  Low Power Wide Area (LPWA) networks are making spectacular progress from
design, standardisation, to commercialisation. At this time of fast-paced
adoption, it is of utmost importance to analyse how well these technologies
will scale as the number of devices connected to the Internet of Things (IoT)
inevitably grows. In this letter, we provide a stochastic geometry framework
for modelling the performance of a single gateway LoRa network, a leading LPWA
technology. Our analysis formulates unique peculiarities of LoRa, including its
chirp spread-spectrum modulation technique, regulatory limitations on radio
duty cycle, and use of ALOHA protocol on top, all of which are not as common in
today's commercial cellular networks. We show that the coverage probability
drops exponentially as the number of end-devices grows due to interfering
signals using the same spreading sequence. We conclude that this fundamental
limiting factor is perhaps more significant towards LoRa scalability than for
instance spectrum restrictions. Our derivations for co-spreading factor
interference found in LoRa networks enables rigorous scalability analysis of
such networks.
