Stochastic Analysis of the Recursive Least Squares Algorithm for Cyclostationary Colored Inputs

This paper studies the stochastic behavior of the recursive least squares (RLS) algorithm in a system identification framework for a cyclostationary colored input. The input cyclostationary signal is modeled by a colored random process with periodically time-varying power. The system parameters vary according to a random-walk. Mathematical models are derived for the mean and mean-square-deviation (MSD) behavior of the adaptive weights as a function of the input cyclostationarity. The MSD behaviors of the RLS and LMS algorithms are compared for cyclostationary colored input. Monte Carlo simulations provide strong support for the theory. A separate analysis for white Gaussian and non-Gaussian inputs is presented in support of the assumptions made for the mathematical model above.