  This paper investigates ground-aerial uplink non-orthogonal multiple access
(NOMA) cellular networks. A rotary-wing unmanned aerial vehicle (UAV) user and
multiple ground users (GUEs) are served by ground base stations (GBSs) by
utilizing the uplink NOMA protocol. The UAV is dispatched to upload specific
information bits to each target GBSs. Specifically, our goal is to minimize the
UAV mission completion time by jointly optimizing the UAV trajectory and
UAV-GBS association order while taking into account the UAV's interference to
non-associated GBSs. The formulated problem is a mixed integer non-convex
problem and involves infinite variables. To tackle this problem, we efficiently
check the feasibility of the formulated problem by utilizing graph theory and
topology theory. Next, we prove that the optimal UAV trajectory needs to
satisfy the \emph{fly-hover-fly} structure. With this insight, we first design
an efficient solution with predefined hovering locations by leveraging graph
theory techniques. Furthermore, we propose an iterative UAV trajectory design
by applying successive convex approximation (SCA) technique, which is
guaranteed to coverage to a locally optimal solution. We demonstrate that the
two proposed designs exhibit polynomial time complexity. Finally, numerical
results show that: 1) the SCA based design outperforms the fly-hover-fly based
design; 2) the UAV mission completion time is significantly minimized with
proposed NOMA schemes compared with the orthogonal multiple access (OMA)
scheme; 3) the increase of GUEs' quality of service (QoS) requirements will
increase the UAV mission completion time.
