A Variational Bayesian Learning Approach for Nonlinear Acoustic Echo Control

In this work, we present novel Bayesian algorithms for acoustic echo cancellation and residual echo suppression in the presence of a memoryless loudspeaker nonlinearity. The system nonlinearity is modeled using a basis-generic nonlinear expansion. This allows us to express the microphone observation in the DFT domain in terms of the nonlinear-expansion coefficients and the acoustic echo path. We augment the observation model with first-order Markov models for the echo-path vector and the nonlinear-expansion coefficients to arrive at a composite state-space model. The echo path vector and each nonlinear-expansion coefficient are designated as the unknown random variables in our Bayesian model. The posterior estimators for the random variables and the learning rules for the a priori unknown model parameters are then derived via the maximization of the variational lower bound on the log likelihood. We further show that a Bayesian post-filter for residual echo suppression can be derived by optimizing a minimum-mean-square error (MMSE) cost function subject to marginalization with respect to the posteriors estimated in the echo cancellation stage. The effectiveness of the approach is supported by simulation results and an analysis using instrumental performance measures.