GeneralizedWiener Filter for Nonlinear Acoustic Echo Control

Many contributions to the problem of nonlinear acoustic echo control (AEC) rely on model-based adaptive filtering combined with elements from deep learning, if not they pursue an all-neural treatment end-to-end. Those frequently two-stage hybrid implementations resemble the traditional linear AEC design consisting of an echo canceler and a postfilter. This paper delivers a mathematical derivation to support and optimize these implementations while taking the possibility of nonlinearities in the acoustic system into account. Specifically, we describe a Wiener filter framework, where the filtering statement employs two general complex-valued linear spectral weights. The theoretical result then guides the synthesis of an AEC system from elements of model-based processing and deep learning, which are here implemented by a model-based frequency-domain Kalman filter (FDKF) for echo cancellation and by a deep-learning-based long short-term memory (LSTM) network for postfiltering. Our experimental investigation includes verification of good complementarity of FDKF and LSTM network in the proposed framework and a study of the input signals suitable for the network part of the system. The analysis relies on moderatesize networks trained on original AEC challenge data.