Performance Analysis of Sparsity-Penalized LMS Algorithms in Channel Estimation

Abstract

Least mean squares (LMS) algorithm was considered as one of the effective methods in adaptive system identifications. Different from many unknown systems, LMS algorithm cannot exploit any structure characteristics. In case of sparse channels, sparse LMS algorithms are proposed to exploit channel sparsity and thus these methods can achieve better estimation performance than standard one, under the assumption of Gaussian noise environment. Specifically, several sparse constraint functions, $\ell_{1}$-norm, reweighted $\ell_{1}$-norm and $\ell_{\text{P}}$-norm, are developed to take advantage of channel sparsity. By using different sparse functions, these proposed methods are termed as zero-attracting LMS (ZA-LMS), reweighted ZA-LMS (RZA-LMS), reweighted $\ell_{1}$-norm LMS (RL1-LMS) and $\ell_{\text{p}}$-norm LMS (LP-LMS). Our simulation results confirm the priority of the new algorithm and show that the proposed sparse algorithms are superior to the standard LMS in number scenarios.