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

Abstract

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.

Third-order Volterra MMSE receivers for enhanced single and multiple antenna interference cancellation

“…Relations ( 53) and ( 54) prove that the LC-( 1) and LC-(3) MMSE receivers perform SAIC because SINR L−C (1) and SINR L−C(3) do not decrease to zero when π j → ∞. Relation ( 52) is the SINR given by the linear MMSE receiver without CCI (see (37)) which shows that for synchronized QPSK SOI and CCI, the CCI is completely removed at the output of L-C(1, 3) receiver whatever α (including for N = 1 for which |α| = 1) thanks to an power's discrimination between the SOI and CCI. In this case, the performance gain with respect to the linear MMSE receiver (37) increases with j .…”

“…We clearly see from (37) that SINR L tends to zero for a strong CCI ( j 1) for |α| = 1 and thus cannot perform SAIC.…”

“…We compare now in Fig. 7, the theoretical SINR at the output of the linear, WL and WL-C(1) MMSE beamformers against their equivalent MVDR 1 beamformers, which take into account the non-circularity and/or the non-Gaussiannity of the interference only (i.e., linear MVDR or Capon [34], WL MVDR 1 [35] and WL-C(1) MVDR 1 beamformers [25], [37]) for N = 2, BPSK synchronized SOI and CCI symbols (τ j = 0) in the worst case φ = 0, as a function of |α| for SNR π s /η 2 = 10dB, INR π s /η 2 = 30dB and a roll-off ω = 0.3. Note that for the MVDR 1 beamformers, the comparison is shown with the time-averaged theoretical SINR because these beamformers have no knowledge of the SOI.…”