  Aerial relays have been regarded as an alternative and promising solution to
extend and improve satellite-terrestrial communications, as the probability of
line-of-sight transmissions increases compared with adopting terrestrial
relays. In this paper, a cooperative satellite-aerial-terrestrial system
including a satellite transmitter (S), a group of terrestrial receivers (D),
and an aerial relay (R) is considered. Specifically, considering the randomness
of S and D and employing stochastic geometry, the coverage probability of R-D
links in non-interference and interference scenarios is studied, and the outage
performance of S-R link is investigated by deriving an approximated expression
for the outage probability. Moreover, an optimization problem in terms of the
transmit power and the transmission time over S-R and R-D links is formulated
and solved to obtain the optimal end-to-end energy efficiency for the
considered system. Finally, some numerical results are provided to validate our
proposed analysis models, as well as to study the optimal energy efficiency
performance of the considered system.
