Performance of the stochastic MV-PURE estimator in highly noisy settings

摘要

The stochastic MV-PURE estimator has been developed to provide linearestimation robust to ill-conditioning, high noise levels, and imperfections inmodel knowledge. In this paper, we investigate the theoretical performance ofthe stochastic MV-PURE estimator under varying level of additive noise. Moreprecisely, we prove that the mean-square-error (MSE) of this estimator in thelow signal-to-noise (SNR) region is much smaller than that obtained with itsfull-rank version, the minimum-variance distortionless estimator, and that thegap in performance is the larger the higher the noise level. These results shedlight on the excellent performance of the stochastic MV-PURE estimator inhighly noisy settings obtained in simulations so far. We extend here previouslyconducted numerical simulations to demonstrate a new insight provided byresults of this paper in practical applications.