Placement and Power Assignment for Hierarchical UAV Networks Under Hovering Fluctuations in mmWave Communications

In this article, we investigate the successful transmission probability of an aerial cellular network in which an unmanned aerial vehicle (UAV), as a macrocell base station (UAV-BS) serves other UAVs as aerial users. The antennas with beamforming capability are mounted on the UAVs, to increase the throughput of the network. The random effects of inner forces such as controlling errors or outer forces like the air conditions, result in the random fluctuations in the hovering UAVs. We assume Rician fading distribution over the links between the UAV-BS and other UAVs. Then, we calculate the distribution of the corresponding channel gain under hovering fluctuations and we derive the closed form expressions for successful transmission probability for each user. Defining an optimization problem on the average successful transmission probability of the network, we obtain the best placement of UAV-BS along with the resource allocation. The problem turns out to be a non-convex problem and time consuming via numerical exhaustive search methods. We obtain a lower bound for the average successful transmission probability and we solve the optimization problem for this lower bound. Maximization problem for the achieved lower bound is equivalent to maximize the main problem. Using some approximations, we convert the problem to a low complex one, then, the problem becomes convex which is solved by KKT conditions and yields the location of UAV-BS. The theoretical results reveal the influence of fluctuations on the throughput of the network and show that optimizing the lower bound probability achieves the suboptimal solution for power assignment and placement problem, which is verified by simulation results.