## Time-Domain Beamforming and Blind Source Separation: Speech Input in the Car EnvironmentThe development of computer and telecommunication technologies led to a revolutioninthewaythatpeopleworkandcommunicatewitheachother.One of the results is that large amount of information will increasingly be held in a form that is natural for users, as speech in natural language. In the presented work, we investigate the speech signal capture problem, which includes the separation of multiple interfering speakers using microphone arrays. Adaptive beamforming is a classical approach which has been developed since the seventies. However it requires a double-talk detector (DTD) that interrupts the adaptation when the target is active, since otherwise target cancelation occurs. The fact that several speakers may be active simulta- ouslymakesthisdetectiondi?cult,andifadditionalbackgroundnoiseoccurs, even less reliable. Our proposed approaches address this separation problem using continuous, uninterrupted adaptive algorithms. The advantage seems twofold:Firstly,thealgorithmdevelopmentismuchsimplersincenodetection mechanism needs to be designed and no threshold is to be tuned. Secondly, the performance may be improved due to the adaptation during periods of double-talk. In the ?rst part of the book, we investigate a modi?cation of the widely usedNLMSalgorithm,termedImplicitLMS(ILMS),whichimplicitlyincludes an adaptation control and does not require any threshold. Experimental ev- uations reveal that ILMS mitigates the target signal cancelation substantially with the distributed microphone array. However, in the more di?cult case of the compact microphone array, this algorithm does not su?ciently reduce the target signal cancelation. In this case, more sophisticated blind source se- ration techniques (BSS) seem necessary. |

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### Contents

1 | |

2 | |

3 | |

13 Outline of the Book | 4 |

Source Separation as a Multichannel Linear Filtering Problem | 6 |

22 The Separation Filters | 10 |

222 Multiple Output Systems | 13 |

223 The Spatial Response | 14 |

63 Experimental Results | 100 |

631 Experiments with the FourElement Compact Array Mounted in the RearView Mirror | 101 |

632 Experiments with the TwoElement Distributed Array Mounted on the Car Ceiling | 106 |

633 Comparison with Other BSS Algorithms in the Frequency Domain | 108 |

64 Summary and Conclusion | 111 |

On the Convergence and Stability in SecondOrder Statistics BSS | 113 |

711 Difficulty of a Global Convergence Analysis | 114 |

712 Convergence Analysis for a Simpliﬁed Algorithm | 116 |

224 Particular Cases | 17 |

23 Spatial Filtering vs Spectral Filtering | 18 |

231 Minimum Filter Length for Spatial Separation | 20 |

232 Particular Cases | 21 |

24 Performance Measures | 22 |

241 Compact Microphone Array | 23 |

243 StartUp Performance and Performance after Initial Convergence | 24 |

Linearly Constrained Minimum Variance Beamforming | 27 |

32 From LCMV to Generalized Sidelobe Canceler GSC | 30 |

33 Constraints for Compact and Distributed Setups | 31 |

332 Constraint for Distributed Microphone Array | 33 |

34 The Target Signal Cancelation Problem | 34 |

341 The EnergyInversion Effect | 35 |

On the Necessity of a DoubleTalk Detector | 36 |

35 Summary and Conclusion | 37 |

Implicit Adaptation Control for Beamforming | 39 |

42 Implicit Adaptation Control | 42 |

43 Analysis of the ILMS Algorithm | 43 |

432 ILMS Transient Behavior and Stability | 46 |

Transient Convergence and Divergence | 47 |

44 Robustness Improvement | 51 |

45 Experiments | 52 |

451 Experiments with the FourElement Compact Array Mounted in the RearView Mirror | 55 |

452 Experiment with the TwoElement Distributed Array Mounted on the Car Ceiling | 59 |

46 Summary and Conclusion | 61 |

SecondOrder Statistics Blind Source Separation | 63 |

51 Problem and Notations | 65 |

512 Separation Ambiguities | 68 |

52 Nonstationarity and Source Separation | 69 |

522 NonstationarityBased Cost Function | 70 |

53 GradientBased Minimization | 73 |

532 Natural Gradient | 74 |

54 Natural Gradient Algorithm for NonSquare Systems | 75 |

55 Summary and Conclusion | 79 |

Implementation Issues in Blind Source Separation | 80 |

611 Gradient in the Sylvester Subspace | 82 |

612 From Matrices to zTransforms | 84 |

613 SelfClosed and NonSelfClosed Natural Gradients | 87 |

614 From zTransforms Back to the Time Domain | 89 |

615 Application to NGSOSBSS | 91 |

Which Natural Gradient is Best? | 93 |

62 Online Adaptation | 97 |

622 SampleWise Adaptation | 98 |

72 Local Stability | 121 |

73 Summary and Conclusion | 123 |

Comparison of LCMV Beamforming and SecondOrder Statistics BSS | 125 |

81 Properties of the Cost Functions | 126 |

812 On the Estimation Variance | 128 |

82 Complexity | 133 |

821 NLMS Complexity | 134 |

822 Complexity of NGSOSBSS Algorithms | 135 |

823 Comparison of NLMS and NGSOSBSS Complexities | 138 |

83 Links with the ILMS Algorithm | 140 |

84 Experimental Comparison | 141 |

85 Summary and Conclusion | 145 |

Combining SecondOrder Statistics BSS and LCMV Beamforming | 147 |

91 Existing Combinations | 148 |

92 BSS and Geometric Prior Information | 149 |

921 Causality Information | 150 |

922 Prior Information on the Source Direction of Arrival | 151 |

923 Geometric Information at the Initialization | 154 |

924 Geometric Information as a Soft Constraint | 156 |

925 Geometric Information as a Preprocessing | 160 |

93 Combining SOSBSS and the Power Criterion | 163 |

Prior Information and the Power Criterion | 165 |

95 Experimental Results on Automatic Speech Recognition | 167 |

96 Summary and Conclusion | 171 |

Summary and Conclusions | 173 |

Experimental Setups | 179 |

A3 Acoustic Characteristics of the Car Cabin | 181 |

Far and FreeField Acoustic Propagation Model and Null Beamforming | 184 |

B2 Null Beamforming | 186 |

The RGSC According to Hoshuyama et al | 189 |

C2 RGSC for the TwoElement Distributed Array Mounted on the Car Ceiling | 191 |

GSC vs RGSC | 192 |

C31 Experiments with the FourElement Compact Array Mounted in the RearView Mirror | 194 |

C32 Experiments with the TwoElement Distributed Array Mounted on the Car Ceiling | 195 |

C4 Conclusion | 196 |

Stability Analysis | 198 |

D2 Linearization of the NGSOSBSS Updates | 200 |

D3 Local Stability Conditions | 203 |

Notations | 207 |

215 | |

222 | |

### Other editions - View all

Time-Domain Beamforming and Blind Source Separation: Speech Input in the Car ... Julien Bourgeois,Wolfgang Minker No preview available - 2009 |

Time-Domain Beamforming and Blind Source Separation: Speech Input in the Car ... Julien Bourgeois,Wolfgang Minker No preview available - 2010 |

### Common terms and phrases

acoustic adaptive beamforming aQIC blind source separation block-wise batch blocking matrix BSS algorithms car ceiling causal codriver compact array mounted complexity computation constraint G1 convolution correlation matrix cost function cross-correlation decorrelation deﬁned denoted depicted in Fig desired signal diagonal diﬀerent distributed array mounted double-talk DTD-NLMS eﬃcient estimate experimental ﬁlter coeﬃcients ﬁrst four-element compact array frequency frequency-domain geometric prior information global convergence gradient descent Hoshuyama ILMS algorithm implementation impulse response input signals instantaneous interference reference iteration LCMV beamforming linear microphone array microphone signals MISO mutual information natural gradient NG-SOS-BSS algorithms Niter NLMS non-self-closed online algorithms output signal parameter PBSS performance permutation rear-view mirror RGSC sample sample-wise Sect self-closed update separation ﬁlters separation matrix shown in Fig signal power SIR improvement SOS-BSS source signals spatial response speech step-size suﬃcient Sylvester matrices target signal cancelation time-domain two-element distributed array vector Wopt yn(p z-transform zero