Joint Power and Beamformer Optimization in Multi-Antenna Relay Covert System: Exploiting Public Users as Shelter

The environmental shelters such as public links can enable covert communication by covering covert transmission. To further exploit shelters, this paper focuses on a two-hop system where multiple pairs of public users and one pair of covert users communicate through a multi-antenna relay. We aim to improve covertness performance while satisfying the covertness constraints of two hops and quality of service (QoS) requirements of public users. The covert throughput maximization problem is formulated via jointly optimizing transmit power and beamformer, which is challenging to solve. We introduce successive convex approximation (SCA) and semidefinite relaxation (SDR) techniques to convert the problem into convex, where the joint optimization algorithm is developed. Considering the computational complexity, we further design a block diagonalization (BD) beamformer at the relay, which translates the beamformer optimization into a power allocation problem and derives the optimal solution in a closed form. We analytically show that the covert throughput first increases and then decreases as the number of public pairs increases in BD-based design, which has been verified numerically and can be generalized in other designs. Numerical results also evaluate the superiority of the joint optimization algorithm and the effectiveness of the BD-based efficient design. In particular, the BD-based design is very close to the joint optimization under small maximum transmit power of users or large maximum transmit power of relay.