  This paper aims to exploit the fundamental limits on the downlink coverage
and spatial throughput performances of a cellular network comprised of a tier
of unmanned aerial vehicle (UAV) base stations (BSs) using the millimeter wave
(mmWave) band and a tier of ground BSs using the ultra high frequency (UHF)
band. To reduce handover signaling overhead, the ground BSs take charge of
control signaling delivery whereas the UAVs are in charge of payload data
transmission so that users need to be simultaneously associated with a ground
BS and a UAV in this network with a control-data plane-split architecture. We
first propose a three-dimensional (3D) location distribution model of the UAVs
using stochastic geometry which is able to generally characterize the positions
of the UAVs in the sky. Using this 3D distribution model of UAVs, two
performance metrics, i.e., multi-cell coverage probability and volume spectral
efficiency, are proposed. Their explicit low-complexity expressions are derived
and their upper limits are found when each of the UAVs and ground BSs is
equipped with a massive antenna array. We further show that the multi-cell
coverage probability and the volume spectral efficiency can be maximized by
optimally deploying and positioning the UAVs in the sky and thereby their
fundamental maximal limits are found. These important analytical findings are
validated by numerical simulations.
