Robust adaptive sparse channel estimation in the presence of impulsive noises

Broadband wireless channels usually have the sparse nature. Based on the assumption of Gaussian noise model, adaptive filtering algorithms for reconstructing sparse channels were proposed to take advantage of channel sparsity. However, impulsive noises are often existed in many advanced broadband communications systems. These conventional algorithms are vulnerable to performance deteriorate by the impulsive noise. In this paper, sign least mean square algorithm (SLMS) based robust sparse adaptive filtering algorithms are proposed to estimate channels as well as to mitigate impulsive noise. By using different sparsity-inducing penalty functions, i.e., zero-attracting (ZA), reweighted ZA (RZA), reweighted L1-norm (RL1) and Lp-norm (LP), the proposed SLMS algorithms are termed as SLMS-ZA, SLMS-RZA, LSMS-RL1 and SLMS-LP. Simulation results are given to validate the proposed algorithms.