Steady-state analysis of the Normalized Least Mean Fourth algorithm without the independence and small step size assumptions

In this work, the steady-state analysis of the normalized least mean fourth (NLMF) algorithm under very weak assumptions is investigated. No restrictions are made on the dependence between input successive regressors, the dependence among input regressor elements, the length of the adaptive filter, the distribution of noise and the filter input. Moreover, in our approach, there is no restriction made on the step size value and therefore the analysis holds for all the values of the step size in the range where the NLMF algorithm is stable. The analysis is based on the effective weight deviation vector performance measure. This vector is the component of weight deviation vector in the direction of the input regressor. The asymptotic time-averaged convergence for the mean square effective weight deviation, the mean absolute excess estimation error, and the mean square excess estimation error for the NLMF algorithm are derived. Finally, a number of simulation results are carried out to corroborate the theoretical findings.