Title :
Stochastic Analysis of the LMS and NLMS Algorithms for Cyclostationary White Gaussian Inputs
Author :
Bershad, Neil J. ; Eweda, Eweda ; Bermudez, Jose C. M.
Author_Institution :
Dept. of Electr. Eng. & Comput. Sci., Univ. of California, Irvine, Newport Beach, CA, USA
Abstract :
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.
Keywords :
Gaussian processes; Monte Carlo methods; signal processing; stochastic systems; MSD; Monte Carlo simulations; NLMS algorithms; cyclostationary signal; cyclostationary white Gaussian inputs; cyclostationary white Gaussian process; mathematical models; mean-square-deviation; stochastic analysis; system identification framework; time-varying power; white Gaussian random process; Adaptation models; Algorithm design and analysis; Analytical models; Least squares approximations; Mathematical model; Signal processing algorithms; Vectors; Adaptive filters; LMS algorithm; NLMS algorithm; analysis; stochastic algorithms;
Journal_Title :
Signal Processing, IEEE Transactions on
DOI :
10.1109/TSP.2014.2307278
