Capacity of UAV-Enabled Multicast Channel: Joint Trajectory Design and Power Allocation

This paper studies an unmanned aerial vehicle (UAV)-enabled multicast channel, in which a UAV serves as a mobile transmitter to deliver common information to a set of $K$ ground users. We aim to characterize the capacity of this channel over a finite UAV communication period, subject to its maximum speed constraint and an average transmit power constraint. To achieve the capacity, the UAV should use a sufficiently long code that spans over its whole communication period. Accordingly, the multicast channel capacity is achieved via maximizing the minimum achievable time-averaged rates of the $K$ users, by jointly optimizing the UAV's trajectory and transmit power allocation over time. However, this problem is non-convex and difficult to be solved optimally. To tackle this problem, we first consider a relaxed problem by ignoring the maximum UAV speed constraint, and obtain its globally optimal solution via the Lagrange dual method. The optimal solution reveals that the UAV should hover above a finite number of ground locations, with the optimal hovering duration and transmit power at each location. Next, based on such a multi-location-hovering solution, we present a successive hover-and-fly trajectory design and obtain the corresponding optimal transmit power allocation for the case with the maximum UAV speed constraint. Numerical results show that our proposed joint UAV trajectory and transmit power optimization significantly improves the achievable rate of the UAV-enabled multicast channel, and also greatly outperforms the conventional multicast channel with a fixed-location transmitter.