Analysis of the hierarchical LMS algorithm

Author

Nascimento, Vìtor H.

Author_Institution

Electron. Syst. Eng. Dept., Univ. de Sao Paulo, Brazil

Volume

10

Issue

3

fYear

2003

fDate

3/1/2003 12:00:00 AM

Firstpage

78

Lastpage

81

Abstract

We analyze the hierarchical least mean-square (HLMS) algorithm, providing expressions for its steady-state mean-square error (MSE). We find conditions for the hierarchical structure to be equivalent to the optimal (full-length) Wiener solution. When these conditions are not satisfied, we show that HLMS will compute biased estimates. Our analysis also shows that even when these conditions hold, the MSE obtained using HLMS may be much larger than that obtained using LMS, since the potentially large MSEs at the subfilters in the first hierarchical level directly affect the output MSE.

Keywords

Wiener filters; adaptive filters; adaptive signal processing; filtering theory; least mean squares methods; stochastic processes; MSE; adaptive filters; full-length Wiener solution; hierarchical LMS algorithm; hierarchical least mean-square algorithm; optimal Wiener solution; optimum length estimation filter; output MSE; steady-state mean-square error; stochastic analysis; subfilters; Algorithm design and analysis; Computational efficiency; Convergence; Councils; Filters; Least squares approximation; Least squares methods; Robustness; Steady-state; Stochastic systems;

fLanguage

English

Journal_Title

Signal Processing Letters, IEEE

Publisher

ieee

ISSN

1070-9908

Type

jour

DOI

10.1109/LSP.2002.807863

Filename

1182090