Convergence analysis of LMS filters with uncorrelated Gaussian data

Statistical analysis of the least mean-squares (LMS) adaptive algorithm with uncorrelated Gaussian data is presented. Exact analytical expressions for the steady-state mean-square error (mse) and the performance degradation due to weight vector misadjustment are derived. Necessary and sufficient conditions for the convergence of the algorithm to the optimal (Wiener) solution within a finite variance are derived. It is found that the adaptive coefficient μ, which controls the rate of convergence of the algorithm, must be restricted to an interval significantly smaller than the domain commonly stated in the literature. The outcome of this paper, therefore, places fundamental limitations on the mse performance and rate of convergence of the LMS adaptive scheme.