Stochastic Analysis of a Stable Normalized Least Mean Fourth Algorithm for Adaptive Noise Canceling With a White Gaussian Reference

The least mean fourth (LMF) algorithm has several stability problems. Its stability depends on the variance and distribution type of the adaptive filter input, the noise variance, and the initialization of the filter weights. A global solution to these stability problems was presented recently for a normalized LMF (NLMF) algorithm. Here, a stochastic analysis of the mean-square deviation (MSD) of the globally stable NLMF algorithm is provided. The analysis is done in the context of adaptive noise canceling with a white Gaussian reference input and Gaussian, binary, and uniform desired signals. The analytical model is shown to accurately predict the results of Monte Carlo simulations. Comparisons of the NLMF and NLMS algorithms are then made for various parameter selections. It is then shown under what conditions the NLMF algorithm is superior to NLMS algorithm for adaptive noise canceling.