Random matrix theory analysis of the dominant mode rejection beamformer

Abstract

The Dominant Mode Rejection (DMR) beamformer developed by Abraham and Owsley [Proc. Oceans, 1990] determines the beamformer weights from the sensor covariance matrix eigendecomposition. The weights are designed to reject signals contained in the dominant subspace, which is defined by the eigenvectors associated with the largest eigenvalues. In previous work, we developed a model for the mean notch depth (ND) of the DMR beamformer from random matrix theory (RMT) results on the sample eigenvector fidelity [IEEE Stat. Sig. Proc. workshop, 2012]. While ND is useful, other metrics such as white noise gain (WNG) and signal to interference and noise ratio (SINR) are of great interest. WNG characterizes the beamformer robustness to mismatch, and SINR quantifies overall performance. SINR loss is defined as the ratio of the SINR for a beamformer designed using sample statistics to the SINR for the optimal beamformer designed using ensemble statistics. This talk extends our previous work by considering the relationship among ND, WNG, and SINR for the DMR beamformer. A surprising result obtained from RMT is that for a single loud interferer and twice as many snapshots as sensors, the expected SINR loss depends only on the number of snapshots. [Work supported by ONR.]