P-norm based Fractional-Order Robust Subband Adaptive Filtering Algorithm for Impulsive Noise and Noisy Input

Abstract

Building upon the mean p-power error (MPE) criterion, the normalized subband p-norm (NSPN) algorithm demonstrates superior robustness in $\hat{I}\pm$-stable noise environments ($1<\hat{I}\pm \le 2$) through effective utilization of low-order moment hidden in robust loss functions. Nevertheless, its performance degrades significantly when processing noise input or additive noise characterized by $\hat{I}\pm$-stable processes ($0<\hat{I}\pm \le 1$). To overcome these limitations, we propose a novel fractional-order NSPN (FoNSPN) algorithm that incorporates the fractional-order stochastic gradient descent (FoSGD) method into the MPE framework. Additionally, this paper also analyzes the convergence range of its step-size, the theoretical domain of values for the fractional-order ${\hat{I}}^2$, and establishes the theoretical steady-state mean square deviation (MSD) model. Simulations conducted in diverse impulsive noise environments confirm the superiority of the proposed FoNSPN algorithm against existing state-of-the-art algorithms.

5 pages, 4 figures, published to IEEE SPL