Leaky delayed LMS algorithm: stochastic analysis for Gaussian data and delay modeling error

This paper presents a stochastic analysis of the delayed least-mean-square (DLMS) adaptive algorithm with leakage. This analysis is obtained taking into account that mismatches between the system delay and its estimate may occur. Such an approach is not considered in previous models. In addition, it is shown that the introduction of a leakage factor into the adaptive algorithm keeps the adaptive algorithm stable under an imperfect delay estimate condition. Recursive difference equations for the first and second moments of the adaptive filter weights are derived. An expression for the critical value of the step size is also determined. Results of Monte Carlo simulations present excellent agreement with the proposed model for both white and colored Gaussian inputs.