A Bayesian network approach to linear and nonlinear acoustic echo cancellation

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.