非圆信号宽线性MVDR波束形成器的全二阶分析
A Full Second-Order Analysis of the Widely Linear MVDR Beamformer for Noncircular Signals
摘要：
对宽线性最小方差无失真响应波束形成器进行了全面的性能分析。虽然已知WL MVDR优于其严格线性对应物Capon波束形成器，但对于非圆形复信号，现有方法提供有限的物理见解，因为它们显式或隐式地省略了输出干扰和噪声（IN）的互补二阶（SO）统计。为此，我们利用输出IN的完整SO统计来引入WL MVDR波束形成器的完整SO性能分析框架。这使得可以将WL MVDR波束形成器的总体信号与干扰加噪声比（SINR）增益与Capon一个转换为沿同相（I）和正交（Q）信道的单独贡献。接下来，通过考虑由任意数量的正交非圆干扰损坏的未知感兴趣的信号（SOI）的接收，我们进一步揭示了在I和Q信道的SINR增益的分布，并表明，在几乎所有的空间的情况下，这些性能优势是更明显的SO非圆率的干扰增加时。说明性的数值模拟提供支持的理论结果。
英文摘要：
A full performance analysis of the widely linear (WL) minimum variance distortionless response (MVDR) beamformer is introduced. While the WL MVDR is known to outperform its strictly linear counterpart, the Capon beamformer, for noncircular complex signals, the existing approaches provide limited physical insights, since they explicitly or implicitly omit the complementary second-order (SO) statistics of the output interferences and noise (IN). To this end, we exploit the full SO statistics of the output IN to introduce a full SO performance analysis framework for the WL MVDR beamformer. This makes it possible to separate the overall signal-to-interference plus noise ratio (SINR) gain of the WL MVDR beamformer w.r.t. the Capon one into the individual contributions along the in-phase (I) and quadrature (Q) channels. Next, by considering the reception of the unknown signal of interest (SOI) corrupted by an arbitrary number of orthogonal noncircular interferences, we further unveil the distribution of SINR gains in both the I and Q channels, and show that in almost all the spatial cases, these performance advantages are more pronounced when the SO noncircularity rate of the interferences increases. Illustrative numerical simulations are provided to support the theoretical results.
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