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Random Matrix Theory Analysis of the Dominant Mode Rejection Beamformer White Noise Gain with Overestimated Rank

Adaptive beamformers (ABFs) can mitigate loud interferers and improve detection and estimation of low power sources given enough snapshots to estimate the sample covariance matrix. The dominant mode rejection (DMR) ABF splits the covariance spectrum into dominant and noise subspaces, improving performance in snapshot-limited scenarios. White noise gain (WNG) is a key performance metric that characterizes a beamformer’s robustness to array perturbations and other errors. The DMR ABF’s WNG is highest when the rank of the dominant subspace matches the number of interferers in the environment and decreases when the rank is overestimated. This paper introduces a model of DMR WNG, based on random matrix theory, that matches the Monte Carlo sample mean when the DMR rank is greater than or equal to the number of interferers.