Third order widely non linear Volterra MVDR beamforming

It is now well known that time invariant (TI) linear beamformers, such as the Capon´s beamformer, are only optimal for stationary Gaussian observations whose complex envelope is necessarily second order (SO) circular. However in many applications such as in radiocommunications, most of the signals are nonGaussian and their complex envelope presents very often some SO and/or higher order (HO) non circularity properties. For this reason we propose in this paper a third order widely non linear Volterra minimum variance distortionnless response (MVDR) beamformer taking into account both the potential non Gaussian character and the potential HO non circularity (up to sixth order) of interferences. Some properties, performance and adaptive implementation of this new beamformer are presented in the paper. Illustrations shows the great interest, with respect to the existing beamformers, of this new beamformer for non Gaussian and HO non circular interferences, omnipresent in practice.