Low-power wide-area network (LPWAN) technologies are gaining momentum for Internet-of-things applications since they promise wide coverage to a massive number of battery operated devices using grant-free medium access. LoRaWAN, with its physical (PHY) layer design and regulatory efforts, has emerged as the widely adopted LPWAN solution. By using chirp spread spectrum modulation with qausi-orthogonal spreading factors (SFs), LoRa PHY offers coverage to wide-area applications while supporting high-density of devices. However, thus far its scalability performance has been inadequately modeled and the effect of interference resulting from the imperfect orthogonality of the SFs has not been considered. In this paper, we present an analytical model of a single-cell LoRa system that accounts for the impact of interference among transmissions over the same SF (co-SF) as well as different SFs (inter-SF). By modeling the interference field as Poisson point process under duty cycled ALOHA, we derive the signal-to-interference ratio distributions for several interference conditions. Results show that, for a duty cycle as low as 0.33%, the network performance under co-SF interference alone is considerably optimistic as the inclusion of inter-SF interference unveils a further drop in the success probability and the coverage probability of approximately 10% and 15%, respectively, for 1500 devices in a LoRa channel. Finally, we illustrate how our analysis can characterize the critical device density with respect to cell size for a given reliability target.

中文翻译：

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不完全正交下的LoRa网络的可伸缩性分析

低功耗广域网（LPWAN）技术在物联网应用中获得了发展势头，因为它们有望通过无授权媒体访问的方式为大量电池供电的设备提供广泛的覆盖范围。LoRaWAN凭借其物理（PHY）层设计和监管工作，已成为被广泛采用的LPWAN解决方案。通过使用具有正交正交扩展因子（SF）的线性调频扩展频谱调制，LoRa PHY可以覆盖广域应用，同时支持高密度设备。但是，到目前为止，它的可扩展性性能还没有得到足够的建模，并且还没有考虑到由SF的不完全正交性引起的干扰影响。在本文中，我们提出了一种单细胞LoRa系统的分析模型，该模型说明了在相同SF（co-SF）和不同SF（inter-SF）上的传输之间的干扰影响。通过在占空比ALOHA下将干扰场建模为泊松点过程，我们得出了几种干扰条件下的信号干扰比分布。结果表明，对于低至0.33％的占空比，仅在co-SF干扰下的网络性能就相当乐观，因为将SF间干扰包括在内会显着降低成功率，并且覆盖率进一步降低约10％ LoRa频道中的1500个设备分别为15％和15％。最后，我们说明了我们的分析如何针对给定的可靠性目标来表征与单元大小有关的关键设备密度。