Optimum variable step-size sequence for LMS adaptive filters

An optimum time-varying step-size sequence for adaptive filters employing the least mean squares algorithm is proposed. This step-size sequence is obtained after minimising the mean square error cost function with respect to the step size on an iterative, block-by-block basis. The effect of the various parameters on the optimum step-size sequence is described and a simple approximation of the optimum sequence is proposed. As compared with other optimum approaches, the proposed one gives a considerable reduction in convergence time and is implemented with just one extra multiplication. Computer simulations are performed to confirm the effectiveness of the new approach