Multicast Secrecy Rate Maximization for MISO Channels with Multiple Multi-Antenna Eavesdroppers

Recently, there has been growing interest in secure communication via multi-antenna physical-layer designs. In this paper, we consider a transmit covariance design for a secrecy rate maximization problem under a multicast scenario, where a multi-antenna transmitter delivers a common confidential message to multiple single-antenna receivers in the presence of multiple multi-antenna eavesdroppers. This multicast secrecy rate maximization (SRM) problem is nonconvex by nature. By resorting to a convex approximation, we provide an upper bound and lower bounds of the multicast secrecy rate by solving a semidefinite program. In particular, for the case of either i) no more than three legitimate receivers and one eavesdropper, or ii) one legitimate receiver and arbitrary number of eavesdroppers, these bounds are shown to be tight and transmit beamforming is an optimal transmit strategy. We also demonstrate by simulations that the multicast SRM problem can be accurately approximated by the proposed method.