Title :
Analysis of mean-square error and transient speed of the LMS adaptive algorithm
Author :
Dabeer, Onkar ; Masry, Elias
Author_Institution :
Dept. of Electr. & Comput. Eng., California Univ., San Diego, La Jolla, CA, USA
fDate :
7/1/2002 12:00:00 AM
Abstract :
For the least mean square (LMS) algorithm, we analyze the correlation matrix of the filter coefficient estimation error and the signal estimation error in the transient phase as well as in steady state. We establish the convergence of the second-order statistics as the number of iterations increases, and we derive the exact asymptotic expressions for the mean square errors. In particular, the result for the excess signal estimation error gives conditions under which the LMS algorithm outperforms the Wiener filter with the same number of taps. We also analyze a new measure of transient speed. We do not assume a linear regression model: the desired signal and the data process are allowed to be nonlinearly related. The data is assumed to be an instantaneous transformation of a stationary Markov process satisfying certain ergodic conditions
Keywords :
Markov processes; Wiener filters; adaptive filters; adaptive signal processing; convergence of numerical methods; correlation methods; filtering theory; least mean squares methods; matrix algebra; statistical analysis; transient analysis; LMS adaptive algorithm; Wiener filter; correlation matrix; ergodic conditions; exact asymptotic expressions; filter coefficient estimation error; least mean square algorithm; linear regression model; mean-square error; second-order statistics convergence; signal estimation error; stationary Markov process; transient speed; Algorithm design and analysis; Convergence; Error analysis; Estimation error; Filters; Least squares approximation; Mean square error methods; Signal analysis; Steady-state; Transient analysis;
Journal_Title :
Information Theory, IEEE Transactions on
DOI :
10.1109/TIT.2002.1013131
