A nonlinear analytical model for the quantized LMS algorithm-the power-of-two step size case

Author

Bershad, Neil J. ; Bermudez, José Carlos M

Author_Institution

Dept. of Electr. & Comput. Eng., California Univ., Irvine, CA, USA

Volume

44

Issue

11

fYear

1996

fDate

11/1/1996 12:00:00 AM

Firstpage

2895

Lastpage

2900

Abstract

Presents a study of the quantization effects in the finite precision LMS algorithm with power-of-two step sizes. Deterministic nonlinear recursions are presented for the mean and second-moment matrix of the weight vector about the Wiener weight for white Gaussian data models and small algorithm step size μ. The numerical solutions of these recursions are shown to agree very closely with the Monte Carlo simulations during all phases of the adaptation process. Design examples demonstrate the selection of the number of quantizer bits and the adaptation step size μ to yield a desired transient behavior and cancellation performance. The results obtained indicate that previous models are too conservative in predicting the converged MSE for a given number of bits

Keywords

Gaussian noise; Monte Carlo methods; adaptive filters; circuit noise; interference suppression; least mean squares methods; matrix algebra; nonlinear filters; recursive filters; transient analysis; white noise; Monte Carlo simulations; Wiener weight; adaptation process; adaptation step size; cancellation performance; converged MSE; design examples; nonlinear analytical model; nonlinear recursions; power-of-two step size case; quantized LMS algorithm; quantizer bits; second-moment matrix; transient behavior; weight vector; white Gaussian data models; Adaptive filters; Analytical models; Computer aided software engineering; Data models; Equations; Fixed-point arithmetic; Least squares approximation; Predictive models; Process design; Quantization;

fLanguage

English

Journal_Title

Signal Processing, IEEE Transactions on

Publisher

ieee

ISSN

1053-587X

Type

jour

DOI

10.1109/78.542451

Filename

542451