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

In this paper, 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 beamforming capable antennas 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. We assume Rician fading distribution over the links between the UAVs, then, we calculate the distribution of the channels under hovering fluctuations. Also, we derive the closed form expressions for successful transmission probability. 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. Instead, we solve the optimization problem for its lower bound. Maximization problem for the achieved lower bound is equivalent to maximize the main problem. Then, we use some approximations to convert it to a low complex problem to find the solution. We use the entity of the low complex problem to obtain the allocated power for each UAV and in the following, the problem becomes convex which is solved by KKT conditions to obtain the location of UAV-BS. The theoretical results show that optimizing the lower bound probability achieves the suboptimal solution for power assignment and placement problem, which is verified by simulation results.