Transient Theoretical Analysis of Diffusion RLS Algorithm for Cyclostationary Colored Inputs

TL;DR

This paper provides a theoretical analysis of the transient convergence behavior of the diffusion RLS algorithm when applied to cyclostationary colored inputs, filling a gap in existing literature.

Contribution

It introduces the first transient analysis of the diffusion RLS algorithm for complex cyclostationary colored inputs, enhancing understanding of its convergence dynamics.

Findings

Analytical models accurately predict transient behavior.

Simulation results validate theoretical models.

Convergence behavior characterized in mean and mean-square error.

Abstract

Convergence of the diffusion RLS (DRLS) algorithm to steady-state has been extensively studied in the literature, whereas no analysis of its transient convergence behavior has been reported yet. In this letter, we conduct a theoretical analysis of the transient behavior of the DRLS algorithm for cyclostationary colored inputs, in the mean and mean-square error sense. The resulting analytical models allows us to thoroughly investigate the convergence behavior of the algorithm over adaptive networks in such complex scenarios. Simulation results support the accuracy and correctness of the theoretical findings.