An improved stochastic model for the least mean fourth (LMF) adaptive algorithm

This paper presents a new statistical analysis of the least mean fourth (LMF) adaptive algorithm behavior. Nonlinear recursive equations are derived which predict the behavior of the first and second order moments of the adaptive weights for Gaussian inputs. These recursions can be used to predict the mean square error (MSE) behavior. The new model improves the available models in that it predicts both the transient and steady-state behaviors for measurement noise having any zero-mean probability density function (pdf) and for any signal-to-noise ratio. This is important because the LMF algorithm is known to outperform the LMS algorithm for non-Gaussian noise distributions and for large signal-to-noise ratios. In addition, the new model explicitly shows the dependence of the algorithm's dynamics on the initial weight conditions. Computer simulations illustrate the accuracy of the new model in predicting the algorithm behavior.