A Model for the Behavior of the Least Mean Kurtosis (LMK) Adaptive Algorithm with Gaussian Inputs

Pedro I. Hübscher; José C. M. Bermudez

doi:10.14209/its.2002.448

A Model for the Behavior of the Least Mean Kurtosis (LMK) Adaptive Algorithm with Gaussian Inputs

Pedro I. Hübscher, José C. M. Bermudez

DOI: 10.14209/its.2002.448

Evento: 2002 International Telecommunications Symposium (ITS2002)

Keywords:

Abstract

"The LMK algorithm is a stochastic gradient algorithm which seeks to minimize the negated kurtosis of the error signal. It outperforms the LMS algorithm in several applications of practical interest, with little increase in computational complexity. This paper presents a statistical analysis of the Least Mean Kurtosis (LMK) adaptive algorithm. Deterministic nonlinear recursive equations are derived for the mean weight behavior and for the weight error correlation matrix, for a Gaussian reference signal and slow learning. The new model describes the algorithm behavior during transient and steady-state for a white measurement noise with any even probability density function (pdf). The accuracy of the model is demonstrated by Monte Carlo simulations."

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