Performance analysis of diffusion least mean fourth algorithm over network

The diffusion least mean fourth (DLMF) algorithm was initially presented for distributed estimate over network with the sub-Gaussian node noise, which can obtain better performance than diffusion least mean square (DLMS) algorithm. Unfortunately, due to the higher order moment of the weight error in the DLMF algorithm and complexity of the network, it is difficult to analyze the mean square performance of the DLMF algorithm. In this paper, the stochastic behaviors including mean behavior and mean square behavior are investigated when the input signals of all nodes are Gaussian processes and the background noises have symmetric probability density functions. The analytical models of the mean weight error and the mean square deviation (MSD) are derived by using a novel manner, which can accurately predict the algorithm behavior. The simulations are carried out to verify the validity of the analysis and compare the performance of DLMF algorithm with that of the DLMS algorithm under different background noise distributions.