On the sensitivity of third-order Volterra MVDR beamformers to interference-pulse shaping filter.

• A closed-form expression of the SINR at the output of a family of third-order Volterra MVDR beamformers is given. • Interpretable closed-form expressions of this SINR are derived in the particular case of 2 sensors in the presence of single digitally linearly modulated interference. • These closed-form expression allow us to quantify the impact of the pulse-shape filtering (pulse shape filter, oversampling factor and initial sampling time). • This sensitivity study proves that the high performance gain of these third-order Volterra MVDR beamformers with respect to the Capon algorithm for a square pulse shape filter are lost in the presence of intersymbol interference. Linear beamformers are optimal, in a mean square (MS) sense, when the signal of interest (SOI) and observations are jointly Gaussian and circular. Otherwise, optimal beamformers become non-linear with a structure depending on the unknown joint probability distribution of the SOI and observations. In this context, third-order Volterra minimum variance distortionless response (MVDR) beamformers have been proposed recently to improve the performance of linear beamformers in the presence of non-Gaussian and potentially non-circular interference, omnipresent in practical situations. High performance gains have been obtained for binary phase shift keying (BPSK) and quadrature phase shift keying (QPSK) interference having a square pulse shaping filter in particular. However in practice, for spectral efficiency reasons, most of signals use non-square pulse shaping filters, such as square root raised cosine filter. It is then important to analyze the sensitivity of third-order MVDR beamformers to interference pulse shaping filter, which is the purpose of this paper. [ABSTRACT FROM AUTHOR]