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This paper considers the regularized estimation of covariance matrices (CM)of high-dimensional (compound) Gaussian data for minimum variancedistortionless response (MVDR) beamforming. Linear shrinkage is applied toimprove the accuracy and condition number of the CM estimate forlow-sample-support cases. We focus on data-driven techniques that automaticallychoose the linear shrinkage factors for shrinkage sample covariance matrix($\text{S}^2$CM) and shrinkage Tyler's estimator (STE) by exploiting crossvalidation (CV). We propose leave-one-out cross-validation (LOOCV) choices forthe shrinkage factors to optimize the beamforming performance, referred to as$\text{S}^2$CM-CV and STE-CV. The (weighted) out-of-sample output power of thebeamfomer is chosen as a proxy of the beamformer performance and conciseexpressions of the LOOCV cost function are derived to allow fast optimization.For the large system regime, asymptotic approximations of the LOOCV costfunctions are derived, yielding the $\text{S}^2$CM-AE and STE-AE. In general,the proposed algorithms are able to achieve near-oracle performance in choosingthe linear shrinkage factors for MVDR beamforming. Simulation results areprovided for validating the proposed methods.

Cross-Validated Tuning of Shrinkage Factors for MVDR Beamforming Based on Regularized Covariance Matrix Estimation