power, carrier phase

indecision and the measured variation in correlator output power. These metrics were

recommended as test statistics to monitor the operational integrity of the GPS receiver

[8]. Additionally, AGC, ADC, and antenna based techniques are utilized in the pre-

processing stage of the receiver to detect RFI [67].

Narrowband CW interference affects the acquisition process of the GNSS receiver. The

study of those effects lead to the development of a descriptive statistical model. The

author presented theoretical results of probability of detection and false-alarm of a GNSS

receiver when CW interference was existent [68]. Additionally, [8] proposed a low

complexity solution that enhances the receiver performance in terms of quantization and

acquisition metrics and contributes to the improvement of consumer-grade GPS receivers

in terms of robustness to interference. Also, an adaptive FIR notch filter based on least

mean squares is proposed and implemented to adaptively detect, locate and mitigate

narrowband interferences. Z. Jiang proposed an algorithm that relied on spectral analysis

to mitigate high power interference [10]. It was concluded that a fixed detection

threshold, as implied in previous studies is insufficient. Therefore, an adaptive detection

threshold that is a function of the standard deviation of the normalized spectrum and the

correlators’ power output was suggested. Related to the same field of detection metrics,

the combination of the AGC levels and the correlators’ output power was exploited to

detect and characterize the RFI but the difference is that the receiver simply relied on a

standard correlator [67].

63

3.3 Proposed Method

Recognizing the importance of CW jamming and understanding the damage it can

cause, an accurate method for the detection and frequency estimation of single and

multiple simultaneous CW jamming signals using high resolution spectral estimation is

proposed. The spectral variant of FOS is presented to improve the detection and

frequency estimation of jammers obtained from FFT. Figure 3-6 depicts the proposed

jamming detection method, after obtaining a digitized signal from the front-end, the

proposed method is applied to the received signal and if a single or multiple jammers is

included in the signal, it is recognized. The method operates in the pre-correlation section

of the receiver.

Figure 3-6: Proposed jamming detection method applied in the pre-correlation stage of the

receiver

Radio Frequenc Frontend

Local

Oscillator

Signal Processing

-

64

3.4 Jammer Detection

This section introduces a new high resolution technique capable of detecting single and

multiple CW jamming signals and accurately estimating their frequencies. The proposed

technique is highly efficient compared to FFT which is widely adopted as a spectral

estimation method for jammer detection. Figure 3-7 demonstrates how a relatively small

window size (1ms) can lead to failure in the accurate estimation of the jamming signal

which is located at 10.2 kHz. FFT would only able to either detect the jammer at 10 or at

11 kHz as shown. The jammer was detected at 10 kHz due to the higher magnitude at that

frequency.

Figure 3-7 Estimated jammer frequency due to FFT (window size = 1 ms)

The proposed method is based on a general purpose modelling technique called FOS.

Several techniques have been proposed for pre-correlation jamming detection [69,70,71].

An Eigenvalue-based jamming detection method is proposed in [69]. This method

provided jamming detection of narrowband as well as wideband signals provided that the

baseband complex signals are sampled at a suitable sampling rate. In [70] jamming

detection is achieved using statistical testing that is based on Short Time Fourier

Transform (STFT) of the received signals. Similarly, time filtering was employed to

detect jammers in [71] followed by a transformation of the signal to the frequency

9.4 9.6 9.8 10 10.2 10.4 10.6 10.8 11 11.20

5

10

window time=0.001sec Window offset of 1 MAX TTA = 3 JSRdB

=0 msethresh=1e-06

Ma

gn

itu

de

Frequency (KHz)

FFT

Jammer

9.4 9.6 9.8 10 10.2 10.4 10.6 10.8 11 11.20

5

10


=0 msethresh=1e-06

Ma

gn

itu

de

Frequency (KHz)

FOS

FFT

9.4 9.6 9.8 10 10.2 10.4 10.6 10.8 11 11.20

5

10


=0 msethresh=1e-06

Ma

gn

itu

de

Frequency (KHz)

FOS

FFT

9.4 9.6 9.8 10 10.2 10.4 10.6 10.8 11 11.20

5

10


=0 msethresh=1e-06

Ma

gn

itu

de

Frequency (KHz)

FOS

FFT

9.4 9.6 9.8 10 10.2 10.4 10.6 10.8 11 11.20

5

10


=0 msethresh=1e-06

Ma

gn

itu

de

Frequency (KHz)

FOS

FFT

9.4 9.6 9.8 10 10.2 10.4 10.6 10.8 11 11.20

5

10


=0 msethresh=1e-06

Ma

gn

itu

de

Frequency (KHz)

FOS

FFT

9.4 9.6 9.8 10 10.2 10.4 10.6 10.8 11 11.20

5

10


=0 msethresh=1e-06

Ma

gn

itu

de

Frequency (KHz)

FOS

FFT

9.4 9.6 9.8 10 10.2 10.4 10.6 10.8 11 11.20

5

10


=0 msethresh=1e-06

Ma

gn

itu

de

Frequency (KHz)

FOS

FFT

9.4 9.6 9.8 10 10.2 10.4 10.6 10.8 11 11.20

5

10


=0 msethresh=1e-06

Ma

gn

itu

de

Frequency (KHz)

FOS

FFT

Estimated

frequency

Frequency (kHz)

65

domain by means of FFT. Generally, numerous jamming detection methods depend on

spectral analysis methods such as FFT to estimate the frequency content of the signal.

The basic principle of the FFT-based RFI detection is to identify the frequency and

amplitude of the interfering source [72,73]. This technique is limited by FFT spectral

resolution given by:

where f𝑠 is the sampling frequency and 𝑁𝑠 is the number of points in the record. Subject

to the SNR, it has been shown that FOS can achieve frequency resolutions up to 10 times

the frequency resolution of the FFT [74]. From Eq. 3-1, one can conclude that a long

record length yields improved spectral resolution, which is needed to accurately model a

time-series. This imposes a limitation on the FFT resolution; therefore relatively long

data records are required to achieve adequate detection of jamming sources. This results

in potential inaccuracies in the spectral estimation of the CW jammers’ frequencies. This

spectral estimate can degrade significantly in the presence of multiple CW jammers with

contiguous frequencies as clearly shown in Figure 3-8, where FFT will only detect one

jammer at 10 kHz although three jamming signals were applied to the received signal.

Figure 3-8 FFT detection of multiple simultaneous CW jammers

FFT Resolution = f𝑠/𝑁𝑠 Eq. 3-1

9.2 9.4 9.6 9.8 10 10.2 10.4 10.6 10.8 11 11.20

50

100


=3 msethresh=1e-05

Mag

nit

ud

e

Frequency (KHz)

FFT

FOS

9.2 9.4 9.6 9.8 10 10.2 10.4 10.6 10.8 11 11.20

50

100

150


=6 msethresh=1e-05

Mag

nit

ud

e

Frequency (KHz)

FFT

FOS

9.2 9.4 9.6 9.8 10 10.2 10.4 10.6 10.8 11 11.20

100

200


=9 msethresh=1e-05

Mag

nit

ud

e

Frequency (KHz)

FFT

FOS

9.2 9.4 9.6 9.8 10 10.2 10.4 10.6 10.8 11 11.20

100

200

300


=12 msethresh=1e-05

Mag

nit

ud

e

Frequency (KHz)

FFT

FOS

9.2 9.4 9.6 9.8 10 10.2 10.4 10.6 10.8 11 11.20

100

200

300


=15 msethresh=1e-05

Mag

nit

ud

e

Frequency (KHz)

FFT

FOS

9.2 9.4 9.6 9.8 10 10.2 10.4 10.6 10.8 11 11.20

200

400


=18 msethresh=1e-05

Mag

nit

ud

e

Frequency (KHz)

FFT

FOS

9.2 9.4 9.6 9.8 10 10.2 10.4 10.6 10.8 11 11.20

200

400

600


=21 msethresh=1e-05

Mag

nit

ud

e

Frequency (KHz)

FFT

FOS

9.2 9.4 9.6 9.8 10 10.2 10.4 10.6 10.8 11 11.20

200

400


=24 msethresh=1e-05

Mag

nit

ud

e

Frequency (KHz)

FFT

FOS

9.2 9.4 9.6 9.8 10 10.2 10.4 10.6 10.8 11 11.20

200

400

600


=27 msethresh=1e-05

Mag

nit

ud

e

Frequency (KHz)

FFT

Jammers

9.2 9.4 9.6 9.8 10 10.2 10.4 10.6 10.8 11 11.20

500

1000


=30 msethresh=1e-05

Mag

nit

ud

eFrequency (KHz)

FFT

FOS

9.4 9.6 9.8 10 10.2 10.4 10.6 10.8 11 11.20

5

10


=0 msethresh=1e-06

Ma

gn

itu

de

Frequency (KHz)

FFT

Jammer

9.4 9.6 9.8 10 10.2 10.4 10.6 10.8 11 11.20

5

10


=0 msethresh=1e-06

Ma

gn

itu

de

Frequency (KHz)

FOS

FFT

9.4 9.6 9.8 10 10.2 10.4 10.6 10.8 11 11.20

5

10


=0 msethresh=1e-06

Ma

gn

itu

de

Frequency (KHz)

FOS

FFT

9.4 9.6 9.8 10 10.2 10.4 10.6 10.8 11 11.20

5

10


=0 msethresh=1e-06

Ma

gn

itu

de

Frequency (KHz)

FOS

FFT

9.4 9.6 9.8 10 10.2 10.4 10.6 10.8 11 11.20

5

10


=0 msethresh=1e-06

Ma

gn

itu

de

Frequency (KHz)

FOS

FFT

9.4 9.6 9.8 10 10.2 10.4 10.6 10.8 11 11.20

5

10


=0 msethresh=1e-06

Ma

gn

itu

de

Frequency (KHz)

FOS

FFT

9.4 9.6 9.8 10 10.2 10.4 10.6 10.8 11 11.20

5

10


=0 msethresh=1e-06

Ma

gn

itu

de

Frequency (KHz)

FOS

FFT

9.4 9.6 9.8 10 10.2 10.4 10.6 10.8 11 11.20

5

10


=0 msethresh=1e-06

Ma

gn

itu

de

Frequency (KHz)

FOS

FFT

9.4 9.6 9.8 10 10.2 10.4 10.6 10.8 11 11.20

5

10


=0 msethresh=1e-06

Ma

gn

itu

de

Frequency (KHz)

FOS

FFT

Estimated

frequency

Frequency (kHz)

66

A solution for the detection of multiple CW jammers was proposed in [71] by cascading

a fixed number of filters to detect multiple jammers. A major limitation presents itself

when the number of jammers is higher than the number of cascaded filters. Furthermore,

the presence of multiple jammers with frequency separation less than FFT resolution has

not yet been addressed. Finally, having the ability to detect low power jammers (i.e., far

from the receiver and potentially approaching it) creates an opportunity for early jammer

warning and detection. Accordingly, the performance of jamming detection based on

spectral estimation can be significantly enhanced by using a robust spectral estimation

method that overcomes the limitations of FFT.

This chapter explores the application of an innovative high resolution spectral estimation

method to pre-correlation frequency based jamming detection. The new method is

introduced to extend the capabilities of pre-correlation detection by substantially

increasing its accuracy when dealing with single jammers; and by enabling the

simultaneous detection of multiple in-band CW jamming signals transmitted at close-by

frequencies.

3.4.1 Application of FOS to Spectral Estimation

FOS is a general purpose modelling technique that can be used for time series analysis

and frequency analysis [75] .It possesses features that can significantly enhance CW

jamming detection based on spectral estimation [76,77,75]. These features include the

remarkably high frequency resolution spectrum of FOS and its noise rejection capabilities

for white and colored noise.

67

FOS constructs a functional expansion of an input, namely 𝒚(𝑛) using an arbitrary set of

non-orthogonal candidate functions. The functional expansion of the input in terms of

the arbitrary candidate functions is given by:

𝒚(𝑛) = ∑ 𝑎𝑚 𝑝𝑚(𝑛) + 𝑒(𝑛)

𝑀

𝑚=0

Eq. 3-2

where 𝑎𝑚 are the weights of the functional expansion where 𝑚 = 0,1 … 𝑀 and 𝑒(𝑛) is

the modelling error. FFT produces a functional expansion of the input using a set of

complex sinusoidal functions that ensure an integer number of cycles in the record length

[78]. Thus, when FFT models a frequency that does not have an integer number of cycles

in the record length, energy is spread into all the other frequencies, which is a

phenomenon known as spectral leakage [79]. By using candidate functions that are non-

orthogonal, FOS is more likely to enable modeling of this frequency between two FFT

bins with a single term [77]. FOS calculations are based on a functional expansion using

orthogonal basis functions such that

𝒚(𝑛) = ∑ 𝑔𝑚𝑤𝑚(𝑛) + 𝜀(𝑛)

𝑀

𝑚=0

Eq. 3-3

where 𝑤𝑚(𝑛) is a set of orthogonal functions derived from the candidate functions

𝑝𝑚(𝑛), 𝑔𝑚is the weight, and 𝜀(𝑛) is an error term. The orthogonal functions are

obtained from the candidate functions 𝑝𝑚(𝑛)using the Gram Schmidt (GS)

orthogonalization algorithm. The GS algorithm relates the orthogonal functions to the

candidate functions through GS coefficients 𝛼𝑚𝑟 given by:

𝛼𝑚𝑟 =𝑝𝑚(𝑛)𝑤𝑟(𝑛)̅̅ ̅̅ ̅̅ ̅̅ ̅̅ ̅̅ ̅̅ ̅̅

𝑤𝑟2̅̅ ̅̅ ̅

Eq. 3-4

68

The GS coefficients mr and the orthogonal weights gm can be found recursively using

the equations [80]:

𝑤0(𝑛) = 𝑝0(𝑛) Eq. 3-5

𝐷𝑚0 = 𝑝𝑚(𝑛)𝑝0(𝑛)̅̅ ̅̅ ̅̅ ̅̅ ̅̅ ̅̅ ̅̅ ̅ Eq. 3-6

𝐷𝑚𝑜 = 𝑝𝑚(𝑛)𝑝𝑟(𝑛)̅̅ ̅̅ ̅̅ ̅̅ ̅̅ ̅̅ ̅̅ ̅ − ∑ 𝛼𝑟𝑖

𝑟−1

𝑖=0

𝐷𝑚𝑖 Eq. 3-7

𝛼𝑚𝑟 =𝑝𝑚(𝑛)𝑤𝑟(𝑛)̅̅ ̅̅ ̅̅ ̅̅ ̅̅ ̅̅ ̅̅ ̅̅

𝑤𝑟2̅̅ ̅̅ ̅

=𝐷𝑚𝑟

𝐷𝑟𝑟 Eq. 3-8

𝐶0 = y(𝑛)𝑝0(𝑛)̅̅ ̅̅ ̅̅ ̅̅ ̅̅ ̅̅ ̅ Eq. 3-9

𝐶𝑚 = y(𝑛)𝑝𝑚(𝑛)̅̅ ̅̅ ̅̅ ̅̅ ̅̅ ̅̅ ̅̅ − ∑ 𝛼𝑚𝑟

𝑚−1

𝑟=0

𝐶𝑟 Eq. 3-10

and

𝑔𝑚 =𝐶𝑚

𝐷𝑚𝑚 Eq. 3-11

Accordingly, FOS skips the point-by-point computation of 𝑤𝑚(𝑛) as it is implicitly

defined by the Gram-Schmidt coefficient 𝛼𝑚𝑟.

In its final stage, FOS recursively computes the original functional expansion’s weights,

𝑎𝑚 (Eq. 3-2), based on the weights of the orthogonal series expansion, 𝑔𝑚. The value of

𝑎𝑚 can be found recursively using

𝑎𝑚 = ∑ 𝑔𝑖

𝑀

𝑖=𝑚

𝑣𝑖 , 𝑣𝑚 = 1 Eq. 3-12

where,

69

𝑣𝑖 = − ∑ 𝛼𝑖𝑟

𝑖−1

𝑟=𝑚𝑣𝑟 𝑖 = 𝑚 + 1, 𝑚 + 2, … , 𝑀 Eq. 3-13

From the previous equations, it is observed that FOS requires the calculation of the

correlation between the candidate functions as shown in Eq. 3-6 and Eq. 3-7 and the

calculation of the correlation between the input and the candidate functions as shown in

Eq. 3-9 and 3-10. The correlation between the input and the candidate function

𝑦(𝑛)𝑝𝑚(𝑛)̅̅ ̅̅ ̅̅ ̅̅ ̅̅ ̅̅ ̅̅ ̅ is normally calculated point-by-point once at the start of the algorithm and

then stored for later quick retrieval.

The MSE of the orthogonal function expansion is demonstrated as [75]:

𝜀2̅̅ ̅ = 𝑦2(𝑛)̅̅ ̅̅ ̅̅ ̅̅ − ∑ 𝑔𝑚2

𝑀

𝑚=0𝑤𝑚

2(𝑛)̅̅ ̅̅ ̅̅ ̅̅ ̅̅ Eq. 3-14

Subsequently, the MSE reduction attributed to the 𝑚𝑡ℎ candidate function is given by:

𝑄𝑚 = 𝑔𝑚2𝑤𝑚

2(𝑛)̅̅ ̅̅ ̅̅ ̅̅ ̅̅ = 𝑔𝑚2𝐷𝑚𝑚 Eq. 3-15

FOS can fit a model with a small number of model terms; this is achieved by fitting terms

that minimize the mean squared error (MSE) in order of their significance. There are

three conditions that are responsible for stopping the search algorithm. If any of them

becomes true the search is halted. If a predefined maximum number of terms to be fitted

is reached, the search stops. In addition, if the ratio of MSE to the mean squared value of

the input signal is less than a pre-determined limit, the search is stopped. Finally, if the

addition of an extra term to the model would yield an MSE reduction that is not greater

than that expected if the current residual 𝜀(𝑛) were white Gaussian noise, the search will

stop. Spectral analysis with FOS is accomplished by selecting candidates 𝑝𝑚(𝑛)that are

70

pairs of sine and cosine terms at each of the frequencies of interest. The candidate

functions 𝑝𝑚(𝑛)are given by:

𝑝2𝑚(𝑛) = cos(𝜔𝑚𝑛)

𝑝2𝑚+1(𝑛) = sin (𝜔𝑚𝑛)

Eq. 3-16

Where = 1, … , 𝑃 , 𝜔𝑚 is the digital frequency of the candidate pair while 𝑃 is the number

of candidate pairs. When a sinusoidal pair (sine and cosine pair) is fitted at each

candidate frequency, the magnitude and phase at that candidate frequency is computed

[81]. Two noteworthy differences exist between FOS and conventional Fourier transform

techniques (i.e. discrete Fourier transform (DFT) or FFT) [74,77,80]. The first difference

is that FOS produces a sinusoidal series representation that is more efficient and frugal

(selects fewer components) by choosing the most significant sinusoidal components first.

Meanwhile, the second difference is that the frequencies of the selected sinusoids

shouldn’t necessarily be commensurate nor integer multiples of the fundamental

frequency corresponding to the record length [80]. Therefore, finer frequency resolution

in the spectral model is achieved.

3.4.2 FOS-based Jamming Detection

In this research FOS is employed for narrowband CW jamming detection. As FOS is

generally known to be a data dependent algorithm [76,82,74,77]; the accuracy of the

model produced by FOS depends on the data record being modelled, the candidate

functions being used to compute correlations, and the stopping conditions (thresholds) in

the algorithm. The chosen FOS candidate frequencies have a finer resolution compared to

FFT in order to achieve better detection accuracy. Candidate frequencies can be selected

so that the candidate functions focus on a particular frequency range of interest. For

71

example, the candidates can be spaced with high resolution on a range of interest and

outside the range of interest; the candidates can be spaced by FFT resolution intervals.

It is desirable to have the minimum number of candidate frequencies in the spectral

estimate which represent the most significant components of received signal. However,

creating a model that incorporates fewer than necessary terms will result in an inaccurate

representation of the received signal. On the other hand, the excessive inclusion of terms

will add noise terms into the received signal’s spectral estimate as well as increase the

computation time.

FOS stops modeling when the addition of a new frequency pair does not increase the

MSE reduction more than the reduction obtained from fitting white Gaussian noise

(WGN). Thus, a candidate acceptance threshold, requiring a frequency pair to fit a

minimum percentage of the overall energy in the signal, is set. Such a threshold allows

FOS to reject frequency terms that model the noise.

3.4.3 Experimental Work

The proposed narrowband CW jamming detection method is assessed using simulated

data records. The main simulated data included raw digitized GPS and jamming signals.

GPS simulated data was obtained using Spirent GSS 6700 GPS simulator and Novatel

FireHose Digital Frontend. The jamming signals were simulated using Matlab and added

to the recorded GPS data sets.

The Spirent GSS 6700 GPS L1 simulator was employed to simulate the GPS signals

based on scenarios created using Spirent’s SimGEN platform and controlled by the

SimReplay Plus software. These signals were used in all the conducted experiments.

Subsequently, the output of the simulator is a raw RF GPS signal that is fed to the

72

Novatel FireHose frontend [83]. The FireHose is responsible for digitizing and down-

converting the GPS signal (obtained from the GSS 6700) into a baseband sampled In-

phase/Quadrature (I/Q) signal. The FireHose, shown below in Figure 3-9, is a dual

frequency L1/L2 software receiver and frontend designed for software receiver and

interference detection systems. The FireHose is patented by NovAtel and is not available

for commercial use. It encloses a NovAtel dual frequency OEMV-1DF GNSS receiver,

along with a GNSS frontend processor which is based on a Smart Fusion

FPGA/Microprocessor chip. Samples are provided for L1 and L2 frequency bands at

sampling frequencies that span from 2.5 to 20 MHz. The experimental setup in the

NavINST lab at the Royal Military College is shown in Figure 3-10 , it consists of the

Spirent GSS 6700 connected to the FireHose frontend. The simulated GPS data was

digitized and recorded using the FireHose Frontend at a sampling frequency of 2.5 MHz.

Data extracted from the FireHose together with the simulated jamming signals was

processed using MATLAB.

Figure 3-9: The Novatel FireHose Frontend Figure 3-10: Simulation setup using the

Spirent GSS 6700 in the NAVINST lab.

73

3.4.4 Simulation Scenarios

All scenarios were conducted according to the procedure demonstrated in

Figure 3-11.The proposed technique was examined through 5 simulation scenarios. The

first scenario studied the case of single CW jammer using simulated single tone CW

jammer signal at frequency 10.2 kHz. The performance of the proposed method based

versus the FFT based one was examined at different sizes of the data records (i.e. window

size) and variable JSR’s. In the second scenario, two CW Jammers at equal power were

added to GPS simulated data. In this scenario, the window size was maintained constant

at 1 ms which is the length of the L1 C/A code while JSR was varied. The third scenario

was similar to the second with a slight variation of adding a third CW jammer. In

Scenario 5 the effects of increasing the window size to 2 ms were studied. Finally, in

scenario 6, the case of three jammers of unequal power was studied at different window

sizes.

Figure 3-11: Demonstration of the procedure for conducting scenarios

G

U G

6700

G

b

74

3.4.5 Results and Discussions

In the first scenario, window sizes were varied from 1 ms to 20 ms and JSR was

increased from 0 dB to 40 dB. The obtained results did not show significant variation at

different JSRs. The results displayed in Figure 3-12 correspond to a JSR of 0 dB.

Frequency detection error was approximately zero for FOS and it reached 200 Hz in case

of FFT.

Figure 3-12 also illustrates the decrease in frequency detection error for FFT as window

sizes increased. On the other hand, FOS preserved a steady performance among the

different widow sizes. The cases of 5, 10, 15 and 20 ms windows differ from other

window sizes. The FFT resolutions corresponding to the aforementioned windows are

200, 100, 66.67 and 50 Hz. The error demonstrated by FFT occurred due to spectral

leakage when the jammer frequencies were not aligned with the frequency bins. On the

other hand, the leakage disappeared when the bins located at multiples of the window

sizes coincided with the jammer frequency of 10.2 kHz.

75

Figure 3-12: Detection error of FOS vs FFT at JSR = 0 dB

The effect of different values of JSR on detection accuracy was studied in the second

scenario. Two jammers having frequencies located at 10.2 kHz and 10.3 kHz, whose

difference is lower than the FFT window size of 1 kHz were introduced in scenario 2.

The window size was maintained constant and JSR of each source was varied from 0 dB

to 15 dB. As shown in Figure 3-13, FOS successfully detected both jammers; frequency

estimation was accurate for one jammer; as for the second, estimation was slightly

erroneous until the JSR of each jammer was increased to 13 dB. It is clear from this

experiment that increasing the number of jammers while maintaining the same window

size poses a challenge in detection accuracy at lower JSR. When FFT was employed for

detection in this scenario, only one signal was detected at 10 kHz thus highlighting the

substantial advantage of using FOS over FFT.

0 2 4 6 8 10 12 14 16 18 200

20

40

60

80

100

120

140

160

180

200

FOS vs FFT jammer detection error in Hz at JSRdB

=0dB with MSE=1e-05

window size in milliseconds

Err

or

in d

ete

cti

on

(H

z)

FOS 0dB

FFT 0dB

Window size (ms)

76

Figure 3-13: Detection error of the second jammer component.

The third scenario studied the effect of adding another closely spaced jammer totaling the

number of jammers to 3 at frequencies 10.2, 10.3 and 10.4 kHz. In this scenario, the

window size was kept constant at 1 ms and JSR was varied from 0 dB to 30 dB per

jammer. Figure 3-14 shows the effect of a weak jammer signal on accurate detection. At

first, only two signals are correctly detected out of three within the desired FFT

resolution of 1 kHz, although other higher magnitude frequency components exist outside

the search spectrum. Increasing the JSR minimizes the error in frequency estimation for

the two visible components. This trend continues until the JSR of each signal is 11 dB.

Figure 3-15 represents a superimposition of the individual subplots that are found in

Figure 3-14. It illustrates the effect of increasing combined JSR from 0 to 90 dB. The

0 5 10 15 20 25 300

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

Combined JSR of the two equal power jammers(dB)

Magnitude e

rror

in F

OS

dete

ction (

KH

z)

first component

second component

Mag

nit

ud

e er

ror

in F

OS

det

ecti

on

(H

z)

77

highest magnitude was observed using FFT at the 10 kHz frequency; it corresponds to the

final iteration where the combined JSR was 90 dB. At that iteration, FFT yielded higher

magnitudes due to spectral leakage. When all three jammers were not powerful enough,

the proposed method produced erroneous frequency estimates. The low magnitude

components highlighted in green correspond to iterations where JSR values were small,

and subsequently insufficient for correct frequency estimation. The error in frequency

estimation is attributed to the low JSR.

78

Figure 3-14: Effect of jammer power on FOS detection of three jammers.

9.2 9.4 9.6 9.8 10 10.2 10.4 10.6 10.8 11 11.20

20

40

60

window time=1 msec JSRdB

=0 M

ag

nit

ud

e

Frequency (KHz)

FFT

FOS

9.2 9.4 9.6 9.8 10 10.2 10.4 10.6 10.8 11 11.20

50

100


=3

Mag

nit

ud

e

Frequency (KHz)

FFT

FOS

9.2 9.4 9.6 9.8 10 10.2 10.4 10.6 10.8 11 11.20

50

100

150


=6

Mag

nit

ud

e

Frequency (KHz)

FFT

FOS

9.2 9.4 9.6 9.8 10 10.2 10.4 10.6 10.8 11 11.20

100

200

window time= 1 msec JSRdB

=9

Mag

nit

ud

e

Frequency (KHz)

FFT

FOS

9.2 9.4 9.6 9.8 10 10.2 10.4 10.6 10.8 11 11.20

100

200

300


=12

Mag

nit

ud

e

Frequency (KHz)

FFT

FOS

9.2 9.4 9.6 9.8 10 10.2 10.4 10.6 10.8 11 11.20

100

200

300


=15

Mag

nit

ud

e

Frequency (KHz)

FFT

FOS

9.2 9.4 9.6 9.8 10 10.2 10.4 10.6 10.8 11 11.20

200

400


=18

Mag

nit

ud

e

Frequency (KHz)

FFT

FOS

9.2 9.4 9.6 9.8 10 10.2 10.4 10.6 10.8 11 11.20

200

400

600


=21

Mag

nit

ud

e

Frequency (KHz)

FFT

FOS

9.2 9.4 9.6 9.8 10 10.2 10.4 10.6 10.8 11 11.20

200

400


=24

Mag

nit

ud

e

Frequency (KHz)

FFT

FOS

9.2 9.4 9.6 9.8 10 10.2 10.4 10.6 10.8 11 11.20

200

400

600


=27

Mag

nit

ud

e

Frequency (KHz)

FFT

FOS

79

Figure 3-15: Effect of JSR on correct detection.

Scenario 4 bares a similarity to scenario 3; although window size was increased to 2 ms thus

increasing the FFT resolution from 1 kHz to 0.5 kHz. JSR was progressively increased from 0 to

15 dB as shown in Figure 3-16. The FOS-based method enabled precise detection of the 3

jammers at 0 dB JSR. Figure 3-16 also shows that although FFT resolution was increased to 0.5

kHz, FFT was incapable of detecting all three jammers. This suggests that FOS detection

performance can be enhanced by increasing data record length but at the same time this will

increase the computational load of the jamming detection. In scenario 5, three jammers were

added at frequencies 10.2, 10.3 and 10.4 kHz and two cases were studied. In this scenario each

jammer had a different power level, as shown in Figure 3-17 and Figure 3-18. Additionally, the

window sizes ranged from 1 to 10 ms. The JSR attributed to jammers 1, 2 and 3 in case (A) was

0, 10 and 15 dB respectively as shown in Figure 3-17. For case (B) JSR was 10, 0 and 15 dB as

shown in Figure 3-18. Case (A) results showed that using a 1 ms window, only two jammers

9.2 9.4 9.6 9.8 10 10.2 10.4 10.6 10.8 11 11.20

100

200

300

400

500

600

700

800

Mag

nit

ud

e

Frequency (kHz)

FFT

FOS

80

were detected out of three. Contrarily, case (B) results detected three jammers accompanied by a

frequency estimation error of 200 Hz for the first component. It can be established that accurate

results are achieved using FOS for both cases (A and B) after increasing the window size to a

value of 2 ms and above. Furthermore, FOS detection performance remained constant after 2 ms,

therefore eliminating the need for larger window sizes. FFT performance became comparable to

FOS from a frequency estimation perspective after increasing the FFT window size to 10 ms.

However, FOS outperformed FFT in terms of the accuracy of the detected components

amplitudes.

81

Figure 3-16: FOS vs FFT jammer detection at different JSR and a 2 ms window size

9.2 9.4 9.6 9.8 10 10.2 10.4 10.6 10.8 11 11.20

5

10

15

20

25

30

window size= 2 msec JSR 1 dB

=0 JSR 2 dB

=0 JSR 3 dB

=0

Magnitude

Frequency (KHz)

FFT

FOS

9.2 9.4 9.6 9.8 10 10.2 10.4 10.6 10.8 11 11.20

5

10

15

20

25

30

35

40

45


=5 JSR 2 dB

=5 JSR 3 dB

=5

Magnitude

Frequency (KHz)

FFT

FOS

9.2 9.4 9.6 9.8 10 10.2 10.4 10.6 10.8 11 11.20

10

20

30

40

50

60

70


=10 JSR 2 dB

=10 JSR 3 dB

=10

Magnitude

Frequency (KHz)

FFT

FOS

9.2 9.4 9.6 9.8 10 10.2 10.4 10.6 10.8 11 11.20

20

40

60

80

100

120


=15 JSR 2 dB

=15 JSR 3 dB

=15

Magnitude

Frequency (KHz)

FFT

FOS

82

Figure 3-17: FOS vs FFT jammer detection at different window sizes for 3 jammers at different JSR (A)

9.2 9.4 9.6 9.8 10 10.2 10.4 10.6 10.8 11 11.20

50

100

150

window size=1 ms JSR 1 dB

=0 JSR 2 dB

=10 JSR 3 dB

=15

Magnitude

Frequency (kHz)

FFT

FOS

9.2 9.4 9.6 9.8 10 10.2 10.4 10.6 10.8 11 11.20

50

100

150


=0 JSR 2 dB

=10 JSR 3 dB

=15

Magnitude

Frequency (kHz)

FFT

FOS

9.2 9.4 9.6 9.8 10 10.2 10.4 10.6 10.8 11 11.20

50

100

150


=0 JSR 2 dB

=10 JSR 3 dB

=15

Magnitude

Frequency (kHz)

FFT

FOS

9.2 9.4 9.6 9.8 10 10.2 10.4 10.6 10.8 11 11.20

50

100

150


=0 JSR 2 dB

=10 JSR 3 dB

=15

Magnitude

Frequency (kHz)

FFT

FOS

9.2 9.4 9.6 9.8 10 10.2 10.4 10.6 10.8 11 11.20

50

100

150


=0 JSR 2 dB

=10 JSR 3 dB

=15

Magnitude

Frequency (kHz)

FFT

FOS

83

Figure 3-18: FOS vs FFT jammer detection at different window sizes for 3 jammers at different JSR (B)

9.2 9.4 9.6 9.8 10 10.2 10.4 10.6 10.8 11 11.20

50

100

150


=10 JSR 2 dB

=0 JSR 3 dB

=15

Magnitude

Frequency (kHz)

FFT

FOS

9.2 9.4 9.6 9.8 10 10.2 10.4 10.6 10.8 11 11.20

50

100

150


=10 JSR 2 dB

=0 JSR 3 dB

=15

Magnitude

Frequency (kHz)

FFT

FOS

9.2 9.4 9.6 9.8 10 10.2 10.4 10.6 10.8 11 11.20

50

100

150

window size= 4 ms JSR 1 dB

=10 JSR 2 dB

=0 JSR 3 dB

=15

Magnitude

Frequency (kHz)

FFT

FOS

9.2 9.4 9.6 9.8 10 10.2 10.4 10.6 10.8 11 11.20

50

100

150


=10 JSR 2 dB

=0 JSR 3 dB

=15

Magnitude

Frequency (kHz)

FFT

FOS

9.2 9.4 9.6 9.8 10 10.2 10.4 10.6 10.8 11 11.20

50

100

150


=10 JSR 2 dB

=0 JSR 3 dB

=15

Magnitude

Frequency (kHz)

FFT

FOS

84

3.5 Conclusion

This chapter introduced a new jamming detection method based on high resolution

spectral estimation for GPS signals using FOS. The proposed method featured several

spectral estimation capabilities including high frequency resolution, elimination of

spectral leakage and rejection of background noise. The aforementioned abilities resulted

in a significant enhancement to the GPS jamming detection process.

The performance of the proposed method was examined using GPS data sets generated

by the Spirent GSS 6700 and acquired by the Novatel FireHose frontend GPS receiver.

The proposed method demonstrated more consistent and accurate jamming detection than

conventional FFT based methods in the presence of a single jammer with less sensitivity

to window size. FFT could only match FOS-based detection in specific cases. It provided

resolutions similar to that of the proposed method at a window size 10 times larger than

that used by FOS. Moreover, our method accurately and efficiently estimated the number

and frequencies of multiple in-band CW jammers whose frequency separation is lower

than that of FFT as demonstrated in scenarios 2 and 3. Nevertheless, increasing the

number of jammers degrades the detection accuracy at lower JSR. In General, the

proposed FOS-based method can expand the capabilities of present GPS receivers to

provide robust anti-jamming in challenging environments.

85

Chapter 4

DoA Estimation of GPS Narrowband Interference

4.1 Introduction

GPS interference detection can be achieved in the time, space, or frequency

domain as previously demonstrated in Chapter 3 or in joint variables domain such as

time-frequency or space–time. Generally, spatial signal processing using antenna arrays

is considered one of the most effective techniques for narrowband interference detection

and especially suppression. In Chapter 2, it was stated that antenna arrays enable

interference mitigation through spatial nulling and beamsteering using adaptive

beamforming and high-resolution DoA estimation methods [84] .

DoA estimation of signals from multiple sources plays a key role in the

interference suppression process. Adaptive antenna arrays use the DoA information to

produce nulls in DoA of interference signals and steer the main beam towards the desired

GPS signal. Various DoA estimation algorithms have been developed for array signal

processing applications. The selection of the DoA estimation algorithm is a crucial

element of adaptive antenna array design. Selecting the proper DoA estimation algorithm

enables proper signal DoA estimation, which directly affects null steering and

beamforming processes. Moreover, one of the main problems of null steering and

beamforming occurs when the jammer is in the same direction or very close to the GPS

signal’s DoA. This implies that jamming detection that is based on high resolution DoA

estimation can significantly enhance the anti-jamming process. The DoA estimation

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techniques that are predominantly used are those that are based on Classical DoA, Capon

and MUSIC algorithms [84]. It has been reported that, Eigen-decomposition based

methods such as MUSIC have high resolution DoA estimation performance [85]. These

methods are based on exploiting the Eigen-structure of the input covariance matrix.

Applying MUSIC to GPS anti-jamming has shown significant enhancement to overall

system performance [86]. However, the performance of MUSIC is limited by coherence

of the jamming sources [87].

This thesis proposes a new high-resolution DoA estimation method to enhance the

GPS jamming detection capabilities using antenna arrays. The proposed method is based

on the orthogonal search technique in order to create bases for the steering function. The

coefficients of the steering function are determined via a unique orthogonal search

method that provides high accuracy DoA estimation. The main advantage of this method

is based on its super high resolution and robust DoA estimation. This method can

enhance anti-jamming techniques based on adaptive array systems, specifically in

situations where the DoA of jamming signals is very close to the DoA of the GPS signal.

Hence, it can enhance the null-steering process and avoid reduction in GPS signal levels

while rejecting jamming signals. Furthermore, the high-resolution capabilities of the

proposed method can resolve jamming signals arriving at very close DoAs and hence

improves the overall performance of the anti-jamming method.

The proposed method is compared to Classical DoA estimation and MUSIC using GPS

L1 signals obtained from a Spirent 6700 simulator; the arrays utilized were linear and

circular arrays. The jamming signals were simulated as CW sources originating from

different directions. In addition, this thesis studies the effect of array geometry on DoA

87

estimation efficiency and proposes an optimum array configuration for enhancing GPS

jamming detection and mitigation. The recommended configuration is examined using

GPS data obtained from the Spirent 6700. A comparison between the performance of the

proposed method and the aforementioned predominant DoA estimation methods is

conducted using the recommended array configuration. For each array configuration, the

performance of the investigated methods is evaluated in case of single and multiple

interference signals. Our results showed that the proposed method could introduce

significant enhancement to GPS jamming detection and hence provide significant

improvement for overall system performance.

4.2 DoA Estimation Using Nonlinear Signal Modeling

This research studies the application of FOS in DoA estimation of jamming

signals. FOS is a highly efficient general purpose modeling method that can be used for

time series analysis and frequency analysis [76]. FOS is known to have features that can

significantly enhance the DoA estimation of CW jamming signals [76,88,82]. They

include a high frequency resolution spectrum and an ability of rejecting white and

colored noise. FOS has been used in numerous applications, including identification of

generalized nonlinear difference equation models, spectrum estimation and DoA

estimation for uniform linear arrays [88,82]. The original orthogonal search (OS)

algorithm is mainly based on suboptimal minimization of the mean squared error (MSE)

between observed and modeled data. The algorithm constructs a functional expansion of

an input using an arbitrary set of non-orthogonal candidate functions. The functional

expansion of the input in terms of the arbitrary candidate functions is given by:

88

𝒚(𝑛) = ∑ 𝑎𝑚 𝑝𝑚(𝑛) + 𝑒(𝑛)

𝑀

𝑚=0

Eq. 4-1

Where the weights 𝑎𝑚 , (where 𝑚 = 0, … , 𝑀) are the weights of the functional

expansion, and 𝑒(𝑛) is the modelling error. Generally, the signal arriving at the antenna

array is a superposition of complex sinusoidal signals and noise. The total signal received

at the 𝑛𝑡ℎ sensor at time 𝑡𝑖 from 𝑆 sources is given by [88]:

𝑦𝑚(𝑡𝑖) = ∑ 𝑃𝑘(𝑡𝑖) exp (𝑗2𝜋𝑓𝑘(𝑡𝑖 − 𝜏𝑚(𝜃𝑘))) +

𝑆−1

𝑘=0

𝑒𝑚(𝑡𝑖) Eq. 4-2

where 𝑖 = 0, … , 𝑇 − 1 is the signal time index

𝑚 = 0, … , 𝑀 − 1 is the sensor index number

𝑘 = 0, ⋯ , 𝑆 − 1 is the signal index number

𝜃𝑘 Is the DoA of the signal from 𝑘𝑡ℎ source

𝑃𝑘 is the complex amplitude of the 𝑘𝑡ℎ source

𝑃𝑘(𝑡𝑖) = |𝑃𝑘(𝑡𝑖)| exp(𝑗𝜑(𝑡𝑖)) and

𝜑(𝑡𝑖) is the phase of the 𝑘𝑡ℎ signal at its source

For 𝐿 real signals 𝑆 = 2𝐿 and the complex amplitudes are conjugate pairs (i.e. 𝑃𝑘+1 =

𝑃𝑘∗ and 𝑓𝑘+1 = −𝑓𝑘 ). The reference is taken at the first element=0, thus 𝜏0(𝜃𝑟𝑘) = 0.

The following model may describe the received signal at the antenna array:

𝑦(𝑛) = ∑ 𝑎𝑘(𝜃𝑘)𝑠𝑘(𝑛)

2𝐿−1

𝑘=0

+ 𝑒(𝑛) Eq. 4-3

where 𝑎𝑘(𝜃𝑟) is 𝑀 × 1 antenna array steering vector for kth

source

𝑠𝑘 is the kth

source signal received by the antenna array

89

When dealing with real signals, each parameter 𝜃𝑘 has two linearly independent steering

vectors: either complex-conjugate exponentials with complex coefficients incorporating

signal phase information, or sine and cosine components with real coefficients may be

used. In this research real (sine and cosine) steering vectors were used. Nevertheless, the

complex exponential notation is retained for consistency with the literature.

OS uses Gram-Schmidt procedure to create an orthogonal basis for the steering vectors,

and a model equivalent to Eq. 4-3 is formed using a set of orthogonal basis vectors{𝑤𝑘}:

𝑦(𝑛) = ∑ 𝑤𝑘(𝜃0, 𝜃1, ⋯ , 𝜃𝑟)𝑔𝑘(𝑛)

2𝐿−1

𝑘=0

+ 𝑒(𝑛) Eq. 4-4

where 𝑟 = 𝑘/2 for 𝑘 even and 𝑟 = (𝑘 − 1)/2 for 𝑘 odd

𝑤𝑗∗ = 𝑤𝑘 for 𝑖 ≠ 𝑘 and * denotes complex-conjugate transpose.

{𝑔𝑘(𝑛)} are the coeffecients of orthogonal basis vectors. The orthogonal basis vectors

{𝑤𝑘} are derived from the candidate functions {𝑎𝑘(𝜃𝑟)} using the following formula:

𝑤𝑘 = 𝑎0 − ∑ α𝑘𝑖𝑤𝑖

𝑘−1

𝑖=0

Eq. 4-5

where 𝛼𝑘𝑖 = 𝑤𝑘∗𝑎𝑘

𝑤𝑘∗𝑤𝑘

and 𝑤0 = 𝑎0

The estimated coefficient 𝑔𝑘(𝑛) that should minimize the mean square error (MSE) are

given by:

𝑔𝑘(𝑛) =𝑤𝑘

∗ 𝑦(𝑛)

𝑤𝑘∗𝑤𝑘

Eq. 4-6

The total MSE is:

90

𝜀2̅̅ ̅ =1

𝑇∑

1

𝑀

𝑇−1

𝑛=0

‖𝒚(𝑛) − ∑ 𝑔𝑘(𝑛)𝑤𝑘

𝑆−1

𝑘=0

‖

2

=1

𝑀𝑇∑ 𝑦∗(𝑛)𝑦(𝑛)

𝑇−1

𝑛=0

− ∑ 𝑄𝑘

𝑆−1

𝑘=0

Eq. 4-7

where

𝑄𝑘 =1

𝑀𝑇∑

[ 𝑤𝑘∗𝒚(𝑛)]2

𝑤𝑘∗𝑤𝑘

𝑇−1

𝑛=0

=𝑤𝑘

𝐻𝑤𝑘

𝑀𝑇∑ 𝑔𝑘(𝑛)

𝑇−1

𝑛=0

Eq. 4-8

𝑄𝑘 is the amount of reduction in MSE gained by adding the candidate basis vector 𝑤𝑘 to

the model. The calculation of 𝑄𝑘 involves the correlations of 𝑤𝑘 with themselves, the

steering vectors 𝑎𝑘 and the data 𝒚(𝑛) are. Therefore, the orthogonal search can discard

the need to explicitly create the orthogonal basis vectors 𝑤𝑘.

FOS works by exploiting these observations and uses Cholesky factorization to calculate

the aforementioned correlations. It starts by creating a variable 𝐷𝑘𝑚, which represents the

correlation between the candidate and the steering vector. This is given by:

𝐷𝑘𝑚 = 𝑤𝑚𝑎𝑘 = 𝑎𝑘∗ 𝑎𝑘 − ∑ 𝛼𝑚𝑗

∗

𝑚−1

𝑗=0

𝐷𝑘𝑗 Eq. 4-9

where 𝑚 = 1 … 𝑘 and 𝛼𝑘𝑗 =𝐷𝑘𝑗

𝐷𝑗𝑗

Another variable 𝐶𝑛𝑘 is used to denote the correlation between the candidate and the

observations vector and defined by:

91

𝐶𝑛𝑘 = 𝑤𝑘∗𝒚(𝑛) = 𝑎𝑘

∗𝒚(𝑛) − ∑ 𝛼𝑘𝑗∗

𝑘−1

𝑗=0

𝐶𝑛𝑗 Eq. 4-10

Accordingly the coefficients of orthogonal basis vectors 𝑔𝑘(𝑛) and the amount of

reduction in MSE 𝑄𝑘 are given by:

𝑔𝑘 (𝑛) =𝐶𝑛𝑘

𝐷𝑘𝑘 Eq. 4-11

𝑄𝑘 = ∑𝐶𝑛𝑘

2

𝑀𝑇𝐷𝑘𝑘

𝑇−1

𝑛=0

Eq. 4-12

The fact that 𝑤𝑘∗𝑤𝑘 = 𝑤𝑘

∗𝑎𝑘 , was utilized in formulating Eq. 4-11 and Eq. 4-12. Given

that 𝑤0 = 𝑎0 the initial values for 𝐷𝑘𝑚 and 𝐶𝑛𝑘 are given by:

𝐷𝑚0 = 𝑎0∗𝑎𝑚 and 𝐶𝑛0 = 𝑎0

∗𝑦(𝑛) Eq. 4-13

The model in Eq. 4-4 is created by adding the candidate functions corresponding to one

direction of arrival at a time. To choose the following estimate θ𝑟, the set of parameters

are accessed to provide the value that yields maximum MSE reduction 𝑄𝑘 Since a real

signal with sine and cosine components is used, the MSE reduction contributed by a

single candidate parameter is in fact the sum of the MSE reductions induced by the two

corresponding steering vectors of that candidate (i.e. 𝑄𝑘 and𝑄𝑘+1). Hence the succeeding

estimate θ𝑟 is given by:

θ𝑟 = 𝑎𝑟𝑔[max (𝑄𝑘 + 𝑄𝑘+1)] Eq. 4-14

Once θ𝑟 is chosen, a set of two terms 𝑔𝑘(𝑛)𝑤𝑘 and 𝑔𝑘+1(𝑛)𝑤𝑘+1 is added to the model

terms. This procedure is repeated L times, once the L parameter estimates are chosen; the

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values of the signal coefficients 𝑠𝑘(𝑛) can be found recursively using the following

formula:

�̂�𝑘(𝑛) = ∑ 𝑔𝑚(𝑛)𝑣𝑚

𝑆−1

𝑚=𝑘

Eq. 4-15

where 𝑣𝑘 = 1

𝑣𝑚 = − ∑ 𝛼𝑚𝑗

𝑚−1

𝑗=𝑘𝑣𝑗 𝑚 = 𝑘 + 1, k + 2, … , 𝑆 − 1

4.2.1 Stopping Conditions for FOS Algorithm

FOS algorithm can be stopped using one of the following criteria:

a) Reaching a predefined maximum number of terms to be fitted.

This requires the knowledge of the number of narrowband interference signals

impinging upon the antenna array. However, the orthogonal search

approaches may be combined with any of a number of statistical criteria to

determine when to stop adding terms to the model, thus providing an estimate

of the number of signals [88].

b) Reaching a pre-defined threshold for MSE Reduction.

This criterion is achieved when the ratio of MSE to the mean squared value of

the input signal is below a pre-defined threshold. Accordingly, the limitation

of knowing the number of expected interference signals is waved. However, it

may lead to an increase in the processing time. Thus this ratio should be

carefully selected to avoid excessive processing time.

93

c) When adding another term to the model, the MSE reduction is less than the

MSE reduction that would be gained if white Gaussian noise was added.

4.2.2 FOS complexity:

FOS necessitates floating point operations of the order of 𝐶𝑀𝑇 + 𝐶𝐿2 where 𝐶 is the

number of candidate steering vectors searched [82]. Moreover, if the elements of the

array and therefore the data samples are not equally spaced, FOS will require a higher

order which becomes 𝐶𝑀𝑇 + 𝐶𝐿2 + 𝐶𝑀𝐿 [88].

4.2.3 Candidate Function Selection for FOS Algorithm

The process of candidate function selection plays a key role in the FOS algorithm.

In this research, the selected candidate functions are pairs of sine and cosine functions

corresponding to the DoAs of the search domain. Accordingly, the selected candidate

functions for a ULA using the model shown in Eq. 4-3 are given by [82]:

𝑎𝑘(𝜃𝑟) = {𝑎𝑘(𝑚, 𝜃𝑟)} Eq. 4-16

where 𝜃𝑟 is the DoA of 𝑟𝑡ℎ signal .

When 𝜃𝑟 is measured from the line of the antenna array, Eq. 4-17 is used.

𝑎𝑘(𝑚, 𝜃𝑟) = cos (2𝑚𝜋(𝑑

𝜆)cos (𝜃𝑟))

𝑎𝑘+1(𝑚, 𝜃𝑟) = sin (2𝑚𝜋 (𝑑

𝜆) cos(𝜃𝑟)) Eq. 4-17

On the other hand, when 𝜃𝑟 is measured from the line perpendicular to the antenna array

the utilized equation is Eq. 4-18, which is shown below:

𝑎𝑘(𝑚, 𝜃𝑟) = cos (2𝑚𝜋(𝑑

𝜆)𝑠𝑖𝑛(𝜃𝑟))

94

𝑎𝑘+1(𝑚, 𝜃𝑟) = sin (2𝑚𝜋(𝑑

𝜆)sin (𝜃𝑟)) Eq. 4-18

where 𝑚 = 0,1, … , 𝑀 − 1 , 𝑖 = 0,1 … , 𝑇 − 1, 𝑑 is the spacing between elements, and 𝜆

is the wavelength of the received signal.

The coefficients 𝑠𝑘(𝑛) are given by [82]:

𝑠𝑘 = √2𝑃𝑟 cos (𝜋𝑡𝑖 + 𝜑𝑟(𝑡𝑖))

𝑠𝑘+1 = √2𝑃𝑟 sin (𝜋𝑡𝑖 + 𝜑𝑟(𝑡𝑖)) Eq. 4-19

where 𝑃𝑟 and 𝛹𝑟(𝑡𝑖) are the power and phase of 𝑟𝑡ℎsource respectively.

4.3 Antenna Array Design

In the following sections, array design for several array geometries will be studied

from a different perspective that will ultimately serve the goal of DoA estimation.

Therefore, in order to adhere to the common literature notations, the total number of

elements in an array will be referred to as 𝑁 elements while 𝑛 will represent the index of

an element in the array and 𝑛 = 0, 1, … , 𝑁 − 1.

4.3.1 Uniform Linear Array

The ULA is capable of filtering the electromagnetic environment in which it

operates, based on the location of the signals in its vicinity. Array geometry has a crucial

effect on the DoA estimation abilities of antenna arrays. Recently, array geometry

optimization has been extensively studied using various methods. In general, the impact

95

of array arrangement on performance was investigated by considering standard arrays

such as the uniform linear array shown below in Figure 4-1 [89].

Figure 4-1:Uniform linear array

For the general ULA shown in Figure 4-1 with inter-element spacing 𝑑𝑛 and M identical

elements, the signal received by the antenna array is given by:

𝑦(𝑡) = 𝑠(𝑡) ( ∑ 𝑒−𝑗𝑘.𝑑𝑛

𝑀−1

𝑛=0

) Eq. 4-20

where 𝑠(𝑡) is the transmitted signal.

The quantity in parenthesis is known as the array factor (AF). This factoring is regularly

termed pattern multiplication. It can be utilized when the identical array elements are

oriented in the same direction. Moreover the radiation pattern of the array is the result of

the multiplication of element radiation pattern and array factor.

When the elements of the ULA are all located on the z-axis, 𝑑𝑛 = (0,0, 𝑧𝑛). The AF then

becomes:

M M-1

dn dn dn dn dn dn

96

𝐴𝐹 = ( ∑ 𝑒−𝑗2𝜋𝜆

𝑧𝑛𝑐𝑜𝑠𝜃

𝑀−1

𝑛=0

) Eq. 4-21

where 𝑛 = 0, … , 𝑀 − 1

𝜃 is the direction of arrival of received signal.

For an M-element ULA let 𝑑𝑛 = (0,0,𝑛𝜆

2) , hence the AF becomes

𝐴𝐹 = ∑ 𝑒−𝑗𝑛𝜋𝑐𝑜𝑠𝜃

𝑀−1

𝑛=0

Eq. 4-22

The array factor formula can be simplified using the following identity [89]

∑ 𝑐𝑛 =1 − 𝑐𝑀

1 − 𝑐

𝑀−1

𝑛=0

Eq. 4-23

Therefore the array factor for ULA is given by:

𝐴𝐹 =1 − 𝑒−𝑗𝑀𝜋𝑐𝑜𝑠𝜃

1 − 𝑒−𝑗𝜋𝑐𝑜𝑠𝜃 Eq. 4-24

After factoring, Eq. 4-24 reduces to:

𝐴𝐹 = (𝑒−𝑗

𝑀𝜋2

𝑐𝑜𝑠𝜃

𝑒−𝑗𝜋2

𝑐𝑜𝑠𝜃)

𝑠𝑖𝑛 (𝑀𝜋

2 𝑐𝑜𝑠𝜃)

𝑠𝑖𝑛 (𝜋2 𝑐𝑜𝑠𝜃)

Eq. 4-25

The AF magnitude pattern for ULA is shown in Figure 4-2. The magnitude of the array

factor is plotted for an array with 𝑀 = 9 elements. Based on the magnitude of the array

factor, maximum energy is received or transmitted by the array when𝜃 = 90° or when 𝜃

= 270°. Introducing weights and varying the orientation of the ULA can manipulate this

array factor. Since the array factor is a linear function of the weights, therefore, choosing

weights is a minor procedure [90,91,92]. On the other hand, the array factor is a nonlinear

97

exponential function of the element positions; consequently, array geometry optimization

is more challenging [89].

Figure 4-2 Array factor for ULA

Other important parameters of array factors include beamwidth and sidelobe level. The

beamwidth is usually defined as null-to-null or half-power beamwidth. The null-to-null

beamwidth is the angular distance between the first nulls around the main beam [89]. The

half-power beamwidth is the angular distance between the half-power points (i.e. 3 dB

points on the array factor) around the main beam. The sidelobe level is usually defined as

the maximum value of the array factor that is found outside the main beam.

4.3.2 Two-Dimensional Arrays

The one-dimensional array factor is either a function of the DoA elevation or the

DoA azimuth depending on its orientation. Hence, the array can filter the received signals

based on single parameter which is the elevation angle 𝜃 or azimuth angle 𝜙 but cannot

2

4

6

8

10

30

210

60

240

90

270

120

300

150

330

180 0

98

accommodate both parameters in filtering received signals. That is why two-dimensional

arrays are used in order to distinguish between received signals based on azimuth and

elevation [93]. The most common configurations for two-dimensional arrays are

rectangular and circular arrays [84].

4.3.2.1 Rectangular Arrays

For a two-dimensional rectangular array with elements on the x-y plane such as the one

shown in Figure 4-3, the array factor becomes [89]:

𝐴𝐹 = ( ∑ 𝑒−𝑗2𝜋𝜆

(𝑥𝑛𝑠𝑖𝑛𝜃𝑐𝑜𝑠𝜙+𝑦𝑛𝑠𝑖𝑛𝜃𝑠𝑖𝑛𝜙)

𝑀−1

𝑛=0

) Eq. 4-26

Figure 4-3 Rectangular array geometry

a

𝑟

z

y

x

𝜙

b

M

99

The array factor is a function of both spherical angles and can therefore filter the

received signals based on their azimuth and elevation angles. The effect of the array on

the received signal as a function of the angle of arrival can be demonstrated by examining

the array factor. The array factor for rectangular array (𝑚 × 𝑚) with uniform weights

and 𝑑 = (𝑎𝜆

2,

𝑏𝜆

2, 0) where 𝑎, 𝑏 = 0,1,2, … . . 𝑚 − 1 is given by:

𝐴𝐹 = ( ∑ ∑ 𝑒−𝑗𝜋 𝑠𝑖𝑛𝜃(𝑎𝑐𝑜𝑠𝜙+𝑏𝑠𝑖𝑛𝜙)

𝑚−1

𝑎=0

𝑚−1

𝑏=0

) Eq. 4-27

by applying the identity formula

𝐴𝐹 = (1 − 𝑒−𝑗𝑚𝜋𝑠𝑖𝑛𝜃𝑐𝑜𝑠𝜙

1 − 𝑒−𝑗𝜋𝑠𝑖𝑛𝜃𝑐𝑜𝑠𝜙) (

1 − 𝑒−𝑗𝑚𝜋𝑠𝑖𝑛𝜃𝑠𝑖𝑛𝜙

1 − 𝑒−𝑗𝜋𝑠𝑖𝑛𝜃𝑠𝑖𝑛𝜙)

= (𝑒−𝑗𝑚𝜋𝑠𝑖𝑛𝜃𝑐𝑜𝑠𝜙 2⁄

𝑒−𝑗𝜋𝑠𝑖𝑛𝜃𝑐𝑜𝑠𝜙 2⁄) (

𝑒−𝑗𝑚𝜋𝑠𝑖𝑛𝜃𝑠𝑖𝑛𝜙 2⁄

𝑒−𝑗𝜋𝑠𝑖𝑛𝜃𝑠𝑖𝑛𝜙 2⁄)

∗ (𝑠𝑖𝑛(𝑚𝜋𝑠𝑖𝑛𝜃𝑐𝑜𝑠𝜙 2⁄ )

𝑠𝑖𝑛(𝜋𝑠𝑖𝑛𝜃𝑐𝑜𝑠𝜙 2⁄ )) (

𝑠𝑖𝑛(𝑚𝜋𝑠𝑖𝑛𝜃𝑠𝑖𝑛𝜙 2⁄ )

𝑠𝑖𝑛(𝜋𝑠𝑖𝑛𝜃𝑠𝑖𝑛𝜙 2⁄ ))

Eq. 4-28

To simplify the process of plotting, the following variables are presented:

𝑢 =𝑘𝑥𝜆

2𝜋= 𝑠𝑖𝑛𝜃𝑐𝑜𝑠𝜙 and 𝑣 =

𝑘𝑦𝜆

2𝜋= 𝑠𝑖𝑛𝜃𝑠𝑖𝑛𝜙

hence,

𝐴𝐹 = (𝑒−𝑗

𝑚𝜋𝑢2

𝑒−𝑗𝜋𝑢2

) (𝑒−𝑗

𝑚𝜋𝑣2

𝑒−𝑗𝜋𝑣2

) (sin (𝑚𝜋𝑢 2)⁄

sin (𝜋𝑢 2)⁄) (

sin (𝑚𝜋𝑣 2)⁄

sin (𝜋𝑣 2)⁄)

Eq. 4-29

The array factor formula for two-dimensional arrays and the beamwidth are more

difficult to study in 3D. Usually, two dimensional arrays are studied in certain planes (i.e.

elevation and azimuthal planes) and given in half-power or null-to-null form, similarly to

100

the one-dimensional case. The sidelobe level remains, similar to the previous section, the

peak value of the array factor outside of the main beam.

An illustration of the AF magnitude pattern is shown in Figure 4-4, Figure 4-5 and

Figure 4-6. The shown pattern corresponds to a square array of 9 elements uniformly

arranged in the x,y plane with equal space of 𝜆/2. Rectangular arrays have the

disadvantage of the edge effect, where the outer elements in the finite array have

degraded performance when compared with the central array elements. It can also be

depicted from the AF magnitude shown in Figure 4-4 that the rectangular array response

varies along the elevation direction which limits the capabilities of rectangular antenna

arrays in beam steering.

Figure 4-4 Array factor magnitude for rectangular array

101

Figure 4-5 Array factor pattern for rectangular array

Figure 4-6 XY-Plane view of array factor pattern for rectangular array

102

4.3.2.2 Circular Array

The planar array geometries can be divided into three other sub-categories;

circular, rectangular, and square. The circular arrays stand out of the three as they do not

have edge elements. In the absence of edge constraints, the beam pattern of a circular

array can be electronically rotated. Moreover, the circular arrays also have the capability

to compensate the effect of mutual coupling by breaking down the array excitation into a

series of symmetrical spatial components [94,95].

Figure 4-7 Circular array geometry

The array factor of a circular antenna array which is shown in Figure 4-7 is given by [94]:

𝐴𝐹(𝜃, 𝜙) = ∑ 𝑒𝑗(𝑘𝑏𝑠𝑖𝑛𝜃 cos(𝜙−𝜙𝑛))

𝑀

𝑛=1

Eq. 4-30

where 𝜙𝑛 is the angular position of element 𝑛

b

n n +1

z

y

x

𝜙𝑛

M

𝜙

103

𝑀 is the number of antenna elements

𝑏 is the radius of the circle

and 𝑘 is the wave number , 𝑘 =2𝜋

𝜆.

The array factor for circular antenna array is a function of both spherical angles and can

therefore filter the received signals based on their azimuth and elevation angles. The

effect of the array on the received signal as a function of the angle of arrival can be

demonstrated by examining the array factor. The magnitude pattern of the circular array

factor is shown in Figure 4-8, Figure 4-9 and Figure 4-10. This pattern is drawn for a

circular array of nine elements that are equally spaced on a circular circumference with

radius of 𝜆

2. Circular arrays configuration does not have the edge effect. It is clear from

the AF magnitude shown in Figure 4-8 that the circular array response is symmetrical

around the elevation direction, which enhances the capabilities of circular antenna arrays

in beam steering.

104

Figure 4-8 Array factor magnitude for circular array

Figure 4-9 Array factor pattern for circular array

105

Figure 4-10 XY-plane view of array factor pattern for circular array

A major factor that is considered in array design is aliasing. Aliasing occurs when signals

propagating in separate directions yield similar steering vectors. In that case, the array’s

response towards the two directions will be identical, so that the array cannot differentiate

between the two directions. Equivalently, in spectral analysis, when the sampling rate is

too small in time, frequency distinction cannot be achieved.

For a ULA, plane waves from distinct directions with duplicate steering vectors will exist

if the spacing between elements is larger than λ / 2. Similarly, for uniformly spaced

rectangular arrays with elements arranged on the x-y plane, there distinct directions with

duplicate steering vectors will exist if the element spacing in either the x or y directions is

larger than λ / 2. Upon the occurrence of aliasing, the main beam may be replicated

somewhere else in the pattern. These replicated beams are denoted as grating lobes.

106

For arrays not having a non-uniform structure, the distance between elements can be

much larger than λ / 2 without introducing aliasing. In this case, two distinct DoAs will

not produce duplicate steering vectors. Nevertheless, although aliasing technically does

not occur, there may be steering vectors that are very similar, hence, grating lobes could

exist. Determining whether or not this takes place for an arbitrary array is very

challenging. In general, if a non-uniform array is utilized, the array factor can be tested to

guarantee that grating lobes are not created [89]. Mathematical studies on the uniqueness

of steering vectors can be found in [96].

4.4 Array Geometry Optimization

An antenna array is commonly used for communication systems operating in

environments with a large quantity of co-channel interference. In this case, an antenna

array is necessary for blocking interference spatially separated from the desired signal

direction. Given that interference signals’ DoAs are unknown, it would not be practical to

optimize the array geometry for specific interference conditions.

Statistical characterization of expected interference DoAs and relative power may

enhance interference rejection. However, these characteristics cannot be ensured in

highly dynamic environments. GPS receivers can reject some interference arriving at

relatively low elevations [28]. Consequently, the DoA of interference signals can be

limited to a defined range of elevations. By optimizing array geometry with respect to

interference characteristics, it is possible to reduce the expected interference power that is

not mitigated by the array.

107

Optimal array geometry was determined in [89] by solving an optimization problem. The

solution was based on the autocorrelation matrix of received signal, given by:

𝑅𝑋𝑋 = 𝐸[𝑋(𝑡)𝑋𝐻(𝑡)] Eq. 4-31

In this equation the expectation is over time. The autocorrelation matrix 𝑅𝑋𝑋 varies for

each interference condition. Hence the expected autocorrelation matrix 𝑆𝑋 provides a

general representation of interference conditions, 𝑆𝑋 is defined as

𝑆𝑋 = 𝐸𝐼 [𝑅𝑋𝑋 ] Eq. 4-32

where the expectation operator is now over the interference situations. If all the antenna

elements have similar physical orientation, 𝑆𝑋 can then be otherwise calculated by

considering the antenna array elements as isotropic antenna elements and adjusting the

power levels in the interference environment.

In GPS systems, the majority of jamming signals have a larger power than the

signal of interest. Otherwise, they would be rejected to an extent at the stage of signal

despreading. Therefore, the array’s main goal is to minimize the output power while

restricting one of the weights in the array to be unity. This is analogous to sidelobe

cancellation [86] and was previously utilized in a 7-element adaptive array developed by ,

American weapons contractor, Raytheon for battling interference in GPS systems [97].

The power minimization technique significantly enhances the antenna array

capabilities to reduce the amount of received interference power. This is considered a

suboptimal technique with respect to MSE since the power minimization does not attempt

to place the maximum of the array factor towards the signal of interest. However, when

the interference power is much stronger than the power of the desired signal, this

108

technique can be employed to produce weights that are close to those produced by the

minimum mean square error (MMSE) techniques [89].

The output power from the array at any time is

𝑦∗𝑦 = 𝑤𝐻𝑋𝑋𝐻𝑤 Eq. 4-33

In fixed interference cases, the average output power �̅� becomes

�̅� = 𝑤𝐻𝑅𝑋𝑋𝑤 Eq. 4-34

𝑃 is therefore a measure of the average output power for a given interference

environment

𝑃 = 𝑤𝐻𝑆𝑋𝑤 Eq. 4-35

One of the weights is restricted to be unity so that the power minimization algorithm does

not nullify all the weights. Furthermore, in order to minimizing the effect of mutual

coupling, the separation between elements is required to be at least 𝜆

4. Let 𝑑𝑖𝑗 be the

separation between elements i and j. The problem of finding an optimal array for

interference suppression can be written as an optimization problem. The minimization

variables are the complex weights and the values of 𝑑𝑖𝑗 . It is desired to obtain

min(𝑤𝐻𝑆𝑋𝑤) where the minimization is subject to 𝑤𝐻𝑒1 = 1, where 𝑒1𝑇 = [1 0 0 ⋯ 0],

such that Eq. 4-36 is achieved.

𝑑𝑖𝑗 ≥𝜆

4 , 𝑓𝑜𝑟 𝑖 ≠ 𝑗 Eq. 4-36

Assuming the locations of the antenna elements are known (or held fixed), the optimal

weight vector for this problem can be found by using Lagrange multipliers. The

minimum value of the objective function for a fixed geometry becomes

109

min(𝑤𝐻𝑆𝑋𝑤) =1

𝑒1𝑇𝑆𝑋

−1𝑒1

Eq. 4-37

The optimization procedure minimizes the objective function over all array geometries

that meet the optimization problem in Eq. 4-36.

The results in [97,89] suggested that the interference suppression capabilities are greatest

when array elements are spaced as closely as possible. Therefore, a trade-off is to be had

between interference suppression and largely spaced arrays used for either diversity or

mutual coupling minimization. Based on array configuration analysis, the selected

optimum array configuration in this research is circular array of 7-elements and central

element. The selected array configuration is shown in Figure 4-11.

Figure 4-11 Circular array with central element

b

n n +1

z

y

x

𝜙𝑛

M

𝜙

110

The radius of the circle is equal to 𝜆

2 and the 7 antenna elements are equally spaced on a

circular circumference with angular spacing of 2𝜋

7. The array factor of the selected

configuration is given by [94]:

𝐴𝐹(𝜃, 𝜙) = 1 + ∑ 𝑒𝑗(𝑘𝑏𝑠𝑖𝑛𝜃 cos(𝜙−𝜙𝑛))

𝑀

𝑛=1

Eq. 4-38

where 𝜙𝑛 is the angular position of element 𝑛

𝑀 is the number of antenna elements

𝑏 is the radius of the circle

𝑘 is the wave number , 𝑘 =2𝜋

𝜆

The array factor magnitude pattern for the selected optimum configuration is shown in

Figure 4-12, Figure 4-13 and Figure 4-14.

Figure 4-12 Array factor magnitude for circular array with central element

111

The AF magnitude for circular array with central element is similar to that of the circular

array previously shown in Figure 4-8, except that it is superior in the aspect of lower

side lobes levels. This provides the circular array with a central element a more enhanced

capability of interference rejection.

Figure 4-13: Array factor pattern for circular array with central element

112

Figure 4-14 XY-Plane view of array factor pattern for circular array with central

element

4.5 High resolution FOS-based DoA Estimation Using a 2D Circular Array with

Central Element

The high resolution FOS-based-DoA estimation algorithm was modified for processing

signals received by a circular array with central element. The received signal model

defined by Eq. 4-3 was modified using the array factor of 2D circular array with central

element given in Eq. 4-36. Generally, the direction of arrival estimate for a 2D array is

defined by elevation 𝜃 and azimuth 𝜙. Accordingly, the received signal model in Eq. 4-3

was modified to include the azimuth variable in the steering vector. The modified

received signal model is given by:

𝑦(𝑛) = ∑ 𝑎𝑘(𝜃𝑟𝑘, 𝜙𝑟𝑘)𝑠𝑘(𝑛)

2𝐿−1

𝑘=0

+ 𝑒(𝑛) Eq. 4-39

113

where 𝑎𝑘(𝜃𝑟𝑘, 𝜙𝑟𝑘) is an 𝑀 × 1 antenna array steering vector for the kth

source

𝑠𝑘 is the kth

source signal received by the antenna array.

Similarly, the orthogonal basis model for Eq. 4-39 is modified to include the azimuth

direction. Therefore the orthogonal basis signal model is defined as:

𝑦(𝑛) = ∑ 𝑤𝑘(𝜃0, 𝜃1, ⋯ , 𝜃𝑟 , 𝜙0, 𝜙1, ⋯ , 𝜙𝑟)𝑔𝑘(𝑛)

2𝐿−1

𝑘=0

+ 𝑒(𝑛) Eq. 4-40

where 𝑟 = 𝑘/2 for 𝑘 even and 𝑟 = (𝑘 − 1)/2 for 𝑘 odd

𝑤𝑗∗ = 𝑤𝑘 for 𝑖 ≠ 𝑘 and * denotes complex-conjugate transpose.

The model in Eq. 4-40 is created by adding the candidate functions corresponding to one

direction of arrival at a time. To choose the succeeding estimate (θ𝑟 , ϕ𝑟), the set of

parameter is accessed to provide the value that yields maximum MSE reduction 𝑄𝑘 Since

a real signal with sine and cosine components is used, the MSE reduction contributed by

a single candidate parameter is in fact the sum of the MSE reductions induced by the two

corresponding steering vectors of that candidate (i.e 𝑄𝑘 and 𝑄𝑘+1). Hence the succeeding

estimate (θ𝑟 , ϕ𝑟), is given by:

(θ𝑟 , ϕ𝑟), = 𝑎𝑟𝑔[max (𝑄𝑘 + 𝑄𝑘+1)] Eq. 4-41

Once (θ𝑟 , ϕ𝑟) are selected, a set of two terms 𝑔𝑘(𝑛)𝑤𝑘 and𝑔𝑘+1 (𝑛)𝑤𝑘+1 is added to the

model terms. This procedure is repeated L times, once the L parameter estimates are

chosen; the values of the signal coefficients 𝑠𝑘(𝑛) can be found recursively using the

same formulas shown in Eq. 4-15.

114

Candidate function selection for FOS algorithm

The selected candidate functions for a circular array with central element were

defined using the new steering vector form. The general form of the candidate function is

given by:

𝑎𝑘(𝜃𝑟 , 𝜙𝑟) = {𝑎𝑘(𝑚, 𝜃𝑟 , 𝜙𝑟)} Eq. 4-42

where 𝜃𝑟 𝑎𝑛𝑑 𝜙𝑟 are the elevation and azimuth of the DoA of the 𝑟𝑡ℎ signal

respectively.

The candidate functions for the circular array with central element, 𝜃𝑟 measured

from the line perpendicular to the antenna array are given by:

𝑎𝑘(𝑚, 𝜃𝑟 , 𝜙𝑟) = cos (2𝑘𝑏𝜋𝑠𝑖𝑛𝜃𝑟 cos(𝜙𝑟 − 𝜙𝑚))

𝑎𝑘+1(𝑚, 𝜃𝑟 , 𝜙𝑟) = sin (2𝑘𝑏𝜋𝑠𝑖𝑛𝜃𝑟 cos(𝜙𝑟 − 𝜙𝑚))

Eq. 4-43

where 𝑚 = 1, … , 𝑀 − 1 , 𝑖 = 0,1 … , 𝑇 − 1

𝑎𝑘(0, 𝜃𝑟 , 𝜙𝑟) = 1 𝑎𝑛𝑑 𝑎𝑘+1(0, 𝜃𝑟 , 𝜙𝑟) = 0

𝜙𝑛 is the angular position of element n

𝑀 is the number of circular antenna elements

and 𝑏 is the radius of the circle.

In this research, an initial candidate number is defined for 360 azimuth angles and

90 elevation angles. Hence the number of candidates is 360 X 90.

4.6 Experimental Setup

In order to verify the proposed method, examination in a controlled environment

such as a hardware simulator is necessary. In this research Novatel Digital GNSS

Antenna (DGA) with software receiver and SPIRENT GSS6700 simulator running

115

SimREPLAYPlus software are utilized to verify the proposed method. The simulation of

antenna array requires DGA for each array element which imposes additional complexity

in data processing to synchronize received data among array elements and ensure that all

elements of the array are identical. In this thesis a new method that enables the

simulation of multi-dimensional GPS antenna array systems using limited hardware

resources is introduced.

One RF-frontend and a single RF output SPIRENT GSS6700 simulator running

SimREPLAYPlus software are utilized to verify the proposed method. Initially, the

desired experimental parameters such as number of antenna elements, array geometry,

GPS signal frequency (i.e. L1, L2 and L5), and consequently antenna element spacing,

are defined. Upon designating the zero-phase element’s (reference element) location in

terms of latitude, longitude and height, the remaining elements of the array are mapped

according to the pre-defined experimental configuration. Once the locations of all

antenna elements are set, a simulation scenario is created using the simulator software.

The simulator software enables the reiteration of the simulation scenario without

changing any parameters except for the location of the antenna element in 3D space.

Figure 4-15 illustrates the simulation sequence for a given 𝑀-element array, where each

iteration corresponds to one of the array elements where 𝑛 = 1, … , 𝑀.

Figure 4-15: Simulation sequence of an M-element array of GPS antennas

Simulation #1 Simulation #2 Simulation #n

116

The RF GPS signal output from the hardware simulator is acquired, digitized, down-

converted and stored using DGA. Finally, post-processing software implemented in

Matlab is used for further testing. The developed technique substitutes for the presence of

a physical array and multiple frontends. Hence, he array is assumed to be calibrated and

hence mutual coupling is neglected. As mentioned earlier, single RF output Spirent

GSS6700 GPS simulator running SimREPLAYPlus software was employed. The former

generates RF GPS L1 signals while the latter controls the simulator and provides scenario

editing and replaying capabilities. The simulator is connected to the Novatel FireHose

frontend which provides the raw I and Q baseband samples as shown in Figure 4-16a.

The FireHose settings adopted for the experiment are shown in Table 4-1 below. The

antenna configuration used in the first experiment was a 7 element ULA with constant

element spacing of 9.5 cm.

Table 4-2 shows the locations of the 7 elements, which were used in the simulation runs.

Table 4-1: Settings adopted for data collection using FireHose frontend

Simulation Parameter Parameter Value

Sampling Frequency (MHz) 2.5

Sampling Complex ( I and Q )

Quantization Bits 8

117

Table 4-2: Location of the array elements used in the experiment

Latitude Longitude Altitude (m)

Degrees Minutes Degrees Minutes

38 41.1306350753688 -96 30.2343023307719 100

38 41.1306387187878 -96 30.2342370968847 100

38 41.1306423622068 -96 30.2341718630009 100

38 41.1306460056250 -96 30.2341066291172 100

38 41.1306496490418 -96 30.2340413952265 100

38 41.1306532924587 -96 30.2339761613428 100

38 41.1306569358752 -96 30.2339109274590 100

The raw samples obtained from the frontend are post-processed and tested using software

developed by the NavINST research group. The experiment was conducted on March

18th

, 2014 at 10:00 am. Ten GPS satellites were available at the time of the experiment.

Figure 4-16b shows the skyplot of the available satellites. Only 5 satellites were used for

the DoA estimation methods verification. The 5 satellites’ space vehicle numbers (SVN)

are: 2,4,5,9 and 30. They were chosen specifically due to their positions and elevations in

order to prevent any two satellites from having similar elevations since this is a one

dimensional array and azimuth is not measured. The concentric circles and the diameters

represent the elevation and azimuth angles in degrees respectively.

118

Figure 4-16: Experimental setup and Skyplot of the experiment.

(a) Experimental setup of the Spirent 6700 and the Firehose

(b) Skyplot of available satellites and the ones used, provided by the developed software receiver.

The acquisition results, shown in Figure 4-17, produced by the NavINST software

receiver using the data obtained from the FireHose verified the correctness of the data by

acquiring 5 satellites as planned in the Spirent simulation scenario. Furthermore, DoA

estimates using classical DoA estimation method were computed as shown in Table 4-3.

15

30

45

60

75

30

210

60

240

90270

120

300

150

330

180

0

04

10

1214 05

24

02

09

30

29

GPS (Used)

GPS (Available)

15

30

45

60

75

30

210

60

240

90270

120

300

150

330

180

0

04

10

1214 05

24

02

09

30

29

GPS (Used)

GPS (Available)

(a)

(b)

119

Comparing the estimated DoAs of selected satellite signals with their simulated elevation

and azimuth, four satellites were successfully detected which confirms the accuracy of

the proposed simulation technique.

Figure 4-17: Acquisition results confirming the utilized satellites after the rest of the

available satellites have been switched off using SimReplay Plus

0 5 10 15 20 25 300

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5Acquisition results

PRN number (no bar - SV is not in the acquisition list)

Acq

uisi

tion

Met

ric

Not acquired signals

Acquired signals

120

Table 4-3: Experimental results for DoA estimation of 5 satellites.

PRN 4 9 2 5 30

Elevation type Low Low/

Moderate

Moderate/

High

High Moderate

Elevation angle 24° 153° 59.67° 106° 132.12°

Classical 38.8 155.8 64.9° N/A 125.6

Error 14.8° 2.8° 5.23° N/A 6.52

4.7 Simulation and Results

The method explained in the previous section was used to generate the GPS L1

signals that were used in this chapter; the simulated signals’ synchronization was later

conducted. This ensures perfect time stamp alignment of recorded sections of GPS

signals. Although mutual coupling was not considered, the experimental setup arranged

the array elements as wide as possible to ensure that the effect of mutual coupling is

negligible since the effect was not considered in this research and the simulated data had

to conform to this assumption.

Two antenna array geometries were examined in this research, namely one-

dimensional and two-dimensional arrays. The former involved a ULA configuration

composed of 7 equally spaced elements separated by 𝜆𝐿1

2 . The latter encompassed two

array configurations which are the 7 element UCA and its expansion, the optimum array

geometry, which was constructed using 8 elements. Seven elements were arranged on the

circumference of a circle with radius of 𝜆𝐿1

2 and one element at the center of the circle.

The elements were arranged on the circle’s circumference with an equal angular space of

121

2𝜋

7. The performance of the proposed method is evaluated in terms of the number of

jammers detected and the resolution of the method. Therefore, several scenarios have

been devised; they differ depending on the geometry of the array, the number of jammers,

their power and their spatial locations.

Three sets of scenarios are studied; namely for the three geometries 1) ULA, 2)

UCA and 3) the optimum array (UCA with central element). Scenarios tested the

detection capabilities of the proposed method and compare it to MUSIC and Classical

DoA estimation methods. The scenarios test a single jammer and multiple closely spaced

jammers with equal Jamming to signal ratios. For all array configurations the test

jamming signal levels were 15 and 45 dB. The process of introducing jamming signals is

achieved by adding sinusoidal signals to the output of DGA. The simulated jammer

frequencies ranged between 100 to 400 Hz. This is to ensure that the introduced jamming

signals fall within the bandwidth of the DGA output L1 signals which are baseband

signals with 2 kHz bandwidth.

4.7.1 Results for ULA

The following section demonstrates the results obtained from the different

scenarios that were implemented in order to evaluate the performance of the developed

high resolution DoA estimation method for the ULA geometry. The proposed method

was tested with single and multiple jamming signals arriving at different JSRs.

4.7.1.1 Single Jammer

The results obtained for a single jammer simulated at a frequency of 100 Hz and

arriving at an elevation angle of 50o are shown in Figure 4-18 and Figure 4-19. The

122

figures illustrate the normalized output for Classical DoA, MUSIC and FOS DoA

methods.

Figure 4-18 DoA estimation of one jammer at JSR=15 dB

It can be demonstrated from the figures that Classical DoA, MUSIC and FOS detected

the single jammer with high accuracy at JSRs of 15 and 45 dB. When detection of a

single GPS jamming signal is required, the performance of all three methods is

satisfactory as the jammer of interest is usually arriving at relatively high power.

0 20 40 60 80 100 120 140 160 1800

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Angle in degrees

Norm

aliz

ed S

patial S

pectr

um

Classical

Proposed Method

MUSIC

123

Figure 4-19: DoA estimation of one jammer at JSR=45 dB

The main contribution of the proposed method when estimating the DoA of a single

jammer is the high accuracy in the detection of jamming signals’ amplitude. This is

mainly related to the nature of operation of FOS on which the method is built. It operates

by constructing a signal model determined by candidate functions corresponding to the

detected signals.

4.7.1.2 Multiple Jamming Signals

The performance analysis of FOS versus MUSIC and classical DoA was

examined in terms of resolution, tolerance to JSR and tolerance to jamming signals

coherence. For this purpose, three Jamming signals were simulated with frequencies of

0 20 40 60 80 100 120 140 160 1800

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Angle in degrees

Classical

Proposed Method

MUSIC

124

100 Hz, 200 and 300 Hz and arriving at elevations of 500, 600 𝑎𝑛𝑑 700 respectively.

The tolerance to jamming signals coherency was examined by repeating this scenario

with three jamming signals at frequencies of 100,105 and 110 Hz.

The results obtained for 3 jammers arriving at elevations of (500, 600 𝑎𝑛𝑑 700 ) are

shown in Figure 4-20 and Figure 4-21 at different JSR’s. The figures show the

normalized output for Classical DoA estimation, MUSIC and FOS-based DoA estimation

methods. The JSRs of the jamming signals used in Figure 4-20 and Figure 4-21 are 15

and 45 dB respectively.

Figure 4-20 DoA estimation of 3 jammers at JSR=15 dB and frequencies of 100Hz, 200Hz

and 300Hz

0 20 40 60 80 100 120 140 160 1800

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Angle in degrees

Norm

aliz

ed S

patial S

pectr

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Classical

Proposed Method

MUSIC

125

Figure 4-21 DoA estimation of 3 jammers arriving at JSR=45 dB and frequencies of 100Hz,

200Hz and 300Hz

The results shown in the above figures demonstrate that the proposed method

FOS-based method outperformed both of MUSIC and Classical DoA due to its high

tolerance to variation of JSR and jamming signals coherency. MUSIC showed good

performance in detecting three jammers at JSR of 45 dB with zero error in estimated

DoAs, but its performance degraded at JSR of 15 dB as it detected two jammers only. On

the other hand FOS had stable performance in terms of the number of jammers detected

at JSR of 15 dB and 45 dB as it detected 3 jammers accurately with zero error in

estimated DoAs. FOS had a slight degradation at JSR of 15 dB where its power allocation

for detected jammer was not equally divided among the three jammers that were initially

simulated with equal power.

0 20 40 60 80 100 120 140 160 1800

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Proposed Method

MUSIC

126

4.7.2 Results for UCA

The proposed method (FOS) performance was examined using a UCA

configuration described earlier with 7 elements equally spaced on the circumference of a

circle with a radius of 𝜆𝐿1

2.


A single jammer was simulated as a 100 Hz sinusoidal signal arriving at elevation

of 400 and an azimuth of 400. Figure 4-22, Figure 4-23 and Figure 4-24, demonstrate

that the performance of FOS, MUSIC and Classical DoA in 2D single jammer detection

is almost identical and shows clear detection of the jamming signal with zero error in

both elevation and azimuth. The advantage of FOS and MUSIC is that their spatial

spectrum has much higher resolution compared to that of Classical DoA.

Figure 4-22 DoA estimation of one jammer using Classical DoA at JSR=45 dB

0

20

40

60

80

100

0

100

200

300

400

0

0.2

0.4

0.6

0.8

1

Elevation (Degrees)

X: 40

Y: 40

Z: 1

Classical Number of Jammers=1 JSRdB

= 45

Azimuth (Degrees)

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127

Figure 4-23: DoA estimation of a single jammer using MUSIC at JSR = 45 dB

Figure 4-24 DoA estimation of one jammer using FOS at JSR = 45 dB

02040

6080100

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MUSIC Number of Jammers=1 JSRdB

= 45

Azimuth (Degrees)

X: 40

Y: 40

Z: 1

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X: 40

Y: 40

Z: 1

FOS Number of Jammers=1 JSRdB

=15

Elevation (Degrees)

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128


In this scenario, three equal power jammers were simulated at frequencies of 100,

200 and 300 Hz with elevations and azimuths separations of 10°. The DoAs of the three

jammers were simulated at (30°, 30°), (40°, 40°) and (50°, 50°). This experiment is

conducted at JSRs of 15 and 45dB. Results obtained from MUSIC and Classical DoA

estimation methods are shown in Figure 4-25 to Figure 4-28. In this scenario the

performance of FOS is compared to MUSIC only as their performance versus Classical

DoA method was already examined for ULA and showed superior performance in all

cases over Classical DoA.

Figure 4-25: DoA estimation of 3 closely spaced jammers using MUSIC at JSR = 15 dB

0 10 20 30 40 50 60 70 80 900

200

400

0

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1

Azimuth (Degrees)

Elevation (Degrees)

X: 48

Y: 48

Z: 1


= 15

X: 33

Y: 33

Z: 0.4891

Norm

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129

Figure 4-26: DoA estimation of 3 closely spaced jammers using FOS at JSR = 15 dB

Table 4-4: Simulation results of 3 closely spaced jammers at JSR=15dB

Jammer 1 2 3

Elevation 30° 40° 50°

Azimuth 30° 40° 50°

MUSIC (33°,33°) N/A (48°, 48°)

Error (3°, 3°) N/A (2°, 2°)

FOS (29°,29°) (40°,40°) (50°,50°)

Error (1°, 1°) (0°, 0°) (0°, 0°)

0 10 20 30 40 50 60 70 80 900

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0.8

0.9

1

X: 50

Y: 50

Z: 0.2353

Azimuth (Degrees)


=15

X: 40

Y: 40

Z: 1

X: 29

Y: 29

Z: 0.2347

Norm

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0

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130

Figure 4-27: DoA Estimation of 3 closely spaced jammers using MUSIC at JSR = 45 dB


0102030405060708090 0200

4000

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0.8

0.9

1

Azimuth (Degrees)

X: 30

Y: 30

Z: 0.2455

Elevation (Degrees)

X: 39

Y: 39

Z: 0.4481


= 45

X: 49

Y: 49

Z: 1

Norm

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0

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1

Elevation (Degrees)

X: 50

Y: 50

Z: 0.9535

Azimuth (Degrees)

X: 40

Y: 40

Z: 1


=45

X: 29

Y: 29

Z: 0.9535

Norm

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131


Jammer 1 2 2


Azimuth 30° 40° 50°

MUSIC (30°,30°) (39°, 39°) (49°, 49°)

Error (0°, 0°) (1°, 1°) (1°, 1°)

FOS (29°,29°) (40°,40°) (50°,50°)

Error (1°, 1°) (0°, 0°) (0°, 0°)

Results shown in Figure 4-26 and Figure 4-28 showed steady performance for

FOS in terms of resolution and number of detected jammers for both cases of JSR 15 dB

and 45 dB. The degradation in FOS was observed in its allocation of power to jamming

signals as it was not accurately allocated for jammers arriving at JSR of 15 dB. The

increase in the level of noise affected FOS performance and caused most of the power to

be allocated to the jammer arriving at 40°. MUSIC performed similarly to FOS at JSR of

45 dB as shown in Figure 4-27 with a slight decrease in accuracy as shown in Table 4-5

with maximum error of 1° in both elevation and azimuth of the jamming signals.

Additionally, MUSIC had a much lower accuracy in power allocation for the three

jamming signals. The degradation in MUSIC performance was more evident at lower

JSR where MUSIC was able to detect only two jamming sources as shown in

Figure 4-25. The accuracy of the detected DoA elevation and azimuth of jamming signals

132

at 15 dB JSR are close for both FOS and MUSIC as shown in Table 4-4 with slight

increase of 1° in the error of jamming signals detected by MUSIC.

Examining the performance of FOS versus MUSIC in resolving very closely spaced jammers:

In this scenario, the performance of 2D FOS is compared to that of MUSIC by

introducing 2 close-by signals at 100 Hz and 200 HZ separated by 5° in both azimuth and

elevation, thus further challenging the detection methods. The two jammers under

investigation were simulated with DoA elevation and azimuth of (400, 400)

and (450, 450) respectively. Results are shown in Figure 4-29 to Figure 4-32 and

numerical results are listed in Table 4-6 and Table 4-7.


0 10 20 30 40 50 60 70 80 900

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X: 43

Y: 43

Z: 1

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133



Jammer 1 2

Elevation 40° 45°

Azimuth 40° 45°

MUSIC (43°,43°) N/A

Error (3°, 3°) N/A

FOS (40°,40°) (45°,45°)

Error (0°, 0°) (0°, 0°)

0 10 20 30 40 50 60 70 80 900

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1

X: 45

Y: 45

Z: 0.8815

Elevation (Degrees)


= 15

X: 40

Y: 40

Z: 1

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134



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200400

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Elevation (Degrees)

X: 40

Y: 40

Z: 0.4602

X: 45

Y: 45

Z: 1


= 45

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X: 45

Y: 45

Z: 1

Elevation (Degrees)

FOS Number of Jammers= 2 JSRdB

= 45

X: 40

Y: 40

Z: 0.979

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135


Jammer 1 2

Elevation 40° 45°

Azimuth 40° 45°

MUSIC (40°,45°) (40°, 45°)

Error (0°, 0°) (0°, 0°)

FOS (40°,40°) (45°,45°)

Error (0°, 0°) (0°, 0°)

The above results of the FOS-based method and MUSIC performance in detecting

two very-closely spaced jammers at a separation of 5° showed similar performance in

accuracy of jammer detection with an advantage of FOS having zero error detection in

both cases of JSR 15 dB and 45 dB and almost steady performance in resolving the two

jammers. On the other hand MUSIC was affected by the increase in noise level as it

failed to resolve the two jammers at JSR 15 dB and had an error of 3 degrees in detecting

the DoAs of jamming signals at JSR 15dB.

4.7.3 Results of Optimum Array

The procedures followed in uniform circular array experiments were used to

examine the performance of FOS versus MUSIC in jamming detection using optimum

array configuration. The configuration of optimum array is similar to UCA configuration

136

with 7 elements equally spaced on circumference of a circle with radius of 𝜆𝐿1

2 and an

additional element at the center of the circle.


The results obtained for a single jammer arriving at an elevation of 400 and an

azimuth of 400are shown in Figure 4-33 to Figure 4-36. The figures show the normalized

output for, MUSIC and FOS DoA methods. Both methods had similar detection

performance of single jammer.

Figure 4-33: DoA estimation of one jammer using MUSIC at JSR=15 dB (optimum array)

01002003000 10 20 30 40 50 60 70 80 90

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Azimuth (Degrees)

X: 40

Y: 40

Z: 1


=15

Elevation (Degrees)

Norm

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137

Figure 4-34: DoA estimation of one jammer using FOS at JSR=15 dB (optimum array)

Figure 4-35 DoA estimation of one jammer using MUSIC at JSR=45 dB (optimum array)

01002003000 10 20 30 40 50 60 70 80 90

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X: 40

Y: 40

Z: 1


=15

Elevation (Degrees)

Nor

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Spa

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rum

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4060

80100

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400

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X: 40

Y: 40

Z: 1

Azimuth (Degrees)

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138

Figure 4-36: DoA estimation of one jammer using FOS JSR=45 dB (optimum array)


The results obtained for 3 jammers arriving at an elevation of (300, 400 𝑎𝑛𝑑 500 )

and azimuth angles of (300, 400 𝑎𝑛𝑑 500) respectively are shown in Figure 4-37 to

Figure 4-40. The figures below show the normalized output for MUSIC and 2D FOS

DoA methods. The performance of MUSIC in jamming detection using optimum array

configuration did not show significant improvement compared to UCA performance.

Conversely, FOS performance showed more significant improvement compared to

MUSIC when the central element was added at the center of UCA as described in the

optimum array configuration. The performance of FOS at JSR of 15 dB and 45 dB has

become almost steady in terms of resolution of jamming sources and power allocation for

each source as demonstrated in Table 4-8 and Table 4-9.

0100

200300

400

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X: 40

Y: 40

Z: 1


=45

Elevation (Degrees)

Nor

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Spa

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rum

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139

Figure 4-37: DoA estimation of 3 jammers using MUSIC at JSR=15 dB (optimum array)

Figure 4-38: DoA estimation of 3 jammers using FOS at JSR=15 dB (optimum array)

0 10 20 30 40 50 60 70 80 900

0.1

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0.8

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1

X: 48

Y: 48

Z: 1

Elevation (Degrees)


= 15

X: 32

Y: 32

Z: 0.3793

Norm

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Azimuth (Degrees)

Elevation (Degrees)

X: 50

Y: 50

Z: 0.7044


=15

X: 40

Y: 40

Z: 1X: 29

Y: 29

Z: 0.704

Norm

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140

Table 4-8: Simulation results of 3 closely spaced jammers using optimum array at

JSR=15dB

Jammer 1 2 3


Azimuth 30° 40° 50°

MUSIC (32°,32°) N/A (48°, 48°)

Error (2°, 2°) N/A (2°, 2°)

FOS (29°, 29°) (40°,40°) (50°,50°)

Error (1°, 1°) (0°, 0°) (0°, 0°)

Normalized Amplitude 0.704 1 0.7044

Figure 4-39: DoA estimation of 3 jammers using MUSIC at JSR=45 dB (optimum array)

0 10 20 30 40 50 60 70 80 900

200

400

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

X: 49

Y: 49

Z: 1


= 45

Elevation (Degrees)

X: 39

Y: 39

Z: 0.3543

X: 30

Y: 30

Z: 0.2667

Norm

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Azimuth (Degrees)

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141

Figure 4-40: DoA estimation of 3 jammers using FOS at JSR=45 dB (optimum array)


JSR=45dB

Jammer 1 2 3


Azimuth 30° 40° 50°

MUSIC (30°, 30°) (39°, 39°) (49°, 49°)

Error (0°, 0°) (1°, 1°) (1°, 1°)

Normalized Amplitude 0.2267 0.3543 1

FOS (29°,29°) (40°,40°) (50°,50°)

Error (1°, 1°) (0°, 0°) (0°, 0°)

Normalized Amplitude 0.9642 1 0.9642

0

2000 10 20 30 40 50 60 70 80 90

0

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0.3

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0.9

1

X: 50

Y: 50

Z: 0.9642


=45

Elevation (Degrees)

X: 40

Y: 40

Z: 1

X: 29

Y: 29

Z: 0.9642

Azimuth (Degrees)

Norm

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142

Examining the performance of FOS versus MUSIC in resolving very closely spaced jammers:

A similar procedure to the one used on the UCA in 4.7.2 was applied to examine

the resolution capabilities of the proposed method versus MUSIC using the optimum

array configuration. Results are shown in Figure 4-41 to Figure 4-44 and in Table 4-10

and Table 4-11 for JSRs of 15 and 45 dB respectively. Similar to section 4.7.2 MUSIC

was not able to detect both the jammers at JSR of 15 dB and was only able to do so when

the JSR was higher at 45 dB

Figure 4-41: DoA estimation of 2 closely spaced jammers using MUSIC at JSR=15 dB

(optimum array)

0 10 20 30 40 50 60 70 80 900200

400

0

0.1

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0.5

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0.9

1

X: 43

Y: 43

Z: 1

Elevation (Degrees)


= 15

Azimuth (Degrees)

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143

Figure 4-42 DoA estimation of 2 closely spaced jammers using FOS at JSR=15 dB (optimum

array)


JSR=15dB

Jammer 1 2

Elevation 40° 45°

Azimuth 40° 45°

MUSIC (43°,43°) N/A

Error (3°, 3°) N/A

FOS (40°,40°) (45°,45°)

Error (0°, 0°) (0°, 0°)

Normalized Amplitude 1 0.9225

02000 10 20 30 40 50 60 70 80 90

0

0.1

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0.4

0.5

0.6

0.7

0.8

0.9

1

Azimuth (Degrees)

X: 45

Y: 45

Z: 0.9225

Elevation (Degrees)


=15

X: 40

Y: 40

Z: 1

Nor

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Spa

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rum

0

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144

Figure 4-43: DoA estimation of 2 closely spaced jammers using MUSIC at JSR=45 dB

(optimum array)

Figure 4-44: DoA estimation of 2 closely spaced jammers using FOS at JSR=45 dB

(optimum array)

0 10 20 30 40 50 60 70 80 90

0200

400

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Azimuth (Degrees)

Elevation (Degrees)

X: 45

Y: 45

Z: 1


= 45

X: 40

Y: 40

Z: 0.5817

Nor

mal

ized

Spa

tial S

pect

rum

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

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1

0

2000 10 20 30 40 50 60 70 80 90

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Azimuth (Degrees)

X: 45

Y: 45

Z: 0.9974

Elevation (Degrees)


=45

X: 40

Y: 40

Z: 1

Nor

mal

ized

Spa

tial S

pect

rum

0

0.1

0.2

0.3

0.4

0.5

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1

145

Table 4-11: Simulation results of 2 closely spaced jammers using optimum array at JSR=45

dB

Jammer 1 2

Elevation 40° 45°

Azimuth 40° 45°

MUSIC (40°,40°) (45°,45°)

Error (0°, 0°) (0°, 0°)

Normalized Amplitude 0.5817 1

FOS (40°,40°) (45°,45°)

Error (0°, 0°) (0°, 0°)

Normalized Amplitude 1 0.9974

The above results showed similar improvement in comparison to UCA

performance for both FOS and MUSIC with slight improvement in the power allocation

of the FOS-based proposed method for jamming signals at JSR = 15 dB. MUSIC

performance at JSR of 15 dB was not improved by using optimum array configuration

and its detection capabilities for two very closely spaced jammers remained limited at

JSR of 15 dB. The results displayed in Table 4-11 demonstrate MUSIC’s drawbacks in

terms of power assignment and sensitivity to noise.

146

4.8 Conclusion

In this chapter, the DoA estimation for interference detection was studied. The main

factors impacting the process of interference detection through DoA were investigated in

order to design an optimum jamming detection system using antenna array. The

suggested optimum configuration is intended for the process of jamming detection and

can be also beneficial in jamming mitigation. A new procedure was introduced to

simulate GPS received signals using a single RF output Spirent GSS 6700 GPS simulator

and a single RF input Novatel FireHose frontend. Post-processing validated the GPS

signals used.

Several Antenna array configurations were reviewed to demonstrate their effect on DoA

estimation capabilities of antenna arrays. Furthermore, this section of the thesis

investigated the process of optimum array design using mathematical optimization. The

main contribution of this chapter is the application of nonlinear signal modeling

techniques for jamming detection utilizing ULAs and UCAs. The nonlinear signal

modeling technique employed for DoA estimation was based on FOS. The nature of

operation of the proposed method provides additional capabilities to DoA estimation.

This was shown in its capability of achieving steady performance in jamming detection at

different JSR’s. Moreover, when the optimum array configuration was studied, the

proposed method showed significant improvement in estimating the magnitude of the

spatial spectrum when compared to MUSIC. The proposed method consistently

outperformed MUSIC, which only started to show similar performance improvements

from the optimum array configuration when more powerful jamming signals were

simulated.

147

Spirent simulated GPS signals received by antenna arrays were used in the conducted

simulations to test the performance of the propose method against MUSIC and Classical

DoA estimation. Jammer signals were simulated using MATLB and added to the

simulated GPS signals. Configurations such as the ULA, UCA and the optimized UCA,

which is constructed by adding a central element to the circular antenna array, were

utilized in this study. The main benefit gained from applying FOS was to achieve higher

accuracy in interference DoA estimation in terms of magnitude and angle. This was

illustrated in single and multiple jamming detection scenarios for the aforementioned

array configurations. The proposed method demonstrated an improved ability to

accurately detect the amplitudes of the single jammers. As for multiple interference

detection, for ULA, the capabilities of jamming detection of Classical DoA are limited by

the resolution; MUSIC on the other hand is much more sensitive to noise and performs

worse at lower signal power. This became evident when the proposed method detected all

three jammers and MUSIC only detected two at relatively low JSR. The method also

demonstrated higher accuracy in detection of the 3 sources of interference with slight

variations in their amplitude at relatively low JSR 15 dB. Since the proposed method is

not optimized for real time operation, it is limited by its higher computational complexity

compared to the Classical method. Nevertheless, the added complexity is justified by the

high gains in accuracy. The proposed method is also limited by the number of elements in

the array and will therefore perform better and detect a higher number of closely spaced

jammers when applied to larger arrays.

148

Chapter 5

Conclusions and Recommendations

The enhancement of the anti-jamming capabilities of GPS receivers was the main

objective of this thesis. The research conducted herein focused on increasing the overall

detection accuracy of the GPS receivers in both the frequency and space domains by

introducing new methods that are based on high resolution signal processing. A brief

outline of the outcomes of this thesis along with the conclusions reached is given in this

chapter. Moreover, the future research that can extend and improve the work

accomplished by this thesis is presented in addition to the recommendations that are

based upon its findings.

5.1 Conclusions

To realize the objectives of this thesis, two new methods that are based on high

resolution signal processing techniques were introduced. The first method which operated

in the frequency domain and relied on spectral analysis was introduced for regular users

which constitute the vast majority of GPS receivers in mind. Using this method, these

receivers that only rely on one antenna can detect jammers with higher accuracy than that

provided by the predominant methods such as FFT. The second method targeted

professional grade anti-jamming equipment that takes advantage of the space domain.

The proposed method is based on high resolution DoA estimation of jammers in order to

provide smart antennas with the most accurate estimate of the jammers’ DoAs such that

beam steering and null steering processors nullify the jammer signals without erroneously

149

nullifying parts of the GPS signal thereby decreasing its effectiveness. These methods

were designed to operate in the pre-correlation section of GPS receivers where mitigation

is more effective.

An overview of the GPS system and receiver structures, followed by an

introduction to the types of interference, jamming and anti-jamming techniques was

provided in Chapter 2. It was concluded by a review of different DoA estimation

methods. Special interest was given to CW interference and jamming in Chapter 3, in

which an enhanced GPS narrowband jamming detection method, that uses high resolution

spectral estimation, was introduced. The proposed method is based on orthogonal search

and has featured several spectral estimation capabilities including high frequency

resolution, elimination of spectral leakage and rejection of background noise; which

subsequently resulted in a significant enhancement to the GPS jamming detection

process. The proposed method consistently demonstrated a twofold superiority over the

predominant FFT for both the accuracy of the jammers’ frequency estimation and the

ability to detect multiple closely spaced jammers.

FFT could only match the proposed detection method in specific cases. It

provided resolutions similar to that of the proposed method at an FFT window size which

was 10 times larger than that used by FOS. Moreover, our method accurately and

efficiently estimated the number and frequencies of multiple in-band CW jammers whose

frequency separation is lower than that of FFT resolution step. This twofold advantage

was as demonstrated in scenarios 2 and 3. Nevertheless, increasing the number of

jammers degrades the detection accuracy at lower JSRs. As previously demonstrated, at

low JSRs and using a 1 ms window, the proposed frequency domain method was only

150

able to detect the three closely spaced jammers (100 Hz separation between each other)

when their individual JSRs reached 27 dB. On the other hand, FFT’s disadvantage

became clear when it detected the three jammers as one jammer regardless of the

individual JSR levels. This inability to detect multiple jammers can only be improved by

increasing the window size.

The spatial domain aspect of the GPS jamming detection enhancement by DoA

estimation of jammers was tackled in Chapter 4. In addition to accurate DoA estimation,

the introduced method achieved high resolution detection of jammers whose spatial

separation is minimal; which is a major goal of this part of the thesis. The method was

studied, developed and tested for both one-dimensional and two dimensional arrays in the

form of ULA, UCA and optimum UCA. Its performance was compared to Classical DoA

estimation and MUSIC using several scenarios that differ in the number of jammers, their

spacing and their power levels. Additionally, a new method that enables the simulation of

multi-dimensional GPS antenna array systems using limited hardware resources was

developed and introduced in order to test the effectiveness of the proposed high

resolution DoA estimation method.

The proposed FOS-based method uses nonlinear signal modeling to provide the DoA

estimates. The method is based on an orthogonal search technique that creates a basis for

the steering function of the array. The steering function coefficients are determined via a

unique orthogonal search method that provides the high accuracy DoA estimates of the

jammers. When applying FOS, one candidate was generated per degree, so when 360

degrees were searched, FOS generated 360 candidates, which subsequently gave control

over the angle being searched. In addition, sub-degree resolution searches became

151

accessible. When these searches were conducted using Classical DoA estimation, a

multitude of DoA estimates that have the same magnitude was provided for the jammer

being search for.

The proposed method clearly outperformed the predominant methods in terms of

accuracy at lower JSRs and in terms of the number of closely spaced jammers detected as

previously demonstrated in Chapter 4. The proposed method prevailed against MUSIC in

both close-by jammers’ scenarios. When two jammers with a 5 degree separation were

being tested at 15 dB JSR, MUSIC detected them as only one jammer with a 40 percent

prediction error; in contrary to the proposed method which successfully detected the

presence of two jammers and accurately estimated their DoAs without error.

Additionally, in a more demanding scenario which involved three closely spaced

jammers, the proposed method demonstrated superiority by correctly detecting the

presence of all three, accurately estimating the DoAs of two jammers and erring in the

DoA estimation of the third jammer by one degree. MUSIC was only able to detect two

of the three jammers thus suffering a 33 percent detection error. Moreover, both

estimations incurred a two degree error which corresponds to a 50 percent higher error

for that jammer compared to the proposed method.

5.2 Recommendations and Future Work

The research conducted in this thesis along with the provided experimental results brings

forth the following recommendations:

152

1. The detection accuracy achieved in both the frequency and spatial domains by

using the proposed methods imply that further optimization and real-time

implementations of the methods are in order.

2. Since the proposed frequency domain method is designed to operate in the pre-

correlation section of the receiver, it can be easily implemented as a hardware

add-on structure to receivers or as a software upgrade to current software

receivers.

3. The proposed DoA estimation method merits the same attention for the

substantial improvements an anti-jamming system stands to gain by applying this

method, although it is not recommended for consumer grade GPS receivers due to

the supplementary cost incurred by the necessary added hardware. Nevertheless it

is highly recommended for military grade anti-jamming receivers.

4. It is highly recommended to use a central element with circular arrays and apply

the interference power minimization optimization because its yields more

accurate jammer amplitude estimation.

Based on the scope and findings of the thesis, the predicted future research work is

presented as follows:

1. In this thesis, only the GPS L1 signal has been experimented on, mainly due to

the fact that GPS is the most dominant and widespread GNSS. Other systems such

as Galileo, GLONASS and BeiDou operate on different frequencies; nevertheless,

they are still prone to jamming. As these systems become more established and

integrated into mainstream receivers, so will the jammers designed to impede the

receivers’ performance. Therefore, it is recommended that this work be expanded

153

into other GNSS frequencies and systems in addition to bearing in mind a unified

jamming detection platform that operates on multi-GNSS receivers.

Modifications to the methods proposed in this thesis should be applied when

considering other GNSSs, nonetheless, the approaches and the methodologies

followed remain similar. It is foreseeable that the application of this research to

different GNSSs will pose different challenges depending on the signals under

study.

2. The prevalence of CW interference and jamming is among the motivating factors

of this study. Unfortunately, other jamming techniques are steadily making their

way into the GPS jamming market, thus increasing the likelihood of GPS

jamming and complicating the anti-jamming receiver’s design and

implementation in order to combat such signals. Hence, the methods proposed in

this thesis should be applied to other jamming types (based on bandwidth and

modulation) that specifically target GPS and should be modified accordingly.

3. External aiding sensors such as INS are typically integrated on different levels

with GPS receivers in order to provide a position solution in case of GPS outages.

A study of the benefits of augmenting integrated GPS/INS systems with a

jamming detection and potentially a jamming mitigation system on the overall

performance of the receiver is deemed required and beneficial.

4. Since the DoA estimation was conducted on one and two dimensional arrays, the

proposed method should be extended to include three dimensional array

geometries, which would highly benefit the anti-jamming process by exploiting

154

the advantages provided by three dimensional arrays such as spatially mitigating

low elevation satellite multipath and similar direction jamming.

155

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