A Novel Generalization of Modified LMS Algorithm to Fractional Order

In this letter, the modified least mean squares (MLMS) algorithm proposed by Kretschmer is generalized to fractional order α (0 <; α
_{≤ 1}
). Such generalization is achieved by replacing the first order difference of the weight updating equation with a fractional one. The convergence speed, weight noise and implementation issue of the generalized MLMS (GMLMS) algorithm are examined. It is shown that for smaller step size, the fractional order α functions the same as the step size, which means that a smaller α will give smaller weight noise while a bigger α will give faster convergence speed.