Convergence analysis of RL1-SLMS-based robust adaptive sparse channel estimation

Robust adaptive sparse channel estimation problem has been attracted highly attention in the next-generation wireless communications systems. Re-weighted L1-norm penalized sign least mean square error (RL1-SLMS) algorithm is considered as one of attractive methods to estimate unknown sparse system as well as to mitigate impulsive noises. However, the convergence performance of RL1-SLMS is very ambiguous comparing with its preliminary version. This paper provides comprehensive convergence analysis for the RL1-SLMS algorithm under non-Gaussian impulsive noise environment. Numerical simulations are given to show the fast convergence and robustness with respect to system sparsity as well as non-Gaussian noise.