Mathematical model of LoRaWAN channel access

While 3GPP has been developing NB-IoT, the market of Low Power Wide Area Networks has been mastered by cheap and simple Sigfox and LoRa/LoRaWAN technologies. Being positioned as having an open standard, LoRaWAN has attracted also much interest from the research community. Specifically, many papers address the efficiency of its PHY layer. However MAC is still underinvestigated. Existing studies of LoRaWAN do not take into account the acknowledgement and retransmission policy, which may lead to incorrect results. In this paper, we carefully take into account the peculiarities of LoRaWAN transmission retries and show that it is the weakest issue of this technology, which significantly increases failure probability for retries. The main contribution of the paper is a mathematical model which accurately estimates how packet error rate depends on the offered load. In contrast to other papers, which evaluate LoRaWAN capacity just as the maximal throughput, our model can be used to find the maximal load, which allows reliable packet delivery.