LMS adaptive filter with optimum step-size for tracking time-varying channels

In this paper, an adaptive step-size LMS algorithm for tracking time-varying channels is presented. It is well known that in the case of such channels, the output steady-state mean square error (MSB) is a nonlinear function of the algorithm step-size and so, an optimum step-size that minimize the MSE exist. Here we propose an algorithm which adaptively adjust the step-size of the LMS toward its optimum value, such that the steady-state MSE is minimized. The nonlinear relation between the steady-state MSE and the step-size is parametrized such that, during the adaptation, estimates of the optimum step-size are easily obtained. These estimates are obtained independent from the channel statistical parameters, therefore, no prior information about the channel parameters is needed.