Nonlinear acoustic echo cancellation based on a parallel-cascade kernel affine projection algorithm

In acoustic echo cancellation (AEC) applications, oftentimes an acoustic path from a loudspeaker to a microphone is estimated by means of a linear adaptive filter. However, loudspeakers introduce nonlinear distortions which may strongly degrade the adaptive filter performance, thus nonlinear filters have to be considered. This paper proposes two adaptive algorithms namely the parallel and cascade sliding-window kernel based affine projection algorithm (PSW-KAPA and CSW-KAPA) to solve the problem of nonlinear AEC (NLAEC) while keeping the computational complexity low. They are based on a leaky KAPA which employs the theory and algorithms of kernel methods. The basic concept is to perform adaptive filtering in a linear space that is nonlinearly related to the original input space. A kernel specifically designed for acoustic applications is proposed, which consists in a weighted sum of the linear and the Gaussian kernels. The motivation is basically to separate the problem into linear and nonlinear subproblems. The weights in the kernel also impose different forgetting mechanisms in the sliding window which in turn translates to a more flexible regularization. Simulation results show that PSW-KAPA and CSW-KAPA consistently outperform the linear NLMS, and generalize well both in high and low linear to nonlinear ratio (LNLR).