Data record-based criteria for the selection of an auxiliary vector estimator of the MMSE/MVDR filter

When the auxiliary vector (AV) filter generation algorithm utilizes sample average estimated input data statistics, it provides a sequence of estimates of the ideal minimum mean-square error or minimum-variance distortionless-response filter for the given signal processing/receiver design application. Evidently, early nonasymptotic elements of the sequence offer favorable bias/variance balance characteristics and outperform in mean-square filter estimation error the unbiased sample matrix inversion (SMI) estimator as well as the (constraint) least-mean square, recursive least-squares, "multistage nested Wiener filter", and diagonally-loaded SMI filter estimators. Selecting the most successful (in some appropriate sense) AV filter estimator in the sequence for a given data record is a critical problem that has not been addressed so far. We deal exactly with this problem and we propose two data-driven selection criteria. The first criterion minimizes the cross-validated sample average variance of the AV filter output and can be applied to general filter estimation problems; the second criterion maximizes the estimated J-divergence of the AV filter output conditional distributions and is tailored to binary phase-shift-keying-type detection problems.