Optimal Placement of UAVs for Minimum Outage Probability

Abstract

We consider multiple unmanned aerial vehicles (UAVs) serving a density of ground terminals (GTs) as base stations. The objective is to minimize the outage probability of GT-to-UAV transmissions. Optimal placement of UAVs under different UAV altitude constraints and GT densities is studied. A practical variant of the Rician fading model, which has been developed by Azari <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">et al.</i> (2018) specifically for UAV systems, is used to model the communication channels. First, the structure of optimal deployments is determined when the common altitude constraint is large. For a wide class of GT densities, it is shown that all UAVs should be placed to the same location in an optimal deployment. A design implication is that one can use a single multi-antenna UAV as opposed to multiple single-antenna UAVs without loss of optimality. Next, using a random deployment argument, a general upper bound on the optimal outage probability is found for any density of GTs and any number of UAVs. Further, for any arbitrary user density, centralized and distributed numerical algorithms are designed using particle swarm optimization and modified gradient descent algorithms, respectively. Simulations show that our distributed algorithm provides almost optimal results even with considerably reduced communication and sensing ranges at the UAVs.