Stochastic analysis for the leaky Delayed LMS algorithm: A new model without invoking the independence assumption

This paper presents a stochastic analysis of the Delayed LMS adaptive algorithm with leakage. Such an analysis is derived without invoking the independence assumption, giving rise to a new model. It permits explicitly to take into account mismatches between the system delay and its estimate. This feature is not available in previous models. In addition, through the introduction of a leakage factor, we can keep the adaptive algorithm stability under imperfect delay estimate. Recursive difference equations are derived for the first and second moments of the weight vector. Simulation results are presented to support the proposed model.