Random Matrix Theory Models for Predicting Dominant Mode Rejection Beamformer Performance
Abstract
Adaptive beamformers (ABFs) use a spatial sample covariance matrix (SCM) that is estimated from data snapshots, i.e., temporal samples from each sensor, to mitigate directional interference and attenuate uncorrelated noise. Thus, ABFs improve signal-to-interference-plus-noise ratio (SINR), an optimal criteria for many detection and estimation algorithms, over that of a single sensor and the conventional beamformer. SINR is a function of white noise gain (WNG), the beamformer’s array gain versus spatial white noise, and interference leakage (IL), the interference power in the beamformer output. Dominant mode rejection (DMR) is a variant of the classic minimum variance distortionless response (MVDR) algorithm that replaces the smallest SCM eigenvalues by their average. By not inverting the smallest eigenvalues, DMR achieves a higher WNG than MVDR. Moreover, DMR still suppresses the loud interferers as the largest eigenvalues are unmodified, yielding a higher SINR than MVDR. This dissertation derives analytical models of WNG and IL for the DMR ABF. The model predictions are shown to match the sample mean, computed via Monte Carlo simulations, for a broad range of scenarios including with and without the signal of interest (SOI) in the training data. Both cases for the SOI in the training data are analyzed when the number of interferers is known, and when the number of interferers is overestimated. The models leverage a new random matrix theory (RMT) spiked covariance model that is derived in this dissertation. The new RMT model more accurately predicts the SCM eigenspectrum, and hence the ABF metrics, when the number of snapshots is on the same order or less than the dimension and there are a large number of interferers relative to the SCM dimension. Assuming the SOI is not in the training data and a known number of interferers are loud, the analytical models show DMR achieves an average SINR loss of -3 dB when the number of snapshots is approximately twice the number of interferers, an analogous result to the Reed-Mallett-Brennan rule for MVDR.
Description
Keywords
Beamforming, Dominant mode rejection (DMR), Random matrix theory (RMT), Sample covariance matrix, SINR