Optimal widely linear MVDR beamforming for noncircular signals

This paper introduces the optimal widely linear (WL) minimum variance distorsionless response (MVDR) beamformer for the reception of an unknown signal of interest (SOI) corrupted by potentially second order (SO) noncircular background noise and interference. The SOI, whose waveform is unknown, is assumed to be SO noncircular with arbitrary noncircular properties. In the steady state and for SO noncircular SOI and/or interference, this new WL beamformer, that is derived from an original orthogonal decomposition, is shown to always improve the performance of both the well-known Capon's beamformer and a WL MVDR beamformer introduced recently in the literature. This optimal WL MVDR beamformer is first introduced and some of its performance are analyzed. Then, several adaptive implementations of this optimal WL beamformer are presented.