A tractable stochastic geometry model of coverage and an approach to energy efficiency estimation in LPWAN networks

In this paper, we consider two types of low-power wide area network (LPWAN): LoRa wide area network (LoRaWAN) and narrow-band internet of things (NBIoT) network. We first propose a framework to calculate the average number of retransmissions in LoRaWAN networks and NBIoT networks based on stochastic geometry. Combining the average number of retransmissions, we give an approximate method to calculate both networks' energy efficiency and estimate the battery lifetime in LoRaWAN networks and NBIoT networks. The numerical results show that the battery lifetime is mainly influenced by the number of active UEs and the spreading factor in LoRaWAN networks and sleeping mode in NBIoT networks, when the data size transmitted each day is fixed. In NBIoT networks, the UEs can work for much longer with power saving mode (PSM) than with extended idle-mode discontinuous reception cycle (eDRX), even exceeding LoRaWAN networks in some cases.