Stochastic Analysis of the LMS and NLMS Algorithms for Cyclostationary White Gaussian Inputs

This paper studies the stochastic behavior of the LMS and NLMS algorithms for a system identification framework when the input signal is a cyclostationary white Gaussian process. The input cyclostationary signal is modeled by a white Gaussian random process with periodically time-varying power. Mathematical models are derived for the mean and mean-square-deviation (MSD) behavior of the adaptive weights with the input cyclostationarity. These models are also applied to the non-stationary system with a random walk variation of the optimal weights. Monte Carlo simulations of the two algorithms provide strong support for the theory. Finally, the performance of the two algorithms is compared for a variety of scenarios.