  LoRa is one of the promising techniques for enabling Low Power Wide Area
Networks (LPWANs) for future Internet-of-Things (IoT) devices. Although LoRa
allows flexible adaptations of coverage and data rates, it is subject to
intrinsic types of interferences: co-SF interferences where end-devices with
the same Spreading Factors (SFs) are subject to collisions, and inter-SF
interferences where end-devices with different SFs experience collisions. Most
current works have considered perfect orthogonality among different SFs. In
this work, we provide a theoretical analysis of the achievable LoRa throughput
in uplink, where the capture conditions specific to LoRa are included. Results
show the accuracy of our analysis despite approximations, and the throughput
losses from imperfect SF orthogonality, under different SF allocations. Our
analysis will enable the design of specific SF allocation mechanisms, in view
of further throughput enhancements.
