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

Abstract

This paper considers the regularized estimation of covariance matrices (CM) of high-dimensional (compound) Gaussian data for minimum variance distortionless response (MVDR) beamforming. Linear shrinkage is applied to improve the accuracy and condition number of the CM estimate for lowsample-support cases. We focus on data-driven techniques that automatically choose the linear shrinkage factors for shrinkage sample covariance matrix (S 2 CM) and shrinkage Tyler's estimator (STE) by exploiting cross validation (CV). We propose leaveone-out cross-validation (LOOCV) choices for the shrinkage factors to optimize the beamforming performance, referred to as S 2 CM-CV and STE-CV. The (weighted) out-of-sample output power of the beamfomer is chosen as a proxy of the beamformer performance and concise expressions of the LOOCV cost function are derived to allow fast optimization. For the large system regime, asymptotic approximations of the LOOCV cost functions are derived, yielding the S 2 CM-AE and STE-AE. In general, the proposed algorithms are able to achieve near-oracle performance in choosing the linear shrinkage factors for MVDR beamforming. Simulation results are provided for validating the proposed methods.

Performance analysis of repeater spoofing suppression based on GNSS multi-beam receiver

“…Studied the influence of signal arrival angle on the performance of MVDR algorithm [33]. Analyzed the desired (SNR), the interference-to-noise ratio (INR) of the jamming, and the signal-to-interference ratio (SIR), signal arrival angle, array element structure, correlation between jamming and desired signal and other factors on the output signal-to-interference plus noise ratio (SINR), but the derivation process is very complicated [34]. Proposed leave-one-out cross-validation (LOOCV) choices for the shrinkage factors to optimize the beamforming performance [35].…”