Geometric MMSE for one-sided and two-sided vector linear predictors: From the finite-length case to the infinite-length case

In the present paper we derive a formula for the geometric minimum mean square error (GMMSE) for one-sided and two-sided finite-length vector linear predictors. This formula is written only in terms of the autocorrelation matrix of the vector process being predicted. We also obtain a formula for the GMMSE for one-sided and two-sided infinite-length vector linear predictors of any wide sense stationary (WSS) vector process. This GMMSE expression for the infinite-length case is derived from the GMMSE expression obtained for the finite-length case.

► We compute the GMMSE for one and two-sided finite-length vector linear predictors.
► We obtain the GMMSE for one and two-sided infinite-length vector linear predictors.
► The infinite-length cases are derived from the finite-length cases.