Energy-minimizing 3D circular trajectory optimization of rotary-wing UAV under probabilistic path-loss in constrained hotspot environments

In this paper, we consider a Software Defined Networking (SDN)/Network Function Virtualized (NFV) networked computing system, which is composed of a serving Rotary Wing (RW) Unmanned Aerial Vehicle (UAV), a Ground Controller Station (GCS) and a number of resource-limited (possibly, heterogeneous) Ground Users (GUs) that randomly move in environments affected by fading-induced probabilistic path-loss. The focus of this paper is on the joint and adaptive optimization of the 3D trajectory parameters (i.e., altitude, radius, and speed) of the RW-UAV that circulates over the served hotspot area for providing communication and/or computing support to the GUs. The objective is the minimization of the RW-UAV propulsion energy under constraints on the maximum allowed average path-loss, maximum tolerated outage probability, and finite beam-width of the UAV antenna. Due to the acceleration-dependent terms present in the considered RW-UAV energy propulsion model, the formulated problem is non-convex, and up to now, its solution still appears not to be addressed in the literature. Hence, to tackle this challenging problem: 1) we develop a (seemingly new) convexification approach to turn the problem into a Geometric Programming (GP) one; 2) after characterizing the related feasibility conditions, we develop an adaptive solving approach that relies on primal-dual gradient-based iterations; and, then, 3) we perform a joint co-design of the main blocks of the SDN/NFV-based communication/computing architectures equipping the serving RW-UAV and controlling GCS, in order to provide support for the orchestration of the computing/communication microservices possibly required by the served GUs. The conducted numerical tests confirm that the performance gains of the proposed optimization framework against the ones of a number of baselines may reach 22%, while the corresponding performance gaps against the ultimate performance of a brute force search-based benchmark remain typically limited up to 3%-4%.