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