  The support for aerial users has become the focus of recent 3GPP
standardizations of 5G, due to their high maneuverability and flexibility for
on-demand deployment. In this paper, probabilistic caching is studied for
ultra-dense small-cell networks with terrestrial and aerial users, where a
dynamic on-off architecture is adopted under a sophisticated path loss model
incorporating both line-of-sight and non-line-of-sight transmissions.
Generally, this paper focuses on the successful download probability (SDP) of
user equipments (UEs) from small-cell base stations (SBSs) that cache the
requested files under various caching strategies. To be more specific, the SDP
is first analyzed using stochastic geometry theory, by considering the
distribution of such two-tier UEs and SBSs as Homogeneous Poisson Point
Processes. Second, an optimized caching strategy (OCS) is proposed to maximize
the average SDP. Third, the performance limits of the average SDP are developed
for the popular caching strategy (PCS) and the uniform caching strategy (UCS).
Finally, the impacts of the key parameters, such as the SBS density, the cache
size, the exponent of Zipf distribution and the height of aerial user, are
investigated on the average SDP. The analytical results indicate that the UCS
outperforms the PCS if the SBSs are sufficiently dense, while the PCS is better
than the UCS if the exponent of Zipf distribution is large enough. Furthermore,
the proposed OCS is superior to both the UCS and PCS.
