Optimal deployment and movement of multiple unmanned aerial vehicles (UAVs) is studied. The considered scenario consists of several ground terminals (GTs) communicating with the UAVs using variable transmission power and fixed data rate. First, the static case of a fixed geographical GT density is analyzed. Using high resolution quantization theory, the corresponding best achievable performance (measured in terms of the average GT transmission power) is determined in the asymptotic regime of a large number of UAVs. Next, the dynamic case where the GT density is allowed to vary periodically through time is considered. For one-dimensional networks, an accurate formula for the total UAV movement that guarantees the best time-averaged performance is determined. In general, the tradeoff between the total UAV movement and the achievable performance is obtained through a Lagrangian approach. A corresponding trajectory optimization algorithm is introduced and shown to guarantee a convergent Lagrangian. Numerical simulations confirm the analytical findings. Extensions to different system models and performance measures are also discussed.

We consider multiple unmanned aerial vehicles (UAVs) serving a density of ground terminals (GTs) as mobile base stations. The objective is to minimize the outage probability of GT-to-UAV transmissions. In this context, the optimal placement of UAVs under different UAV altitude constraints and GT densities is studied. First, 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. Lower bounds on the performance of optimal deployments are also determined. The upper and lower bounds are combined to show that the optimal outage probability decays exponentially with the number of UAVs for GT densities with finite support. Next, the structure of optimal deployments are studied when the common altitude constraint is large. In this case, 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. Numerical optimization of UAV deployments are carried out using particle swarm optimization. Simulation results are also presented to confirm the analytical findings.Index Terms-UAV-aided communications, optimal placement, outage probability.

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