On the convergence analysis of a variable step-size LMF algorithm of the quotient form

The least-mean fourth (LMF) algorithm is best known for its fast convergence and low steady-state error especially in non-Gaussian noise environments. Recently, there has been a surge of interest in the LMF algorithm with different variants being proposed. The fact that different variable step-size least-mean square algorithms have shown to outperform its fixed step-size counterpart, a variable step-size least-mean fourth algorithm of the quotient form (VSSLMFQ) is proposed here. Therefore in this work, the proposed algorithm is analysed for its performance in the steady-state and it is shown to achieve a lower steady-state error then the traditional LMF algorithm. Finally, a number of computer simulations are carried out to substantiate the theoretical findings.