  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.
