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

• Published in: IEEE transactions on signal processing Vol. 62; no. 9; pp. 2238 - 2249
• Main Authors: Bershad, Neil J., Eweda, Eweda, Bermudez, Jose C. M.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.05.2014; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Adaptation models; Adaptive filters; Algorithm design and analysis; Algorithms; analysis; Analytical models; Applied sciences; Computer simulation; Detection, estimation, filtering, equalization, prediction; Exact sciences and technology; Gaussian; Information, signal and communications theory; Least squares approximations; LMS algorithm; Mathematical model; Mathematical models; NLMS algorithm; Optimization; Signal and communications theory; Signal processing; Signal processing algorithms; Signal, noise; stochastic algorithms; Stochasticity; Telecommunications and information theory; Transaction processing; Vectors; Performance evaluation; Monte Carlo method; stochastic algorithms; Non stationary system; Input signal; Non-local means method; Random walk; Adaptive filters; Non stationary condition; Adaptive filter; Non stationary process; Stochastic process; analysis; Algorithm; Time variation; Stochastic analysis; Gaussian process; Signal processing; LMS algorithm; Numerical simulation; System identification; Mathematical model; Least mean squares methods; NLMS algorithm
• ISSN: 1053-587X; 1941-0476
• DOI: 10.1109/TSP.2014.2307278

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.