Capacity of a LoRaWAN Cell

In this paper, we consider the problem of evaluating the capacity of a LoRaWAN cell. Previous analytical studies investigated LoRaWAN performance in terms of the Packet Delivery Ratio (PDR) given a number of devices around a gateway and its range. We improve the model for PDR by taking into consideration that the following two events are dependent: successful capture during a collision and successful frame decoding despite ambient noise. We consider a realistic traffic model in which all devices generate packets with the same inter-transmission times corresponding to the duty cycle limitation at the highest SF, regardless of the distance to the gateway. Based on the developed model, we optimize the Spreading Factor (SF) boundaries to even out PDR throughout the cell. We validate the analytical results with simulations, compare our model with previous work, and experimentally validate the hypothesis of Rayleigh fading for the LoRa channel. The important conclusion from our results is that a LoRa cell can handle a relatively large number of devices. We also show that there is practically no inter-SF interference (cross interference between transmissions with different SFs): interference from higher SFs comes from nodes located farther away, so they face greater attenuation and thus, they do not interfere with lower SF nodes.