Sparse Adaptive Filters for Echo Cancellation

✍ Scribed by Jacob Benesty, Constantin Paleologu, Silviu Ciochina

• Publisher: Morgan and Claypool Publishers
• Year: 2010
• Tongue: English
• Leaves: 125
• Series: Synthesis Lectures on Speech and Audio Processing
• Category: Library

✦ Synopsis

Adaptive filters with a large number of coefficients are usually involved in both network and acoustic echo cancellation. Consequently, it is important to improve the convergence rate and tracking of the conventional algorithms used for these applications. This can be achieved by exploiting the sparseness character of the echo paths. Identification of sparse impulse responses was addressed mainly in the last decade with the development of the so-called ``proportionate''-type algorithms. The goal of this book is to present the most important sparse adaptive filters developed for echo cancellation. Besides a comprehensive review of the basic proportionate-type algorithms, we also present some of the latest developments in the field and propose some new solutions for further performance improvement, e.g., variable step-size versions and novel proportionate-type affine projection algorithms. An experimental study is also provided in order to compare many sparse adaptive filters in different echo cancellation scenarios. Table of Contents: Introduction / Sparseness Measures / Performance Measures / Wiener and Basic Adaptive Filters / Basic Proportionate-Type NLMS Adaptive Filters / The Exponentiated Gradient Algorithms / The Mu-Law PNLMS and Other PNLMS-Type Algorithms / Variable Step-Size PNLMS Algorithms / Proportionate Affine Projection Algorithms / Experimental Study

✦ Table of Contents

Echo Cancellation......Page 12
Double-Talk Detection......Page 14
Sparse Adaptive Filters......Page 15
Notation......Page 16
Vector Norms......Page 18
Sparseness Measure Based on the 0 Norm......Page 20
Sparseness Measure Based on the 1 and 2 Norms......Page 21
Sparseness Measure Based on the 1 and Norms......Page 22
Sparseness Measure Based on the 2 and Norms......Page 23
Mean-Square Error......Page 26
Echo-Return Loss Enhancement......Page 27
Misalignment......Page 28
Wiener Filter......Page 30
Efficient Computation of the Wiener-Hopf Equations......Page 33
Deterministic Algorithm......Page 35
Stochastic Algorithm......Page 39
Variable Step-Size NLMS Algorithm......Page 42
Convergence of the Misalignment......Page 44
Sign Algorithms......Page 45
General Derivation......Page 48
The Proportionate NLMS (PNLMS) and PNLMS++ Algorithms......Page 50
The Signed Regressor PNLMS Algorithm......Page 51
The Improved PNLMS (IPNLMS) Algorithms......Page 52
The Regular IPNLMS......Page 53
The IPNLMS with the 0 Norm......Page 55
The IPNLMS with a Norm-Like Diversity Measure......Page 56
Cost Function......Page 58
The EG Algorithm for Positive Weights......Page 59
The EG Algorithm for Positive and Negative Weights......Page 60
Link Between NLMS and EG Algorithms......Page 62
Link Between IPNLMS and EG Algorithms......Page 64
The Mu-Law PNLMS Algorithms......Page 66
The Sparseness-Controlled PNLMS Algorithms......Page 70
The PNLMS Algorithm with Individual Activation Factors......Page 71
Considerations on the Convergence of the NLMS Algorithm......Page 76
A Variable Step-Size PNLMS Algorithm......Page 81
Classical Derivation......Page 84
A Novel Derivation......Page 86
A Variable Step-Size Version......Page 90
Experimental Conditions......Page 98
IPNLMS Versus PNLMS......Page 99
MPNLMS, SC-PNLMS, and IAF-PNLMS......Page 103
VSS-IPNLMS......Page 106
PAPAs......Page 107
Bibliography......Page 114
Index......Page 122
Authors' Biographies......Page 124