A Bayesian network approach to linear and nonlinear acoustic echo cancellation

Christian Huemmer,Walter Kellermann,Christian Hofmann,Roland Maas

doi:10.1186/s13634-015-0282-2

Christian Huemmer, Walter Kellermann + Show 2 more

Open Access

https://doi.org/10.1186/s13634-015-0282-2

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Abstract

This article provides a general Bayesian approach to the tasks of linear and nonlinear acoustic echo cancellation (AEC). We introduce a state-space model with latent state vector modeling all relevant information of the unknown system. Based on three cases for defining the state vector (to model a linear or nonlinear echo path) and its mathematical relation to the observation, it is shown that the normalized least mean square algorithm (with fixed and adaptive stepsize), the Hammerstein group model, and a numerical sampling scheme for nonlinear AEC can be derived by applying fundamental techniques for probabilistic graphical models. As a consequence, the major contribution of this Bayesian approach is a unifying graphical-model perspective which may serve as a powerful framework for future work in linear and nonlinear AEC.

Highlights

The problem of acoustic echo cancellation (AEC) is one of the earliest applications of adaptive filtering to acoustic signals and yet is still an active research topic [1, 2]
Depending on the definition of the state vector and its mathematical relation to the observation, we illustrate that the application of different probabilistic inference techniques to the same graphical model straightforwardly leads to the normalized least mean square (NLMS) algorithm with fixed/adaptive stepsize value, the Hammerstein group model, and a numerical sampling scheme for nonlinear AEC
7 Conclusions In this article, we derived a set of conceptually different algorithms for linear and nonlinear AEC from a unifying graphical model perspective

Summary

Introduction

The problem of acoustic echo cancellation (AEC) is one of the earliest applications of adaptive filtering to acoustic signals and yet is still an active research topic [1, 2]. Depending on the definition of the state vector (modeling a linear or nonlinear echo path) and its mathematical relation to the observation, we illustrate that the application of different probabilistic inference techniques to the same graphical model straightforwardly leads to the NLMS algorithm with fixed/adaptive stepsize value, the Hammerstein group model (considered from this perspective here for the first time), and a numerical sampling scheme for nonlinear AEC. This consistent Bayesian view on conceptually different algorithms highlights the probabilistic assumptions underlying the respective derivations and provides a powerful framework for further research in linear and nonlinear AEC.

Review of Bayesian networks and state-space modeling

LIC model

Conclusions