Adaptive Sparse Channel Estimation under Symmetric alpha-Stable Noise

We tackle the problem of channel estimation in environments that exhibit both sparse, time-varying impulse responses and impulsive noise with Symmetric alpha-Stable (S alpha S) statistics. Two novel frameworks are proposed for designing online adaptive algorithms that exploit channel sparseness and achieve robust performance against impulses. The first framework generates recursive least-squares (RLS)-type algorithms based on a differentiable cost function that combines robust non-linear methods with sparse-promoting L-0 norm regularization. The second framework employs the natural gradient (NG) and incorporates non-linear methods for the channel prediction error as well as the L-0 norm of the channel taps. From these frameworks, we derive linear and quadratic complexity algorithms. The improved performance of the proposed RLS-type and NG-type algorithms relative to conventional robust algorithms, such as the recursive least M-estimate (RLM) algorithm and the recursive least p-norm (RLP) algorithm, is validated by using extensive computer simulations as well as signal analysis from an underwater acoustic communications experiment. In addition, we discovered that RLM is not robust under specific S alpha S noise conditions, contrary to the claim in [34]. Finally, our results also demonstrate the clear superiority of the NG-type algorithms over their RLS-type counterparts.