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 alpha (0 < alpha <= 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 functions the same as the step size, which means that a smaller will give smaller weight noise while a bigger will give faster convergence speed.