Gradient-Limited Affine Projection Algorithm for Double-Talk-Robust and Fast-Converging Acoustic Echo Cancellation

Abstract

We propose a gradient-limited affine projection algorithm (GL-APA), which can achieve fast and double-talk-robust convergence in acoustic echo cancellation. GL-APA is derived from the M-estimation-based nonlinear cost function extended for evaluating multiple error signals dealt with in the affine projection algorithm (APA). By considering the nonlinearity of the gradient, we carefully formulate an update equation consistent with multiple input-output relationships, which the conventional APA inherently satisfies to achieve fast convergence. We also newly introduce a scaling rule for the nonlinearity, so we can easily implement GL-APA by using a predetermined primary function as a basis of scaling with any projection order. This guarantees a linkage between GL-APA and the gradient-limited normalized least-mean-squares algorithm (GL-NLMS), which is a conventional algorithm that corresponds to the GL-APA of the first order. The performance of GL-APA is demonstrated with simulation results.