Non-optimal convergence of adaptive LMS with uncorrelated data

Convergence analysis of the adaptive least mean square (LMS) algorithm is based on the fundamental assumption that the data vector is uncorrelated with the weight vector at each iteration. This assumption has been taken to mean that successive data vectors are uncorrelated. However, when adaptation of the algorithm is performed at intervals less than the filter length plus the prediction delay and the input is a sinusoid in white noise, it is shown that the convergent weight vector no longer satisfies the minimum mean squared error optimality criterion. Furthermore, it is shown that the adaptation proceeds with a time constant determined by the input noise power. Results of a computer experiment verify the analytic description of the non-optimal convergence.