Title :
Convergence characteristics of LMS and LS adaptive algorithms for signals with rank-deficient correlation matrices
Author_Institution :
Codex Corp., Mansfield, MA, USA
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;
Conference_Titel :
Acoustics, Speech, and Signal Processing, 1988. ICASSP-88., 1988 International Conference on
Conference_Location :
New York, NY
DOI :
10.1109/ICASSP.1988.196887
