Stochastic analysis of the LMS algorithm for cyclostationary colored Gaussian inputs

• Published in: Signal processing Vol. 160; pp. 127 - 136
• Main Authors: Bermudez, José C.M., Bershad, Neil J., Eweda, Eweda
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.07.2019
• Subjects: Adaptive filters; Analysis; Cyclostationary signals; LMS Algorithm; Stochastic algorithms; Cyclostationary signals; Stochastic algorithms; LMS Algorithm; Adaptive filters; Analysis
• ISSN: 0165-1684; 1872-7557
• DOI: 10.1016/j.sigpro.2019.02.018

•We study the stochastic behavior of the LMS algorithm when the input signal is a cyclostationary colored Gaussian process.•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.•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. This paper studies the stochastic behavior of the LMS algorithm for a system identification framework when the input signal is a cyclostationary colored Gaussian process. The unknown system is modeled by the standard random walk model. 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. Monte Carlo simulations provide strong support for the theory.