Convergence characteristics of LMS and LS adaptive algorithms for signals with rank-deficient correlation matrices

Author

Ling, Fuyun

Author_Institution

Codex Corp., Mansfield, MA, USA

fYear

1988

fDate

11-14 Apr 1988

Firstpage

1499

Abstract

The author investigates the convergence characteristics of the last mean square (LMS) and the recursive least squares (RLS) adaptive algorithms when the correlation matrix of the input signal does not have a full rank. It is shown that the initial convergence rate of the LMS algorithm is inversely proportional to the rank of correlation matrix, or equivalently, the number of nonzero eigenvalues. The same conclusion holds for the RLS algorithms if the minimum norm solution (MNS) is used in each iteration. A simple time-recursive method to obtain approximate MNSs in each iteration is presented and proven. The effect of additive noise is discussed

Keywords

convergence of numerical methods; filtering and prediction theory; iterative methods; least squares approximations; signal processing; LMS algorithm; RLS algorithms; adaptive algorithms; adaptive filtering; additive noise; convergence characteristics; iteration; last mean square; minimum norm solution; rank-deficient correlation matrices; recursive least squares; time-recursive method; Adaptive algorithm; Convergence; Data communication; Eigenvalues and eigenfunctions; Equations; Filtering; Least squares approximation; Least squares methods; Resonance light scattering; Vectors;

fLanguage

English

Publisher

ieee

Conference_Titel

Acoustics, Speech, and Signal Processing, 1988. ICASSP-88., 1988 International Conference on

Conference_Location

New York, NY

ISSN

1520-6149

Type

conf

DOI

10.1109/ICASSP.1988.196887

Filename

196887