Adaptive Channel Equalization using Variable Step-size Least Mean Fourth Algorithm

Transmission of information over communication channel has been made possible by the use of adaptive equalizers. Adaptive equalizers are dependent on the Least Mean Square (LMS) algorithm for equalization. However, the LMS algorithm does not provide satisfactory results in the real world which is largely dominated by interference signals that are non-Gaussian in nature. To overcome this shortcoming, the Least Mean Fourth algorithm was proposed. Variable step-size algorithm outperforms the fixed step-size algorithm in terms of convergence as well as the level of misadjustment. In this paper, variable step-size least mean fourth algorithm has been proposed to perform channel equalization over a linear time-invariant channel. The adaptation of step size is performed such that the step-size is lowered when the error becomes low, while the algorithm adapts fast when the error is large. Our work constitutes the comparison between the fixed step-size LMS, LMF and VSSLMF algorithms in terms of the inverse channel response and the mean square steady-state error.