Distributionally Robust Secure Multicast Beamforming With Intelligent Reflecting Surface

Recently, the intelligent reflecting surfaces (IRSs)-aided wireless transmission has drawn considerable attention. This paper investigates the use of IRS in enhancing the physical-layer security of the multiuser multiple-input single-output (MU-MISO) broadcast system, where a base station (BS) transmits a common data stream to multiple legitimate receivers in the presence of multiple eavesdroppers (Eves). The BS is assumed to have only some erroneous channel state information (CSI) of the Eves. The CSI error is modeled by a moment-based random error model, in which the BS only knows the first- and second-order statistics of the error, but not the exact distribution. Under this CSI error model, we investigate the joint robust design of the secure beamforming at the BS and the phase shift at the IRS to maximize the worst legitimate user’s SNR, while keeping the Eves’ SNR below certain threshold with high probability, evaluated with respect to any distribution fulfilling the given first and second-order statistics. This robust secure transmission design problem is a semi-infinite chance-constrained problem, which is in general intractable. We show that the considered problem admits an equivalent conic reformulation, which can be handled by alternately optimizing the beamformer at the BS and the phase shift at the IRS via semidefinite relaxation (SDR) and penalty convex-concave procedure (CCP), respectively. To further improve the secrecy performance, we also study another rank-two beamformed Alamouti transmission scheme at the BS, which can be seen as a generalization of conventional rank-one beamforming. Simulation results demonstrate that the proposed designs are robust against the error distribution, and that the inclusion of IRS is not only helpful for enhancing the security, but also useful for promoting a low-rank SDR solution.