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

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.