A New Noise-Assistant LMS Algorithm for Preventing the Stalling Effect

TL;DR

This paper presents a novel Added Noise LMS (AN-LMS) algorithm that enhances the LMS adaptive filter's resistance to the stalling effect by incorporating noise into the weight update process, maintaining similar convergence and complexity.

Contribution

It introduces the AN-LMS algorithm with added noise to prevent stalling, providing theoretical analysis of its properties and convergence, and demonstrating its effectiveness.

Findings

AN-LMS improves resistance to stalling effect.

Convergence rate is comparable to standard LMS.

Complexity remains linear, similar to LMS.

Abstract

In this paper, we introduce a new algorithm to deal with the stalling effect in the LMS algorithm used in adaptive filters. We modify the update rule of the tap weight vectors by adding noise, generated by a noise generator. The properties of the proposed method are investigated by two novel theorems. As it is shown, the resulting algorithm, called Added Noise LMS (AN-LMS), improves the resistance capability of the conventional LMS algorithm against the stalling effect. The probability of update with additive white Gaussian noise is calculated in the paper. Convergence of the proposed method is investigated and it is proved that the rate of convergence of the introduced method is equal to that of LMS algorithm in the expected value sense, provided that the distribution of the added noise is uniform. Finally, it is shown that the order of complexity of the proposed algorithm is linear as the conventional LMS algorithm.