Time-Domain Beamforming and Blind Source Separation (eBook)

Preface 6
Acknowledgments 8
Contents 9
1 Introduction 13
1.1 Existing Approaches: A Brief Overview 14
1.2 Scope and Objective of the Book 15
1.3 Outline of the Book 16
2 Source Separation as a Multichannel Linear Filtering Problem 18
2.1 The Mixing Channels 18
2.2 The Separation Filters 21
2.3 Spatial Filtering vs. Spectral Filtering 29
2.4 Performance Measures 33
2.5 Summary and Conclusion 35
3 Linearly Constrained Minimum Variance Beamforming 37
3.1 LCMV Beamforming 37
3.2 From LCMV to Generalized Sidelobe Canceler ( GSC) 40
3.3 Constraints for Compact and Distributed Setups 41
3.4 The Target Signal Cancelation Problem 44
3.5 Summary and Conclusion 47
4 Implicit Adaptation Control for Beamforming 49
4.1 Adaptive Interference Canceler 49
4.2 Implicit Adaptation Control 52
4.3 Analysis of the ILMS Algorithm 53
4.4 Robustness Improvement 61
4.5 Experiments 62
4.6 Summary and Conclusion 71
5 Second-Order Statistics Blind Source Separation 73
5.1 Problem and Notations 75
5.2 Nonstationarity and Source Separation 79
5.3 Gradient-Based Minimization 83
5.4 Natural Gradient Algorithm for NonSquare Systems 85
5.5 Summary and Conclusion 89
6 Implementation Issues in Blind Source Separation 90
6.1 Natural Gradient in the Convolutive Case 90
6.2 Online Adaptation 106
6.3 Experimental Results 109
6.4 Summary and Conclusion 120
7 On the Convergence and Stability in Second- Order Statistics BSS 122
7.1 Global Convergence 122
7.2 Local Stability 130
7.3 Summary and Conclusion 132
8 Comparison of LCMV Beamforming and Second- Order Statistics BSS 134
8.1 Properties of the Cost Functions 135
8.2 Complexity 142
8.3 Links with the ILMS Algorithm 149
8.4 Experimental Comparison 150
8.5 Summary and Conclusion 154
9 Combining Second-Order Statistics BSS and LCMV Beamforming 156
9.1 Existing Combinations 157
9.2 BSS and Geometric Prior Information 158
9.3 Combining SOS-BSS and the Power Criterion 172
9.4 Combining SOS-BSS with Geometric Prior Information and the Power Criterion 174
9.5 Experimental Results on Automatic Speech Recognition 176
9.6 Summary and Conclusion 180
10 Summary and Conclusions 182
A Experimental Setups 187
A.1 The Four-Element Compact Array Mounted in the Rear- View Mirror 187
A.2 The Two-Element Distributed Array Mounted on the Car Ceiling 187
A.3 Acoustic Characteristics of the Car Cabin 189
A.4 Illustration of the Difficulty in the Design of a Reliable DTD 189
B Far- and Free-Field Acoustic Propagation Model and Null Beamforming 192
B.1 Far- and Free-Field Model 192
B.2 Null Beamforming 193
C The RGSC According to Hoshuyama et al. 195
C.1 RGSC for the Four-Element Compact Array Mounted in the Rear- View Mirror 195
C.2 RGSC for the Two-Element Distributed Array Mounted on the Car Ceiling 197
C.3 Experimental Comparison: GSC vs. RGSC 198
C.4 Conclusion 202
D Stability Analysis 204
D.1 Mixing and Separation Models 204
D.2 Linearization of the NG-SOS-BSS Updates 205
D.3 Local Stability Conditions 208
E Notations 211
References 219
Index 226