Summary: Convergence Analysis of the LMS Algorithm with a
General Error Nonlinearity and an IID Input
Tareq Y. Al-Naffouri Azzedine Zerguine Maamar Bettayeb
Dept. of Physics
Stanford University KFUPM KFUPM
Stanford, CA 9305 Dhahran 31261 Dhahran 31261
U.S.A Saudi Arabia Saudi Arabia
Dept. of Electrical Eng. Dept. of Electrical Eng.
The class of least mean square (LMS) algorithms
employing a general error nonlinearity is considered.
A linearization approach is used to characterize thc
convergence and performance of this class of algo-
rithms for an independent and identically distributed
(aid) input. The analysis results are entirely consis-
tent with those of the LMS algorithm and several of its
variants. The results also encompass those of a recent
work that considered the same class of algorithms for
arbitrary and Gaussian inputs.