On Semi-Blind Source Separation-Based Approaches to Nonlinear Echo Cancellation Based on Bilinear Alternating Optimization

Acoustic echo cancellation (AEC) is a crucial task in full duplex communications. As conventional linear filtering approaches are ineffective to deal with double-talk, various semi-blind source separation (SBSS)-based AEC algorithms are deceived, most of which are formulated and implemented in the frequency domain based on the multiplicative transfer function (MTF) model for computational efficiency. To avoid large latency and in order to deal with loudspeaker nonlinearities, the convolutive transfer function (CTF) model and odd power series expansion are leveraged, which are employed by numerous SBSS-based nonlinear AEC (SBSS-NAEC) algorithms. Conventional SBSS-NAEC methods estimate the series expansion coefficients and the CTF filter simultaneously making the number of free parameters to estimate large. Hence, the corresponding algorithms are computationally expensive and are difficult to optimize. In this work, we propose to decouple the series expansion coefficients and the CTF filters into a bilinear form and present a bilinear alternating optimization framework for estimating the model parameters. An alternating iterative projection (AIP) algorithm and an alternating element-wise iterative source steering (AEISS) algorithm are proposed. As the bilinear representation consists of less parameters compared to the conventional methods, the proposed algorithms not only improve the AEC performance but also reduce the computational complexity, which is validated by comprehensive simulations and experiments.