New results on the stability analysis of the LMF (least mean fourth) adaptive algorithm

This paper presents a new analysis for the convergence of the LMF (least mean fourth) adaptive algorithm. The analysis improves previous results because it explicitly shows how the stability of the algorithm depends on the initial conditions of the weights, i.e., the analysis is also valid when the algorithm is initialized far from the optimum weight vector. Analytical expressions are derived relating the limiting values of the adaptation constant and the initial weight error vector. The analysis assumes a white zero-mean Gaussian reference signal and a white measurement noise with any even probability density function (p.d.f.) and finds conditions for convergence in the mean square sense.