The Probability Density Function of SINR Loss of the Dominant Mode Rejection Beamformer

The dominant mode rejection (DMR) adaptive beamformer (ABF) is a reduced rank subspace algorithm, which replaces the covariance matrix in the Minimum Variance Distortionless Response (MVDR) beamformer with an eigenvalue reshaped covariance estimate out of the sample covariance matrix (SCM). Signal-to-interference-plus-noise ratio (SINR) loss quantifies the performance of an ABF designed with SCM with respect to its nominal version designed with the true ensemble covariance matrix (ECM). This paper conjectures that the SINR loss of the DMR beamformer is beta-distributed, derives and provides an approximated expression for the beta probability density function. For the simple case of single interferer present in white noise, the performance of the DMR beamformer only depends on the number of snapshots. Monte-Carlo simulations are carried out to verify our derived results.