Statistical Analysis of the LMS Algorithm for Proper and Improper Gaussian Processes

TL;DR

This paper develops a more general and accurate statistical model of the LMS algorithm applicable to both proper and improper Gaussian signals, improving upon existing models and verified through simulations.

Contribution

It introduces a comprehensive LMS algorithm model that accounts for improper signals without restrictive independence assumptions, enhancing adaptive filtering accuracy.

Findings

The new model outperforms existing models in simulations.

It accurately captures the behavior of LMS with improper signals.

The approach broadens the applicability of LMS in adaptive filtering.

Abstract

The LMS algorithm is one of the most widely used techniques in adaptive filtering. Accurate modeling of the algorithm in various circumstances is paramount to achieving an efficient adaptive Wiener filter design process. In the recent decades, concerns have been raised on studying improper signals and providing an accurate model of the LMS algorithm for both proper and improper signals. Other models for the LMS algorithm for improper signals available in the scientific literature either make use of the independence assumptions regarding the desired signal and the input signal vector, or are exclusive to proper signals; it is shown that by not considering these assumptions a more general model can be derived. In the presented simulations it is possible to verify that the model introduced in this paper outperforms the other available models.