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Short-data-record adaptive filtering: The auxiliary-vectoralgorithm

Karystinos Georgios, Haoli Qian, Medley Michael J., Batalama Stella N.

Πλήρης Εγγραφή

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Περίληψη

Based on statistical conditional optimization criteria, we developed aniterative algorithm that starts from the matched filter (or constraint vector)and generates a sequence of filters that converges to the minimumvariance distortionless response (MVDR) solution for any positive defi-nite input autocorrelation matrix. Computationally, the algorithm is a simplerecursive procedure that avoids explicit matrix inversion, decomposition,or diagonalization operations. When the input autocorrelation matrixis 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 rises slowlyand asymptotically to the covariance trace of the familiar sample matrixinversion (SMI) estimator. For short data records, the early, nonasymptotic,elements of the generated sequence of estimators offer favorablebias–covariance balance and are seen to outperform in mean-square estimationerror constraint-LMS, RLS-type, and orthogonal multistage decompositionestimates (also called nested Wiener filters) as well as plainand diagonally loaded SMI estimates. The problem of selecting the mostsuccessful (in some appropriate sense) filter estimator in the sequence fora given data record is addressed and two data-driven selection criteria areproposed. The first criterion minimizes the cross-validated sample averagevariance of the filter estimator output. The second criterion maximizesthe estimated J-divergence of the filter estimator output conditional distributions.Illustrative interference suppression examples drawn from thecommunications literature are followed throughout this presentation.

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