A Modified Pseudo-Huber Loss Based Zero-Attraction LMS Algorithm for Sparse Systems

Abstract The zero-attraction based least mean square (LMS) algorithms have gained popularity for sparse system identification due to their low computational complexity and easy implementation. This paper introduces a new sparsity aware function based on pseudo-Huber loss (P-HL), namely modified P-HL (MP-HL). This is then utilized to develop a novel sparsity-aware zero-attraction-based MPHL- LMS (ZA-MP-HL-LMS) adaptive filter. The paper also presents mean and mean square error (MSE) theoretical analysis. Additionally, the condition of the zero attraction parameter to obtain a lower steady-state MSE than LMS is also derived. The simulation results demonstrate that the proposed algorithms outperform state-of-the-art approaches in the system identification examples.