Analytical Optimal Joint Resource Allocation and Continuous Trajectory Design for UAV-Assisted Covert Communications

In this paper, we focus on an unmanned aerial vehicle (UAV)-assisted covert communication scenario, and introduce an optimal joint resource allocation and continuous UAV trajectory design. We aim at maximizing the information throughput between UAV and a ground user, while protecting the transmission behavior from being detected by a warden. Due to the continuity of UAV trajectory in both time and space, the formulated problem has infinitely large number of variables to be optimized, i.e., being not only cutting-edge, but also very challenging to be coped with. To address this issue, we provide an artificial potential field (APF)-based approach, with which a closed-form optimal solution is for the first time obtained for considered UAV-assisted covert communication. In particular, first based on investigation on the covertness constraint, the maximal transmit power is characterized as a closed-form binary decision function with respect to UAV position. Following the characterization, we then transform the joint optimization problem to one of pure UAV trajectory design. Subsequently, via conducting an APF to covert transmission rate between the UAV and the user, the trajectory design problem is completely equivalent to a mechanical problem, i.e., a density-variable rope shape design problem in the APF, based on mechanical equivalence technique. Such mechanical problem can be optimally solved. Specifically, the force field in the conducted APF corresponding to a covert communication is actually twisted due to the presence of the warden, for which we reorganize a brand new mechanical analysis process accordingly, including reanalyzing the direction of the force field and updating the force balance expression. Then, according to the minimum total potential energy principle, the closed-form solution of the optimal rope shape is constructed following the equilibrium analysis. In addition, acknowledging that the lowest potential point of APF changes with the covert requirement, we also discuss all the three cases for optimal trajectory distinguishing in hovering behavior of the UAV.