Asymptotic behavior of an adaptive estimation algorithm with application to M-dependent data

Theoretical results are presented concerning the asymptotic behavior of the parameter estimates generated by an adaptive algorithm in stationary dependent random situations. Proofs are exhibited in the general case and derived for the case of statistical dependence in the input for a finite number of lags. It is found that the estimate mean-error norm converges to an asymptotic bound, giving a finite bias, generally nonzero, and that the asymptotic mean-norm square error is bounded and can be arbitrarily reduced by decreasing the adaptation factor.