Convergence analysis of adaptive linear estimation for dependent stationary processes

The convergence properties of an adaptive linear mean-square estimator that uses a modified LMS algorithm are established for generally dependent processes. Bounds on the mean-square error of the estimates of the filter coefficients and on the excess error of the estimate of the signal are derived for input processes which are either strong mixing or asymptotically uncorrelated. It is shown that the mean-square deviation is bounded by a constant multiple of the adaptation step size and that the same holds for the excess error of the signal estimation. The present findings extend earlier results in the literature obtained for independent and M-dependent input data