A Full Second-Order Analysis of the Widely Linear MVDR Beamformer for Noncircular Signals

A full performance analysis of the widely linear (WL) minimum variance distortionless response (MVDR) beamformer is introduced. While the WL MVDR is shown to outperform its linear counterpart, the Capon beamformer, for noncircular complex signals, its analysis provides limited physical insights, since the existing approaches 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 and propose a full SO performance analysis framework for the WL MVDR beamformer, which enables the separation of 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. 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 examples are provided to support the theoretical results.