Broadband wireless channels usually have the sparse nature. Based on theassumption of Gaussian noise model, adaptive filtering algorithms forreconstruction sparse channels were proposed to take advantage of channelsparsity. However, impulsive noises are often existed in many advance broadbandcommunications systems. These conventional algorithms are vulnerable todeteriorate due to interference of impulsive noise. In this paper, sign leastmean square algorithm (SLMS) based robust sparse adaptive filtering algorithmsare proposed for estimating channels as well as for mitigating 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), theproposed SLMS algorithms are termed as SLMS-ZA, SLMS-RZA, LSMS-RL1 and SLMS-LP.Simulation results are given to validate the proposed algorithms.
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