Joint 3D Beamforming-and-Trajectory Design for UAV-Satellite Uplink Covert Communication

In this paper, we study uplink covert communication in a space-air system, where an unmanned aerial vehicle (UAV) transmits sensitive data to a Geosynchronous Earth Orbit (GEO) satellite while preventing the transmission action from being discovered by a warden. We derive the optimal decision threshold of the warden. We investigate the 3-dimensional (3D) beamformer and 3D trajectory design for the transmitter UAV against this optimum warden to maximize the covert transmission rate in the presence of imperfect channel state information and uncertain noise. Due to the non-convex structure and dependence between beamforming vectors and locations of the transmitter UAV, we develop a decoupling method that specifies a feasible flight region of the transmitter UAV at each time slot, enabling the decomposition of the original optimization problem into two sub-problems that optimize the trajectory and beamforming vectors individually. We design an iterative algorithm with a new initialization method to solve the sub-problems alternately with the semi-definite relaxation (SDR) and the successive convex approximation (SCA) technique. Numerical results show that the average covert rate of our design approaches the ideal case without the warden and increases by about 102.3% and 19.1% compared with benchmark schemes that do not employ beamforming or design 2D trajectory, respectively.