Robust Variable Zero Attractor Controller Based ZA-LMS Algorithm for Variable Sparsity Environment

Abstract

The zero attraction least mean square algorithm (ZA-LMS) provides excellent performance than LMS algorithm when the system is sparse. But when the sparsity level decreases, the performance of ZA-LMS is worse than standard LMS. Hence a novel approach is proposed to work in variable sparsity environment, i.e. the fixed zero attractor controller is replaced by a variable one and the variation is done by comparing the instantaneous error with a threshold which is based on steady state mean square error (MSE) of standard LMS algorithm. Simulations were performed to compare the proposed variable ZA-LMS (VZA-LMS) algorithm with LMS and ZA-LMS algorithms. The proposed algorithm is tested for non sparse, semi sparse and sparse systems and it is found that it converges to a steady state value equal to LMS when the system is non sparse and in case of sparse and semi sparse systems, the steady state MSE is less than LMS and ZA-LMS, thus making the algorithm robust against variable sparsity conditions.