Learning Coefficient and Convergence Speed for Stereo Echo Cancelers with Pre-Processing

Abstract

It is well-known that the so-called non-uniqueness problem appears in adaptive filters for stereo acoustic echo cancelers and one of the effective solutions is the input-sliding method that utilizes a time-varying preprocessor. In this paper, the convergence speed of the input-sliding method is examined. For adaptive algorithms based on orthogonal projection, such as the normalized LMS algorithm, the convergence speed is maximized when the learning coefficient is unity since the orthogonal projection is completed then. However, if the input signal vectors do not span the whole space but exist in a subspace which varies in time, then the learning coefficient which achieves the fastest convergence is found to be not unity but between one and two. The geometrical consideration of the tap-weight vector explains the phenomena and the theoretical results agree well with those of computer simulations.