The meta distribution of the SIR for LoRaWANs with power control

To reduce energy consumption, a device in a LoRa (Long Range) wide area network (LoRaWAN) needs to adjust its transmit power according to the distance from its tagged Gateway (GW). It is important to measure the performance of the LoRaWANs uplink with power control. In this paper, we focus on the analysis of the coverage probability and the meta distribution of the signal-to-interference ratio (SIR) for a LoRaWAN uplink with fractional power control (FPC). The LoRaWAN uplink is analysed based on the Poisson point process (PPP). We present the possible reductions in transmit power of devices whilst ensuring that the received signal power is greater than the receiver sensitivity. We derive the coverage probability of a LoRaWAN uplink, and show how power control influences it. Finally, utilizing the meta distribution of SIR, the fine-grained information of the LoRaWAN is revealed. The results show that the power control greatly increases the successful probability of edge-devices with little effect on the probability of inner-devices if an appropriate FPC coefficient is chosen. This is because the LoRa signal can be demodulated at a very low required SIR threshold.