A Variational Bayesian Learning Approach for Nonlinear Acoustic Echo Control

• Published in: IEEE transactions on signal processing Vol. 61; no. 23; pp. 5853 - 5867
• Main Authors: Malik, Sarmad, Enzner, Gerald
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.12.2013; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Acoustics; Adaptation models; Algorithms; Applied sciences; Bayes methods; Bayesian analysis; Cancellation; Cascade modeling; Detection, estimation, filtering, equalization, prediction; Exact sciences and technology; Information, signal and communications theory; Learning; Mathematical analysis; Mathematical model; Mathematical models; Miscellaneous; nonlinear echo cancellation; Nonlinearity; Operations research; post-filtering; Random variables; recursive Bayesian estimator; Signal and communications theory; Signal processing; Signal, noise; State-space methods; state-space model; Telecommunications and information theory; Vectors; Vectors (mathematics); Cascade modeling; Microphone; Variational methods; Noise reduction; Discrete Fourier transformation; Loudspeaker; Non linear phenomenon; Composite material; Learning; Acoustic noise; post-filtering; Random variable; Lower bound; Probabilistic approach; Acoustic signal; recursive Bayesian estimator; state-space model; nonlinear echo cancellation; Markov model; State space method; Acoustic signal processing; Echo suppression; Algorithm; Residual impurity; First order; A priori estimation; Signal processing; Bayes methods; Non linear effect
• ISSN: 1053-587X; 1941-0476
• DOI: 10.1109/TSP.2013.2281021

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.