Short data record adaptive filtering: The auxiliary-vector algorithm

Based on statistical conditional optimization criteria, we developed an iterative algorithm that starts from the matched filter (or constraint vector) and generates a sequence of filters that converges to the minimum variance distortionless response (MVDR) solution for any positive definite input autocorrelation matrix. Computationally, the algorithm is a simple recursive procedure that avoids explicit matrix inversion, decomposition, or diagonalization operations. 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 rises slowly and asymptotically to the covariance trace of the familiar sample matrix inversion (SMI) estimator. For short data records, the early, nonasymptotic, elements of the generated sequence of estimators offer favorable bias-covariance balance and are seen to outperform in mean-square estimation error constraint-LMS, RLS-type, and orthogonal multistage decomposition estimates (also called nested Wiener filters) as well as plain and diagonally loaded SMI estimates. The problem of selecting the most successful (in some appropriate sense) filter estimator in the sequence for a given data record is addressed and two data-driven selection criteria are proposed. The first criterion minimizes the cross-validated sample average variance of the filter estimator output. The second criterion maximizes the estimated J-divergence of the filter estimator output conditional distributions. Illustrative interference suppression examples drawn from the communications literature are followed throughout this presentation. (C) 2002 Elsevier Science (USA).