Short-data-record estimators of the MVDR/NMSE filter

We show that statistical conditional optimization criteria lead to the development of a simple iterative algorithm that starts from the matched filter (or constraint vector of interest) and generates a sequence of filters that converges to the minimum-variance-distortionless-response (MVDR) solution for any positive definite input autocorrelation matrix. When the input autocorrelation matrix is replaced by a conventional sample-average (positive definite) estimate, the algorithm effectively generates a sequence of MVDR filter estimators; the bias converges rapidly to zero and the covariance trace raises slowly and asymptotically to the covariance trace of the familiar sample-matrix-inversion (SMI) estimator. For short-data-records, the early elements of the generated sequence of estimators offer favorable bias/covariance balance and are seen to outperform in mean-square estimation error (constrained-)LMS, RLS-type, and, certainly, SMI estimates