Leaky LMS algorithm: MSE analysis for Gaussian data

Despite the widespread usage of the leaky LMS algorithm, there has been no detailed study of its performance. This paper presents an analytical treatment of the mean-square error (MSE) performance for the leaky LMS adaptive algorithm for Gaussian input data. The common independence assumption regarding W(n) and X(n) is also used. Exact expressions that completely characterize the second moment of the coefficient vector and algorithm steady-state excess MSE are developed. Rigorous conditions for MSE convergence are also established. Analytical results are compared with simulation and are shown to agree well.