Performance of a Third-Order Volterra Mvdr Beamformer in the Presence of Non-Gaussian and/or Non-Circular Interference

Linear beamformers are optimal, in a mean square (MS) sense, when the signal of interest (SOI) and observations are jointly Gaussian and circular. When the SOI and observations are zero-mean, jointly Gaussian and non-circular, optimal beamformers become widely linear (WL). They become non-linear with a structure depending on the unknown joint probability distribution of the SOI and observations when the latter are jointly non-Gaussian, assumption which is very common in radiocommunications. In this context, a third-order Volterra minimum variance distortionless response (MVDR) beamformer has been introduced recently for the reception of a SOI, whose waveform is unknown, but whose steering vector is known, corrupted by non-Gaussian and potentially non-circular interference, omnipresent in practical situations. However its statistical performance has not yet been analyzed. The aim of this paper is twofold. We first introduce an equivalent generalized sidelobe canceller (GSC) structure of this beamformer and then, we present an analytical performance analysis of the latter in the presence of one interference. This allows us to quantify the improvement of the performance with respect to the linear and WL MVDR beamformers.