A variable step size algorithm with generate-and-evaluate function

A new variable step-size algorithm which has a framework similar to the variable step (VS) adaptive filter algorithm given by R. W. Harris et al. (1986) is introduced. The methodology is to periodically invoke a generate-and-evaluate function during the adaptation. The new function will first generate a new step-size by increasing or decreasing the current step-size value by a factor of α according to the sign change of the gradient. Then the performance of the current step-size and the newly generated step-size will be evaluated and the better one will be chosen for the next stage of adaptation. Empirically, the value of α is almost linearly related to the invocation period T. The smaller values of α and T give better tracking capability. Simulation results show that the new algorithm outperforms the LMS with fixed step-size and the VS algorithm in terms of convergence and steady-state misadjustment. In addition, the new algorithm can be implemented with only modest increase in complexity over the LMS algorithm by using a fast implementation scheme