Signal Processing for mmWave MIMO Radar - diva …826028/FULLTEXT01.pdf · Signal Processing for mmWave MIMO Radar ... improved resolution and detection capabilities will be achieved

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FACULTY OF ENGINEERING AND SUSTAINABLE DEVELOPMENT

Signal Processing for mmWave MIMO Radar

Óscar Faus García

June 2015

Master’s Thesis in Electronics

Master’s Program in Electronics/Telecommunications

Examiner: Daniel Rönnow

Supervisor: André Bourdoux / Wim Van Thillo

Óscar Faus García Signal Processing for mmWave MIMO Radar

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Preface

I would like to thank my advisor, André Bourdoux, for his supervision, valuable guidance and helpful

suggestions during my 6 months of internship in IMEC. Having the opportunity to take part in such an

interesting and innovative project like the mmWave radar has been a valuable and enriching

experience for me. I am also grateful to Wim Van Thillo for his support during my arrival to IMEC.

I also want to thank all the colleagues in the mmWave group and in the wireless communication

department who at some point have helped me with any issue and whose comments and discussions

have been highly valuable. I am also grateful to IMEC for providing me with the facilities and means

to develop my thesis and to KU Leuven for their help and support during my international scholar stay

in Leuven.

While many people have contributed to my experience during my thesis, I would like to thank a few

people in particular; Bilal, Georgi, Nico and Yi, for sharing these intense months with me and for

offering their professional and personal friendship. It was truly a great experience to share all that time

in IMEC, Wisteria and ultimately in Belgium; I am very grateful and I believe that the best is yet to

come.

I am especially grateful to Georgi G. for his help, support and suggestions during the writing of my

thesis, and also to Hou Yi for his special life approach that so many good fun moments has brought

among us.

Also, I want to thank Darya for her help in important moments during these last months. I would also

like to thank my family, and specially my parents and sister, for the unconditional support they have

always sent me from Spain during all these years that I have been abroad in Sweden, Belgium and

Poland. Gracias.


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Abstract

This thesis addresses the design study, implementation and analysis of signal processing algorithms

for a 79 GHz millimeter-wave Phase Modulated Continuous Wave (PMCW) Multi Input Multi Output

(MIMO) short range radar; performed in IMEC research institute (Leuven, Belgium). The radar

system targets high resolution performance with low power consumption in order to integrate a full

MIMO radar transceiver with digital processor and antennas in a compact package featuring a size of 1

cm2. Achieving such radar system characteristics requires the exploitation of a highly demanding

digital architecture with signal processing gain and high range, speed and angle resolutions. The

improved resolution and detection capabilities will be achieved by performing signal processing

algorithms on the reflected waveform. The digital front-end implements parallel range gate processing

with a bank of correlators that perform: pulse compression, coherent accumulation to further increase

Signal to Noise Ratio (SNR) and N-point FFT to extract the Doppler information. The use of MIMO is

proposed implementing a code domain technique in the PMCW waveform, the Outer Hadamard Code

MIMO. This concept makes use of a unique sequence for all the transmitting antennas that is rendered

by an outer sequence to ensure the orthogonality of the transmitted waveforms. The outer code makes

use of the good cross-correlation properties of the Hadamard sequences and the waveform uses

sequences that exhibit perfect auto-correlation profile, the Almost Perfect Autocorrelation Sequences

(APAS). The MIMO implementation results in higher angular resolution and extra processing gain.

The use of beamforming techniques in the radar allows the angle estimation of the detected targets;

using rough and fine beamforming that provides with coarse and precise Angle of Arrival (AoA)

estimation in an early and late stage respectively. A Constant False Alarm Rate (CFAR) processing

stage is implemented in the stage of the system where higher signal processing gain is achieved. This

algorithm allows the variation of the CFAR parameters and analyzes the detections in order to

improve the probability of detection (𝑃𝑑) while decreasing the probability of false alarm (𝑃𝑓𝑎). A

series of simulations with different scenarios and variable parameters are set in order to analyze the

performance of the system. The simulations analyze the gain achieved in each stage and their

outcomes show an impressive processing gain that can reach SNR improvements as high as 77 dB for

a small virtual array while keeping the 𝑃𝑓𝑎 low with the CFAR adjustment. The use of bigger arrays

demonstrates the possibility to enable clear detections for low Radar Cross Section (RCS) targets in

far distances of the unambiguous range. The use of beamforming shows interference reduction

improvement as the beam widths narrow with the increasing number of virtual array antennas. These

results have been achieved while keeping the system design parameters to a range resolution of 7.5 cm

for a maximum range of 37.5 meters with speed resolution of 0.2 m/s and a maximum detectable

speed of 12.66 m/s. The outcomes support the good performance of the signal processing techniques

implemented and the benefits in applying them in a SoC mmWave MIMO radar.


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Table of Contents

Preface ...................................................................................................................................................... i

Abstract .................................................................................................................................................. iii

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

Table of Figures ..................................................................................................................................... ix

List of Tables ........................................................................................................................................ xiv

1 Introduction ..................................................................................................................................... 1

1.1 Historical Overview ................................................................................................................ 1

1.2 Radar in Brief .......................................................................................................................... 4

1.3 Proposed Radar System ......................................................................................................... 12

1.4 Outline of the Thesis ............................................................................................................. 15

2 Theory ........................................................................................................................................... 17

2.1 Radar Technology ................................................................................................................. 17

2.1.1 Important System Parts ................................................................................................. 17

2.1.2 Radar Main Parameters and Concepts ........................................................................... 20

2.1.3 Radar Equation .............................................................................................................. 24

2.1.4 PMCW vs FMCW Radar............................................................................................... 26

2.1.5 Radar Waveform and Pulse Compression ..................................................................... 32

2.2 Fundamentals of Signal Processing for Radar ....................................................................... 38

2.2.1 Basic Signal Processing Concepts ................................................................................. 38

2.2.2 Matched filter ................................................................................................................ 39

2.2.3 Pulse Integration ............................................................................................................ 42

2.2.4 Doppler Processing ........................................................................................................ 43

2.2.5 Ambiguity Function ...................................................................................................... 48

2.3 Constant False Alarm Rate (CFAR) ...................................................................................... 50

2.3.1 Introduction ................................................................................................................... 50

2.3.2 Cell Averaging CFAR ................................................................................................... 53


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2.3.3 Greatest Of / Smallest Of Cell Averaging with CFAR ................................................. 56

2.3.4 Order Statistics CFAR ................................................................................................... 57

2.4 MIMO Radar ......................................................................................................................... 58

2.4.1 Introduction ................................................................................................................... 58

2.4.2 Virtual Array Concept ................................................................................................... 60

2.4.3 Outer Code MIMO ........................................................................................................ 63

2.4.4 Range Domain MIMO ................................................................................................... 65

2.5 Beamforming ......................................................................................................................... 66

2.5.1 Introduction ................................................................................................................... 66

2.5.2 Linear Phased Array Antenna ....................................................................................... 68

2.5.3 Conventional Methods .................................................................................................. 69

2.5.4 Adaptive Methods ......................................................................................................... 72

3 System Implementation ................................................................................................................. 74

3.1 Radar System Description ..................................................................................................... 74

3.1.1 Overview ....................................................................................................................... 74

3.1.2 Required System Parameters ......................................................................................... 76

3.1.3 Digital Front-End .......................................................................................................... 86

3.1.4 Simulation Chain Structure ........................................................................................... 94

3.2 MIMO Implementation ....................................................................................................... 103

3.2.1 Overview ..................................................................................................................... 103

3.2.2 Outer Hadamard Code ................................................................................................. 104

3.2.3 Range Domain Separation ........................................................................................... 112

3.3 Constant False Alarm Rate (CFAR) Detector ..................................................................... 117

3.3.1 Overview ..................................................................................................................... 117

3.3.2 SISO CFAR ................................................................................................................. 118

3.3.3 MIMO CFAR .............................................................................................................. 129

3.4 Fine Angle of Arrival (AoA) ............................................................................................... 137

3.4.1 Overview ..................................................................................................................... 137

3.5 System Review .................................................................................................................... 140


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4 Simulations and Discussion ......................................................................................................... 145

4.1 Simulations Information ...................................................................................................... 145

4.2 CFAR results ....................................................................................................................... 155

4.2.1 Probability of False Alarm .......................................................................................... 160

4.2.2 Number of Training Cells ............................................................................................ 163

4.2.3 Guard Cells .................................................................................................................. 165

4.2.4 Algorithm .................................................................................................................... 167

4.3 MIMO results ...................................................................................................................... 170

4.3.1 Small Array and High RCS ......................................................................................... 170

4.3.2 Small Array and Low RCS .......................................................................................... 175

4.3.3 Big Array and Low RCS ............................................................................................. 183

4.4 Angle of Arrival .................................................................................................................. 191

4.4.1 Rough Beamforming ................................................................................................... 191

4.4.2 Fine Angle of Arrival .................................................................................................. 202

4.5 Main PMCW system parameters variation .......................................................................... 206

4.5.1 Unambiguous range ..................................................................................................... 206

4.5.2 Range Resolution ........................................................................................................ 211

4.5.3 Velocity Resolution ..................................................................................................... 216

4.5.4 Unambiguous velocity ................................................................................................. 219

4.5.5 M-Sequences ............................................................................................................... 224

5 Conclusions ................................................................................................................................. 228

5.1 Future Work ........................................................................................................................ 232

References ........................................................................................................................................... 234

Summary of Main Parameters .............................................................................................................. A1


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Table of Figures

Fig. 1: Maxwell electromagnetism equations............................................................................................................................. 1

Fig. 2: Telemobiloscope [1]. ....................................................................................................................................................... 2

Fig. 3: Radar basic operation principle. ...................................................................................................................................... 5

Fig. 4: Scheme of a bistatic radar design. ................................................................................................................................... 6

Fig. 5: Scheme of a monostatic radar design. ............................................................................................................................. 6

Fig. 6: Block diagram of a monostatic architecture pulsed radar system. ................................................................................ 8

Fig. 7: Block diagram of the architecture of a FMCW radar. ...................................................................................................... 9

Fig. 8: Spectrum with the location of the traditional microwave bands and the mmWave bands. ......................................... 11

Fig. 9: Attenuation in the atmosphere of electromagnetic waves according to their working frequency. .............................. 12

Fig. 10: Radar short and long range types with the mmWave frequencies and capabilities. ................................................... 13

Fig. 11: Basic block diagram of a general monostatic radar system [37].................................................................................. 18

Fig. 12: Two targets closely placed being radiated by a radar. ................................................................................................. 20

Fig. 13: Spectrum of a pulse of duration τ, with a sinc shape [26]. .......................................................................................... 21

Fig. 14: Several transmitted pulses separated in time by the PRI. ........................................................................................... 22

Fig. 15: Two unambiguous and one ambiguous mesuarement [9]. a)Transmitter: three pulses with a pulse width 𝜏𝑝 and

PRI=Tp.b) Receiver: Echoes caused by the first pulse. .................................................................................................... 23

Fig. 16: A basic FMCW radar block diagram. ............................................................................................................................ 27

Fig. 17: Representation of the FMCW transmitted and reflected signals [9]. .......................................................................... 28

Fig. 18: Representation of the final FMCW signal in the output mixer [9]. .............................................................................. 29

Fig. 19: Block diagram architecture of a basic pseudo-noise modulated radar system. .......................................................... 30

Fig. 20: Time representation of a biphase sequence with its parameters [9]. ......................................................................... 30

Fig. 21: An M-Sequence representation in the frequency domain [9]. .................................................................................... 31

Fig. 22: A pulse being spread through time in order to reduce to peak energy and keep the BW........................................... 33

Fig. 23: Biphase code diagram of pulse compression. .............................................................................................................. 33

Fig. 24: A 13-Barker code and its respective autocorrelation function . .................................................................................. 35

Fig. 25: Autocorrelation response of a m-sequence code with 1023 chips length. .................................................................. 36

Fig. 26: APAS code processing of its autocorrelation function [36]. ......................................................................................... 37

Fig. 27: Autocorrelation response of an APAS code of 4080 chips length. ............................................................................... 37

Fig. 28: Coherent and non-coherent signals. In a) a coherent signal generated from the reference b), in c) a non-coherent

pulse. .............................................................................................................................................................................. 42

Fig. 29: After the Doppler processing the matrix transforms to range/Doppler from fast/slow time to matrix [33]. ............. 45

Fig. 30: Shape of the received signal after DFT processing [33]. .............................................................................................. 47

Fig. 31: Thumbtack-like ambiguity function [33]. ..................................................................................................................... 49

Fig. 32: Basic block diagram of the signal processing in the receiver until the detection stage. .............................................. 50

Fig. 33: Cell analysis procedure of a CFAR analysis. ................................................................................................................. 52

Fig. 34: Block diagram of the CA CFAR detector. ...................................................................................................................... 54

Fig. 35: CA CFAR masking occurring in a multi-target situation with N=32 and 𝑃𝑓𝑎 = 10 − 6 [46]. ...................................... 55

Fig. 36: MIMO radar system principle. ..................................................................................................................................... 59

Fig. 37: Three transmitter antennas and four receiver antennas with their matched filters detectors. .................................. 61


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Fig. 38: NM virtual antenna arrays formed with the physical antennas from Fig. 36. ............................................................. 61

Fig. 39: Transmission part for the signal generation of a MIMO outer code system. .............................................................. 64

Fig. 40: MIMO processing for one range gate in one receiver antenna. .................................................................................. 64

Fig. 41: Transmitter side of the Range Domain Separation MIMO method with four transmitters. ........................................ 65

Fig. 42: Receiver side of the Range Domain Separation MIMO method showing one receiver antenna. ................................ 66

Fig. 43: Geometry of a Uniform Linear Array (ULA).................................................................................................................. 68

Fig. 44: Conventional Beamformer basic block diagram. ......................................................................................................... 70

Fig. 45: Adaptive Beamformer basic block diagram. ................................................................................................................ 72

Fig. 46: 3D simulation of the targeted SoC radar, featuring the size of 1 𝑐𝑚2 [9]. .................................................................. 75

Fig. 47: Chip duration for each sequence 𝐿𝑐 symbol. .............................................................................................................. 77

Fig. 48: Unambiguous range detection field of a radar system. ............................................................................................... 78

Fig. 49: One PMCW sequence with a certain chip period. ....................................................................................................... 83

Fig. 50: Relation between the unambiguous Doppler frequency and the dwell time. ............................................................. 85

Fig. 51: Relation between the number of N and the narrowing of the filter in the Doppler bank filter. ................................. 85

Fig. 52: System design structure of the mmWave radar project. ............................................................................................. 86

Fig. 53: Basic block diagram of the PMCW radar system under study. .................................................................................... 87

Fig. 54: Repetition of the transmitted sequence, S, a number of M times. ............................................................................. 88

Fig. 55: Radar system transmitting the needed N times M sequences repetition. .................................................................. 88

Fig. 56: Digital front-end with a bank of parallel correlators for PMCW radar system [20]. .................................................... 89

Fig. 57: Transmitter part of a radar system reaching two targets at different range gates. .................................................... 90

Fig. 58: Receiver part of a radar system echoing the signals from the two targets of the Fig. 56. ........................................... 91

Fig. 59: Complete parallel range gate processor block diagram of a PMCW radar. ................................................................. 92

Fig. 60: Detailed parallel gate processing for the example of the Fig. 58. ................................................................................ 93

Fig. 61: Matlab chain PMCW radar simulation flow. ................................................................................................................ 95

Fig. 62: Two dimensional model of the SISO data structure, a radar data matrix. ................................................................... 98

Fig. 63: Block diagram of the digital front-end processing a single range gate and saving its samples in each component of

the vector that composes the first row of the radar data matrix. .................................................................................. 99

Fig. 64: Digital front-end processing and storing of samples for the full parallel range gate system. .................................... 100

Fig. 65: Conversion of the fast/slow time radar data matrix to the range/Doppler radar data matrix. ................................. 101

Fig. 66: Location of the MIMO processing part in the radar system. ..................................................................................... 103

Fig. 67: Three dimensional model of the MIMO data structure, a radar data cube. .............................................................. 104

Fig. 68: A MIMO radar system with N_tx=4 and N_rx=2 and its correspondent virtual array. .............................................. 105

Fig. 70: Simplified diagram of the signals the TX signals being summed and reflected. ........................................................ 106

Fig. 69: Forming of the transmitter side of an Outer Hadamard Code MIMO radar system. ................................................. 106

Fig. 71: Receiver side of an Outer Hadamard Code MIMO radar system. .............................................................................. 107

Fig. 72: Data structure size that each receiver will take after the MIMO processing. ............................................................ 108

Fig. 73: Separation of each transmitter signal part with a Hadarmard matrix and radar data cube storage. ........................ 109

Fig. 74: Separation of each transmitter signal part for every N repetitions and radar data cube storage. ............................ 109

Fig. 75: Separation of each transmitter signal part for every N repetitions with the full parallel range gate processing besides

its storing in a radar data cube. .................................................................................................................................... 110

Fig. 76: Separation of each received signal for every N repetitions with the full parallel range gate processing and for each

receiving antenna, besides its storing in a radar data cube.......................................................................................... 111


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Fig. 77: Signal forming of the transmitter side of a Range Domain Separation MIMO radar system. .................................... 112

Fig. 78: Range Domain MIMO receiver after having correlated a full sequence Lc, giving as a result the unambiguous range

of each antenna. ........................................................................................................................................................... 113

Fig. 79: Range Domain MIMO receiver detailed process after having correlated a full sequence Lc, giving as a result the

unambiguous range of each antenna. .......................................................................................................................... 114

Fig. 80: Detections of each antenna with a Range Domain Separation MIMO processor. ..................................................... 114

Fig. 81: One dimension matrix with the information related to each antenna with length 𝐿𝑐 x M x N. ................................ 115

Fig. 82: Radar data cube after the reorganization of the one dimensional receiver output with dimension 𝐿𝑐 x 𝑁𝑣 x N. .... 116

Fig. 83: Range Domain Separation structure adjustment with m-sequences. ....................................................................... 116

Fig. 84: Location of the CFAR processing part in the radar system. Upper figure for a SISO radar configuration, lower figure

for a MIMO radar configuration. .................................................................................................................................. 117

Fig. 85: Data structures in the input of the CFAR detector stage. Left figure, a SISO matrix filled with data, right figure a

MIMO data cube structure. .......................................................................................................................................... 118

Fig. 86: Difference in the profile views between the Doppler domain and the Range domain.............................................. 119

Fig. 87: CFAR analysis along the range domain for each doppler bin. .................................................................................... 120

Fig. 88: CFAR analysis along the range domain for each doppler bin. .................................................................................... 121

Fig. 89: Detection in the radar data matrix and saving of the detected’s coordinate in the detection matrix. ..................... 122

Fig. 90: Block diagram of the CA/GOCA/SOCA CFAR algorithms. ........................................................................................... 123

Fig. 91: Block diagram of an OS CFAR algorithm. ................................................................................................................... 123

Fig. 92: Final detection matrix with several detections. ......................................................................................................... 124

Fig. 93: False alarms in consecutive Doppler bin and range gate clearance algorithm. No consecutive/adjacent found. ..... 125

Fig. 94: False alarms in consecutive Doppler bin and range gate clearance algorithm. Range migration found. .................. 126

Fig. 95: False alarms in consecutive Doppler bin and range gate clearance algorithm. Doppler spreading and range migration

found. ........................................................................................................................................................................... 127

Fig. 96: Final detection matrix result after the post-detection processing to eliminate false alarms. ................................... 128

Fig. 97: Rough radar scanning along the equidistant angles of the radar aperture, for 4 antennas. ..................................... 130

Fig. 98: First angle under evaluation in beamforming. ........................................................................................................... 131

Fig. 99: Beamforming using the radar data cube 𝐿𝑐 𝑥 𝑁𝑣 𝑥 𝑁 and a weighting vector of certain angle, besides new radar

data cube structure with the angles dimension. .......................................................................................................... 132

Fig. 100: Vector beamforming using the radar data cube 𝐿𝑐 𝑥 𝑁𝑣 𝑥 𝑁 and a weighting vector of certain angle, besides a new

radar data cube structure with the angles dimension. ................................................................................................. 133

Fig. 101: Angles’ radar data cube completed for all the angles of the rough beamforming .................................................. 134

Fig. 102: Beamforming completed for the first angle of the rough beamforming. ................................................................ 134

Fig. 103: CFAR detector along each matrix linked with an angle............................................................................................ 135

Fig. 104: Consecutive angles' radar data matrix analysis. ...................................................................................................... 135

Fig. 105: Target causing a double detection in different angles. ............................................................................................ 136

Fig. 106: Location of the fine beamforming processing part in the radar system. ................................................................. 137

Fig. 107: Fine beamforming around a rough beamforming wide lobe linked to a target in a detected angle. ...................... 138

Fig. 108: Data sets selection from the radar data cube using the CFAR detection coordinates. ............................................ 138

Fig. 109: Beamforming evaluation in different angles around the angle where the detection 1 was located with the rough

beamforming. ............................................................................................................................................................... 139

Fig. 110: Block diagram of the transmitter part of the PMCW radar system, SISO and MIMO configurations. ..................... 142


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Fig. 111: Block diagram of the receiver side of the PMCW radar system. .............................................................................. 143

Fig. 112: Simulation 1, detection in the range – Doppler domain 3D representation of the radar data cube. ...................... 149

Fig. 113: Simulation1, detection showed in the range profile of the radar data cube taken before the FFT processing. ...... 150

Fig. 114: Simulation 1, detection in the Doppler profile of the radar data cube taken after the FFT processing. ................. 151

Fig. 115: Simulation 1, detection cuts in the Doppler domain cuts and the range domain cuts where there have been

detections. .................................................................................................................................................................... 151

Fig. 116: Simulation 1, Detection matrixes; after CFAR detection(left) and after post-processing algorithm(right). ............ 154

Fig. 117: Simulation 2, detections of the simulation 2 showed in the detection matrixes. ................................................... 158

Fig. 118: Simulation 2, detections showed in Range and Doppler cuts. ................................................................................ 158

Fig. 119: Simulation 2, detections of the targets of the simulation 2 in Range and Doppler profiles. ................................... 159

Fig. 120: Simulation 2, detections over the system noise floor for 𝑃𝑓𝑎 = 10 − 4(left) and 𝑃𝑓𝑎 = 10 − 2 (right). ............. 160

Fig. 121: Simulation 2, detection matrixes of the detections for 𝑃𝑓𝑎 = 10 − 4(left) 𝑃𝑓𝑎 = 10 − 2 (right). ....................... 161

Fig. 122: Simulation 2, Detection profiles of the detections in Simulation 2 for 𝑃𝑓𝑎 = 10 − 4 (up) and 𝑃𝑓𝑎 = 10 − 2

(down). ......................................................................................................................................................................... 162

Fig. 123: Simulation 2, detection profiles of the targets with RCS=-20 dBsm, with 𝑃𝑓𝑎 = 10 − 6 (up) and 𝑃𝑓𝑎 = 10 − 4

(down). ......................................................................................................................................................................... 163

Fig. 124: Simulation 3, detection profile of a CA CFAR algorithm for 𝑁𝑡𝑐=2 (up), 𝑁𝑡𝑐 =10 (middle) and 𝑁𝑡𝑐=16 (down). .. 164

Fig. 125: Simulation 3, Doppler profile with a target causing range migration. ..................................................................... 165

Fig. 127: Simulation 3, detection matrix of a range migrated detection with 0 guard cells (left) and 1 guard cell (right) ..... 166

Fig. 126: Simulation 3, detection profiles varying the number of guard cells, from 0(up) to 8(down). ................................. 166

Fig. 128: Simulation 3, CA algorithm applied for two contiguous detections with 𝑁𝑡𝑐= 12 (left) and 𝑁𝑡𝑐= 20 (right). ......... 167

Fig. 129: Simulation 3, GOCA algorithm applied for two contiguous detections with 𝑁𝑡𝑐= 12 (left) and 𝑁𝑡𝑐= 20 (right). .... 167

Fig. 130: Simulation 3, SOCA algorithm applied for two contiguous detections with N_tc= 12 (left) and N_tc= 20 (right). .. 168

Fig. 131: Simulation 3, OS algorithm applied for two contiguous detections with 𝑁𝑡𝑐= 12 (left) and 𝑁𝑡𝑐= 20 (right). ......... 169

Fig. 132: Simulation 4, targets in the range – Doppler domain 3D representation of the radar data cube. .......................... 172

Fig. 133: Simulation 4; range profile of the received signal after the pulse compression. ..................................................... 173

Fig. 134: Simulation 4, range profile after M accumulations and MIMO, before the FFT processing. ................................... 173

Fig. 135: Simulation 4, Doppler cuts of the radar data cube after the FFT processing. .......................................................... 174

Fig. 136: Simulation 4, Doppler cut of the radar data cube after the rough beamforming processing. ................................. 175

Fig. 137: Simulation 5, range profile after pulse compression. .............................................................................................. 178

Fig. 138: Simulation 5, range profile after the pulse compression and M accumulation. ...................................................... 178

Fig. 139: Simulation 5, Doppler profile of the radar data cube after the FFT. ........................................................................ 179

Fig. 140: Simulation 5, range profile of the radar data cube after the FFT processing. .......................................................... 180

Fig. 141: Simulation 5, 3D representation of the radar data cube data after the rough beamforming processing. .............. 180

Fig. 142: Simulation 5, range profile of the radar data cube after the rough beamforming processing. ............................... 181

Fig. 143: Simulation 5, CFAR profile cuts of the detections. ................................................................................................... 182

Fig. 144: Simulation 5, detection matrixes. ............................................................................................................................ 183

Fig. 145: Simulation 6, Doppler profile of the radar data cube after the FFT. ........................................................................ 185

Fig. 146: Simulation 6, Doppler profile of the radar data cube after the rough beamforming. ............................................. 185

Fig. 147: Simulation 6, targets in the range – Doppler domain 3D representation of the radar data cube. .......................... 186

Fig. 148: Simulation 6, range profile of the radar data cube after the rough beamforming processing. ............................... 186

Fig. 149: Simulation 6, targets in the range – Doppler domain 3D back representation of the radar data cube. .................. 187


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Fig. 152: Simulation 7, angle of arrival cut for the Target 1. .................................................................................................. 193



Fig. 155: Simulation 7, Doppler cuts for the Target 1, angle 12 degrees. ............................................................................... 195


Fig. 157: Simulation 7, Doppler cuts for the Target 3, angle -36 degrees. ............................................................................. 196

Fig. 158: Simulation 7, target 3 in the range – Doppler domain 3D for the angle = -36 degrees. .......................................... 197




Fig. 162: Simulation 7, range profile for the angle 30. ........................................................................................................... 200

Fig. 163: Simulation 8, range profile for the angle 30. ........................................................................................................... 201

Fig. 164: Simulation 7, Bartlett beamforming algorithm applied for the detected targets. ................................................... 202

Fig. 165: Simulation 7, Capon beamforming algorithm applied for the detected targets. ..................................................... 203

Fig. 166: Simulation 7, MUSIC beamforming algorithm applied for the detected targets. .................................................... 203

Fig. 167: Simulation 8, Bartlett beamforming algorithm applied for the detected targets. ................................................... 204

Fig. 168: Simulation 8, Capon beamforming algorithm applied for the detected targets. ..................................................... 205

Fig. 169: Simulation 8, MUSIC beamforming algorithm applied for the detected targets. .................................................... 205

Fig. 170: Simulation 9, CFAR profile cuts for the detections. ................................................................................................. 209


Fig. 172: Simulation 9, CFAR profile cuts for the detections with range resolution decreased.............................................. 213

Fig. 173: Simulation 9, detection matrixes for the range resolution decreased. ................................................................... 214

Fig. 174: Simulation 9, detection matrixes for a decreased velocity resolution. .................................................................... 218

Fig. 175: Simulation 9, CFAR profile cuts for the detections with unambiguous velocity decreased. .................................... 221

Fig. 176: Simulation 9, detection matrixes for unambigous velocity decreased. ................................................................... 222

Fig. 177: Simulation 9, detection matrixes for increased unambiguous speed. ..................................................................... 224

Fig. 178: Simulation 10, CFAR profile cuts for the detections. ............................................................................................... 227


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List of Tables

Table 1: Summary of the main PMCW radar system parameters. ........................................................................................... 76

Table 2: Final Values of the Parameters after recalculation. ................................................................................................... 81

Table 3: Some of the functionalities that are included in the digital front end and back end of the radar system. ................ 87

Table 4: Matlab chain parts and main functionalities. ............................................................................................................. 94

Table 5: Simulation 1, targets scenario initialization parameters. ......................................................................................... 146

Table 6: Simulation 1, main design parameters chosen for the radar system under simulation. .......................................... 146

Table 7: Simulation 1, theoretical PMCW link budget of the targets. .................................................................................... 147

Table 8: Simulation 1, summary of the main PMCW system parameters. ............................................................................. 148

Table 9: Simulation 1, CFAR Performance. ............................................................................................................................. 153

Table 10: Simulation 1, detected targets coordinates and interpretation. ............................................................................ 153

Table 11: Simulation 1, radar system performance at different stages of simulation, theoretical and simulated. ............... 155

Table 12: Simulation 2, targets scenario initialization parameters. ....................................................................................... 156

Table 13: Simulation 2, theoretical PMCW link budget of the targets. .................................................................................. 156

Table 14: Simulation 2, values of the CFAR parameters chosen. ........................................................................................... 157

Table 15: Simulation 2, CFAR performance. ........................................................................................................................... 157



Table 18: Simulation 3, new targets location to show the variation in training cells effect. .................................................. 163

Table 19: Simulation 4, summary of the main PMCW system parameters. ........................................................................... 170

Table 20: Simulation 4, selectable parameters of the MIMO stage. ...................................................................................... 171


Table 22: Simulation 5, simulated targets initialization parameters. ..................................................................................... 176

Table 23: Simulation 5, theoretical PMCW link budget of the targets. .................................................................................. 176

Table 24: Simulation 5, MIMO configuration. ........................................................................................................................ 176







Table 31: Simulation 6, radar system performance at different stages of the system. .......................................................... 184


Table 33: Simulation 6, CFAR detected targets coordinates and interpretation. ................................................................... 188



Table 36: Simulation 7, simulated targets initialization parameters. ..................................................................................... 192



Table 39: Simulation 7, CFAR detected targets coordinates and interpretation. ................................................................... 198


xv




Table 43: Variable PMCW system design parameters. ........................................................................................................... 206

Table 44: Simulation 9, simulated targets initialization parameters ...................................................................................... 206

Table 45: Simulation 9, decreased unambiguous range variation.......................................................................................... 207

Table 46: Simulation 9, summary of main PMCW system parameters for decreased unambiguous range. .......................... 208

Table 47: Simulation 9, theoretical PMCW link budget for the targets scenario. .................................................................. 208



Table 50: Simulation 9, increased unambiguous range. ......................................................................................................... 210

Table 51: Simulation 9, summary of main PMCW system parameters for increased unambiguous range. ........................... 211

Table 52: Simulation 9, decreased range resolution. ............................................................................................................. 212

Table 53: Simulation 9, summary of the main PMCW system parameters for decreased range resolution. ......................... 212

Table 54: Simulation 9, detected targets coordinates and interpretation for a decreased range resolution. ....................... 213

Table 55: Simulation 9, increased range resolution. .............................................................................................................. 214

Table 56: Simulation 9, summary of the main PMCW system parameters for increased range resolution. .......................... 215

Table 57: Simulation 9, detected targets coordinates and interpretation for a increased range resolution. ........................ 215

Table 58: Simulation 9, decreased velocity resolution. .......................................................................................................... 216

Table 59: Simulation 9, summary of the main PMCW system parameters for decreased velocity resolution....................... 216

Table 60: Simulation 9, detected targets coordinates and interpretation for decreased velocity resolution........................ 217

Table 61: Simulation 9, increased velocity resolution. ........................................................................................................... 218

Table 62: Simulation 9, summary of the main PMCW system parameters for increased velocity resolution. ....................... 219

Table 63: Simulation 9, detected targets coordinates and interpretation for increased velocity resolution. ........................ 219

Table 64: Simulation 9, decreased unambiguous speed. ....................................................................................................... 220

Table 65: Simulation 9, summary of the main PMCW system parameters for decreased unambiguous velocity. ................ 220

Table 66: Simulation 9, detected targets coordinates and interpretation for decreased unambiguous velocity. ................. 221

Table 67: Simulation 9, increased unambiguous velocity. ..................................................................................................... 222

Table 68: Simulation 9, summary of main PMCW system parameters for increased unambiguous velocity. ....................... 223

Table 69: Simulation 9, detected targets coordinates and interpretation for increased unambiguous velocity. .................. 223

Table 70: Simulation 10, simulated targets initialization parameters. ................................................................................... 225

Table 71: Simulation 10, theoretical PMCW link budget of the targets. ................................................................................ 225

Table 72: Simulation 10, summary of the main PMCW system parameters. ......................................................................... 226

Table 73: Simulation 10, radar system performance at different stages of simulation, theoretical and simulated. ............. 226

Table 74: Simulation 10, detected targets coordinates and interpretation. .......................................................................... 227


xvi


1

1 Introduction

In this chapter, an historical overview of the radar technology from its beginnings through its

evolution is presented. The chapter also reviews the basic concepts of radar; the main functions and

characteristics, the main classification groups in which the different radar systems are included, the

frequency bands where the different types of radar work and some applications. A background of

automotive radars is also presented; the technology motivation and development during the last years,

the technologies used with their advantages and drawbacks besides future needs. An introduction to

the mmWave radar that this thesis focuses in is also provided, besides a description of the aim of the

thesis. Finally, in the last part of the chapter an outline of the thesis is included, where the content that

each chapter develops is described.

1.1 Historical Overview

The origin of radar cannot be attributed to any particular person or country in particular. The

development of the technology was pushed by certain circumstances that lead to its appearance. The

‘discovery’ was boosted by several factors and actors which contribution summed up to the

materialization of the final product. However there are some milestones and historical moments that

are worth mentioning since they added significant and relevant tools and inventions to the process.

In 1865, a Scottish physicist named James Clerk Maxwell, introduced a relevant and very important

theory for the future development and growth of wireless technologies included in the radar. ‘A

Dynamical Theory of the Electromagnetic Field’ was the third article that Maxwell published

regarding electromagnetism [1]. This paper is of vital importance since it introduced the famous set of

equations shown in Fig. 1, today referred as ‘the four Maxwell’s equations’; that describe how the

magnetic and electric fields are related to each other. The basic demonstration of this theory was the

fact that the magnetic and electric fields are moving through the space as waves and with a constant

speed.

∇ ∙ 𝐸 = 𝜌

𝜀0

∇ ∙ 𝐵 = 0

∇ × E = −𝜕𝐵

𝜕𝑡

∇ × 𝐵 = 𝜇0𝐽 + 𝜇0휀0𝜕𝐸

𝜕𝑡

Fig. 1: Maxwell electromagnetism equations.


2

These Maxwell’s papers gave birth to the use of electromagnetism as we know it today. Thanks to

these foundations was possible for the next vital actor to appear. A further improvement of

electromagnetism theory was developed by Heinrich Rudolf Hertz, a German physicist, who in the late

19th century demonstrated that the electromagnetic waves are reflected by metallic surfaces [2]. He

studied the response to electromagnetic radiation, soon to be called radio waves, of different

conductors of dielectrics, demonstrating in fact what was theorized by the Maxwell’s equations.

Another important milestone was achieved by Guglielmo Marconi. After conducting some

experiments, consisting on tests transmitting waves throughout the countryside, he indicated the

potential use of the technology in order to help ships avoid coastline points in bad weather conditions.

The achievement of his long distance electromagnetic transmissions [3] and his presented ideas to

apply the technology were the key kick off for a wide interest in the development of the technologies

that will later come out as the so called radar.

In 1904, Christian Hülsmeyer started to give demonstrations of a device characterized by the use of

the echos produced by radio waves [4]. The invention was called ’telemobiloscope’(Fig. 2) and

consisted on a gap where a signal was generated using a dipole antenna with a reflector, as the

transmitter.

The reflected echoes were taken by a similar receiver coherent antenna and when a detection happened

a bell ringed. The device was very useful for sea traffic control thanks to its capable range capability

covering up to 3000 meters. The device did not provide range information yet, just the warning of a

nearby object, but it was the first practical invention applying the work of G. Marconi.

A parallel invention of significant importance happened in 1921. The Magnetron emerged as an

efficient transmitter invented by the Albert Wallace Hull [5]. The discovery took place when A. Hull

was researching the movement of electrons under the influence of a magnetic field and he realized that

there was a possibility of controlling the electron current by varying the produced magnetic field.

Fig. 2: Telemobiloscope [1].


3

Almost at the same time as Hull’s discovery, Albert Hoyt Taylor and Leo C. Young were conducting

transmitting experiments in the US Naval Aircraft Radio Laboratory, when they realized they had an

interference in the system, which was actually a detected wooden vessel. Later in 1930, Lawrence A.

Hyland decided to use an analogous arrangement with purpose of detecting an airplane. This directed

to a patent proposition [6] to use the technique to detect boats and aircrafts for what it would now be

called CW radar (Continuous Wave Radar).

By that time, the invention could detect the existence of an object, but could not determine its velocity,

nor its location. Leo C. Young suggested the use of pulsing techniques to overcome this limitation.

Robert Morris Page implemented Young’s idea and in 1934 his invention was tested to detect a plane.

Even though the results were poor they were good enough to show the potential of the technology and

resulted in the world first real radar device.

In 1936 William C. Hahn and George Metcalf developed an important component which will be useful

for the radars, as an oscillator and amplifier, the Klystron. During this time period important efforts

and investigations were put in place to further develop the technology, mainly in countries such as

United Kingdom, Germany, US, URSS and Japan.

The British, directly threaten and facing possible attacks coming by air, developed the famous Chain

Home surveillance radar network that remained working until the end of the World War II. In 1939,

after numerous rudimentary tests and developments in United Kingdom, the engineers John Turton

Randall and Henry Albert Howard Boot constructed a radar using a multicavity magnetron [7]. The

device was light and high powered due to its short wavelength and suitable to be mounted on aircrafts

to effectively German submarines during night or with bad visibility conditions.

After the beginning of the Second World War (WWII), in 1940, the US and United Kingdom started a

cooperation to further upgrade the radar technology. Until then, most of the existing radar systems

were functioning at HF (High Frequency) and VHF (Very High Frequency) wavelengths, but with the

progresses of the microwave magnetron by the British and the creation of the Radiation Laboratory in

the MIT (Massachusetts Institute of Technology), the radar based on microwave frequencies was

settled and remained dominant until nowadays.

The development of the radar technology was guided by the war defense’s needs, while currently

military applications are still the main market and reason for development, the use of radar has been

widely extended to a number of varied civilian applications. The most known might be the traffic

radars, used to measure the speed of cars, or the meteorological radars with which the weather

forecasts are shown in TV news. Another radar very important for nowadays functioning of the

transport is the air traffic control radar, used to control the aircraft traffic over the congested air space.

Aviation also uses radars for determining speed and avoiding bad weather conditions. One of the late

developments for which radar is being used for and where many efforts and investment are being put,

is in the scope of the automotive industry, for aid driving and autonomous cars. Ultimately, it is

foreseen that their miniaturization, radars will be used in small devices making up the Internet of


4

Things. It is precisely in these latest applications in the medium term and automotive applications in

the short term, where the radar system presented in the following document chapters is intended to be

used in.

1.2 Radar in Brief

The word Radar stands for RAdio Detecting and Ranging, and it was given by Samuel M. Tucker and

F. Furth in 1940 [8]. It describes the electronic systems that are able to detect the presence and speed

of one or several objects, by means of electromagnetic waves. The fundamentals of radar can be seen

as an analogy to the reflection caused by a sound wave. When a shout is generated a series of echoes

can be received back as a result of reflections from objects surrounding the origin. Moreover, the

distance of the reflecting object can be easily computed, by knowing the speed of the sound and the

coefficient of the medium through which the sound is being propagated.

Radar, instead of sound waves, uses electromagnetic waves. Radar can be defined as an

electromagnetic sensing device for locating and derive further information regarding the detected

object, through processing and analysis of the information contained in the signals coming back from

the reflecting objects. The summarized radar operation, shown in Fig. 3, is outlined as follows:

- Initially the radar transmitter, by means of an antenna, radiates energy in space, in

the shape of electromagnetic waves

- Through space, electromagnetic waves might come across with an object, called

target. Depending on the reflectivity of the target, a portion of the energy will be

reflected back.

- The electromagnetic energy hitting the target, is reflected in multiple directions.

One of the directions comes to be the same direction of the initially radiated

electromagnetic wave. This energy is received by the radar receiver antenna.

- After an amplification and with the assistance of convenient signal processing a

decision has to be made in whether there is a detection or not in the signal received.

- After the decision is made, other information about the target can be extracted for

further analysis and processing.


5

The basic operation principles of radar systems are based on the physics of electromagnetism

mechanisms. Basically:

- The reflection of electromagnetic waves: the energy is reflected when the wave

front come across with an electrically conductive surface.

- Electromagnetic waves move through the space at a constant velocity, roughly the

speed of light, 𝑐 = 3 ∙ 108 𝑚/𝑠. Due to the fact that the speed is constant, the

distance between the reflecting targets and the signal source can be measured.

- The waves travel in a straight line, unless slight deviations due to atmospheric

conditions, meaning that with special antenna arrangements and processing, the

energy can be centered into a desired direction. So that way, also the direction of

the detected targets can be measured.

Radars main functionalities are; the detection, ranging, speed measurement and angle location:

Detection and Ranging: It is one of the main features of a radar and describes its ability to determine

the distance from a target. As mentioned before, this is done by measuring the time that the

electromagnetic wave reflected back to the receiver takes from the moment it has left the transmitter.

Depending on the distance at which the target is located and other parameters (such as the pulse

duration), the precision of the range can be as good as few centimeters.

To be able to measure the time difference, there has to be included a tool that will allow the receiver to

differentiate the wanted signal from clutter and/or other undesired detections. This timing label can be

thought in several ways: from a determined length pulse, a phase modulation or a frequency

modulation. The main parameter for a good ranging precision will be the bandwidth, as it will be

explained in Chapter 2.

Fig. 3: Radar basic operation principle.

Radar Antenna

Echo from Target

Transmitted Signal


6

Velocity: Radars can also be used to obtain the information concerning the speed of a moving target.

This information can be gathered from the distance variation over certain duration of time. Another

used method is by means of the changes in the measurement of the Doppler frequency. The Doppler

frequency accuracy will vary depending on the time of observation; meaning that an accurate

frequency Doppler measurement will require long integration time. This concept will be explained in

more detail in Chapter 2.

Angle of arrival: Another relevant parameter that will be used to improve the characteristics of the

presented radar system is the angle. Using the angle information embedded in the reflected waves will

allow us to determine the direction to a target by doing a sweep along the sight of the antenna. Further

explanation will be provided in the Chapter 2 of the present document.

Even though there is not an official taxonomy of the existing radar technologies, this paragraph will

present the main groups and their characteristics:

Monostatic/Bistatic: Firstly, there can be distinguished different radar architectures, the monostatic

and bistatic. The difference between them can be found in the design of the transmitter and receiver

antennas sides of the system. While the bistatic radars are characterized by a design where the

transmitter and receiver antennas are separated spatially (Fig. 4 [9]), the monostatic architecture is

based on the transmission and reception of the signal in the same antenna, without any spatial

separation. This is usually performed with a circulator, as shown in Fig. 5 [9].

The radar systems can also be classified according to the way they radiate the electromagnetic waves,

basically in the pulse radars or continuous wave radars (CW).

Pulse radar: This type of radar radiates multiple and repetitive short and high energy pulses

modulated in order to be able to also obtain the speed information out of the Doppler shifts. The

The radars can also be classified according to the way they radiate electromagnetic waves, in the pulse

radars and continuous wave radars (CW).

Fig. 4: Scheme of a bistatic radar design. Fig. 5: Scheme of a monostatic radar design.


7

Pulse radar: This type of radar radiates multiple and repetitive short and high energy pulses

modulated in order to be able to also obtain the speed information out of the Doppler shifts. The

method is method is characterized by the shortness of its transmission pulses, which are usually in the

order of the microseconds. After a pulse has been transmitted there is a long period of lack of

transmission (T >> pulse length). This period is typically named ‘receiving time’, since the length of

this silent time interval will be used to interpret the time between the transmitted pulse and reflected

one, thus, giving the range unambiguously. In this type of radar is important to consider the control of

the timing since the correct calculation of the range depends on the time accuracy calculation.

The pulse is going to be targeting one particular direction, defined by the directivity of the antenna, at

each given moment. The distance from the target can be easily measured in an oscilloscope, evaluating

the time between the two observed pulses in the screen (as far as there have not been any other

transmitted pulses in the meantime). The traveling of the pulse is a two way trip, thus, the time

measured must be divided by two in order to obtain the one way time interval that the electromagnetic

wave needed to reach the object. Leading to be the following simple equation [33]:

𝑅 =

𝑐0∙𝑡

2 (1)

Derived from,

𝑣 =𝑠

𝑡 and 𝑡 =

2∙𝑅

𝑐0 (2)

Where

R = distance

𝐶0 = vacuum speed of light

v = the speed

t = time interval

Therefore, once obtained the half round trip time t/2, simply by a multiplication by the speed of light

the distance is easily computable. Fig. 6 shows the block diagram of a pulsed radar system, in this

case with a monostatic architecture.


8

A wave signal is generated with the local oscillator (LO) with certain constant frequency 𝑓0 and,

during transmission, radiated from the antenna, then, the received RF signal is processed at an

intermediate frequency IF by mixing it with the LO frequency. The name “pulsed” is given because of

the modulation induced by the switch in series with the antenna.

The radiated signal can be defined according to the following waveform formula [37]:

𝑠(𝑡) = 𝐴(𝑡) ∙ sin [2𝜋𝑓(𝑡) ∙ 𝜑(𝑡)] (3)

Where A(t) is the square wave signal shape varying according to the time, will be logical one in the

short time when there is a transmission and zero otherwise (in echoes’ waiting mode) and

𝑠𝑖𝑛 [2𝜋𝑓(𝑡) ∙ 𝜑(𝑡)] is the carrier sine wave generated by the local oscillator. The pulsed radars were

basically designed having in mind long distances applications.

Continuous Wave Radars (CW): This radar technology uses a continuous sinus wave at high

frequency. It also uses the Doppler frequency shift in order to detect non-standing targets or their

relative speed. The spectrum of standing targets would look centered in 𝑓0, if the targets are moving

this will be shifted by 𝑓𝑑 (Doppler frequency). This characteristic makes the CW radars highly

accurate when estimating the speed. In order to prevent the transmission disruption of the continuous

radiation, two separate antennas need to be used. Thus, all the CW radars are bistatic.

There can be distinguished two main types of CW radar systems depending on the modulation they

use; Frequency Modulated CW radars (FMCW) and Phase Modulated CW (PMCW) radars. A deeper

comparison between FMCW and PMCW radars is given in Chapter 2.

Fig. 6: Block diagram of a monostatic architecture pulsed radar system.


9

- FMCW Radars: This type of modulated radar uses frequency modulation in the

source. A VCO (Voltage Controlled Oscillator) generates the signal with up and down chirps with a

period of Tp and 50% duty cycle. The signal is continuously radiated, and a small part of it, through

the couples, is mixed with the echoes received, as shown in Fig. 7.

- PMCW radars: This type is also called phase-coded radar[10]. In contradiction with

the pulsed radar systems (energy radiated in a short time interval), in this type of modulated radar a

method of pulse compression can be used to generate a spread spectrum signal which will span the

energy over a long period of time. For this purpose the phase modulation can be achieved with

pseudo-random binary sequences, M-sequences or any other codes that will reduce the peak power of

the system. As the radar system type presented in the document is going to be this type, a more

detailed explanation of this method is given in Chapter 2.

Radars can be operated at a wide range of frequencies. Varying from frequencies as low as few MHz

to as high as some hundred GHz, inside, what is called, the millimeter-wave region. A frequency range

where radar systems can be found working covers from the 5 MHz up to the 95 GHz bands, as can be

observed in Fig. 8. The used frequencies in radar vary in a wide frequency range. Thus, it is expected

that the technologies associated are different and their use is linked to very different applications with

very different capabilities and characteristics. Depending on the application, one frequency of

operation is preferred to another. In Fig. 9(modified from [11]), an attenuation graph depending on the

operating frequency can be found with a mark in the carrier frequency of the radar under study.

Fig. 7: Block diagram of the architecture of a FMCW radar.


10

As a first thought; the high frequency bands show an obvious advantage in applications that need

small antennas; due to the small wavelength a more efficient antenna is possible. The short

wavelengths permit high gain antennas with a convenient small size. But it is also easier to achieve

better accuracy in range and placement of the target due to the wider band used in such frequency’s

bands. By the other hand, low frequencies work better for applications with long distances goals since

is more feasible to get high power antennas and the electromagnetic waves are less attenuated while

propagating in the air. Also, high frequency radars will be more affected by weather conditions (water

absorption peak) than a low frequency band radar, in long ranges. Following, an overview of the radar

operating bands and applications:

- HF / VHF (< 300 MHz) – A/B bands: nowadays the technologies that use these frequency bands

are called Over The Horizon radars (OTH). The main positive characteristics of this band are; the

immunity to weather conditions, the long range capability out to 3500 km (since it is easier to

obtain high power transmitters) and the low attenuation they suffer. However, their drawbacks are

their low efficiency. Mainly useful for applications over the oceans. The low part of this band

takes advantage on the ionosphere reflections to reach longer distances.

- UHF (300 MHz to 1 GHz) – C band: characterized by low or medium accuracy and resolution,

but still very seldom weather conditions affection. It is a good frequency band to early detection

of aircrafts and Airborne Moving Target Indication (AMTI). It is also good for tracking missiles

and satellites. At the upper part of this frequency band there can be found the so-called ‘wind

profiler radars’ that are capable of measuring the direction and velocity of the wind. Another

application of this frequency band is the Ground Penetrating Radars (GPR), which usually

extends further than the UHF band to get better accuracy. These ranges are appropriate to locate

big objects under the ground.

- L band (1 – 2 GHz): It is commonly used for radars operating in ranges up to 400 km for air

surveillance applications. The weather phenomenon starts to be slightly more noticeable in this

range, and the more the frequency increases the more the rain effect will be significant. This band

is also used for missile surveillance and low orbit satellite tracking.

- S band (2 – 4 GHz): used for short range surveillance, up to 120 km. This band is where regional

airspace surveillance radars for aviation are located. It has medium accuracy and it can be said

that is a band of compromises, relatively long range coverage with relative accuracy. Another

radar application that uses this band is the surveillance aircraft AWACS (Airborne Warning and

Control System).

- C band (4 – 8 GHz): Used for short range surveillance and long range tracking with good

accuracy. It takes properties from the C and X bands and is highly sensitive to bad weather. Some

examples of applications working in this band are: the weather radars to locate rains and,

surveillance of military battlefield.


11

- X band (8 – 12 GHz): Meant to short range surveillance in good weather conditions. It is well

known to be used for military applications, mainly for airborne radars, and it is also common for

police speed meters. They are usually very convenient due to the size of the antennas so they are

very popular for applications where weight and mobility are the main factors to take into account.

- Ku / Ka bands (12 – 40 GHz): Mainly for short-range tracking. Since the higher the frequency the

more is the atmosphere absorption, this band is good for applications where weather conditions

are not taken into account. This band is attractive when it comes to applications that require very

little installation space and don’t need long ranges. An application working in this range is the

Surface Radar in the major airports.

- V / W / mm-Wave bands (40 – 100+ GHz): This range is clearly limited to short or very short

ranges, depending on the weather conditions, and mainly work besides smart antennas which are

able to point their very thin beams. In this wide band there is particular interest around the 96

GHz zone, since there is a relative minimum of attenuation. The effects and technology of the

mm-wave technology are different than those of the microwave radar technology, and both are

more limiting in the mm-wave radar technology. The use of this band has lately become more

popular because of many advantages. The main one, is the availability of a wide band of

frequencies, there is a lot of unused space, so that the radar systems to be developed in this region

can have a wide bandwidth which will give higher range resolution and narrower beams with

smaller antennas. It is also very well considered for its robustness, for example, for military

applications where countermeasures are expected. Nowadays there are big investments in mm-

wave radar for automotive applications due to its small size and very good values of accuracy and

resolution. Usually these automotive systems operate in the range from 73 to 81 GHz. Further

explanations and development on this precise application, technology and frequency band will be

provided throughout the present document. The working frequency of the radar system here

presented is going to be in this band, with working frequencies located in the mm-wave band.

L S C X Ku K Ka U V / mmWave

Microwave Bands mmWave Bands

Rad

ar

Fig. 8: Spectrum with the location of the traditional microwave bands and the mmWave bands.


12

1.3 Proposed Radar System

The radar system described in this thesis has its main application goal in the automotive industry.

Concretely, the specifications were established in order to focus in the so called short range radar

(SRR) systems [12], which reaches distances around 30 meters in the direct proximity of the vehicle,

as can be seen in Fig. 10.

There have been developments of automotive radar systems in the band of the 24 GHz with

technology built on SiGe (Silicon Germaium) blocks [13], [14]. Other frequencies have also been

explored (under 10 GHz or over 100 GHz) but their role is insignificant. Being that the market pursues

for higher integration achievements with lower power consumption, which cannot be achieved with

these technologies and frequency bands. The use of the mmWave band is more challenging and

complex from the technical point of view, but it provides higher performance possibilities. A key

characteristic for an easy integration is the sensor size, which is determined by the antenna aperture.

Fig. 9: Attenuation in the atmosphere of electromagnetic waves according to their working frequency.


13

At high frequency the antenna size is allowed to be small keeping a good angular resolution. In order

to achieve the same performance in the 24 GHz band, a three times larger aperture would be required

[12]. Furthermore, the mmWave band is not affected by tough atmospheric phenomena as rain, snow,

sand storms, lightning, etc. Nevertheless, their small form factor means very low transmitted energy

and narrow beams, which provide interference immunity. The 79 GHz band [77 – 81 GHz] has arisen

as the standard initiative to locate the worldwide vehicular radar frequencies and it will be worldwide

used for SRR [15].

The first disclosed use of a radar system based on millimeter-wave technology for automotive

purposes dates back in the 1970s [12]. Nonetheless, their use did not go further than the building of

prototypes. The main reasons for its market failure were the large size and high production costs that

the systems represented by that time. It was not until 1998 when the first mmWave was ready for use.

By 2003 the majority of car makers had a radar option based on this technology [16].

Nowadays the mmWave band radar market production is experiencing a rapid growth in terms of

volume, with a consequent drop of the prizes, and allowing, for example, driver assistance systems

available for middle class vehicles [17].

SRR 77-81 GHz

Range < 30 mResolution < 10 cm

LRR 76-77 GHz

Range < 200 mResolution > 1 m

Fig. 10: Radar short and long range types with the mmWave frequencies and capabilities.


14

Since the market and development of these systems is still undergoing and the technical background

behind its development is complex, there is an important assortment of different market solutions.

Despite these differences, all the available sensors in the market count on the FMCW modulation

technique [18]; for example the LRR3 sensor of Bosch [19], the ARS 300 by Conti [20] or the Denso

sensor [21]. However, the implementation of the FMCW technique faces challenges due basically to

the big amount of energy that the synthesizer needs and the limited performance of the frequency

slope. The target resolution is important and in FMCW this resolution is linked to the sweep

bandwidth of the transmitting signal which requires a VCO with a big tuning range. Besides the

difficulties to realize the system for big bandwidths, VCO’s linearity also limits the accuracy of the

measurements.

One alternative to FMCW is the PMCW technique using pseudo-noise signals; it is easier to realize

and its accuracy does not depend on the linearity of the transmitter signal. The resolution depends on

the bandwidth of the modulation which is given by the clock frequency of the code generator. There

have been some published studies, in [22], [23], [24], and implementations with SiGe technology [25]

and [13].

In the last years, the functions implemented in cars with radar technology solutions have been mainly

comfort services, such as: warning systems for a near collision, assistance in lane changes, blind spots

monitors, park assistance, etc. There also exist some advances in active safety, however in the

immediate future; the 79 GHz frequency band will add high-resolution radar performance, therefore

allowing the increase of the safety for car occupants and pedestrians, also improving the comfort and

services onboard for the driver and companions.

In order to be able to develop and apply these safety systems with assurance, there are improvements

that need to be implemented. The systems need to be able to differentiate better the objects in the road

in front and nearby the car. The development and exploitation of the 79 GHz band brings the

opportunity of using systems with a much broader bandwidth comparing to the existing solutions, thus

increasing the capability of the radar systems. It will permit the implementation of proactive safety

characteristics. Using the technologies associated will allow a better resolution and accuracy to

analyze the objects on the road. The wide bandwidth together with the investigation in signal

processing will allow functionalities such as autonomous emergency braking against collisions or

pedestrians.


15

In the medium term, the 79 GHz technology will be the cornerstone of a new generation of fully

autonomous vehicles. Other than vehicles, the high resolution radar systems are nowadays being

implemented in industrial control environments, medical sign monitoring, security systems and

building automation. Thanks to the tiny size of the Radar implementation in Chip, consumer

electronics is other scope in which the new generation of radar systems will experience growth; for

example in the sports’ scope for monitoring the speed, position and distance or in the man to machine

interaction systems.

It is due to this increasing demand for higher integration and lower power consumption that CMOS

(Complementary Metal Oxide) emerge as the natural successor to the SiGe technology that nowadays

prevails in the automotive radar market. The desired lower power used in these systems leads to the

need of exploiting a digital intensive architecture. The technologies that will make possible the

achievement of these challenging characteristics are going to be implemented in the radar system

proposed, a 79 GHz phase-modulated 4 GHz bandwidth continuous wave radar in 28 nm CMOS.

When it comes to analyze the behavior of the detection part of the system, the basic parameters to

consider are the probability of false alarm (𝑃𝑓𝑎) and the probability of detection (𝑃𝑑). The possible

final outcome (detection or not detection) will depend on to the interference statistics and the signal to

interference ratio (SNR). For radar tracking the main quality parameters to take into account are: the

range accuracy, velocity and angle. The aim of radar signal processing techniques and methods is to

improve these quality parameters, like for example, by applying pulse integration or MIMO (Multi

Input Multi Output) processing techniques.

1.4 Outline of the Thesis

The present work will focus on the development, implementation and simulation analysis of the signal

processing methods and techniques that will allow the proposed radar system to get high resolution

detections and high signal processing gain. The high resolution performance is implemented in range,

speed and angle. The radar system will use low output power antennas; with the achievement of high

processing gain, the system will improve the SNR of the detected targets and will allow the detection

of small targets in the limits of the short range detections.

In the present thesis there are covered a lot of aspects of the radar system: Theoretical background

with fundamental radar parts and parameters are explained in Chapter 2 alongside fundamentals of

the radar signal processing used in the digital front-end of the receiver side. The theory covered will


16

include all the necessary concepts that are used in the implementation of the signal processing

methods. The CFAR will be developed and the algorithms used in the implementation described. The

MIMO part will be explained with the description of the methods implemented and the main MIMO

concepts necessary to understand its functioning. The beamforming concept and techniques will be

introduced in the end of the chapter. Therefore, the theoretical background in order to understand the

radar system presented in Chapter 3 will be fully developed besides aspects of related technologies,

such as PMCW versus FMCW, for a better understanding of the methods and technologies chosen in

the development of the radar system. Moreover a series of important tools necessary for the complete

understanding of the system will be presented and explained as well.

Chapter 3 will focus on the implementation of the methods and techniques explained in Chapter 2.

Firstly, the description of the PMCW radar system under study and its main design parameters. Then,

it is going to be provided a description of the digital front-end and how it works. The system

description will be closed with the explanation of the simulation chain implemented in Matlab to

evaluate the system. The second part describes the process of implementation of the methods

explained in Chapter 2 and the development data structures used in the simulation chain. Firstly; the

MIMO implementation in Matlab is explained besides how the information is managed, then the

CFAR implementation algorithms and to finish the Angle of Arrival techniques. In the last part of the

Chapter 3 a resume of the implemented system parts will be showed with the different methods and

technologies developed in the first part of the Chapter 3 and backed by the theory of the Chapter 2.

In Chapter 4 a series of simulations are performed and their results are showed and discussed. The

methods and techniques are discussed and a resume of the strong and weak parts of them will be

reported. These results will be based on the use of different CFAR parameters and methods applied to

different scenarios, the MIMO processing effects and the different Direction of Arrival techniques.

The simulations 1 and 2 are focused in the CFAR behavior. The simulations 3, 4 and 5 are focused in

the setting of the MIMO parameters and its dependence with the results in different scenarios. The

simulations 7 and 8 are set to show the results of the application of the angle of arrival techniques.

There will also be presented several simulated scenarios for given different design parameters, the

simulations 9 and 10. The simulations will be varying the number of targets, the speed of the targets,

their position, RCS, along with other parameters in order to understand how the changes affect the

system performance and behavior.

In Chapter 5 a resume of the work developed throughout the thesis period will be exposed. The

important results and conclusions will be presented, ending with suggestions on the possible

continuation and future improvements of the developed system.


17

2 Theory

This chapter focuses in the technical background behind radar systems in general and the mmWave

radar system under study in particular. Firstly a section where the general parts of a radar system and

the main technologies available are explained. Following, the signal processing fundamentals used to

process the information of the radar systems is introduced. Later on, the specific theory behind the

techniques used in the mmWave radar system are introduced; the CFAR method and its different

algorithm alternatives, the MIMO processing besides the different proposed implementations and the

beamforming technique, its justification, parameters and different types of beamforming technique

groups depending on the information they use. The aim of the chapter is to pave the way to understand

the justification of the technologies implemented in the radar system that will be introduced in the

Chapter 3 and the simulation results achieved in the Chapter 4.

2.1 Radar Technology

In this first part of the Chapter 1, the main functionalities and technologies of radar are going to be

explained thoroughly. So that, the reader can has an understanding of the structure and functioning of

any radar and which parameters and concepts influence more in its performance. Some specific

techniques used in the mmWave radar are also developed; pulse compression, PMCW and pseudo-

noise sequences.

2.1.1 Important System Parts

Fig. 11 shows the block diagram of the typical monostatic radar, although this configuration is not

unique and the radar system under study will need to be bistactic, is a good example to explain the

main parts of a radar system. The transmitter modulates the waveform depending on the wanted radio

frequency and increases its power to the required power level. The signal is conducted through the

circuit to the antenna through a duplexer. The reflected signals are managed by this same device, the

duplexer, up to the receiver of the system. Commonly the receiver is a super heterodyne with a Low

Noise Amplifier (LNA) as a first stage. After this there can be found several stages to achieve an

intermediate manageable frequency, each of which are managed by a local oscillator and mixer.

Once the signal is ready to be treated by the signal processor, which will perform several operations to

improve the recovered signal and take as many information as possible from it. The processed

information is then sent to a display or another processor, as required.


18

Transmitter - Waveform generator: These two parts are of main importance in the characteristics of

the radar system. The transmitter will generate a convenient waveform for the concrete job that the

radar system is designed, and, as previously introduced in Chapter 1, this can be either a waveform

with varying frequency or varying phase, among others. In the case of study of this thesis, the

waveform is going to be phase modulated. Depending on the frequency of operation of the radar, the

power of the transmitter will change substantially. The higher the frequency, the smaller the power

that the antenna will be able to manage. This power can vary from the few milliwatts up to megawatts.

Given that the central frequency of operation of the radar system here presented is situated in the range

of the mm-wave band, the transmitter power is expected to be around the milliwatts range. The

duplexer is very important to avoid any burn outs from the strong transmitting signal on the sensitive

receivers, in the case of monostatic radars.

The radar under consideration here will be bistatic, so that, duplexers will not be needed. However due

to the fact that the chip will be so small, the proximity of the receiver and transmitter antennas will

cause energy leakages that will need to be tackled either via signal processing or analogically.

The antenna will be the apparatus that will allow a controlled radiation. It will also allow gathering the

energy from the echoes coming back to the system with an identical process as during transmission.

In radar systems the antennas are practically always directive, allowing to produce a directive beam

with narrow width allowing to focus the power in a certain preferential direction and also permits to

determine the angle of arrival of the echo, thus, localizing the target.

Fig. 11: Basic block diagram of a general monostatic radar system [37].


19

Typical beam widths vary from as narrow widths as less than 1 degree to tenths of degrees. Depending

on the application considered, the antennas can intentionally have very narrow or broad beams in

azimuth or/and elevation. In practice, the bigger the antenna is, the better will be the overall

performance (for both power and atmospheric attenuation advantages). But, in the presented

applications their size cannot be big due to the operating frequency, situated in the 79 GHz range. As

already shown in Chapter 1, and reported again in Fig. 9, the attenuation experienced by a radar

system operating at 79 GHz is around 0.4 dB/Km.

Receiver: The receiver amplifies the weak reflected signal coming into the receiver antenna up to the

necessary level to be able to detect its existence. It also demodulates the signal and will feed it to the

indicator.

A crucial specification of the receivers is the noise level since this is the main limitation on the

performance of a radar to make a decision on whether there is going to be a detection or not. Therefore

the noise level in the receivers must be kept as low as possible.

Another important specification of the receiver is the dynamic range. The dynamic range is usually

specified as the difference between the maximum signal that the receiver is capable to manage and the

minimum that is able to detect. In environments where there is a big number of reflections (caused by

clutter), and constructive interference among them could lead to high amplitude signals at the receiver,

the required dynamic range is wider. If the receiver has a large enough dynamic range, closely located

targets with big RCS differences, are more likely to be detected.

Signal processor: In the signal processor the signal is already at intermediate frequency. This block is

responsible in differentiating a target from clutter depending on the Doppler information and power

levels, and then detecting the correct location and speed of the wanted target. In general, the signal

processing part of radars include an I&Q (In phase and Quadrature, amplitude and phase information)

detector, a Moving Target Indicator and a Constant False Alarm Rate Detection (CFAR), but also

further advance processing, to improve the gain or amount of data acquired, can be introduced in this

block, as for example; MIMO techniques or/and, beamforming. The detecting decision is made in the

output, being a target detected when the power exceeds certain threshold. If the level of detection is set

to be very low, a high number of false alarms is expected, if it is too high, many targets may go

missing. The norm which will establish the threshold value can vary with the application of one

algorithm or another, which choice will depend on the scope of the concrete application. This will be

further developed later in this chapter.

Another part of the receiver, connected to the signal processor, is the data processor, where the

previously processed information will be shown on display, or might be used for further processing to

extract more information about the target. The signal processing block includes also matched filters,

explained later.


20

2.1.2 Radar Main Parameters and Concepts

There are some parameters to be chosen on a radar system that directly affect the performance of the

system. Depending on the application and on the actual circumstances the variation of these

parameters will allow the system to give proper outcomes.

-Parameters

Bandwidth: It is one of the most important parameters to take into account when designing a radar

system. This is due to the fact that the bandwidth is proportional to the resolution performance of the

radar. The larger the bandwidth, the narrower the spectrum peak and the higher performance

resolution can be achieve. There are two different bandwidth types that can be defined, the signal

bandwidth (regulated by the width of the pulse of the signal or by its modulation) and the radar

bandwidth. If the system requires a big resolution in range to differentiate among targets, the

bandwidth needs to be large. This is because the bandwidth is directly related to the range resolution

(Eq. (6)). Bandwidth is defined with the Rayleigh criterion and is expressed as Eq. (4) [48].

𝐵 =

1

𝜏

(4)

Range resolution: It is the ability of a radar system to discriminate between different targets. It is

usually a high desired property in radar, but it also brings some constraints that will limit other aspects

of the radar performance, as it will be explained in Chapter 3. Fig. 12 [26], shows and example of

range resolution calculation.

Fig. 12: Two targets closely placed being radiated by a radar.


21

Knowing Eq. (1) and given the case when there are two targets, the time difference from echo to echo

is going to be Eq. (5):

2(R + ∆R)

c−2R

c=2∆R

c (5)

Setting the time difference as 𝜏 and simplifying the space difference obtaining Eq. (6):

∆R =cτ

2 (6)

The radar reflecting signal is processed with pieces of range extent, usually called ‘range bins’ or

‘range gates’.

The time expression of a pulse of rectangular shape with duration 𝜏 is described in Eq. (7):

Which is a ‘Sinc’ function with centre in 𝜔0, as shown in Fig. 13 [48],

With a bandwidth at -3 dB which equals to 𝐵 = 1/𝜏

Therefore the space difference between distinguishable targets can be rewritten as Eq. (9):

𝑓(𝑡) = 𝐴𝑐𝑜𝑠𝜔0𝑡 , 𝜏

2≤ 𝑡 ≤

𝑡

2 (7)

𝐹(𝜔) =

𝜏

2(sin(𝜔 + 𝑤0)𝜏/2

(𝜔 + 𝑤0)𝜏/2) (8)

Fig. 13: Spectrum of a pulse of duration τ, with a sinc shape [26].


22

So it can be observed that the larger the bandwidth of the transmitted wave, the smaller the range

resolution will be. Note that the term ‘resolution’ should not be confused with ‘accuracy’. Accuracy is

the degree of correspondence between the calculated position speed and the actual speed or real

position of the target. It is normally studied as a statistical measure in the radio navigation scope.

Pulse Repetition Frequency (PRF): Pulses use to be transmitted at constant periods. The difference of

time between two consecutive pulses is defined as Pulse Repetition Interval (Fig. 14), and the

reciprocal is the PRF (Number of pulses transmitted per second).

Maximum Unambiguous Range (𝑅𝑚𝑎𝑥): It is closely related to the PRF since any echo being detected

after the transmission of the next pulse (not related with the echo incoming), will cause unambiguity,

being the system unable to determine the real range of the detected echo. All the returning echoes that

take longer than the PRI will appear in incorrect locations (wrong range gate). So that, the maximum

range distance at which the system can detect is not just going to be given by the radar equation

(explained later), but also by the time duration that the system allows between sending one signal and

the next one. An example of an unambiguous measurement can be observed in Fig. 15.

Figure a) shows the transmitter side of a radar system where there are three pulses sent with a PRI

separation of Tp. Figure b) shows the receiver side of the system, there are represented three echoes.

The dotter shapes represent the transmitted pulses; the colour shapes represent the unambiguous

echoes and the stripped shape the ambiguous echo. Two of them have taken less time than the PRI

time to be received, so that the delay can be computed correctly and a good range result is expected.

The last one has taken longer than the PRI to be detected, so that it has been received after the

transmission of the next pulse. It can be observed that the distance to the target is going to be wrongly

∆𝑅 =𝑐

2𝐵 (9)

Fig. 14: Several transmitted pulses separated in time by the PRI.


23

calculated as ∆𝑡3 instead of the real range which turns to be 𝑇𝑝 + ∆𝑡3. It can be concluded that the

maximum unambiguous range is:

Angular Resolution (𝑆𝑎): The angular resolution of a radar system can be defined as the smallest angle

separation at which two targets can be detected when they are placed at the same distance. The

parameter is given by the width of the antenna beam at half power (-3 dB). Consequently, two equally

targets located at the same distance can be differentiated if their mutual separation is bigger than the

width of the antenna in the point of half power. Therefore; the smaller the beamwidth (higher

directivity), the higher the angular resolution. The angular resolution can be computed by [33]:

Where 𝜃 = Antenna beam width [deg].

𝑅 = Distance from the system to targets[m].

Concepts:

Radar Cross Section (RCS): It can be defined as the capability of an object to reflect energy, which

has the dimensions of area (𝑚2). THE RCS is defined as Eq. (12) [33]:

𝑅𝑚𝑎𝑥 =

𝑐 ∙ 𝑃𝑅𝐼

2 (10)

𝑆𝑎 = 2𝑅 ∙ sin

𝜃

2 (11)

Fig. 15: Two unambiguous and one ambiguous mesuarement [9]. a)Transmitter: three pulses with a pulse width

𝜏𝑝 and PRI=Tp.b) Receiver: Echoes caused by the first pulse.


24

Where 4𝜋𝑟2 takes into account that the power distributes in the shape of a sphere, 𝜎 is the RCS, r is

the distance, 𝑆𝑟 is the reflected power density [W/𝑚2] and 𝑆𝑟 is the power density that is intercepted

by the object [W/𝑚2]. Note that this number does not necessarily have to be the same as the cross

section area of the object, since not all the incident energy will be reflected in the direction of the

radar. In other words, is the measurement of the difference between the reflected power density in the

same direction of the radar system and the power density which is actually taken by the object.

Clutter: The radar reflected signals are produced when the radar is radiating in the direction of any

surface. Hence, when the radar receiver is detecting the echo signals it will also receive echoes from

many different sources. The unwanted signals in radar are defined as clutter, and it includes the

reflections from all kind of objects or natural phenomena, i.e. birds, rain, houses, trees, etc.

2.1.3 Radar Equation

The radar equation is not just useful for the determination of the capable range of detection depending

on the system features but also to guide the radar system design.

The development of the radar equation starts with the supposition of an isotopic antenna, which power

density at range R will be Eq. (13). However, given that any radar practical antenna will be isotropic,

the power density in the maximum gain direction will be have a certain gain G. This power density

will intercept a target which scattering characteristics are given by its Radar Cross Section (RCS),

identified as 𝜎 in Eq. (14), which gives the power intercepted by the object [31].

Where 𝑃𝑡 = Transmission power [W]

𝑃𝑑 = Detected power [W]

G = Gain [dB]

𝜎 = RCS [𝑚2]

R = Distance to target [Km]

𝜎 =

4𝜋𝑟2𝑆𝑟𝑆𝑡

(12)

𝑃𝑑 = 𝑃𝑡

1

4𝜋𝑅2 (13)

𝑃𝑑 =

𝑃𝑡𝐺

4𝜋𝑅2∙ 𝜎 (14)


25

The detected power 𝑃𝑑 is obtained back in the radar system, so that the power detected by the radar

antenna is given by Eq. (15) [31].

Where 𝜆 = Wavelength [m].

𝐴𝑒 = Effective area [𝑚2].

The receiver noise power is 𝑃𝑛, resulting from the superimposition of the noise received from the

surroundings and the one cause by the receiver electronics itself. The total noise power 𝑃𝑛, and the

system noise figure F, are found as [31]:

Where, 𝑇𝑠 = Source noise temperature [K]

𝑇0 = Noise temperature of reference 290[K]

B = Receiver Bandwidth [Hz]

K = Boltzmann’s constant (1.38x10−23 [W/K/Hz])

Using the noise figure definition and adding several system losses (L) comes out to be Eq. (18) or Eq.

(19) when cleared for the maximum range given a target:

The previous equation is a general form of the radar equation in which there have been made a series

of assumptions for our case of study. For example, that the emitter and receiver antennas are equal or

that the bandwidth is matched to the pulse length as B ≈ 1/𝜏. But each concrete radar application has

to adapt the radar equation to the specific circumstances of the application.

𝐺 =4𝜋𝐴𝑒

𝜆2 𝑃𝑟 =

𝑃𝑡𝐺2𝜎𝜆2

(4𝜋)3𝑅4 (15)

𝑃𝑛 = 𝑘𝑇0𝐵 + 𝑘𝑇𝑠𝐵 (16)

𝐹 = 1 +

𝑇𝑠𝑇0

(17)

𝑃𝑟𝑃𝑛=


(4𝜋)3𝑅4𝑘𝑇0𝐵𝐹𝐿 (18)

𝑅𝑚𝑎𝑥 = [


(4𝜋)3𝑘𝑇0𝐵𝐹𝐿(𝑆/𝑁)]

1/4

(19)


26

2.1.4 PMCW vs FMCW Radar

The radar system under study is going to be transmitting a Continuous Wave (CW). The concepts and

system structure are going to be very similar to the ones used for pulsed radar and defined in 2.1.3, so

that most of the theory of pulsed radars applies with the exception of some variations that will be

presented in the development of the document. What in traditional radars were ‘pulses’ now they will

be sequence instead, as will be exposed in the next subchapter.

Working for automotive applications, as for other applications that ask for a very good range

resolution, require radars with a large bandwidth. The available bandwidth is going to depend on the

pulse duration (as seen in Chapter 1), and to get very short pulses is in general difficult. The smaller

the pulse (so the better the range resolution), the higher the peak instantaneous power will have to be.

There are arcing effects occurring at high peak powers, and this effect is strengthening at high

frequencies. The arcing effect causes that the rectangular shape of the pulses becomes not so

rectangular and then causing a less sharp shapes after the FFT processing and thus, affecting the

detecting performance.

In traditional pulsed radar systems the energy is radiated in a very short period of time. However,

using pulse compression enables to substitute a pulse waveform which would require large amounts of

energy in very short time by spreading spectrum signals which will distribute the energy along a large

period of time. So, comparing to pulsed radars, CW radars will have higher energy with a lower peak

power and no blind range for detection.

Continuous Wave radars send a continuously generated high frequency signal and meanwhile, there is

a continuous flow of income signal processed from the reflections coming back to the receiver. The

main issues to take into account are: the big difference between the incoming and outgoing signal

power levels (which can cause leakage from the transmitter to the receiver) and the processing of the

continuous flow of incoming signals to be able to solve the detections. For the first issue a solution is

to use a space separation between antennas, but since one of the goals of the development is to reduce

the size of the system, this solution will not be considered. There can be implemented digital solutions

or other analogic circuits to mitigate its effects, which are currently being under development [27].

Unmodulated CW radar systems radiate a stable frequency with fixed amplitude signal. These radars

determine the speed of moving targets by means of the frequency shift caused by the Doppler Effect,

but cannot determine the range of the target due to the lack of modulation in the source. The

importance of modulation lies in the possibility of using time references in the transmitted/received

signals to be able to determine extra information.


27

Frequency Modulated Continuous Wave Radar (FMCW): These systems use modulation in the origin

varying the frequency so can use measurement of the propagation delay to find out the distance from

target. FMCW radars need a transmitter capable to sweep certain range of frequencies in a short period

of time, so that it can measure the range and velocity of the targets. Usually a frequency synthesizer is

used to implement it. A basic architecture for FMCW radar is showed in Fig. 16. A Voltage Controlled

Oscillator (VCO) produces a chirp and then there is a frequency change of bandwidth B in a Tp period.

Usually FMCW uses a linear-triangular frequency chirp to be modulated as the shown in Fig. 17. Eq.

(20) and (21) give the expression for a FM modulation using increasing and decreasing chirps [33].

With,

Where B = Bandwidth

Tp = Chirp duration

𝑓0 = Working frequency

𝑓𝑡 = Frequency modulation

Since the signal is a RF sinusoid the modulation scheme can be described as follows [33]:

𝑓𝑡(𝑡) = 𝑓0 + 𝑘𝑡 (20)

𝑘 =

2𝐵

𝑇𝑝 (21)

𝑠𝑡 = 𝐴𝑡 cos(2𝜋𝑓𝑡(𝑡)𝑡) = 𝐴𝑡cos (2𝜋𝑓0t + 2𝜋𝑘𝑡2) (22)

Fig. 16: A basic FMCW radar block diagram.


28

After that, the reflected signal coming from the target after a delay will enter the receiver and mix with

the part of the transmitter signal that was coupled to the mixer as a reference. Resulting in the

following equation, which includes the propagation delay and the Doppler shift.

Where ∆𝑡 = Propagation delay.

𝑓𝑑 = Doppler frequency shift.

In Fig. 17 there can be distinguished a variation of the frequency with time for both the radiated and

received signals. It can be observed that there is a frequency shift 𝑓𝑑. In Fig. 18 there can also be seen

the difference between the transmitted and received signals in absolute values. Taking into account the

two frequencies, range R and speed 𝑣𝑟 can be solved using the following equations [9]:

The implementation of the FMCW radar system is quite challenging since many digital building

blocks are required and there is high power consumption due to the use of the frequency synthesizer.

This is a limiting factor since, as previously stated, high range resolution radar systems require large

bandwidth. It is clear that the more bandwidth is needed, the more energy will the synthesizer need

and therefore more problematic the implementation will be. Moreover, the FMCW radars are

𝑠𝑟(𝑡 − ∆𝑡) = 𝐴𝑟 cos(2𝜋𝑓0t + 𝑓𝑑) (𝑡 − ∆𝑡) + 2𝜋𝑘(𝑡 − ∆𝑡)2) (23)

𝑅 =

𝑐𝑇𝑝

2𝐵

𝑓1 + 𝑓22

(24)

𝑣𝑟 =

𝑐

2𝑓𝑐

𝑓1 − 𝑓22

(25)

Fig. 17: Representation of the FMCW transmitted and reflected signals [9].


29

bandwidth limited due to the loss of linearity of the slope of the FM PLL when exceeding 1 GHz [28],

therefore not allowing high resolution systems.

So far, radar for automotive applications developments have been characterize for the implementation

of FMCW technology. These technologies are already available in the market and have sufficient

performance for certain applications; however the medium – term performance require the

development of new methods that improve the previously stated issues of FMCW.

Phase Modulated Continuous Wave Radar (PMCW): Binary phase-modulated continuous wave radar

is the modulation that is used in the radar system under study. It is also known in literature as phase-

coded radar, and it is a spread spectrum radar which binary symbols are set at 0 and 180 degree phase

shifts of a continuous wave (CW) frequency carrier signal. This spread spectrum sequence is also

called ‘code’. The sequence of phase shifts depends on the use of certain codes with special properties,

which will be presented in the next subchapter.

PMCW has some advantageous performance characteristics. The waveform generation is very simple;

being that the chips can directly modulate the local oscillator. The phase modulation in the transmitter

can be used to add information in the signal, like for example an ID [29], which could be very useful

to avoid interferences of twin systems that at some point could interfere between each other. The

codes are also named Pseudo Noise sequences (PN), since their spectrum is noise-like. Even though

the PN sequences are created deterministically, to an observer they look like random. Some of these

codes have almost perfect correlation properties, which will be a very important and determinant

factor for the performance improvement. PMCW radars also can deliver high interference robustness

and accomplish one of the short range radar high resolution requirements, which is the range

resolution. This performance can be achieved with many fewer constraints than using FMCW. The

PMCW modulation will not need synthesizers with fast-settling and very high speed properties [25],

nor will need to be highly linear as it had to be in the case of FMCW (which will turn in a higher range

Fig. 18: Representation of the final FMCW signal in the output mixer [9].


30

resolution possibilities with low energy consumption). Last but not least, the existing technology and

patents related to the technology are few and the development in its beginnings, which will translate in

attractiveness for market entrance.

Moreover using PMCW there is the possibility to use MIMO in the code domain (explained in section

2.4), which will enable high angular resolution performance and extra processing gain. In Fig. 19 can

the block diagram of a basic PMCW transmitter can be observed.

The linear feedback shift register (LFSR) generates a code that will be multiplied by the carrier

frequency 𝑓0 using a biphase modulator and then transmitter with the antenna. As an example, in Fig.

20 there is a biphase sequence with its main parameters. The sequence will be generated in the

transmitter periodically and constantly, with a period Tp.

Fig. 19: Block diagram architecture of a basic pseudo-noise modulated radar system.

Fig. 20: Time representation of a biphase sequence with its parameters [9].


31

Along the previous figures and explanations can be observed the equivalency between the duration of

a pulsed period (including its silent time), the duration of a chirp period for FMCW and the period in

PMCW sequences. The period in PMCW is the duration of the code, in FMCW is the duration of the

upchirp and/or downchirp, while in pulsed radar is the total time between the start of the transmission

of one pulse and the beginning of the next one. So that, for a code the total period will be equal to the

number of the elements of the code times the chip duration Tc, as observed in Fig. 20. The chip

duration is the inverse of the bandwidth, fc.

To reach a further understanding on how these parameters will affect the radar system performance, in

Fig. 21 there is a representation of the power spectrum of an M-Sequence, obtained after computing its

autocorrelation function.

The S(f) resulting shape comes out to be a 𝑠𝑖𝑛𝑐2 function, Eq. (26) [33]:

The space between a peak and the next one comes given by the period Tp of the code. Therefore, there

is a relation between the bandwidth used for the code and the range resolution, which will also lead to

the calculation of the maximum unambiguous range, just as in the pulse radar case.

𝑆(𝑓) =

𝑠𝑖𝑛𝑐2(𝜋𝑓𝑡𝑐)

(𝜋𝑓𝑡𝑐)2

(26)

∆𝑟 =𝑐

2𝑓𝑐 (27)

𝑅𝑚𝑎𝑥 =

𝑐𝑁

2𝑓𝑐 (28)

Fig. 21: An M-Sequence representation in the frequency domain [9].


32

From the formulas it can be concluded that the smaller the chip duration Tc, the better range resolution

will be achieved. The achievement of the unambiguous range will depend in this case on the length of

the code, so that, there is going to be needed long codes combined with small chip durations, in this

way high resolution for short range systems will be designed. Another important factor to take into

account when choosing the length of the Pseudo Noise code is the interference capabilities. The longer

the code, the better autocorrelation function will have and this fact will make the cross correlation

function to be lowered, so that the better will the system differentiate between different receivers.

Unfortunately, there are also some disadvantages in PMCW radars to be taken into account. The

baseband bandwidth of PMCW radars is very big, being its half of the RF bandwidth. As an example,

there can be named a system at 79 GHz using the 4 GHz of the spectrum with possible range

resolution of 3.75 cm, but there will be needed an ADC sampling at 4 Gsps [30]. So that, the

resolution of the converter will necessarily need to be maintained as low as possible in order to use

adequate energy consumption. This is going to depend on the specifications and presents a trade-off. If

the energy consumption can be kept low, the whole radar system can be implemented as a whole

system-on-chip in CMOS technology [31], implementing the ADCs with all the digital processing [32]

in a single chip, hence reducing the cost for volume production.

2.1.5 Radar Waveform and Pulse Compression

The main advantage of modulating the radar waveform with biphased pseudo noisy sequences is that

in this way there can be achieved high resolutions in both Doppler and range domains. This is because

with the use of the technique, these parameters can be controlled independently, varying the

integration time T and the bandwidth B.

Pulse Compression: The design of a radar system aim to achieve high range resolution and high

sensitivity to detect targets. The sensitivity to detect targets improves as the energy increases, the

range resolution increases with the increase of the used bandwidth. If the radar transmits a pulse of

rectangular envelope, the signal needs to be extended in order to achieve certain power level. But,

extending the pulse means a decrease the instantaneous bandwidth, thus degrading the resolution.

Pulse compression implements a solution to this conflict. The Pulse compression technique radiates a

long coded pulse to get a large bandwidth compared to that of a pulse not modulated of the same

duration. The process can be thought as the development of a waveform design and its appropriate

matched filter (presented in next subchapters), such that the output of the filter in the receiver focuses

its energy in a small period of time, resulting in a good range resolution and letting the total energy be

high. With this technique a compromise can be reached transmitting a long pulse that has the

advantage of a short pulse (large bandwidth). To achieve such a compromise the pulse needs to be


33

coded to have sufficient bandwidth and processed to obtain the desired range resolution. The goal is

that the energy contained in a long duration pulse will be equivalent to that in a high short power

pulse. In order to achieve such a result the energy needs to be spread through time, so that the peak

energy at each moment is very low, but the total accumulated energy is equivalent. This concept is

graphically explained in Fig. 22. If the technique is not used, having a very small pulse length for a

given energy need, would lead to a huge amount of power needed, 𝜏1 ≪ 𝜏2 and 𝑃1 ≫ 𝑃2.

The coded pulse is created at a low power level and radiated. In the receiver, the signal is processed

using a pulse compression filter, which is a matched filter, in order to achieve the maximum SNR.

Each code duration should be designed with time length according to the desired bandwidth, and will

have a processing gain such that Fig. 23 and Eq. (28):

𝑇𝑖𝑚𝑒 𝑥 𝐵𝑎𝑛𝑑𝑤𝑖𝑑𝑡ℎ =

𝑇

𝜏= 𝐵𝑇 (29)

Fig. 22: A pulse being spread through time in order to reduce to peak energy and keep the BW.

Fig. 23: Biphase code diagram of pulse compression.


34

In the end, the technique simply consists on sub-dividing a long energy spread pulse into shorter N

pulses of equal duration 𝜏. As previously stated, PMCW is used in the radar system under study. The

phase of each chip is selected depending on the pseudo-noise type code. The phase of the code

waveform chips [10] changes from 0 to 180 degrees depending on a binary sequence, as shown in Fig.

23. Choosing the right codes is essential for a good radar system behaviour. When choosing a proper

code with certain properties the output detection will have a thumbtack-like and very sharp shape

(which implies a lack of range-Doppler ambiguities), due to the ambiguity function shape (explained

in the next subchapter). Therefore the detection will be much easier than otherwise. The advantage of

using pulse compression is not only the previously mentioned but, moreover, its spread-spectrum

nature will make the system very robust to interferences that are different from the transmitted code.

In the traditional pulsed radars, a short pulse is sent followed by a long period of silence. In such a

case, the properties of the codes that are going to be explained below would require further

optimization. But, keeping in mind that the chosen system under study will be using Continuous Wave

(CW) signal, the system will radiate the pseudo noise codes continuously with no silences in between

pulses. Actually, there are not pulses itself anymore, there is a continuous flow of codes repeated

periodically; therefore the used codes should present good periodic autocorrelation properties. The

periodic auto correlation (PAC) of the code should preferably draw a sharp peak once the code is

adjusted by itself when performing the autocorrelation operation, in all the other cases the

autocorrelation should be zero. Other important property to take into account is the resistance to

Doppler shifts of the code.

-Golay codes[33]: Also called complementary sequences, they are based in the

concatenation of two sequences with the same number of elements N. They are characterized for

having an aperiodic autocorrelation function with equal magnitude sidelobes but with opposite sign.

When summing up the two autocorrelations from both concatenated sequences there is a peak of 2N

and its sidelobe level is zero. Therefore, this type of codes can offer a wide dynamic range. However,

practically a Doppler shift will cancel the zero lobe property when both of the parts are summed in the

receiver. Due to this frequency shift constraint, they have not been used a lot in radar applications.

- Barker codes: They are a limited set of biphased codes with good autocorrelation

behaviour; the sidelobes of the autocorrelation are either zero or one. The maximum length of Barker

codes that have been discovered has been 13. However, the concatenation of codes is possible if

longer codes are needed. The peakside level varies depending on the number of elements of the code

as Eq. (30), in Fig. 24 can be observed the autocorrelation function of a Barker code of 13 elements

[34]:

𝑃𝑆𝐿 = −20𝑙𝑜𝑔10𝑛 (30)


35

These sequences have good properties but are not very useful for a case where the length of the

sequence needed is going to depend on certain main parameters, since there exist just thirteen different

lengths in Barker codes. Therefore the use of Barker codes was discarded for this project.

-Maximum Length – Sequences (M-Sequences): Maximal length sequences are well

known and their structure is very similar to random sequences, for that reason they have very desirable

autocorrelation functions. Usually they are made using shift registers with different stages and selected

outputs connected in feedback. If the connections are well chosen the resulting sequence will have the

maximum length that the sequence can have before getting repeated, being the length of the sequence

𝑁 = 2𝑛 − 1, and being n the number of stages of the shift register. There is a big list of generated m-

sequences that was made by Peterson and Weldon [35].

These sequences possess wanted autocorrelation properties, however they do not guarantee the lowest

sidelobes results. They have a sidelobe level that can even reach -1[36], which is still too much for the

planned radar system. For example; the maximum signal to noise ratio achieved with a m-sequence of

length 63 is going to be 36 dB [37]. According to [38], measurements taken at 76 GHz demonstrates

that pedestrians can have as small RCS as -8 dBsm with variations on the measure of up to 20 dB if

the measure was taken from a bad angle. Big vehicles have an RCS of around 30 dBsm [39].

Therefore there can be a range of 50 dB which will need to be covered to be able to differentiate a

small person from a big bus and do not let one target overcome the other. By the other hand, m-

sequences are interesting to use in our radar system since there are many available code lengths and

with a long length. M-Sequences will be used for some simulations in this project, some results can be

observed in the Chapter 4. In Fig. 25 can be observed the response of the autocorrelation function of

an m-sequence.

Fig. 24: A 13-Barker code and its respective autocorrelation function .


36

-Almost Perfect Auto-Correlation Sequences (APAS) [36]: This type of sequence is

appropriate for CW radars and conciliates the constraints presented previously. They were introduced

defining them as a type of periodic complex sequences in which all of the out of phase periodic

autocorrelation coefficients are zero with the exception of one point [38]. Given an APAS code of

length N, the main properties are: its positive autocorrelation coefficient is placed at N/2, there is a

negative peak with amplitude –N+4, the length of the code will be necessarily a multiple of four and

the second half of the code has to be like the first half but opposite excepting for one element.

Therefore the APAS codes will have a zero lobe part equals to N/2 length, meaning that it will be

possible to achieve perfect zero side lobes.

Therefore, an APAS sequence S is made up of two halves, named S1 and S2. With the CW

transmission, the sequence S will be periodically transmitted, as shown in Fig. 26. The main peak N

occurs when the periodic sequences are exactly aligned in the correlator. Then there is a zero

correlation zone level period of N/2-1 of duration, and just at N/2 the negative peak of 4-N amplitude

appears. Next to the peak there are again N/2-1 samples with zero value. As it can be seen, the

negative peak avoids the perfect auto-correlation property; therefore the usable range of the sequence

will be equal to N/2.

When choosing a sequence length according to the design parameters, the length of the sequence will

need to be twice longer than the calculated, after the correlation the second half of the sequence will

not be needed and the negative peak will be cut besides the second half. The number of available

possible APAS sequences depending on their length will increase as the sequence length N increases.

-1000 -500 0 500 1000 1500 2000 2500 3000 3500 4000

0

100

200

300

400

500

600

700

800

900

1000

1100

X: 0

Y: 1023

M-Sequence Crosscorrelation for a 1023 chips code

X: 645

Y: -1

Fig. 25: Autocorrelation response of a m-sequence code with 1023 chips length.


37

The good behaviour of the APAS sequences, regarding to sidelobes, will make them very useful for

the purpose of the radar system described in this document, so that the simulations presented in

Chapter 4 will be performed using previously generated APAS codes. The sequence needs periodicity

in order to achieve a clean behaviour in the crosscorrelation. It will work perfectly for standing targets

(zero frequency shifts); the phase shifts between the receiving signals will be zero. However there will

start to appear sidelobes as the speed of the target increases; the phase will have changed due to the

Doppler effect, thus the crosscorrelation will not be multiplying anymore by totally coherent data. Fig.

27 contains the autocorrelation response of a long 4080 chips APAS code.

-4000 -2000 0 2000 4000 6000 8000 10000 12000 14000 16000

-4000

-3000

-2000

-1000

0

1000

2000

3000

4000X: 4080

Y: 4080

APAS Crosscorrelation for a 4080 chips code

X: 5033

Y: -2.72e-14

Fig. 27: Autocorrelation response of an APAS code of 4080 chips length.

Fig. 26: APAS code processing of its autocorrelation function [36].


38

2.2 Fundamentals of Signal Processing for Radar

In this section is presented a background of the basic and specific signal processing techniques used

for radars and the mmWave radar proposed in particular. The important techniques that will provide

the system with high SNR gain and resolution are developed; the matched receivers, pulse integration

procedures and Doppler frequency processing, besides some complementary concepts.

2.2.1 Basic Signal Processing Concepts

-Convolution: Is a mathematical operation that takes two signals and produces a third signal; it

describes the relationship between these three signals of interest, which are: the input signal, the

impulse response and the output signal. The input signal can be broken up into a group of impulses;

each of them can be thought as simple delta function that is scaled and shifted. While the output signal

can be thought as the derived output from the input signals that are a shifted and scaled version

depending on the impulse response. The global output signal is found adding these individual scaled

and shifted impulse responses belonging to each of the decomposed input impulses. Mathematically,

and for discrete signals it is described as in Eq. (31) [40]:

Each individual sequence value can be viewed as triggering a response, then all the responses are

added together to arrange the total output.

-Correlation: Just as the convolution operation, it is a mathematical operation that uses two signals to

generate a third signal. The third signal is called the correlation of the two input signals. The

amplitude of the samples in the correlation output signal is the similarity degree between the received

signal and the sample signal, at that location. The value of the correlation output is maximized when

the input signal is aligned with the same characteristics in the received signal. The correlation is the

optimal technique in order to detect a previously known waveform [40]; using correlation in order to

detect a known waveform is frequently called matched filtering. Mathematically, it can be described as

Eq. (32) [40]:

𝑦[𝑛] = ∑ 𝑥[𝑘] ∙ ℎ[𝑛 − 𝑘]

+∞

𝑘=−∞

= 𝑥[𝑛] ∗ ℎ[𝑛] (31)

𝑦[𝑛] = ∑ 𝑥[𝑛 − 𝑘] ∙ ℎ[𝑘]

+∞

𝑘=−∞

= 𝑥[𝑛] ∗ ℎ[−𝑛] (32)


39

The signal flipping is the only mathematical difference between the convolution and the correlation.

The correlation requires reversing one of the signals being correlated. However, the concepts are

totally different; the correlation attempts to quantize the extent to which two signals are alike.

-DFT: The discreet Fourier Transform is a mathematical tool that decomposes any discreet function

into a group of sinusoidal functions and vice versa. The functions are a complex exponential which

contain different frequencies. Therefore, it is a tool that allows the transformation of time domain

signals into frequency domain signals, allowing a much easier interpretation of the information

contained. The Fourier transformation is mathematically defined as Eq. (33) [40]:

Where

𝑥𝑛 = the input signal amplitude of certain sample

𝑋𝑘 = spectrum of 𝑥𝑛

𝑁 = the number of samples

𝑘 = kth frequency sample

The DFT will be used to obtain the frequency shift change of the radar echoes samples in order to

obtain their speed. The FFT, an algorithm that reduced its computation time, will be applied along the

final samples.

2.2.2 Matched filter

Most of radars are meant to have a good performance in both sensitivity and high resolution.

Detectability becomes better as the energy increases, and resolution improves as the bandwidth is

larger. As previously seen, applying pulse compression in the wave form allows to address both issues

with great results.

When the echo signal is received the system should maximize the information contained. By definition

a matched filter is a radar receiver filter that is conceived to maximize the SNR at the filter’s output

[33]. The impulse response of a perfect matched filter would be the same waveform which was

transmitted but just conjugated and reversed in time, like that both the transmitted and received signals

would be matched.

Let’s say that the radiated waveform is presented as u(t), its spectrum is going to be Eq. (34):

𝑋𝑘 ≜ ∑ 𝑥𝑛 ∙ 𝑒−2𝜋𝑖𝑘𝑛/𝑁

𝑁−1

𝑛=0

(33)

𝐹(𝜔) = ∫ 𝑢(𝑡)𝑒−𝑗𝜔𝑡𝑑𝑡

∞

−∞

(34)


40

And, if the transfer function of the receiver is 𝐻(𝜔), the output signal is going to be (35):

In (36) the maximum value of g(t) is 𝑔(𝑡0) and the noise spectrum of power in the filter output is [37]:

Being 𝑁0

2 the spectral density of the noise at the output. The average noise at the output and the signal

input energy are (37) and (38).

So the SNR at the radar detector will be [37]:

There can be seen in (39) that the SNR depends on the frequency response of the receiver. Since we

are searching for the maximum possible SNR, the 𝐻(𝜔) that maximises the SNR is wanted. Using the

Schwarz inequality follows that [33]:

Which is the maximum possible energy in the receiver output, which will only occur when the impulse

response will be [33]:

𝑔(𝑡) = ∫ 𝐹(𝜔)𝐻(𝜔)𝑒−𝑗𝜔𝑡𝑑𝑓

∞

−∞

(35)

𝐺(𝜔) =

𝑁02|𝐻(𝑤)|2 (36)

𝑁 =

𝑁02∫ |𝐻(𝑤)|2𝑑𝑓∞

−∞

(37)

𝐸 = ∫ |𝐹(𝑤)|2𝑑𝑓

∞

−∞

(38)

|𝑔(𝑡)|2

𝑁=|∫ 𝐹(𝜔)𝐻(𝜔)𝑒−𝑗𝜔𝑡𝑑𝑓∞

−∞|2

𝑁02 ∫

|𝐻(𝜔)|2𝑑𝑓∞

−∞

(39)

|𝑔(𝑡)|2

𝑁≤2𝐸

𝑁0 (40)

𝐻(𝜔) = 𝛼𝐹∗(𝜔)𝑒−𝑗𝜔𝑡0 or ℎ(𝑡) = 𝛼𝑓∗(𝑡0 − 𝑡) (41)


41

Where 𝛼 = constant gain

𝑡0 = time delay through the filter

Then, the impulse response needed comes to be time-delayed inverse and conjugate of the waveform

multiplied by a constant, set to unity. Therefore the time domain output of the receiver filter will be set

as [33]:

The Eq. (42) can be identified as the cross-correlation of the transmitted waveform 𝑓(𝜏) with the noise

and target signal. So that, the matched filter is a correlator. The idea behind it is simply use a flipped

convolution; the output amplitude of each point will be a measure of how exact the filter matches the

equivalent section of the input signal. Finally, the maximum SNR ratio is achieved; the peak is higher

over the mean noise power using the correlation than with other filter.

From Eq. (40) can be extracted that this maximum energy will not depend on anything else but on the

energy contained in the waveform, not on its modulation or shape. The energy contained in the

waveform is spread using pulse compression, as explained in the section 2.1.5. Consequently the SNR

gain due to pulse compression after the matched filter in each range gate will depend on the length of

the waveform sequence used to modulate the carrier.

The matched filter principle is going to be used in the radar system under study and its system

implementation will be presented in more detail working inside the radar in the system description of

the Chapter 3. The detection of the targets is the main feature of radar systems. In the system under

study several targets are expected to be detected in the same or different ranges.

The time 𝑇𝑚 at which the output is maximum should be chosen, if it is selected to be 𝑇𝑚 = 𝜏 the

output will be just the correlation of the received and delayed reflected signal with the impulse

response of the matched filter [33]. The peak will be occurring at correlation lag zero, when 𝑡𝑝𝑒𝑎𝑘 =

𝑡0 + 𝜏 which corresponds with the delay of the target (due to the range) plus the delay of the matched

filter. Therefore the target range can be computed as 𝑅0 = 𝑐(𝑡𝑝𝑒𝑎𝑘 − 𝜏)/2. It is deduced that the

choice

of the parameter 𝑇𝑚 is arbitrary, and normally will be 𝑇𝑚 = 𝜏 , the duration of one sequence (one

sequence chip). In the radar system implementation under study the solution is going to be

implemented using parallel range gate processing; each branch of the parallel system will use the

echoed signal correlated with the delayed sequence. The delayed is equal to the chip duration, 𝑇𝑚 = 𝜏.

𝑦(𝑡) = ∫ 𝑓(𝜏)𝑓(𝜏 + 𝑡0 − 𝑡)𝑑𝜏

∞

−∞

(42)


42

2.2.3 Pulse Integration

Another method to increase the SNR of the system is the pulse integration. It is a fundamental

operation. The integration in the radar system under study is going to be coherent. Let’s first introduce

the concept of coherence and explain the reason why it is so important.

-Coherent Radar: Coherent signal processing is defined as ‘the echo integration, filtering, or detection

using amplitude and phase of the signal referred to a coherent oscillator’ by the IEEE SRD. It means

that the radiated signal should have a unique phase reference for consecutive pulses, in practice each

pulse of consecution of sequences must be referenced to the same starting time and phase.

Fig. 28 shows the difference between a coherent pulse and a non-coherent one. In the case a) the two

pulse signals look as if they were taken from the same continuous and stable sinusoid signal. In the

case c) the pulse is not in the same phase than the reference even though it keeps its frequency. The

most important advantage of this kind of systems is that they achieve the capability in making a

distinction among relatively small speed differences (since this differences match with the small phase

differences). Coherence provides Doppler estimation and also helps to protect the signal against

interferences. For obvious reasons the radar system under study in this document is fully coherent.

Once the concept of coherence is clear, the processing of coherent pulse integration is easily defined.

The integration of returns from consecutive pulses is performed in order to increase the energy

received from a concrete target. The pulse integration in the system under study is going to be

coherent, meaning that the integration is going to be made in both the imaginary and the real part of

the signal data (i.e., phase and magnitude).

Fig. 28: Coherent and non-coherent signals. In a) a coherent signal generated from the reference b), in c)

a non-coherent pulse.


43

Let’s say that a transmitted pulse comes across with a target and the signal reflected is detected at a

certain delay in the receiver of the radar system. The measured signal consists on a complex echo with

some added noise. The power of this single pulse would be:

Where

A = Complex signal amplitude.

𝜎𝑤2 = Random additive noise.

If the measurement is repeated N-1 more times for n identical pulses with a known initial phase, the

echo received should be the same but with a different noise sample (since it will vary randomly). If out

of the N-1 samples a single measurement is built with the integration of all and each of the different

measurements, a sum of complex samples is going to take place. The summation of all the samples

will keep the same phase information because of the coherent nature of the system; therefore it is a

coherent integration, given by Eq. (44):

Where the phase 𝜑 is known and is the same for each of the pulses. This model assumes that the train

of pulses received encounter the same propagation distortion. Since the operation is coherent, the total

energy received from n pulses is equivalent to 𝑛2 of a single pulse energy; the total noise variance is

proportional to n. Thus the power of the signal is 𝑁2𝐴2 and the noise power is now 𝑁𝜎𝑤2 . The SNR at

the output of the accumulator increases linearly with n. Therefore the coherent integration has

improved the SNR by a N factor, called integration gain. That is ideally, but in practice, achieving

coherent integration in a radar receiver is tricky. The accumulation occur along the period [0, 𝑁 ∙ 𝑇],

and during this period the target may be not stationary, besides the propagation channel could change.

This can lead to a mismatch of the amplitudes and phases of between the return pulses, which may not

be totally known.

2.2.4 Doppler Processing

-Doppler Effect: When a wave is radiated, received or reflected by a target which is moving drifted

further or closer to a source or receiver, there is an effect that performs an apparent frequency change.

This is called the Doppler Effect and applies to every wave in motion. Using the phase change rate

allows to compute the distance. The apparent change is due to the motion difference between two

𝑔𝑝 =

𝐴2

𝜎𝑤2

(43)

𝑧 = ∑{𝐴𝑒𝑗𝜑 +𝑤[𝑛]}

𝑁−1

𝑛=0

= 𝑁 𝐴𝑒𝑗𝜑 +∑{𝑤[𝑛]}

𝑁−1

𝑛=0

(44)


44

points. If one transmitter point radiates while moving toward another point, the receiver will perceive

a higher frequency wave. This is caused because the receiver is going to get a higher number of waves

each second and interpret it as a higher frequency wave. The total phase change after two way

propagation is given by Eq. (45) [37]:

Where

𝜆 =Wavelength

R = Range

Therefore, after differentiating the phase change over time, the phase change rate (angular frequency)

will be given by Eq. (45), and the Doppler frequency 𝑓𝑑 cleared, resulting in Eq. (46) [37]:

When performing Doppler processing usually indicates the employment of the Fast Fourier Transform

(FFT) algorithm and other few techniques in order to calculate the echo data’s spectrum for a concrete

range. If the targets are in movement, the different Doppler shifts will allocate the energy in different

parts of the spectrum, thus permitting the separation and detection of the targets. Even though Doppler

processing is a more complex method making it more energy consuming due to higher processing

complexity, it is able to provide more information about the target than other methods like Moving

Target Indicator (MTI) [33].

CW radars, like the radar system under study here, observe the Doppler shift produced by a moving

target during the integration time, in the carrier frequency of the received echo, relative to the transmit

signal.

The result of the Doppler processing will be a data matrix. This matrix will have two domains, the

slow-time domain and the fast-time domain (they will explain further in the system description in

Chapter 3). After the Doppler processing, the slow-time domain will result into a spectral domain that

will be called Doppler Domain and the fast-time into the range domain. The spectral analysis is going

to be performed for each range bin. The conversion can be observed in Fig. 29:

𝜑 =

2𝜋

𝜆∙ 2𝑅 =

4𝜋𝑅

𝜆 (45)

𝜔𝑑 =

𝑑𝜑

𝑑𝑡=4𝜋 ∙ 𝑑𝑅

𝜆 ∙ 𝑑𝑡=4𝜋𝑣𝑟𝜆

= 2𝜋𝑓𝑑 (46)

𝑓𝑑 =

2𝑣𝑟𝜆𝑐𝑜𝑠𝜃 (47)


45

Depending on the parameters chosen for the processing, the pulse Doppler processing will supply with

the radial velocity data of the targets and also if the target is coming closer or leaving further. It will

also support the identification of multiple targets depending on whether the parameters of the system

have been chosen to have a fine enough Doppler resolution to separate the different targets in speed (if

they are in the same range).

The drawback is the increased processing complexity which will require higher energy usage and

larger dwell times since there will be a need for gathering more pulses (sequences in our system being

that is a CW system). The complete description of the system and how each point of the data matrixes

will be acquired will be explained in the system description of the radar system under study, in

Chapter 3.

In order to understand the functioning of the technique, it will be considered just one target at a certain

range moving at a constant speed such that the frequency shift is Fd as given by the complex sinusoid

signal in Eq. (48). To effectively compute the Doppler frequency there is going to be needed a long

period of acquisition. One method to do this is simply transmit the same sequence a certain number of

times, thus like this they will give us a better Doppler frequency resolution. In this case, during a dwell

time there are going to be transmitter M sequences [33]:

Fig. 29: After the Doppler processing the matrix transforms to range/Doppler from fast/slow time to matrix [33].


46

Where

m = Number of sequence over the dwell time m = [0 M-1]

Fd = Frequency shift.

T = Pulse repetition interval.

A = Amplitude.

As previously stated, m is the usually referred as slow time index and t is named as the fast time index.

If the system is using a matched filter, as in the case of the radar system under study, the matched

output filter will be given by Eq. (49):

Where

𝑟𝑦𝑦 = Autocorrelation function

To obtain the Doppler data, the matched filter output related to the range can be sampled, thus the

peaks belonging to the received signal can be taken as [33]:

The Fourier transform of this signal gives (51):

Being

𝐹 ∈ [−𝑃𝑅𝐹

2,𝑃𝑅𝐹

2]

𝑦[𝑚] = ∑ 𝐴𝑒𝑗2𝜋𝑓𝑑𝑇𝑚𝑀−1

𝑚=0

(48)

𝑦(𝑡) = 𝐴 ∑ 𝑟𝑦𝑦𝑒𝑗2𝜋𝑓𝑑𝑚𝑇

𝑀−1

𝑚=0

(49)

𝑦𝑞 = 𝑦(𝑞𝑇) = 𝐴 ∑ 𝑟𝑦𝑦𝑒𝑗2𝜋𝑓𝑑𝑚𝑇𝑞 ≈

𝑀−1

𝑚=0

𝐴 ∑ 𝑟𝑦𝑦𝑒𝑗2𝜋𝑓𝑑𝑞𝑚𝑇

𝑀−1

𝑞=0

(50)

|𝑌(𝐹)| = |∑ 𝑦𝑞𝑒−𝑗2𝜋𝑓𝑞

𝑀−1

𝑞=0

| = |𝐴𝑟𝑦𝑦 ∑ 𝑒−𝑗2𝜋𝑓𝑞𝑀−1

𝑞=0

| = |𝐴𝑟𝑦𝑦sin (𝜋𝑀(𝐹 − 𝐹𝑑))

sin (𝜋(𝐹 − 𝐹𝑑))| (51)


47

The magnitude of the previous equation is showed in Fig. 29. For a frequency PRF/4, 20 sequences

and amplitude equals to 1.

As expected, the main lobe is centred at F = Fd. The main lobe performance is going to determine the

Doppler resolution of the system. So that, the Doppler resolution is going to be determined by the

dwell time, in this case the inverse of MT. Therefore, the resolution will be improved as the dwell time

increases. Integrating the slow time samples of the echo mean that a matched filter is applied for zero

frequency, which will come out as a constant value. What it is done to detect a frequency shift is to

implement a matched filter in the fast time for an expected Doppler shift. If the signal has the form

Aexp(j𝑤𝑑m), after time-reverse and conjugation the filter coefficients will be h[m]=exp(+j𝑤𝑑m), and

the filter peak happens when the data sequence and response are overlapped.

After the previous considerations we can already define the Doppler resolution on a radar system, as

seen in Eq. (52):

Where

M = Number of sequence repetitions

T = Duration of the sequence [s]

𝐹𝑟𝑒𝑠 =

1

𝑀 ∙ 𝑇=1

𝑇𝑑 (52)

Fig. 30: Shape of the received signal after DFT processing [33].


48

In the results part of the Chapter 4, there are going to be showed some simulation of different targets

detected at the same dwell time and even the same range. This is possible since the echo detected

signal will have different frequency components, so the spectrum will be showed with two peaks

separated in the spectrum each other.

The Doppler part of the system can be seen as a Doppler filter bank composed by as many filters as

number of sequences repetitions. The lobes should be as narrow as possible in order to allow high

resolution Doppler measurements and, at the same time, improve the SNR. Even though the main lobe

bandwidth should be theoretically infinitesimal (corresponding to continuous sinusoidal signal of

infinite duration), it cannot exist in the real system, therefore it corresponds to the CW waveform,

which is the dwell time between sequence chips. As a result of the finite number of samples, spectral

leakage will occur for strong signals, meaning that a signal will appear not just in its frequency(speed)

but also in its surrounding frequencies, increasing the probability of false alarms in the detection

process.

Since the number of operations in a radar system application is expected to be very high, it is common

to compute the DFT with the Fast Fourier Transform (FFT) algorithm. A further explanation of the

Doppler system processing is developed in the section 3.1.

This processing will be performed for each range and after all, there is going to be further signal

processing to find out what can be considered target detection or not, as is presented in the section 2.3.

2.2.5 Ambiguity Function

Since all the main radar system parameters have been discussed in previous sections, a useful tool that

makes use of them is going to be briefly introduced in this section.

Overall, the radar system resolution is a combination of Doppler resolution, range resolution and angle

resolution. The final radar system resolution can be characterized by a special function.

The ambiguity function (AF) can be considered as a very useful analytical tool that can be used to

design the waveform of the system and analyse its behaviour together with the response of the

waveform processed with the matched filter [41]. The function is beneficial to examine all the

parameters that are going to affect the radar system, such as the resolutions (Doppler and range), side

lobes levels, ambiguities (Doppler and range) and other phenomena.


49

In a generic radar system, the ambiguity function is given by Eq. (53) [42]:

Where 𝑢(𝑡) is the radar waveform; it can be noticed that the function is bidimensional. It indicates the

output of the matched filter when certain mismatched delay 𝜏 and Doppler shift 𝜐 happen. If the

function in (0, 0) is very sharp, it will mean that the range and Doppler resolutions are very good. This

is because the value of the function |𝜒(0, 0)| symbolizes a perfect matched filter output, with no

mismatch. When a mismatch happens, it means that either in range or in Doppler there has been a

widening in the shape of the lobe in frequency or a range migration in the range domain. In Fig. 31

there is represented a thumbtack-like ambiguity function.

The ambiguity function of the Fig. 31 is characterized by a single central peak. This narrow peak

means good resolutions (in both range and Doppler domains), and, the fact that there is a lack of any

other peak, indicates that there will not be any ambiguities (range nor Doppler). There are not side

lobes either so masking effects are not expected. Even though it seems the ideal system, this singular

system is designed to maximize the resolutions. However there are other applications where a trade-

off is required to benefit other parameters of the system against the resolution, like the processing

complexity or energy consumption. Therefore, the perfect ambiguity function response will depend on

the design of the waveform for a concrete system application.

𝜒(𝜏, 𝜐) = |∫ 𝑢(𝑡)𝑢∗(𝑡 + 𝜏)𝑒𝑗2𝜋𝑣𝑡𝑑𝑡

∞

−∞

| (53)

Fig. 31: Thumbtack-like ambiguity function [33].


50

2.3 Constant False Alarm Rate (CFAR)

The concept of CFAR, its justification and its main parameters are introduced in this subsection. The

functioning of CFAR in a typical system is exposed. The algorithms that are going to be implemented

in the system are also explained, besides its main characteristics and behaviour under given

circumstances.

2.3.1 Introduction

Once the pulse compression is performed and the output of the Doppler processor is available, there

will be a matrix of data with information, included clutter. The information will be available in the

domain of range and in the domain of Doppler, but to get the useful information there will be needed a

technique that will find out whether each of these data cells signals is the wanted or not. Coming back

to the fundamental goal of radar systems; this is to detect targets. The decisions are normally taken

comparing the level of the signal, amplitude A(t) of the output to a threshold T(t) which may be pre-set

in the design or calculated with the aid of signal processing. In order to separate the interference

echoes from the wanted signals, digital processing must be used. The signal processing of the data is

oriented to determine certain threshold with which the data will be compared, thus deciding on the

likeliness of the signal being a desirable target or an unwanted signal. If the decision made is positive,

i.e., it indicates the presence of a target, further processing is performed.

The detections can be performed in different stages of the radar system depending on the needs of the

application. In the case under study, the detection stage location is in the stage after which the

maximum SNR gain has been achieved, so it is easier for the threshold to get a detection and avoid

false alarms.

Targets and interference are usually best characterized by statistical models [43]. Therefore, it seems

logical that the tools to decide whether a signal is wanted or not should be of statistical hypothesis

analysis.

There are two only situations that will always repeat, either the detection is only interference

(Hypothesis 0) or the measurement is a combination of the echo from a valid target plus interferences

(Hypothesis 1). Therefore the detector should check each measurement and select one of the two

Fig. 32: Basic block diagram of the signal processing in the receiver until the detection stage.


51

possible hypotheses as most likely concerning that certain signal. If the decision obtained is less likely

than more, then the hypotheses of only interference apply and it is declared that there is no target.

Otherwise, if the measurement accounts best for a target, a target presence declaration of the

coordinates will be made and further processing is expected.

The statistical nature of the signals bring us to approach the problem with a description of the

probability density function (pdf), which will characterize the detection, taking into account the two

possible outcomes. If the signal being studied is named as y, there will be two pdfs:

- 𝑝𝑦(𝑦|𝐻0): pdf of the signal given not presence of a target

- 𝑝𝑦(𝑦|𝐻1): pdf of the signal given the presence of a target

Therefore, to solve the detection challenge there should be models that solve the previous pdfs. The

model designs are going to depend on the environment where the radar is going to be used and in the

system design itself; thus chosen in order to experience the most favourable performance in detection.

Concretely, the detections will be sustained by several samples of data from the radar data matrix. The

next probabilities’ concepts are described since they will be used in every CFAR algorithm:

- Probability of Detection (𝑃𝑑): It is the probability that a target is resolved to be

present when it actually is present at the detection coordinates under study.

- Probability of False Alarm (𝑃𝐹𝐴): It is the probability that a target is resolved to be

present when it is actually not present at the detection coordinates under study.

In general, the False Alarm Rate (FAR) is computed with Eq. (54):

Once the necessary parameters are defined, in order to make a decision there is a need for a rule. The

decision outcome will be based on this rule. In radar, it is popular to use a criterion named Neyman-

Pearson [44], by which the 𝑃𝑑 is maximized under the limitation of the 𝑃𝐹𝐴 being set at a constant

value which should not be exceeded. The 𝑃𝐹𝐴 value allowed will be decided by the system designer

and it will depend on the implications for that concrete radar system. Commonly, the 𝑃𝐹𝐴 should be

low. The probability of detection will mainly depend on the target SNR.

So far, the description above gives for granted that the clutter and noise level is known and also not

variable at each moment. This supposition permits to set up a system which threshold guarantees an

accurate and specific probability of false alarm. However, in real applications the levels of interference

use to be a difficult space and time varying stochastic process, consequently the 𝑃𝐹𝐴 would be

unpredictable, which is not desirable. Therefore, there is a need for an adaptive system that will work

with variable threshold depending on a clutter situation with different fluctuation, intensity and range,

𝐹𝐴𝑅 =

𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝐹𝑎𝑙𝑠𝑒 𝐴𝑙𝑎𝑟𝑚 𝑒𝑎𝑐ℎ 𝑃𝑅𝐼

𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑟𝑎𝑛𝑔𝑒 𝑐𝑒𝑙𝑙𝑠 𝑢𝑠𝑒𝑑 (54)


52

in real time. Ideally, the algorithm would vary the parameters depending on the environment in that

concrete moment to provide an accurate and controlled rate of 𝑃𝐹𝐴.

Radar systems can make even hundreds of thousands detections per second. Fortunately, as the

hardware has decreased in prize and the processing has become faster, the radar systems have become

automated. Constant False Alarm Rate (CFAR) detection is a group of techniques which are

developed to allow detections given a controlled 𝑃𝐹𝐴, using foreseen real and changing scenarios.

The first step to take in a CFAR analysis is to define a window of fixed size along the data cells of the

data matrix (Fig. 33), to estimate the signal level in the range around the cell. The general procedure to

detect can be followed in Fig. 33:

This window, which will be called sliding window, will be moving all along the data with its centre in

the Cell Under Test (CUT). The window will have a fixed pre-set size, being this one of the

parameters to take into account in the CFAR system design. The window is divided in two parts, the

leading part and the lagging part, both surrounding the CUT. Optionally, there is the possibility to

introduce some cells which will not be taken into account in the estimation around the CUT. These

cells are named guard cells and they are useful to decrease the self-interferences in the case where a

target is present near the CUT under study.

The data contained in the window is going to be used to approximate the statistical parameters of the

clutter and interferences in the background, so that the adaptive threshold can be set to a proper level.

The cells used to estimate this value are called training cells.

The length of the window needs to be chosen according to rough expectations that the designer will

make depending on the application where the radar system will be used. For example, to get proper

Cell Under Test

Xm X1Xm+1Xn CUT

Training Cells Training Cells

Guard Cells

Fig. 33: Cell analysis procedure of a CFAR analysis.


53

low variance estimation in a homogeneous background noise environment the size of the window

should be as large as possible. But it is not always possible to set it as long as possible. The size

should be adapted so it matches the typical length of homogeneous clutter areas of the scenario.

Otherwise the requirement of equally distributed clutter random variables would not be fulfilled [45].

This is the reason why there have appeared many different CFAR techniques; each of them is designed

to be applied in a certain environment conditions to minimize the number of false alarms and

maximize the probability of detection.

2.3.2 Cell Averaging CFAR

Also referred as CA-CFAR, the technique uses adjacent cells’ signal data to estimate the level of noise

and adapt the threshold to an optimum level. The processing approach in CA CFAR is based on two

assumptions. The first one is that the neighbouring cells do not contain any other target, just

interference. The second; the neighbouring cells have the same statistical interference as the CUT.

Under this situation, the optimized technique is simply to make an estimation of the interference

power level in the reference cells according to Eq. (55) [46], with the use of the arithmetic mean of the

power levels inside the window under study, around the CUT.

Where

N = Number of cells under test.

𝑋𝑖 = Power of each cell, since a square law detector is used.

Once we get the estimation performance in Z, the second step is to multiply the estimated power Z

with a scaling factor T (which will depend on the estimation method applied and in the 𝑃𝐹𝐴 set [46]).

Then, the result will be the threshold level that should be applied in that certain moment, as can be

seen in Fig. 34.

𝑍 =1

𝑁∑𝑋𝑖

𝑁

𝑖=1

(55)


54

The threshold will be calculated as a multiplication of the estimated power of each cell:

Substituting Eq. (56) in (55), the estimation of power comes out to be the arithmetic mean of the cells

under study scaled with T [46]:

Knowing that the interferences have random variable behaviour and the goal of adaptive threshold is

to be able to get a predictable behaviour, there can be found an analytical formula of the probability of

false alarm [33]. It can be seen that the 𝑃𝐹𝐴 is affected by the scaling factor T and the number of cells

N, as expected.

𝑆 = 𝑇𝑍 (56)

𝑍 =𝑇

𝑁∑𝑋𝑖

𝑁

𝑖=1

(57)

𝑃𝐹𝐴 = (1 +

𝑇

𝑁)−𝑁

(58)

Xm X1Xm+1Xn CUTSquare-law

detector

Range

∑ ∑

1/N ∑

Scaling Factor: TCA

Comparator

Detection

No Detection

Estimated Power Z

Vt = Z TCA

Input

Samples

Fig. 34: Block diagram of the CA CFAR detector.


55

Now, given a 𝑃𝐹𝐴 there is the possibility to find the scaling factor that will make it constant, clearing

on Eq. (59) [45]:

If there would be given the case when there is range migration, this method would not be appropriate,

unless guard cells are used to avoid self-interference.

Main Limitations: The main limitations of the CA algorithm come given by the assumptions that were

exposed above. If either or both of these assumptions are broken in a real application, the behaviour of

the technique will not be the expected.

- If the first assumption fails: Target masking will happen when several targets exist inside the same

reference window under study. Their existence will make the threshold rise and, therefore, the real

target will not be detected or will be much more probable to be missed, as the example in Fig. 35:

- If the second assumption fails: Clutter edges appear when the test cells are around the limits of two

differentiated clutter regions, therefore the statistics in the window will not be heterogeneous since the

clutter is not uniformly distributed. These edges will cause false alarms, or also masking, depending

on the situation.

𝑇 = (𝑃𝐹𝐴

−1𝑁 − 1) (59)

Fig. 35: CA CFAR masking occurring in a multi-target situation with N=32 and 𝑃𝑓𝑎 = 10−6 [65].


56

2.3.3 Greatest Of / Smallest Of Cell Averaging with CFAR

The limitations of CA CFAR described in the previous section led to the appearance of new

techniques which goal was to fight these limitations. Some of these techniques are the smallest of cell

averaging CFAR (SOCA) and greatest of cell averaging CFAR (GOCA).

SOCA technique is meant to tackle the problem of masking caused by interfering targets close to the

CUT. Using this approach, the lead and lagging windows are averaged independently, instead of as a

whole as in the CA case. Then, the useful threshold is chosen as the smallest estimated among the two

different averaged windows.

GOCA technique is meant to tackle the problem of nonhomogeneous clutter in determined

environments in which an increase of false alarms would be more worrying than masking. Following

the same logic as with SOCA, the different windows would be averaged independently, however, with

GOCA the threshold will be depending on the greater among the two values. The threshold, depending

on a scale factor T can be seen in Eq. (60) and (61) [47]:

SOCA would avoid missing targets due to target masking but, instead, the 𝑃𝐹𝐴 would increase, mostly

close to crossing areas with different distributed clutter. Therefore, this method is suitable to be used

in heterogeneous environments.

GOCA used in nonhomogeneous areas makes that the false alarms drop but also the probability of

detection is slightly reduced. Therefore, this technique shows a good advantage in transition areas of

big power level difference but at the same time drops the sensitivity in homogeneous background

noise situations.

Even though it could be tempting to say that the scaling factors of both methods, 𝑇𝐺𝑂 and 𝑇𝑆𝑂, could

be computed using the Eq. (59) since there is just a change of N by N/2, the power interfering will be

half and therefore the scaling factor will be increased. Weiss [46] showed in 1982, that the scaling

factor is the solution of the Eq. (62) [45], which must be solved with iterations.

𝑍 = 𝑇𝐺𝑂 ∙ max

(

[ 2

𝑁∑𝑋𝑖

𝑁2

𝑖=1]

, [2

𝑁∑ 𝑋𝑖

𝑁

𝑖=𝑁2+1

]

)

(60)

𝑍 = 𝑇𝑆𝑂 ∙ min

(

[ 2

𝑁∑𝑋𝑖

𝑁2

𝑖=1]

, [2

𝑁∑ 𝑋𝑖

𝑁

𝑖=𝑁2+1

]

)

(61)

𝑃𝐹𝐴2= (1 +

𝛼𝑔𝑜/𝑠𝑜

𝑁/2)−𝑁/2

− (2+𝛼𝑔𝑜/𝑠𝑜𝑁2

)

−𝑁/2

𝑥

{

∑ (

𝑁2 − 1 + 𝑘

𝑘)

𝑁2−1

𝑘=0

(2 +𝛼𝑔𝑜/𝑠𝑜𝑁2

)

−𝑘

}

(62)


57

2.3.4 Order Statistics CFAR

This technique is an alternative to the previous ones since there is no use of averaging power anymore.

Instead, order statistic CFAR (OS CFAR) selects the samples of the reference window to make an

ascending ordered sequence of samples depending on their power value. So, all the amplitudes are

sorted increasingly as [47]:

The kth element is the kth order statistic, which is selected as the estimated value of the interference

level and the threshold will be selected as a multiple of the value given by the kth element, as in (64):

To be called CFAR, the 𝑃𝐹𝐴 should not depend on the interference power, which is validated in [33],

given that the 𝑃𝐹𝐴 is:

Where

𝑌0= Noise sample with exp. distribution [46].

Then, the right 𝑇𝑜𝑠 value in order to accomplish certain 𝑃𝑓𝑎 can be computed using Eq. (66) [47]:

It can be checked that 𝑃𝐹𝐴 is not dependent on the interference power, so that it is also a CFAR

method.

It has been demonstrated in the previous sections that Cell Averaging techniques have very sensitive

behaviour when there are several targets in the scenario and also they have masking problems when

crossing high range power levels. OS CFAR has in these situations very good performance since it is

not based in the assumption of homogeneous clutter inside the window under study. The threshold is

not influenced by several other targets inside the same window.

In OS CFAR, guard cells do not make sense to be used since other targets amplitudes will not have

practically effect on the noise level estimate. The main disadvantage is the increase in processing

complexity.

𝑋(1) ≤ 𝑋(2) ≤ ⋯ ≤ 𝑋(𝑁) with 𝑍 = 𝑋(𝑘) (63)

𝑍 = 𝑇𝑜𝑠𝑋𝑘 (64)

𝑃𝐹𝐴 = 𝑃[𝑌0 ≥ 𝑇𝑜𝑠𝑋𝑘] (65)

𝑃𝑓𝑎 = 𝑘 (

𝑁

𝑘)(𝑘 − 1)! (𝑇𝑜𝑠 +𝑁 − 𝑘)!

(𝑇𝑜𝑠 + 𝑁) (66)


58

2.4 MIMO Radar

In this section, the MIMO principle is introduced; its technical background and physical approach are

developed, along the concept of virtual array. An introduction to two MIMO methods is presented, for

short range and for long range radar; the MIMO Outer Code technique and the range domain

separation method. Their justification, main technical background and basic structure are described.

2.4.1 Introduction

In the last decade the development rhythm in the MIMO radar’s scope has been very high. It is

actually a new concept for radar systems in which MIMO stands for Multiple Input Multiple Output.

The concept has been borrowed from the communications scope, where the technique follows that has

been very useful allowing the increase of the throughput, among other characteristics, for

communication channels. This has implied the ‘borrowing’ of many settled ideas from classical

MIMO telecommunications. This can be an advantage because it allows the use of certain results from

theory and practice from communications, but it does not take into account particular characteristics in

the radar’s scope which, therefore, may lead to errors.

MIMO radars can be split into two types [48]; radars which include separated antennas by a wide

distance, called Statistical MIMO Radars, and MIMO radars with coded waveforms and collocated

antennas.

Statistical MIMO Radars: These systems’ goal is to improve the sensibility of the detector by

separating the sensors an appropriate distance. Both of the arrays, the transmitter antennas and the

receiver antennas are broadly separated if compared with their signal wavelength, thus supplying

independent dispersed reflections for each couple of transmitter-receiver antennas. In this scenario,

each antenna illuminates differently the target. In consequence the RCS are going to be independent

random variables for each of the paths and thus, the information gathered by the receiver will have

independent characteristics about the target. This type of radar systems are not going to be developed

further in this document, they will not be used in the radar system under study.

Coherent MIMO Radar: Differing from the previous MIMO system, the Coherent MIMO Radar aims

to achieve a better spatial resolution, among other improvements.

In these MIMO radar systems, the transmitters and the receiver antennas are very near located so that

the targets are seen in the far field respect to the arrays. In this case the assumption that the scatters

back from the targets are the same for each pair of antennas, up to some small delay, is true. Differing

from the previous scenario, now the RCS in each transmitting path are the same. The signals gathered

in each of the antennas of the receiving array will hold the information coming from one specific

transmitting antenna each. This collocated antennas’ system will be the type that the radar system


59

under study will be using. As stated in the introduction of the document, one of the goals of the radar

system proposed is to integrate the system in a very small area, which leads us to the use of collocated

transmitter and receiver antennas.

MIMO radars can be simply defined saying that; it is a system of multiple antennas. In a MIMO radar

system there are several transmitting and receiving points, as can be seen in Fig. 36, therefore each

antenna in the transmission array independently radiates a waveform signal, which is going to be

different than the radiated from the other antennas [49]. In the receiver array, the reflected signals

belonging to each transmitter antennas are detected by the different receiver antennas. The receivers

will be able to differentiate among transmitted signals, due to the different waveforms used in the

transmitters, and create new sets of information coming from the different transmitter antennas for

each receiver, creating a virtual array.

The key aspect of MIMO radar systems lies in the assumption that all the M elements of a transmitter

array generate M signals that are mutually orthogonal. Each is radiated from M different phase centres.

Therefore, each of the antennas of the receiving array will detect all the coded signals together and

will attempt to separate them. The received waveforms will be extracted using a set of matched filters

in the receiver, and then, the information contained in each of the waveforms will be available.

Even though in most of the literature the orthogonality of the signals coming from each transmitting

antenna is assumed, it is not a requirement for MIMO radar systems, actually the main MIMO method

used for the system under study is going to use a technique that does not use different sequences for

each transmitting antenna, as it is explained in the oncoming section 2.4.3.

Fig. 36: MIMO radar system principle.


60

Using PMCW as a modulation technique for the MIMO radar system under study is a big advantage.

The use of binary symbols brings advantages for MIMO radars. MIMO radars require orthogonal

waveforms on the transmitting antennas that are going to be transmitting simultaneously. The

orthogonality is achieved with binary codes (presented in the section 2.1.5), which are simple to

modulate in PMCW with direct bi-phase modulation.

2.4.2 Virtual Array Concept

Bearing in mind a collocated MIMO system; since each waveform extracted contains independent

measurements an improved target detection performance can be achieved [50], [51]. The use of M

transmitters and N receivers in a MIMO system combined with several matching detectors, results in

the increase of antennas independent information, but, with fewer physical antennas to be used. Being

one of the main goals of the radar system design under study, the system-on-chip implementation [29],

there is no freedom of antennas’ number usage. This would lead to high hardware complexity and

increased power consumption from the extra independent channels generated by each transmitter

antenna. The use of the Virtual Array concept in MIMO radar allows keeping the advantages of the

usage of many antennas, but without using a huge number of physical antennas.

If there are considered M transmitting antennas with the waveform such as 𝑠𝑘(𝑡), the radiated

waveforms are being orthogonal such as Eq. (67):

And considering that there are 𝑁𝑟 receiving antennas, in the received each of these receiver antennas

will use a bank of 𝑁𝑡 matched filters, being 𝑁𝑡 = 𝑀. Each of these filters will extract the orthogonal

waveforms from the transmitter antennas. As a result, the number of independent signals with which

the virtual array will be defined is 𝑁𝑡𝑁𝑟 .

The target echo response in each of the 𝑚𝑡ℎ outputs of the receiver matched filters of each of the 𝑛𝑡ℎ

physical receiver antennas has the following expression [48]:

Where

𝑉𝑇 = Vector from the radar system heading the target.

𝐴(𝑡) = The echo signal reflected from the target.

𝑋𝑇,𝑚 & 𝑋𝑅,𝑛 = Phase difference given in the transmitting and receiving antennas’

locations.

𝜆 = The wavelength of the signal.

∫𝑠𝑘(𝑡)𝑠𝑚

∗ (𝑡) 𝑑𝑡 = 𝛿[𝑘 − 𝑚] (67)

𝑦𝑛,𝑚(𝑡) = 𝐴(𝑡)𝑒

(𝑗2𝜋𝜆𝑉𝑇(𝑡)(𝑋𝑇,𝑚+𝑋𝑅,𝑛)) (68)


61

The phase differences are created by the transmitting and receiving antennas locations. The target echo

response of (68) is equivalent to the responses detected by an array of NM antennas placed at the

following phase differences:

This is what is called a virtual array of NM antennas. As an example [48], in Fig. 37 there can be

observed the transmitting array (left) using 3 TX antennas and 4 RX antennas (right), each receiver

antenna uses a matched filter corresponding to each of the transmitting antennas, therefore, separating

the three of them.

In Fig. 38, the resulting virtual array is showed; it can be seen that an NM virtual array has been

created using just N + M real physical antennas.

{𝑋𝑇,𝑚 + 𝑋𝑅,𝑛|𝑛 = 0, 1, … ,𝑁 − 1,𝑚 = 0, 1, … ,𝑀 − 1} (69)

Fig. 37: Three transmitter antennas and four receiver antennas with their matched filters detectors.

Fig. 38: NM virtual antenna arrays formed with the physical antennas from Fig. 36.


62

If Fig. 37 and 38 are considered, the antennas location can be described as,

Where

𝑑𝑅 = Separation between receiver antennas

𝑑𝑇 = Separation between transmitter antennas

The targets response expression presented in (68) is now expressed as (72) [48]:

Where

𝜃 = Angle location of the target with respect to the array

The phase differences caused by the wave front heading towards 𝜃 in the transmitter and in the

receiver are related; in order to create a virtual array the distance between the transmitter antennas has

to be spared as much as the number of receivers. Therefore, the phase difference in the receiver is Eq.

(73) [48]:

And the separation between the receiver antennas depends on the number of antennas in the reception

side, if we follow the called Nyquist virtual array [48], is given by:

Substituting Eq. (73) and (74) in Eq. (72) and simplifying, the expression becomes:

If the number of receiving chosen antennas is 𝑁𝑟𝑥 = 𝑁, the set given by Eq. (69) becomes as [0,𝑁 ∙

𝑀 − 1]. Thus, the received signals of Eq. (75) become 𝑁 ∙ 𝑀 signals each of which have a phase

difference between them of 𝑃𝑑𝑖𝑓,𝑟𝑥. Consequently; it creates the virtual array of 𝑁 ∙ 𝑀 elements with

just using 𝑁 +𝑀 physical antennas. It can be thought as if the system is sampling the electromagnetic

𝑥𝑅,𝑛 = 𝑛 ∙ 𝑑𝑅 𝑛 ∈ [0, 𝑁 − 1] (70)

𝑥𝑇,𝑚 = 𝑚 ∙ 𝑑𝑇, 𝑚 ∈ [0,𝑀 − 1] (71)

𝑦𝑛,𝑚(𝑡) = 𝐴(𝑡)𝑒(𝑗

2𝜋𝜆(𝑛∙𝑑𝑅+𝑚∙𝑑𝑇)∙𝑠𝑖𝑛𝜃 )) (72)

𝑃𝑑𝑖𝑓,𝑟𝑥 =

𝑑𝑅𝜆𝑠𝑖𝑛 𝜃 (73)

𝑁𝑟𝑥 =

𝑑𝑇𝑑𝑟

(74)

𝑦𝑛,𝑚(𝑡) = 𝐴(𝑡)𝑒

(𝑗2𝜋

𝜆𝑃𝑑𝑖𝑓,𝑟𝑥(𝑛+𝑁𝑟𝑥∙𝑑𝑇)) (75)


63

wave in the spatial domain. The different samples created by the 𝑁 ∙ 𝑀 elements can be used for

getting the direction of arrival of the echoes, thus increasing the spatial resolution.

2.4.3 Outer Code MIMO

As previously stated, the waveform that is going to be used will consist on binary values mapped in a

0 or 180 degrees shift of a continuous RF signal. There exist ‘families’ of codes that were originally

developed for the communications scope whose properties are useful in the radar system under study.

If MIMO wants to be enabled, the waveforms being radiated by the different transmitter antennas must

be made orthogonal to each other. Thus, allowing the matching filters in the receiver to separate them

and so that, creating a MIMO virtual array.

The classical transmitter orthogonality approach by sequence design (code division) consists on the

use of different sequences of the same family for each of the different transmitters. The cross-

correlation properties for all delays are important, the final performance of the system will depend on

the cross-correlation properties [52]; the signals will be received with all the delays corresponding to

the ranges that the radar covers. If the codes have any non-zero cross-correlation sidelobe this will

become an energy leak from one waveform to the other during the process of detection in the receiver.

This would lead to a bad performance when it will come to the beamforming processing and to a

higher level of false alarms in the CFAR detector. The approach requires zero cross-correlation level

between the family codes, i.e., completely orthogonal. It comes out that the sequences with the desired

autocorrelation behaviour do not have the desired cross-correlation properties; therefore the classical

approach is not feasible.

Then, is when the concept of Outer Code turns out to be very useful. If the waveforms are

‘outercoded’ over the existing code sequence, i.e. with an outer code which have good cross-

correlation properties, the different waveforms will be separated in each matched filter with virtually

zero interferences, creating the wanted virtual array.

Resuming; the transmitting waveform of each antenna use one single sequence (M-Squence or APAS,

discussed in 2.1.5) of length 𝐿𝑐, identical for each of the transmitting antennas. Then, an outer

sequence is used to render the transmitting antennas orthogonal between them.

Sequences with zero cross-correlation in zero-delay exist; one common example is the Walsh-

Hadamard family of codes [53]. Hadamard codes exist for all lengths multiple of 2, from 4 to 664. The

length of the needed outer code will be the same as the number of transmitter antennas.

If there are four transmitting antennas, the transmitter of the system will look like in Fig. 39:


64

The Hadamard code in this case will be of length four, since there are four transmitter antennas,

therefore it will have 4 rows, each of them with 4 elements, as in (76):

At the receiver side of the system (see Fig. 40), for each antenna there will be a unique correlator

which will match with the S sequence (since there is just one code sent). Later on, each MIMO block

is separated in sections that, computed as dictated as the Hadamard matrix, will give the corresponding

output of each transmitter antenna.

𝐻 = [

1 11 −1

1 11 −1

1 1 1 −1

−1 −1−1 1

] (76)

Fig. 39: Transmission part for the signal generation of a MIMO outer code system.

Fig. 40: MIMO processing for one range gate in one receiver antenna.


65

2.4.4 Range Domain MIMO

With the goal of improving the performance and lower the complexity besides power consumption of

the system, another MIMO technique was implemented. The sequences used are still binary, actually,

the same type of sequences used without MIMO and with Outer Code MIMO are going to be used,

i.e., M-Sequences and APAS.

There has been discussed in the section 2.4.3 that to achieve orthogonality between the signal

waveforms there is a need to use a zero cross-correlation family of codes.

The main characteristic of this new MIMO approach is the use of just one code sequence, without any

kind of other outer code, without regard of the number of antennas transmitting at the same time.

To be able to achieve virtual array results with this new approach, the length of one single sequence S

will be longer than ‘needed’ according to the design system parameters. The sequence will be as many

times longer as the number of transmitter antennas, but it will only contain one sequence. Therefore

the new sequences will have a length:

Where

𝑆𝑟𝑑 = Range Domain sequence length.

𝐿𝑐 = Sequence length needed.

𝑁𝑡𝑥 = Number of transmitting antennas.

Each of the transmitter antennas will also need to delay the sequence certain period of time, depending

on the number of transmitting antennas, so that the sequences for each antenna are delayed an equal

time as Eq. (78):

A block diagram concept of the transmitter side of the Range Domain MIMO concept can be

observed in Fig. 41. The antennas radiate at the same time but delayed versions of the sequence with

respect the previous one.

𝑆𝑟𝑑 = 𝐿𝑐𝑁𝑡𝑥 (77)

𝑆𝑒𝑞. 𝑑𝑒𝑙𝑎𝑦 =

𝐿𝑐𝑁𝑡𝑥

(78)

Fig. 41: Transmitter side of the Range Domain Separation MIMO method with four transmitters.


66

Each of the receiver antennas will use one single correlator of full length to detect the targets. Targets

that are place further than the ambiguous range will be considered as if they are detected with another

antenna, therefore from a wrong antenna.

The receiver is going to detect the echoes with a delay of the same length as the delay of the sequence.

This will happen with all the antennas excepting for the first one. Once the whole sequence is

correlated, in each receiver there will be as many echoes in a row as transmitter antennas. For

example, if we use the transmitter side of Fig. 41. The receiver side in each of the receiver antennas

will look like in Fig. 42:

2.5 Beamforming

This section focuses on the beamforming algorithms. The technical background behind beamforming

is presented besides the particular situation for a linear phased array antenna, which is the case of the

antenna array used in the mmWave radar system under study. The beamforming techniques that are

going to be used at a given point in the radar system are also explained; the conventional techniques

and the adaptive methods.

2.5.1 Introduction

There have been discussed the ranging computation, the detection techniques and the speed

measurements; but there is another important parameter that plays a main role in the radar systems, the

angle. The angle information, alongside the distance estimation, provides the system with the complete

picture about where the detected target is located. The location of the target can be defined with three

different parameters, i.e., (𝑟, 𝜃, 𝜑), being 𝜃 the angle of the azimuth, 𝜑 the angle of the elevation and 𝑟

the range. Since the main application of the radar system under consideration is the automotive, the 𝜑

angle is going to be neglected, to focus just on the azimuth angle, 𝜃.

The radar data cube structure has three dimensions; the range domain dimension; where the data

related to each of the range bins of the radar system is contained, the Doppler dimension; where the

information related to the frequency shift is contained and the antenna phase centre dimension. The

Fig. 42: Receiver side of the Range Domain Separation MIMO method showing one receiver antenna.


67

phase centre dimension allows the study and processing of the signals in certain range bin depending

on the frequency content, which is the same as saying the angle of arrival.

Considering an antenna with a particular beam pattern 𝐵(𝜃) with big gain in 0 degrees and low gain in

all the other angles, it is clear that the antenna is very good to detect targets at 0 degrees, but not if the

target’s location is in different angles than zero. Rotating the antenna mechanically would fix the

problem, but it is space consuming, costly and slow, therefore not suitable for the radar system

application under study. Digital beamforming allows changing the beam pattern using electronic

means, with the only physical requirement of the disposal of multiple antennas.

The beamforming concept can be defined as the coherent combination of signals from several different

phase centres that help to add selectivity in the angle of arrival direction of the front wave, i.e., to

build and steer the antenna beam in the right direction in order to achieve a series of requirements, in

the presence of interfering signals and noise. The technique is appropriate just if the radar antenna is

an array with different phase centre signals, concept that will be introduced in the next section. It can

be used in TX/RX signals to/from a concrete direction, meaning that it behaves as a spatial filter [54].

In the present radar system, the beamforming technique will be just used in the receiver side of the

system, as a result what the system will be doing can be thought as a beamforming in reverse. When

performing beamforming, the signals are delayed to steer the antenna array gain in certain direction.

However, when calculating the AoA, the delay between the elements is measured and that translated

into AoA measurement. A radar beamforming receiver combines its outputs using a spatial filter such

that the reflections that are coming from the wanted direction are let go through without any

distortions. However, signals coming from other directions are attenuated.

If a wave is incoming from the angle 𝜃, the received signal in each antenna is defined as Eq. (79):

Where

𝐴(𝑡) = The echo signal reflected from the target.

𝑑 = The distance between antennas.

𝑛 ∈ [0, N-1], being N the number of antennas.

The exponential term represents the phase difference caused by the different path distances that the

wave front experiences when approaching the array from the angle 𝜃, as can be observed in Fig 43. In

order to get the signal from certain angle 𝜃, the received signals can be linearly combined as expressed

in Eq. (80) [48]:

𝑅𝑥𝑛(𝑡) = 𝐴(𝑡)𝑒

(𝑗2𝜋𝜆∙𝑑∙𝑛∙𝑠𝑖𝑛𝜃)

(79)


68

Where

𝑤𝑛 = Weighting coefficient related with the nth antenna.

𝐵(𝜃) = Beampattern of the signal.

From Eq. (80) can be extracted that 𝑦(𝑡) will achieve different gain depending on the signals coming

from different angles 𝜃. The spatial resolution of the beamformer is going to depend on the number of

antennas of the array.

There are several beamforming methods, they are classified according to the technique or the

data/criterion used. The most known algorithms involve two different groups; the conventional and the

adaptive beamformers [55]. The benefits of beamforming are diverse and involve the control of

several beams, improved range of dynamics, energy efficiency, etc.

2.5.2 Linear Phased Array Antenna

As previously stated; the use of multiple antennas is the only physical requirement in order to be able

to implement the beamforming technique. The characteristics of the individual antennas are based on

the amplitude, phase centres of the signals and their geometrical location.

The antenna’s distribution in the radar system under study is going to use uniform linear array

distribution antennas, as shown in Fig. 43. A phased array antenna samples the wavefront incoming at

each isolated antenna placement, as a result there is a need to choose in a right way the space in

between the antenna elements.

𝑦(𝑡) = ∑ 𝑤𝑛 ∙ 𝑅𝑥𝑛(𝑡)

𝑁−1

𝑛=0

= 𝐴(𝑡)∑ 𝑤𝑛

𝑁−1

𝑛=0

∙ 𝑒(𝑗2𝜋𝜆∙𝑑∙𝑛∙𝑠𝑖𝑛𝜃)

= 𝐴(𝑡) ∙ 𝐵(𝜃) (80)

Fig. 43: Geometry of a Uniform Linear Array (ULA).


69

The wavenumber [rad/m] of a signal incoming to a linear array and its spatial frequency [cycle/m]

equivalent is given by Eq. (81) [33]:

It is known that the angle of arrival can be defined from -90 to 90 degrees depending on the target

position respect to the centre of the array, therefore the spatial frequency bandwidth [cycle/m] is:

Following the Nyquist criterion it comes out that the necessary spatial sampling interval, and

therefore, the antenna’ separation must be Eq. (84) to avoid spatial frequency aliasing:

Due to the radar frequency use, 79 GHz, the allowed spacing is going to be very small. A phased array

antenna is made up of different phased radiating antennas. The front wave beams are created shifting

the phase in each antenna so that there are constructive and destructive effects that steer the signal in

the wanted direction. The main lobe will always point the same direction towards where the increasing

phase shift is heading to. Note that in this system it is just applied in the reception.

2.5.3 Conventional Methods

They are also called fixed beamformers as they are non-adaptive [55]. Their principle is focused on the

process of combination of the outputs of each signals’ phase centres to build a narrow directive gain

pattern, as seen in Fig. 44. As a result, the main lobe will be high gain and the sidelobes will be low,

translating in an improved selectivity of the echoes and at the same time the power lowering of the

scatterers coming from other directions. The conventional beamformers’ outputs work using a

weighting vector for a determinate direction of arrival (DOA) which just depends on the response of

the array [55], which are fundamentally the delays measured in each of the receiver antennas caused

by the path difference of the incoming signals. The output is simply summed up with the outputs

coming filtered from each antenna. The response does not depend on the received data; therefore they

are data independent beamformers which response is constant for all the environments. They are low

complex methods but also low resolution.

𝐾𝑥 =

2𝜋

𝜆𝑠𝑖𝑛𝜃 (81)

𝐹𝑥 =

1

𝜆𝑠𝑖𝑛𝜃 (82)

𝛽𝑥 =

1

𝜆sin (

𝜋

2) −

1

𝜆sin (−

𝜋

2) =

2

𝜆 (83)

𝑑 ≤

1

𝛽𝑥=𝜆

2 [𝑚]

(84)


70

-Delay and Sum Method

As presented in the section 2.5.1, the Delay and Sum method is a conventional method that does not

depend on the data contained in the signals. Assuming a linear array like the showed in Fig 43, and

omnidirectional antennas, the signal that each antenna will receive is expressed as Eq. (85) [48]:

Where

n = The number of antenna of the array.

d = The separation between the different antennas.

a(t) = The signal envelope.

𝜃 = The azimuth angle with which the signal is incoming the array.

The signal is combined in the receiver to obtain Eq. (86):

Where

𝑤𝑛 = The weighting coefficient corresponding to each of the antennas.

𝑟𝑛(𝑡) = 𝑎(𝑡)𝑒

𝑗2𝜋𝜆𝑛𝑑𝑠𝑖𝑛𝜃

(85)

𝑦(𝑡) = ∑ 𝑤𝑛𝑟𝑛(𝑡)

𝑁−1

𝑛=0

= 𝑎(𝑡)∑ 𝑤𝑛𝑒𝑗2𝜋𝜆𝑛𝑑𝑠𝑖𝑛𝜃

𝑁−1

𝑛=0

(86)

Fig. 44: Conventional Beamformer basic block diagram.


71

Thus, Eq. (86) shows that combining the signals, the beam patter can be synthesized and controlled

with the variations of the weighting coefficients, also called beamformer coefficients. The pattern can

be expressed as Eq. (87) [48]:

Where

𝑊(𝑒𝑗𝜔) = The Fourier Transform of the beamformer 𝑤𝑛.

It follows then, that this beamformer design can be thought as a FIR filter. The frequency resolution of

a filter depends on the filter order, equivalently, it has been shown is the section 2.5.2 that the spatial

resolution of a beamformer will depend on the number of the antennas that the array has.

-The Bartlett Algorithm

It follows the same not data dependence as the previous technique, but it improves the behaviour of

the beamformer [56]. It estimates the power spectrum over an angle using the averaging operation

over the power output of the beamformers, using the covariance operation. Each spatial filter is a

narrowband filter centred on a concrete angle. Each of the outputs of the filters are averaged over time

and normalized, providing an estimation of the power contained in this band. In other words, it

maximizes the power collected from a given angle, 𝜃. Its weight vector is defined in Eq. (88) [55]:

So that, the signal’s power spectrum at a given angle, 𝜃 is:

Where

𝑎(𝜃) is a ULA, given by: 𝑎(𝜃) = [1 𝑒𝑗𝜃… 𝑒𝑗(𝑁−1)𝜃]

The method has an approximate resolution of 100/N [57], and is characterized by being robust against

interferences and simple to implement. However, the resolution achievable is quite limited; translating

in not very sharp lobes and generation of strong side lobes.

𝐵(𝜃) = ∑ 𝑤𝑛𝑒−𝑗𝜔𝑛|

𝑤=2𝜋𝜆𝑑𝑠𝑖𝑛𝜃

𝑁−1

𝑛=0

= 𝑊(𝑒𝑗𝜔)|𝑤=

2𝜋𝜆𝑑𝑠𝑖𝑛𝜃

(87)

𝑤𝐵𝐴 =

𝑎(𝜃)

√𝑎𝐻(𝜃)𝑎(𝜃) (88)

𝑃𝐵𝐴 =

𝑎𝐻(𝜃)�̂�𝑎(𝜃)

𝑎𝐻(𝜃)𝑎(𝜃) (89)


72

2.5.4 Adaptive Methods

The idea underlying here implies the use of the data of the signals received; hence the technique is

now data dependent. They use the correlation properties among the signals received such that it is

possible to adapt the weighting vectors to the existence of noise, clutter, etc., thus optimizing the

performance. Basic block diagram can be seen in Fig. 45. These techniques have increased angle

resolution and more capabilities than the conventional beamformers. They offer higher accuracy and

resolution, but they also require higher computational complexity. The performance depends strongly

on the correct estimation of the sources (which can happen in the case of multipath fading).

-Capon Algorithm: This data dependent algorithm was proposed by Capon [58]. It is also called

Minimum Variance Distortionless Response algorithm (MVDR). The main feature of this algorithm is

to minimize the total output power of the system (including noise and other signals) but keep high that

which is heading the desired angle direction, 𝜃. The algorithm is based on the following premises [59]:

Meaning that, the system should minimize the total collected power and keep the gain in the desired

direction, 𝜃, as 1. In other words, to implement a sharp bandpass filter. Applying the previous

conditions, the weight vector is found to be [58]:

𝑚𝑖𝑛𝑤𝑃(𝑤) subject to 𝑤𝐻𝑎(𝜃) = 1 (90)

𝑤𝐶𝐴𝑃 =

�̂�−1𝑎(𝜃)

𝑎𝐻(𝜃)�̂�−1𝑎(𝜃) (91)

Fig. 45: Adaptive Beamformer basic block diagram.


73

So that, the Capon output power spectrum at a given angle, 𝜃 is:

Capon’s algorithm main advantage is that it provides with a much narrower beamwidth comparing to

conventional beamforming algorithms [60]. This goal is achieved nulling all the directions that are

close to the wanted angle. Capon algorithm has lower computation complexity than subspace based

methods, as MUSIC. However, some of the drawbacks are that the noise performance is a bit

sacrificed [61], and the resolution has still some dependence on the size of the array and the SNR.

-Multiple Signal Classification (MUSIC) Algorithm: It is a subspace based method [62], the covariance

matrix is decomposed in signal subspace and noise subspace by means of the use of eigenvectors and

eigenvalues decomposition. Basically the idea is to sweep 𝜃 and check where it makes 0.

It gives an approximation of the number of incoming signals, therefore giving their direction of arrival

[62]. The estimation is taken from either of the subspaces assuming that: the noise is highly

uncorrelated and the signal subspace is orthogonal to the noise subspace, it is expressed by Eq. (93):

Therefore, the MUSIC spectrum power is given by Eq. (94) [62]:

Where,

Π̂⊥ = �̂�𝑘�̂�𝑛𝐻

This subspaced based algorithm provides high resolution, very sharp lobes and more accuracy without

being limited by the size of the array aperture. The disadvantage is that the complexity of the

algorithm is increased. But the main drawback is shared with the Capon algorithm, and it is that; the

measured signals 𝑎(𝜃) might not be ideal at all, therefore the Eq. (93) and (94) would be degraded and

large DoAs errors would occur [55]. This can happen in realistic systems where the environment or

antennas are imprecise. Hence, the robustness of these adaptive techniques against imperfections or

uncertainties is their main drawback.

𝑃𝐶𝐴𝑃 =

1

𝑎𝐻(𝜃)�̂�−1𝑎(𝜃) (92)

𝑈𝑛𝐻𝑎(𝜃) = 0 (93)

𝑃𝑀 =

𝑎𝐻(𝜃)𝑎(𝜃)

𝑎𝐻(𝜃)Π̂⊥𝑎(𝜃) (94)


74

3 System Implementation

In this chapter, a full description of the 79 GHz PMCW mmWave MIMO radar under study is

developed. A deep description of the proposed radar system and its design parameters are presented

and their parameters’ dependences established and explained. The functioning of the digital front-end

is explained besides a brief description of the structure of the Matlab chain that is used to perform the

system implementation and simulations. All along the implementation explanations, the concepts are

justified and linked with the improvement achievements that are expected to occur in each of the

stages. In the second part of the chapter, the implementation of the MIMO methods exposed in the

chapter 2 is thoroughly described besides how the Matlab implementation manages the data. The

CFAR implementation is also developed and explained; how the algorithm analyses the data with and

without MIMO enabled and each of the algorithms implementation. The AoA implementation is also

commented. The last part of the chapter is focused in providing a general overview of the complete

mmWave radar implementation and the foreseen results; the transmitter and receiver sides are

presented together and the main system theoretical gains in each stage of the system are pointed out.

3.1 Radar System Description

In this first section, an accurate description of the system is presented. The main parameters selection

is justified; its dependence with other important system parameters is demonstrated and linked with

the radar system performance. The digital front-end of the system is deeply described and its

functioning reviewed in detail. A brief explanation of the Matlab flow and its main parts is also

revealed.

3.1.1 Overview

The goal of every radar system is to detect the presence, placement and other relevant parameters of

the targets under interest, all of it with as small latency as possible. Until recently, the applications of

these systems have not been widespread used and thus mass production has not happened. This is due

to different factors, among them; the size of the radar systems limits the number of applications where

its use could be an advantage. The nowadays technology is not a constraint anymore when it comes to

the size of the system parts or energy consumption, and there are technologies available to overcome

this historical constraint.

The goal of the radar system project presented in this document is to develop and integrate

technological solutions that lead to the drastic size reduction of a complete radar system. A full

system-on-chip like the presented in Fig. 3 (SoC) is targeted, with an integrated transceiver of four

transmission and reception antennas and an integrated digital processor mounted on a 1 𝑐𝑚2 board.


75

The reduction of the form factor would kick off the emergence of a whole new batch of applications

that could use the advantageous features of an extremely robust radar against bad environmental

conditions, such as; harsh weather situations, heat, lightning, vibrations, etc.

The automotive industry is the main targeted scope in which the research efforts are being encouraged

last years. Final application products are already in the market as [12] foresaw. Nevertheless, the

market demand pursues higher integration with lower power consumption. Once all the constraints are

overcome, the system could be integrated in never explored applications, like smart cities or consumer

devices, which would lead to a mass production and consequently, to prize reduction. CMOS

technology could supply with advantages the current radar dependability in SiGe multichip [29]. The

radar system presented is millimetre wave MIMO radar with PMCW modulation. The FMCW radar

systems present non linearities when their bandwidth is bigger than 1 GHz. In order to obtain a range

resolution better than 10 cm it is not enough with a bandwidth of 1 GHz [63], so that the PMCW

technology is needed. The choosing of this modulation will also allow the implementation of MIMO

in the code domain and no range-Doppler ambiguities.

This thesis signal processing implementation and results are focused on the automotive application

scope, which is the primary target for this radar system technology at these early stages. In particular,

the so-called short-range radars [12], which permit the detection of a person along a 30 meters range

with a resolution smaller than 10 cm. The proposed system considers a 4 GHz bandwidth with the

carrier frequency in the 79 GHz band, targeting a range resolution of 7.5 cm. The maximum speed

foreseen is around the 13 m/s (47 km/s), with a resolution around the 0.2 m/s.

Fig. 46: 3D simulation of the targeted SoC radar, featuring the size of 1 𝑐𝑚2 [9].


76

3.1.2 Required System Parameters

Being the application focus put in the automotive scope, the parameters need to be set according to the

needs that the constraints of the scenario involve. Table 1 defines the main radar system parameters.

Table 1: Summary of the main PMCW radar system parameters.

Parameter Symbol Value Unit

Carrier Frequency 𝐹𝑐 79 GHz

Bandwidth 𝐵𝑊 4 GHz

Sampling Rate 𝑅𝑐 2 Gsps

Range Resolution 𝑅𝑟𝑒𝑠 75 mm

Unambiguous Range 𝑅𝑚𝑎𝑥 37.5 m

Maximum Unambiguous Velocity 𝑣𝑚𝑎𝑥 12.86 m/s

Velocity Resolution 𝑣𝑟𝑒𝑠 0.25 m/s

The large bandwidth configuration implies two major drawbacks in the system; the need of high speed

ADCs (which imply the use of big amounts of energy), and high levels of noise. The sampling rate

needed is 2 Gsps [29] and the only way to keep the ADC power consumption low is to set the ADC at

a low resolution. Short-range radar to detect pedestrians demonstrates [64] that it is enough to use a 4

bits ADC, since it does not present degradation. The problem of the high noise levels can be

diminished with the use of signal processing algorithms in order to increase the SNR level. The

processing gain methods and implementation will be explained and shown in each of its stages all

along the present Chapter 3. The achievement of signal gain by means of digital processing implies a

very demanding digital implementation on chip, thus, the advantages of CMOS technology in 28 nm

will be used [29].

-Parameters Dependence: To reach the main system parameter’s values there are other dependent

parameters which need to be calculated or adjusted according to their dependence.

The dwell time, is the total time that the system takes to process a batch of data, the time elapsed

between the start of one data batch and the start of the next one. The dwell time is going to depend on

many other system’s parameters and their variation will always modify this value. In the system under

study is given by Eq. (95) and represented in Fig. 55 [page 89]:

𝑇𝑑 = 𝑇𝑐 ∙ 𝐿𝑐 ∙ 𝑀 ∙ 𝑁 (95)


77

Where,

𝑇𝑑 = Dwell Time

𝑇𝑐 = Chip Duration

𝑀 = Number of accumulations

N = Number of FFT points

The Chip Duration (𝑇𝑐), is the time duration of each of the code chips, see Fig. 47. It depends on the

sampling rate of the system as Eq. (96) and is represented in Fig. 47. Being that the sampling has been

set to 2 Gsps:

Ultimately, the range resolution (see Fig. 48) is going to be fixed by the chip rate, so it should be as

high as possible in order to provide fine resolution, in this case the dependent range resolution is given

in Eq. (97):

The unambiguous range of the radar (see Fig. 48) is the maximum distance that the system will be

able to process without ambiguities; it depends on the repetition frequency of the pulse, or sequence

(since the system works in CW with sequences). The unambiguous range is given by Eq. (98):

𝑇𝑐 =

1

𝑅𝑐=1

2𝐺= 0.5 𝑛𝑠 (96)

𝑅𝑟𝑒𝑠 =

𝑐

2𝑅𝑐=3 ∙ 108

2 ∙ 2𝐺= 0.075 𝑚 (97)

𝑅𝑚𝑎𝑥 =

𝑐

2𝑃𝑅𝐹=𝑐𝑃𝑅𝐼

2 (98)

. . .

LCxTC

TC

Fig. 47: Chip duration for each sequence 𝐿𝑐 symbol.


78

The Pulse Repetition Interval (PRI) or its equivalent PRF, is the time that takes a whole pulse

(sequence) to be transmitted. Using PMCW the pulse length is given by the sequence number of chips

(Fig. 47). Since the chip rate is already known in Eq. (96), the PRF can be defined as Eq. (99):

The system requirement for the maximum unambiguous range was set to 𝑅𝑚𝑎𝑥 = 37.5 𝑚, according

to the Table 1. So that, clearing the PRF in Eq. (98) results in a minimum PRF of 4 MHz which

translates, after substituting and clearing in Eq. (99), in a code length (𝐿𝑐) of at least 500 symbols. In

the section 2.1.5 of the Chapter 2, several codes have been described to be coded as the PMCW

waveform.

The waveform used is going to be initially considered an APAS code, which characteristics mean the

need of a code twice times as long as the initially needed (see section 2.1.5). Therefore, the necessary

sequence length will be set to 𝐿𝑐 = 1000.

𝑃𝑅𝐹 =

𝑅𝑐𝐿𝑐

(99)

Radar System

Fig. 48: Unambiguous range detection field of a radar system.


79

By the other hand, the velocity resolution of the system is set to be 𝑣𝑟𝑒𝑠 = 0.25 𝑚/𝑠, which is the

resolution with which the system will be able to differentiate the speed of a target. The velocity

resolution is defined in Eq. (100):

Where

𝜆𝑐 = Wavelength of the RF carrier

Given the working frequency of the radar band at 𝐹𝑐 = 79 𝐺𝐻𝑧, the wavelength results as Eq. (101):

So that, after substituting (101) in (100) and clearing for the dwell time, it results on 𝑇𝑑 ≈ 10 𝑚𝑠.

Having this dwell time between one processing period and the next one, and knowing the size of a

range gate from Eq. (97), leads to know the maximum speed at which a target can cross a range gate

without ambiguous measurement:

Meaning that the maximum equivalent Doppler frequency at which the system will be able to detect a

moving target will be 𝑣𝑚𝑎𝑥 = 7.5 𝑚/𝑠.

The number of FFT points N, is the number of points that the FFT will need to have in order to

implement a “bank of filters”, thus filtering the equivalent Doppler spectrum (an interval from 0 to the

maximum detectable speed, 𝑣𝑚𝑎𝑥 = 7.5 𝑚/𝑠). N needs to be chosen so that the filter width is narrow

enough such that the achievable speed resolution is 𝑣𝑟𝑒𝑠 = 0.25 𝑚/𝑠. In order to compute the number

of FFT points, we need to know the number of intervals (Doppler bins) that need to be filtered and

take into account that the value can be positive or negative (depending on whether the target is

approaching the radar system or getting further), which implies a factor 2. Then, the closest upper

integer power of 2 needs to be found, so the condition is always accomplished and the implementation

in hardware is efficient, resulting in Eq. (103):

𝑣𝑟𝑒𝑠 =

𝜆𝑐2 ∙ 𝑇𝑑

(100)

𝜆𝑐 =

𝑐

𝐹𝑐=3 ∙ 108

79𝐺= 0.038 𝑚 (101)

𝑣𝑚𝑎𝑥 =

𝑠

𝑡=0.075

0.01≈ 7.5 𝑚/𝑠 (102)

𝑁 = 2

⌈log22∙𝑣𝑚𝑎𝑥𝑣𝑟𝑒𝑠

⌉= 128 (103)


80

So that, for the previously parameters set and the computed frequency values, the number of needed

N-points is 128. The implications of this number will be explained later in succesive sections.

Checking the Eq. (95), it can be noticed that all the parameters are already known, excepting M. In

order to make all fit and work according to the specifications, the accumulation parameter need to be

adjusted. Substituting all the previous parameters in Eq. (95) and clearing for M, it results in Eq. (104):

There are needed 150 accumulations in order to achieve the desired parameters, meaning that the

𝐿𝑐 sequences will be repeated 150 times each time.

Since there have been some adjustments and rounding in the parameters choosing, the calculation to

the back should be done to get the final values, which are given in Table 2.

The previous parameters are related to three different digital signal processing operations that will

allow the functioning of the radar main features, granting the SNR improvement by means of signal

processing gain in the receiver side of the system. The blocks involved in the digital front-end gain

are; the correlators, the accumulations and the Doppler processing. They are described further in the

section 3.1.3.

The processing gain achieved in each of these operations is given by the previous parameters. In the

case of the parameters of the example:

- Processing gain before the FFT, 𝐺𝑝𝑟𝑒𝐹𝐹𝑇 = 10 log10(𝐿𝑐 ∙ 𝑀) = 52 𝑑𝐵

- Processing gain after the FFT, 𝐺𝐹𝐹𝑇 = 10 log10(𝑁) = 21 𝑑𝐵

- Total processing gain, 𝐺𝑃𝑜𝑠𝑡−𝑃𝑟𝑜 = 73 𝑑𝐵

Even though the processing gain is high, it is not going to be enough in certain detection situations.

More processing gain will be needed. The use of the radar equation developed in the Chapter 2, Eq.

(18) demonstrates this statement:

Taking as a theoretical example a system of a single antenna radiating with a transmitter power

𝑃𝑇 = 10 𝑑𝐵𝑚 and a target located at 30 m, with an RCS of – 8 dBsm(equivalent to a pedestrian [38]),

considering the gains of the antennas G = 0 dBi, and free space path loss, the power received would be

as little as 𝑃𝑟 = −139 𝑑𝐵𝑚. Using Table 1 parameters, the noise power with at the output given by

[63] is around -72 dBm. The results show off a theoretical final SNR of 6 dB, clearly pointing the need

of further processing gain. Similar results can be checked in the simulations Chapter 4.

𝑀 =

𝑇𝑑𝑇𝑐 ∙ 𝐿𝑐 ∙ 𝑁

= 156.25 ≈ 150 (104)


81

Table 2: Final Values of the Parameters after recalculation.

Parameter Symbol Value Unit

Carrier Frequency 𝐹𝑐 79 GHz

Bandwidth 𝐵𝑊 4 GHz

Sampling Rate 𝑅𝑐 2 Gsps

Range Resolution 𝑅𝑟𝑒𝑠 75 mm

Unambiguous Range 𝑅𝑚𝑎𝑥 37.5 m

Dwell Time 𝑇𝑑 9.6 ms

Sequence Length 𝐿𝑐 1000 chips

Coherent Accumulations M 150 []

FFT Size N 128 Doppler Bins

Maximum Unambiguous Velocity 𝑣𝑚𝑎𝑥 12.97 m/s

Velocity Resolution 𝑣𝑟𝑒𝑠 0.2 m/s

-Other Dependencies: The dependencies of the main system parameters have been described above.

The parameters are dependent on each other and the modification of one of them in order to improve

certain feature performance, would lead to the variation on another parameter that would contribute to

a performance dropping on another system feature. It is important to be aware on which effects would

take the variation of each of the parameters in the system. Usually, the main design parameters of the

system are set and all the other parameters that depend on them are calculated. If for any reason some

of the design parameters are not possible to be reached (energy consumption, processing complexity,

etc), a trade-off needs to be made adjusting their dependent parameters.

Following there are going to be exposed some important radar system parameters’ equations that will

demonstrate their dependency with the variation of other system variables.

Doppler Range and Resolution:

Where,

𝐹𝑑𝑟𝑒𝑠 = Doppler frequency resolution

𝐹𝑑𝑎𝑚𝑏 = Ambiguous Doppler frequency

𝐹𝑑𝑟𝑒𝑠 =

𝑅𝑐𝑀 ∙ 𝑁 ∙ 𝐿𝑐

=𝑃𝑅𝐹

𝑀 ∙ 𝑁 (105)

𝐹𝑑𝑎𝑚𝑏 =

𝑅𝑐2 ∙ 𝑀 ∙ 𝐿𝑐

=𝑃𝑅𝐹

2 ∙ 𝑀 (106)


82

Or their speed equivalents:

As can be noticed from the equations above, the Doppler frequency resolution depends on the number

of accumulations and number of FFTs that are performed, but so it does from the chip rate. The higher

the chip rate, the more number of accumulations and N points will be needed to reach a fine Doppler

resolution, if the 𝐿𝑐 is kept. This is because there will be more samples to take as M and N increase.

The dwell time, as stated in Eq. (95), depends on the numbers of M, N and 𝐿𝑐, since the bigger the

number the more time the system needs to transmit it. Therefore, if the dwell time 𝑇𝑑 is a parameter

that constraints the system, it will affect the frequency resolution, given that M, N and 𝐿𝑐 depend on it.

The frequency resolution computed with the Table 2 data would result in; 𝐹𝑑𝑟𝑒𝑠 = 104.16 𝐻𝑧.

Therefore the system would be able to differentiate frequency shifts with each 104.16 Hz. The speed

resolution is its equivalent and the factor 2 indicates the possibility of a positive or negative speed in

the spectrum, thus resulting in; 𝑣𝑟𝑒𝑠 = ±0.197 𝑚/𝑠. This value can be affected by the windowing

performed in the FFT when it comes to the simulation of the system.

The ambiguous Doppler frequency is not going to depend any longer on the number of the FFTs, but it

does on the number of accumulations, which will mark the maximum time period along which the

system is able to detect a frequency change. Equivalently in Eq. (108) the maximum speed is

calculated. The factor 2 indicates again the separation in the spectrum in negative and positive speeds

depending on whether the target approaches of leaves. Eq. (106) stands for the achievement of a

maximum Doppler frequency shift free of ambiguities, the factor 2 is found for the need to accomplish

the Nyquist sampling theorem. It is known that the Doppler sampling rate, 𝐹𝑠,𝐷𝑜𝑝, is given by Eq.

(109). The sampling rate needs to be 2 times the bandwidth of the signal, here given by the

unambiguous frequency 𝐹𝑑𝑎𝑚𝑏.

If the parameters of the Table 2 are applied the Doppler ambiguous speed would be 𝐹𝑑𝑎𝑚𝑏 =

6.67 𝐾𝐻𝑧, meaning that the maximum frequency shift able to be detected cannot be higher than this

frequency change. The maximum Doppler speed would be 𝑣𝑚𝑎𝑥 = 12.66 𝑚/𝑠. Being the Doppler

sampling frequency equal to 𝐹𝑠,𝐷𝑜𝑝 = 13.33 𝐾𝑠𝑝𝑠, which accomplishes Nyquist for a signal of 6.67

KHz bandwidth.

𝑣𝑟𝑒𝑠 =

𝐹𝑑𝑟𝑒𝑠 ∙ 𝜆

2=

𝑅𝑐 ∙ 𝜆

2 ∙ 𝑀 ∙ 𝑁 ∙ 𝐿𝑐 (107)

𝑣𝑚𝑎𝑥 = 𝑣𝑎𝑚𝑏 =

𝐹𝑑𝑎𝑚𝑏 ∙ 𝜆

2=

𝑅𝑐 ∙ 𝜆

4 ∙ 𝑀 ∙ 𝐿𝑐 (108)

𝐹𝑠,𝐷𝑜𝑝 =

𝐵𝑊

𝑀 ∙ 𝐿𝑐 (109)


83

Unambiguous Range and Resolution: The following equations have been developed previously.

They show that the resolution in the range is determined by the bandwidth, as discussed in Chapter 2,

and that the maximum range depends on the length of the pulse or sequence in the system. The

sequence duration is, as seen in Fig. 49 given by Eq. (112):

Therefore, the maximum unambiguous range depends on the length of the sequence (the number of

chips), sn the case studied before, 𝐿𝑐 = 1000. The longer the sequence, the more ranges the system

will be able to interpret without ambiguities. Nevertheless, it has to be taken into account that if APAS

sequences are used, the practical range is going to be reduced to half due to the properties of this type

of code. Consequently, the signal waveform after being processed will have half-length and so that

half of the maximum ambiguous range. 𝑅𝑎𝑚𝑏 also depends on the chip duration, which is the time

value that takes to a chip of the sequence to be processed, and comes given by the sampling speed:

𝑅𝑟𝑒𝑠 =𝑐

2 ∙ 𝐵𝑊 (110)

𝑅𝑎𝑚𝑏 =

𝐿𝑐 ∙ 𝑇𝑐 ∙ 𝑐

2 (111)

𝑆 = 𝐿𝑐 ∙ 𝑇𝑐 (112)

𝑇𝑐 =

1

𝑅𝑐 (113)

Fig. 49: One PMCW sequence with a certain chip period.


84

In the case of the Table 2, the chip duration would be 𝑇𝑐 = 0.5 𝑛𝑠. A slow sampling rate would

provide a larger range but a wider range resolution and vice versa.

Once the range resolution and the ambiguous speed are available, one can calculate how long it will

take to cross a range gate in the limit situation, i.e., when a target moves as fast as the system is

capable to detect. This value should match with the system dwell time. From Eq. (95) and Eq. (108) it

appears that:

As it has been seen above, the change of a parameter has an effect in the whole system. However, the

range and Doppler domains are independent due to the use of pulse compression with PMCW, and its

selection can be managed independently.

In the following figures, the interpretation of the results from the previous equations can be observed;

the side lobes of the matched filters response have been neglected for simplification purposes.

As introduced in the section 2.2.4, the ambiguous Doppler frequency can be thought as a limited

bandwidth signal with its ranges set to the maximum frequency shift of a target, both negative and

positive limits. The Doppler frequency resolution can be thought as a series of narrow filters among

the bandwidth of the signal, the more FFT points the more resolution will the filters have and

therefore, the system will be able to differentiate among smaller frequency shifts (different velocities)

with a higher resolution. As seen in Eq. (106) the ambiguous Doppler shift, which gives the maximum

speed at which a target can be detected without ambiguities, is given by the PRF of the system. After

implementing the M accumulations, the system has a PRF equal to:

In Fig. 50 is shown a representation of the maximum frequency window that the system will be able to

process given the time that the PRF will require to process a single sequence, taking into account the

accumulations, and with a one half factor for both signs Doppler shifts. The maximum frequency

range possible to detect after the FFTs is then given by Eq. (116):

As the number of N repetitions increase, the number of ‘filters’ also increases inside the same size of

Doppler unambiguous range and therefore, the Doppler resolution increases.

𝑅𝑟𝑒𝑠𝑣𝑎𝑚𝑏

=2 ∙ 𝑀 ∙ 𝐿𝑐 ∙ 𝐹0(𝐵𝑊)2

≈ 10 𝑚𝑠 (114)

𝑃𝑅𝐹 =

1

𝑇𝑐 ∙ 𝐿𝑐 ∙ 𝑀 (115)

[

−1

2 ∙ 𝑇𝑐 ∙ 𝐿𝑐 ∙ 𝑀 ;

1

2 ∙ 𝑇𝑐 ∙ 𝐿𝑐 ∙ 𝑀] (116)


85

Fig. 50: Relation between the unambiguous Doppler frequency and the dwell time.

The Doppler filter bank is implemented using FFTs. If the size of the FFT is N, each of the bins of the

FFT has a frequency width 𝐹𝑑𝑟𝑒𝑠, which is the Doppler resolution frequency in Eq. (105).

Consequently, the total Doppler bandwidth available is 𝑁 ∙ 𝐹𝑑𝑟𝑒𝑠, but the bandwidth is used for both

positive and negative Doppler shifts Therefore the effective Doppler effective bandwidth is half.

Fig. 51: Relation between the number of N and the narrowing of the filter in the Doppler bank filter.

The Doppler filter bank is able to determinate the moving speed of a target as long as the Doppler shift

is less than half of the bandwidth of each filter, i.e., 𝐹𝑑𝑟𝑒𝑠/2. In the case that the speed of a target is

high enough the detection ‘falls’ inside the adjacent the consecutive filter, creating a speed

measurement error with a maximum error equal to 𝐹𝑑𝑟𝑒𝑠/2. In the case of detection of a single target,

just one of these frequencies will contain the target complementary phase that will allow the rise of the

maximum possible value of the signal, therefore showing a detection peak in the correspondent

frequency shift.

S S∙ ∙ ∙

M sequences = 1 x PRF

S S∙ ∙ ∙ S S∙ ∙ ∙

N=1 N=2

After matched filter and FFTAfter matched filters and FFTs

S S∙ ∙ ∙ S S∙ ∙ ∙ S S∙ ∙ ∙∙ ∙ ∙

N=1 N=2 N

∙ ∙ ∙∙ ∙ ∙

After matched filters and N-FFTs


86

3.1.3 Digital Front-End

The mmWave Radar development in IMEC is a wide project with different working areas; the present

document has described a part of the system design area of the project. This area includes: digital

front-end, digital back-end, analogical & mmWave, antenna & packaging and target propagation parts,

as can be observed in Fig. 52.

The parts of the system design involved in the present document include elements of the digital and

algorithms parts. The digital part of the Fig. 52 is considered the digital front-end of the system and

the algorithms part is considered the digital back-end of the system. In these sections is where this

document is focused in. The design, implementation and simulation of the digital part are the previous

steps to the chip implementation and is of vital importance in order to obtain good demo outcomes.

Digital front-end is called to the processing of the data from the moment it leaves the ADC converter

until it is ready to be interpreted, and vice versa. While, digital back-end is called to the treatment and

processing of the obtained data in the digital front-end output in order to get useful information or

improve the digital processing of the system. In Table 3 there are some of the functionalities that are

included in the digital front-end and digital back-end of the radar system.

Fig. 52: System design structure of the mmWave radar project.


87

Table 3: Some of the functionalities that are included in the digital front end and back end of the radar system.

Digital Front End Digital Back End

Tx Waveform generation CFAR Processing

Rx correlator, accumulator, MIMO Targets location and classification

Radar Data Cube generation DoA estimation

System parameters adjustment Display of information

The PMCW radar system digital front-end under study is elementarily summarized in the block

diagram illustrated in Fig. 53. The transmitter TX uses the binary code of length 𝐿𝑐 in order to

modulate the RF carrier with a chip rate 𝑅𝑐. The sequence is mapped onto 0 or 𝜋 phase shifts in the

CW signal. The technique is known as direct-sequence modulation.

The used LO is the same in the transmitter and in the receiver RX, therefore the signal is down-

converted using the same RF carrier, thus the received data is referenced. This signal enters the

matched filter described in the section 2.2.2, which is a correlation operation with the same sequence

that was mapped in the transmitter. This is a known sequence, therefore it will present a correlation

peak in the case that the signal being processed is the signal wanted at the moment of sequence perfect

alignment.

Fig. 53: Basic block diagram of the PMCW radar system under study.


88

The code is delayed certain 𝜏 time (𝑇𝑐), one sequence chip, belonging to each range gate. Thus, the

echoed signal at certain range gate will encounter the same sequence delay as delayed code, depending

on the range where the target is located. In the transmitter part, the sequence has been transmitted not

just once, but M times, as seen in Fig. 54. Therefore, the M received sequences are accumulated, and

by these means, the SNR is substantially increased.

After the accumulation, the next operation is a Discreet Fourier Transform (DFT) of N points. This

will allow the system to present the information in the frequency domain, allowing the frequency

shift’s detection and, thus, the speed estimation of the targets detected. In order to be able to do this,

the M sequences need to be sent as many times as N-FFT points will be performed by the FFT in the

receiver, as seen in Fig. 55.

Once in the receiver, the total N times M sequences are processed and there will be N points available

to perform the FFT. The problem is that performing using the processing showed in the previous

explanation, there is just the possibility to process the detections in a certain pre-tuned range gate

where the delayed sequence is set. This is because the cross-correlation of the sequence with the signal

received will only present a high peak, indicating a detection, when the code and the signal are

perfectly aligned, i.e., for zero lag. Therefore, for all the other range gates there will not appear a peak

even though there could be other detections.

Fig. 55: Radar system transmitting the needed N times M sequences repetition.

Fig. 54: Repetition of the transmitted sequence, S, a number of M times.


89

To fix this issue, the sequence should be delayed as many times as range gates are expected to be

covered. Therefore, each delayed sequence would be useful in order to detect all the possible targets in

one concrete range gate. In order to implement this solution, a bank of correlators is a good solution,

as seen in Fig. 56:

The implementation of multiple correlators can be done in parallel, so that, the range scans are

processed simultaneously. Each correlator spacing (sequence delay) is equal to the range resolution.

This means that the processing described for Fig. 53 one time, is now done 𝐿𝑐 times simultaneously,

one for each range gate. Taken as an example a PMCW radar system with the parameters of the Table

2, there should be implemented 1000 (500 if the sequence used is APAS) parallel correlators with their

corresponding accumulations and 500 parallel FFT operations of 128 points each, in order to extract

the Doppler domain data. Since all the correlators are digitally operated in parallel there are no

theoretical limits regarding to the quantity of targets that can be detected simultaneously.

The correlator performs the correlation and integration of the pulses, as explained in the section 2.1.5,

acting as a matched filter for the whole sequence and as an integrator with each of the “subpulses” that

the sequence 𝐿𝑐 is made of (Pulse Compression presented in section 2.2.2). The code length signal

values are integrated (𝐿𝑐) by means of the correlation. Then coherently accumulated when taking the

next M sequences of the same range gate branch and summing up their values. In the end of this

process there will be left one only value. This operation is going to happen as many times as parallel

range gates branches are available. After a period 𝑀 ∙ 𝐿𝑐 ∙ 𝑇𝑐 there will be 𝐿𝑐 values ready to be further

processed, one per range gate branch.

This process is going to be repeated as many times as the number of points set for the FFT. Using as

an example the data of the Table 2, it is N=128. So we will be able to get a FFT of 128 points along

each range gate. After a period 𝑀 ∙ 𝐿𝑐 ∙ 𝑇𝑐 ∙ 𝑁, which is equal to the system dwell time, there will be

available 128 data points for each range gate. After the performance of the FFT, the Doppler

frequency shifts will give out the speed of the targets detected in each of the range gates.

Fig. 56: Digital front-end with a bank of parallel correlators for PMCW radar system [20].


90

In order to have a clearer idea of the detailed radar system processing concept, in Fig. 57 can be

observed a broad example of a couple of targets being reached by the radar waveforms and their

subsequent reflected signals, in Fig. 58.

Fig. 57: Transmitter part of a radar system reaching two targets at different range gates.

In Fig. 57 there is a representation of two targets situated at different range gates. The target 1 is

located in the range gate 3, while the target 2 is situated in the last range gate. Both of the sequences S

are in reality the same transmitted signal, shown in different places for better understanding purposes.

The signal reaches first the target 1, since it is located in RG #2. Even though there is just one

sequence depicted, the signal flow keeps being sent M times for accumulations and N more times for

the N-FFT later processing, for each dwell time, as seen in Fig. 55.

In Fig. 58 the echoes reflected from the targets and clutter, have been already generated and are

coming back to the radar system to be processed with the parallel range gate processing. The grey

blocks represent the echoes that did not find any target in their way (so, there is no echo, or just noise).

For simplicity purposes, just the 2 first echoes, belonging to possible targets in the two first ranges

gates, are depicted. Since there was not target in either of those range gates, just noise or clutter will be

processed. The same for the rest of reflections, excepting for those of the echoes caused by the targets

1 and 2. The target 1 is found in the third range gate, therefore its echo starts to arrive to the receiver

3 ∙ 𝑇𝑐 seconds later. The target 2 creates an echo from the range gate 𝐿𝑐, therefore its echo is delayed

𝐿𝑐 ∙ 𝑇𝑐 when it starts to arrive input into the receiver.

Due to the time difference caused by the echoes in the different locations of the targets, the detection

will be produced in a different range gate. The target distance will be calculated in the receiver,

performing a range resolution which is equal to Eq. (97).

Target 1

RangeGates #0 #1 #2 #3 #4 #5 #6 #7 #8 #9 #10 #11

TX

#

Target 2

∙ ∙ ∙

S

S

∙ ∙ ∙


91

Fig. 58: Receiver part of a radar system echoing the signals from the two targets of the Fig. 56.

Once the echoes are sampled by the ADC and are ready to be processed, the parallel range gate

processing starts with the matched filtering of each of the echoes and for each of the range gates of the

unambiguous range.

Parallel range gate processing: The processing of the echoes arriving from the targets happens as

follows; the sequence generator shares with the receiver the same sequence as the used for the

mapping of the RF carrier in the transmitter. Each of the branches of the receiver represents the

possible detection in a different range gate of the unambiguous maximum range field. For each range

gate detector, the sequence is delayed by one chip, so the first branch sequence will be delayed once

and the last branch will be delayed as much as the length of the sequence minus 1, as can be seen in

Fig. 59.

RX

. . .

S SS SS S

S

t=0

∙ ∙ ∙

1

#1#2

#3

Echo from Range Gate:

#

∙ ∙∙

∙ ∙ ∙∙ ∙ ∙


92

As the echoes are arriving to the receiver antenna and after the ADC, they are correlated with their

correspondent delayed original sequence signal. It means that if the target was located in the first

range gate, it will be detected in the first correlator branch of the correlator bank. The sequence with

which is correlated is just delayed by one chip. When a correlator gives out a powerful peak is because

the signal was echoed by a target or clutter, having then a likely detection in the distance

corresponding to the range gate where it has been detected. The range resolution is known; therefore

the range is easily computed.

Focusing in Fig. 60, there is a more detailed block diagram with the process; the first range gate 0

would expect an echo which is delayed by 0, therefore the sequence with which is evaluated is the

same sequence without any delay. Since there is not a target in the range gate 0, there will not be any

target signal coming from range gate 0, i.e., delayed by 0. The matched filter output for the branch of

the RG #0 will not show a detection peak, just some noise or/and clutter.

Fig. 59: Complete parallel range gate processor block diagram of a PMCW radar.


93

The branch associated with the RG #1 will show the same behaviour than all the other branches where

a target is not present in their respective range gate, therefore a strong peak will not be detected.

However there was a target located in the RG #2; as previously stated, the signal coming back

reflected from the target 1 will have a delay of two chips, corresponding to the 2 range gates of

distance where it is located. When the signal will be perfectly aligned with the delayed code of the

branch associated with the RG #2, the matched filter will present a peak; therefore a target will have

been detected in the range gate 2.

Fig. 60: Detailed parallel gate processing for the example of the Fig. 58.

. . .

. . .

. . .

. . .

. . .

. . .

. . .

1

1

1

1

. . .

. . .

Branch RG #0

Branch RG #1

Branch RG #2

Branch RG #Lc-1

. . .

SequenceGenerator

Code length Lc

Rc

Rc

RX

TX


94

The target 2 is located in the last unambiguous range gate, therefore its echo reaches the detector with

a delay of Lc-1. When the delayed original sequence is perfectly aligned with the echo it will produce

a peak and, therefore, a likely detection when applying CFAR later. The sequences keep arriving M

times to be summed up, then at the end of the process of pulse compression plus integration, a single

value will be kept at the output of each of the parallel range gate processing branches. If there has been

a detection in the branch, the value will have big amplitude, otherwise the value will just carry noise or

clutter, which are expected to be of a low amplitude.

3.1.4 Simulation Chain Structure

In order to simulate the PMCW radar system explained in the sections above, the system has been

implemented in Matlab software. The radar system is analyzed working with simulations operated

using an end to end Matlab simulation chain. The simulation chain bears in mind the complete system;

the system parameters besides their dependent parameters, the waveform specific design, the chip

implementation, the targets and their specifics, the channel propagation effects and environment

scenario. The Table 4 includes the relation of content of each part of the Matlab chain structure.

Table 4: Matlab chain parts and main functionalities.

Part Main Utilities

Scenario - System main parameter’s definition

- Simulated targets parameters

Analog Part & mm

Wave

- TX analog baseband

- TX analog RF & Mixers

- PLL

- RX analog baseband

- RX analog RF & mixers

- Spillover

Antenna - TX antenna array

- RX antenna array

Digital Part

- Signal Waveform generation

- Dependent parameters adjustment

- Receiver Implementation

- Data processing

- Data interpretation

Algorithms

- RX Doppler bank

- MIMO

- CFAR

- DoA

During the development of the thesis, the work has been focused in the development and improvement

of the Matlab code in the parts of: Digital, Algorithms, Antennas and Scenario. Most of the work has

taken place in the algorithms part with the development of radar CFAR, different MIMO processing


95

methods, DoA algorithms, the receiver processing implementation, the data structures management

and interpretation, and the display of the results in a user friendly and intuitive way.

In the diagram of the Fig. 61 the Matlab chain flow of the PMCW MIMO radar can be observed in

detail.

There can be differentiate three main levels of the chain; the “script” (in purple), which runs the

simulation and sets the parameters design values introduced by the user. The “Dependent Parameters”

and “Main” functions (in blue), use the data provided by the script to complete the initialization of the

needed parameters and the simulation flow. The script calls the functions that simulate the system

itself depending on the previous two levels (in green).

Fig. 61: Matlab chain PMCW radar simulation flow.

SCRIPT

DependentParameters

MAIN

- Doppler Resolution / Ambiguity- Range Resolution / Ambiguity- Sequence Generation- MIMO parameters- Theoretical SNRs- CFAR parameters- Beamforming parameters- Other PMCW dependent params.

- Scenario- Regulation- Specifications- Targets- Digital FE- CFAR- PMCW- FMCW- Digital BE- Analog FE- Antenna- Quantization

Selection of System Design Parameters

Calculation of System design dependent parameters

Transmitter Propagation Receiver Digital RX FE Digital RX BE

- SISO/MIMO signal forming.

- Initialize Objects

- Noise effectsgeneration in TX

- Pulsetransmission

- Updating targetspositions.

- Pulse radiation

- Pulse propag.

- Reflection of pulse in the targets

- Add simulatedspillover/noises

- Collect echoes

- Link budgetverification

- Data saving of simulated signal

Correlation

Accumulation

MIMO Processing

Radar Data Cube saving

Doppler Processing

RoughBeamforming

CFAR detector

DoA Processing

SNRscalculation

Display simulation

results


96

-Script: In this function is where all the Matlab chain simulation starts. It is the place where all the

constant parameters and system main parameters are defined and set. It initializes all the structures’

parameters of data that are going to be needed during the simulation chain. The data structures are

declared to contain preset parameters but they will also increase their size with new parameters as the

simulation execution is running. The data structures declared are the following: Scenario, Results,

Regulation, Specifications, Targets, Digital front-end, CFAR, PMCW, FMCW, Digital Back-End,

Analog Front End, Antenna and Quantization. Once all the parameters are set, the script itself calls for

the calculation of the dependent parameters.

-Dependent Parameters: This function calculates the parameters that are going to depend on the

previously set main parameters. Including the scenario dependent parameters, the Doppler and range

resolution/ambiguous system parameters, the sequence generation, the MIMO processing adjustments

(in case that MIMO is used), the Beamforming parameters, CFAR factors, the calculation of the

theoretical SNR levels in different points of the chain and all the other PMCW dependent parameters

that are likely going to be further used in the execution chain. It also displays a resume of the main

system parameter’s values before returning the execution to the script function.

-Main: Once all the system parameters are set, the main function is called from the script. If there is

not data saved from a previous simulation, a real simulation starts, otherwise it loads the data to be

only interpreted. The simulation starts with the initialization of some system objects (explained further

in the section 3.5). The transmitter part is called to generate the transmitter wave, and then the

waveform is prepared to be propagated through a simulated channel. Once the propagation simulation

is done, the receiver part comes into play. It simulates the possible noises and interferences and the

reception of the echoes from the targets that were previously set. The simulated data information is

then saved to possible future loadings. Coming up next, the analog receiver and digital receiver front

run. The PMCW receiver function is called to process the received signals and fill up the radar data

cube in order to have the information well organized for entering the algorithms part. Then, the MIMO

processing takes places, if activated. After, the data is ready to be processed in the Digital Back-End

part, including the range and Doppler estimation, the CFAR detector, the DoA processing and the

display of the results.

-Transmitter: The signals are generated using the created sequence. The generation of a SISO radar

signal will be different than that of a MIMO. The MIMO will also vary its waveform generation

depending on the MIMO type chosen: Range Domain or Outer Code. The system objects are

initialized using the chosen parameters of the script in order to enable the simulation. At the same

time, if the user has chosen to add noise effects in the transmitter, those will be added to the created

waveform and finally the pulse will be simulated to be sent.


97

-Propagation: The propagation will take care of the time changing situation of the targets in order to

achieve a fine simulation. It will also take care of the pulse propagation through a free space

environment and the simulation of the radiation itself, depending on the type of antenna/s chosen in

the transmitter/receiver parts. It will also simulate the reflection of the waveform given the targets

settings and its way back through a free space environment.

-Receiver: If the user has set the adding of spill-over effects or receiver noises, those will be added to

the collected signal here. The link budget of the system is also verified in the receiver part. All the

flow of data simulated between the transmitter side and the receiver part of the radar system is saved

for the next steps; the processing of the information.

-Digital RX FE: Once the simulated data is completely ready, the flow of the simulation chain leads to

the digital receiving part of the system. In this step is where most of the work of this thesis has been

developed, both the digital front-end and the digital back-end.

The digital front-end is the part that has been explained in the previous section, 3.1.3. It comprises the

matched filter receiver where the waveform is correlated in order to find the detections of the echoing

signals. After the bank of correlators (using the parallel range gate technique explained), the M

samples are accumulated for each branch of the bank. Then the MIMO processing is performed

depending on the MIMO type chosen (as explained in the next section). The final radar data cube with

all the data is saved and prepared in order to make it easily accessible for further signal processing and

interpretation, which will take place in the digital back-end.

Digital Front-End processing: Given the theoretical and practical importance of the digital front-end

processing and management of the data, an explanation with the main concepts and parts is going to be

exposed as follows.

The received signals are processed in the digital front-end as explained in section 3.1.3. The process of

data management occurs in a certain manner that the samples end up stored in a radar data matrix, as

the one in Fig. 62. The vertical dimension of the matrix is the range domain and the horizontal

dimension is the Doppler domain. Sometimes these dimensions are also called, slow time and fast time

dimension, due to the difference of sampling intervals in subsequent rows of a column and those in

subsequent columns of a row.

Many of the radar signal processing computations that are going to be performed in the next sections

are going to make use of a radar data matrix as the depicted in Fig. 62(For a simple case of one

receiver), or a radar data cube (for a more complex case as with MIMO processing, presented in next

section).


98

Fig. 62: Two dimensional model of the SISO data structure, a radar data matrix.

Each of the rows of the matrix will be called Range Gate (or Range Bin) and each of the columns

Doppler Bin. The Doppler bin of the radar has an interval of 𝑇𝑠, which is the processing time between

one processed sample and the next one, and is equal to the time that the system spends to process one

data sample; 𝑇𝑠 = 𝑇𝑐 ∙ 𝐿𝑐 ∙ 𝑀.

The Fig. 63 depicts the processing of one only range gate, the first one. Each of the M sequences (𝐿𝑐

length) are processed in the matched filter and compressed as explained in the section 3.1.3. At the

output there will be just one sample that will be stored in the first row of the first column of the radar

matrix. Successive M sequences of 𝐿𝑐 will be processed in the same fashion until the N samples of the

first range gate are filled up.

In the example of Fig. 63 can be observed that the first block (blue) of M sequences will be processed;

correlated and compressed, accumulated along the M sequences repetitions and then the FFT will be

applied along the N samples. The outcome will be one sample (blue), the consecutive block (red) will

follow the same process, and so all the other blocks of M sequences until the last block, the N, that

after the processing will fill up the last sample in the last component of the first row.

NDoppler Bin

Doppler dimension

Ran

ged

imen

sio

n

Range Gate


99

In Fig. 64 the digital front-end processing is complete; in this figure the bank of correlators besides the

parallel range gate processing as a whole is showed. All the range gates echoes are going to be

processed in parallel. The range gate 1 is the same as showed in Fig. 63, however the bank of

correlators allows the parallel processing for all delays (all range gates). The second range gate

(RG#1) signal will be delayed by one chip time (because the second range gate is one range gate

further) and it will be correlated with the sequence delayed the same period, as explained in Fig. 60. In

this way, the second row of the radar data matrix will be filled up. These operations will be performed

in parallel for each range gate and the samples will be stored in consecutive rows of the radar data

matrix. The last range gate of the system will arrive with a delay of 𝐿𝑐 − 1 and will be correlated with

the same original sequence delayed by 𝐿𝑐 − 1, its N samples will be stored in the last row of the radar

data matrix.

Since the processing is parallel, the total dwell time of the system will still be 𝑇𝑑, equivalent to the

dwell time of each of the range gates processing.

1 N

N-FFT

M accumulation

RX

TXSequencegenerator

LO

S S∙ ∙ ∙

M sequences (

S S∙ ∙ ∙ S S∙ ∙ ∙∙ ∙ ∙

N ( )

M Block N=1 M Block N=2 M Block N

Co

rrel

atio

n

2

Fig. 63: Block diagram of the digital front-end processing a single range gate and saving its samples in each

component of the vector that composes the first row of the radar data matrix.


100

Each range gate has now N samples. The DFT on N samples can already be performed to extract the

Doppler profile. The DFT is performed by FFTs all along each of the 𝐿𝑐 range gates. Therefore, Lc N-

FFTs, one per range gate, as can be observed in Fig. 64. Before the FFT is applied, windowing is

performed along the range gates in order to achieve low Doppler sidelobes; the window type applied is

Blackman. After the FFT, for each range gate where there have been detections, the peaks will appear

arranged in the Doppler bin number belonging to the frequency shift. Since the velocity resolution is

known, it will be easy to interpret which is the speed value that this Doppler bin is associated with.

In the end, each coordinate [Range Bin, Doppler Bin] will contain a complex value which, depending

on the power level, will mean a detection or not in the CFAR.

-Digital RX BE: Once the matrix is filled up with all the samples, it is ready to be further processed.

The next step is to process the data in order to obtain information and interpret it. The first step of the

back-end part of the digital receiver is to perform the Doppler processing of the radar data matrix. This

will be done along the range dimension of the matrix (along each range gate), see Fig. 65. If there have

been detections in the range gate, a peak will appear in a certain Doppler bin, otherwise the noise will

be predominant among the range gate data. Thus, the Doppler information will be available to be

interpreted in the performing of the CFAR detection (section 3.3) and the DoA (section 3.4).

1

1

1

1

1

1

1

1

1

1

1

1

1

N

N

N

N

N

N

N

N

N

N

N

N

N

1 N

1 N

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2 Branch RG #0

Branch RG #1

Branch RG #Lc - 1

RX

TX

(Sequence Block #)

(Ran

geG

ate

#)

Fig. 64: Digital front-end processing and storing of samples for the full parallel range gate system.


101

Later on, the data resulting from this processing will be plotted and displayed for interpretation and the

SNR of the signals of the echoes reflected by the targets will be calculated and showed.

Fig. 65: Conversion of the fast/slow time radar data matrix to the range/Doppler radar data matrix.

Sampling in the fast time and slow time dimension:

From the previous explanation some other conclusions can be drawn; each of the final taken data

points can be considered as a sample point of a certain signal. The signals in this case are the range

and the frequency shifts that the system is sampling along the Doppler domain and the range domain.

The common approach, in order to choose the rate of the sampling process, is the Nyquist criterion.

This criterion chooses the sampling rate in such a rate that the original signal can be reassembled. The

same criterion can be practiced in radar, however in radar the signal is actually never rebuilt, the

samples are taken to evaluate information. The sampling criterion has to be appropriate for the use that

is going to be done of the samples.

Regarding to the fast time dimension sampling; it has been showed that the received signal is taken

into matched filters that perform the convolution of the flipped modulated sequence of the transmitted

waveform with the echoed signal. Consequently, the spectrum of the received signal is limited by the

bandwidth of the transmitter signal, which leads to the conclusion that the Nyquist rate in the fast time

domain is just the bandwidth of the transmitted signal. The transmitted signal bandwidth corresponds

to each of the chips of the transmitted sequence generated at 𝑅𝑐 rate, the inverse of the chip period.

1

1

1

1

1

1

1

1

1

1

1

1

1

N

N

N

N

N

N

N

N

N

N

N

N

N

1 N

1 N

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

- FFTs

1

1

1

1

1

1

1

1

1

1

1

1

1

N

N

N

N

N

N

N

N

N

N

N

N

N

1 N

1 N

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

(Sequence Block #)

(Ran

geG

ate

#)

( Doppler Bin #)

1


102

The corresponding sampling rate of the range domain (fast time dimension) corresponds with each of

the range gates, i.e., the bandwidth of the transmitter pulse:

Being

𝑇𝑐 = Sampling interval rate / chip period.

This sampling interval decides the spacing between the range gates, as (118):

On the other hand, the slow time dimension sampling rate is based on the PRI, which is the time

passed between successive column samples in a given row of the radar data matrix. These samples

describe the received signal after identic delay from the transmission time of successive sequences.

The sampling interval of the Doppler range is just the repetition interval 𝑇𝑠 = 𝑃𝑅𝐼, Eq. (119), which is

equivalent to the unambiguous Doppler bandwidth or Doppler spectrum.

Each sample represents the reflectivity from each concrete location. When a relative motion of a target

occurs along the sampling period (from one sample to the next one), the phase of subsequent echoes

will change from on sample to other sample (besides the amplitude variation due to noise changes).

This phase changing sampling corresponds to a Doppler shift, i.e., the sample related to each row of

the radar data matrix will have certain Doppler bandwidth. The Doppler spectrum also needs to be

sampled in order to achieve frequency resolution. The required spectrum sampling is given then by the

Eq. (109) applying the Nyquist criterion. This is equivalent to say that the Doppler spectrum is

evaluated at the different F frequencies, with certain bandwidth depending on its 𝐹𝑟𝑒𝑠 as [33]:

𝐹𝑠 =

1

𝑇𝑐 (117)

∆𝑅𝑠 =

𝑐 ∙ 𝑇𝑐2

(118)

𝑇𝑠 = 𝑀 ∙ 𝐿𝑐 ∙ 𝑇𝑐 =

1

𝐹𝑑𝑎𝑚𝑏 (119)

𝐹 = ∑𝑘∆𝐹𝑑𝑟𝑒𝑠

𝑁

𝑘=1

(120)


103

3.2 MIMO Implementation

The MIMO principles described in the section 2.4 are implemented in the Matlab chain and its

implementation process is explained in this section. Firstly, the MIMO block is situated inside the

system chain and a general review of the data management and structures used is introduced. Later on,

the MIMO methods implementation is thoroughly explained while linking the explanation with their

theoretical contributions to the system performance.

3.2.1 Overview

The MIMO processing itself takes place in the receiver side of the digital processing part. Focusing in

the receiver side; when the MIMO processing is enabled, the radar data matrix presented in the

previous section is modified before the FFT processing occurs, so that, the data stored is not FFT

processed yet. Therefore, the MIMO processing part starts after the accumulation of the M samples

step following the matched filters output. It is located preceding the FFT processing, as can be seen in

Fig. 66:

The data available in the input of the MIMO processing is a radar data cube, three dimensions of data

(in the Hadamard method), or a radar data matrix (in SISO or Range Domain method), depending on

the method used, as it will be explained in the subsections below. The output of the MIMO processing

will be the data of each of the antennas that form the virtual array of antennas (concept introduced in

the section 2.4.2). Consequently the output will be a radar data cube of 3 dimensions; 𝐿𝑐 𝑥 𝑁𝑡𝑥 ∙

𝑁𝑟𝑥 𝑥 𝑁. The second dimension will be the virtual antenna array (𝑁𝑣), with a size equivalent to the

number of transmitter antennas times the number of receiving antennas. This new dimension

represents the spatial dimension; it contains the data of each antenna necessary to be able to spatially

sample. The information gathered by the different antennas positioned along the array is different in

each of them; the array antennas are actually sampling the wavefront, therefore the spacing of the

array is another sampling interval, as explained in the section 2.5.2. The data contained is used later to

get the DoA using beamforming.

MIMOM Accum.

N-FFT

N-FFT

N-FFT

Fig. 66: Location of the MIMO processing part in the radar system.


104

Depending on the MIMO method used, there is also the need to prepare the transmission

implementation in different ways, as it is going to be explained in the following subsections.

3.2.2 Outer Hadamard Code

As explained in theory Chapter 2, section 2.4: in order to be able to separate the signal waveforms

coming from different transmitting antennas, orthogonality between the transmitting signals need to be

achieved, since the signals are going to be transmitted simultaneously.

Given the example of an array of 4 transmitting antennas and 2 receiving antennas; the MIMO

implementation with the outer code method starts with the separation of the receiver antennas by 0.5𝜆.

Represented by the array vector:

RX = [1 1]

The transmission array is sparse with a length between the antennas equal to the length of the

receiving arrays. This is done inserting zeros in the transmitting vector; i.e., separating the transmitting

antennas by 𝜆

2∙ 𝑁𝑟𝑥 , the result is 𝜆 for the case under study. Consequently the virtual array generated

will have the same separation as if there would be in reality this number of transmitter antennas:

TX = [1 0 1 0 1 0 1 0]

As seen in Fig. 68, the final virtual array will be resulting from the convolution of the vectors, and will

have, in this case, 8 elements:

Virtual Array = [1 1 1 1 1 1 1 1]

N

Fig. 67: Three dimensional model of the MIMO data structure, a radar data cube.


105

To get this virtual array, achieving orthogonality between the transmitted signals is a must. Applying

the outer code method, it will be possible to recover the signal of each transmitter antenna separately.

Transmitter: As explained in the section 2.4.3, the outer code will be used to render the transmitting

antennas orthogonal to each other. Firstly, the transmitting antennas’ spacing will be set as previously

presented. The number of antennas is selectable in the script menu, but in order to use the Hadamard

codes, the number of transmitting antennas need to be 2 or a multiple of 4. This is because the

Hadamard codes’ length are limited to length 2 or multiple of 4 up to 664. The Hadamard code length

is picked up depending on the number of transmitter antennas; in the example case of 4 transmitting

antennas, the Hadamard code length will be 4.

The set-up of the transmitter side is showed in Fig. 69; a single sequence, named S is used for all the

transmitting antennas. The sequence with a length Lc is repeated M times, so that it will support the

coherent accumulations later. Then, it is repeated as many times as number of antennas 𝑁𝑡𝑥 with the

possibility of having a sign inversion depending on the rows of the Hadamard matrix. Therefore there

will be 𝐿𝑐 𝑥 𝑀 𝑥 𝑁𝑡𝑥 samples. At the same time, there are needed N samples to perform the FFT later,

consequently the process will be repeated N times. There should also be remembered that all the

transmitter antennas are radiating simultaneously.

TX Array RX Array Virtual Array

Fig. 68: A MIMO radar system with 𝑁𝑇𝑋=4 and 𝑁𝑅𝑋=2 and its correspondent virtual array.


106

Receiver: If it is considered the processing of the reflected echoes per MIMO blocks; each MIMO

block is the piece of data showed in Fig. 69. Since all the antennas radiate at the same time through the

same path, the signals are summed up in their way to the target and back when reflected.

Consequently, to the detectors of the receiving antennas, the signal will look like one alone, as showed

in Fig. 70:

Fig. 70: Simplified diagram of the signals the TX signals being summed and reflected.

TX-1

TX-2

TX-3

TX-4

Target 1

Target 2

Far Field

RX-1

RX-2

∙ ∙ ∙

H =

S S∙ ∙ ∙

x 1

M sequences

S S∙ ∙ ∙

x 1

S S∙ ∙ ∙

x 1

S S∙ ∙ ∙

x 1

S S∙ ∙ ∙

x 1

S S∙ ∙ ∙

x -1

S S∙ ∙ ∙

x 1

S S∙ ∙ ∙

x -1

S S∙ ∙ ∙

x 1

S S∙ ∙ ∙

x 1

S S∙ ∙ ∙

x -1

S S∙ ∙ ∙

x -1

S S∙ ∙ ∙

x 1

S S∙ ∙ ∙

x -1

S S∙ ∙ ∙

x -1

S S∙ ∙ ∙

x -1

TX-1

TX-2

TX-3

TX-4

N = 1 N = 2 ∙ ∙ ∙N

LC chips S

One sequence

=

∙ ∙ ∙

∙ ∙ ∙

∙ ∙ ∙

∙ ∙ ∙

MIMO Block 1 MIMO Block 2 MIMO Block 3 MIMO Block 4 MIMO Block 1 ∙ ∙ ∙

Fig. 69: Forming of the transmitter side of an Outer Hadamard Code MIMO radar system.


107

Each MIMO block is received with matched filters, which correlate and compress the signal until there

are just M samples left. After that, the signal is accumulated as usually, letting as a result just one

sample. The four MIMO blocks are represented in Fig. 69 and Fig. 71 in an orange scale. The first

MIMO block sample is first obtained, the second MIMO block will follow the same process, and so

the third and fourth. Therefore there are now 4 samples after compression and accumulation of each of

the MIMO blocks. Each of these samples has a portion of the signal sent by each of the transmitter

antennas (4 transmitter antennas in this example). For each receiver there is going to be a bank of

correlators to process all the range gates, as usual, the same approach as the showed in Fig. 60 but with

the MIMO processing variation. For simplification purposes here it will be showed just one range gate

processing, but the same process is repeated in parallel for all the range gates.

For each receiver, after the filter bank correlations and accumulations, the data will be organized in a

radar data cube which dimensions will be 𝐿𝑐𝑥𝑁𝑡𝑥𝑥𝑁, as seen in Fig. 72. Where 𝐿𝑐 are the compressed

samples of each range gate of the filter bank of correlators, 𝑁𝑡𝑥 are the accumulated MIMO block

samples of a certain transmitting antenna (which size is equal to the number of transmitting antennas),

i.e., each of the MIMO blocks multiplied by a different Hadamard coefficient, and N the needed size

to create as many samples as needed for the later FFT.

The four samples linked with each of the MIMO blocks, Fig. 71, need to be separated so that the

signal value portion coming from each transmitter is conveniently distinguished. The use of the

H =

M Accum. H

RX-1

1 sampleM samples

1 sample

Correlator(length LC)

M ∙ LC samples

Block 1Block 2

Block 3

Block 4

4 samples

Fig. 71: Receiver side of an Outer Hadamard Code MIMO radar system.


108

Hadamard code matrix in each of the MIMO blocks and its zero-cross correlation properties will allow

the separation of each transmitting antenna samples.

The samples are split in 𝑁𝑡𝑥 sections of 1 sample each that will be combined together according to the

Hadamard matrix coefficients. The Hadamard matrix code is symmetric and 𝑁𝑡𝑥 blocks were

transmitted, when it is multiplied by the samples vector, (each of the signal samples was

added/substracted when the signal is summed up together in the transmission path), the signal will be

separated and each portion belonging to each different transmitting antenna will be obtained. It can be

seen in Fig. 73 which samples will be taken if just the first range gate processing is considered and the

N = 1. An auxiliary empty matrix with the size 𝐿𝑐𝑥𝑁𝑡𝑥𝑁𝑟𝑥𝑥𝑁 is created.

The samples from each transmitter antenna will be saved there as they are separated. Then the second

batch of 4 samples (each one belonging to the sum of the 4 transmitted antennas) of the N point

number 2 will be processed with the Hadamard matrix, and again, 4 different samples will be

separated and saved in their correspondent place on the new matrix where the data from the different

antennas is saved. As can be observed in Fig. 71 and Fig. 73, this will be repeated for the four different

batches of MIMO blocks, therefore the same sample is going to be accumulated 𝑁𝑡𝑥 times, in the case

under study, 4 times. This will give the system an extra gain.

N

1

11

Fig. 72: Data structure size that each receiver will take after the MIMO processing.


109

This process will be repeated N times until all the necessary N-FFT samples are obtained (see Fig. 74),

filling up the first radar data matrix. However, in this first matrix there is just the information of each

of the 4 transmitting antennas related to the first range gate of the system.

x H

N

1

11

1 sample1 sample

1xRG

1 1 1 1

N

1

11

x H1xRG

N

N

N

N

∙ ∙ ∙

∙ ∙ ∙

∙ ∙ ∙

∙ ∙ ∙

N=1N N

1

1

1

1

∙ ∙ ∙

∙ ∙ ∙

∙ ∙ ∙

∙ ∙ ∙

N N N

Fig. 73: Separation of each transmitter signal part with a Hadarmard matrix and radar data cube storage.

Fig. 74: Separation of each transmitter signal part for every N repetitions and radar data cube storage.


110

Once all the first range samples are obtained, the second range samples need to be processed in the

same way and so they will all the consequent range gates until the last unambiguous range gate, 𝐿𝑐.

See Fig. 75. The MIMO processing is happening in parallel for all the range gates.

At the output of each receiver antenna the data from the 𝑁𝑡𝑥 transmitter antennas will be obtained,

consequently obtaining range data from 𝑁𝑟𝑥𝑁𝑡𝑥 virtual array antennas, with the necessary number of

samples to be able to perform the N-FFT which will provide the Doppler information later. In Fig. 76;

the whole MIMO processing plus a simplified parallel range gate is depicted.

M Accum.Correlator(length LC)

x H

N

N

N

N

∙ ∙ ∙

∙ ∙ ∙

∙ ∙ ∙

∙ ∙ ∙

N=1N

1

1

1

1

∙ ∙ ∙

∙ ∙ ∙

∙ ∙ ∙

∙ ∙ ∙


x H

N

N

N

N

∙ ∙ ∙

∙ ∙ ∙

∙ ∙ ∙

∙ ∙ ∙

N=1N

1

1

1

1

∙ ∙ ∙

∙ ∙ ∙

∙ ∙ ∙

∙ ∙ ∙

Range Gate #

Range Gate #

1 1 1 1

N

1

11

∙ ∙∙

N N N N∙ ∙

∙

Fig. 75: Separation of each transmitter signal part for every N repetitions with the full parallel range gate processing

besides its storing in a radar data cube.


111

The same process is being done in parallel in each of the receiver antennas, i.e., 𝑁𝑟𝑥 times, see Fig. 76:

If the example is followed, after the filter bank of correlators (Lc) and accumulations of each receiving

antenna for each range gate, a 3 dimensional data structure of size is 𝐿𝑐𝑥𝑁𝑣𝑥𝑁 is obtained; where 𝑁𝑣

is the number of virtual antenna created, 8 in the case under study.

The new radar data cube structure is filled with the information related to each virtual antenna, the

whole unambiguous range and sampled N times, as the radar data cube seen in Fig. 76.


x H

N

N

N

N

∙ ∙ ∙

∙ ∙ ∙

∙ ∙ ∙

∙ ∙ ∙

N=1N

1

1

1

1

∙ ∙ ∙

∙ ∙ ∙

∙ ∙ ∙

∙ ∙ ∙


x H

N

N

N

N

∙ ∙ ∙

∙ ∙ ∙

∙ ∙ ∙

∙ ∙ ∙

N=1N

1

1

1

1

∙ ∙ ∙

∙ ∙ ∙

∙ ∙ ∙

∙ ∙ ∙

Range Gate #

Range Gate #

∙ ∙∙


x H

N

N

N

N

∙ ∙ ∙

∙ ∙ ∙

∙ ∙ ∙

∙ ∙ ∙

N=1N

1

1

1

1

∙ ∙ ∙

∙ ∙ ∙

∙ ∙ ∙

∙ ∙ ∙


x H

N

N

N

N

∙ ∙ ∙

∙ ∙ ∙

∙ ∙ ∙

∙ ∙ ∙

N=1N

1

1

1

1

∙ ∙ ∙

∙ ∙ ∙

∙ ∙ ∙

∙ ∙ ∙

Range Gate #

Range Gate #

∙ ∙∙

RX-1

RX-

∙ ∙∙

1 1 1 11

1

N N N N

N

1

1 1 1 1

N N N N

Fig. 76: Separation of each received signal for every N repetitions with the full parallel range gate processing

and for each receiving antenna, besides its storing in a radar data cube.


112

3.2.3 Range Domain Separation

The implementation of the range domain separation method is simpler. The approach here is

different; as explained in the section 2.4.4, in this case the same sequence without any variation will be

sent in all the transmitter antennas.

As with the outer Hadamard code method, even though the MIMO processing occurs in the receiver

side of the digital processing, there are also some parameters that need to be arranged before, in the

transmitter side of the system. When working with the MIMO method there has to be taken into

account the type of code used to generate the waveform. Thus, the implementation is going to be

divided depending on the different implemented codes.

-With APAS codes:

Transmitter: The first change in the transmission is that the code should be 𝑁𝑡𝑥 times longer than the

needed length for the specified system parameters, continuing with the previous example, 𝑁𝑡𝑥 = 4

and 𝑁𝑟𝑥 = 2 . The code should be the same in all the transmitter antennas, but it has to be delayed by

𝐿𝑐

𝑁𝑡𝑥 . See Fig. 77:

The sequence will be repeated in every antenna M times in order to enable accumulation and N times

to enable the Doppler processing later on. All the flow between consecutive antennas will be delayed

by 𝐿𝑐

𝑁𝑡𝑥. In this case APAS codes have been used; all the APAS codes are multiple of 2, and therefore

the delay can be done properly in delays of the same length.

The antennas will radiate at the same time, therefore, the delayed signals from all the transmitting

antennas will be summed up in its way to the target and back after reflections, in the same manner as it

was explained in the previous section and showed in Fig. 70.

TX 1

TX 2

TX 3

TX 4

Sequence 4 times longer than desired Rambig

S S S S

S

S

S

S

S Sequence length necessary given the system parameters

NM Sequences

S S S S

S S S S

S S S S

Fig. 77: Signal forming of the transmitter side of a Range Domain Separation MIMO radar system.


113

Receiver: The receiver part can be simplified in this case when compared with the Outer Code

processing. There will be needed just one correlator in each receiver antenna. The size of the correlator

will be the same size as the code used in the transmission, full length. The correlator output will look

like in Fig. 78.

When the sum of the transmissions is detected in each receiver, the full length correlator will correlate

a sum signal of the 4 delayed sequences: the first whole sequence, the second sequence up to ¾ of its

lengths, the third sequence up to ½ of its length and the forth sequence up to ¼ of its length, as seen in

Fig. 79.

Fig. 78: Range Domain MIMO receiver after having correlated a full sequence Lc, giving as a result the

unambiguous range of each antenna.

When the original sequence will be aligned with the first full length sequence reflected signal, it will

show the first antenna detections in all its unambiguous range gates. The first ¼ part of the resulting

output after will be the whole unambiguous range gates of the first antenna, and it is in this part where

the targets should be. The rest ¾ of the resulting signal should be just noise.

In consequence, when the sequences are correlated at lag zero; the first 𝐿𝑐

𝑁𝑡𝑥 of the resulting correlation

will show the unambiguous range of the system (which is 𝐿𝑐

𝑁𝑡𝑥) and is associated with the first ¼ of the

first antenna signal (which is actually the sequence length of the system design).

Since the other sequences in the other antennas were delayed, there will not be a correlation in their

portion of the received signal until they are perfectly aligned. However, when the signal coming from

the second antenna into the correlator will be aligned there will be a correlation of the unambiguous

range of the second antenna (see second stage of Fig. 79), that now will be correlating at zero lag.

Same logic applies to the other antenna signals, for the third and fourth antenna (see third and fourth

stage in Fig. 79).

In the last stage of Fig. 79, can be observed that after the last sequence of the first sequences batch, a

new first sequence (red, belonging to the first antenna), will be aligned again. This is the second

sequence of an M block, the process starts again.

FIR = S*

Rambig 2Rambig 3Rambig 00

Return from TX

antenna 1

Return from TX

antenna 2

Return from TX

antenna 3

Return from TX

antenna 4

Return from TX

antenna 1

. . .

RX


114

Once the full length correlator has finished computing a full length correlation, the output of the

receiver will look like if there have been repeated detections, as many repetitions as 𝑁𝑡𝑥. For example,

given that there were three targets in the first range gates of the field, it would look like showed in Fig.

80:

S

SSSS

SSSS FIR = S*RX

S

Original Sequence

FIR = S*

Rambig 2Rambig 3Rambig00

S

SSS FIR = S*


S

SSS FIR = S*


S S

FIR = S*


0

S S

S

S

SS

SSSS

SSSS

SSSS

S

S

Rambig

S

Original Sequence

S

Original Sequence

S

Original Sequence

S

Original Sequence

Rambig

Rambig

Rambig

S S S S

Sequence 2

Sequence 1

S

FIR = S*


0

S SSSSSS S

Rambig

S

Original Sequence

Return from TX antenna

1


2


3


4


1

S

Fig. 79: Range Domain MIMO receiver detailed process after having correlated a full sequence Lc, giving as a result

the unambiguous range of each antenna.

Rambig 2Rambig 3Rambig0 Rambig

Fig. 80: Detections of each antenna with a Range Domain Separation MIMO processor.


115

Afterwards, the signal flow will continue arriving M times to enable accumulation gain and then N

other repetitions to obtain the number of points for the FFT, in the same way as in the previous

method.

The difference also comes in the way to manage the information; before we had a radar data cube of

information with mixed information from all the antennas, waiting to be split, and classified according

to their N number of sample, 𝐿𝑐 range gate and 𝑁𝑡𝑥 antenna. However now there is a flow of

information of 1 dimension, in which each 𝐿𝑐 sequence contains the echo caused by each of the

antennas. The only thing needed to do is to break up the flow in 𝑁𝑇𝑋 parts, for each antenna. The first

𝐿𝑐 samples of each M block will belong to the first antenna; the second consecutive 𝐿𝑐 samples of

each M block will contain the echoes produced by the second antenna, and so on for the rest of the

antennas (See Fig. 81). This is for one receiving antenna, if there are two as in the example system,

the same exact process will happen in all the receiver antennas, creating two times one dimensional

data.

Using Matlab operations the 𝐿𝑐 sequences are split in four, as seen in Fig. 82, and consecutively

added to a matrix, first for N=1 and the same process for N=2 until N=N. Since the APAS sequences

lengths are always even, each of the pieces will have the same length.

Thus, at this point, half of the final radar data cube is formed; adding in the same way the data from

the other receiving antenna, extra information from other 4 antennas is added.

Once the information is reorganized, the M sequences belonging to each antenna have been

accumulated to increase the system gain and there is a radar data cube of dimensions 𝐿𝑐 𝑥 𝑁𝑣 𝑥 𝑁.

Now there is the information about all the range gates for each virtual antenna and with N repetitions,

letting the information ready to perform the N-FFT that will provide with the Doppler information.

In this case APAS codes have been used; all the APAS codes are multiple of 2, and therefore the delay

could be done properly in delays of the same duration. The only thing to take into account here is that

the second half of the range gates should be eliminated, due to the second autocorrelation peak

characteristic of the APAS codes.

M Sequences

N

1 2 N

Fig. 81: One dimension matrix with the information related to each antenna with length 𝐿𝑐 x M x N.


116

With M-Squences: The use of Range Domain Separation MIMO for M-Sequences follow the same

process explained for the APAS codes. However it shows an extra challenge to be solved. As

mentioned in the section 2.1.5, the M-Sequences lengths are odd: 𝑁 = 2𝑛 − 1, therefore the number of

range gates of each antenna will not have the same length.

To fix this issue without interfering with the correct functioning of the system, the solution is to take

out the last sample of every antenna excepting for the last antenna. This is done after the correlation

and reorganization of the data with a simple operation in Matlab, as seen in Fig. 83. The only change

affecting the system will be the availability of one less range gate, the last one.

N N

1

N

1

1

N

1 M 1 M

RX-1 RX-2

N N

1

N

11 1

-1

Fig. 82: Radar data cube after the reorganization of the one dimensional receiver output with dimension 𝐿𝑐 x 𝑁𝑣 x N.

Fig. 83: Range Domain Separation structure adjustment with m-sequences.


117

3.3 Constant False Alarm Rate (CFAR) Detector

In this section, the CFAR block is placed in the system and the way the algorithm manages and

analyzes the information is exposed. The algorithm implementation and performance is explained; in

the pre-processing part, in the detection part with each of the algorithms’ implementation and in the

post-processing part. The detection process in case that MIMO is enabled is also thoroughly

explained; the rough beamforming concept and implementation is exposed and the difference in the

detection process is clarified, besides the managing of the structures where the information is

contained (radar data cube).

3.3.1 Overview

The place of the CFAR implementation in the Matlab chain is reserved after the FFT processing of the

samples (in case of SISO system) or after the rough beamforming stage (in case of MIMO system),

and before the Angle of Arrival stage, once the signals have been processed in the receiver with the

matched filter bank and their correspondent parallel range gate processing and the samples are

correctly placed inside the radar data cube. See Fig. 84:

Fig. 84: Location of the CFAR processing part in the radar system. Upper figure for a SISO radar

configuration, lower figure for a MIMO radar configuration.

N-FFT

N-FFT

N-FFTCFAR DoA

N-FFT

N-FFT

N-FFT

N-FFT

N-FFT

N-FFT

RoughBeamforming CFAR DoA

Ang.


118

Therefore the CFAR function takes as an input the radar data cube; which is going to be a bi-

dimensional matrix in the case of a SISO system simulation with dimensions 𝐿𝑐 𝑥 𝑁, or tri-

dimensional in the case of a MIMO system simulation with dimensions 𝐿𝑐 𝑥 𝑁 𝑥 𝑁𝐴. See Fig 85:

The output of the CFAR stage is going to be the coordinates of the detected targets after the CFAR

analysis.

3.3.2 SISO CFAR

In order to make the implementation easier, firstly the CFAR was implemented taking into account

just one transmitting and one receiving antenna. Therefore the data to be processed and analyzed by

the function in order to make the detection decisions is a bi-dimensional matrix. However, the

algorithm will be the bases of a multifunctional CFAR which will work with MIMO as well and just a

few changes will be needed to adapt it, as it is explained in the next section.

The approach to make the detections depends on the dimensions along which the decisions need to be

taken. The detections are going to be performed along 1 dimension and the data available is organized

in a matrix of two dimensions; the Doppler dimension has the FFT performed along its samples and

the range dimension has the information of each of the ranges where the detections have been

performed. The Doppler dimension will present a peak if a target is detected; this peak will not be

perfect but will have a width. Also, along the Doppler range under determined conditions, side lobes

are expected. However, the profile of the range domain will present neat peaks in case of detections in

this range gate (unless there is range migration, explained later).

N

11

1

N

Fig. 85: Data structures in the input of the CFAR detector stage. Left figure, a SISO matrix filled with

data, right figure a MIMO data cube structure.


119

Hence, it makes sense to perform the detections along the range dimension, i.e., with each of the

Doppler bins, see Fig. 86. Less false alarms and masking situations are expected with the neat peaks

that will appear along each of the Doppler bins profiles. Nonetheless, a system object detection along

the range gates will usually be showed besides the normal detection, in Chapter 4.

Fig. 86: Difference in the profile views between the Doppler domain and the Range domain.

The black squares represent likely detections that the CFAR system would have activated in case of a

detection performed along the Doppler domain. The width of the signal may include adjacent bins and

its power might be high enough to induce a false alarm in a different position than the exact location.

Implementation Process: Below the steps of the CFAR implementation process are shown using block

diagrams for aid and better understanding of the algorithm.

-Detection decision: As exposed in the section 2.3.1, the main parameters to choose when it comes to

prepare the data in order to estimate the power in the detection process are: window size, guard cells

and the cell under test (CUT). The matrix will be traveled from up to down along the range gates, and

from left to write, from the first Doppler bin until the last one, N, as can be seen in Fig. 87.

Range Domain Profile View

Doppler Domain Profile View

Ran

geD

om

ain

Doppler Domain


120

At each iteration, the CUT will be the next cell down and when the column (Doppler bin) is finished,

the next column will start to be studying.

The size of the sliding window will depend on the training cells and the number of guard cells to take.

These will be selectable parameters of the simulation, their choosing will make the results vary, as it

will be showed in Chapter 4.

Each time there is a cell under test, the power data from each of the training cells is saved. A detection

decission will be taken depending on the CFAR algorithm chosen and the threshold calculated. The

threshold is set depending on the algorithm chosen (see section 2.3), which will be determined by the

probability of false alarm chosen and the number of training cells.

N

Cell Under Test

Ran

geD

om

ain

Doppler Domain

Fig. 87: CFAR analysis along the range domain for each doppler bin.


121

The value of the original radar data matrix is compared with the threshold value given by the

algorithm; if the value in this concrete [Doppler bin, Range gate] coordinate is bigger than the

calculated threshold, a detection is marked in a new matrix of the same size as the radar data matrix.

This matrix will be called detection matrix, the detection will be placed in the same coordinates where

the detection has been found out in the original radar data matrix. See Fig 89:

N

Ran

geD

om

ain

Doppler Domain

Sliding Window

CUT

Training Cells Training CellsGuard Cells

Xn Xm+1 Xm X1

Cell Under Test

Fig. 88: CFAR analysis along the range domain for each doppler bin.


122

Fig. 89: Detection in the radar data matrix and saving of the detected’s coordinate in the detection matrix.

Algorithms: Following there is a description of the algorithms implemented and how they work. The

use of averaging algorithms as CA, GOCA and SOCA is common. The averaging operation is

common to them. After it will be used to perform the algorithm in different ways. The scaling factors

will be automatically calculated (depending on the fixed 𝑃𝑓𝑎) with iterative procedures, following the

equations of the section 2.3, for each different algorithm.

Cell Averanging (CA): Takes the data from both of the windows and averages it, as explained in the

section 2.3.2, then it multiplies the value with a scaling factor and it results in a threshold value for this

CUT. See Fig. 90.

Greatest of Cell Averaging (GOCA): Takes the biggest value after averaging both training windows,

then it also multiplies this value for its particular scaling factor. See Fig. 90.

Smallest of Cell Averaging(SOCA): Takes the smallest value after averaging both training windows,

then it also multiplies this value for its particular scaling factor. See Fig. 90.

Detection Matrix

N

Ran

geD

om

ain

Doppler Domain

Radar data Matrix

NDoppler Domain

Ran

geD

om

ain


123

Fig. 90: Block diagram of the CA/GOCA/SOCA CFAR algorithms.

Order Statistic (OS): The order statistic algorithm does not use averaging. Therefore, a rank value is

chosen as a decisive parameter. Depending on the rank value, a power value from the ascending sorted

vector is picked up and multiplied with the OS scaling factor, presented in Fig. 91:


detector

Range

∑ ∑1/N ∑

Scaling Factor:

TCA TGOCA TSOCA

Comparator

Estimated Power Z

Vt = Z Tx

Input

Samples

1/N MAX

MIN1/N

Detection (CUT > Vt)

No Detection (CUT < Vt)

CA

SOCA

GOCA


detector

Range

Input

Samples

SSort the ‘n’ training cells in increasing

power order and select the Kth order

Scaling Factor: TOS

Z = Xk

ComparatorVt = Z Tos

Detection (CUT > Vt)

No Detection (CUT < Vt)

Fig. 91: Block diagram of an OS CFAR algorithm.


124

Order Statistic Greatest Of: It performs a separate order statistic in the lagging and forward training

windows and chooses the biggest value of them, then it is multiplied by a scaling factor.

After every sample (cell in the diagrams) of the radar data matrix have gone through the CFAR

algorithm, there will be a completed detection matrix, like the one showed in Fig. 92:

Detection Matrix: Each time that there is a detection, it should be marked in the detection matrix as

one point, in one range gate and Doppler bin at a time. As it can be noticed in Fig. 92 that even though

the detections have been performed along the Doppler bins, there are some consecutive (range and

Doppler) detections. This will happen in real situations as will be checked later in Chapter 4.

If there are several consecutive detections along the Doppler bins it can mean two things:

- The target is moving at an unambiguous speed (for the design of the system), i.e., the

target is moving faster than the system is design to detect correctly.

N

Detection Matrix

Fig. 92: Final detection matrix with several detections.


125

- There is spectral leakage happening; the target is very close to the radar system or the

target has a big RCS value and thus, the energy is leaked to neighbor frequency cells.

If there are several consecutive detections along range gates it can also mean two things:

- The target is at an ambiguous range (for the design of the system), i.e., the target is

further than the maximum range for which the system is design to detect correctly.

- There is range migration, i.e., the target initial position is close to the edge of a range

gate and its speed is high enough to be detected (energy transfer) in the next range gate

before the end of the dwell time. In the Chapter 4 there can be observed several

simulations showing this effect.

There are many times when the previous issues are not going to be possible to be solved improving the

system design. The CFAR algorithm also includes post-detection processing to help reduce the

number of false alarms due to the previously exposed issues.

Post-detection processing: The algorithm analyses now the detection’s matrix in order to reduce the

final number of false alarms. Each of the Doppler bin’s columns is checked for detections, if there are

any detection, the range gate where the detection is located, is analyzed. New detections are searched

along the range gate where the detection is located and heading towards the consecutive right cells, as

seen in Fig 92:

N

Detection Matrix

N

Detection Matrix

Range gatecoordinate saved

Final detectioncoordinate saved

Consecutive doppler binWithout detection

Consecutive range gateWithout detection

Fig. 93: False alarms in consecutive Doppler bin and range gate clearance algorithm. No consecutive/adjacent found.


126

When there is not any other detection in the next consecutive cell (next Doppler bin), the range gate

coordinate is saved. This will be the final Doppler bin, associated to a certain frequency shift, where

the target will be localized. But there is still the possibility of a range migration effect, i.e., in the next

consecutive range gate after the final Doppler bin detection. Therefore the next consecutive is also

checked, if there is no consecutive detection, as in Fig. 93, the second coordinate (belonging to the

range gate) is saved, thus having a final detection.

If there is another detection (Fig. 94), it means there has been range migration. Both of the consecutive

range gate detections are checked and compared, the smallest value will be cleared and finally, there

will just be one detection, the true one, without false alarms around. In the case of the Fig. 94 no

spectrum broadening was found, just range migration. The power value of the final selected sample

will be the highest value compared with all the false detections that have been discarded around it.

Fig. 94: False alarms in consecutive Doppler bin and range gate clearance algorithm. Range migration found.

If consecutive detections are found along Doppler bins, all the consecutive Doppler bins with

detections are checked, and the one with the highest value is obtained and saved, as in the case studied

in Fig. 94. All the other false alarm detections in this detection range gate are then cleared. For the

Doppler bin with the highest value, the consecutive range gate will be checked for range migration,

see Fig. 95, and then the one with minimum power will be discarded, leaving the final detection

coordinate.

N

Detection Matrix

N

Detection Matrix

Consecutive Doppler binWithout detection

Consecutive range gateWith detection. (Power comparison)


127

Fig. 95: False alarms in consecutive Doppler bin and range gate clearance algorithm. Doppler spreading and

range migration found.

This operation is going to be repeated again in the same way if there is another target in the same

Doppler bin under analysis. Once all the detections of the same Doppler bin have been cleared, the

analysis starts over again in the next Doppler bin.

The action is repeated until the analysis reaches the last range bin of the last Doppler bin. Then the

matrix is clear of false alarms caused by the effects previously described, and will look like Fig. 96.

The algorithm just checks the right-consecutive possible detections (and not the left-consecutive)

because by the way the algorithm is implemented, it is impossible to find a left-consecutive detection.

The algorithm runs from left to right Doppler bins, therefore any possible false alarms are discarded

before the next Doppler bin is checked, thus not being under study this hypothetic false alarm any

more.

The same applies for the range migration; a target might migrate between previous range gates or next

range gates (depending on whether the target is approaching or leaving the system), however, since the

algorithm runs from the closest range gate to the furthest, it discards any hypothetic range migration to

a previous false alarm for next range gate studies.

N

Detection Matrix

N

Detection Matrix

Doppler bin Of highest Power

Consecutives Doppler binsWith detection

(Power comparison)

Consecutive range gateWith detection.

(Power comparison)

False detectioncleared

Final targetcoordinate saved


128

Detection Checking: There has been implemented a checking algorithm to compare the final detected

targets in the detection matrix with the theoretical coordinates (speed and range) where the targets are

calculated to be detected. The number of targets, their position, speed and angle, are set in the script

function of the Matlab chain. The length of each Doppler bin and range gate is also known according

to the system design. As a result, it is easy to calculate in which range gate and Doppler bin a target

should be detected in the simulation. This will be helpful to check the reliability of the detection’s

system with a quick review. The theoretical targets will be compared with the final detections and the

system algorithm will be able to differentiate among:

- Confirmed detections: Detections that are expected in certain range gate and

Doppler bin and indeed, have been detected in the correct range gate and Doppler

bin.

- Confirmed detection with range migration: The target is detected in the expected

Doppler bin but it is not detected in the expected range gate. This situation will

happen when there is range migration to the previous or to the next range gate, due

to the movement of the target across range gates during the dwell system time.

N

Detection Matrix

Final target Coordinate saved

[Range gate, Doppler bin]

False alarm Detections cleared

Fig. 96: Final detection matrix result after the post-detection processing to eliminate false alarms.


129

- False alarm detection: There is a target detection where it was not expected to be a

target. It will depend on the 𝑃𝑓𝑎 settings of the CFAR, the noise level and the side

lobes that the waveform generates in the matched filter. They are expected to

increase as the speed of the targets increase.

Detections plotting: The function will also plot the profiles of the expected detections. This means that

both the confirmed detections and the expected detections which were not actually detected will be

showed. In the one hand the range domain profile will be showed; the values of all the range gates of

the Doppler bin where the detection happen, besides the threshold calculated by the CFAR algorithm.

By the other hand, the Doppler range profile; the values of all the Doppler bins of the range gate where

the target is detected, besides the threshold given by the system object. The Doppler domain profile

will just be given for information since it does not play a role in the CFAR detections functions. These

simulations results are shown in the Chapter 4.

The final detections coordinates will be saved in the targets structure for its use in later functions of

the simulation.

3.3.3 MIMO CFAR

If MIMO processing has been applied after the receiver, the CFAR detections will work slightly

different than when using one single antenna in both of the sides of the system. In this case the input

of the CFAR function will not be a radar data matrix anymore but a radar data cube.

As it has been explained in the section 3.2; after the MIMO processing there is a radar data cube

available, thus one dimension more than processing the signals when just one antenna. The cube

contains the same two dimensions that the SISO CFAR input had (one dimension with the all range

gates values, 𝐿𝑐, and one dimension with the Doppler bins, N) and a new dimension which contains

the information received by each of the antennas of the virtual array, 𝑁𝑣.

The virtual antennas dimension will contain the information of each reflection with certain phase angle

shift, due to their different location distance in the antenna array. As a result the angle information can

be used to perform detections taking advantage on the angle difference. For that, a rough beamforming

needs to be introduced. Thus, the radar data cube of dimensions 𝐿𝑐 𝑥 𝑁𝑣 𝑥 𝑁 , will be transformed into

a radar data cube of dimensions 𝐿𝑐 𝑥 𝑁𝐴 𝑥 𝑁, where 𝑁𝐴 are the different angles scanned.

Rough Beamforming: Even though next section 3.3.4 is going to talk about Direction of Arrival

(DoA), the rough beamforming needs to explained here to understand how the CFAR works when

simulating MIMO processing. The beamforming applied is going to be rough, i.e., a low resolution

solution. The angle resolution with which it will be performed is going to be big. There are going to be


130

scans in as many angles as twice the number of the virtual array antennas. Therefore if 𝑁𝑣 = 8,

𝑁𝐴 = 16. In the following figures, just 8 lobes out of 16 are depicted for visual simplicity.

The rough beamforming is going to be useful to carry out a first quick scan of the angle aperture of the

antenna array, enough to be able to roughly know the angle around which the targets are positioned, as

can be seen in Fig. 97:

With this information, a finest beamforming will be performed around the angles where the targets

have been detected, after the CFAR, with beamforming subspace methods that will provide better

resolution performances.

The input of the rough beamformer is the radar data cube after the MIMO and FFTs processing, with

𝐿𝑐 𝑥 𝑁𝑣 𝑥 𝑁 dimensions, and its output will have 𝐿𝑐 𝑥 𝑁𝐴 𝑥 𝑁 dimensions, going directly to the input

of the CFAR, where detections will be processed along the range gates for the different studied angles

and frequency shifts (Doppler bins, N), as has been showed in Fig. 85 and the Fig. 96.

Target 1

Target 2

60

Fig. 97: Rough radar scanning along the equidistant angles of the radar aperture, for 4 antennas.


131

The beamforming method used to process the rough beamforming is conventional; the fast and simple

Delay and Sum method. The antenna array has a broadside configuration, and then the distance from

each antenna element to the reference of the array is known. The antenna aperture is chosen as a

parameter in the script function; it is chosen 120 degrees, i.e., 60 degrees from the reference center of

the array to each side.

Since the FFTs have been performed, the Doppler data is already available; therefore the rough

beamforming will work at all the unambiguous speeds. The rough beamforming process will start

calculating the weight vector at certain angle; the weight vector will have as many values as the

number of virtual antennas has the array. It will be calculated as stated in the section 2.5.3 and will be

always the same for each angle under study. Given the first angle to study (Fig. 98) and using the

radar data cube obtained after the MIMO processing (Fig. 76), the weight vector will be evaluated

along each virtual antenna signal value in certain range gate and at a certain frequency (Doppler bin)

at a time, see Fig. 99.

Target 1

Target 2

60

Fig. 98: First angle under evaluation in beamforming.


132

The weight vector contains the weighting values related to each of the antennas of the array for certain

angle, and each range gate vector of the virtual antennas contains the signal for each phase shift due to

the array elements. If we evaluate one vector with the other and the phase shift coincides with this of a

detection in the concrete range gate and Doppler shift (speed), a detection will have been found. The

evaluation is performed as a multiplication which will lead to just one value, as seen in Fig. 99:

As previously mentioned, the output of the rough beamforming will be a radar data cube of

dimensions 𝐿𝑐 𝑥 𝑁𝐴 𝑥 𝑁, (Fig. 76). The beamforming values will be saved consecutively in their

correspondent range gates, angle columns and Doppler shifts.

To save processing time, a whole matrix at certain frequency shift (𝑁𝐹𝐹𝑇) will be evaluated, with

dimensions 𝐿𝑐 𝑥 𝑁𝑉. It will contain all the range gates information of all the virtual antennas at a

certain frequency (𝑁𝐹𝐹𝑇). After evaluating it with the weighting vector, a new 𝐿𝑐 vector will be

1

1

N

1

Weight Vector for the First angle under study.

First range gate data belonging to each virtual antenna.

Beamforming resultfor the first angle in

the first range gate andFor the firt Doppler bin.

N=1

= 1

1

1

N

1

Virtual Antennas’Radar Data Cube

Angles’ Radar Data Cube

Fig. 99: Beamforming using the radar data cube 𝐿𝑐 𝑥 𝑁𝑣 𝑥 𝑁 and a weighting vector of certain angle, besides

new radar data cube structure with the angles dimension.


133

obtained. The information contained will be the beamforming evaluation in certain angle and at certain

speed, as seen in Fig. 100:

Fig. 100: Vector beamforming using the radar data cube 𝐿𝑐 𝑥 𝑁𝑣 𝑥 𝑁 and a weighting vector of certain angle,

besides a new radar data cube structure with the angles dimension.

After the beamforming all along the range gates for a certain frequency shift is finished, the same

process is repeated for the next Doppler bin (next frequency shift) until all the possible frequency

shifts have been evaluated. The results of the evaluation will be stored in the new angles matrix, one

after the other. If there is any target at the angle considered at any speed, a power peak will appear.

Therefore, once the beamforming belonging to the first angle studied is already performed, see Fig.

101. Then, the very same process will be repeated with the next angle but with a new weighting

vector, until all the angles of the rough beamforming have been covered, Fig. 102, and the Range-

Doppler-Angles matrix is completed. The radar data cube resulting will be then ready for the CFAR

detections.

1

1

N

1

All range gates data belongingto each virtual antenna for N=1.

Beamforming resultfor the first angle in every range gate and

for the first Doppler bin.

N=11

1

1


1

1

N

1

Angles’ Radar Data CubeVirtual Antennas’Radar Data Cube


134

Fig. 101: Beamforming completed for the first angle of the rough beamforming.

1

N

1

All range gates data belongingto each virtual antenna for N=N.

Beamforming resultfor the first angle in every range gate and

for the last Doppler bin.

N=N1

1

1


1

1

N

1


1

Virtual Antennas’Radar Data Cube

Beamforming data for the first angle

Target 1

Target 2

60

1

1

N

1


Beamforming data for each angleOf the rough beamforming .

Target 1

Target 2

60

Fig. 102: Angles’ radar data cube completed for all the angles of the rough beamforming.


135

Implementation process: The implementation of the MIMO CFAR introduces some necessary changes

comparing to the normal CFAR. Now the input of the algorithm is a 3 dimensional structure, with 𝑁𝑣

times the data that the SISO CFAR was processing. The same detection algorithm chain will be looped

𝑁𝑣 times for each matrix angle, as seen in Fig. 103:

All the post-detection process algorithm and cell selection is performed in the same way as for a SISO

configuration. The first angle matrix will be processed for detections in exactly the same way. After

the final detections’ coordinates are made and saved is when the new piece of algorithm plays its role.

Besides the number of the range gate and the Doppler bin where the target is detected, the information

of the angle is also saved, besides the power of the detection. As a result, the available information

related to each detection is increased. After the first matrix (belonging to the first checked angle), the

CFAR algorithm loop will process the second matrix, belonging to the information of the next angle,

as seen in Fig. 103.

1

1

N

1


1

1

Normal detection algorithmmatrix angle by matrix angle.

Fig. 103: CFAR detector along each matrix linked with an angle.

1

1

Detection Matrix of a certain Angle

1

1

Detection Matrix of the consecutive Angle

Fig. 104: Consecutive angles' radar data matrix analysis.


136

The detections’ coordinates will be normally saved, but, now the detected targets are compared with

the previous detections, i.e., with the detections saved from the previous angle matrix, as seen in Fig.

104. Firstly, for each detected target, the algorithm will check if there is any previous target

detected(in other angle matrix) in this same range gate. If there is not, then this is a new target that was

not detected in other angles and its information is stored in the targets result’s matrix. If it turns out

that there was a previous detection in the same range gate where the target under analysis is located,

there is the possibility that is the same target that was also detected for another angle. To verify it, the

algorithm checks if also the Doppler bin matches. If it does not match, i.e., the target is at the same

distance but moving at a different speed, then is a new target, see Fig.104. Its coordinates, angle of

detection and power level are stored. Anyhow, if the Doppler bin also matches, it means that a target

that was detected in another angle is also detected at the present angle. This situation can happen when

a target is located between two consecutive angle lobes or moving between them, see Fig. 105. When

a coincident target is found in a new angle, the power levels of both of the detections are checked, the

one with the higher power level will be the final value stored for this target, substituting the angle

value and power associated to the previous one, see Fig. 103.

The process will be repeated for all the angles and when all the angles have been checked a final cube

of detections will remain. Each of the detections will be associated with a certain angle and power

level. Later, the CFAR algorithm will continue normally showing the checking of the detections

compared with the theoretical results and the profile plots, just the same as with the SISO type.

As a result, the output of the algorithm will be a structure of detected targets with valuable information

to be used in later processing.

60

Target 1

Target 2

Fig. 105: Target causing a double detection in different angles.


137

3.4 Fine Angle of Arrival (AoA)

In this section, the beamforming implementation is exposed besides a brief explanation of the different

algorithms implemented to determine the angle of arrival with higher precision.

3.4.1 Overview

The computation of the angle of arrival is performed after the CFAR detections, as seen in Fig. 106.

Once the exact range gate and Doppler bin of the targets detected is exactly known (given the system

design resolutions), and the angle is roughly known, it will be easier to compute a finest angle

resolution.

The beamforming algorithms that provide fine beamforming resolution are computationally heavier;

therefore it makes sense to apply them after the CFAR detection, just in the range gates and Doppler

bins where the targets have been detected and assessing the angles around which the target has been

found. In this way the target angle will be located with much finer angle resolution using much less

processing power than if it is done before the rough beamforming + CFAR detection.

The data with which the beamforming will be processed is going to come from the output of the bank

of FFTs. Therefore the solution is going to be fed with detections data found in the MIMO CFAR

stage and the radar data cube obtained after the FFTs, with 𝐿𝑐 𝑥 𝑁𝑉 𝑥 𝑁𝐹𝐹𝑇 dimensions.

RoughBeamforming CFAR AoA

Ang.

Fig. 106: Location of the fine beamforming processing part in the radar system.


138

When selecting the data samples from each of the virtual antennas, it will just be selected the data set

belonging to the range gate and Doppler bin where the target was detected. These sets of samples will

be extracted from the radar data cube after the FFT, as seen in Fig 108.

Target 1

Target 2

1

1

1

N

1

Radar Data Cube

ata set from detection 2 incertain Range gate and Doppler bin

ata set from detection 1 incertain Range gate and Doppler bin

Data sets from the different virtual antennas in a detected target coordinate [Range Gate, Doppler Bin]

Range GateDetection 2

Range Gate Detection 1

Doppler Bin ofDetection 2

Doppler Bin ofDetection 1

Fig. 107: Fine beamforming around a rough beamforming wide lobe linked to a target in a detected angle.

Fig. 108: Data sets selection from the radar data cube using the CFAR detection coordinates.


139

At the same time, the assessing angles will come determined by the angle where the specific target

was detected after the MIMO CFAR. There will be taken; [ −𝑁𝑣 , 𝑁𝑣 ] angles around the rough

estimated angle. The difference between the angles will be determined by the width of the lobes. i.e., if

the angle where the target under study was at 40 degrees and the 𝑁𝑣 = 8 , the weighting vector will be

generated for 16 angles around the 40 degrees angle.

The beamforming results are stored in a vector with the estimation for the different studied angles as

seen in Fig. 109. Now it is easy to find the highest power value along the angles vector and store this

angle as the new angle where the detection is located, thus experimenting an increase of angular

resolution.

After the rough beamforming + CFAR, each detection is located in a different [range, Doppler, angle],

therefore each detection data set will be evaluated in the angles around their rough detection angle.

The solution is implemented in three finer resolution algorithms: Bartlett, Capon and MUSIC

algorithms. The three algorithms generate the beamforming according to the equations given in the

section 2.5 of the theory. One common operation that the three methods perform in their algorithms is

the covariance calculation.

Covariance: The covariance operation provides with a measure of the correlation of two sets of

random variables, and is defined as Eq. (121) [40]:

𝑐𝑜𝑣(𝑋, 𝑌) =∑(𝑥𝑖 − �̅�)(𝑦𝑖 − �̅�)

𝑁

𝑁

𝑖=1

(121)

Weight Matrix made of the weighting vectors for the angles around the detected

angle location of target 1.

Data set for Detection 1 taken fromRadar Data Cube from its coordinate

[Range Gate, Doppler Bin]Fine AoA for the detection 1in the angle range [-Nv, Nv]

Fig. 109: Beamforming evaluation in different angles around the angle where the detection 1 was located with

the rough beamforming.


140

Bartlett: It generates a covariance matrix with the data set taken from the different virtual antennas,

for a given range angle and Doppler bin. This matrix will be used when assessing the beamforming for

each angle.

Capon: This method also uses the covariance of the data set selected, but also makes its inverse. The

resultant matrix is multiplied by the weighting vector as normally, for each angle under study.

MUSIC: Uses the assumption that noise in each channel is highly uncorrelated and therefore the

covariance matrix is diagonal [59], after it computes the covariance in terms of eigenvalues and

eigenvectors (using the Singular Value Decomposition) and multiplies it with the weighting vector,

giving as a result the expected signals data.

3.5 System Review

After studying each of the main parts of the PMCW radar system and its implementation blocks, a

system review with all the connected blocks linked to the Matlab chain implementation can be

presented to be simulated. The block diagrams of the digital part of the radar system are showed in

Fig. 110 and Fig. 111. The transmitting part is represented in Fig. 110; the receiving part is showed in

Fig. 111.

Transmitter: It shows how the waveform is generated for each of the case methods; when the system

just uses one transmitter antenna, the system picks up the code length according to the system design

parameters. Depending on whether the waveform selected uses APAS codes or M-Sequences, the final

sequence length will be doubled or not. The sequences will be repeated M times, this makes up each

PRI. Then they are repeated N more times, in total 𝑀 𝑥 𝑁 sequences of length 𝐿𝑐. Each chip of the

flow is going to be mapped with 𝜋 shifts depending on whether the chip value is a ‘0’ or ‘1’.

When MIMO is activated, the number of the transmission array is selected. Then, depending on the

type of MIMO processing selected; each antenna PRI information gets weighted with the Hadamard

Matrix or each antenna uses the same code. In the case of Range Domain Separation method, the code

length is taken 4 times longer than the needed and then transmitted from each array antenna with a

delay. If APAS codes are used, the code length will be need to be double.

The type of antenna or antenna array and its characteristics, the simulation of the radiation, the

transmission, the radiator itself, the free space model, the collector and the targets characterization are

simulated using Matlab System Object functions belonging to the Phased Array Toolbox package.


141

System Objects: The system objects are a special kind of Matlab object specially designed to

implement and/or simulate active systems with input information that changes over the time due to

different parameters. They can be thought as black boxes that use our data input to generate processed

outputs. They are useful to simulate generic scenarios or functions, like the simulation of the free

space model acting as a filter for our generated transmitter signals or the models of the antennas’

behavior used to radiate these signals. These generic simulations can be done quicker and more

efficiently with Matlab system objects, however they cannot be access or modified. They also save the

user time since these generic functions do not need to be implemented manually, and the

implementation can be focused in those specific elements of the simulation chain of the radar system

under study which need to be specifically implemented.

Once the transmission of the signals have been propagated through the channel, reflected from the

targets and the echoes collected back in the receiver (system objects simulation), the digital receiver

front end of the system implementation starts to work with the signal as seen Fig. 58.

Receiver: As the signal arrives to the receiver it gets processed by the matched filter of each of the

different receiver antennas (in the case that MIMO is activated). Each receiver implements a parallel

range gate processing as it was seen in Fig. 60 in the section 3.1.3. If MIMO is enabled, the processing

is done (according to the MIMO method) and the different signals separated and then conducted to

perform the FFT along the N dimension of each range gate belonging to its radar data cube (in this

moment the radar data cube have dimensions 𝐿𝑐 𝑥 𝑁𝑉 𝑥 𝑁𝐹𝐹𝑇). Once the FFTs are performed, the

Doppler information is available and the rough beamforming can be processed along the virtual

antenna dimension of the radar data cube (dimensions 𝐿𝑐 𝑥 𝑁𝐴 𝑥 𝑁𝐹𝐹𝑇), then the square law detector

data comes into the CFAR, where the detections are performed along the three dimensions of the radar

data cube. The targets can be at a different range gate, speed and angle, and the radar data cube

contains all these dimensions of information. Once the detections are final, the information is

transferred to the fine angle of arrival part. The targets detected coordinates will be used to improve

the angle resolution where the target has been detected, taking the radar data cube data from the FFTs

output, which is the 𝐿𝑐 𝑥 𝑁𝑉 𝑥 𝑁𝐹𝐹𝑇 dimension radar data cube.


142

Sequence (Lc) Generator

TX

LO


TX1

LO

S

S

∙ ∙ ∙ S S∙ ∙ ∙ S S∙ ∙ ∙S S∙ ∙ ∙

N=2 N = 1 (M Sequences)N

M-Sequences

APAS Sequences

. . .

1

SISO

-TX

Dwell System Time =

PRF = M

IMO

-TX

∙ ∙∙

Had.

Had.

Had.

Had.

Hadamard Weighting

S S∙ ∙ ∙

x 1

S S∙ ∙ ∙

x 1

S S∙ ∙ ∙

x 1

S S∙ ∙ ∙

x 1

S S∙ ∙ ∙

x 1

S S∙ ∙ ∙

x -1

S S∙ ∙ ∙

x 1

S S∙ ∙ ∙

x -1

S S∙ ∙ ∙

x 1

S S∙ ∙ ∙

x 1

S S∙ ∙ ∙

x -1

S S∙ ∙ ∙

x -1

S S∙ ∙ ∙

x 1

S S∙ ∙ ∙

x -1

S S∙ ∙ ∙

x -1

S S∙ ∙ ∙

x -1

∙ ∙ ∙

M Sequences

TX2

TX-

TX- -1

N

S

∙ ∙ ∙S

∙ ∙ ∙S

∙ ∙ ∙S

Dwell System Time =


D

D

D

LO

TX1

TX- -1∙ ∙∙

TX-

TX2

S S S S

S

N

S S S S

S S S S

S

S S S S

S

S

N=1 (M Sequences)

Dwell System Time =

Sequence longer

Ou

ter

Had

amar

Co

de

Ran

ge D

om

ain

Se

par

atio

n

Fig. 110: Block diagram of the transmitter part of the PMCW radar system, SISO and MIMO configurations.


143

M Accum.Integrate

RX-1

RX-

∙ ∙∙

N-FFT

N-FFT

N-FFT

CFAR Detector

Fine BFDoA

Radar Data Cube- Rough Angles

x x

MIMO

Sequence ( )

M Accum.Integrate

M Accum.Integrate

M Accum.Integrate

M Accum.Integrate

M Accum.Integrate

Sequence ( )

N-FFT

N-FFT

N-FFT

MIMO

RoughBeamforming

RG #1

RG #2

RG #

RG #1

RG #2

RG #

Correlator/ Pulse Compression

x N

x N

Radar Data Cube -Virtual Antennas

x N x

=1

Detection’sCoordinates

Radar Data Cube- After FFTsx x

Radar Data Cube -Doppler spectrum

x x

Pulse Compression Gain Accumulations Gain Outer Code Gain Doppler Processing Gain Rough Beamforming Gain

Max. System Gain

Fig. 111: Block diagram of the receiver side of the PMCW radar system.


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Processing gain: In each part of the process there are system power level gains (indicated in green

color), depending on the parameters used. All the processing gain performed in the system is coherent,

i.e., the phase is preserved until the last moment. The power is then added as ‘voltages’, it is squared.

Since the noise is uncorrelated, it will just be summed up as ‘power’, therefore the SNR improvement

in each stage will be of 10 log10(𝑥). The noise floor will increase with the gain but half of what the

signal level will increase by Eq. (122):

-Digital Receiver Front End:

Most of the system gain is produced in the digital front-end of the digital receiver. The first stage

where SNR gain is achieved is in the digital receiver front-end. When the parallel range gate

processing inputs the signal, it is correlated and compressed in each of the matched filters of the bank

of correlators. The pulse compression gain depends on the length of the sequence by 𝐺𝑝𝑐 = 10 ∙

log10 𝐿𝑐. Afterwards, the flow of 𝐿𝑐 sequences is accumulated along the range domain bins. The SNR

processing gain depends on M by 𝐺𝑎𝑐 = 10 ∙ log10𝑀.

The signal flow continues to run and if MIMO with outer code is enabled there is going to be a gain

after the MIMO processing depending on the number of transmitter antennas used, 𝐺𝑂𝐶 = 10 ∙

log10𝑁𝑇𝑋. Following, the radar data cube with information related to each virtual array antenna will

be processed with FFTs along the range gates; with the computation of the FFTs, the gain depends on

the number of points that the FFT takes by 𝐺𝑁𝐹𝐹𝑇 = 10 ∙ log10𝑁.

Therefore, the total gain of the digital receiver front-end can achieve as high levels as:

-Digital Back End:

The transmitter side of the system does not use beamforming, therefore, there is not extra gain here.

However, the receiver side does; the beamforming used in the receiver produces a gain that will

depend on the number of the virtual array antennas. The number of virtual antennas is 𝑁𝑣 = 𝑁𝑇𝑋 ∙ 𝑁𝑅𝑋

At the receiver side the signals combine coherently resulting in an SNR gain equal to 𝐺𝐵𝐹 = 10 ∙

log10𝑁𝑣. Ultimately the total SNR gain of the system is achieved just before the CFAR detections

block, so that the SNR is optimum to get the best CFAR possible performance, given by Eq. (124).

𝑆𝑁𝑅𝑖𝑚𝑝 = 𝑆𝐺 −𝑁𝐺 = 20 ∙ log10 𝑆 − 10 ∙ log10𝑁 = 10 ∙ log10 𝑥 (122)

𝐺𝑝(𝑑𝐵) = 10 log10(𝐿𝑐 ∙ 𝑀 ∙ 𝑁 ∙ 𝑁𝑇𝑋) (123)

𝐺𝑠𝑦𝑠(𝑑𝐵) = 10 log10(𝐿𝑐 ∙ 𝑀 ∙ 𝑁 ∙ 𝑁𝑇𝑋 ∙ 𝑁𝑣) (124)


145

4 Simulations and Discussion

In this chapter, a variety of simulations is showed. Each simulation has been set in order to show a

particular constraint or important achievement thanks to the implementation of all the signal

processing methods and techniques explained along the theory in the Chapter 2 and in the system

implementation in the Chapter 3. Along the Chapter 4, the target scenarios are being changed, the

targets parameters are varied according to the purpose of the simulation and the selectable parameters

of the system processing stages are also varied. The results are continuously being commented in order

to link them with the expected results and describe the details of the radar system performance.

Discussions of the advantages of the implementation, the drawbacks and the achievements drawn from

the simulations results are expected all along each of the subsections of the chapter.

Firstly, the information resulting from the simulations chain in Matlab is going to be described. The

simulation 1 is used to show the way the information is going to be treated, along the description of a

SISO system example. Secondly, the simulations 2 and 3 will be used to analyze the effect of the

CFAR parameter variations in the detection performance of the radar system. In the third place, the

simulations 4, 5 and 6 are used to analyze the performance of the MIMO implementation in different

target scenarios and arrays’ configurations. The simulations 7 and 8 are set to analyze the rough

beamforming stage performance and the differences among the different beamforming methods. The

last part of the chapter is focused in showing how the system performance would vary depending on

the variation of the main design system parameters, with the simulations 9 and 10.

4.1 Simulations Information

Firstly, the general information that is displayed after each radar system simulation is going to be

introduced for a better understanding of the results that will be further shown.

As a simulation example; a simple system with one standing target is going to be set; in Table 5 the

initialization parameters of the simulated targets are shown. The number of targets set; their RCS, the

position, speed and angle. The position represents a 3 dimensional referential system [x, y, z]; for

simplicity in the interpretation of the results, all the targets are placed along the x axis of the reference

system. The speed describes the same referential system and it is considered that the target just moves

along the x axis as well. If the speed is positive, the target is moving away from the radar system, if the

speed is negative, the target is getting closer. The angle describes the angle off bore-sight taking as a

reference the center of the radar transmitting antenna or array.


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Table 5: Simulation 1, targets scenario initialization parameters.

Targets Value Unit

Number 1 -

RCS 30.0 dBsm

Position [1.2525, 0, 0] m

Velocity [0, 0, 0] m/s

Angle 0 deg

The Table 6 describes the main specified parameters of the system to be simulated. The parameters are

the minimum performance design values that the system needs to achieve in the end of the simulation.

These values are used to calculate all the other dependent parameters of the system that will make the

whole Matlab simulation chain work.

Table 6: Simulation 1, main design parameters chosen for the radar system under simulation.

Parameter Value Unit

Required Unambiguous Range 30 m

Required Range Resolution 7.5 cm

Required Scan Range 120 deg

Required Angular Resolution 5 deg

Req. Rad. Velocity Resolution 0.2 m/s

Required ambiguous velocity 12.66 m/s

The design parameters presented in Table 5 and Table 6 are just a small part of all the parameters that

need to be specified in the script function before running the radar system simulation, as can be seen in

Fig. 61 of the section 3.1.4. These are targets parameters and the scenario parameters; with the

development of the chapter 4 and the need to set new parameters, the antenna, PMCW and CFAR

design parameter structures are introduced as well. Once all the design parameters are set, the

simulation can start following the simulation chain flow described in the section 3.1.4.


147

The parameters presented the Table 7 describe the theoretical values that set the link budget and some

theoretical general power levels and references of the system to be simulated. The transmitted output

power is always set to 10 dBm, the antennas gain is the sum of the TX and RX gains, and it is always

kept to 0 dB. The path loss is the theoretical losses calculated for the current scenario and position of

the initialized target/s. The receiver power is the calculated theoretical power of the received signal

after the target echo before the ADC converter. The noise power at the RX is the theoretical value of

the noise before the ADC and the SNR is the theoretical value that the target will have after the whole

digital signal processing. The processing gain is the system gain due to the signal processing with the

pulse compression, M accumulations and N-FFT processing.

Table 7: Simulation 1, theoretical PMCW link budget of the targets.


Transmit Power 10.0 dBm

Antenna Gain 0.0 dB

Path Loss -85.3 dB

Receiver Power -45.3 dBm

Noise Power at RX output -67.8 dBm

Target SNR 95.3 dB

Processing Gain 72.8 dB

Besides all the previous parameters, another important set of data of the PMCW radar simulation is the

main system parameters of the Table 8, the design values of the Table 6 are used to compute them.

The parameters showed match with the design parameters of the example that has been developed

along Chapter 3, since the same design parameters have been chosen for this simulation. Some of the

parameters in Table 8 are fixed and do not vary (carrier frequency, chip rate), but most of them are

variable.


148

Table 8: Simulation 1, summary of the main PMCW system parameters.


Carrier Frequency 79 GHz

Chip Rate 2000 Msps

PRF 2000 KHz

Doppler Sampling Rate 13.42 KHz

Doppler Resolution 104.87 Hz

Sequence Length (𝐿𝑐) 1000 Chips

Number of Accum. (M) 149 -

FFT Size (N) 128 -

System Dwell Time 9.54 ms

Unambiguous Range 75.0 m

Range resolution 7.5 cm

Max. Unambiguous Velocity 12.74/45.88 [m/s km/h]

Velocity Resolution 0.2/0.72 [m/s km/h]

It can be noticed that even though some of the parameters were set in Table 6 to certain value, their

final value after the dependent parameters calculation is slightly changed. This is due to rounding

reasons as explained in the section 3.2.1.

Following the simulation flow of the Fig. 61 of the section 3.1.4, the simulation starts. The simulation

process can take from few minutes up to hours, depending on the system parameters chosen and the

processing capacity of the computer used for the simulation. The messages presented in the command

window for the example simulation, during the course of the simulation are given as follows:

-- Simulation started @ Feb.11,2015 12:38:53 --

Simulating SISO block 10 of 128












-- Signal propagation simulation stopped @ Feb.11,2015 12:40:58 --


149

It can be seen that the type of antenna used is a single input single output configuration, so it is a

simple simulation that does not take a long time. The waveform is firstly composed and once all the

data is ready, the signal propagation is simulated per blocks. Later on, all the data is processed and

managed following the matlab chain flow as presented in the Chapter 3 for the system implementation.

The first results of the simulation appear, as seen in Fig. 112, where the mesh of the radar data cube

after the FFT processing is presented:

In Fig. 112 it can be observed a 3D mesh made up from the data contained in the radar data cube after

the simulation and after all the digital signal processing of the digital front-end, i.e, after the FFT

processing stage. The peak is surrounded by a noise floor and the graph is normalized to 0 dB. The

peak is the echo signal of the target that was set for the example simulation. It can be observed some

signal spreading spectrum shape due to its high energy level.

The target was set to a 0 speed, therefore the target appears in the center of the Doppler domain

centered at zero. For a better view of both of the domains, a cut of each of them is also plotted; see

Fig. 113 and Fig. 114:

Fig. 112: Simulation 1, detection in the range – Doppler domain 3D representation of the radar data cube.


150

In Fig. 113 the cut of the range domain is showed, leading to a much clearer interpretation of the range

domain information. The range can be seen as from the range 0 up to the last unambiguous range, 37.5

meters. According to the Table 8 the necessary sequence length to match the system design parameters

is 1000 chips. Given that the range resolution is 7.5 cm, the maximum unambiguous range should be

75 meters. But it is correct, since APAS codes have been chosen as waveform to simulate. The

characteristics of APAS codes are explained in the section 2.1.5; their characteristics lead to the need

of choosing a double length code for a design that needs half the length in order to accomplish the

design parameters.

A peak occurs at 1.275 meters displaying a clear detection among the noisy floor and showing where

the target is placed, the graph is normalized to 0 dB. The target was placed at 1.2525 meters and the

detections shows that it occurs at 1.275 meters, the error is 0.025 meters which accomplishes the

required range resolution set in the system design, 2.5 cm < 7.5 cm.

In Fig. 114 the cut of the Doppler domain is showed, leading to a much clearer interpretation of the

Doppler domain information. The Doppler domain starts at -12.7 meters and goes up to 12.7 meters.

The sidelobes shape is now clearly visible with the main side lobes over the noise floor and the rest of

them hidden under the rest of the noise floor. The peak is perfectly centered at 0 speed.

The data of Fig. 113 is taken after the pulse compression processing and accumulation, before the FFT

processing, it can be noticed that the SNR level is around 75 dB. However, the Doppler profile (Fig.

114) is the representation of the data taken after the FFT, there is a noticeable change in the gain of

around 15 dB.

0 5 10 15 20 25 30 35

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X: 1.275

Y: 0

Range profile

Range [m]

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]

Fig. 113: Simulation1, detection showed in the range profile of the radar data cube taken before the FFT processing.


151

After all the signal processing has been developed to accomplished the highest possible signal level,

the CFAR detector is executed to automatically detect the targets, as it has been explained in the

section 3.3. The Fig. 115 is plotted:

-10 -5 0 5 10-100

-90

-80

-70

-60

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-30

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-10

0

Doppler [m/s]

Magnitude [

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Doppler cuts

Fig. 114: Simulation 1, detection in the Doppler profile of the radar data cube taken after the FFT processing.

0 20 40 60 80 100 120 140-60

-40

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80Detection of trgt #1 in RG cut # 18

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Range gates

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Fig. 115: Simulation 1, detection cuts in the Doppler domain cuts and the range domain cuts where there have been

detections.


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Fig. 115 is subdivided in two subplots; the upper plot is the real CFAR implementation performed

along the range domain, which results are used in the system. The lower plot is the CFAR detection

along the Doppler domain using the system object, just depicted for information and analysis

purposes. In the title of the figure can be seen the Doppler cut used to represent the range profile of the

detected target, or the range cut used to represent the Doppler profile of the detected target. In the

CFAR detection figures, the domains do not appear in distance or speed units but in range gates and

Doppler bins. The detected coordinates [Range gates, Doppler bins] are the location that the detections

will use for further processing.

The blue line of the upper part of Fig. 115 is the plotting of all the range gates data belonging to the

Doppler bin where the detection has been found, taken from the radar data cube after the FFT

processing. The red line defines the CFAR behavior, it is the CFAR threshold; every data sample

under the red line is not considered a detection, every sample over the line is considered a detection.

The data of the threshold level comes given by every single threshold calculated by the CFAR

algorithm along each of the Doppler bins of the radar data cube under study, as explained in the

section 3.3. As can be observed, just one detection is made along the Doppler bin 65. The confirmed

detected targets are showed in the plots, also the failed to detect targets, but not the false alarm

detections.

The CFAR algorithm presents valuable information in the command line, it appears show as

following:

****************

CFAR performance

****************

---------------------------------------

CFAR detections through the doppler bins

---------------------------------------

7 cells exceed the threshold.

----------------------

Final targets detected

----------------------

Range gate Doppler bin

Target 1 : 3 22

Target 2 : 18 65

Target 3 : 18 70

Checking the detections:

-------------------------

There is a false alarm in the Range gate 3 with the Doppler bin 22 .


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There is a CONFIRMED DETECTION in the Range gate 18 with the Doppler bin 65 .

There is a false alarm in the Range gate 18 with the Doppler bin 70 .

== == == == == == == == == == == == == == == == == == == == == == == == ==

-Target 1 is detected at 1.275m. (Range gate: 18) traveling at 0 m/s(Doppler bin: 65).

The interpretation of the previous data is done as follows: After performing the CFAR throughout the

radar data cube there have been 7 samples (CUT) which value was higher than the threshold calculated

in its sliding window. These are potential targets that need to be studied with the post-detection

algorithms of CFAR. After the post-detection algorithms there are 3 detections left. The detection

checking algorithm compares the coordinates of the final coordinates with the theoretical coordinates

where the target/s should be detected and finds out that two of the detections are false alarms and one

of the detections is actually the target, as a confirmed detection. The relevant data of the confirmed

targets detected is presented; in this case the target was not moving and was located at a 1.275 m.

distance. The Table 9 confirms the data given by the system. The information will be shown in the

shape of tables in future simulations results, as seen in Table 9 and 10.

Table 9: Simulation 1, CFAR Performance.

CFAR Info Number

Exceeded Thresholds 7

Targets Detected 3(1)

False Alarms 2

Confirmed Detections 1

Table 10: Simulation 1, detected targets coordinates and interpretation.

CFAR Info Range Gate Doppler Bin Interpretation

Detection 1 3 22 False Alarm

Detection 2 18 (1.275 m.) 65 (0 m/s) Confirmed Detection


In Fig. 116 the detections can be seen in the shape of two detection matrixes, representing the range

domain and the Doppler domain of the radar data matrix. The white dots are the detections, the black

dots are the not detections. The left detection matrix shows the detections obtained just right after the

CFAR algorithm, the right detection matrix shows the detections just right after the post-detection

algorithm has been applied. The subfigure zooms in the field region where the targets are detected.


154

It can be noticed the false alarm detected in the third range gate with the doppler bin 22 circled in red.

After the post-detection algorithm, the number of detections has decreased from 7 to 3, as can be

noticed comparing both matrixes. In green the confirmed detection in the range gate 18 with the

doppler bin 65 and next to it, the other false alarm in the same range gate but in the Doppler bin 70.

Before the post-detection algorithm, most of the false alarms are consecutively surrounding the real

target coordinate; if the Fig. 114 and the lower part of the Fig. 116 are compared, the width of the

main lobe peak is noticeable. The excessive wideness of the main lobe of the detection peak cause

most of the false alarms, this can be caused by the proximity of the target to the radar system and its

high RCS, which causes a high power level detection, but it could also be caused by a bad selection of

the CFAR tuning parameters. The consecutive false alarms can be cleared by the post-processing

algorithm without problem. However, the false alarm appearing in the same range gate but in a further

doppler bin cannot be cleared by the post-processing algorithm. This false alarm is caused by the side

lobes of the peak, as can clearly be seen in Fig. 114. Again, these side lobes can be due to the high

power of the signal reflected or a bad selection of the sequence waveform, which causes other

correlation peaks other than for lag zero. The later is not the case since the sequence used is APAS.

Over threshold cells

Doppler Bins

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Fig. 116: Simulation 1, Detection matrixes; after CFAR detection(left) and after post-processing

algorithm(right).


155

After the detections coordinates have been saved, the Matlab chain continues running and ends up

with the presentation of the radar system performance results, which are the SNR of the targets along

the different stages of the system, see Table 11:

Table 11: Simulation 1, radar system performance at different stages of simulation, theoretical and simulated.

Targets SNR Value [dB]

Before ADC - Theory 22.5

Before ACD - Simulation 22.4

Before FFT - Theory 74.2

Before FFT - Simulation 75.3

After FFT - Theory 95.3

After FFT - Simulation 92.8

After FFT/BF - Theory 95.3

After FFT/BF - Simulation 92.8

In Table 11 the SNR levels of the target are checked at different simulation stages, both the

theoretically calculated and the obtained after the simulation. Before any signal processing the SNR

level of the target was 22.4 dB, practically the same as obtained in theory. Nonetheless, after the signal

processing (due to the pulse compression and accumulation), the SNR gets improved up to 75.3 dB,

which is still 17.5 dB below respecting to the SNR after the FFT processing. Since there is no

beamforming, being that the antenna configuration used is SISO, the SNR keeps being the same.

Ultimately, the radar system gets a gain of 70.3 dB, just 2.5 dB under the total processing gain

predicted, according to Table 11.

4.2 CFAR results

To show the variability of the detection results, a generic simulation scenario is chosen. With the

variation of the CFAR selectable parameters there can be seen and analyzed different detection

outcomes. The scenario chosen is very similar to the scenario under study in the section 4.1; the main

design parameters of the simulation are the ones described in Table 6, therefore the summary of the

main system parameters will have an identical outcome as in Table 8. However, there have been

added new simulated targets and in different locations, as described in Table 12. These changes will

lead to the variation of the theoretical values of the PMCW link budget of the targets; the new data is

presented in Table 13, the antennas gain and the transmitted power is not showed since is always

going to be the same.


156

Table 12: Simulation 2, targets scenario initialization parameters.

Targets Parameters Value Unit

Number 3 -

RCS 30 dBsm

Position [3, 0, 0] / [4.5, 0, 0] / [6.375, 0, 0] m

Velocity [-4, 0, 0] / [4, 0, 0] / [8, 0, 0] m/s

Angle 0 deg



Path Loss -100.5 / -107.5 / -113.6 dB

Receiver Power -60.5 / -67.5 / -73.6 dBm


Targets SNR 80.1 / 73.1 / 67 dB


Once the chosen generic scenario is defined and clear, the selectable parameters that give the CFAR

algorithm its configurability are presented. All the parameters importance was presented in the

sections 2.3.1 and 3.3.1. The CFAR structure initialization is part of the system design parameters that

need to be set in the script function preceding a simulation, as seen in the Matlab chain diagram of

Fig. 61.

Firstly, the number of training cells at each side of the sliding windows must be chosen, besides the

number of guard cells at each side of the cell under test (CUT). The type of CFAR algorithm selected

to evaluate the data inside the sliding window can also be selected; the possible selections for the

simulation are: CA, GOCA, OS, SOCA, OSGO, which implementation was presented in the section

3.3.2. In the case of Order Statistic algorithms (OS and OSGO) the rank needs to be selected. The

maximum selectable rank will be twice as much as the number of total sliding window cells. Another

parameter to select is the scaling factor, it can be set to be manual or automatic; the automatic

adjustment is just implemented for CA, GOCA and OS. If any of the other algorithms is selected the

manual option should be chosen, besides the scaling factor to consider, in another field. The main

parameter in a CFAR detector is the desired probability of false alarm, which will also be selectable in

the CFAR initialization structure.

In Table 14, the CFAR parameters chosen for the simulation under consideration are presented:


157

Table 14: Simulation 2, values of the CFAR parameters chosen.

CFAR Parameter Value

Training Cells (𝑁𝑡𝑐) 6

Guard Cells (𝑁𝑔𝑐) 1

Algorithm OS

Probability of False Alarm (𝑃𝑓𝑎) 10−6

Rank 9

Scale Factor Auto 1

Scale Factor if Manual (𝑇𝑚𝑎𝑛) /

The results of the CFAR detections with the previous configuration can be checked in Table 15 and

16:

Table 15: Simulation 2, CFAR performance.

CFAR Info Number

Exceeded Thresholds 16


False Alarms 1





Detection 2 41 (3 m.) 85 (4 m/s) Confirmed Detection

Detection 3 62 (4.575 m.) 45 (-4 m/s) Confirmed Detection

with Range Migration


As can be noticed the three targets are correctly detected. However, the detection 3 shows a target in a

range gate where it should not be. The targets, according to the theoretical calculations, should be

located in the range gate 61, but it is detected in the range gate 62. This is due to the fact that the target

was positioned in the edge of the range gate 61, the furthest range edge from the radar. Since the

system started to gather information until it finished (𝑇𝑑), the target was moving at a speed of -4 m/s;

the target was so close to the next range gate that during most of this time it was in the next range gate.

Therefore most of the energy was sampled in the next range gate and the detection is located there. In

Fig. 117 and 118 the detections matrixes and the detection profiles can be observed.


158

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40


Doppler Bins

Pow

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[dB

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[dB

]

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[dB

]

Fig. 118: Simulation 2, detections showed in Range and Doppler cuts.


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Fig. 117: Simulation 2, detections of the simulation 2 showed in the detection matrixes.


159

For a view of their Doppler spectrum and range profile the Fig. 119 can be observed. The spectrum

peaks in this case, are placed in different Doppler bins, indicating that during the dwell time there have

been frequency shifts due to movement of the targets.

The SNR of the targets at different points of the simulation can be compared with the target levels

from the Fig 118 and 119, as presented in Table 17:



Before ADC - Theory 7.3 / 0.3 / -5.8

Before ACD - Simulation 8.4 / 1.4 / -5.5

Before FFT - Theory 59.1 / 52 / 46

Before FFT - Simulation 59.9 / 52.6 / 45.5

After FFT - Theory 80.1 / 73.1 / 67

After FFT - Simulation 77.3 / 70.1 / 63

After FFT/BF - Theory 80.1 / 73.1 / 67

After FFT/BF - Simulation 77.3 / 70.1 / 63

From the Table 17, the levels of the simulations with the theoretical are consistent.

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Fig. 119: Simulation 2, detections of the targets of the simulation 2 in Range and Doppler profiles.


160

Following, the different selectable parameters will be varied in order to discuss the behavior change

that this will cause and the scenarios when certain parameters values would likely give more

advantage than the others.

4.2.1 Probability of False Alarm

Probability of false alarm: The change in the probability of false alarm will lead to the increasing or

decreasing of the whole threshold in the same manner for every evaluated point. While reducing the

𝑃𝑓𝑎 the threshold is expected to be lowered, decreasing it should rise the threshold level. A simple way

to see the effects of the 𝑃𝑓𝑎 over the detections is leaving the field to be detected without any targets

and ‘detect’ only the noise floor. In the simulation under consideration, the number of range gate

existing cells are 500, while the number of Doppler bin cells are 128; giving a total of 64000 cells

inside which there is one sample of the signal received. If the 𝑃𝑓𝑎 is set to 10−2, there should be 1

‘detection’ each 100 cells, or what is the same; 640 detections for the whole matrix. If the 𝑃𝑓𝑎 is

decreased up to 10−4 the threshold over the noise floor should rise and around 6.4 detections should

appear. Checking the Fig 120, can quickly be seen the difference. The system has detected 681

detections over the threshold with 𝑃𝑓𝑎 = 10−2 and 11 for 𝑃𝑓𝑎 = 10

−4, which is close enough to the

640 and 6.4 theoretical values respectively.


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Fig. 120: Simulation 2, detections over the system noise floor for 𝑃𝑓𝑎 = 10−4(left) and 𝑃𝑓𝑎 = 10

−2 (right).


161

Varying the 𝑃𝑓𝑎 but while keeping the targets of the simulation 2 give a clearer picture of what is

happening. In Fig. 121 the targets can still be seen but surrounded by false alarm detections.

Fig. 122 shows the signal and the CFAR threshold level along the Doppler bins where each of the

confirmed detected targets is located. The upper side of the figure are the profiles for 𝑃𝑓𝑎 = 10−4; it

can be seen that the threshold (red line), has been lowered some dB if it is compared with the profile

of Fig. 118 when the 𝑃𝑓𝑎 was set to 10−6. This threshold level lowering has caused the inclusion of

the highest noise peaks of the noise floor over the threshold. In the lower part of the figure, for

𝑃𝑓𝑎 = 10−2 can clearly be seen how the threshold level has decreased and it is very close to the noise

floor. With so high probability of false alarm, there are many noise floor peaks that overcome the

threshold level.

In the case under study, the targets where placed close to the radar and their RCS values were high.

This situation is perfect to obtain all the detections without problems; since the signal power levels

received are high. Therefore a low threshold level is not desired in order to avoid false alarms, i.e., a

low 𝑃𝑓𝑎. However, in situations where the targets are very small or they are far in the range (implying

a low power signal level), a low 𝑃𝑓𝑎 will be beneficial in order to lower the threshold as much as

possible in order to detect them.


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Fig. 121: Simulation 2, detection matrixes of the detections for 𝑃𝑓𝑎 = 10−4(left) 𝑃𝑓𝑎 = 10−2 (right).


162

To keep the 𝑃𝑓𝑎 low allows avoiding false alarms but it can also skip targets that would have been

detectable if the 𝑃𝑓𝑎 was higher. To set the 𝑃𝑓𝑎 high allows the detection of low power level signals

caused by small or far targets, but also raises the number of false alarms. The results of Fig. 123 show

the same targets of the simulation 2 but with a much lower RCS, set to -20 dBsm. It can be observed

that setting a too low 𝑃𝑓𝑎 makes the threshold to not consider the target as a detection; the threshold is

over the target detection in the most right figure. In this situation, a low 𝑃𝑓𝑎 would have been

beneficial to detect the lowest signal targets.

The furthest located target (RG #86) has the lowest power level due to the higher path losses, using a

𝑃𝑓𝑎 = 10−6 (upper figure) to set the threshold, is too low and the CFAR does not detect it as a

detection. However, in this case, setting the 𝑃𝑓𝑎 = 10−4 helps with the detection (lower part of Fig.

123), now it is detected. Nonetheless there are a couple more of false alarms, since the threshold is

lowered in the same level all over the detection field.

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Fig. 122: Simulation 2, Detection profiles of the detections in the simulation 2 for 𝑃𝑓𝑎 = 10−4 (up) and 𝑃𝑓𝑎 = 10−2

(down).


163

4.2.2 Number of Training Cells

Number of training cells: Now, all the values of the Table 14 are kept as they were initially set and the

number of training cells is varied at each side of the sliding window. Increasing the number of training

cells makes the algorithm to consider more values in its evaluation to decide the threshold; therefore if

there is clutter inside the training cells under consideration, the threshold value will be modified.

Depending on the other parameters settings the change could make the target unnoticed. However, a

larger number of samples also mean a better estimate of the background around the CUT. A better

estimate could achieve higher probability of detection with a lower probability of false alarms.

In order to be able to see the effects of the training window variation, the algorithm type is change to

CA (Cell Averaging), since the algorithm used so far is not so easily affected by this variation. The

other change introduced in the simulation is the location of one of the targets. A complicated situation

where two targets are moving at the same speed and near between them is chosen to illustrate the

scenario. The target 1 now changes the direction of speed and the target two is located just 60 cm

further than the target 1, as can be seen in Table 18:

Table 18: Simulation 3, new targets location to show the variation in training cells effect.

Position [3, 0, 0] / [3.6, 0, 0] / [6.375, 0, 0] m

Velocity [4, 0, 0] / [4, 0, 0] / [8, 0, 0] m/s

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Fig. 123: Simulation 2, detection profiles of the targets with RCS=-20 dBsm, with 𝑃𝑓𝑎 = 10−6 (up) and 𝑃𝑓𝑎 = 10

−4

(down).


164

The CA CFAR algorithm uses power averaging as explained in the section 3.3.2, and it is one of its

drawbacks, as it will be explained later. There are two targets in the same Doppler bin and in very

close range gates (60 cm = 8 range gates). In the upper simulation 𝑁𝑡𝑐 = 2, therefore the neighbor

target power is not present inside the training cells of the sliding window. As a consequence, both of

the targets are detected; In Fig. 124; the first two graphs of the upper figure are the same, since both of

the targets are detected in the same Doppler bin, in the middle graph the detail of the threshold and the

signal can be observed. The thresholds are separated and do not interfere in the other targets, being

capable of detecting both them. However, if the number of training cells is set to 10, as in the middle

figure, the value of the neighboring target is already included in the sliding window, being averaged.

As a result, the threshold is increased and the targets mask each other, resulting in a missed detection.

As the number of training cells increase, the threshold line smoothers, as can be observed in the same

figure.

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Fig. 124: Simulation 3, detection profile of a CA CFAR algorithm for 𝑁𝑡𝑐=2 (up), 𝑁𝑡𝑐 =10 (middle) and 𝑁𝑡𝑐=16

(down).


165

4.2.3 Guard Cells

Number of guard cells: The guard cells are meant to avoid self-interferences caused by the CUT itself,

when the signal is too strong or there is range migration. If the side-lobes are too high, their power will

be evaluated besides the rest of the training cells, degrading the estimation of noise and triggering a

wrong threshold level. By the other hand, if there are too many guard cells selected, the real estimation

of power around the CUT could be not real and also give bad threshold estimation. To show these

effects, the modified initial simulation has been used with the variation of some scenario elements and

parameters: one target has been moved further and purposely placed in the edge of a range gate while

moving at a sufficient speed to make it cross the range gate and cause range migration, its RCS level

has been also decreased to avoid excessive spectral leakage due to range migration.

In Fig. 125 is clear that the energy is found in two different range gates for the fastest target, depicted

by two different peak colored shapes. The target has been moving from one range gate to the next one

while the data was being gathered, therefore there is energy detected in both of the range gates. If the

number of guard cells is set to 0, there is a false alarm due to this range gate migration. When the

threshold is estimated around a target, the power in the training cells is high due to the high level of

the other target, and makes the threshold rise. If the number of guard cells is 1, the neighbor high

power signal is avoided in the power estimation and therefore the threshold is not affected, avoiding a

false alarm detection, as seen in Fig. 126:

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Fig. 125: Simulation 3, Doppler profile with a target causing range migration.


166

In Fig 127 can be seen how the threshold varies around the CUT when the guard cells are set to 8

(down) comparing with set to zero (up).

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Fig. 127: Simulation 3, detection profiles varying the number of guard cells, from 0(up) to 8(down).

X: 105 Y: 132

Index: 1

RGB: 1, 1, 1


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Fig. 126: Simulation 3, detection matrix of a range migrated detection with 0 guard cells (left) and 1 guard cell

(right)


167

4.2.4 Algorithm

Algorithm: The variation of the CFAR algorithm used has the biggest effect in the final results.

However, it is difficult to present their characteristics with a realistic simulated scenario where clutter

and background noise variations that affect each algorithm. To evaluate the behavior of each algorithm

the same scenario as in the previous simulations is kept, i.e., uniform background noisy environment

with multiple target situations. This is just one of the multiple different situations that in practice can

happen and is not enough to comprehend these algorithms but shows how each algorithm behaves.

A two targets situation is presented, where each of the targets is located in the same Doppler bin at a

close distance (10 range gates away) and the number of training cells (12) is big enough to take both

targets’ echoes within the reference window. The signal power found in the proximities of the cut is,

because of the oversimplified assumptions and lack of other signals or clutter, interpreted as clutter.

Therefore the threshold is raised, which leaves one or both of the targets undetected, as seen in Fig.

128. These situations can be improved to a certain degree with the variation of the number of training

cells (𝑁𝑡𝑐) or/and the probability of false alarm (𝑃𝑓𝑎 ) but it is not really the solution.

The targets are presented with very similar power levels. In Fig. 128 the CA algorithm is applied with

𝑁𝑡𝑐=12 and 𝑁𝑡𝑐=20, both of the targets are detected.

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Fig. 128: Simulation 3, CA algorithm applied for two contiguous detections with 𝑁𝑡𝑐= 12 (left) and 𝑁𝑡𝑐= 20 (right).

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Fig. 129: Simulation 3, GOCA algorithm applied for two contiguous detections with 𝑁𝑡𝑐= 12 (left) and 𝑁𝑡𝑐= 20 (right).


168

In Fig. 129, the GOCA algorithm appears to mask one of the targets, the other target is detected. The

main difference between CA and GOCA is that CA is based on the assumption of a situation with

uniform clutter in the neighbourhood, while GOCA takes into account clutter edges happening in the

studied area. For the presented situation, CA is beneficial, since the clutter is uniform, but in case of

clutter edges presence GOCA would be superior.

The SOCA algorithm is applied in Fig. 130 and both of the targets are detected without problems.

SOCA algorithm chooses the smallest averaged value of the sliding windows parts to set the threshold,

as explained in the theory chapter. This is beneficial in this situation but for situations where more

targets and with more different levels will be present, it will cause masking of lower power targets.

In order to solve these issues, the OS algorithm is also tested. As explained in previous chapters, this

algorithm does not average the noise and clutter power in the reference window, instead, one of the

values is chosen as the threshold. Therefore the assumption of uniform clutter does not apply anymore.

In Fig. 131 can be seen that now the threshold is not so sensitive to the peaks of the targets and

therefore the detections are perfectly recognized by the decision.

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0 50 100 150 200 250 300 350 400 450 500-60

-50

-40

-30

-20

-10

0

10


Range gates

Pow

er

[dB

]

0 20 40 60 80 100 120 140-60

-50

-40

-30

-20

-10

0


Doppler Bins

Pow

er

[dB

]

0 50 100 150 200 250 300 350 400 450 500-60

-50

-40

-30

-20

-10

0

10


Range gates

Pow

er

[dB

]

0 20 40 60 80 100 120 140-60

-50

-40

-30

-20

-10

0


Doppler Bins

Pow

er

[dB

]

0 50 100 150 200 250 300 350 400 450 500-60

-50

-40

-30

-20

-10

0

10


Range gates

Pow

er

[dB

]

0 20 40 60 80 100 120 140-60

-50

-40

-30

-20

-10

0


Doppler Bins

Pow

er

[dB

]

0 50 100 150 200 250 300 350 400 450 500-60

-50

-40

-30

-20

-10

0

10


Range gates

Pow

er

[dB

]

Fig. 130: Simulation 3, SOCA algorithm applied for two contiguous detections with N_tc= 12 (left) and N_tc= 20 (right).


169

The conventional CFAR algorithms suffer from the matter that they are designed to assume uniform

distributed statistics in the reference window, i.e, no clutter or other target presence in the window

under test. Under this assumption, the larger the number of cells used to estimate the power level, the

better the estimation. However for rapidly changing clutter or strong clutter edges, false alarm increase

is expected. GOCA case should reduce the number of false alarms at clutter edges but at the same

time, it would decrease the probability of detection in the presence of several targets.

As checked in the previous figures, applying OS algorithm has a clear advantage due to its robustness

in multiple target situations compared to CA and GOCA, since OS is does not work on the assumption

of homogeneous clutter inside the reference window. The threshold is rarely controlled by other

targets inside the reference window. Moreover, OS estimation makes the reference window size less

influential and can be chosen freely according to other aspects. All in all, OS CFAR seems the best

choice for the scenario under consideration and it is chosen for the rest of the simulations of the radar

system presented in this document.

The environment variations in background noise, clutter presence and targets density make vary the

conditions under which the CFAR work. For certain environment a CFAR algorithm could be

advantageous to use, but in other moment, other algorithm would be more beneficial to use. The

changing conditions make very difficult the choice of one of the algorithms. In the simulation chain,

the 5 CFAR algorithms described in 3.3.2 are implemented. Yet, none of them guarantees the perfect

behavior under all kind of situations. The variation of the related parameters, 𝑁𝑡𝑐, 𝑁𝑔𝑐 and 𝑃𝑓𝑎 might

help to adjust the performance to the different scenarios under test (samples size, target density, etc),

so a preset set of parameters could be loaded depending on the foresighted scenario under which the

radar is going to work. Yet, in a real situation these parameters preset should also change to adapt,

since the conditions for which the parameters were preset may also change.

0 20 40 60 80 100 120 140-60

-50

-40

-30

-20

-10

0


Doppler Bins

Pow

er

[dB

]

0 50 100 150 200 250 300 350 400 450 500-60

-50

-40

-30

-20

-10

0


Range gates

Pow

er

[dB

]

0 20 40 60 80 100 120 140-60

-50

-40

-30

-20

-10

0


Doppler Bins

Pow

er

[dB

]

0 50 100 150 200 250 300 350 400 450 500-60

-50

-40

-30

-20

-10

0


Range gates

Pow

er

[dB

]

0 20 40 60 80 100 120 140-60

-50

-40

-30

-20

-10

0


Doppler Bins

Pow

er

[dB

]

0 50 100 150 200 250 300 350 400 450 500-60

-50

-40

-30

-20

-10

0


Range gates

Pow

er

[dB

]

0 20 40 60 80 100 120 140-60

-50

-40

-30

-20

-10

0


Doppler Bins

Pow

er

[dB

]

0 50 100 150 200 250 300 350 400 450 500-60

-50

-40

-30

-20

-10

0


Range gates

Pow

er

[dB

]

Fig. 131: Simulation 3, OS algorithm applied for two contiguous detections with 𝑁𝑡𝑐= 12 (left) and 𝑁𝑡𝑐= 20 (right).


170

4.3 MIMO results

In order to show the differences in the system when MIMO is enabled, the PMCW system parameters

of the Table 6 are used, however some tiny changes are noticed due to the calculation of the dependent

parameters, as can be seen in Table 19. This is due to the adjustments that need to be done in the

dependent parameters to adapt the design parameters to the reality of the MIMO TX. The value that

substantially varies is the number of accumulations, M, as it is explained later. Also, the targets

initialization parameters of the simulation 2 are used again, as seen in Table 12, therefore the

theoretical PMCW link budget of the Table 13 should be the same. The CFAR values are also kept

according to Table 14, consequently the CFAR performance of Tables 15 and 16 is identical.



Chip Rate 2000 Msps

PRF 2000 KHz





FFT Size (N) 128 -






Once the generic scenario is defined, the selectable parameters that give the MIMO stage

configurability are presented. The MIMO methods variations were introduced in the sections 2.4.3 and

2.4.4. The MIMO parameters structure is another part of the design parameters that can be selected in

the script of the Matlab data flow and can be located in the Matlab chain diagram of the Fig. 61.

4.3.1 Small Array and High RCS

In Table 20, the selectable parameters of the MIMO stage are showed. The number of transmitter and

receiving antennas is selectable, but in the case of applying Outer Hadamard Code MIMO, the number

of antennas just can be set to 4 or its multiples, since there just exist Hadamard codes for such lengths.


171

The receiver antenna should be set to a minimum of 2 antennas. The method is chosen among the

Outer Hadamard Code(1) and the Range Separation Domain(2).

Table 20: Simulation 4, selectable parameters of the MIMO stage.

MIMO Parameter Value

Number of TX antennas (𝑁𝑡𝑥) 4

Number of RX antennas (𝑁𝑟𝑥) 2

MIMO method 1 ( Outer Hadamard Code )

Regarding to the dependent parameters that MIMO sets; the spacing in the receiver antennas depends

on the number of transmitting antennas. The length of the sequence is also going to be changed

depending on the MIMO method chosen; if Outer code is chosen, the length of the code would be the

same as without MIMO radar, but if Range domain is chosen, the length of the sequence should be

𝑁𝑡𝑥 times longer than the given by the design specifications. The previous applies for both APAS and

M-Sequences. When Outer Code is chosen, there has to be taken into account the transitions between

MIMO blocks for the Hadamard code, therefore adding 2 extra M sequences in the PRI. This is not

necessary for Range domain code, since it does not use rendering codes.

The M needed to satisfy the design parameters follows the same rule based on the Eq. (104). However,

if the Outer Hadamard method is applied, the length of the Hadamard code MIMO blocks needs to be

taken into account; the formula would change to:

The dwell time in this case also includes the number of extra deliveries due to the use of Hadamard

codes implemented along each antenna MIMO block. The dwell time needs to be maintained the same

to keep the rest of the specifications in the design values, therefore the M accumulations have to be

reduced. The Hadamard code chosen needs to be the same length as the number of transmitting

antennas, therefore, the dwell time is divided by this number as well. The number of necessary

accumulations is reduced, in the case applied and for 𝑁𝑡𝑥 = 4 , M comes down to 36. The gain due to

M accumulations will be smaller, but after the Outer Code MIMO processing other gain will be

obtained which is equivalent to the gain lost in the accumulations number decreasing, as can be

checked in Fig. 73. This extra gain will contribute to achieve the total gain that the system would have

with the normal number of M accumulations if Outer Hadamard Code would not have been applied.

After the MIMO processing, the SNR level is expected to increase by 10 ∙ 𝑙𝑜𝑔10𝑁𝑡𝑥 , which would be

around 6 dB more. Added to the 15.56 dB of the 36 M accumulations, give a total of 21.6 dB. The

same gain that the system would have achieved using M = 149.

𝑀 =

𝑇𝑑𝑇𝑐 ∙ 𝐿𝑐 ∙ 𝑁 ∙ 𝑁𝑡𝑥

(125)


172

Following, the results of the MIMO radar simulation with the settings of the Table 20 are going to be

showed. The range power level profile will be showed in each step where the signal processing gets

gain. Firstly, the signal level is showed after the pulse compression and accumulation, then after the

FFT processing and finally the gain due to the use of MIMO when the rough beamforming is used. All

the profile figures that are shown below are normalized to zero in order to have a better read of the

SNR in each stage of the signal processing. In Table 21 the simulation and theoretical resulting values

of the targets’ SNR are presented.



Before ADC - Theory 7.3 / 0.3 / -5.8

Before ADC - Simulation 8.4 / - / -

After Pulse Compression – Theory 37.3 / 30.3 / 24.25

After M Accumulations – Theory 52.9 / 45.85 / 39.8

Before FFT - Theory 59.1 / 52 / 46

Before FFT - Simulation 60 / 52.8 / 46.6

After FFT - Theory 80.1 / 73.1 / 67

After FFT - Simulation 75.4 / 68.2 / 63.3

After FFT/BF - Theory 89.1 / 82.1 / 76

After FFT/BF - Simulation 83.4 / 76.2 / 71.3

In Fig. 132 the range-Doppler three-dimensional representation of the radar data cube for maximum

gain can be observed. After the full signal processing gain, the targets can be clearly seen:

The theoretical SNR of the targets is quite low in the input of the receiver. Since the signals have not

been correlated in this point yet, it is not possible to show a range profile of the signals.

Fig. 132: Simulation 4, targets in the range – Doppler domain 3D representation of the radar data cube.


173

In Fig. 133 the range profile of the signal can be seen after the pulse compression in the matched filter;

the SNR gain is expected to be 𝐺𝐿𝑐 = 10 ∙ 𝑙𝑜𝑔101000 = 30 dB. The SNRs of the targets can be

observed in the range of the expected levels, with the 30 dB gain already increased.

In Fig. 134 the range profile is showed measured after the M accumulations; the difference in SNR is

expected to be 𝐺𝑀 = 10 ∙ 𝑙𝑜𝑔1036 = 15.56 dB, but due to the Hadamard extra 𝑁𝑡𝑥 = 4 blocks, the

total gain is 𝐺𝑝𝑟𝑒𝐹𝐹𝑇 = 59.1. The theoretical values are practically matching the simulated SNR.

0 5 10 15 20 25 30 35-90

-80

-70

-60

-50

-40

-30

-20

-10

0

Range Profile after the Pulse Compression

Range [m]

Magnitude [

dB

]

Fig. 133: Simulation 4; range profile of the received signal after the pulse compression.

0 5 10 15 20 25 30 35

-60

-50

-40

-30

-20

-10

0

Range profile before FFT

Range [m]

Magnitude [

dB

]

Fig. 134: Simulation 4, range profile after M accumulations and MIMO, before the FFT processing.


174

After the FFT processing, the Doppler cuts appear already with the peaks centered in the velocity

value where the targets are moving. In Fig. 135 the SNR level is showed after the FFT processing, the

expected FFT gain is 𝐺𝑀 = 10 ∙ 𝑙𝑜𝑔10128 = 21.07 dB. The SNRs gain is appreciable, the total SNR

after the pulse compression, accumulations and FFT processing sums up around 52 dB for each target.

Due to the MIMO configuration of the system, with 4 antennas in the transmitter side and 2 other in

the receiver part, a virtual array of 8 antennas is formed. As explained in 3.3.3, a rough beamforming

is made along different angles, this processing stage allows an expected extra gain of 𝐺𝐵𝐹=10∙

𝑙𝑜𝑔10 4 = 9 𝑑𝐵, for 8 virtual antennas. In Fig 136 the Doppler cut profile of the radar data cube after

the rough beamforming is showed. It can be noticed that there is a gain of around 9 dB between the

signal after the FFT processing of the Fig. 135 and the profile showed in Fig. 136 after the rough

beamforming processing.

-10 -5 0 5 10-100

-90

-80

-70

-60

-50

-40

-30

-20

-10

0

Doppler [m/s]

Magnitude [

dB

]

Doppler cuts after FFT

Fig. 135: Simulation 4, Doppler cuts of the radar data cube after the FFT processing.


175

Overall, the theoretical gain was expected to be around 𝐺𝑃𝑟𝑜𝑐 = 10 ∙ 𝑙𝑜𝑔10(𝐿𝑐 ∙ 𝑀 ∙ 𝑁 ∙ 𝑁𝑡𝑥 ∙ 𝑁𝑣) =

10 ∙ 𝑙𝑜𝑔10(1000 ∙ 36 ∙ 128 ∙ 4 ∙ 8) = 81.7 𝑑𝐵, the achieved simulation gain of the targets is around

76 dB. The differences can be due to simulation inaccuracies, not perfectly coherent gains due to the

Doppler shift effect or the Blackman window applied in the FFT. When compared with the results of

the Table 11 for the SISO configuration, the SNR levels are maintained similar excepting for the extra

rough beamforming gain achieved in the last stage, which gives the MIMO configuration an extra

gain. Moreover, now the angles information is available for angle of arrival estimation.

4.3.2 Small Array and Low RCS

For the next simulations, a new scenario is set; in the previous simulations, the RCS of the targets

were set to high values that would correspond to big targets (i.e., large tracks), thus the SNR levels of

the detections were very high and easy to detect. In the next simulations, the RCS of targets are set to a

more realistic value for average pedestrians, -8 dBsm. The number of targets and their locations and

velocities are changed, as described in Table 22:

-10 -5 0 5 10-100

-90

-80

-70

-60

-50

-40

-30

-20

-10

0

Doppler [m/s]

Magnitude [

dB

]

Doppler cuts after the Rough Beamforming

Fig. 136: Simulation 4, Doppler cut of the radar data cube after the rough beamforming processing.


176

Table 22: Simulation 5, simulated targets initialization parameters.


Number 4 -

RCS -8 dBsm

Position [4.5, 0, 0] / [11.25, 0, 0] / [13.5, 0, 0] / [17.7, 0, 0] m

Velocity [10, 0, 0] / [-7, 0, 0] / [12, 0, 0] / [1, 0, 0] m/s

Angle 0 deg

The new simulated targets settings will raise the change of the theoretical values of the PMCW link

budgets; the updated data is presented in Table 23:



Path Loss -107.5 / -123.4 / -126.6 / 131.2 dB

Receiver Power -105.5 / -121.4 / -124.6 / -129.2 dBm


Targets SNR 41 / 25.1 / 21.7 / 17.3 dB


As it can be observed, the path losses are high and the expected received power of each target are low

due to the smaller RCS of the targets in this simulation.

Table 25 describes the main PMCW system parameters, most of them are kept as in the previous

simulations since the main design parameters have not changed. However, the number of transmitting

antennas has been reduced to 2, the same number of receiving antennas, Table 24:

Table 24: Simulation 5, MIMO configuration.






177




Chip Rate 2000 Msps

PRF 2000 KHz





FFT Size (N) 128 -




Max. Unambiguous Velocity 12.66 /45.57 [m/s km/h]


The set CFAR parameters are kept exactly in the same values as the ones presented in Table 14.

In Table 26, the final SNR theoretical and simulated values are showed:



Before ADC - Theory -37.5 / -53.6 / -56.8 / -61.4

Before ADC - Simulation -

After Pulse Compression – Theory -7.7 / -23.6 / -26.8 /-31.4

After M Accumulations – Theory 10.9 / -5 / -8.2 / -12.8

Before FFT - Theory 13.9 / -2 / -5.1 / -9.8

Before FFT - Simulation 12.8 / 2.1 / 0.5 / 0.2

After FFT - Theory 35 / 19.1 / 15.9 / 11.3

After FFT – Simulation 30.7 / 16.6 / 9.6 / 9.1

After FFT/BF - Theory 41 / 25.1 / 21.9 / 17.3

After FFT/BF - Simulation 35.6 / 20.7 / 15.6 / 14.8


178

In Fig. 137 the range profile after the pulse compression is represented. Even though the theoretical

gain is 30 dB, it is not enough to differentiate the signals over the noise floor since the signals are still

kept under the noise floor mixed with the noise.

0 5 10 15 20 25 30 35

-35

-30

-25

-20

-15

-10

-5

0

5

X: 4.575

Y: -12.95

Range profile after Pulse Compression

Range [m]

Magnitude [

dB

]

X: 11.25

Y: -7.284

X: 13.57

Y: -13.19

X: 17.63

Y: -5.792

Fig. 137: Simulation 5, range profile after pulse compression.

Fig. 138: Simulation 5, range profile after the pulse compression and M accumulation.

0 5 10 15 20 25 30 35

-15

-10

-5

0

5

X: 4.575

Y: 0

Range profile before FFT (After pulse compression + accum.)

Range [m]

Magnitude [

dB

]

X: 11.25

Y: -10.66X: 13.57

Y: -12.19

X: 17.63

Y: -11.96


179

In Fig. 138, the signal after the accumulations show already some higher values; the closest target has

a higher SNR and therefore after the 18.6 dB of theorical gain due to 73 accumulations, is able to rise

over the noise floor, reaching a SNR of around 13 dB. The second closest target has just overcome the

noise floor while the other two are not able yet to leave the noise mix.

After the FFT processing, the SNR is expected to improve by 21 dB. In Fig. 139 the Doppler profile

view of the radar data cube is showed after the FFT processing; the strongest target has already a very

good SNR level, while the second closest target is completely on sight. The two furthest targets now

are visible just over the noise floor. A curious effect can be observed among the two weaker targets;

even though the target positioned 17.7 meters away and traveling at 1 m/s should have around 4 dB

lower SNR than the target travelling at 12 m/s (13.5 m. far), after the FFT processing they have similar

SNR levels. The effect can be explained by diverse factors, one of them the speed difference between

them. While the furthest target is traveling at 1 m/s, the other one travels at 12 m/s. The high speed of

the second target can cause that the coherent gain does not match as much as the coherent gain of the

slow target, therefore resulting in a degradation of the SNR gain for the fast target. Another reason can

be found in the application of the Blackman window before the computation of the FFT, which could

have decrease the power level of the detection.

-10 -5 0 5 10-100

-90

-80

-70

-60

-50

-40

-30

-20

-10

0

X: -10.09

Y: 0

Doppler [m/s]

Magnitude [

dB

]

Doppler cuts after the FFT

X: 6.922

Y: -13.17

X: -12.06

Y: -19.86

X: -0.9889

Y: -19.83

Fig. 139: Simulation 5, Doppler profile of the radar data cube after the FFT.


180

Fig. 140 gives another interesting view of the range profile after the FFT. The speeds and distances of

each target can be checked with the results presented by the CFAR in Table 27. In Fig. 121 the radar

data cube data can be seen in 3D; the faster the targets are, the closest to the extremes of the Doppler

domain. In this graph the results presented are taken after the rough beamforming processing and show

that the SNR has improved by around 5 dB. Since the formed virtual array has 4 antennas; 𝑁𝑣 = 𝑁𝑡𝑥 ∙

𝑁𝑟𝑥 = 4, the theoretical gain is 𝐺𝑣 = 10 ∙ 𝑙𝑜𝑔10 4 = 6 𝑑𝐵.

Fig. 140: Simulation 5, range profile of the radar data cube after the FFT processing.

Fig. 141: Simulation 5, 3D representation of the radar data cube data after the rough beamforming processing.


181

If the range profile at this point is observed (see Fig. 142), it can be noticed that the noise floor is now

5 dB further from the targets’ peaks than in the case of Fig 140, in the stage after the FFT processing.

The gain in signal power is squared incremented (20 ∙ 𝑙𝑜𝑔10 𝐺𝑝𝑤) because of the signal coherence, the

noise gain is produced as unity since the noise is random (10 ∙ 𝑙𝑜𝑔10 𝐺𝑛). Therefore, the final SNR

gain remains (10 ∙ 𝑙𝑜𝑔10 𝐺).

At this point the gain of the system is maximum and is when the CFAR detection should be

performed. Therefore, the SNR is also maximum and this will give advantage in the detection of the

targets that are small. After the simulation, the CFAR stage shows the performance given by Table 27

and the detections information given by Table 28:


CFAR Info Number

Exceeded Thresholds

2(-60°) / 4(-42.85°) / 3(-25.71°) / 6(-

8.57°) / 8(8.57°) / 2(25.71°) / 4(42.85°)

/ 3(60°)


False Alarms 0


Since MIMO is being used, the CFAR is performed after the rough beamforming stage in order to get

the highest possible SNR before the CFAR detection process. MIMO is processed in this case as

Fig. 142: Simulation 5, range profile of the radar data cube after the rough beamforming processing.


182

explained in the section 3.3.3, therefore the detections are performed in each of the angles under

scanning. There is a total virtual array of 4 antennas; therefore there are 8 angles to be scanned from

-60 to 60 degrees. The interpretation of the detection is described by the CFAR as given in Table 28:



Detection 1 61 (4.575) 14 (-10 m/s) Confirmed Detection





- 235 (17.625 m.) 60 (1 m/s) Expected Detection

From Table 28 can be seen that there are two targets that were in the edge of their range gate and due

to their high speed they crossed the range gate where originally where placed and ended up reflecting

most of their energy in the consecutive range gate from where they were expected. There is also an

expected detection that was not able to be detected, it has been missed. In Fig. 143 the detection

profiles are showed; the targets with the highest SNR are easily detected while the two further targets

are very difficult.

When the targets RCS is small or they are located very far, the detections are difficult to be

guaranteed. One of the targets with small SNR has been missed by the CFAR threshold, as can be seen

in the most right profile of the Fig. 143. A variation of the parameters in the CFAR could have helped

to finally detect the missed target; also the increasing of the array antennas can raise the SNR. There

are cases where the targets RCS is weaker or they are further located; in such cases the CFAR

adjustments will not be useful.

0 50 100 150-50

-40

-30

-20

-10

0

10


Doppler Bins

Pow

er

[dB

W]

0 100 200 300 400 500-60

-40

-20

0


Range gates

Pow

er

[dB

W]

0 50 100 150-50

-40

-30

-20

-10

0


Doppler Bins

Pow

er

[dB

W]

0 100 200 300 400 500-50

-40

-30

-20

-10


Range gates

Pow

er

[dB

W]

0 50 100 150-60

-50

-40

-30

-20

-10

0


Doppler Bins

Pow

er

[dB

W]

120 140 160 180 200 220 240

-18

-16

-14

-12

-10

-8

-6

-4


Range gates

Pow

er

[dB

W]

0 50 100 150-60

-50

-40

-30

-20

-10

0


Doppler bins

[dB

W]

220 240 260

-12

-11

-10

-9

-8

-7

-6

Trgt #4 NOT detected in Doppler cut 60

Range gates

[dB

W]

Fig. 143: Simulation 5, CFAR profile cuts of the detections.


183

In Fig. 144 the detection matrix is showed, after and before the post-detection algorithm. It can be seen

that the detections are very clean even before the cell selection; this is due to the good parameters

balance chosen under this scenario in the CFAR.

4.3.3 Big Array and Low RCS

In Simulation 6, all the parameters of the system in Simulation 5 are kept the same as well as the

targets settings and CFAR parameters. However the number of transmitting and receiving antennas is

increased, Table 29. The theoretical SNR final values of the targets will be increased and some

variations in the dependent parameters of the system will be introduced to compensate the number of

antennas configuration. The PMCW parameters summary can be checked in Table 30:







Doppler Bins

Range G

ate

s

20 40 60 80 100120

50

100

150

200

250

300

350

400

450

500


Doppler Bins

Range G

ate

s

20 40 60 80 100120

50

100

150

200

250

300

350

400

450

500


Doppler Bins

Range G

ate

s

20 40 60 80 100120

50

100

150

200

250

300

350

400

450

500


Doppler Bins

Range G

ate

s

20 40 60 80 100120

50

100

150

200

250

300

350

400

450

500

Fig. 144: Simulation 5, detection matrixes.


184





Number of Accum. (M) 17 []




The gain process is expected to be exactly the same from the pulse accumulation until the stage after

the FFT processing, therefore all the gains and data showed in the figures of the simulation 5 are

identical. The difference will come after the rough beamforming stage, where the number of antennas

makes a big difference in the final gain. The virtual array achieved with this MIMO configuration is

𝐺𝐵𝐹 = 𝑁𝑇𝑋 ∙ 𝑁𝑅𝑋 = 32. Thus, the gain due to MIMO rough beamforming is expected to be 𝐺𝐵𝐹 =

10 ∙ 𝑙𝑜𝑔1032 = 15 𝑑𝐵. In Table 31, the final SNR theoretical and simulated values are showed:

Table 31: Simulation 6, radar system performance at different stages of the system.


Before ADC - Theory -37.5 / -53.6 / -56.8 / -61.4


After Pulse Compression – Theory -7.7 / -23.6 / -26.8 /-31.4

After M Accumulations – Theory 4.6 / -11.3 / -14.5 / -19.1

Before FFT - Theory 13.6 / -2.3 / -5.5 / -10.1

Before FFT - Simulation 12.8 / 2.2 / 0.6 / 0.2

After FFT - Theory 34.7 / 18.8 / 15.6 / 11.0

After FFT – Simulation 31.3 / 16.7 / 9.6 / 9.8

After FFT/BF - Theory 49.8 / 33.8 / 30.7 / 26.0

After FFT/BF - Simulation 45.4 / 30.2 / 24.5 / 22.6


185

In Fig. 145, the Doppler profile after the FFT processing is showed. The SNR levels are practically

identical as the ones of the simulation 5.

However, when comparing with the Doppler profile after the rough beamforming processing, the

results come out to be quite different, as can be seen in Fig. 146:

The SNR level has notably increased in all the targets. Even the weakest targets now enjoy a good and

clean SNR peak around to 22 and 24 dB of SNR, respectively. Fig. 148 shows a clear capture of their

profile. The SNR levels are higher than the same capture of the simulation 6, Fig. 142.

-10 -5 0 5 10

-70

-60

-50

-40

-30

-20

-10

0X: -9.954

Y: 0

Doppler [m/s]

Magnitude [

dB

]

Doppler cuts after the FFT

X: 7.027

Y: -14.18

X: -11.91

Y: -19.84 X: -0.9759

Y: -21.2

Fig. 145: Simulation 6, Doppler profile of the radar data cube after the FFT.

-10 -5 0 5 10-100

-90

-80

-70

-60

-50

-40

-30

-20

-10

0

X: -9.954

Y: 0

Doppler [m/s]

Magnitude [

dB

]

Doppler cuts after the Rough Beamforming

X: -0.9759

Y: -22.77 X: 7.027

Y: -15.24

X: -11.91

Y: -20.87

Fig. 146: Simulation 6, Doppler profile of the radar data cube after the rough beamforming.


186

The strongest peaks have increased in the same manner to reach up to 45 and 30 dB SNR levels,

respectively. In Fig. 147 the 3D representation of the radar data cube is found. It looks more defined

than the one obtained with just 4 antennas in the virtual array. However, due to the strong gain

increase experienced, a detail can be noticed.

The most left detections in Fig. 147 are those belonging to targets with velocities of 10 and 12 m/s

respectively, approaching the radar system. It was found in Table 28 that these high speed targets

suffer range migration.

Fig. 147: Simulation 6, targets in the range – Doppler domain 3D representation of the radar data cube.

Fig. 148: Simulation 6, range profile of the radar data cube after the rough beamforming processing.


187

In Fig. 149 the energy level belonging to the previous range is visible in both of the targets. The power

contained in the previous range gate was small enough (meaning that the target did not spend most of

the dwell time in this range gate but in the next) to be hidden under the noise floor, and thus, not

detected. However, after the extra gain introduced by the big virtual antenna array, it is raised on top

of the noise floor and is now visible, as seen in Fig. 149 inside the dotted circles.

Again, at this point the gain is maximum and the SNR higher than in previous steps and in Simulation

5. The CFAR performance shows the results presented in Table 32:


CFAR Info Number

Exceeded Thresholds 75 total. 25(-0.95) / 24(0.95)


False Alarms 9


In this case, the virtual array is composed by 32 virtual antennas, consequently the information after

the rough beamforming is contained in twice as many scanning angles, i.e, 64 angles. The targets are

placed at 0 angle from the center of the array, therefore the beams closer to the angle zero will get

most of the detections. In the previous simulation, this fact was not so evident due to the fact that there

were many fewer scanning beams, and as a result the beams were wider, thus the detection of the

Fig. 149: Simulation 6, targets in the range – Doppler domain 3D back representation of the radar data cube.


188

targets could spread among the different angled beams. In this case the beams are much thinner, thus

the system has a much better angle resolution. Since the targets were set in angle zero, there are not

detections in most of the angles; the central angles get most of the detections (0.95 deg), as seen in

Table 33. The detections in other angles are due to sidelobes reasons due to the bad performance of the

sum and delay beamforming technique. The interpretation of the detections is showed in Table 33:

Table 33: Simulation 6, CFAR detected targets coordinates and interpretation.





Detection 4 61 (4.575 m.) 14 ( -10 m/s) Confirmed Detection

with range migration







with range migration




The 4 targets are now correctly detected; however there is a noticeable increase of false alarms. In

Fig. 150 the detection profiles are showed, the high SNR levels (more than 20 dB for the weakest

targets) of the targets make the detections easy and the OS algorithm sets the threshold with a good

distance to the noise floor, avoiding false alarms in the proximities of the target detections.

0 50 100 150-40

-20

0

20


Doppler Bins

Pow

er

[dB

W]

0 100 200 300 400 500-60

-40

-20

0

20


Range gates

Pow

er

[dB

W]

0 50 100 150-40

-30

-20

-10

0

10


Doppler Bins

Pow

er

[dB

W]

0 100 200 300 400 500-40

-30

-20

-10

0

10


Range gates

Pow

er

[dB

W]

0 50 100 150-40

-30

-20

-10

0

10


Doppler Bins

Pow

er

[dB

W]

0 100 200 300 400 500-50

-40

-30

-20

-10

0


Range gates

Pow

er

[dB

W]

0 50 100 150-40

-30

-20

-10

0


Doppler Bins

Pow

er

[dB

W]

0 100 200 300 400 500-50

-40

-30

-20

-10

0


Range gates

Pow

er

[dB

W]



189

In Fig. 151 the detection matrixes belonging to the simulation 6 are depicted. In the detection matrix

before the post-processing, the first target detection print appears broader than the rest of detections

(detected in two different range gates). This is due to the fact that the power level of the signal in the

migrated range gate is high enough, to be detected. Thus, letting two consecutive range gates with

detections.

However the second speedy target, at the left of the figure, does not show the same detection footprint.

Its previous range gate’s power level is just a bit higher than the noise floor and is not enough to be

taken over the CFAR threshold. In the figure in the left, after the post-processing there are less

detections left, leaving a total of 9 false alarms.

Most of the final false alarms occur due to noise peaks in range gates where there are no targets

present. These false alarms occur because the gain also acts in the noise floor, letting the highest

values of the noise floor closer to the CFAR threshold. Since the targets do not mask the high peaks,

the CFAR threshold level is lowered and these spurious are casually detected. If the noise floors of the

Fig. 143 and Fig. 150 are compared, the highest value of the simulation 5 noise floor can be seen

around the – 15 dBW, while for the simulation 6 is around -5 dBW; a +10 dB difference caused by the

extra gain given by the 32 virtual antenna array (+15 dB).


Doppler Bins

Range G

ate

s

20 40 60 80 100120

50

100

150

200

250

300

350

400

450

500


Doppler Bins

Range G

ate

s

20 40 60 80 100120

50

100

150

200

250

300

350

400

450

500


Doppler Bins

Range G

ate

s

20 40 60 80 100120

50

100

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350

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450

500


Doppler Bins

Range G

ate

s

20 40 60 80 100120

50

100

150

200

250

300

350

400

450

500



190

Range Domain Separation: The initial goal of the radar system under study reaches the scope of short

range detections with high range gate resolution. The orthogonality of MIMO using outer Hadamard

method is very positive because it only relies on the cross-correlation of the Hadamard code at zero

delay, which is zero. An extension of the scope of the radar system could reach the long range

detections, not just short range.

For long ranges while keeping the same range gate resolution, longer sequences are going to be

needed. When computing the system dependent parameters under long 𝑅𝑢𝑛𝑎𝑚𝑏, the code selection

length grows and the M accumulations number decrease (the longer the code is, the more time each

PRI takes to send it, and in order to accomplish the system dwell time the number of M needed is

smaller). Moreover, long range detections make sense to detect higher speed targets (which require

higher N), therefore leaving less room for the M accumulations.

One characteristic of the Outer Hadamard code method is that it needs one extra M accumulation in

the beginning and the end of each PRI. These are needed because two sequences must be discarded at

the transitions of the Hadamard coefficients. The transitions between one Hadamard sequence and the

next one break the PAC (Periodic Auto-Correlation) property that has the sequence. Therefore, the

smaller the M number is, the smaller the efficiency of the system is, as seen in Eq. (126):

The value of M should be around 50 in order to minimize this overhead loss and never below 8. This

situation will show up when applying long range design system parameters, as explained in the

previous paragraph. That is the reason for introducing the new MIMO method based on range domain

separation. This MIMO method does not need the extra overhead M accumulations and therefore the

code efficiency is not reduced.

The simulation of the range domain separation method takes place in the same manner as the

simulations processes described for the Outer Hadamard Code in the previous simulations. The gains

and produced in the same stages of the system and the detections are processed in the same way. The

method implementation is different, as explained in the Chapter 3. However, in practice the only

difference is that it allows the efficient functioning of the radar system under long range detection

application scenario. The design parameters are chosen differently; longer unambiguous ranges, lower

range resolutions and higher unambiguous speeds, which take advantage of the characteristics of the

range domain separation method explained in the section 3.2.3. Since the results are practically the

same and the initial goal of the radar system under study are the short range detections, the simulations

results have just been showed applying outer Hadamard code, which is more efficient for short ranges.

𝜂𝑙𝑜𝑠𝑠 = log10 (

𝑀

𝑀 + 2) [𝑑𝐵] (126)


191

4.4 Angle of Arrival

In this section, the beamforming techniques and their contributions to the system improvement are

analyzed and discussed. The simulations 7 and 8 are used to draw results; firstly with the rough

beamforming analysis and later on with the fine beamforming application in the last stage of the

system.

4.4.1 Rough Beamforming

The first place in the system where an angle of arrival processing is performed is before the CFAR

detections. The rough beamforming is used to increase the targets SNR and provide angle information

in a first quick scan. Afterwards, the different angles are analyzed with the CFAR to get at which

angle, speed and range gate the detections are located, as explained in the section 3.3.3.

In the previous simulations all the targets were centered in the angle zero from the array center. So, the

detections were taking place in the central angle lobes of the rough beamforming. If the targets are

located at different angles, the detections will be found in different matrixes’ angles. After the rough

beamforming, each range gates – Doppler bins matrix contains the information of Doppler and speed

related to the scan of a certain angle in the radar field under scan. The higher is the number of the

virtual array, the more angle information the system can use to estimate the correct angle where the

target is located, i.e., the higher angle resolution.

For the next simulation, the same main system parameters as used in the previous simulations are

going to be used. The MIMO configuration in Table 34 is used, which will make the dependent

parameters be the ones presented in Table 35.







192









The setting of the CFAR parameters is kept as well, as the described in Table 14. However the targets

initialization scenario is changed and their new scenario data is presented in Table 36:



Number 3 -

RCS 0 dBsm

Position [3 ∙ cos(10°), 3 ∙ sin(10°), 0] / [4.5 ∙ cos(30°), 4.5 ∙ sin(30°),

0] / [5.625 ∙ cos(−35°), 5.625∙ sin(−35°), 0] m

Velocity [-4, 0, 0] / [3.5, 0, 0] / [6.5, 0, 0] m/s

Angle [10°, 30°, -35°] deg

As can be seen from Table 36, each target has been placed at an angle difference. With these angle

settings, the correct functioning of the angle of arrival is going to be checked. The CFAR algorithm is

going to search for the detections in each of the angles of the rough beamforming. Since there are 4

transmitting antennas and 2 receiving antennas, the virtual array has a size 𝑁𝑣 = 8, and the angles for

the quick scan in the rough beamforming will be double, 16.

The theoretical and simulated SNR values of the simulation 7 are showed in Table 37:


193



Before ADC - Theory -22.7 / -29.7 / -33.6

Before ADC - Simulation -21.9 / - / -

After Pulse Compression – Theory 7.3 / 0.3 / -3.6


Before FFT - Theory 28.7 / 21.6 / 17.8

Before FFT - Simulation 31.7 / 18 / 15.4

After FFT - Theory 49.7 / 42.7 / 38.8

After FFT – Simulation 49 / 35.3 / 30.7

After FFT/BF - Theory 64.8 / 57.8 / 53.9


The simulation follows the same gain steps as presented in the previous simulations and performs the

rough beamforming processing with the consequent energy gain. Since the targets are placed at

different angles, the angle of arrival cuts after the beamforming process draws a characteristic shape.

In the following figures, the rough beamforming shape can be observed in each of the target’s angle of

arrival cuts.

-60 -40 -20 0 20 40 60-100

-90

-80

-70

-60

-50

-40

-30

-20

-10

0

X: 12

Y: 0

Angle of arrival [degrees]

Magnitude [

dB

]

Angle of arrival cuts for Target 1

Fig. 152: Simulation 7, angle of arrival cut for the Target 1.


194

As can be noticed in Fig. 152, 153 and 154, the level of the side lobes is high. This high level is the

reason why there were extra detections in other angles in simulation 6, even though the targets were

placed in the angle 0. Nonetheless, the beamforming method forms the highest energy peak in the

angle scan close to the target’s location angle. The power difference will be enough to make the CFAR

algorithm discard the detections of lower energy in other angles and keep the correct angles as final

detections.

In order to check the Doppler cuts of the targets, the angle of detection where this Doppler cut is

represented, needs to be chosen. In order to see the Doppler cut of the Target 1, the angle 12 needs to

be selected, since for all the other angles the power level of the target 1 will not be maximum. In the

following figures the Doppler cuts of each of the targets are depicted. It can be observed that, even

though the angle is selected to represent the Doppler cut of certain target, also the other targets appear.

This power levels belong to the side-lobes of the other targets at this angle of representation. This is

due to the same reason discussed before, the Delay and Sum beamforming method produces big side

lobes that let the other targets be seen in other angles through their side lobes. The Doppler cuts of the

targets in the detected angles are given in Fig. 155, 156 and 157.


-60 -40 -20 0 20 40 60-80

-70

-60

-50

-40

-30

-20

-10

0

X: 28

Y: 0


Magnitude [

dB

]

Angle of arrival cut for Target 2


195

-60 -40 -20 0 20 40 60-80

-70

-60

-50

-40

-30

-20

-10

0

X: -36

Y: 0 Angle of arrival cuts for Target 3


Magnitude [

dB

]


-10 -5 0 5 10-100

-90

-80

-70

-60

-50

-40

-30

-20

-10

0

Doppler [m/s]

Magnitude [

dB

]

Doppler cuts for Angle = 10 degrees

X: 3.904

Y: 0

Fig. 155: Simulation 7, Doppler cuts for the Target 1, angle 10 degrees.


196

The same is going to happen in the 3D representation with the range and speed information of the

radar data cube for each target; the angle in which the power level wants to be checked will need to be

selected. As an example, in Fig. 158 the radar data cube 3D representation for the target 3 can be

observed.

-10 -5 0 5 10-100

-90

-80

-70

-60

-50

-40

-30

-20

-10

0

X: -3.513

Y: 0

Doppler [m/s]

Magnitude [

dB

]

Doppler cuts for the Angle = 28


-10 -5 0 5 10-90

-80

-70

-60

-50

-40

-30

-20

-10

0

X: -6.636

Y: 0

Doppler cuts for Angle = -36 degrees

Doppler [m/s]

Magnitude [

dB

]

Fig. 157: Simulation 7, Doppler cuts for the Target 3, angle -36 degrees.


197

At this point of maximum gain, the MIMO CFAR algorithm is applied, the performance of the CFAR

is showed in Table 38:


CFAR Info Number

Exceeded Thresholds 100 total. 12 (12°) / 12 (15°) / 12 (28°) /

10 (30°) / 12 (-36°)


False Alarms 1


The CFAR works for the angles [-60°, -52°, -44°, -36°, -28°, -20°, -12°, 4°, 4°, 12°, 20°, 28°, 36°, 44°,

52°, 60°], 16 angles scanned after the rough beamforming. As can be noticed by the number of

thresholds overcome, most of the detections occur in angles close to the angles where the targets are

located. But there are still detections in all the other angles, in a lower number. Even though there are

not targets located in the other angles, the beamforming used is conventional (Delay and sum) and

forms big sidelobes around the main lobe, causing detections of the targets in other angles. Even

though there are detections in all the angles, in the end, there are just 4 targets detected, one false

alarm; this is due to the fact that the CFAR algorithm always discriminates by power level when

checking among the same [Range Gate; Doppler Bin] coordinate along different angles, just letting as

a detection the coordinate [Range Gate; Doppler Bin; Angle] with the highest power level. This

process was explained in the section 3.3.3. The interpretation of the detections is showed in Table 39:

Fig. 158: Simulation 7, target 3 in the range – Doppler domain 3D for the angle = -36 degrees.


198

Table 39: Simulation 7, CFAR detected targets coordinates and interpretation.

CFAR Info Range Gate Doppler Bin Angle Interpretation

Detection 1 40 (3) 85 (4.2 m/s) 10 (12°) Confirmed Detection

Detection 2 61 (4.575 m.) 47 (-3.5 m/s) 12 (28 °) Confirmed Detection

Detection 3 76 (5.7 m.) 31 (-6.5 m/s) 4 (-36 °) Confirmed Detection


Detection 4 359 8 - False Alarm

The detections have new coordinates where their highest power level is found, which is the angle scan

that is closer to the angle location where they have been set in Table 36. In Fig. 159 the detections

profiles of the targets can be observed, and in Fig. 160 the detection matrix that comes out after all the

angles detection sum.

0 50 100 150-60

-40

-20

0

20


Doppler Bins

Pow

er

[dB

W]

0 100 200 300 400 500-60

-40

-20

0

20


Range gates

Pow

er

[dB

W]

0 50 100 150-60

-40

-20

0

20


Doppler Bins

Pow

er

[dB

W]

0 100 200 300 400 500-60

-40

-20

0

20


Range gates

Pow

er

[dB

W]

0 50 100 150-50

-40

-30

-20

-10

0

10


Doppler Bins

Pow

er

[dB

W]

0 100 200 300 400 500-60

-40

-20

0


Range gates

Pow

er

[dB

W]



Doppler Bins

Range G

ate

s

20 40 60 80 100120

50

100

150

200

250

300

350

400

450

500


Doppler Bins

Range G

ate

s

20 40 60 80 100120

50

100

150

200

250

300

350

400

450

500


Doppler Bins

Range G

ate

s

20 40 60 80 100120

50

100

150

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500


Doppler Bins

Range G

ate

s

20 40 60 80 100120

50

100

150

200

250

300

350

400

450

500



199

In Simulation 8, the number of antennas is increased with the configuration of Table 40. All the other

parameters and targets settings are kept in the same values as the ones presented for the simulation 7.






The virtual antenna array then becomes of the size 𝑁𝑣 = 32, and the number of scanning angles that

are performed in the rough beamformer are 64. The results are in line with those of the simulation 5

for the same MIMO configuration but now the targets are positioned in different angles. The SNR

levels of the system are presented in Table 41:





After Pulse Compression – Theory 7.3 / 0.3 / -3.6


Before FFT - Theory 28.7 / 21.6 / 17.8


After FFT - Theory 49.7 / 42.7 / 38.8

After FFT – Simulation 49.2 / 35.5 / 32.4


After FFT/BF - Simulation 61.5 / 51 / 44.8

The increased number of scanning angles causes higher resolution in the rough beamforming, as can

be seen in Fig. 161, for the target 2. This increase in the resolution cause the cancellation of many

side-lobes that with the simulation 7 were raising. Also causes the sharpening of the other side – lobes

levels. This fact besides the beamforming gain increase results in more power level difference that is

beneficial for the CFAR in situations of low power level targets.


200

In Fig. 161 the Doppler cuts of the targets 3 are showed; when compared with the Doppler cuts of the

same target with the previous configuration in simulation 7, Fig. 157; it can be observed that other

than the extra gain due to the increased number of antennas, the difference between the target 2 and

the power level belonging to the side lobes of the target 1 has been increased from 6 dB to 24 dB.

Even the target 3 side lobe signal does not appear anymore in the scan angle 30.

Fig. 162: Simulation 7, range profile for the angle 30.


-10 -5 0 5 10-100

-90

-80

-70

-60

-50

-40

-30

-20

-10

0

X: -3.513

Y: 0

Doppler [m/s]

Magnitude [

dB

]

Doppler cuts for the Angle = 30 degrees


201

The differences can be clearly seen in Fig. 162 and 163. The detections results show an increase of

number of false alarms, since the CFAR parameters were not changed, as it also happened in

Simulation 5, leading to the same conclusions. But also an increase in the accuracy of the angle where

the targets are detected which leads to an increased level of power when the beamforming operation is

taking place, as shown in Table 42.


CFAR Info Range Gate Doppler Bin Angle Interpretation

Detection 1 40 (3) 85 (4.2 m/s) 10 (10.47 °) Confirmed Detection

Detection 2 61 (4.575 m.) 47 (-3.5 m/s) 12 (29.52 °) Confirmed Detection

Detection 3 76 (5.7 m.) 31 (-6.5 m/s) 4 (-35.24 °) Confirmed Detection







Fig. 163: Simulation 8, range profile for the angle 30.


202

4.4.2 Fine Angle of Arrival

Once the CFAR detection is performed after the rough beamforming, the coordinates of the detections

are found, included the angle of detection for each target. Thus, the procedure explained in the section

3.4.1 is followed in order to search for the detection angle in the highest angle resolution.

Below instead, the fine angle of arrival is performed along the whole [-60, 60] degrees range for the

simulations 7 and 8, in order to show the differences between the angle of arrival algorithms’

performance. An angle resolution of 0.5 degrees has been chosen in order to apply the fine

beamforming algorithms which gives a total of 241 beamformed angles between the angle -60 and the

angle 60.

-For the Simulation 7, the number of virtual antennas given by the array is 𝑁𝑣 = 8. In Fig. 164 the

Bartlett algorithm is applied; the three detected targets beam patterns are depicted in red, blue and

green colored lines. For each target, a main lobe of around 20 dB wide can be observed, besides side

lobes starting at around -23 dB. Thus, the Bartlett algorithm does not provide with good angular

resolution.

-60 -40 -20 0 20 40 60-80

-70

-60

-50

-40

-30

-20

-10

0

X: -35

Y: -31.87


Magnitude [

dB

]

Angle of arrival cuts - Conventional (Bartlett)

X: 10

Y: 0

X: 30

Y: -20.65

Target 1 - Range Bin: 40, Doppler Bin: 85, Angle: 10 deg


Target 3 - Range Bin: 76, Doppler Bin: 31, Angle: -35 deg

False Alarm

Fig. 164: Simulation 7, Bartlett beamforming algorithm applied for the detected targets.


203

In Fig. 165, the Capon algorithm is applied. The difference is noticeable, as explained in section 2.5.4

this is an adaptive and data dependent algorithm. It produces much narrower beam widths that

improve greatly the angular resolution and the directivity. The sidelobes practically are inexistent

which translates in the filtering of interfering signals. Capon minimizes the total system power as can

be observed by the signal levels compared to Bartlett, this is one of the drawbacks of the algorithm.

In Fig. 166 the MUSIC algorithm is applied; it can be observed that the beam widths are still narrower

than the produced by the Capon algorithm, this is due to the subspace processing that MUSIC runs, as

explained in the section 2.5.4. It is very selective and the noise cancellation is very good, there are not

side lobes. The complexity of this algorithm is higher though.

-60 -40 -20 0 20 40 60-40

-35

-30

-25

-20

-15

-10

-5

0

X: 30

Y: 0


Magnitude [

dB

]Angle of arrival cuts - MVDR (Capon)

X: 10

Y: -11.27

X: -35

Y: -14.86




False Alarm

Fig. 165: Simulation 7, Capon beamforming algorithm applied for the detected targets.

-60 -40 -20 0 20 40 60-80

-70

-60

-50

-40

-30

-20

-10

0

X: -34.5

Y: -22.14


Magnitude [

dB

]

Angle of arrival cuts - MUSIC

X: 30

Y: 0

X: 10

Y: -9.686




False Alarm

Fig. 166: Simulation 7, MUSIC beamforming algorithm applied for the detected targets.


204

-For the simulation 8, the number of virtual antennas given by the array is 𝑁𝑣 = 32.

In Fig. 167 the Bartlett beamforming algorithm is applied. It can be observed that the number of

elements plays an important role in its beamforming generation. As explained in the section 2.5.3, the

conventional methods, as Bartlett, just depend on the array response, i.e., the measured delays in the

antennas caused by the different paths lengths. In Simulation 8, the array size has been substantially

increased; therefore there is more phase information available, which is used by the algorithm to create

a narrower lobes pattern. The increasing of information causes the appearance of narrower multiple

different side lobes due to the cancellation at some angles that in Simulation 7 did not exist. When

compared to Fig. 167; in Fig. 164 higher side lobe level continuity can be observed due to the lack of

enough information in the intermediate angles.

The Fig. 168 depicts the beamforming applying Capon algorithm. The difference when comparing

with Fig. 165 of the simulation 7 is not so evident at a first sight, as it was in the case of the Bartlett

algorithm. This is due to the fact that Capon does not rely on the array size as Bartlett does, therefore

the size array increasing does not affect it in a dramatic manner. However, there can also be noticed an

improvement in the beam width of the lobes due to the availability of more data to nullify neighbor

angles around the signal angle.

-60 -40 -20 0 20 40 60-90

-80

-70

-60

-50

-40

-30

-20

-10

0

X: -35

Y: -32.43


Magnitude [

dB

]

Angle of arrival cuts - Conventional (Bartlett)

X: 30

Y: -20.63

X: 10

Y: 0

False Alarm

False Alarm




False Alarm

False Alarm

Fig. 167: Simulation 8, Bartlett beamforming algorithm applied for the detected targets.


205

In Fig. 169 the MUSIC algorithm shows the same behavior than the Capon when comparing to the

simulation 7; its behavior is not very affected by the size of the anntena array. It also experiences side

lobes narrowing with comparing to the simulation 7. The sharpness of the lobes is now very high

which will translate in a big interference signals’ cancellation.

-60 -40 -20 0 20 40 60-50

-45

-40

-35

-30

-25

-20

-15

-10

-5

0

X: 30

Y: 0

Angle of arrival cuts - MVDR (Capon)


Magnitude [

dB

]

X: 10.5

Y: -20.55

X: -35

Y: -27.96

False Alarm

False Alarm




False Alarm

False Alarm

Fig. 168: Simulation 8, Capon beamforming algorithm applied for the detected targets.

-60 -40 -20 0 20 40 60-60

-50

-40

-30

-20

-10

0

X: -35

Y: -18.31


Magnitude [

dB

]

Angle of arrival cuts - MUSIC

X: 10

Y: -0.8166

X: 30

Y: 0

False Alarm

False Alarm




False Alarm

False Alarm

Fig. 169: Simulation 8, MUSIC beamforming algorithm applied for the detected targets.


206

4.5 Main PMCW system parameters variation

In the previous simulations, the main system parameters have been kept to the same values; the values

given in Table 1 of the section 3.1.2. These parameters are the performance parameters that were

decided to be established as goal to be implemented in the final commercial product. However, the

main system parameters can also be varied and that would translate in an improvement or deterioration

of the radar system performance. Below, the main radar parameters are varied to show how their

variation affects the general behavior of the system. In Table 43 the main variable PMCW system

parameters, together with their normal values, are presented:

Table 43: Variable PMCW system design parameters.


Unambiguous Range 30 m

Range Resolution 0.075 m

Velocity Resolution 0.2 m/s

Max. Unambiguous Velocity 12.66 m/s

4.5.1 Unambiguous range

A new simulation scenario is set, simulation 9. The CFAR parameters are kept at the same parameters

values as the presented in Table 14. The MIMO configuration is the same as the presented in Table 20

for the simulation 4. The new targets scenario initialization is showed in table 44.

Table 44: Simulation 9, simulated targets initialization parameters

Targets Value Unit

Number 3 -

RCS 0 dBsm

Position [5.625, 0, 0] / [9.375, 0, 0] / [15, 0, 0] m

Velocity [-3.5, 6, 8.5] m/s

Angle 0 deg

The unambiguous range parameter is going to be varied for a shorter range configuration; the rest of

parameters are kept the same, as can be seen in Table 45:


207

Table 45: Simulation 9, decreased unambiguous range variation.






The variation of the maximum unambiguous range will cause the variation of some parameters that

were depending on this parameter. As seen in the section 3.1.5, the unambiguous range depends on the

PRI, which itself depends on the length of the sequence and the chip rate. The chip rate is fixed and

the maximum unambiguous range has changed, therefore the PRI will vary, as can be seen in Table

46.

The PRF increases since the minimum period that a sequence will need to be transmitted and reflected

is going to be smaller, given by Eq. (99). The code selection depends on the PRI and the chip rate; for

a given chip rate and a determined minimum PRI a sequence will need to be shorter or longer to

satisfy the unambiguous minimum time. Since the PRI has been reduced, the code length needed is

also reduced, according to Eq. (127):

The 𝐿𝑐𝑚𝑖𝑛 for a 𝑅𝑢𝑛𝑎𝑚𝑏 = 15 is 200 chips length. Since APAS codes are used, the needed length is

double, 𝐿𝑐𝑚𝑖𝑛 = 400. Therefore the sequence length need to be 400 long or more; there are not APAS

codes of 400 length, thus, the next closer code is selected, which has 𝐿𝑐 = 504. It accomplishes the

minimum length required for such unambiguous range. With this sequence length adjustment, the final

unambiguous length gets increased from the 15 meters required to the 18.9 meters (252*𝑅𝑟𝑒𝑠), as

showed in Table 46.

The necessary minimum dwell time, does not vary because it depends on the Doppler resolution and

its unchanged, therefore to keep the same dwell time with a shorter PRI requirement, the system

adjusts the number of accumulations needed, M.

𝐿𝑐𝑚𝑖𝑛 = ⌈

𝑃𝑅𝐼𝑚𝑖𝑛𝑐

⌉ (127)


208

Table 46: Simulation 9, summary of main PMCW system parameters for decreased unambiguous range.



Chip Rate 2000 Msps

PRF 3968.5 KHz



Sequence Length (𝑳𝒄) 504 Chips


FFT Size (N) 128 []


Unambiguous Range 37.80 (18.9) m




There is no gain variation due to these changes; even though the sequence is shorter, (the pulse

compression gain will be reduced), the system increasing of the M will level this loss. The lost gain in

the pulse compression stage will be recovered during the pulse accumulation. The theoretical link

budget of the targets is showed in Table 47, and the radar system performance in Table 48.

Table 47: Simulation 9, theoretical PMCW link budget for the targets scenario.


Path Loss -111.4 / -120.3 / -128.4 dB

Receiver Power -101.4 / -110.3 / -118.4 dBm


Targets SNR 48.1 / 39.3 / 31.1 dB



209





After Pulse Compression – Theory -6.6 / -15.4 / -23.6

After M Accumulations – Theory 12 / 3.1 / -5

Before FFT - Theory 18 / 9.2 / 1


After FFT - Theory 39.1 / 30.2 / 22.1

After FFT - Simulation 36.9 / 24.8 / 20.9



After the signal processing steps described in the previous simulations, the detections are performed

with the CFAR algorithm, giving as performance outcome the data showed in Table 49:










The detection profiles and detection matrixes can be seen in Fig. 170 and 171:

Fig. 170: Simulation 9, CFAR profile cuts for the detections.

0 50 100 150-40

-30

-20

-10

0

10

20


Doppler Bins

Pow

er

[dB

W]

0 50 100 150 200 250-60

-40

-20

0

20


Range gates

Pow

er

[dB

W]

0 50 100 150-50

-40

-30

-20

-10

0

10


Doppler Bins

Pow

er

[dB

W]

0 50 100 150 200 250-50

-40

-30

-20

-10

0

10


Range gates

Pow

er

[dB

W]

0 50 100 150-50

-40

-30

-20

-10

0


Doppler Bins

Pow

er

[dB

W]

0 50 100 150 200 250-60

-50

-40

-30

-20

-10

0


Range gates

Pow

er

[dB

W]


210

As can be seen in the previous figures, the range is now shorter, any targets located further than the

maximum unambiguous range will not be detected or its detection will be unambiguous, i.e., wrongly

located.

The range variation has not affected the rest of the main PMCW system parameters of Table 47 or

processing gain, since the dependability of these parameters (𝐹𝑟𝑒𝑠) with the maximum range has been

leveled with the variation of other parameters, (M ).

The increase of the unambiguous range will have an opposite effect. If the 𝑅𝑢𝑛𝑎𝑚𝑏 is increased as

pointed in Table 50:

Table 50: Simulation 9, increased unambiguous range.







Doppler Bins

Range G

ate

s

20 40 60 80 100 120

50

100

150

200

250


Doppler Bins

Range G

ate

s

20 40 60 80 100 120

50

100

150

200

250



211

The system parameters vary as follows in Table 51:

Table 51: Simulation 9, summary of main PMCW system parameters for increased unambiguous range.



Chip Rate 2000 Msps

PRF 490.20 KHz





FFT Size (N) 128 []


Unambiguous Range 306 (153) m




The minimum time needed for a signal to go and come back to the last range gate is increased,

therefore the PRF decreases. The dependence of the sequence length with the PRI leads to the need of

a longer sequence, in this case 𝐿𝑐𝑚𝑖𝑛 = 667 , which results in a 1334 length code for APAS. The next

closest available APAS code has 4080 chips. Thus, a final maximum unambiguous range of 153

meters is reached. The large length of the new needed sequence causes that the needed number M

accumulations to satisfy the system dwell time, decreases down to 8.

Since Outer Hadamard code MIMO is applied, 2 extra M accumulations are added for Hadamard

transitions that will be dropped in the received once the signal is processed. As explained in the

section 4.3, such a low number of accumulations damage the system efficiency, therefore in this

situation of long range radar, the application of Range Domain Separation MIMO or the use of a

waveform with more code lengths available would be more efficient and beneficial.

4.5.2 Range Resolution

The range resolution of the system is going to be varied while keeping all the rest of parameters as

their original values. Firstly the resolution is going to be increased, as shown in Table 52:


212

Table 52: Simulation 9, decreased range resolution.






Table 53: Simulation 9, summary of the main PMCW system parameters for decreased range resolution.



Chip Rate 600 Msps

PRF 2272.73 KHz





FFT Size (N) 128 -



Range resolution 25 cm

Max. Unambiguous Velocity 12.54 / 45.16 [m/s km/h]


Table 53 shows the main system parameters changes that decreasing the range resolution has caused.

In the first place, the chip rate depends on the range resolution, as stated by (97), therefore the chip

resolution needed to decrease from the 2 Gsps to 600 Msps. The PRI is kept because the unambiguous

range does not change. The chip rate is related with the sequence length according to (99), therefore

the length of the sequence needed for a smaller chip rate will be shorter, it changes to 120, which

becomes 240 for APAS and the closest APAS code has length 264.

The number of accumulations depends on the chip rate and the sequence length, since these

parameters have been reduced, the number of needed accumulations decreases down to 41. The dwell

time is still kept even though the M and sequence length have been decreased. This is due to the


213

increase on the chip rate. The drawback of this variation comes in the decreased resolution

performance of the detections; in Table 54 this degradation can be checked:

Table 54: Simulation 9, detected targets coordinates and interpretation for a decreased range resolution.








Now, the range gates are wider, i.e., for the same unambiguous range distance, there is the need of less

range gates. This translates in a range error increase produced in the detections. If Table 54 is

compared with the distance where the targets were set, it can be observed that now the error is as big

as 0.25 meters for the Target 3 (15 m.), which is the minimum range resolution margin that the system

has been working with in this simulation.

In Fig. 172 and 173 the detection profiles and the detection matrixes can be observed. It has to be

taken in to account that the size of the data matrix has now decreased; therefore with the probability of

false alarm kept the same, the detection threshold is expected to rise.

0 50 100 150-60

-40

-20

0


Doppler Bins

Pow

er

[dB

W]

0 20 40 60 80 100 120 140-60

-40

-20

0


Range gates

Pow

er

[dB

W]

0 50 100 150-60

-50

-40

-30

-20

-10

0


Doppler Bins

Pow

er

[dB

W]

0 20 40 60 80 100 120 140-60

-50

-40

-30

-20

-10

0


Range gates

Pow

er

[dB

W]

0 50 100 150-60

-50

-40

-30

-20

-10

0


Doppler Bins

Pow

er

[dB

W]

0 20 40 60 80 100 120 140-60

-50

-40

-30

-20

-10


Range gates

Pow

er

[dB

W]

Fig. 172: Simulation 9, CFAR profile cuts for the detections with range resolution decreased.


214

If the range resolution is increased, as stated in Table 55 until 𝑅𝑟𝑒𝑠 = 6 𝑐𝑚 , the process described

earlier is reversed. The chip resolution is expected to be increased due to its dependence with the range

resolution and, therefore, the minimum sequence length is expected to grow. As seen in Table 56; in

this case 𝐿𝑐 becomes 500, which for APAS becomes 1000. Now, all the sequence length is used for

the required range resolution and therefore the maximum unambiguous range is exactly the demanded.

The number of accumulations needed also grow by 16 (4 for each MIMO block).

Table 55: Simulation 9, increased range resolution.






In Table 57 the new CFAR detections can be checked.


Doppler Bins

Range G

ate

s

20 40 60 80 100 120

20

40

60

80

100

120


Doppler Bins

Range G

ate

s

20 40 60 80 100 120

20

40

60

80

100

120

Fig. 173: Simulation 9, detection matrixes for the range resolution decreased.


215

Table 56: Simulation 9, summary of the main PMCW system parameters for increased range resolution.



Chip Rate 2500 Msps

PRF 2500 KHz





FFT Size (N) 128 []



Range resolution 6 cm



Table 57: Simulation 9, detected targets coordinates and interpretation for a increased range resolution.









The new detections have improved their range resolution, now the maximum error is 6 cm. This is due

to the fact that now there are more range gates for the same unambiguous range. It can be thought with

the sampling concept; with the increasing of the range resolution the chip rate increases the frequency

that samples the sequence chips that are used to get the information of each range gate of the

unambiguous range. Thus, the resolution is increased. Until now, the Doppler Domain has been kept

without any changes because the Doppler unambiguity and the range unambiguity can be kept

independent.


216

4.5.3 Velocity Resolution

The velocity resolution is now varied; it is decreased to 𝑣𝑟𝑒𝑠 = 1 𝑚/𝑠 while keeping the other system

main parameter in their normal values, as seen in Table 58.

Table 58: Simulation 9, decreased velocity resolution.




Velocity Resolution 1 m/s


Table 59 shows the main system changes that this action has caused. The 𝐹𝑑𝑟𝑒𝑠 depends on the

velocity resolution according to Eq. (105). Therefore, for a higher resolution value, the Doppler

resolution also increases. The dwell time of the system depends exclusively and inversely on the

frequency resolution, i.e., for a higher value of frequency resolution the dwell time decreases. In this

case the necessary dwell time has dropped from 10 ms to 2 ms. The number of N-FFT points depends

on the maximum unambiguous frequency (which does not vary) and the Doppler frequency resolution,

as seen in Eq. (103).

Table 59: Simulation 9, summary of the main PMCW system parameters for decreased velocity resolution.



Chip Rate 2000 Msps

PRF 2000 KHz





FFT Size (N) 32 []


Unambiguous Range 75 (37.5) m


Max. Unambiguous Velocity 15.82/ 56.96 [m/s km/h]

Velocity Resolution 0.99 / 3.56 [m/s km/h]


217

For the same maximum frequency there is needed less resolution, therefore the number of necessary N

repetitions is decreased down to N=32. Since the number of accumulations also depends on N, the

value of M is also affected and decreases down to 28.

It is noticeable that the number of changing parameters varying now are different than the parameters

that are varying when the range-related parameters are varied, this shows the independence of both

Doppler and range ambiguities. In Table 60 the detections performance can be observed:

Table 60: Simulation 9, detected targets coordinates and interpretation for decreased velocity resolution.







The increase in the error is noticeable; there is 1 m/s error between the real speed and the detected

speed, which is the maximum that the system has been set to work with. This variation can also be

thought as a decrease in the sampling rate of the Doppler shift changes.

The decreased number of points in the FFT make the filter around the speed wider, thus letting more

frequencies in, see Fig. 50 and 51 of the section 3.1.1.

In Fig. 174 the detection matrix for this case is showed; with just N=32 Doppler bins in the Doppler

domain.


218

If the velocity resolution is increased up to 𝑣𝑟𝑒𝑠 = 0.1 (Table 61), the inverse process is expected to

happen. The Doppler equivalent resolution is 51.40 Hz that leads to the need of increasing the system

dwell time up to 19.46 seconds (Table 62). The dwell time parameter has been adjusted in order to

have a sampling time long enough that allows the detection from the minimum speed up to the

maximum, in intervals of 51.40 Hz. The need of the N-FFT points is increased by two times,

according to Eq. (103), and the M accumulations are also affected so that the total necessary dwell

time is achieved.

Table 61: Simulation 9, increased velocity resolution.







Doppler Bins

Range G

ate

s

102030

50

100

150

200

250

300

350

400

450

500


Doppler Bins

Range G

ate

s

102030

50

100

150

200

250

300

350

400

450

500


Doppler Bins

Range G

ate

s

102030

50

100

150

200

250

300

350

400

450

500


Doppler Bins

Range G

ate

s

102030

50

100

150

200

250

300

350

400

450

500

Fig. 174: Simulation 9, detection matrixes for a decreased velocity resolution.


219

Table 62: Simulation 9, summary of the main PMCW system parameters for increased velocity resolution.



Chip Rate 2000 Msps

PRF 2000 KHz





FFT Size (N) 256 -




Max. Unambiguous Velocity 12.49/ 44.97 [m/s km/h]


Table 63: Simulation 9, detected targets coordinates and interpretation for increased velocity resolution.


Detection 1 75 (5.625 m.) 167 (3.9 m/s) Confirmed Detection



Detection 3 201 (15.075 m.) 47 (-8.1 m/s) Confirmed Detection


In Table 63, the detection data after the CFAR is presented; the velocity resolution now is much

higher. The drawback of applying a high speed resolution is that the computational hugely increases.

4.5.4 Unambiguous velocity

The unambiguous velocity is changed and decreased down to 𝑣𝑚𝑎𝑥 = 6 𝑚/𝑠, i.e., the maximum speed

at which the radar system will be able to detect a moving target without ambiguities. Again, the other

main system parameters values are kept in their normal values, as seen in Table 64:


220

Table 64: Simulation 9, decreased unambiguous speed.





Max. Unambiguous Velocity 6 m/s

The new main system parameters are presented in Table 65. The first value to be changed is the

Doppler sampling rate; it depends on the ambiguous Doppler frequency, which is the frequency band

that is going to be needed in order to detect frequency shifts as high as the selected unambiguous

speed. For 𝑣𝑚𝑎𝑥 = 6 𝑚/𝑠 the frequency shift is 𝐹𝑑 = 3160 𝐻𝑧. The Doppler sampling rate is the

frequency with which the system will acquire frequency shift information, i.e., each time that M

accumulations and 𝑁𝑡𝑥 MIMO blocks are transmitted; this happens with a frequency 6.85 KHz, which

is just double as the maximum Doppler shift frequency needed to detect the fastest detectable moving

target; Nyquist is accomplished.

As seen in Eq. (104) the number of N-FFT needed depends on the maximum and minimum Doppler

shifts. Since the velocity resolution is kept and the maximum speed decreased, the N-points number is

going to decrease down to 64. Since the velocity resolution is kept, the dwell time of the system needs

to be the same. Thus, leveling 𝑇𝑑 is the reason why the number of accumulations needs to be so high.

Table 65: Simulation 9, summary of the main PMCW system parameters for decreased unambiguous velocity.



Chip Rate 2000 Msps

PRF 2000 KHz





FFT Size (N) 64 -







221

In Table 66 the detections performance of the CFAR are presented. The two first targets are correctly

detected. However, there is a third detection that the system identifies as a false alarm; the detected

coordinates do not match with the expected coordinates of any target set in the scenario. This false

alarm though, is the detection of the third target at an ambiguous speed. The target is set to speed at 9

m/s and the maximum unambiguous speed of the system is 6 m/s. Therefore the speed of the target is

faster than the value that is set by the system design. This causes the false alarm, which is in reality a

ambiguous detection of a target.

Table 66: Simulation 9, detected targets coordinates and interpretation for decreased unambiguous velocity.


Detection 1 75 (5.625 m.) 53 (4.2 m/s) Confirmed Detection

Detection 2 126 (9.45 m.) 3 (-5.8 m/s) Confirmed Detection


Detection 3 201 (15.075 m.) 51 (2.6 m/s) False Alarm

In Fig. 175 and 176 the detections and the matrix of detections are showed. The ambiguous detection

is showed along the Doppler profile for a clearer view of the detection. The Doppler bin where it is

detected is not correct.

0 10 20 30 40 50 60-40

-30

-20

-10

0

10

20

30

X: 53

Y: 23.11

Detection of trgt #1 in RG cut # 76

Doppler Bins

Pow

er

[dB

W]

0 100 200 300 400 500-60

-40

-20

0

20


Range gates

Pow

er

[dB

W]

0 10 20 30 40 50 60-40

-30

-20

-10

0

10

20

X: 3

Y: 13.84


Doppler Bins

Pow

er

[dB

W]

0 100 200 300 400 500-80

-60

-40

-20

0


Range gates

Pow

er

[dB

W]

0 10 20 30 40 50 60-50

-40

-30

-20

-10

0

10

X: 51

Y: 4.863

Detection of trgt #3 in RG cut # 201 .

Doppler bins

[dB

W]

0 0.2 0.4 0.6 0.8 10

0.2

0.4

0.6

0.8

1

0 10 20 30 40 50 60-40

-30

-20

-10

0

10

20

30

X: 53

Y: 23.11


Doppler Bins

Pow

er

[dB

W]

0 100 200 300 400 500-60

-40

-20

0

20


Range gates

Pow

er

[dB

W]

0 10 20 30 40 50 60-40

-30

-20

-10

0

10

20

X: 3

Y: 13.84


Doppler Bins

Pow

er

[dB

W]

0 100 200 300 400 500-80

-60

-40

-20

0


Range gates

Pow

er

[dB

W]

0 10 20 30 40 50 60-50

-40

-30

-20

-10

0

10

X: 51

Y: 4.863

Detection of trgt #3 in RG cut # 201 .

Doppler bins

[dB

W]

0 0.2 0.4 0.6 0.8 10

0.2

0.4

0.6

0.8

1

Fig. 175: Simulation 9, CFAR profile cuts for the detections with unambiguous velocity decreased.


222

As it can be observed, the detection matrix has been reduced to 64 N-Points. Since the maximum and

minimum speeds to be detected are smaller, the needed points are reduced. The wrong(ambiguous)

detection is marked in the post-processing figure, detected at an ambiguous speed.

If the unambiguous velocity is increased instead, as presented in Table 67, the system parameters will

be rearranged as showed in Table 68.

Table 67: Simulation 9, increased unambiguous velocity.





Max. Unambiguous Velocity 25 m/s


Doppler Bins

Range G

ate

s

20 40 60

50

100

150

200

250

300

350

400

450

500

X: 51 Y: 201

Index: 0

RGB: 0, 0, 0


Doppler Bins

Range G

ate

s

20 40 60

50

100

150

200

250

300

350

400

450

500


Doppler Bins

Range G

ate

s

20 40 60

50

100

150

200

250

300

350

400

450

500

X: 51 Y: 201

Index: 0

RGB: 0, 0, 0


Doppler Bins

Range G

ate

s

20 40 60

50

100

150

200

250

300

350

400

450

500

Fig. 176: Simulation 9, detection matrixes for unambigous velocity decreased.


223

Table 68: Simulation 9, summary of main PMCW system parameters for increased unambiguous velocity.



Chip Rate 2000 Msps

PRF 2000 KHz





FFT Size (N) 256 -






The number of N-Points is increased; since the velocity resolution value is kept, more points are going

to be needed to be able to sample all the speeds. The Doppler sampling rate is increased by 4 times

since there are 4 times more N points where to take a doppler shift sample. The number of N

repetitions thus is high and takes a lot of transmission time, thus the accumulations number is reduced

since there is less need to use them in order to accomplish the required system dwell time. The

detection that was previously wrongly detected now it is not ambiguous anymore and it will be

detected in its location without problems, as can be seen in Fig. 177, matching the information

presented in Table 69.

Table 69: Simulation 9, detected targets coordinates and interpretation for increased unambiguous velocity.








224

Fig. 177: Simulation 9, detection matrixes for increased unambiguous speed.

4.5.5 M-Sequences

In scenario cases as the presented in Table 50, the required unambiguous range is incremented a few

meters and the final unambiguous range ends up having many more meters than the required

minimum. This is due to the few length variety that the APAS codes present; when the minimum

sequence length overcomes by few a sequence length, next available APAS code can be twice as long.

These concrete situations can be avoided with the use of the M-Sequences introduced in the section

2.1.5, provided that sequences of many different lengths can be generated for m-sequences. In

Simulation 10, m-sequences are used instead of APAS codes. The scenario of the targets is also

slightly changed for the one presented in Table 70. One target has been eliminated, while the target 2

has been kept and the target 3 has been moved to a further distance. The RCS of the furthest target

have been reduced to a sensitive case, -20 dBsm, which is the RCS that children can present when

detected from an unfortunate angle [38].


Doppler Bins

Range G

ate

s

50 100 150 200 250

50

100

150

200

250

300

350

400

450

500

X: 83 Y: 201

Index: 0

RGB: 0, 0, 0


Doppler Bins

Range G

ate

s

50 100 150 200 250

50

100

150

200

250

300

350

400

450

500


225


Targets Value Unit

Number 2 -

RCS [0, -20] dBsm

Position [9.375, 0, 0] / [25, 0, 0] m

Velocity [6, 9] m/s

Angle 0 deg

The MIMO configuration and CFAR parameters are kept as in Simulation 4 and the main system

parameters are the same as the presented in Table 50 when the ambiguous range was increased.

In Table 71 the link budget for the targets of the simulation is presented, besides the main system

parameters of Table 72.



Path Loss -120.3 / -137.3 dB

Receiver Power -110.3 / -147.3 dBm


Targets SNR 39.2 / 2.2 dB


The choice of the m-sequence has made a change in the outcome of the main system parameters; the

minimum sequence length needed for an unambiguous range of 50 meters is 𝐿𝑐𝑚𝑖𝑛 = 667. When

using m-sequences, the length of the code does not need to be doubled, therefore the closest m-

sequence found has been of length 1023. It is half of what it was needed for the APAS case. This has

led to the increase of number of M accumulations up to 35 (from 8), which translates in a better system

efficiency. The use of the m-sequence has reduced the unused unambiguous range from the 154 meters

to 76.72 meters.


226




Chip Rate 2000 Msps

PRF 1955.03 KHz





FFT Size (N) 128 []






In Table 73 the radar performance in each stage of the signal processing is showed. It can be observed

the big difference that the different RCS levels have during the signal processing. The long range and

low energy with which the second target reflects the signal, foreseen a complicated scenario for the

CFAR detector.



Before ADC - Theory -42.5 / -79.5


After Pulse Compression – Theory -12.4 / -49.4

After M Accumulations – Theory 3.1 / -34

Before FFT - Theory 9.1 / -27.9

Before FFT - Simulation 7.8 / 0.4

After FFT - Theory 30.2 / -6.9

After FFT - Simulation 23.5 / -13.3

After FFT/BF - Theory 39.2 / 2.2

After FFT/BF - Simulation 34.7 / 0.2


227

The target 1 has the same parameters, also under the same scenario as in Simulation 9; comparing the

system performance results of Tables 73 and 48 there can be observed a slight decrease in SNR along

the signal processing gain process that end up with a 1.6 dB difference in the last stage of gain. This

can be due to the properties of the m-sequences itself, as explained in the section 2.1.5, that provide a

slightly worse SNR due to its non-zero side lobes after the matched filtering.

In Table 74 the CFAR detections are presented; the target with high RCS is detected without

problems, however the far and with low RCS target cannot be detected; its SNR is just 0.2 dB, in the

level of the noise floor and below some noise peaks. In Fig. 178, the detection profiles show the

impossibility to detect the second target and also it can be noticed that the noise floor seems to be

slightly higher than its level when using APAS (Fig. 172).




- 335 (25 m.) 19 (-9 m/s) Not Detected


Even though m-sequences are convenient for scenarios like the presented in Simulation 10, the

drawbacks of APAS can be overcome with compromises in the selection of parameters. As explained

in 2.1.5, a better correlation property in the waveform is preferred for the radar system under study.

0 20 40 60 80 100 120 140-60

-40

-20

0


Doppler Bins

Pow

er

[dB

W]

0 100 200 300 400 500 600 700 800 900 1000-80

-60

-40

-20

0


Range gates

Pow

er

[dB

W]

0 20 40 60 80 100 120 140-50

-40

-30

-20

-10

0


Doppler bins

[dB

W]

0 100 200 300 400 500 600 700 800 900 1000-50

-40

-30

-20

-10

0

X: 335

Y: -19.8

Trgt #2 NOT detected in Doppler cut 19

Range gates

[dB

W]

Fig. 178: Simulation 10, CFAR profile cuts for the detections.


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5 Conclusions

This thesis has presented the signal processing techniques and algorithms implemented in a mmWave

PMCW MIMO radar system that achieved an excellent radar performance in terms of resolution and

detectability. The challenge was tackled by means of different methods and approaches implemented

along the digital front-end and back-end parts of the system. The short range is the application

scenario that the radar system is meant to be used in.

The work started with a theoretical background of the main concepts involving a radar system and the

techniques to be used in the system implementation, in Chapter 2. The proposed solutions were

introduced in detail; the CFAR’s proposed algorithms and main characteristics, the MIMO concepts

and proposed techniques and the beamforming approach and methods. The radar system under design

was presented besides the implementation of the proposed procedures. Also, the Matlab chain

structure used to implement the proposed solutions was shown in Chapter 3.

The description of the implementation was focused in explaining the functioning of the methods while

linking their behavior with the theory, but also in the way that the signal information is managed and

processed in the Matlab structures.

A parallel range gate processing solution was proposed in order to process the signal echoes; it

consists on the use of identical branches (as many as the number of unambiguous range gates) that

take the incoming signal as input. Each of the branches processes the information related to each range

gate exactly in the same way; first a correlator, with a different delay for each branch, carries out the

pulse compression and produces one sample, then the continuous flow is treated in the same manner in

order to produce accumulations and improve the SNR, finally an N-point FFT is used to acquire the

Doppler profile. In all these steps the theoretical gain achieved is high. The waveform to be used in the

transmitting signals is important and APAS sequences besides m-sequences were proposed due to

their desired autocorrelation properties.

The digital front-end part of the system was completed with the MIMO processing of the signal. When

the MIMO configuration is activated, the transmitting waveform is generated in a precise manner so

that it is later correctly processed it in the receiver part.

The MIMO made use of the virtual array technique in order to create virtual antennas that contain

more information, making possible to determine the direction of arrival with more precision. The

different antennas used to transmit the signal need to propagate orthogonal waveforms so that the

system was able to differentiate between the waveform belonging to each transmitter antenna in the

receiver. The proposed outer code method consisted in using just one sequence for all the antennas,

instead of different codes for each of the transmitting antennas. The Hadamard sequence family was


229

used to render the information by blocks. The unique sequence was repeated M times, so that the

system supported samples accumulation in the receiver, and then repeated 𝑁𝑇𝑋 times with a possible

sign inversion given by the rows of the adequate Hadamard matrix. In the receiver a correlator

processed the blocks of samples and then they were split into 𝑁𝑇𝑋 sections that were combined or

subtracted as commanded by the Hadamard matrix coefficients. There is just the need for one

correlator per receiver antenna and range gate, instead of as many as 𝑁𝑇𝑋 (if the orthogonality was

achieved by sequence design). By the other hand, unlike the sequence design option, with outer code

the orthogonality is exact for low Doppler frequency since it relies on the cross-correlation properties

of Hadamard sequences at zero delay, which are zero.

After the digital front-end processing stage the expected gain accomplished by the system on the SNR

level of the targets was 𝐺𝑝 = 10 log10(𝐿𝑐 ∙ 𝑀 ∙ 𝑁 ∙ 𝑁𝑇𝑋 ).

The digital back-end of the system contained the implementation of a rough beamforming stage that

provided with broad angle information when MIMO is enabled. Moreover, in this process there is an

extra gain achieved, thanks to the virtual array, is expected to be 𝐺𝑝 = 10 log10(𝑁𝑉). The total

theoretical processing gain for the reference scenario presented in section 3.1.2 with a nominal MIMO

configuration enabled (𝑁𝑇𝑋 = 4,𝑁𝑅𝑋 = 2) was as high as 𝐺𝑝 = 81.86 𝑑𝐵. The stage where a bigger

portion of gain was achieved was after the pulse compression and accumulation.

After this stage the system gain was maximum and, therefore the SNR; the CFAR algorithm stage was

then executed. The CFAR algorithm contained the choice of different algorithms to be applied that

were useful when the environment scenario was varied. Furthermore, post-processing algorithms were

used to keep the false alarm rate as low as possible.

The digital receiver back-end had as a last component the direction of arrival stage; with the

information gathered with the CFAR detections, a finer direction of arrival processing was performed.

There are several DoA proposed algorithms (MUSIC, Capon and Barlett) that can be applied; each of

them with their advantages and drawbacks.

In Chapter 4, the simulations were performed while varying different system parameters in order to get

a clear picture of the behavior of the radar system under different configurations.

The simulation’s results of the digital front-end happened to show values very close to the expected

gain in each gain stage. The results were checked and checked in each SNR performance table after

each different simulation. The total simulated processing gain for the reference scenario presented in

section 3.1.2 varies between the 73 dB and the 77 dB of processing system gain, depending on the

scenarios, parameters and targets initialization. The values were very close to the theoretical maximum

achievable gain under these parameters. The difference in the theoretical and simulated values of the


230

SNR at different stages of the simulation chain can be due to several factors like the not completely

coherent gain due to Doppler frequency shifts, or the Blackman window applied before the FFTs.

The CFAR implemented algorithms were tested under different scenarios in Simulation 2 and 3;

different targets’ locations, RCS levels, range migration situations and with the variation of their set

parameters. Each CFAR implemented algorithm is aimed to be applied in different scenarios; the

averaging algorithms presented a more sensitive behavior in the set of their threshold level and the

number of training and guard cells used in the process. The CA behavior is optimum for situations of

uniform clutter and GOCA is meant to be used in different level clutter edges. The application of

SOCA is beneficial in a low volume of targets situation, but it would present masked targets in high

density targets scenario. The OS algorithm is not based on the averaging data of the neighbor cells;

therefore its dependence with the size of the training and guard cells is highly reduced. This

characteristic causes its better behavior in scenarios of multiple targets situations. The combination of

possible scenarios is wide and varying in a real situation. The OS algorithm has been chosen for the

simulations in Chapter 4 since, for the controlled situations in which the simulations take place; it

presents the most stable behavior. Yet, in a real situation the values of the algorithm parameters and

the type of algorithm should be adapted to the perceived environment or to a preset scenario.

The MIMO simulations presented a chance to compare the outcomes difference between a SISO radar

system and the extra capabilities of a MIMO configuration. The combination of the MIMO

configuration with the rough beamforming provides the phase difference information under the

selected angles, which allow a rough estimation of the angle of arrival and an extra processing gain.

Different combinations of the number of transmitting and receiving antennas were simulated with

varying targets’ scenarios. At the same time, the CFAR detection profiles were shown; the SNR

increase made easier the target detection under low RCS targets. The system processing gain is

essential for a radar of such low transmitting power as the one presented. Simulation 4 showed how

the gain is achieved along the different system stages, while Simulation 5 presented the importance of

the signal processing gain in a realistic scenario where the target have a low RCS. Simulation 6

showed the consequences of increasing the number of the virtual array, and how the SNR experiences

a high increase that makes the targets easier to be detected by the CFAR, but at the same time

increases the number of false alarm due to an increase in the noise floor level, besides other effects.

The choice in the selection of the MIMO number of transmitters and receivers showed to introduce a

trade-off between the supported computational capacity and the energy consumption of the system.

For a situation where targets have a low RCS a high number of the virtual array size is a must but the

computation processing will be increased.


231

The angle of arrival simulations showed the utility of the information contained in the different

received signals; Simulation 7 presented a realistic scenario where just a few angles were beamformed

before the CFAR detection, which were enough to get a rough angle estimation of the target and a

decent extra processing gain. Simulation 8 described a more complex situation where the increased

number of array size allowed a sharper rough beamforming, which besides increasing the SNR, also

eliminated or reduced the side-lobes caused by the conventional beamforming method, thus avoiding

extra false alarms in different angles. The CFAR characteristics were kept unchanged during these

simulations in order to be able to see the effects of the changing conditions. However a finer selection

on the CFAR parameters (depending on the scenario or chosen parameters), would have provided

better results. For example, if the probability of false alarm would have been increased in Simulation

8, the false alarms would have disappeared due to the high SNR of the targets and good side-lobe level

of the rough beamforming.

The fine angle of arrival simulations were performed using the data of Simulations 7 and 8; the fine

beamforming was applied along all the data points of certain range gate and Doppler bin where the

CFAR detections have confirmed a target. Thus, an easier visualization of each beamforming

characteristics was obtained. The radar system could directly apply the more complex adaptive

beamforming methods in order to achieve high DoA accuracy with a good resolution, as shown in

section 4.4.2. Nevertheless, this operation would imply the increase of the computational complexity.

A more computational friendly approach was the explained in section 3.4.1. However, it all depended

on the needs in a specific scenario.

The simulations were performed with the reference design parameters that the system performance

will need to achieve. Still, the system final specifications may vary due to hardware limitations,

problems encountered during the prototypes development and testing or due to other unforeseen

reasons. Simulation 9 kept a target scenario constant and varied the main system parameters to find

out the effect that these system changes would have in the performance and behavior of the radar

system. The scenario was checked while varying the unambiguous range and velocity, besides the

range and velocity resolution. The results showed the different outcomes, presenting how the system

parameter interacted and depended on each other and, therefore, it helped to better understand how the

radar system works. Simulation 10 was used to show the availability of different options (M-

sequences) that can be convenient in a certain scenario (long range detection) under concrete design

characteristics (APAS and Hadamard Outer Code). Moreover, the difficulties in the detection of very

low RCS targets were presented, envisaging the need of further system improvements in order to cover

all the possible scenarios with good results.


232

5.1 Future Work

To solve the missed detections for low RCS targets in some far ranges, a bigger SNR is needed. The

gain can be increased by expanding the number of used antennas or increasing the number of

accumulations, but also by increasing the number of the radar systems (SoC) working synchronized.

These changes would have effects in the other parameters of the system, as seen in Simulation 9,

which would translate in a general improvement of the system performance. In order to improve the

range resolution, more bandwidth could be allocated or there could be investigated novel waveform

shapes. The increase of angular resolution has been demonstrated to be effectively tackled by

increasing the number of antennas while performing MIMO processing. Other possibility is the

implementation of super-resolution beamforming methods. In order to increase the Doppler resolution,

a micro-Doppler characterization could be studied besides the implementation of flexible FFT

architectures.

The CFAR behavior could also be improved; this may be done with new algorithms that could

specifically be developed in order to identify the environment under which the radar is working and

selecting the proper CFAR algorithm and parameters’ values that would show a better threshold

setting performance.

Nevertheless, the drawback of all the system improvements is the increase of the computational

complexity and thus the required energy; which translates in the variation of other hardware

parameters, etc. The operations that digital front-end of the radar system performs are actually very

simple (correlations, accumulations, etc.), but they need to be done in large number and in parallel.

The pulse compression operation involves the multiplication of 𝐿𝑐 ∙ 𝑀 ∙ 𝑁 with 1 or -1 and add 𝐿𝑐

samples; repeated 𝑀 ∙ 𝑁 times, 𝑀 ∙ 𝑁 ∙ 𝑁𝑇𝑋 time if MIMO is enabled. The coherent accumulation

involves the adding of 𝑀 samples 𝑁 times. Ultimately, the FFT operation involves making N points

windowing, 𝐿𝑐 times and N points FFT another 𝐿𝑐 times. This number is then multiplied by the

number of receiver antennas that the system might have. As it can be noted, the improvement of the

system performance will be obtained with an increased complexity which is not always possible to

achieve.

In order to find a middle point between getting excellent performance capabilities and work with an

acceptable computing complexity, future improvements can be introduced. This future work can

include the implementation of several radar modes depending on the perceived scenario: a detection

mode and a tracking mode. The detection mode would require lower range gate, velocity and angular

resolutions since the main goal is to ‘broadly’ detect. Once there is detection and using the available

information, the tracking mode of the radar would be triggered and the high resolution capabilities


233

would be activated for a proper identification of the target. Once the tracking mode is active, less

range gates would be needed since the target has been already localized; just the range gates

surrounding the target would be activated. The implementation of these techniques would save many

operations and the complexity would be considerably reduced. Ultimately, the interesting future topics

are related with the radar system optimization and efficiency.

Regarding the bigger picture of automotive radar; the systems head towards the sensor fusion where

complementary technologies (such as radar and imaging), would work together to sense the

surrounding with very high detail. This could be done by also combining information from other

sources such as weather, traffic density or car to car information exchange. In order to be able to

afford such a computational complexity in a small surface, faster silicon would be needed. In the

future, these integrated systems could be implemented using mmWave based in FinFET technology.


234

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A1

A1 Summary of Main Parameters

𝐵 ≡ 𝐵𝑎𝑛𝑑𝑤𝑖𝑑𝑡ℎ

𝑃𝑅𝐼 ≡ 𝑃𝑢𝑙𝑠𝑒 𝑅𝑒𝑝𝑒𝑡𝑖𝑡𝑖𝑜𝑛 𝐼𝑛𝑡𝑒𝑟𝑣𝑎𝑙

𝑃𝑅𝐹 ≡ 𝑃𝑢𝑙𝑠𝑒 𝑅𝑒𝑝𝑒𝑡𝑖𝑡𝑖𝑜𝑛 𝐹𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦

𝑅 ≡ 𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑡𝑜 𝑡𝑎𝑟𝑔𝑒𝑡

𝑅𝑚𝑎𝑥 ≡ 𝑈𝑛𝑎𝑚𝑏𝑖𝑔𝑢𝑜𝑢𝑠 𝑅𝑎𝑛𝑔𝑒,𝑀𝑎𝑥𝑖𝑚𝑢𝑚 𝐷𝑒𝑡𝑒𝑐𝑡𝑎𝑏𝑙𝑒 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒

𝜃 ≡ 𝐴𝑛𝑡𝑒𝑛𝑛𝑎 𝑏𝑒𝑎𝑚 𝑤𝑖𝑑𝑡ℎ

𝜎 ≡ 𝑅𝐶𝑆 (𝑅𝑎𝑑𝑎𝑟 𝐶𝑟𝑜𝑠𝑠 𝑆𝑒𝑐𝑡𝑖𝑜𝑛)

fd ≡ 𝐷𝑜𝑝𝑝𝑙𝑒𝑟 𝐹𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦 𝑠ℎ𝑖𝑓𝑡

fc ≡ 𝐶𝑎𝑟𝑟𝑖𝑒𝑟 𝐹𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦

𝜏 ≡ 𝑃𝑢𝑙𝑠𝑒 𝑊𝑖𝑑𝑡ℎ

𝐹𝑟𝑒𝑠 ≡ 𝐹𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦 𝑅𝑒𝑠𝑜𝑙𝑢𝑡𝑖𝑜𝑛

𝑇c ≡ 𝐶ℎ𝑖𝑝 𝐷𝑢𝑟𝑎𝑡𝑖𝑜𝑛

Ts ≡ 𝑆𝑒𝑞𝑢𝑒𝑛𝑐𝑒 𝐷𝑢𝑟𝑎𝑡𝑖𝑜𝑛

𝑇𝑑 ≡ 𝑆𝑦𝑠𝑡𝑒𝑚 𝐷𝑤𝑒𝑙𝑙 𝑇𝑖𝑚𝑒

𝑀 ≡ 𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝐴𝑐𝑐𝑢𝑚𝑢𝑙𝑎𝑡𝑖𝑜𝑛𝑠

𝑁 ≡ 𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑃𝑜𝑖𝑛𝑡𝑠 𝑓𝑜𝑟 𝑡ℎ𝑒 𝐹𝐹𝑇 𝑝𝑟𝑜𝑐𝑒𝑠𝑠𝑖𝑛𝑔

𝑃fa ≡ 𝑃𝑟𝑜𝑏𝑎𝑏𝑖𝑙𝑖𝑡𝑦 𝑜𝑓 𝐹𝑎𝑙𝑠𝑒 𝐴𝑙𝑎𝑟𝑚

Lc ≡ 𝑆𝑒𝑞𝑢𝑒𝑛𝑐𝑒 𝑙𝑒𝑛𝑔𝑡ℎ 𝑜𝑓 𝑡ℎ𝑒 𝑐𝑜𝑑𝑒

Ntx ≡ 𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑡𝑟𝑎𝑛𝑠𝑚𝑖𝑡𝑡𝑒𝑟 𝑎𝑛𝑡𝑒𝑛𝑛𝑎𝑠

Nrx ≡ 𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑟𝑒𝑐𝑒𝑖𝑣𝑒𝑟 𝑎𝑛𝑡𝑒𝑛𝑛𝑎𝑠

𝑅𝑐 ≡ 𝑆𝑎𝑚𝑝𝑙𝑖𝑛𝑔 𝑅𝑎𝑡𝑒

𝐹𝑠,𝐷𝑜𝑝 ≡ 𝑆𝑎𝑚𝑝𝑙𝑖𝑛𝑔 𝐷𝑜𝑝𝑝𝑙𝑒𝑟 𝐹𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦

𝐹𝑑𝑎𝑚𝑏 ≡ 𝐷𝑜𝑝𝑝𝑙𝑒𝑟 𝐹𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦 𝑅𝑒𝑠𝑜𝑙𝑢𝑡𝑖𝑜𝑛

𝐹𝑑𝑟𝑒𝑠 ≡ 𝐷𝑜𝑝𝑝𝑙𝑒𝑟 𝑓𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦 𝑟𝑒𝑠𝑜𝑙𝑢𝑡𝑖𝑜𝑛𝑠

𝑅𝑟𝑒𝑠 ≡ 𝑅𝑎𝑛𝑔𝑒 𝑅𝑒𝑠𝑜𝑙𝑢𝑡𝑖𝑜𝑛

V𝑚𝑎𝑥 ≡ 𝑀𝑎𝑥𝑖𝑚𝑢𝑚 𝑢𝑛𝑎𝑚𝑏𝑖𝑔𝑢𝑜𝑢𝑠 𝑠𝑝𝑒𝑒𝑑

V𝑟𝑒𝑠 ≡ 𝑉𝑒𝑙𝑜𝑐𝑖𝑡𝑦 𝑅𝑒𝑠𝑜𝑙𝑢𝑡𝑖𝑜𝑛

𝑁𝑣 ≡ 𝑉𝑖𝑟𝑡𝑢𝑎𝑙 𝐴𝑟𝑟𝑎𝑦 𝑆𝑖𝑧𝑒

𝑁𝐴 ≡ 𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑆𝑐𝑎𝑛𝑛𝑒𝑑 𝐴𝑛𝑔𝑙𝑒𝑠

𝑤𝑛 ≡ 𝐵𝑒𝑎𝑚𝑓𝑜𝑟𝑚𝑖𝑛𝑔 𝑊𝑒𝑖𝑔ℎ𝑡 𝑉𝑒𝑐𝑡𝑜𝑟

𝐺𝑠𝑦𝑠 ≡ 𝑆𝑦𝑠𝑡𝑒𝑚 𝐺𝑎𝑖𝑛


B1


C2

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Signal Processing for mmWave MIMO Radar - diva …826028/FULLTEXT01.pdf · Signal Processing for mmWave MIMO Radar ... improved resolution and detection capabilities will be achieved