Sparseness Controlled Proportionate RLS Algorithm for Sparse and Non-Sparse Systems

Abstract

This paper proposes a novel sparse adaptive technique to handle variable sparsity. The algorithm is based on the measure of sparseness. A proportionate matrix distributes the gain factor for all filter taps during each iteration. Each filter coefficient of the adaptive filter is updated by the corresponding diagonal element of the proportionate matrix, and that depends on the degree of sparseness. The classical recursive least square algorithm (RLS) is amended by accommodating the proportionate matrix to propose the sparseness-controlled proportionate recursive least square (SC-PRLS) algorithm. The convergence control parameter is incorporated into the algorithm to achieve faster convergence and better steady-state error. The performance of Mean squared error and stead state error of the proposed algorithm are also compared with standard RLS and proportionate RLS (PRLS). The simulation results indicate that SC-PRLS is more effective than PRLS and traditional RLS. An increase in the degree of sparseness leads to an increase in steady-state error and it can be controlled by convergence control parameter, while the convergence rate remains intact in the SC-PRLS. It performs superior in sparse as well as in non-sparse environment so this algorithm can handle large variations in the sparseness. Keywords: SC-PRLS, Sparseness Controlled Proportionate Adaptive Algorithm, Sparse and Non-Sparse Systems, RLS.