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

TL;DR

This paper analyzes the stochastic MV-PURE estimator's performance in high noise environments, demonstrating its superior mean-square-error reduction compared to full-rank estimators, especially as noise increases.

Contribution

It provides a theoretical analysis of the stochastic MV-PURE estimator's performance in noisy conditions, highlighting its advantages over traditional estimators.

Findings

MSE of stochastic MV-PURE is much lower in low SNR regions.

Performance gap widens as noise level increases.

Simulation results confirm theoretical insights.

Abstract

The stochastic minimum-variance pseudo-unbiased reduced-rank estimator (stochastic MV-PURE estimator) has been developed to provide linear estimation with robustness against high noise levels, imperfections in model knowledge, and ill-conditioned systems. In this paper, we investigate the theoretical performance of the stochastic MV-PURE estimator under varying levels of additive noise. We prove that the mean-square-error (MSE) of this estimator in the low signal-to-noise (SNR) region is much smaller than that obtained with its full-rank version, the minimum-variance distortionless estimator, and the gap becomes larger as the noise level increases. These results shed light on the excellent performance of the stochastic MV-PURE estimator in highly noisy settings obtained in simulations so far. Furthermore, we extend previous numerical simulations to show how the insight gained from the results of this paper can be used in practice.