Analysis of the Least Mean Square algorithm with processing delays in the adaptive arm for Gaussian inputs for system identification.

This paper analyzes the effect of a processing delay on the Least Mean Squares (LMS) algorithm for a system identification problem when the processing delay is in the adaptive arm of the filter. Thus the sensing of the input signal is delayed. The input is assumed to be a zero mean stationary Gaussian process. The theoretical mean and mean square behavior of the adaptive weight vector is analyzed. The weight vector is shown to be biased and significantly affects the mean square deviation (MSD). Monte Carlo simulations are presented in support of the assumptions used to derive the theoretical model as a function of the delay, bandwidth and step-size for the LMS algorithm. The results suggest bias problems with other more complicated adaptive filtering algorithms such as Normalized LMS and Recursive Least Squares. • We study the stochastic behavior of the LMS algorithm for a system identification framework when the input signal is a cyclostationary colored Gaussian process. • Well-known results for the LMS algorithm are extended to the cyclostationary case and used for predicting the mean-square weight deviation (MSD) and excess mean-square error (EMSE) behavior of the algorithm. • The analysis is performed for cyclostationary input signals modeled as colored Gaussian random processes with periodically time-varying power. • A new model is proposed for the autocorrelation matrix of an input vector of samples of a second order wide sense cyclostationary signal. • It is shown that the proposed model is a good approximation of the autocorrelation matrix of an autoregressive signal with periodically varying power. • Simulation results show excellent agreement with the theoretically predicted behavior, confirming the usefulness of the analytical model to study the adaptive filter behavior. [ABSTRACT FROM AUTHOR]