Affine Projection Adaptive Filters for the Identification of Sparse Systems

Abstract

In this paper, we focus on the identification of sparse systems, as is often the case in telecommunications and acoustics applications, using sparse affine projection (AP) algorithms, expected to perform better than sparse versions of the LMS and NLMS for a highly correlated input signal. Initially, we offer a concise review on the AP adaptive filter theory, followed by the analysis of sparse AP zero attractors from a geometric point-of-view. Then, we propose a sparse AP based on the SparseStep approximation of the 0-pseudo-norm. Finally, the proposed algorithm is numerically validated by comparing it with well-known sparse AP filters.