Low-complexity cross-validation design of a linear estimator

Linear signal estimators have extensive applications. Under the minimum mean squared error (MMSE) criterion, the linear MMSE (LMMSE) estimator is optimal but requires knowledge of the covariance matrices. The sample matched filter generally performs worse but requires less a priori knowledge. A composite estimator that combines the sample LMMSE estimator and matched filter is studied, which may lead to noticeable improvements in performance. It is shown that such a gain can be achieved by low-complexity parameter tuning methods based on cross-validation using training or out-oftraining data. Numerical results are provided to demonstrate the effectiveness of the proposed approaches.