This paper aims to exploit the fundamental limits on the downlink coverage and spatial throughput performances of a cellular network consisting 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 simultaneously associate 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, we propose the multi-cell coverage probability and the volume spectral efficiency of the network, derive their explicit low-complexity expressions and find their upper limits 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.Index Terms-Unmanned aerial vehicle network, millimeter wave, coverage, throughput, cell association, stochastic geometry. arXiv:1905.06099v3 [cs.IT] 18 Jul 2019 by a clustered channel model consisting of small-scale fading and angle-ofdeparture (AoD)-based transmit array gain vectors. Here we thus assume that all UAVs have a uniform linear array and are able to perfectly align their beam with the angle-of-departure (AoD) of their array in order to maximize their antenna array gain from them to their serving users.

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