Study of a Variable Step Size LMS Adaptive Filtering Algorithm

To solve the problem of stability and the tradeoff between rate of convergence (speed of adaptation) and steady-state excess MSE (quality of adaptation, or accuracy of the adaptive filter) for standard LMS algorithm, this paper presents an adaptive variable step size LMS algorithm (least mean square algorithm) of complex form, where the innovation of the weight-vector depends on the gradient of error surface at the point of new weight. Then the convergence properties and the effects of parameters choice for the algorithm are analyzed. The adaptive variable step size LMS algorithm has fast convergence, robust stability, less computational complexity and easy to implement. Computer simulations confirm the theoretical analysis and show the algorithm performance is practical and superior to the usual LMS algorithm.