Acoustic MIMO Signal Processing (2006) (Signals and Communication Technology)

383 Pages·2006·14.917 MB·English

by  Yiteng Huang, Jacob Benesty, Jingdong Chen,

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Yiteng (Arden) Huang
Jacob Benesty
Jingdong Chen
Acoustic MIMO
Signal Processing
Springer
Dr. Yiteng (Arden) Huang
Bell Labs, Lucent Technologies
600 Mountain Ave.
Murray Hill, NJ 07974
USA
Prof. Dr. Jacob Benesty
INRS-EMT, University of Quebec
800 de la Gauchetiere Quest
Montreal, QC, H5A 1K6
Canada
Dr. Jingdong Chen
Bell Labs, Lucent Technologies
600 Mountain Ave.
Murray Hill, NJ 07974
USA
Acoustic MIMO Signal Processing
Library of Congress Control Number: 2006920463
ISBN 0-387-27674-2 e-ISBN 0-387-27676-9
ISBN 9780387276748
Printed on acid-free paper.
© 2006 Springer Science+Business Media, Inc.
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Contents
Preface xiii
1 Introduction 1
1.1 Acoustic MIMO Signal Processing 1
1.2 Organization of the Book 4
Part I Theory
2 Acoustic MIMO Systems 9
2.1 Signal Models 9
2.1.1 SISO Model 9
2.1.2 SIMO Model 11
2.1.3 MISO Model 12
2.1.4 MIMO Model 12
2.2 Characteristics of Acoustic Channels 13
2.2.1 Linearity and Shift-Invariance 14
2.2.2 FIR Representation 14
2.2.3 Time-Varying Channel Impulse Responses 14
2.2.4 Frequency Selectivity 15
2.2.5 Reverberation Time 15
2.2.6 Channel Invertibility and Minimum-Phase Filter 16
2.2.7 Multichannel Diversity and the Common-Zero Problem 18
2.2.8 Sparse Impulse Response 19
2.3 Measurement and Simulation of MIMO Acoustic Systems 21
2.3.1 Direct Measurement of Acoustic Impulse Responses.... 22
2.3.2 Image Model for Acoustic Impulse Response Simulation 24
2.4 Summary 29
Contents
Wiener Filter and Basic Adaptive Algorithms 31
3.1 Introduction 31
3.2 Wiener Filter 32
3.3 Impulse Response Tail Effect 34
3.4 Condition Number 35
3.4.1 Decomposition of the Correlation Matrix 36
3.4.2 Condition Number with the Frobenius Norm 37
3.4.3 Fast Computation of the Condition Number 39
3.5 Basic Adaptive Algorithms 41
3.5.1 Deterministic Algorithm 41
3.5.2 Stochastic Algorithm 44
3.5.3 Sign Algorithms 46
3.6 MIMO Wiener Filter 48
3.7 Numerical Examples 53
3.8 Summary 56
Sparse Adaptive Filters 59
4.1 Introduction 59
4.2 Notation and Definitions 60
4.3 The NLMS, PNLMS, and IPNLMS Algorithms 61
4.4 Universal Criterion 64
4.4.1 Linear Update 65
4.4.2 Non-Linear Update 67
4.5 Exponentiated Gradient Algorithms 68
4.5.1 The EG Algorithm for Positive Weights 68
4.5.2 The EG± Algorithm for Positive and Negative Weights 69
4.5.3 The Exponentiated RLS (ERLS) Algorithm 71
4.6 The Lambert W Function Based Gradient Algorithm 72
4.7 Some Important Links Among Algorithms 74
4.7.1 Link Between NLMS and EG± Algorithms 74
4.7.2 Link Between IPNLMS and EG± Algorithms 75
4.7.3 Link Between LWG and EG± Algorithms 77
4.8 Numerical Examples 78
4.9 Summary 83
Frequency-Domain Adaptive Filters 85
5.1 Introduction 85
5.2 Derivation of SISO FD Adaptive Algorithms 86
5.2.1 Criterion 86
5.2.2 Normal Equations 89
5.2.3 Adaptive Algorithms 91
5.2.4 Convergence Analysis 93
5.3 Approximation and Special Cases 96
5.3.1 Approximation 96
5.3.2 Special Cases 98
Contents
5.4 FD Affine Projection Algorithm 99
5.5 Generalization to the MISO System Case 101
5.6 Numerical Examples 104
5.7 Summary 106
Blind Identification of Acoustic MIMO Systems 109
6.1 Introduction 109
6.2 Blind SIMO Identification Ill
6.2.1 Identifiability and Principle HI
6.2.2 Constrained Time-Domain Multichannel LMS and
Newton Algorithms 113
6.2.3 Unconstrained Multichannel LMS Algorithm with
Optimal Step-Size Control 120
6.2.4 Frequency-Domain Unnormalized and Normalized
Multichannel LMS Algorithms 122
6.2.5 Adaptive Multichannel Exponentiated Gradient
Algorithm 135
6.2.6 Numerical Examples 141
6.3 Bhnd MIMO Identification 147
6.3.1 Problem Formulation and Background Review 148
6.3.2 Memoryless MIMO System with White Inputs 151
6.3.3 Memoryless MIMO System with Colored Inputs 152
6.3.4 Convolutive MIMO Systems with White Inputs 154
6.3.5 Convolutive MIMO Systems with Colored Inputs 156
6.3.6 Frequency-Domain Blind Identification of Convolutive
MIMO Systems and Permutation Inconsistency 157
6.3.7 Convolutive MIMO Systems with White but
Quasistationary Inputs 158
6.4 Summary 160
6.5 Appendix. Blind SIMO Identification: A Derivation Directly
From the Covariance Matrices of the System Outputs 161
Separation and Suppression of Co-Channel and Temporal
Interference 169
7.1 Introduction 169
7.2 Separating Co-Channel and Temporal Interference 170
7.2.1 Example: Conversion of a 2 x 3 MIMO System to Two
SIMO Systems 170
7.2.2 Generalization to M x N MIMO Systems with M > 2
and M < AT 174
7.3 Suppressing Temporal Interference 177
7.3.1 Direct Inverse (Zero-Forcing) Equalizer 178
7.3.2 MMSE Equalizer 179
7.3.3 MINT Equalizers 179
7.4 Summary 182
Contents
Part II Applications
Acoustic Echo Cancellation and Audio Bridging 185
8.1 Introduction 185
8.2 Network Echo Problem 186
8.3 Single-Channel Acoustic Echo Cancellation 188
8.4 Multichannel Acoustic Echo Cancellation 190
8.4.1 Multi versus Mono 190
8.4.2 Multichannel Identification and the Nonuniqueness
Problem 192
8.4.3 Impulse Response Tail EflPect 194
8.4.4 Some Different Solutions for Decorrelation 195
8.5 Hybrid Mono/Stereo Acoustic Echo Canceler 199
8.6 Double-Talk Detection 200
8.6.1 Basics 200
8.6.2 Double-Talk Detection Algorithms 202
8.6.3 Performance Evaluation of DTDs 206
8.7 Audio Bridging 206
8.7.1 Principle 206
8.7.2 Interchannel Differences for Synthesizing Stereo Sound . 209
8.7.3 Choice of Interchannel Differences for Stereo AEC 211
8.8 Summary 212
Time Delay Estimation and Acoustic Source Localization .215
9.1 Time Delay Estimation 215
9.2 Cross-Correlation Method 217
9.3 Magnitude-Difference Method 219
9.4 Maximum Likelihood Method 220
9.5 Generalized Cross-Correlation Method 223
9.6 Adaptive Eigenvalue Decomposition Algorithm 226
9.7 Multichannel Cross-Correlation Algorithm 227
9.7.1 Forward Spatial Linear Prediction 228
9.7.2 Backward Spatial Linear Prediction 230
9.7.3 Spatial Linear Interpolation 231
9.7.4 Time Delay Estimation Using Spatial Linear Prediction 232
9.7.5 Spatial Correlation Matrix and Its Properties 233
9.7.6 Multichannel Cross-Correlation Coefficient 235
9.7.7 Time Delay Estimation Using MCCC 235
9.8 Adaptive Multichannel Time Delay Estimation 236
9.9 Acoustic Source Localization 238
9.10 Measurement Model and Cramer-Rao Lower Bound 239
9.11 Algorithm Overview 242
9.12 Maximum Likehhood Estimator 243
9.13 Least-Squares Estimators 244
Contents ix
9.13.1 Least-Squares Error Criteria 245
9.13.2 Spherical Intersection (SX) Estimator 247
9.13.3 Spherical Interpolation (SI) Estimator 247
9.13.4 Linear-Correction Least-Squares Estimator 248
9.14 Example System Implementation 254
9.15 Summary 259
10 Speech Enhancement and Noise Reduction 261
10.1 Introduction 261
10.2 Noise-Reduction and Speech-Distortion Measures 263
10.2.1 Noise-Reduction Factor and Noise-Reduction Gain
Function 264
10.2.2 Speech-Distortion Index and Attenuation Frequency
Distortion 265
10.2.3 Signal-to-Noise Ratio 265
10.2.4 Log-Spectral Distance 266
10.2.5 Itakura Distance 266
10.2.6 Itakura-Saito Distance 268
10.2.7 Mean Opinion Score 269
10.3 Single-Channel Noise-Reduction Algorithms: a Brief Overview. 269
10.4 Time-Domain Wiener Filter 270
10.4.1 Estimation of the Clean Speech Samples 270
10.4.2 Estimation of the Noise Samples 273
10.4.3 Noise Reduction versus Speech Distortion 274
10.4.4 A Priori SNR versus a Posteriori SNR 277
10.4.5 Bounds for Noise Reduction and Speech Distortion .... 281
10.4.6 Particular Case: White Gaussian Noise 282
10.4.7 A Suboptimal Filter 283
10.5 Frequency-Domain Wiener Filter 287
10.5.1 Estimation of the Clean Speech Spectrum 287
10.5.2 A Priori SNR versus a Posteriori SNR 290
10.6 Noise Reduction Through Spectral Magnitude Restoration .... 292
10.7 Spectral Subtraction 293
10.7.1 Estimation of the Spectral Magnitude of the Clean
Speech 293
10.7.2 Estimation of the Noise Spectrum 295
10.7.3 Relationship Between Spectral Subtraction and
Wiener Filtering 296
10.7.4 Estimation of the Wiener Gain Filter 299
10.7.5 Simulations 300
10.8 Adaptive Noise Cancellation 302
10.8.1 Estimation of the Clean Speech 302
10.8.2 Ideal Noise Cancellation Performance 304
10.8.3 Signal Cancellation Problem 305
10.8.4 Simulations 307