Performance analysis of LMS filters with non-Gaussian cyclostationary signals

The least mean-square (LMS) filter is one of the most common adaptive linear estimation algorithms. In many practical scenarios, e.g., 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 Gaussian probability distributions of the considered signals. In this work, we provide a transient and steady-state performance analysis that applies to non-Gaussian cyclostationary signals. In the considered analysis, the SOI is modeled as a perturbed response of a linear periodically time-varying system to the input signal. We obtain conditions for convergence and derive analytical expressions for the non-asymptotic and steady-state mean-squared error. We then show how the theoretical analysis can be effectively applied for two common non-Gaussian classes of input distributions, the class of elliptical compound Gaussian distributions, and the broad class of Gaussian mixture distributions. The accuracy of our analysis is illustrated for system identification and signal recovery scenarios that involve linear periodically time variant systems and non-Gaussian inputs.