Beamforming design for covert broadcast communication with hidden adversary

This paper explores covert broadcast communication in a challenging situation in which the transmitter, Alice, faces uncertainty regarding the position of the passive adversary, Willie. In this situation, controlling the signal exposure becomes difficult. Specifically, this paper focuses on the cases where Alice can delimit the suspicious areas where Willie may be located. The suspicious areas can have arbitrary number and shapes. Under the Rician fading model, the analytical expression of Willie’s detection performance is derived. Then, the transmit power, the beamforming direction, and the number of channel uses are jointly designed to minimize the optimal Willie’s detection performance among all the possible positions of Willie, on the premise of satisfying receivers’ quality-of-service requirements. To tackle the formulated knotty problem with an infinite number of irregular and discontinuous Willie’s possible positions, the continuous nature of the antenna pattern is exploited to convert the original problem into the one with a finite number of possible positions, by sampling the suspicious areas. Then, different algorithms are developed to address the resultant non-convex optimization problem for single-antenna Willie and multi-antenna Willie, respectively. Numerical results demonstrate significant performance gains of the proposed scheme over the widely-adopted maximum ratio transmission scheme, which indicates that simply adjusting the main lobe towards the receiver is indeed far away from optimum and shows the importance of leveraging Alice’s limited knowledge of Willie’s position.