  Providing broadband connectivity to airborne systems using ground based
cellular networks is a promising solution as it offers several advantages over
satellite-based solutions. However, limited range of terrestrial base stations
is a key challenge in full realization of this approach. This paper addresses
this problem by proposing a mathematical framework for range extension
leveraging large number of antennas at the base station. In contrast to prior
works where range is not considered as a design parameter, we model the signal
to noise ratio as a function of both number of antennas as well as the range in
line-of-sight ground-to-air systems. This allows us to derive analytical
expressions to determine the number of antennas required to increase range in
different frequency bands and tracking and non tracking scenarios.
