To provide a reliable wireless uplink for users in a given ground area, one
can deploy Unmanned Aerial Vehicles (UAVs) as base stations (BSs). In another
application, one can use UAVs to collect data from sensors on the ground. For a
power-efficient and scalable deployment of such flying BSs, directional
antennas can be utilized to efficiently cover arbitrary 2-D ground areas. We
consider a large-scale wireless path-loss model with a realistic
angle-dependent radiation pattern for the directional antennas. Based on such a
model, we determine the optimal 3-D deployment of N UAVs to minimize the
average transmit-power consumption of the users in a given target area. The
users are assumed to have identical transmitters with ideal omnidirectional
antennas and the UAVs have identical directional antennas with given half-power
beamwidth (HPBW) and symmetric radiation pattern along the vertical axis. For
uniformly distributed ground users, we show that the UAVs have to share a
common flight height in an optimal power-efficient deployment. We also derive
in closed-form the asymptotic optimal common flight height of N UAVs in terms
of the area size, data-rate, bandwidth, HPBW, and path-loss exponent
