A Robust Zero-attracting Proportionate Logarithmic Hyperbolic Cosine Adaptive Filter against Impulsive Noise for Sparse Systems

Abstract

In this paper, a robust adaptive algorithm to mitigate the effect of heavy-tailed impulsive noise in the case of sparse systems is proposed. The recently proposed Zero-attracting Logarithmic Hyperbolic Cosine Adaptive Filter (ZALHCAF) improves the steady-state level of the Logarithmic Hyperbolic Cosine Adaptive Filter (LHCAF) algorithm. This paper incorporates the proportionate idea to the ZA-LHCAF algorithm to improve the convergence rate. However, the convergence rate improves at the cost of increased steady-state level. So, a novel way of updating the gain function parameter is proposed in which the gain function parameter is dynamically updated based on the estimate of error. The simulation results show that the proposed algorithm can attain a better steady-state level and convergence rate.