Optimal deployment of sustainable UAV networks for providing wireless coverage.

Each UAV is constrained in its energy storage and wireless coverage, and it consumes most energy when flying to the top of the target area, leaving limited leftover energy for hovering at its deployed position and providing wireless coverage. The literature largely overlooks this sustainability issue of UAV network deployment to prolong the UAV networku0027s residual lifetime for providing wireless coverage, and we aim to maximize the minimum leftover energy storage among all UAVs after their deployment. We also practically consider the No-Fly-Zones (NFZs) constraint to tell that, UAVs cannot be deployed to anywhere even if their energy storages allow. When all UAVs are deployed from a common UAV station, we propose an optimal deployment algorithm, by jointly optimizing UAVsu0027 flying distances on the ground and final service altitudes in the sky. We also show that, due to NFZs, the optimization problem becomes more difficulty and the whole UAV network consumes more energy. We solve it optimally in $O(n log n)$ time for a number n of UAVs. Moreover, when $n$ UAVs are dispatched from different initial locations, we first prove that any two UAVs will not fly across each other in the flight as long as they have the same initial energy storage, and then design a fully polynomial time approximation scheme (FPTAS) of time complexity $O(n log frac{1}{epsilon})$ to arbitrarily approach the optimum with relative error $epsilon$. Further, we consider that UAVs may have different initial energy storages under the constraint of NFZs, and we prove this problem is NP-hard. Despite of this, we successfully propose a heuristic algorithm to solve it by balancing the efficiency and computation complexity well. Finally, we extend the FPTAS to a 3D scenario and validate theoretical results by extensive simulations.