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

Authors:
Jesús Gutiérrez-Gutiérrez;Iñaki Iglesias;Adam Podhorski
Affiliations:
CEIT and Tecnun (University of Navarra), Manuel de Lardizábal 15, 20018 San Sebastián, Spain;CEIT and Tecnun (University of Navarra), Manuel de Lardizábal 15, 20018 San Sebastián, Spain;CEIT and Tecnun (University of Navarra), Manuel de Lardizábal 15, 20018 San Sebastián, Spain
Venue:
Signal Processing
Year:
2011

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Abstract

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.