Sparse adaptive filters - An overview and some new results

In this paper, we provide an overview of the major developments in the area of sparse adaptive filters, starting from the celebrated works on PNLMS algorithm and its several variants to more recent approaches that use compressed sensing framework, more specifically, LASSO and basis pursuit or matching pursuit, to develop sparse adaptive algorithms with improved mean square error and tracking properties. Subsequently, we also present a new approach to identify sparse systems with time varying sparseness, for which a novel scheme of cooperative learning involving a PNLMS and a NLMS based adaptive filters is developed.