Adaptive MSE estimation

Two basic approaches to adaptive signal processing are in common use. The first and most direct involves substituting data-derived estimates of signal and noise autocorrelations into the standard Wiener-Hopf equation. The second uses a stochastic algorithm, such as the LMS, to minimize the mean square error directly. This paper attempts to unify these approaches by deriving an algorithm which substitutes data-derived estimates of the signal and noise autocorrelations into a recursive version of the Wiener-Hopf equation thus eliminating the need for direct matrix inversion. Although clearly an offshoot of the direct method, this algorithm, in its simplest form, is identical to the well-known LMS stochastic algorithm.