Assessment of the efficiency of the LMS algorithm based on spectral information

Author

Flores, Aaron ; Widrow, Bernard

Author_Institution

Dept. of Electr. Eng., Stanford Univ., CA, USA

Volume

1

fYear

2004

fDate

7-10 Nov. 2004

Firstpage

120

Abstract

The LMS algorithm is used to find the optimal minimum mean-squared error (MMSE) solutions for a wide variety of problems. Unfortunately, its convergence speed depends heavily on its initial conditions when the autocorrelation matrix R of its input vector has a high eigenvalue spread. In many applications such as system identification or channel equalization, R is Toeplitz. In this paper we exploit the Toeplitz structure of R to show that when the weight vector is initialized to zero, the convergence speed of LMS is related to the similarity between the input PSD and the power spectrum of the optimum solution.

Keywords

Toeplitz matrices; adaptive filters; equalisers; least mean squares methods; LMS algorithm; MMSE; Toeplitz structure; adaptive filter; autocorrelation matrix; channel equalization; minimum mean-squared error; system identification; Adaptive algorithm; Autocorrelation; Convergence; Delay lines; Eigenvalues and eigenfunctions; Iterative algorithms; Least squares approximation; System identification; Transient analysis; Vectors;

fLanguage

English

Publisher

ieee

Conference_Titel

Signals, Systems and Computers, 2004. Conference Record of the Thirty-Eighth Asilomar Conference on

Print_ISBN

0-7803-8622-1

Type

conf

DOI

10.1109/ACSSC.2004.1399102

Filename

1399102