Adaptive Array Systems: Fundamentals and Applications

Preface xi

Acknowledgments xv

List of Figures xvii

List of Tables xxix

Introduction xxxiii

I.1 Adaptive Filtering xxxiii

I.2 Historical Aspects xxxiv

I.3 Concept of Spatial Signal Processing xxxv

1 Fundamentals of Array Signal Processing 1

1.1 Introduction 1

1.2 The Key to Transmission 2

1.2.1 Maxwell’s Equations 2

1.2.2 Interpretation 3

1.2.3 Key to Antennas 3

1.3 Hertzian Dipole 5

1.4 Antenna Parameters & Terminology 7

1.4.1 Polarisation 7

1.4.2 Power Density 7

1.4.3 Radiated Power 8

1.4.4 Radiation Resistance 9

1.4.5 Antenna Impedance 9

1.4.6 Equivalent Circuit 10

1.4.7 Antenna Matching 10

1.4.8 Effective Length and Area 10

1.4.9 Radiation Intensity 11

1.4.10 Radiation Pattern 11

1.4.11 Bandwidth 12

1.4.12 Directive Gain, Directivity, Power Gain 12

1.4.13 Radiation Efficiency 14

1.5 Basic Antenna Elements 14

1.5.1 Finite-Length Dipole 15

1.5.2 Mono-pole 17

1.5.3 Printed Antennas 17

1.5.4 Wideband Elements 18

1.5.5 Dual Polarised Elements 20

1.5.6 Sonar Sensors 21

1.6 Antenna Arrays 21

1.6.1 Linear Array 22

1.6.2 Circular Array 23

1.6.3 Planar Array 23

1.6.4 Conformal Arrays 24

1.7 Spatial Filtering 25

1.8 Adaptive Antenna Arrays 27

1.9 Mutual Coupling & Correlation 27

1.10 Chapter Summary 28

1.11 Problems 29

2 Narrowband Array Systems 31

2.1 Introduction 31

2.2 Adaptive Antenna Terminology 32

2.3 Beam Steering 35

2.3.1 Phase Weights 35

2.3.2 Main Beam Steering 36

2.3.3 Null Steering 38

2.4 Grating Lobes 41

2.5 Amplitude Weights 44

2.5.1 Window Functions 44

2.6 Chapter Summary 53

2.7 Problems 53

3 Wideband Array Processing 55

3.1 Introduction 55

3.2 Basic concepts 56

3.3 A Simple Delay-line Wideband Array 59

3.3.1 Angles of Grating Lobes 61

3.3.2 Beam Width 63

3.4 Rectangular Arrays as Wideband Beamformers 65

3.4.1 Rectangular Array Antenna in Azimuth 66

3.4.2 Beamforming using IDFT 69

3.4.3 Beamforming using Matrix Inversion 73

3.4.4 Numerical Examples 75

3.4.5 Summary of Wideband Frequency Selective Rectangular Arrays 82

3.5 Wideband Beamforming using FIR Filters 84

3.5.1 Continuous Linear Wideband Array 84

3.5.2 Beamformer Implementation 85

3.5.3 Sensor Locations 88

3.5.4 Design of Primary Filters 90

3.5.5 Design of Secondary Filters 92

3.5.6 Numerical Examples 92

3.6 Chapter Summary 93

3.7 Problems 94

4 Adaptive Arrays 97

4.1 Introduction 97

4.2 Spatial Covariance Matrix 98

4.3 Multi-beam Arrays 100

4.4 Scanning Arrays 100

4.5 Switched Beam Beamformers 101

4.6 Fully Adaptive Beamformers 104

4.6.1 Temporal Reference Beamforming 106

4.6.2 Spatial Reference Beamforming 107

4.7 Adaptive Algorithms 108

4.7.1 Wiener Solution 109

4.7.2 Method of Steepest-Descent 111

4.7.3 Least-Mean-Squares Algorithm (LMS) 112

4.7.4 Direct Matrix Inversion (DMI) Algorithm 113

4.7.5 Recursive Least-Squares (RLS) Algorithm 115

4.8 Source Location Techniques 116

4.9 Fourier Method 117

4.10 Capon’s Minimum Variance 118

4.11 The MUSIC Algorithm 118

4.12 ESPRIT 121

4.12.1 Unitary ESPRIT 122

4.13 Maximum Likelihood Techniques 124

4.14 Spatial Smoothing 125

4.14.1 Comparison of Spatial Parameter Estimation Techniques 127

4.15 Determination of Number of Signal Sources 127

4.16 Blind Beamforming 129

4.16.1 Decoupled Iterative Least Squares Finite Alphabet Space-Time (DILFAST) Algorithm 130

4.16.2 Spectral Self-Coherence Restoral (SCORE) Algorithm 131

4.16.3 Constant Modulus Algorithm (CMA) 132

4.16.4 Least-Squares Despread Respread Multitarget Constant Modulus Algorithm (LS-DRMTCMA) 133

4.17 Chapter Summary 133

4.18 Problems 134

5 Practical Considerations 135

5.1 Introduction 135

5.2 Signal Processing Constraints 136

5.2.1 Phase Error 136

5.2.2 Element Position Error 137

5.2.3 Element Failure 137

5.2.4 Steering Vector Error 137

5.2.5 Ill-Conditioned Signal Processing Matrices 137

5.2.6 Weight Jitter 138

5.3 Implementation Issues 138

5.3.1 System Linearity 145

5.3.2 Calibration 146

5.3.3 Mutual Coupling 154

5.3.4 Circular Arrays 156

5.4 Radiowave Propagation 160

5.4.1 Narrowband Single Antenna Channel Model 161

5.4.2 Multiple Antenna Channel Model 162

5.4.3 Wideband Multiple Antenna Channel Model 163

5.4.4 Uplink-Downlink Channel Modelling for FDD Systems 168

5.5 Transmit Beamforming 170

5.5.1 Blind Techniques 172

5.5.2 Feedback Based Techniques 177

5.5.3 Switched Beam Techniques 178

5.5.4 Downlink Signal Distribution Schemes 179

5.6 Chapter Summary 181

5.7 Problems 181

6 Applications 183

6.1 Introduction 183

6.2 Antenna Arrays for Radar Applications 183

6.3 Antenna Arrays for Sonar Applications 184

6.4 Antenna Arrays for Biomedical Applications 186

6.4.1 Medical Ultrasonic Arrays 186

6.4.2 Space-Time Beamforming for Microwave Imaging 192

6.5 Antenna Arrays for Wireless Communications 193

6.5.1 Uplink Beamforming for Second-Generation Mobile Wireless Networks 196

6.5.2 Downlink Beamforming for Third-Generation Mobile Wireless Networks 207

6.5.3 User Location and Tracking 219

6.5.4 Beamforming for Satellite Communications 231

6.6 Chapter Summary 235

6.7 Problems 236

References 239

Index 251