  In this paper, we present a device-to-device (D2D) transmission scheme for
aiding long-range frequency hopping spread spectrum (LR-FHSS) LoRaWAN protocol
with application in direct-to-satellite IoT networks. We consider a practical
ground-to-satellite fading model, i.e. shadowed-Rice channel, and derive the
outage performance of the LR-FHSS network. With the help of network coding,
D2D-aided LR-FHSS transmission scheme is proposed to improve the network
capacity for which a closed-form outage probability expression is also derived.
The obtained analytical expressions for both LR-FHSS and D2D-aided LR-FHSS
outage probabilities are validated by computer simulations for different parts
of the analysis capturing the effects of noise, fading, unslotted ALOHA-based
time scheduling, the receiver's capture effect, IoT device distributions, and
distance from node to satellite. The total outage probability for the D2D-aided
LR-FHSS shows a considerable increase of 249.9% and 150.1% in network capacity
at a typical outage of 10^-2 for DR6 and DR5, respectively, when compared to
LR-FHSS. This is obtained at the cost of minimum of one and maximum of two
additional transmissions per each IoT end device imposed by the D2D scheme in
each time-slot.
