Fundamentals of Signal Enhancement and Array Signal Processing

This book is a comprehensive guide to the theory and practice of signal enhancement and array signal processing, including Matlab codes, exercises, and instructor and solution manuals. Written as a course textbook for senior undergraduate and graduate students, it contains a total of 11 chapters, which cover single–channel signal enhancement and multichannel signal enhancement in the time and frequency domains. Other important topics include linear filtering for signal enhancement, fixed beamforming, adaptive beamforming, differential beamforming, and beamforming for broadband signals.

Systematically introduces the fundamental principles, theory and applications of signal enhancement and array signal processing in an accessible manner Offers an updated and relevant treatment of array signal processing with rigor and concision Features a companion website that includes presentation files with lecture notes, homework exercises, course projects, solution manuals, instructor manuals, and Matlab codes for the examples in the book

Written by experienced researchers and teachers, Fundamentals of Signal Enhancement and Array Signal Processing is an essential textbook for senior undergraduate and graduate students of acoustic and array signal processing. Practicing engineers and industry professionals will also find it a comprehensive self–study guide.

Preface vii

1 Introduction 1

1.1 Signal Enhancement 1

1.2 Approaches to Signal Enhancement 9

1.3 Array Signal Processing 11

1.4 Organization of the Book 14

1.5 How to Use the Book 16

2 Single–Channel Signal Enhancement in the Time Domain 21

2.1 Signal Model and Problem Formulation 21

2.2 Wiener Method 22

2.3 Spectral Method 40

2.4 Problems 55

3 Single–Channel Signal Enhancement in the Frequency Domain 61

3.1 Signal Model and Problem Formulation 61

3.2 Noise Reduction with Gains 62

3.3 Performance Measures 63

3.4 Optimal Gains 66

3.5 Constraint Wiener Gains 81

3.6 Implementation with the Short–Time Fourier Transform 87

3.7 Problems 95

4 Multichannel Signal Enhancement in the Time Domain 101

4.1 Signal Model and Problem Formulation 101

4.2 Conventional Method 102

4.3 Spectral Method 116

4.4 Case of a Rank Deficient Noise Correlation Matrix 131

4.5 Problems 136

5 Multichannel Signal Enhancement in the Frequency Domain 143

5.1 Signal Model and Problem Formulation 143

5.2 Linear Filtering 146

5.3 Performance Measures 147

5.4 Optimal Filters 152

5.5 Generalized Sidelobe Canceller Structure 171

5.6 A Signal Subspace Perspective 173

5.7 Implementation with the STFT 182

5.8 Problems 188

6 An Exhaustive Class of Linear Filters 197

6.1 Signal Model and Problem Formulation 197

6.2 Linear Filtering for Signal Enhancement 199

6.3 Performance Measures 200

6.4 Optimal Filters 202

6.5 Filling the Gap Between the Maximum SINR and Wiener Filters 214

6.6 Problems 221

7 Fixed Beamforming 227

7.1 Signal Model and Problem Formulation 227

7.2 Linear Array Model 228

7.3 Performance Measures 229

7.4 Spatial Aliasing 232

7.5 Fixed Beamformers 233

7.6 A Signal Subspace Perspective 253

7.7 Problems 261

8 Adaptive Beamforming 271

8.1 Signal Model, Problem Formulation, and Array Model 271

8.2 Performance Measures 272

8.3 Adaptive Beamformers 274

8.4 SNR Estimation 287

8.5 DOA Estimation 290

8.6 A Spectral Coherence Perspective 294

8.7 Problems 302

9 Differential Beamforming 309

9.1 Signal Model, Problem Formulation, and Array Model 309

9.2 Beampatterns 310

9.3 Front–to–Back Ratios 311

9.4 Array Gains 313

9.5 Examples of Theoretical Differential Beamformers 314

9.6 First–Order Design 317

9.7 Second–Order Design 320

9.8 Third–Order Design 328

9.9 Minimum–Norm Beamformers 335

9.10 Problems 341

10 Beampattern Design 349

10.1 Beampatterns Revisited 349

10.2 Nonrobust Approach 353

10.3 Robust Approach 355

10.4 Frequency–Invariant Beampattern Design 358

10.5 Least–Squares Method 361

10.6 Joint Optimization 367

10.7 Problems 378

11 Beamforming in the Time Domain 383

11.1 Signal Model and Problem Formulation 383

11.2 Broadband Beamforming 386

11.3 Performance Measures 387

11.4 Fixed Beamformers 391

11.5 Adaptive Beamformers 401

11.6 Differential Beamformers 413

11.7 Problems 423

Index 429

Jacob Benesty, INRS, University of Quebec, Canada

Israel Cohen, Technion, Israel Institute of Technology, Israel

Jingdong Chen, Northwestern Polytechnical University, China