Capacity Characterization of UAV-Enabled Multiple Access Channel with Trajectory Optimization

This paper studies an unmanned aerial vehicle (UAV)-enabled multiple access channel (MAC), where multiple ground users transmit individual messages to a mobile UAV. We consider the linear topology case when the users are deployed in a straight line on the ground and the UAV flies at a fixed altitude in the sky. Under this setup, we aim to characterize the fundamental capacity region of the UAV-enabled MAC over a particular communication period, which is defined as the set of all average rate tuples that are simultaneously achievable by users, under the users' individual maximum power and the UAV's maximum flight speed constraints. Towards this end, we maximize the average sum-rate of all users subject to a set of rate profile constraints, by optimizing the UAV's one-dimensional (1D) trajectory design. Although this problem is highly nonconvex and very difficult in general, we present the globally optimal solution, by first showing that any speed-constrained UAV trajectory is equivalent to the combination of a maximum-speed trajectory and a speed-free trajectory, and then employing the Lagrange duality method to solve the equivalent speed-free trajectory design problem. It is shown that the optimal trajectory solution follows an interesting successive hover-and-fly (SHF) structure, i.e., the UAV successively hovers above a number of optimized locations, and flies among them unidirectionally at the maximum speed. Numerical results show that the capacity region achieved by the optimal SHF trajectory design significantly outperforms the achievable rate region by other benchmark schemes.