Nonlinear quantization effects in the LMS and block LMS adaptive algorithms-a comparison

Author

Bershad, Neil J.

Author_Institution

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

Volume

37

Issue

10

fYear

1989

fDate

10/1/1989 12:00:00 AM

Firstpage

1504

Lastpage

1512

Abstract

Digital implementations of the least-mean-square (LMS) and block LMS (BLMS) algorithms are compared with respect to finite word effects. The algorithm stalling phenomenon is studied using Gaussian data models and conditional expectation arguments. It is shown that the BLMS algorithm requires (1/2 log₂ L-K) fewer bits for the same stalling behavior (L=block length and K lies between 0.2 and 1.0, depending on the precise definition of algorithm stalling). On the other hand, the LMS algorithm requires log ₂ L fewer bits than BLMS for the same level of saturation behavior (transient response) at algorithm initialization. Hence, the LMS algorithm requires (1/2 log₂ L+K ) fewer bits than the BLMS algorithm for the same saturation and stalling effects

Keywords

analogue-digital conversion; least squares approximations; ADC; Gaussian data models; LMS algorithm; algorithm stalling phenomenon; block LMS adaptive algorithms; digital implementations; finite word effects; least-mean-square; nonlinear quantisation; saturation behavior; transient response; Algorithm design and analysis; Computational complexity; Data models; Degradation; Filtering algorithms; Helium; Least squares approximation; Predictive models; Quantization; Transient response;

fLanguage

English

Journal_Title

Acoustics, Speech and Signal Processing, IEEE Transactions on

Publisher

ieee

ISSN

0096-3518

Type

jour

DOI

10.1109/29.35388

Filename

35388