Enhancement of target detection using software defined radar (SDR)

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by

Ahmed Youssef

B.Sc., Military Technical College, 2004 M.Sc., Military Technical College, 2012

A Dissertation Submitted in Partial Fulfillment of the Requirements for the Degree of

DOCTOR OF PHILOSOPHY

in the Department of Electrical and Computer Engineering

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Enhancement of Target Detection Using Software Defined Radar (SDR)

by

Ahmed Youssef

B.Sc., Military Technical College, 2004 M.Sc., Military Technical College, 2012

Supervisory Committee

Dr. Peter F. Driessen, Supervisor

(Department of Electrical and Computer Engineering)

Dr. F. Gebali, Supervisor

Dr. Stephen Harrison,

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Supervisory Committee

Dr. Peter F. Driessen, Supervisor

Dr. F. Gebali, Supervisor

Dr. Stephen Harrison,

(National Research Council of Canada)

ABSTRACT

Three novel approaches that are based on a recent communication technique called time compression overlap-add (TC-OLA), are introduced into pulse compression (PC) radar systems to improve the radar waveform shaping and enhance radar performance. The first approach lays down a powerful framework for combining the TC-OLA tech-nique into traditional PC radar system. The new TC-OLA-based radar obtained is compared with other radars, namely traditional linear frequency modulation (LFM), and wideband LFM which has the same processing gain under different background situations. The results show the superiority of the proposed radar over the others. The second approach combines a random phase noise signal with a selected radar signal to build a new radar system, SSLFM radar, that enjoys the low-probability of intercept property, and, therefore, has higher immunity against noise jamming tech-niques compared with other radar systems. The properly recovery of the transmitted signal, however, requires a synchronization system at the receiver side. In this dis-sertation, we propose three synchronization systems each having different pros and cons. The last approach takes the radar waveform design methodology in a different direction and proposes a novel framework to combine any number of radar signal and transmit them simultaneously. Instead of trying to achieve universality through waveform shaping optimization, we do so via pluralism. As a proof of concept, all the

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proposed radars have been implemented and tested on software-defined radar (SDR). The theoretical and the experimental results showed the superiority of all proposed radar systems. Since TC-OLA is fundamental to this work, we add a chapter to propose a new technique called downsample upsample shift add (DUSA) to address the limitations of the existing implementation of TC-OLA.

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List of Tables

Table 2.1 Comparison between Pulse Compression techniques with respect

to PSL and Range resolution . . . 29

Table 3.1 Simulated parameters of the radar model, the target, and the jamming technique . . . 39

Table 3.2 TC-OLA parameters . . . 40

Table 4.1 Simulated parameters . . . 71

Table 4.2 Comparison between SSLFM TC-OLA, TC-OLA-based LFM, and wideband LFM. . . 95

Table 4.3 Experimental parameters . . . 101

Table 5.1 Simulated parameters . . . 115

Table 5.2 Experimental parameters . . . 132

Table 6.1 Parameters used to validate our model. . . 141

Table 6.2 Mapping for DUSA . . . 143

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List of Figures

Figure 2.1 LFM pulse and its power spectral density (Top) and matched

filter output (bottom). . . 11

Figure 2.2 LFM matched filter output before and after applying different weighting windows. . . 12

Figure 2.3 Stepped frequency waveform burst, N = 5 [7]. . . 14

Figure 2.4 Frequency-time array for LFM and Costas code [7]. . . 15

Figure 2.5 Transmitted and received pulse modulated by BC of length 13. 17 Figure 2.6 Autocorrelation function of 5 × 4 combined BCs. . . 18

Figure 2.7 Matched filter output mismatching for different Doppler shift values. . . 19

Figure 2.8 Frank code, N=4 [7]. . . 22

Figure 2.9 Frank code phase to be like LFM phase, N = 4 [7]. . . 23

Figure 2.10Incremental phase of the Frank code, N = 8. . . 24

Figure 2.11Incremental phase of the P1 code, N = 8. . . 25

Figure 2.15Output of matched filter for P4 code, for N = 64. . . 30

Figure 2.16Output of matched filter for Frank code. . . 31

Figure 3.1 Simulated LFM-PC Radar model. . . 36

Figure 3.2 CFAR block diagram for the three selected algorithms, CA-CFAR, GO-CFAR and OS-CFAR. . . 37

Figure 3.3 Generating overlapping segments from the sampled LFM chirp signal (M = 5, R = 1). . . 41

Figure 3.4 The new chirp signal after increasing sampling rate from fs1 to fs2 = M R fs1 (M = 5, R = 1) to ensure non-overlapped segments. . 42

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Figure 3.5 Instantaneous frequency for non-overlapped segments after ap-plying Hanning window. . . 43 Figure 3.6 Spectrogram of LFM chirp signal. . . 44 Figure 3.7 Spectrogram of the TC LFM chirp signal. The spectrum is

spread over M

R fs1. . . 45

Figure 3.8 TC-OLA-based LFM-PC Radar Block. . . 46 Figure 3.9 The response of the proposed TC-OLA-based LFM-PC radar

model. (a) The output of the MF, (b) The Output of MTD, and (c) The Output of the CFAR detector. . . 47 Figure 3.10PD vs SNR curve for traditional LFM-PC and new

TC-OLA-based LFM-PC models at Pf a = 10−6 under AWGN effect. For

new model M

R = 5, 10, 15, and 20. . . 48

Figure 3.11PD vs SNR curve for traditional LFM-PC and new

TC-OLA-based LFM-PC models at PD = 0.5 and Pf a= 10−6under AWGN

effect. For new model M

R = 5, 10, 15, and 20. . . 49

Figure 3.12Jamming pulse only. (a) Jamming pulse before MF; It has twice time duration with respect to radar pulse duration. (b) Jamming pulse after MF; It has three time duration of radar pulse width. 51 Figure 3.13(a) Spectrogram represents CNJ signal based on LFM signal. (b)

Spectrogram represents CNJ signal based on TC LFM signal. . 52 Figure 3.14PD vs SNR curve for traditional LFM-PC radar and under CNJ

at JSR = 10, 25, 30, and 35 dB. . . 53 Figure 3.15PD vs SNR curve for LFM-PC and TC-OLA-based LFM-PC M_R =

5under CNJ at JSR = 10, 25, 30, and 35 dB. . . 55 Figure 3.16PD vs SNR curve for LFM-PC and TC-OLA-based LFM-PC M_R =

10under CNJ at JSR = 10, 25, 30, and 35 dB. . . 56 Figure 3.17PD vs SNR curve for wideband LFM-PC and TC-OLA-based

LFM-PC, M

R = 5, under AWGN. . . 57

Figure 3.18Spectrogram of the wideband LFM chirp signal with B = 75 MHz 59 Figure 3.19Spectrum of the wideband LFM chirp signal with B = 75 MHz

and TC LFM signal, M

R = 5. . . 60

Figure 3.20PD vs SNR curve for wideband LFM-PC and TC-OLA-based

LFM-PC M

R = 5 under CNJ at JSR=30 dB. . . 61

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Figure 4.2 Block diagram of SS#1 for TC-OLA processor. . . 67

Figure 4.5 (a) Spectrogram of LFM signal. (b) Synthesized LFM signal with µ = 1. . . 72

Figure 4.6 Spectrogram of the SSLFM signal with M R = 5 and µ = 1. . . 74

Figure 4.7 Spectrogram of CNJ effect on: (a) wideband LFM signal with bandwidth M RB, (b) TC-OLA-based LFM signal with M R = 5, (c) SSLFM signal with M R = 5. . . 76 (a) . . . 76 (b) . . . 76 (c) . . . 76

Figure 4.8 The response of: (a) the traditional LFM radar, (b) the wideband LFM radar 5B, (c) the TC-OLA-based LFM-PC radar, M R = 5, (d) the SSLFM TC-OLA radar, M R = 5, under JSR = 35 dB. . . 79

(a) . . . 79

(b) . . . 79

(c) . . . 79

(d) . . . 79

Figure 4.9 Output of MF(1) _{for M = 4 and R = 2, and with (a) no shift, (b)} one sample shift, (c) two sample shift, and (d) three sample shift. 81 Figure 4.10The correlation output of MF(2)_{, M = 6, R = 3, for: (a) h}0 M F(2)(n), (b) h1 M F(2)(n), (c) h 2 M F(2)(n). Only the MF with the coefficients x_syn2 d(n) has an apparent correlation peak while the rest do not. 84 Figure 4.11The correlation output of MF(1)_{in the second stage, with M = 6} and R = 3, for (a) 2 sample shifts, (b) 5 sample shifts. . . 85

Figure 4.12The correlation output of MF(2)_{, M = 6, R = 3, for: (a) h}0 M F(2)(n), (b) h1 M F(2)(n), (c) h 2 M F(2)(n), (d) h 3 M F(2)(n), (e) h 4 M F(2)(n), (f) h 5 M F(2)(n), Only the MF with the coefficients x30 syn_d(n) has an apparent cor-relation peak while the rest do not. . . 88

Figure 4.13Time offset problem of 0.45Ts, M = 6, R = 3, and η = 0.5. . . . 90

Figure 4.14The first 20µs of the output of the OLA and denoising processors, M R = 2. (a) Without time offset correction, ρ = 0 (b) With time offset correction, ρ = 0.4Ts. . . 91

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Figure 4.15DPC for traditional LFM, TC-OLA-based LFM, wideband LFM,

and SSLFM TC-OLA radars under AWGN. . . 92

Figure 4.16DPC for traditional LFM, TC-OLA-based LFM, wideband LFM, and SSLFM TC-OLA radars under JSR = 35 dB. . . 93

Figure 4.17DPC for OLA-based LFM, wideband LFM, and SSLFM TC-OLA radars for JSR = 40 dB. . . 94

Figure 4.18Performance of the proposed synchronization systems. (a) M R = 2, (b) M_R = 5, (c) M_R = 10. . . 96

Figure 4.19Output of MF(1) _{for M = 8 and R = 4, and with (a) no shift, (b)} one sample shift, (c) two sample shift, (d) three sample shift, (e) four sample shift, (f) five sample shift, (g) six sample shift, (h) seven sample shift, and (d) eight sample shift. . . 98

Figure 4.20Performance of the proposed synchronization systems. (a) M R = 2, (b) M_R = 5, (c) M_R = 10. . . 100

Figure 4.21(a) LFM signal, B=1MHz, (b) spectrogram of LFM signal. . . . 102

Figure 4.22(a) Received SSLFM signal, (b) spectrogram of received SSLFM signal. . . 103

Figure 4.23Output of the synchronization system - stage 1. The received signal matches the MF number 5. . . 104

Figure 4.24Output of synchronization system - stage 2 after denoising and OLAing processes. (a) recovered LFM signal, (b) spectrogram of recovered LFM signal. . . 105

Figure 4.25MF Output of LFM-PC radar. . . 106

Figure 5.1 Block diagram for N-signal TC-OLA transmitter system. . . 110

Figure 5.2 Block diagram for N-signal TC-OLA receiver system. . . 111

Figure 5.3 Spectrogram of the transmitted signal with M R = 4. . . 116

Figure 5.4 A 5µs of the received signal at the output of the OLA processors. (a) LFM signal, (b) BC signal. The figure shows the additional gain of M R = 4. Note that, selecting different scales in (a) and (b) are for better clarity. . . 117

Figure 5.5 Spectrogram of received signal after the OLA processors. (a) LFM signal, (b) BC signal. . . 118

Figure 5.6 MF outputs for low and high speed targets. (a) LFM signal, (b) BC signal. . . 119

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Figure 5.7 Block diagram for 3-signal TC-OLA receiver system showing the

Doppler cancellation components. . . 120

Figure 5.8 Doppler cancellation algorithm. . . 121

Figure 5.9 MF outputs of BC signal after separation with and without Doppler cancellation module at high-speed target. . . 122

Figure 5.10MTD output at high-speed target case. (a) BC without Doppler cancellation process, (b) BC after Doppler cancellation process, (c) LFM signal with Doppler information. . . 123

(a) . . . 123

(b) . . . 123

(c) . . . 123

Figure 5.11The MF output of CLB waveform for low- and high-speed targets.126 Figure 5.12The MF output of MLB waveform for low- and high-speed targets.127 Figure 5.13The MF output of OLB waveform in the case of low- and high-speed targets. . . 128

Figure 5.14PD curves for LFM and BC after separation of 2-signal TC-OLA system in the case of low and high-speed targets. . . 130

Figure 5.15The real part of the received signal. . . 131

Figure 5.16Received signal after separation (a) LFM signal (b) BC signal. . 133

Figure 5.17Output of the MF detectors; (a) output of LFM MF (b) output of BC MF. . . 134

Figure 6.1 Implementation of DUSA representing the TC-OLA transmitter. 137 Figure 6.2 Implementation of DUSA representing the TC-OLA receiver. . 138

Figure 6.3 The 2 µ sec signal of the DN block with M = 4, R = 2 at the transmitter. (a) Transmitted LFM chirp signal. (b) Path zero downsampled by 2, (c) Path one downsampled by 2, (d) Path two downsampled by 2, (e) Path three downsampled by 2. . . . 143

Figure 6.4 The 2 µ sec signal of the UP block step M = 4, R = 2 at the trans-mitter. (a) path zero upsampled by 4, (b) path one upsampled by 4, (c) path two upsampled by 4, (d) path three upsampled by 4, (e) Transmitted signal after combining the four paths (DUSA method), and (f) Transmitted signal by TC-OLA method. . . . 144

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Figure 6.5 The 2 µ sec signal of the DN block M = 4, R = 2 at the receiver. (a) Received DUSA signal. (b) path zero downsampled by 4, (c) path one downsampled by 4, (d) path two downsampled by 4,

(e) path three downsampled by 4. . . 145

Figure 6.6 The 2 µ sec signal of the UP block M = 4, R = 2 at the receiver. (a) path zero upsampled by 2, (b) path one upsampled by 2, (c) path two upsampled by 2, (d) path four upsampled by 2, (e) Received signal after combining the four lines (DUSA method), and (f) Received signal by TC-OLA method. . . 146

Figure 6.7 Implementation of DUSA that is equivalent to TC-OLA and CDMA transmitter. . . 147

Figure 8.1 Virtual TC-OLA/DUSA technique for M = 4 and R = 1. . . 154

Figure 8.2 Multi-target situation solution using TC-OLA radar system. . . 155

Figure A.1 Radar LFM chirp signal: (a) Single pulse in time domain. (b) Single pulse in frequency domain. . . 159

Figure A.2 (a) The output of the matched filter with total delay. (b) The output of matched filter in dB indicating side lobe level. . . 160

Figure A.3 Storage of radar signal in different domains for moving target detector (MTD). . . 160

Figure A.4 Output of MTD. . . 161

Figure A.5 CA-CFAR and GO-CFAR Detectors. . . 162

Figure A.6 CA-CFAR detector. . . 163

Figure A.7 PD vs SNR curve for Theoretical, CA-CFAR, and GO-CFAR of LFM-PC at Pf a = 10−6 under AWGN. . . 164

Figure C.1 DUSA algorithm for M = 5 and R = 1. . . 168

Figure C.2 The output spectrum (real part) of each path, node A, B, C, D, and E. . . 169

Figure C.3 The output spectrum (real) of DUSA signal of 5 paths around 0 Hz. . . 169

Figure C.4 The output spectrum (real) of DUSA signal of 5 paths around 67Hz. . . 170

Figure C.5 Spectrum of DUSA signal. . . 171

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Figure D.1 Coded-OLA system with N = 2. (a) M

R takes value of 2 (right),

and 4 (left); the signal x is successfully separated from y. (b) M R

takes value of 3 (right), and 5 (left); the signal x is not separated from y. . . 175

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ACKNOWLEDGMENTS

Without the help and support of many people, this work would not have been possible. I would like to thank everyone who supported me during my Ph.D. journey, and I would like to express my sincere gratitude to the following special people:

Dr. Peter Driessen, for his mentorship, encouragement, insight, and all of his interesting inputs on a variety of topics over the years. I have learned from him the way to think, the way to approach the problems, and the way to be a good supervisor.

Dr. Fayez Gebali, for his support, encouragement, and constructive comments. I have learned from him how to be a good teacher.

Dr. Moa Belaid, for his continuous support and conversations by allocating one-to-one sessions with me that ended up with a valuable work. He also helped me to access and speed up my computations on the WestGrid clusters.

Dr. Stephen Harrison, for great inputs and comments that enhanced my work. Dr. Gokhun Tanyer for his great feedback and valuable conversations, and for

reviewing my first journal paper.

My father, Fouad Youssef and my mother, Huda elsyaed, for their great support, love, and continuous prayers for me to excel in my Ph.D.

My wife, Dalia Ali, for her continuous love, patience, emotional support, assurance in difficult and frustrating moments, and encouragement during my Ph.D. She remembered me all the time in her prayers and ensured that I had the proper environment to excel in my studies. I will never forget the tasty coffee that she daily prepared for me!

My sons, Malek Youssef, and Noureldeen Youssef, for their family and social times they spent with me, especially during the weekends.

My brothers Mohammed and Mostafa, and my sisters Marwa and Noura, for their continuous prayers and support.

Ahmed Abo Elfadel, for great conversations and valuable feedbacks on the radar and jamming systems.

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ELW402 Students, Nicholas Bruce, Colter McQuay, and Peter Kremler, for the pleasant time we spent in the lab and for reviewing my papers when asked.

Compute Canada, for the computational resources that made the running time of my analyses take few hours instead of days.

The Programmer Analyst, Kevin Jonesfor his great help with all my technical problems either in software or hardware. He was always available for us and ready to help.

I would like also to thank all my Egyptian, Canadian, and Libyan friends who have supported me.

This document was typeset in LATEX, namely Sublime Text 3 with Zotero inte-gration for references. Simulation results were obtained from MATLAB. Long-running simulations were performed on WestGrid using the MATLAB. Most data plots were generated using the MATLAB. Technical drawings were created using Keynote on Apple machine.

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Acronyms

Acronym Description Page

PD probability of detection 34

Pf a probability of false alarm 34

ACF autocorrelation function 21

AF ambiguity function 13

APPC alternating projection phase control 30

AWGN additive white Gaussian noise 35

BCs Barker codes 17

CA-CFAR cell average CFAR 34

CDMA code devision multiple access 6, 30

CFAR constant false alarm rate 3

CNJ convolution noise jamming 34

CPI coherent pulse interval 38

CUT cell under test 38

D delay 137

DN downsample 137

DUSA downsample-upsample shift-add 5

EA electronic attack 29

EMW electromagnetic wave 1

ES electronic warfare support 29

FDMA frequency division multiple access 31

GO-CFAR greatest-of CFAR 34

JSR jamming to signal ratio 51

KLD Kullback-Leibler divergence 30

LFM linear frequency modulation iii

LFM-PC linear frequency modulation pulse compression 3

LFM-Syn LFM synthesized 30

LPI low probability of intercept 4

MF matched filter 3

MI mutual information 28

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Acronym Description Page

MPS minimum peak sidelobe 18

MTD moving target detector 3

NLFM nonlinear-FM 15

OFDM orthogonal frequency division multiplexing 30

OLA overlap-add 3

OS-CFAR order-statistic CFAR 34

PC pulse compression iii, 3

PRI pulse repetition frequency 14

PSL peak sidelobe level 25

radar Radio detection and ranging 1

RF radio frequency 16

SCNR signal-to-clutter-plus-noise ratio 29

SDR software-defined radar iv, 4

SFW Stepped frequency waveform 13

SINR signal-to-interference-plus-noise ratio 28

SLL sidelobe level 18

SNR signal to noise ratio 2

SS synchronization system 4

SSJ self screening jammer 50

SSLFM smeared synthesized LFM 4

TC time compression 3

TC-OLA time compression overlap-add iii, 3

UP upsample 137

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List of Symbols

Symbol Description Page

B1 signal bandwidth after spreading 71

B bandwidth 8

C(i) DUSA register cell 137

G radar processing gain 56

J(t) pulse jamming signal 75

JSR jamming signal ratio 39

K factor that gives specific Pfa 38

M window size, in samples 3

N(n) noise waveform 86

N_{OL A}(n) OLA output of AWGN 77

Nadapt adapt random phase signal 89

Nint p interpolate phase noise 89

Nup upsample phase noise 89

Rj jamming range 50

Rt target range 39

R hop size, in samples 3

Sj sequence of segment #j 39

Sr j received signal at the jammer 50

Tr pulse repetition interval 39

W CFAR window size 39

XjOL A(n) OLA output of jamming signal 77

XtOL A(n OLA output of SSLFM 77 α shift value 78 δ f frequency step 10 η threshold level 89 µn noise factor 71, 101 µ chirp rate 50 φn Phase state 16

ρ controlled time offset 89

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τ pulse width 10

ξ maximum of maximum peak of MF 81

aβ code sequence 139

c speed of light 43

f1 sample frequency of LFM signal in the DUSA

model

136

f2 low rate sample frequency during step 2 in the

DUSA model

136

f3 higher rate sample frequency in the DUSA model 138

fc carrier frequency 39

fd target Doppler frequency 13

fs1 sample frequency of conventional radar system 40

fs2 sample frequency after time compression 40

hl p impulse response of lowpass filter 89

kt h index of cell used in OS-CFAR 37

n(t) additive white Gaussian noise 50

nj(t) jamming noise 75

r(n) random phase noise 70

td target time delay for a given range R1 10

td target time delay 13, 50

t0 time delay of transmitted jamming signal 50

tj time delay of transmitted signal jammer 50

vr target relative velocity 43

x(n) the digitized version of the LFM radar signal 70 xsynβ _d(n) downsampled of SLFM signal for a given shift

value β

82

xd(n) downsampled of received signal 82

xf(n) reconstruction LFM signal 78

xj(t) received jamming signal 75

xr[n] received radar signal 40, 141

xsα(n) received signal after OLA processor for a given

shift value α

78

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xβ

M F(2)(n) impulse response of downsampled signal 82

xβ[n] downsampled shifted signal 139

xsyn(n) synthesized LFM signal 79

yr[n] received DUSA signal 140

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Chapter 1 Introduction

1.1 Problem Description

Radio detection and ranging (radar) tackles two major tasks: detecting the presence of a target and determining its range. The round trip of a radar signal includes transmitting an electromagnetic wave (EMW) to cover an area of interest, scattering of the wave by target(s) inside this area, receiving the scattered EMW at the receiver side, and finally processing the received signal to extract the desired information [1]. The radar designers have been trying to improve the radar system since World War II. Nowadays, radar systems are not limited to just detecting and measuring the range; they are expanding to include target speed, height, shape, size, and trajectory. In particular, they are used in missile guidance, tracking, and surveillance. Although radar was invented for military purposes, it turns out to have many civilian appli-cations: tracking aircrafts, ships, and vehicles, monitoring earth resources and birds during migration, and detecting elderly falls [2–4].

The achievements of radar were limited in the early 20t h _{century by the power}

limitations of the transmitters used to send the radar waves in the form of repeating short pulses. Even if higher power were supplied, the range resolution was worse due to the wider pulse width [5, 6].

Pulse compression (PC) was proposed to solve this dilemma. The basic idea was to transmit a long pulse of constant amplitude. At the receiver side, the signal is processed through a filter with an impulse response equals to a conjugated time-reversed version of the transmitted signal. The received signal is therefore compressed to a short pulse which accumulates all the energy in the long pulse [6, 7]. By doing

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so, a maximum detection range and a high range resolution can be achieved.

The reliability of detection, including the statistics of hits, misses, and false alarms, depends mostly on the signal level compared to noise, clutter, and jamming levels [6]. In other words, if the incoming radar signal strength of an object of interest is rel-atively low, in sense of being far from radar receiver or has low cross-section area to reflect much of EMW, strong interferences with other signals, especially jamming ones, will negatively affect the detection performance of the radar receiver. In fact, intentional jamming is the most annoying threat against radar. It is sometimes called "soft kill" because it temporarily makes an enemy’s asset ineffective but does not destroy it [8–10]. The basic jamming technique provides false information by transmit-ting an interfering signal along with the radar signal and, therefore, causing the radar receiver to reach incorrect conclusions. The amount of the detection performance degradation depends on the effectiveness of jamming on the radar signal which pre-vents the radar receiver from recovering the required information [11, 12]. Designing a powerful radar system with highly reliable detection in different background situ-ations is the aim of radar designers. Since the classical design can no longer achieve the desired performance, a new waveform is adopted for achieving radar designers’ goal [13].

In radar system design, having a universal waveform is the ultimate goal of many designers. The currently accepted belief that there is no such a universal waveform is not surprising in light of the wide variety of waveforms used in radar and commu-nication fields.

The waveform design should take into account a number of system requirements and constraints including bandwidth, sampling rate, power, Doppler tolerance, duty cycle, sidelobes, range resolution and signal to noise ratio (SNR). A variety of wave-form modulations have been developed since the 1950s to address these requirements as well as others [2]. Radar waveforms can be categorized based on the waveform modulation: frequency and phase modulations [3]. Frequency modulation can be lin-ear or nonlinlin-ear; phase modulation can be bi-phase (two possible states) or polyphase (more than two phase states) [6, 7]. These modulations can be applied in different ways: intrapulse, which is applied to individual pulses, interpulse, applied across the pulses of a multi-pulse waveform, or both [14]. Other waveform types may arise when using a waveform design methodology including information theory and/or machine learning.

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1.2 Contributions

Several attempts are still ongoing to improve the radar waveform shaping and, there-fore, increase the radar target detection [15–21]. In this dissertation, we introduce three novel approaches that incorporate a communication technique, called TC-OLA, into PC radar systems to improve the radar waveform shaping and enhance radar performance. Notice that, all approaches are investigated and implemented under a single target.

1.2.1 TC-OLA-based LFM Radar

TC-OLA is a communication technique that combines two techniques [22, 23]: time compression (TC) and overlap-add (OLA). In TC, the signal at the transmitter is divided into overlapping segments, and re-sampled using higher rates to produce non-overlapping segments. At the receiver, the signal is reconstructed from the segments using the OLA method. Using TC-OLA, the signal spreads its spectrum at the transmitter, and the amplitude of the signal increases linearly at the receiver with the ratio of two parameters M, the length of the segment, and R is the hop size. These two facts are incentive to incorporate TC-OLA into radar systems. In this work, we propose a new PC radar system, the OLA-based LFM radar, that relies on TC-OLA and LFM waveform to achieve better detection performance (More details in Chapter 3, Section 3.3) .

In TC-OLA-based LFM context, we apply TC to the digitized LFM signal, using predetermined M and R, and OLA to the received LFM signal to recover the signal and undistorted information content. Using TC-OLA boosts the SNR by the amount of M

R and provides a robust processing gain compared to the traditional radar

LFM-PC systems. In addition, TC-OLA provides a better immunity against noise jamming techniques [24, 25]. We extend the conventional linear frequency modulation pulse compression (LFM-PC) radar model to simulate and evaluate the performance of the new system, which includes matched filter (MF) processor, moving target detector (MTD), and three common constant false alarm rate (CFAR) algorithms, by suitably adding TC and OLA blocks at the transmitter and receiver, respectively. Using the TC-OLA-based LFM radar system, we have control over the SNR level and the spectrum spread while preserving the same Doppler shift and target time delay as the conventional LFM radar system. Furthermore, we transform LFM chirp signal into a new TC signal that inherits LFM properties. Moreover, the proposed radar

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model relies on high sample rates only when needed and, therefore, does not require changing the conventional radar receiver as is the case for a wideband LFM radar with the same processing gain.

1.2.2 Smeared Synthesized LFM Radar

Although TC-OLA-based LFM showed powerful results compared to the conventional LFM radar, it still needs improvements to deal with convolutional noise jamming when compared to the wideband LFM radar. Convolutional noise jamming techniques are challenging as the spectrum shape of the jammed signal is the same as that of the radar signal. This motivates us to introduce a novel smeared synthesized LFM (SSLFM) TC-OLA radar system to defeat this kind of jamming techniques. The new system allows us to control the SNR level, and, therefore, obtain a higher processing gain compared to the traditional LFM-PC radar systems. In addition, it allows us to control the signal spectrum spreading, making it more immune to convolutional noise jamming. The new SSLFM signal is obtained by either multiplying the LFM waveform with a complex unit signal with random phase, or by encoding the TC signal with random phase at the transmitter. Once the signal is received, the OLA processor is applied to obtain the SSLFM signal with a higher gain depending on the chosen TC-OLA parameters. A denoising processor, used during the OLA processor or after, is deployed to remove the random phase from the SSLFM and forward the resulted LFM signal to the rest of the LFM-PC radar receiver system, namely, the MF processor, the MTD, and the CFAR processor. The new SSLFM TC-OLA radar system enjoys a better low probability of intercept (LPI) feature while maintaining the LFM time sidelobe and Doppler tolerance properties. As such, the SSLFM TC-OLA radar provides a better immunity against powerful noise jamming techniques compare to the traditional LFM, wideband LFM radar with the same processing gain, and TC-OLA-based LFM radar. Moreover, the additional modules in the new radar system still do not require changing the core LFM radar components.

Using TC-OLA and denoising require a synchronization system (SS) to properly recover the LFM signal. We therefore offer three (SSs), each with its own pros and cons. The performance evaluation of the new radar system shows its superiority over the traditional LFM, the wideband LFM and the TC-OLA-based LFM radars, especially under powerful noise jamming. The synchronization system is implemented and tested experimentally using SDR. The result shows that the synchronization

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system successfully detects the first sample of radar received signal and, therefore, guides the OLA and denoising processors to properly recover the received signal.

1.2.3 N-signal TC-OLA Radar

Taking the waveform shaping further and aiming at achieving the universality through pluralism, we present a new radar system based on low-rate coded TC-OLA technique. With this new system, any number and any kind of radar signals can be combined and transmitted. In addition, it allows for signal spectrum spreading, which adds a LPI feature to the system. Moreover, the new system controls the SNR level, based on the predefined TC-OLA parameters, and, therefore, obtains a higher processing gain compared to the conventional pulse-compression radar systems.

Radar designers are usually interested in having a radar system with many features including high-time resolution, high-Doppler tolerance, low-sidelobe level, and LPI. Unfortunately, a single radar signal cannot enjoy all of these features and some of its features might actually be lost in some cases, such as high-speed target and multi-target detection. Since different types of radar signal modulations offer different but complementary features, the proposed system addresses the challenge of having many features in a single waveform by combining different waveforms using low-rate coded TC-OLA. By doing so, the system offers a wide range of design choices according to the waveforms specified, and allows for additional processing such as noise and Doppler cancellation.

The performance evaluation of the new radar system shows its superiority over the traditional radar system by operating on N-radar signals simultaneously, making use of features from each waveform, canceling the Doppler from a Doppler-intolerant signal, and adding an extra processing gain to the proposed system.

1.2.4 Downsample Upsample Shift-Add Technique

Despite the advantages of TC-OLA technique over other schemes, the shortcomings of TC-OLA implementations were presented in [23], namely the high rate data process-ing required in the filter, window function and adder, and the commutator misalign-ment, especially in the case where the hopping size, R, is not equal to 1. Moreover, the upsampling elements used in the TC-OLA implementation rely of the value of M to be a multiple of R [23]. To overcome some of the existing TC-OLA implemen-tation shortcomings, we propose a downsample-upsample shift-add (DUSA) method

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that faithfully implements the TC-OLA technique. The mathematical framework of DUSA relies on three operators: downsample, upsample, shift and add operators, and is shown to yield the same results as TC-OLA. Moreover, at some point of the processing of DUSA is carried out at a lower sampling rate which reduces the com-plexity of the design. Furthermore, DUSA does not depend on the window function and inherently accommodates any values of the parameters M and R. Finally, DUSA can be easily extended to implement other schemes such as code devision multiple access (CDMA).

1.2.5 Summary of Contributions

Summing up, the main contributions of this dissertation are as follows:

• A new TC-OLA-based LFM radar that controls SNR and spreads the signal spectrum without changing in the core of the conventional radar system. The system also gives a promising result against noise jamming techniques.

• A new TC-OLA SSLFM radar with same features of the previous radar in addition to LPI feature that gives higher immunity against jamming technique. • Three algorithms of synchronization systems for properly recovering the

incom-ing signal.

• Implementing a new TC-OLA SSLFM radar on SDR.

• A new N-signal TC-OLA radar for simultaneously transmitting a number of radar signal in order to improve the detection performance and achieve the university.

• Implementing a new N-signal TC-OLA radar on SDR.

• A new DUSA system for enhancing the TC-OLA technique and overcoming some of the existing TC-OLA implementation shortcomings.

1.3 Organization of the Dissertation

The remainder of this dissertation is structured as follows. Chapter 2 discusses the radar pulse compression waveforms. Chapter 3, 4, and 5 introduce and evaluate

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the new TC-OLA LFM, SSLFM TC-OLA, and N-signal TC-OLA radar systems, respectively. Enhancement of TC-OLA techniques using DSUA multirate system is presented in Chapter 6. Chapter 7 and Chapter 8 summarize the work and discuss our short- and long-term future work. The Appendices of the work is for elucidating some points in different chapters.

1.4 Publications

Most of the dissertation chapters have been published or submitted at the time of writing this work.

• Chapter 3 was published as [26, 27].

• Chapter 4 was submitted to IEEE Access, and the reviews received on November 27, 2018 are in Appendix E.2. The chapter has not yet been revised per the reviewer comments.

• Chapter 5 was submitted to IEEE Access and the reviews are in Appendix E.1. The chapter was revised according to these reviews and resubmitted on December 01, 2018 are submitted to IEEE Access.

• Chapter 6 was published as [28].

Notice that the reference numbers in the Chapters do not match the reference numbers in the papers, since the reference numbers in the chapters refer to the bib-liography.

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Chapter 2 Review of Radar Waveform Design

Using Pulse Compression and Other

Approaches

2.1 Introduction

Radars are usually used to detect, track, and control the fire system against targets. One of the key factors of search radar systems is the maximum detection range . With a constant peak output power, the maximum detection range of the radar can be increased by using a wider radar pulse, which, in turn, increases the average radar power. Unfortunately, wider radar pulses limit the radar range resolution. By using pulse compression techniques, the radar designer can satisfy both radar specifications [1, 2].

The basic idea of pulse compression involves the transmission of a relatively long pulse and compress it upon reception. By transmitting a long pulse, the radar main-tains high average power achieving high maximum detection range. On the other hand, compressing the received long pulse to a short pulse provides the radar with a high range resolution. The pulse duration cannot be reduced indefinitely. According to the Fourier transform, the bandwidth, B, cannot have duration shorter than 1/B, i.e. its time-bandwidth product cannot be less than unity [6, 29].

The time-bandwidth product is the important factor that determines the compres-sion gain. Unmodulated pulses give unity gain while the phase or frequency modu-lated signals give values greater than unity depending on the correlation between the

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input signal and the matched filter used [7].

Pulse compression consists of two types: frequency and phase modulation. His-torically, LFM is the first implementation of the pulse compression radars. Although pulse compression phase coded radars were developed later, LFM-PC radars are still widely used in military applications due to their Doppler tolerance, and high pro-cessing gain. This high propro-cessing gain stems from the fact that the same power contained in the transmitted long pulse is contained in the short compressed pulse. After compression, the peak signal to noise ratio is significantly higher, depending on of course on the bandwidth used, compared to the phase coded family radars. The main disadvantage of the LFM signal is its range sidelobes at the output of the matched filter. These sidelobes can, however, be mitigated by using a weighting filter at the radar receiver [2, 6].

There are various implementations of pulse compression that a radar designer can choose from according to the radar application requirements. Below we discuss pulse compression types in more details as well as the state of the art waveforms that stemmed from developing the basic radar signal or optimizing the waveform with its mismatched filter to achieve specific requirements.

2.2 Frequency Modulation

2.2.1 Linear Frequency Modulation

LFM waveform is commonly used in pulse compression radar for both surveillance and tracking radars. This signal has many advantages such as high Doppler toler-ance. LFM-PC is accomplished by adding frequency modulation to a long pulse at transmission, and by using a matched filter receiver in order to compress the received signal. Using LFM, within a rectangular pulse, compresses the matched filter output by a factor, which is directly proportional to the pulse width and bandwidth. Thus, by using long pulses and wideband LFM modulation large compression ratios can be achieved [1, 3, 6, 30]. The normalized complex transmitted signal of a linear-FM pulse is given by [6, 7]:

s(t)= ej2π( f0t+µ₂t2), 0 6 t 6 τ, (2.1)

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• τ is pulse width,

• µ = B/τ, and B is the bandwidth of LFM waveform. • f0 is the initial frequency.

The instantaneous frequency is given by:

f (t) = 1 2π dφt dt , f (t)= f0+ B Tt (2.2)

Eq. 2.2 shows the linear relationship between time and frequency of LFM wave-form. The radar echo signal is similar to the transmitted one with the exception of a time delay and an amplitude that depend on the target radar cross section (RCS). The echo received by the radar from the target is:

sr(t)= Aej2π( f0(t−t1)+

µ

2(t−t1)2), (2.3)

where A is proportional to RCS, antenna gain, and range and spreading-loss attenu-ations. The time delay td is given by:

t1 = 2R1/C. (2.4)

At the receiver side, the frequency f0 is removed by mixing sr(t) with reference signal

whose phase is 2π f0t. The received signal after the reference signal and low pass filter

is given by:

sr(t)= a1ej2π(− f0t1+

µ

2(t−t1)2). (2.5)

Sampling of the quadrature components is then performed. To avoid aliasing problem, sampling must satisfy Shanon theory:

fs > 2B. (2.6)

If the frequency resolution δ f = 1/τ, the minimum required number of samples is given by [7]:

N > 2Bτ (2.7)

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-5 0 5 Time (s) 10-5 -1 -0.5 0 0.5 1 Amplitude Chirp Waveform -1 -0.5 0 0.5 1 Frequency (Hz) 106 0 0.2 0.4 0.6 0.8 1 Amplitude Chirp Spectrum -5 0 5 Time (s) 10-6 0 0.2 0.4 0.6 0.8 1 Amplitude

PC Matched Filter Output

-5 0 5 Time (s) 10-6 -60 -50 -40 -30 -20 -10 0 Amplitude (dB)

PC Matched Filter Output

Figure 2.1: LFM pulse and its power spectral density (Top) and matched filter output (bottom).

number of samples, for positive integer m is:

NF FT = 2m > N (2.8)

The output of the matched filter has a main lobe and many time-sidelobes. The peak time-sidelobe level is ≈ −13.2 dB, which is relatively high. These time-sidelobes can shadow the weak return from small targets and go undetected in the presence of strong return of large targets. Fig. 2.1 shows LFM waveform and the matched filter output.

One solution for this time-sidelobes problem is to weight the amplitude of LFM signal with a suitable window function. However, as the time-sidelobes are reduced by windowing, the width of the main lobe of the LFM signal is increased, thus decreasing

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-5 0 5 Time (s) ₁₀-6 -40 -30 -20 -10 0 Amplitude (dB)

PC Matched Filter - Uniform

PC Matched Filter - Hamming

PC Matched Filter - Hanning

-5 0 5 Time (s) ₁₀-6 -120 -100 -80 -60 -40 -20 0 Amplitude (dB)

PC Matched Filter - Blackman

Figure 2.2: LFM matched filter output before and after applying different weighting windows.

the range resolution of the radar [10]. The following windows may be used for sidelobe suppression process [6, 10]:

• Hamming: w(k) = 0.54 + 0.46 cos(2πk/N). • Hanning: w(k) = 0.5 (1 + cos(2πk/N)).

• Blackman: w(k) = 0.42 + 0.5 cos(2πk/N) + 0.08 cos(4πk/N).

The index k in the above formulas is −N/2, . . ., N/2. Fig. 2.2 shows the LFM matched filter output before and after applying different weighting windows. Notice that the main lobe increases because of the effect of windowing.

If a Doppler shift is presented due to the target motion, the filter is no longer matched with the received pulse and its output is distorted from its original form.

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The distortion is however minimal for most of the practical target velocities as will be discussing in Chapter 3.

An ambiguity function (AF) is a two-dimensional function of time delay and Doppler frequency that represents the distortion of a received signal due to the Doppler shift of the returns from a moving target [2, 6]. This function is widely used in radar to examine the response of the matched filter to a range of Doppler fre-quencies by plotting an AF diagram for a particular waveform in a three-dimensional plane. This diagram displays the square of the magnitude of the matched filter output for different Doppler shifted in the received echo. The magnitude of the output of matched filter is formally defined by [10]:

| X(td, fd)| = ∫ ∞ −∞ U∗(t)U(t + td)ej2π fddt , (2.9)

where td is the target delay and fd is the Doppler frequency.

The main property of AF is that it achieves its maximum value at zero delay and zero Doppler, X(0, 0). If the waveform is normalized to unit energy, X(0, 0) = 1, the volume under the square of the ambiguity surface is unity:

∫ ∞

−∞

∫ ∞

−∞

| X(td, fd)|2= 1 (2.10)

The above equation implies that a waveform designed to lower the response in a given region of the ambiguity function will produce an increase in another region because the total volume must remain constant [6]. In other words, if we attempt to squeeze the ambiguity function to a narrow peak at the origin (thumbtack shape), that peak cannot exceed a value of 1, and the volume squeezed out of that peak must reappear somewhere else. The more Doppler shift the more distortion occurs and in turn the ideal thumbtack shape is lost.

2.2.2 Stepped Frequency Waveform

Stepped frequency waveform (SFW) is an alternative technique for obtaining a large bandwidth and thus fine range resolution without requiring intrapulse frequency mod-ulation. An SFW is a kind of pulse burst waveform. Each pulse in the burst is a simple constant-frequency pulse fi and the frequency of each pulse is increased by the

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The ambiguity function of the matched filter corresponding to Eq. (5.46) can be obtained from that of the coherent pulse train developed in Section 5.2.3 along with property 5 of the ambiguity function. The details are fairly straightforward and are left to the reader as an exer-cise. The result is (see Problem 5.2)

Eq. (5.47)

where is the ambiguity function of the single pulse. Unlike the case in Eq. (5.43), the sec-ond part of the right-hand side of Eq. (5.47) is now modified according to property 5 of Section 5.1. This is true since each subpulse has its own beginning frequency derived from the primary LFM slope.

5.4. Nonlinear FM

As clearly shown by Fig. 5.6, the output of the matched filter corresponding to an LFM pulse

has sidelobe levels similar to those of the signal, that is, 13.4dB below the main

beam peak. In many radar applications, these sidelobe levels are considered too high and may present serious problems for detection particularly in the presence of nearby interfering targets or other noise sources. Therefore, in most radar applications, sidelobe reduction of the output of the matched filter is always required. This sidelobe reduction can be accomplished using

f₀ f₁ f₂ f₃ f₄ f 0 time

Figure 5.12. Example of stepped frequency waveform burst; N = 5.

f f f primary LFM slope B_i f_d ; ₁ –qT f_d B 0 ----+ ; f_d f T ---+ N– q T sin N f_d f T ---+ T sin ---q=–N 1– N 1– = NT ; 1 x sin x2 i

Figure 2.3: Stepped frequency waveform burst, N = 5 [7].

One of the advantages of SFW is using the interval between pulses to adjust the center frequency of other narrowband components of the radar system. The frequency steps can be added to a train of unmodulated pulses as well as to a train of modulated pulses, e.g. LFM pulses [6]. The special case of a stepped-frequency train of unmodulated pulses will be derived from the general expression by setting the LFM slope to zero. SFW takes a long time to generate since the transmission of the pulses is sequential. In case of fast moving targets, this causes a Doppler smear as SFW has to proceed step by step through a lot of frequency steps, especially for large bandwidths [7, 31, 32]. Consider an LFM signal whose bandwidth is Bi and whose

pulse width is τi and refer to it as the primary LFM. Divide this long pulse into N

subpulses each of width τ0 to generate a sequence of pulses whose pulse repetition

frequency (PRI) is denoted by τ. It follows that τi = (n − 1)τ. Define the beginning

frequency for each subpulse as that value measured from the primary LFM at the leading edge of each subpulse, as illustrated in Fig. 2.3:

fi = f0+ i∆ f i = 0, . . ., N − 1, (2.11)

where f0 is a initial frequency and ∆ f is the frequency step from one subpulse to

another. The set of n subpulses is often referred to as a burst. Each subpulse can have its own LFM modulation.

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2.2.3 Nonlinear Frequency Modulation

The nonlinear-FM (NLFM) waveform has one advantage over LFM. NLFM does not need weighting windows as the LFM does to have the required time-sidelobe level [33]. The time-sidelobe level of NLFM is ≈ −33 dB at Doppler offset equal to zero, which is better than LFM without adding window [1]. The NLFM shape is accomplished by increasing the rate of change of frequency modulation near the ends of the pulse and decreasing it near its center.

One of the primary shortcomings of the NLFM waveform is its Doppler intolerance in presence of Doppler shift, the main lobe of the compressed NLFM pulse is distorted and the time-sidelobes tend to be increased compared to those of the LFM [34, 35].

2.2.4 Costas code

In the Costas code, a pulse duration τ is divided into N equal subpulses of duration τc = T/N. In quantized LFM signal, the frequency of each subpulse is increased

lin-early according to Eq. 2.11. Costas codes are similar to quantized LFM signal except

SOLO

Pulse Compression Techniques

Frequency Codes

Costas Codes

In this case a pulse of duration T is divided in N equal sub-pulses of duration

τ

₁

=

T /

N

In Linear Stepped Frequency Modulation (LSFM) the frequency of each sub-pulse is increased linearly according to:

f

_i

=

f

₀

+

i

δ

f

i

=

1 ,

2 ,

!

,

N

where f₀ is a constant frequency and f₀ >> δ f.

The maximum change in frequency is Δ f = N δ f during the time τ.

The pulse has a time-bandwidth of:

₍

₎

2 1 1 2 1

N

f

N

f

N

T

f

⋅

=

⋅

=

⋅

≈

Δ

≈

!

"

!#

$ τ

δ

τ

δ

0 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9 10 0 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9 10

Column number, j (time) Column number, j (time)

Row number

, i (frequency)

Row number

, i (frequency)

Frequency-time array for LFM Frequency-time array for Costas code

Costas codes are similar to LSFM, only the frequency steps are chosen randomly.

Figure 2.4: Frequency-time array for LFM and Costas code [7].

the frequency steps are chosen randomly as shown in Fig. 2.4 [7]. The maximum change in frequency is ∆ f = N∆ f during the time τ. The pulse has time-bandwidth of:

∆f T = N∆ f Nτ1 = N2(∆ fτ1)

| {z }

≈1

≈ N2. (2.12)

In other words, in both signals we find one “dot” in each column and in each row. This means that at any one of the time slices, only one frequency is transmitted, and

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each frequency is used only once during each subpulse [6]. The main advantage is the ambiguity function of Costas codes is approaching the ideal thumbtack shape. Moreover, all sidelobes except for few around the origin, have generally amplitude 1/N. Few sidelobes close to the origin have amplitude 2/N. The compression ratio of Costas codes depends on the number of subpulses which is approximately equal to N [7].

Costas codes have a very sharp AF, which means very low Doppler tolerance, as such, they are unsuitable for fast moving targets. One can overcome this problem by using several matched filters, each one matching to a certain Doppler frequency, but this increases the cost and complexity of the radar receiver [2].

2.3 Phase Modulation

The second major class of PC waveforms is phase coded waveforms. A phase-coded waveform has a constant frequency but an absolute phase that is switched between one or more fixed values at regular intervals within the pulse length. Each pulse is divided into subpulses, which are often referred to as “chips” [31].

x(t)= N−1 Õ n=0 xn(t − nτc) xn(t)=        ejφn, 0 ≤ t ≤ τ c 0, otherwise. (2.13)

where τcis chip duration and φnis phase state. Phase coded waveforms are divided

into Biphase codes and polyphase codes. A Biphase code has only two possible choices for the phase state φn, typically 0 and π. A polyphase code has more than two phase

states. There are several common subcategories of each and we discussed them next.

2.3.1 Biphase (Binary Phase)

A Biphase code switches the absolute phase of the radio frequency (RF) carrier be-tween two states, with π out of phase and bandwidth 1/τ. The Biphase can be digitally implemented, called binary phase codes, with significant range sidelobe re-duction. However, it is sensitive to the Doppler shift.

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2.3.1.1 Barker Codes

The most common Biphase codes used in radar application are the Barker codes (BCs). BCs are a specific set of Biphase sequences that have a maximum sidelobe magnitude of 1 at the matched filter output and therefore attain an N : 1 ratio of the peak to the highest sidelobe, which is the minimum possible value for the autocorrelation function. Note that Biphase codes do not necessarily change phase state at every subpulse transition [6, 31]. There are only seven known BCs that share this property. The BC 13, for example, is transmitted and received pulse as shown in Fig. 2.5. BCs have been found only for N up to 13. This gives insufficient

0 2 4 6 8 10 12 14 16 18 20 22 24 Time (s) 0 3 6 9 12 15 Amplitude 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Time (s) -1.5 -1 -0.5 0 0.5 1 1.5 Amplitude

Figure 2.5: Transmitted and received pulse modulated by BC of length 13. processing gain. Recall that pulse compression waveforms have a bandwidth much greater than 1/τ. The spread spectrum of the BC waveforms may not be obvious due to the phase coded waveforms, in general, having the same frequency in all the subpulses. The discontinuities caused by the phase transitions, however, do spread the signal spectrum. In other words, the spreading depends on the point in the pulse at which the switch occurs [31].

A known drawback of the BCs is their intolerance to Doppler shifts. In fact, a Doppler phase rotation of 2π across the full pulse length is more than enough to distort the signal structure at the matched filter output. As a consequence, BC waveforms are dealing with Doppler frequency that satisfy sufficient matched filter

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output according to the following equation [31]:

FDmaxτ < 1/4 (2.14)

As such, combined or nested BCs were constructed to generate longer BCs with lower sidelobes [6, 7]. One scheme of generating codes longer than 13 bits, for example, is the method of forming combined BCs using the known BCs [7]. However, as shown in Fig. 2.6, the sidelobes of a combined BC autocorrelation function is no longer equal to unity. For example, to obtain a 20:1 pulse compression rate, one may use either a 5 × 4 or a 4 × 5 codes. • BC 4 [+ − ++] • BC 5 [+ + + − +] + − ++ | {z } + + − ++ | {z } + + − ++ | {z } + −+ −− | {z } − + − ++ | {z } +

The 5×4 BC consists of the 5 Barker code, each bit of which is the 4-bit Barker code. The 5 × 4 combined code is the 20-bit code.

0 5 10 15 20 25 30 35 40 Time (s) 0 2 4 6 8 10 12 14 16 18 20 Amplitude

Figure 2.6: Autocorrelation function of 5 × 4 combined BCs.

Another technique to generate longer code is called minimum peak sidelobe (MPS). An MPS code, for example, gives a sidelobe level (SLL) of 2 for N = 20, while nested

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BC gives, for the same N, a SLL of 5. The longest MPS length is 105 with peak sidelobe of 5 [2, 31]. 0 5 10 15 20 25 Time (s) 0 0.2 0.4 0.6 0.8 1 Amplitude

Barker Code Fequency Mismatch

fd/bw=0 0 5 10 15 20 25 Time (s) 0 0.2 0.4 0.6 0.8 1 Amplitude

fd/bw=0.02 0 5 10 15 20 25 Time (s) 0 0.2 0.4 0.6 0.8 1 Amplitude

fd/bw=0.05 0 5 10 15 20 25 Time (s) 0 0.2 0.4 0.6 0.8 1 Amplitude

fd/bw=0.07

Figure 2.7: Matched filter output mismatching for different Doppler shift values.

2.3.1.2 Pseudo Random Code

Pseudo-Random codes are binary-valued sequences similar to BCs. The name pseudo-random (pseudo-noise) stems from the fact that they resemble a pseudo-random sequence. The pseudo-random codes can be easily generated using feedback shift-registers. It can be shown that for N shift-registers we can obtain a sequence of a maximum length of 2N _{− 1} _[36].

To ensure that the output sequence from a feedback shift-register is maximal length, the bits used in the feedback path should be determined by the one coefficients

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of primitive, irreducible polynomials modulo 2. As an example, for N = 4, length 2N − 1= 15, can be written in binary notation as 1 0 0 1 1.

The primitive, irreducible polynomial that this denotes is:

(1)x4+ (0)x3+ (0)x2+ (1)x1+ (1)x0 (2.15)

The last term in every such polynomial corresponds to the closing of the loop to the first bit in the register.

Longer pseudo-random codes can be generated to reduce the sidelobes. The main drawbacks of pseudo-random codes are that their compression ratio is not large enough and low sensitivity to sidelobe degradation in the presence of Doppler fre-quency shift [7].

2.3.2 Polyphase Codes

Biphase codes, as noted in the previous section, have poor Doppler tolerance. Polyphase codes exhibit lower sidelobe levels and greater Doppler tolerance compared to Biphase codes. A number of polyphase codes are in common use. These include Frank codes, P1, P2, P3, and P4 codes. These codes have been derived from a step approxima-tion to linear frequency modulaapproxima-tion waveforms (Frank, P1, P2) and linear frequency modulation waveforms (P3, P4) [37].

Generally, polyphase codes are derived by dividing the waveform into subcodes of equal duration and using phase value for each subcode to achieve the best result at the output of the matched filter [6]. Numerous polyphase codes have been proposed; many are described in [2, 6]. In this section, we give a brief description of the basic polyphase codes, namely, Frank, P1, P2, P3, P4 codes and their properties.

2.3.2.1 Frank Code

Frank code is a digital representation of a quadratic phase shift. In the Frank code, the pulse of width τ is divided in N equal groups; each group is subsequently divided into other N subpulses each of width τc. Therefore, the total number of subpulses is

N2, and the compression ratio is also N2 [6, 38].

A Frank code of N2 _{subpulses is called an N-phase Frank code. The fundamental}

phase increment of the code is ∆φ = 2π

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subpulse is computed from:             0 0 0 0 . . . 0 0 1 2 3 . . . N − 1 0 2 4 6 . . . 2(N − 1) . . . . 0 (N − 1) 2(N − 1) 3(N − 1) . . . (N − 1)2             ∆φ

Each row represents the phases of the subpulses of a group. The phase element of Frank code can be stated as follows [6]:

φm,n = 2π

N (m − 1)(n − 1) (2.16)

where m = 1, 2, . . ., N, and n = 1, 2, . . ., N. If N = 4, For example, the fundamental phase increment of the 4-phase Frank code is ∆φ = 2π

4 = π/2:           0 0 0 0 0 π/2 π 3π/2 0 π 0 π 0 3π/2 π π/2           =           1 1 1 1 1 j −1 − j 1 −1 0 −1 1 − j −1 j          

Therefore, the 4-phase Frank code has the following N2 _{= 16 elements: [1 1 1 1 1 j −}

1 − j 1 − 1 1 − 1 1 − j − 1 j]. The phase increments within each row represent a stepwise approximation of an up-chirp LFM waveform as shown in Fig. 2.8.

If we add 2π phase to the third N = 4 row and 4π phase to the fourth (adding a phase that is a multiple of 2π does not change the signal), an analogy to the discrete FM signal is obtained. If we use ∆ f = 1

τc, the phases of the discrete LFM and the

Frank-coded signals are then identical at all multipliers of 4τc as shown in Fig. 2.9.

Frank code has the largest incremental phase at the center of the code as shown in Fig 2.10. When the code is passed through a bandpass amplifier in a radar receiver, the code is attenuated more in the center of the waveform. This attenuation tends to increase the sidelobes of the Frank code autocorrelation function (ACF) but it is still better than that of the binary phase codes.

(46)

22

Poly-Phase Codes

Frank Codes (continue – 2)

Example: For N=4 Frank code (continue – 1).

If we add 2π phase to the third N=4 Frank phase row and 4π phase to the forth

(adding a phase that is a multiply of 2π doesn’t change the signal) we obtain a

analogy to the discrete FM signal.

0 0 0 0 0 Δφ 2Δφ 3Δφ 2Δφ 4Δφ 6Δφ 3Δφ 9Δφ 0 0

Total number of subpulses (N2₎

Phase increment 2 π 4 π 6 π 6Δφ 12Δφ time Phase increment 4 τ’ 2 π 4 π 6 π 8 π 10 π 12 π 0 0 0 0 0 90 180 270 0 180 0 180 0 270 180 90 Frank code Step chirp 16 τ’ 8 τ’ _{12 τ’} f0+ Δf f0+ 2 Δf f0+ 3 Δf f0

If we use then the

phases of the discrete linear FM

and the Frank-coded signals are

identical at all multipliers of τ’.

'

/

1 τ

=

Δ f

Figure 2.8: Frank code, N=4 [7].

2.3.2.2 P1 Code

In P1 code, the phase element of this signal can be expressed as: φm,n = −π

N(N − (2m − 1))((m − 1)N+ (n − 1)), (2.17) where m, n = 1, 2, . . ., N and N is any positive number that defined the code sequence length N2_.

The P1 code has a small incremental phase group at the center of the code and highest incremental phase at the two ends of the code as shown in Fig. 2.11. When waveforms phase coded with these codes are passed through bandpass amplifier in a radar receiver, P1 code is attenuated most heavily at the two ends of the waveform. This reduces the sidelobes of the P1 code autocorrelation function. This, therefore, exhibits relatively low sidelobes compared with Frank code [32, 39].

2.3.2.3 P2 Code

In P2 code, the phase element can be expressed as: φm,n= hπ 2 N − 1 N − π N(n − 1)) i (N+ 1 − 2m) (2.18)

Enhancement of target detection using software defined radar (SDR)

Contents

List of Tables

List of Figures

Acronyms

List of Symbols

Chapter 1

Introduction

1.1

Problem Description

1.2

Contributions

1.2.1

TC-OLA-based LFM Radar

1.2.2

Smeared Synthesized LFM Radar

1.2.3

N-signal TC-OLA Radar

1.2.4

Downsample Upsample Shift-Add Technique

1.2.5

Summary of Contributions

1.3

Organization of the Dissertation

1.4

Publications

Chapter 2

Review of Radar Waveform Design

Using Pulse Compression and Other

Approaches

2.1

Introduction

2.2

Frequency Modulation

2.2.1

Linear Frequency Modulation

2.2.2

Stepped Frequency Waveform

5.4. Nonlinear FM

2.2.3

Nonlinear Frequency Modulation

2.2.4

Costas code

Pulse Compression Techniques

Frequency Codes

Costas Codes

τ

=

T /

N

f

=

f

+

i

δ

f

i

=

1

,

2

,

!

,

N

(

)

N

f

N

N

f

N

T

f

⋅

=

⋅

=

₍

₎