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.

中文翻译：

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时间相关干扰下的松弛迫零波束形成器

松弛迫零 (RZF) 波束成形器是二次线性约束的最小方差波束成形器。本文解决的中心问题是，在时间相关干扰下，RZF 的性能是否优于广泛使用的最小方差无失真响应和迫零波束成形器。首先，RZF 是通过施加椭圆体约束来重新推导的，该约束限制了干扰泄漏量，以减轻输出方差与源自时间相关性的均方误差 (MSE) 之间的内在差距。其次，对单干扰情况下的 RZF 进行了分析，显示了 MSE 如何受到所需源和干扰源之间的时空相关性以及信号和噪声功率的影响。第三，针对多干扰情况进行了数值研究，展示了 RZF 在其基本性能以及从 EEG 数据重建大脑活动的应用方面的显着优势。分析和实验结果表明，RZF 波束成形器在某些情况下可提供接近最佳的性能。