In low-power wide area networks (LPWAN), a considerable number of end devices (EDs) communicate with the gateway in a certain area, whereas for transmitted data, a low data rate and high latency are allowed. Long-range (LoRa), as one of the LPWAN technologies, considers pure ALOHA and chirp spread spectrum (CSS) in the media access control (MAC) and physical (PHY) layers such that it can improve the energy efficiency while mitigating inter-cell interference (ICI). This paper investigates the system throughput of LoRa networks under the assumption that the interferences between EDs for exclusive regions are ignored using CSS. In order to establish an analytical model for the performance of LoRa, we introduce the pure ALOHA capture model, which is the power threshold model. For this model, we assume that the interfering power is proportional to the length of the time overlapped. In addition, we discuss LoRa gain by comparing the total throughput of LoRa with that of non-CSS.
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