AN‐aided probabilistic robust and secure beamforming with imperfect LCSI and statistical ECSI

Abstract

The probabilistic robust beamforming with the help of artificial noise (AN) is investigated in this study, where a multiple-input-single-output wiretap scenario with K single-antenna eavesdroppers is considered. Based on a more practical assumption that the transmitter derives imperfect legitimate user's channel state information (LCSI) and statistical eavesdroppers' channel state information (ECSI), secrecy rate maximisation (SRM) under a total transmit power constraint and K probabilistic secrecy outage constraints are studied. To deal with it, the K probabilistic constraints are firstly approximated to the deterministic worst-case ones by resorting to sphere bounding. Secondly, by introducing a slack variable the approximated worst-case SRM can be further recast as a series of semi-definite programmings. In this way, the jointly optimised robust beamforming vector and the AN covariance are determined in a tractable convex fashion. Moreover, the authors can prove that the derived AN-aided secure robust beamforming actually is the optimal solution to the approximated worst-case SRM problem. Numerical results reveal that the proposed AN-aided probabilistic secure robust beamforming could achieve outage secrecy rate improvement in comparison with the existing optimal worst-case robust beamforming without AN, optimal outage constrained robust beamforming without AN, the non-robust isotropic AN transmission, and the non-robust AN-aided beamforming scheme.