Control-theoretic design of the LMS and the sign algorithms in nonstationary environments

Author

Kwong, C.P.

Author_Institution

Dept. of Electron., Chinese Univ. of Hong Kong, Shatin, Hong Kong

Volume

38

Issue

2

fYear

1990

fDate

2/1/1990 12:00:00 AM

Firstpage

253

Lastpage

259

Abstract

The feedback structure of the LMS (least mean squared) algorithm proposed by B. Widrow et al. (Proc. IEEE, vol.64, p.1151-62, Aug. 1976) is reexamined from a control system design viewpoint. The minimization of the misadjustments due to gradient noise and lag can then be recast as the disturbance rejection and tracking problems in control. A frequency-domain approach to the latter problems that has the advantages of transparency, ease of computation, and generality compared with the time-domain approach previously used is presented. With the same set of assumptions of white input and a Markovian plant, it is shown that the optimum step size obtained by the present approach is identical to that obtained by Widrow. Applying the same approach, the optimum step size of a simplified version of the LMS algorithm-the sign algorithm-is derived for the case when the plant is slowly varying and the input signals are Gaussian

Keywords

control system synthesis; feedback; frequency-domain synthesis; least squares approximations; time-varying systems; Gaussian input signals; LMS algorithm; Markovian plant; control system design; control theoretic design; feedback; frequency-domain approach; least mean squared algorithm; nonstationary environments; optimum step size; sign algorithm; time varying systems; white input; Algorithm design and analysis; Attenuation; Control systems; Design methodology; Feedback control; Gaussian noise; Least squares approximation; Noise measurement; Random processes; Size measurement;

fLanguage

English

Journal_Title

Acoustics, Speech and Signal Processing, IEEE Transactions on

Publisher

ieee

ISSN

0096-3518

Type

jour

DOI

10.1109/29.103061

Filename

103061