Performance Analysis of LMS Filters for Estimation of Cyclostationary Signals

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.