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.
翻译:对广线性(WL)最低差异不扭曲反应(MVDR)光谱进行全面业绩分析;虽然人们知道WL MVDR光谱超过严格的线性对应方(Capon beamrefer),对于非循环复杂的信号,Capon beamrefor,现有方法提供了有限的实际洞察力,因为它们明确或隐含地忽略了产出干扰和噪音(IN)的第二阶(SO)补充统计数据。为此目的,我们利用输出输出的完整SO统计数据,为WL DR光谱图引入完整的SO性业绩分析框架,从而有可能将WL MVDR总信号-干涉加噪音率(SINR)的收益与纯线性对比(SINR)分开,但是,Capon一号显示,根据(I)阶段和四阶(Q)通道的个别贡献,Capon 明确或隐蔽性影响(SOII)光学分数任意性干扰,我们进一步公布SINR在I和Q频道上的全面信号和噪音比的分布,在SVDRBALBA值上几乎所有的优势是模拟的理论干预。