Random matrix theory analysis of the dominant mode rejection beamformer white noise gain

Abstract

The dominant mode rejection (DMR) beamformer [Abraham and Owsley, IEEE Oceans (1990)] is an adaptive spatial processor that has been effectively used to null interference sources in scenarios where the number of training samples to estimate the sample covariance matrix (SCM) is limited. In these scenarios the ratio of the SCM dimension (array size) to the number of snapshots (training samples) is close to or even greater than one. Whereas classical asymptotic SCM results require the number of samples grow to infinity while keeping the dimension fixed, random matrix theory (RMT) provides a robust mathematical framework to analyze the SCM spectrum in snapshot-limited scenarios. RMT predictions of the SCM eigenvectors have already been applied to predict DMR beamformer notch depth in a single interferer environment (Buck and Wage, IEEE SSP (2012)]. This talk presents an RMT-based asymptotic approximation of the DMR SCM inverse in a loud multi-interferer environment. The RMT SCM model is used to predict the white noise gain (WNG) of the DMR beamformer, accounting for the impact when bulk spectral components are included in the dominant subspace. The performance of the RMT-based WNG prediction is compared to the sample mean using Monte Carlo simulations. [Funded by ONR 321US.]