Microphone array signal processing

In the past few years we have written and edited several books in the area of acousticandspeechsignalprocessing. Thereasonbehindthisendeavoristhat there were almost no books available in the literature when we ?rst started while there was (and still is) a real need to publish manuscripts summarizing the most useful ideas, concepts, results, and state-of-the-art algorithms in this important area of research. According to all the feedback we have received so far, we can say that we were right in doing this. Recently, several other researchers have followed us in this journey and have published interesting books with their own visions and perspectives. The idea of writing a book on Microphone Array Signal Processing comes from discussions we have had with many colleagues and friends. As a c- sequence of these discussions, we came up with the conclusion that, again, there is an urgent need for a monograph that carefully explains the theory and implementation of microphone arrays. While there are many manuscripts on antenna arrays from a narrowband perspective (narrowband signals and narrowband processing), the literature is quite scarce when it comes to s- sor arrays explained from a truly broadband perspective. Many algorithms for speech applications were simply borrowed from narrowband antenna - rays. However, a direct application of narrowband ideas to broadband speech processing may not be necessarily appropriate and can lead to many m- understandings.

1 Introduction	p. 1
1.1 Microphone Array Signal Processing	p. 1
1.2 Organization of the Book	p. 5
2 Classical Optimal Filtering	p. 7
2.1 Introduction	p. 7
2.2 Wiener Filter	p. 8
2.3 Frost Filter	p. 16
2.3.1 Algorithm	p. 16
2.3.2 Generalized Sidelobe Canceller Structure	p. 17
2.3.3 Application to Linear Interpolation	p. 19
2.4 Kalman Filter	p. 21
2.5 A Viable Alternative to the MSE	p. 25
2.5.1 Pearson Correlation Coefficient	p. 26
2.5.2 Important Relations with the SPCC	p. 26
2.5.3 Examples of Optimal Filters Derived from the SPCC	p. 29
2.6 Conclusions	p. 37
3 Conventional Beamforming Techniques	p. 39
3.1 Introduction	p. 39
3.2 Problem Description	p. 40
3.3 Delay-and-Sum Technique	p. 41
3.4 Design of a Fixed Beamformer	p. 46
3.5 Maximum Signal-to-Noise Ratio Filter	p. 49
3.6 Minimum Variance Distortionless Response Filter	p. 52
3.7 Approach with a Reference Signal	p. 54
3.8 Response-Invariant Broadband Beamformers	p. 55
3.9 Null-Steering Technique	p. 58
3.10 Microphone Array Pattern Function	p. 61
3.10.1 First Signal Model	p. 62
3.10.2 Second Signal Model	p. 64
3.11 Conclusions	p. 65
4 On the Use of the LCMV Filter in Room Acoustic Environments	p. 67
4.1 Introduction	p. 67
4.2 Signal Models	p. 67
4.2.1 Anechoic Model	p. 68
4.2.2 Reverberant Model	p. 68
4.2.3 Spatio-Temporal Model	p. 69
4.3 The LCMV Filter with the Anechoic Model	p. 69
4.4 The LCMV Filter with the Reverberant Model	p. 73
4.5 The LCMV Filter with the Spatio-Temporal Model	p. 75
4.5.1 Experimental Results	p. 78
4.6 The LCMV Filter in the Frequency Domain	p. 81
4.7 Conclusions	p. 83
5 Noise Reduction with Multiple Microphones: a Unified Treatment	p. 85
5.1 Introduction	p. 85
5.2 Signal Model and Problem Description	p. 86
5.3 Some Useful Definitions	p. 87
5.4 Wiener Filter	p. 89
5.5 Subspace Method	p. 92
5.6 Spatio-Temporal Prediction Approach	p. 95
5.7 Case of Perfectly Coherent Noise	p. 97
5.8 Adaptive Noise Cancellation	p. 99
5.9 Kalman Filter	p. 100
5.10 Simulations	p. 101
5.10.1 Acoustic Environments and Experimental Setup	p. 101
5.10.2 Experimental Results	p. 103
5.11 Conclusions	p. 114
6 Noncausal (Frequency-Domain) Optimal Filters	p. 115
6.1 Introduction	p. 115
6.2 Signal Model and Problem Formulation	p. 116
6.3 Performance Measures	p. 117
6.4 Noncausal Wiener Filter	p. 120
6.5 Parametric Wiener Filtering	p. 124
6.6 Generalization to the Multichannel Case	p. 126
6.6.1 Signal Model	p. 126
6.6.2 Definitions	p. 128
6.6.3 Multichannel Wiener Filter	p. 129
6.6.4 Spatial Maximum SNR Filter	p. 132
6.6.5 Minimum Variance Distortionless Response Filter	p. 134
6.6.6 Distortionless Multichannel Wiener Filter	p. 135
6.7 Conclusions	p. 136
7 Microphone Arrays from a MIMO Perspective	p. 139
7.1 Introduction	p. 139
7.2 Signal Models and Problem Description	p. 140
7.2.1 SISO Model	p. 141
7.2.2 SIMO Model	p. 141
7.2.3 MISO Model	p. 142
7.2.4 MIMO Model	p. 143
7.2.5 Problem Description	p. 144
7.3 Two-Element Microphone Array	p. 144
7.3.1 Least-Squares Approach	p. 145
7.3.2 Frost Algorithm	p. 146
7.3.3 Generalized Sidelobe Canceller Structure	p. 148
7.4 N-Element Microphone Array	p. 150
7.4.1 Least-Squares and MINT Approaches	p. 150
7.4.2 Frost Algorithm	p. 152
7.4.3 Generalized Sidelobe Canceller Structure	p. 154
7.4.4 Minimum Variance Distortionless Response Approach	p. 156
7.5 Simulations	p. 156
7.5.1 Acoustic Environments and Experimental Setup	p. 156
7.6 Conclusions	p. 163
8 Sequential Separation and Dereverberation: the Two-Stage Approach	p. 165
8.1 Introduction	p. 165
8.2 Signal Model and Problem Description	p. 165
8.3 Source Separation	p. 168
8.3.1 2 x 3 MIMO System	p. 168
8.3.2 M x N MIMO System	p. 172
8.4 Speech Dereverberation	p. 175
8.4.1 Direct Inverse	p. 175
8.4.2 Minimum Mean-Square Error and Least-Squares Methods	p. 177
8.4.3 MINT Method	p. 177
8.5 Conclusions	p. 180
9 Direction-of-Arrival and Time-Difference-of-Arrival Estimation	p. 181
9.1 Introduction	p. 181
9.2 Problem Formulation and Signal Models	p. 184
9.2.1 Single-Source Free-Field Model	p. 184
9.2.2 Multiple-Source Free-Field Model	p. 185
9.2.3 Single-Source Reverberant Model	p. 186
9.2.4 Multiple-Source Reverberant Model	p. 187
9.3 Cross-Correlation Method	p. 188
9.4 The Family of the Generalized Cross-Correlation Methods	p. 190
9.4.1 Classical Cross-Correlation	p. 191
9.4.2 Smoothed Coherence Transform	p. 191
9.4.3 Phase Transform	p. 192
9.5 Spatial Linear Prediction Method	p. 193
9.6 Multichannel Cross-Correlation Coefficient Algorithm	p. 196
9.7 Eigenvector-Based Techniques	p. 200
9.7.1 Narrowband MUSIC	p. 201
9.7.2 Broadband MUSIC	p. 203
9.8 Minimum Entropy Method	p. 205
9.8.1 Gaussian Source Signal	p. 205
9.8.2 Speech Source Signal	p. 206
9.9 Adaptive Eigenvalue Decomposition Algorithm	p. 207
9.10 Adaptive Blind Multichannel Identification Based Methods	p. 209
9.11 TDOA Estimation of Multiple Sources	p. 211
9.12 Conclusions	p. 215
10 Unaddressed Problems	p. 217
10.1 Introduction	p. 217
10.2 Speech Source Number Estimation	p. 217
10.3 Cocktail Party Effect and Blind Source Separation	p. 218
10.4 Blind MIMO Identification	p. 220
10.5 Conclusions	p. 222
References	p. 223
Index	p. 237

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