Snapshot Performance of the Dominant Mode Rejection Beamformer

The dominant mode rejection (DMR) beamformer constructs its weight vector using a structured covariance estimate derived from the eigendecomposition of the sample covariance matrix (SCM). Like all adaptive beamformers (ABFs), the DMR ABF places notches in the direction of loud interferers to facilitate the detection of quiet targets. This paper investigates how DMR performs as a function of the number of snapshots used to estimate the SCM. The analysis focuses on the fundamental case of a single interferer in white noise. Theoretical calculations for the ensemble case reveal the relationships among notch depth, white noise gain, and SINR. The centerpiece of the paper is a detailed empirical study of the single-interferer case, which includes snapshot-deficient scenarios often ignored in previous work. Empirical data demonstrate that the sample eigenvectors determine the mean performance of the DMR ABF. On a log-log plot the mean notch depth is a piecewise linear function of the number of snapshots and the interference-to-noise ratio. The paper interprets the behavior of the DMR ABF using recent results on sample eigenvectors derived from random matrix theory.