Sparsity-Aware Logarithmic Hyperbolic Cosine Adaptive Filter with Variable Center

Abstract

Sparsity-aware adaptive filtering algorithms based on the hyperbolic cosine (HC) and logarithmic HC adaptive filter (AF) called LHCAF have emerged as robust approaches for sparse channel estimation under non-Gaussian noise environments. However, the conventional zero-attracting LHCAF (ZA-LHCAF) algorithm delivers suboptimal performance under non-zero-mean non-Gaussian noise, as it relies on error statistics centered around the origin. To address this issue, we propose a novel ZA-LHCAF with variable center (ZA-LHCAF-VC) algorithm that is robust against non-Gaussian distortions having non-zero mean by incorporating higher-order central moments of error. Furthermore, we propose different variants of sparsity-aware LHCAF-VC (SA-LHCAF-VC) by incorporating the re-weighted L1-norm and the arc-tangent based sparsifying norm into the LHCAF-VC cost function. To further enhance the convergence performance, a variable step size (VSS) mechanism is also integrated into SA-LHCAF-VC to yield a novel VSS-SA-LHCAF-VC algorithm. Simulation results demonstrate that the proposed algorithm exhibits superior convergence performance compared to existing state-of-the-art methods. © 2025 IEEE.