Performance Analysis of LMS Filters with non-Gaussian Cyclostationary Signals

TL;DR

This paper provides a general performance analysis of LMS filters when dealing with non-Gaussian cyclostationary signals, applicable to practical communication systems, without relying on specific distributional assumptions.

Contribution

It introduces a distribution-agnostic, comprehensive analysis of LMS filter performance for cyclostationary signals, including convergence conditions and error expressions.

Findings

Accurate steady-state and transient performance expressions derived.

Analysis validated through simulations in practical communication scenarios.

Conditions for LMS convergence established for non-Gaussian cyclostationary signals.

Abstract

The least mean-square (LMS) filter is one of the most common adaptive linear estimation algorithms. In many practical scenarios, and particularly in digital communications systems, the signal of interest (SOI) and the input signal are jointly wide-sense cyclostationary. Previous works analyzing the performance of LMS filters for this important case assume specific probability distributions of the considered signals or specific models that relate the input signal and the SOI. In this work, we provide a general transient and steady-state performance analysis that is free of specific distributional or model assumptions. We obtain conditions for convergence and derive analytical expressions for the non-asymptotic and steady-state mean-squared error. The accuracy of our analysis is demonstrated in simulation studies that correspond to practical communications scenarios.