  Optimal deployment of unmanned aerial vehicles (UAVs) as communication relays
is studied for fixed-rate variable-power systems. The considered setup is a set
of ground transmitters (GTs) wishing to communicate with a set of ground
receivers (GRs) through the UAVs. Each GT-GR pair communicates through only one
selected UAV and have no direct link. Two different UAV selection scenarios are
studied: In centralized selection, a decision center assigns an optimal UAV
depending on the locations of all terminals. In distributed selection, a GT
selects its relaying UAV using only the local knowledge of its distances to the
UAVs. For both selection scenarios, the optimal tradeoff between the UAV and GT
power consumptions are determined using tools from quantization theory.
Specifically, the two extremal regimes of one UAV and very large number of UAVs
are analyzed for a path loss exponent of $2$. Numerical optimization of UAV
locations are also discussed. Simulations are provided to confirm the
analytical findings.
