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

TL;DR

This paper introduces a fractional-order NSPN algorithm that enhances robustness in impulsive noise environments by integrating fractional-order stochastic gradient descent, with theoretical analysis and simulation validation.

Contribution

It proposes a novel fractional-order NSPN algorithm that improves robustness in impulsive noise, along with convergence analysis and steady-state MSD modeling.

Findings

FoNSPN outperforms existing algorithms in impulsive noise environments.

Theoretical convergence range and steady-state MSD are established.

Simulations confirm the effectiveness of the proposed method.

Abstract

Building upon the mean p-power error (MPE) criterion, the normalized subband p-norm (NSPN) algorithm demonstrates superior robustness in $\alpha$-stable noise environments ($1 < \alpha \leq 2$) 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 $\alpha$-stable processes ($0 < \alpha \leq 1$). 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 $\beta$, 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.