This paper studies an unmanned aerial vehicle (UAV)-enabled multicasting system, where a UAV is dispatched to disseminate a common file to a set of ground terminals (GTs). We aim to design the UAV trajectory to minimize its mission completion time, while ensuring that each GT successfully recovers the file with a desired high probability. The formulated problem is nonconvex and difficult to be solved in its original form. Therefore, we first derive an effective lower bound for the success file recovery probability of each GT. The problem is then reformulated in a more tractable form, where the UAV trajectory only needs to be designed to ensure the minimum connection time constraint with each GT, during which their distance is below a certain threshold. We show that without loss of optimality, the UAV trajectory consists of connected line segments only, which can be obtained by determining the optimal set of waypoints as well as the UAV speed along the path connecting the waypoints. We propose efficient schemes for the waypoint design based on a novel concept of virtual base station placement and by applying convex optimization. Furthermore, for fixed waypoints, the optimal UAV speed is efficiently obtained by solving a linear programming problem. Numerical results show that the proposed UAV-enabled multicasting with optimized trajectory design achieves significant performance gains over other benchmark schemes.
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