  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.
