Robustness Analysis of the Data-Selective Volterra NLMS Algorithm

TL;DR

This paper provides a theoretical analysis of the robustness of the data-selective Volterra NLMS algorithm, establishing stability bounds and demonstrating its noise robustness through simulations.

Contribution

It offers the first theoretical analysis of the data-selective Volterra NLMS algorithm's robustness, including stability bounds and noise resilience.

Findings

The algorithm is robust against noise regardless of parameter settings.

A global error bound for the coefficient vector is derived.

The algorithm improves parameter estimation during updates.

Abstract

Recently, the data-selective adaptive Volterra filters have been proposed; however, up to now, there are not any theoretical analyses on its behavior rather than numerical simulations. Therefore, in this paper, we analyze the robustness (in the sense of l2-stability) of the data-selective Volterra normalized least-mean-square (DS-VNLMS) algorithm. First, we study the local robustness of this algorithm at any iteration, then we propose a global bound for the error/discrepancy in the coefficient vector. Also, we demonstrate that the DS-VNLMS algorithm improves the parameter estimation for the majority of the iterations that an update is implemented. Moreover, we prove that if the noise bound is known, we can set the DS-VNLMS so that it never degrades the estimate. The simulation results corroborate the validity of the executed analysis and demonstrate that the DS-VNLMS algorithm is robust against noise, no matter how its parameters are adopted.