On the properties of the reduction-by-composition LMS algorithm

Author

Chen, Sau-Gee ; Kao, Yung-An ; Chen, Ching-Yeu

Author_Institution

Dept. of Electron. Eng. & Inst. of Electron., Nat. Chiao Tung Univ., Hsinchu, Taiwan

Volume

46

Issue

11

fYear

1999

fDate

11/1/1999 12:00:00 AM

Firstpage

1440

Lastpage

1445

Abstract

The recently proposed low-complexity reduction-by-composition least-mean-square (LMS) algorithm (RCLMS) costs only half the multiplications compared to that of the conventional direct-form LMS algorithm (DLMS). This work intends to characterize its properties and conditions for mean and mean-square convergence. Closed-form mean-square error (MSE) as a function of the LMS step-size μ and an extra compensation step-size α are derived, which are slightly larger than that of the DLMS algorithm. It is shown, when μ is small enough and α is properly chosen, the RCLMS algorithm has comparable performance to that of the DLMS algorithm. Simple working rules and ranges for α and μ to make such comparability are provided. For the algorithm to converge, a tight bound for α is also derived. The derived properties and conditions are verified by simulations

Keywords

adaptive filters; adaptive signal processing; convergence of numerical methods; filtering theory; least mean squares methods; adaptive signal processing; closed-form mean-square error; compensation step-size; mean-square convergence; reduction-by-composition LMS algorithm; tight bound; Adaptive filters; Adaptive signal processing; Convergence; Costing; Costs; Councils; Filtering algorithms; Least squares approximation; Robustness; Signal processing algorithms;

fLanguage

English

Journal_Title

Circuits and Systems II: Analog and Digital Signal Processing, IEEE Transactions on

Publisher

ieee

ISSN

1057-7130

Type

jour

DOI

10.1109/82.803485

Filename

803485