A Novel Family of Sparsity-Aware Robust Adaptive Filters Based on a Logistic Distance Metric

In the recent past, logarithmic hyperbolic cosine based-cost function has been widely applied in adaptive filters as it offers robust performance against outliers. However, the performance of such adaptive filters suffers from high steady-state misalignment due to its significant weight update, even in the presence of outliers. This paper proposes a logistic distance metric-based novel robust cost function, and the corresponding logistic distance metric adaptive filter (LDMAF) has been developed. The proposed LDMAF provides negligible weight update when the desired signals are affected by significant outliers, resulting in low steady-state misalignment. The bound on learning rate has been estimated, and computational complexity comparison of the proposed and other existing algorithms has also been carried out. To further exploit the system's sparse nature and robustness against the outliers, zero attraction-based LDMAF (ZA-LDMAF) and re-weighted zero attraction-based LDMAF (RZA-LDMAF) algorithms have also been developed in this paper. In addition, a new sparse penalty function based on a generalized multivariate Geman-McClure function has been introduced, which provides smooth $l_{0}$ -norm approximation over other existing functions. Based on this new sparse penalty function, this paper has also developed a novel sparsity-aware robust adaptive filter called generalized Geman-McClure LDMAF (GGM-LDMAF). Simulation studies confirmed the improved convergence behaviour achieved by the proposed algorithms over other existing algorithms for system identification and acoustic echo cancellation scenarios.