Relaxed Zero-Forcing Beamformer under Temporally-Correlated Interference

TL;DR

This paper investigates the performance of the relaxed zero-forcing (RZF) beamformer under temporally-correlated interference, demonstrating its advantages over traditional beamformers through analysis and EEG data applications.

Contribution

The paper rederives RZF with an ellipsoidal constraint, analyzes its performance under correlated interference, and shows its advantages in practical EEG brain activity reconstruction.

Findings

RZF outperforms traditional beamformers in correlated interference scenarios.

Analytical results show RZF's near-optimal performance in certain conditions.

Numerical studies confirm RZF's effectiveness in EEG data applications.

Abstract

The relaxed zero-forcing (RZF) beamformer is a quadratically-and-linearly constrained minimum variance beamformer. The central question addressed in this paper is whether RZF performs better than the widely-used minimum variance distortionless response and zero-forcing beamformers under temporally-correlated interference. First, RZF is rederived by imposing an ellipsoidal constraint that bounds the amount of interference leakage for mitigating the intrinsic gap between the output variance and the mean squared error (MSE) which stems from the temporal correlations. Second, an analysis of RZF is presented for the single-interference case, showing how the MSE is affected by the spatio-temporal correlations between the desired and interfering sources as well as by the signal and noise powers. Third, numerical studies are presented for the multiple-interference case, showing the remarkable advantages of RZF in its basic performance as well as in its application to brain activity reconstruction from EEG data. The analytical and experimental results clarify that the RZF beamformer gives near-optimal performance in some situations.