  Broadband frequency-selective fading channels usually have the inherent
sparse nature. By exploiting the sparsity, adaptive sparse channel estimation
(ASCE) methods, e.g., reweighted L1-norm least mean square (RL1-LMS), could
bring a performance gain if additive noise satisfying Gaussian assumption. In
real communication environments, however, channel estimation performance is
often deteriorated by unexpected non-Gaussian noises which include conventional
Gaussian noises and impulsive interferences. To design stable communication
systems, hence, it is urgent to develop advanced channel estimation methods to
remove the impulsive interference and to exploit channel sparsity
simultaneously. In this paper, robust impulsive-mitigation adaptive sparse
channel estimation (IMAC) method is proposed for solving aforementioned
technical issues. Specifically, first of all, the non-Gaussian noise model is
described by Gaussian mixture model (GMM). Secondly, cost function of
reweighted L1-norm penalized least absolute error standard (RL1-LAE) algorithm
is constructed. Then, RL1-LAE algorithm is derived for realizing IMAC method.
Finally, representative simulation results are provided to corroborate the
studies.
