An optimised normalised LMF algorithm for sub-Gaussian noise

The least mean fourth (LMF) algorithm is known for its fast convergence and lower steady state error, especially under sub-Gaussian noise conditions. Meanwhile, the recent work on the normalised versions of LMF algorithm has further enhanced its stability and performance in both Gaussian and sub-Gaussian noise. For example, the normalised LMF (XE-NLMF) algorithm, recently developed, is normalised by the mixed signal power and error power, and weighted by a fixed mixed-power parameter. Unfortunately, this algorithm depends on the selection of this mixing parameter. To overcome this obstacle, in this work, a time-varying mixed-power parameter technique is introduced to optimise its selection. An enhancement in performance is obtained through the use of this procedure in both the convergence rate and steady-state error.