  Integrating the unmanned aerial vehicles (UAVs) into the cellular network is
envisioned to be a promising technology to significantly enhance the
communication performance of both UAVs and existing terrestrial users. In this
paper, we first provide an overview on the two main paradigms in cellular UAV
communications, i.e., cellular-enabled UAV communication with UAVs as new
aerial users served by the ground base stations (GBSs), and UAV-assisted
cellular communication with UAVs as new aerial communication platforms serving
the terrestrial users. Then, we focus on the former paradigm and study a new
UAV trajectory design problem subject to practical communication connectivity
constraints with the GBSs. Specifically, we consider a cellular-connected UAV
in the mission of flying from an initial location to a final location, during
which it needs to maintain reliable communication with the cellular network by
associating with one GBS at each time instant. We aim to minimize the UAV's
mission completion time by optimizing its trajectory, subject to a
quality-of-connectivity constraint of the GBS-UAV link specified by a minimum
receive signal-to-noise ratio target. To tackle this challenging non-convex
problem, we first propose a graph connectivity based method to verify its
feasibility. Next, by examining the GBS-UAV association sequence over time, we
obtain useful structural results on the optimal UAV trajectory, based on which
two efficient methods are proposed to find high-quality approximate trajectory
solutions by leveraging graph theory and convex optimization techniques. The
proposed methods are analytically shown to be capable of achieving a flexible
trade-off between complexity and performance, and yielding a solution that is
arbitrarily close to the optimal solution in polynomial time. Finally, we make
concluding remarks and point out some promising directions for future work.
