  Using a drone as an aerial base station (ABS) to provide coverage to users on
the ground is envisaged as a promising solution for beyond fifth generation
(beyond-5G) wireless networks. While the literature to date has examined
downlink cellular networks with ABSs, we consider an uplink cellular network
with an ABS. Specifically, we analyze the use of an underlay ABS to provide
coverage for a temporary event, such as a sporting event or a concert in a
stadium. Using stochastic geometry, we derive the analytical expressions for
the uplink coverage probability of the terrestrial base station (TBS) and the
ABS. The results are expressed in terms of (i) the Laplace transforms of the
interference power distribution at the TBS and the ABS and (ii) the distance
distribution between the ABS and an independently and uniformly distributed
(i.u.d.) ABS-supported user equipment and between the ABS and an i.u.d.
TBS-supported user equipment. The accuracy of the analytical results is
verified by Monte Carlo simulations. Our results show that varying the ABS
height leads to a trade-off between the uplink coverage probability of the TBS
and the ABS. In addition, assuming a quality of service of 90% at the TBS, an
uplink coverage probability of the ABS of over 85% can be achieved, with the
ABS deployed at or below its optimal height of typically between 250-500 m for
the considered setup.
