Nonlinear Acoustic Echo Cancellation Based on a Sliding-Window Leaky Kernel Affine Projection Algorithm

Acoustic echo cancellation (AEC) is used in speech communication systems where the existence of echoes degrades the speech intelligibility. Standard approaches to AEC rely on the assumption that the echo path to be identified can be modeled by a linear filter. However, some elements introduce nonlinear distortion and must be modeled as nonlinear systems. Several nonlinear models have been used with more or less success. The kernel affine projection algorithm (KAPA) has been successfully applied to many areas in signal processing but not yet to nonlinear AEC (NLAEC). The contribution of this paper is three-fold: (1) to apply KAPA to the NLAEC problem, (2) to develop a sliding-window leaky KAPA (SWL-KAPA) that is well suited for NLAEC applications, and (3) to propose a kernel function, consisting of a weighted sum of a linear and a Gaussian kernel. In our experiment set-up, the proposed SWL-KAPA for NLAEC consistently outperforms the linear APA, resulting in up to 12 dB of improvement in ERLE at a computational cost that is only 4.6 times higher. Moreover, it is shown that the SWL-KAPA outperforms, by 4-6 dB, a Volterra-based NLAEC, which itself has a much higher 413 times computational cost than the linear APA.