On the convergence and MSE of Chen´s LMS adaptive algorithm

Author

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

Author_Institution

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

Volume

3

fYear

1997

fDate

21-24 Apr 1997

Firstpage

2349

Abstract

The previously proposed Chen´s (see IEEE Trans. Circuits Syst.-II: Analog and Digital Signal Processing, vol.43, p.372-8, May 1996) LMS algorithm costs only half the multiplications of the conventional direct-form LMS algorithm (DLMS). Despite of this merit, the algorithm lacked a rigorous theoretical analysis. This article characterizes its properties and conditions for mean and mean-square convergences. The closed-form MSE is derived, which is slightly larger than that of the DLMS algorithm. It is shown, under the condition that the LMS step size μ is very small and an extra compensation step size α is properly chosen, that Chen´s algorithm has a comparable performance to that of the DLMS algorithm. For the algorithm to converge, a tighter bound than before 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; Chen´s LMS adaptive algorithm; DLMS algorithm; LMS step size; MSE; adaptive filtering; closed-form MSE; compensation step size; direct-form LMS algorithm; mean convergence; mean square convergence; multiplications; simulations; stability analysis; Adaptive algorithm; Adaptive filters; Algorithm design and analysis; Convergence; Convolution; Costs; Filtering algorithms; Least squares approximation; Robustness; Stability analysis;

fLanguage

English

Publisher

ieee

Conference_Titel

Acoustics, Speech, and Signal Processing, 1997. ICASSP-97., 1997 IEEE International Conference on

Conference_Location

Munich

ISSN

1520-6149

Print_ISBN

0-8186-7919-0

Type

conf

DOI

10.1109/ICASSP.1997.599524

Filename

599524