An easy demonstration of the optimum value of the adaptation constant in the LMS algorithm [FIR filter theory]

Author

Soria-Olivas, Emilio ; Calpe-Maravilla, Javier ; Guerrero-Martinez, Juan F. ; Martinez-Sober, Marcelino ; Espi-Lopez, J.

Author_Institution

Fac. de Fisica, Valencia Univ., Spain

Volume

41

Issue

1

fYear

1998

fDate

2/1/1998 12:00:00 AM

Firstpage

81

Abstract

The least mean squares (LMS) is the most widely used algorithm among those proposed to adapt the coefficients of an FIR filter in order to minimize the mean-square error (MSE) between its output and the desired signal. Since the introduction of the LMS algorithm, many variants have been proposed to improve its performance. Doubtless, the most popular is the normalized LMS algorithm, which uses a value for the adaptation constant that assures the fastest convergence. This correspondence shows a new demonstration of the algorithm based on a mathematical approach easier than that usually proposed

Keywords

FIR filters; convergence of numerical methods; filtering theory; least mean squares methods; FIR filter; adaptation constant; coefficients adaptation; computational performance; fast convergence; least mean squares algorithm; mathematical demonstration approach; mean-square error; normalized LMS algorithm; Adaptive filters; Convergence; Equations; Finite impulse response filter; Lagrangian functions; Least squares approximation; Minimization methods; Real time systems; Robustness; Stability;

fLanguage

English

Journal_Title

Education, IEEE Transactions on

Publisher

ieee

ISSN

0018-9359

Type

jour

DOI

10.1109/13.660794

Filename

660794