  Based on the assumption of Gaussian noise model, conventional adaptive
filtering algorithms for reconstruction sparse channels were proposed to take
advantage of channel sparsity due to the fact that broadband wireless channels
usually have the sparse nature. However, state-of-the-art algorithms are
vulnerable to deteriorate under the assumption of non-Gaussian noise models
(e.g., impulsive noise) which often exist in many advanced communications
systems. In this paper, we study the problem of RObust Sparse Adaptive channel
estimation (ROSA) in the environment of impulsive noises using variable
step-size affine projection sign algorithm (VSS-APSA). Specifically, standard
VSS-APSA algorithm is briefly reviewed and three sparse VSS-APSA algorithms are
proposed to take advantage of channel sparsity with different sparse
constraints. To fairly evaluate the performance of these proposed algorithms,
alpha-stable noise is considered to approximately model the realistic impulsive
noise environments. Simulation results show that the proposed algorithms can
achieve better performance than standard VSS-APSA algorithm in different
impulsive environments.
