This paper explores the effects of three-dimensional (3D) antenna radiation pattern and backhaul constraint on optimal 3D path planning problem of an unmanned aerial vehicle (UAV), in interference prevalent downlink cellular networks. We consider a cellular-connected UAV that is tasked to travel between two locations within a fixed time and it can be used to improve the cellular connectivity of ground users by acting as a relay. Since the antenna gain of a cellular base station changes significantly with the UAV altitude, the UAV can increase the signal quality in its backhaul link by changing its height over the course of its mission. This problem is non-convex and thus, we explore the dynamic programming technique to solve it. We show that the 3D optimal paths can introduce significant network performance gain over the trajectories with fixed UAV heights.
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