Generalized Soft-Root-Sign Based Robust Sparsity-Aware Adaptive Filters

Robust adaptive filters utilizing hyperbolic cosine and correntropy functions have been successfully employed in non-Gaussian noisy environments. However, these filters suffer from high steady-state misalignment due to significant weight update in the presences of outliers. In addition, several practical systems exhibit sparse characteristics, which is not taken into account by these filters. In this paper, a generalized soft-root-sign (GSRS) function is proposed and the corresponding GSRS adaptive filter is designed. The proposed GSRS provides negligible weight update in the occurrence of large outliers and thereby results in lower steady-state misalignment. To further improve modelling performance for sparse systems and to achieve robustness, sparsity-aware GSRS algorithms are also developed in this paper. The bound on learning rate and the computational complexity of proposed algorithm is also investigated. Simulation studies confirmed the improved convergence characteristics achieved by the proposed algorithms over existing algorithms.