LoRa networks are pivotally enabling Long Range connectivity to low-cost and power-constrained user equipments (UEs) in a wide area, whereas a critical issue is to effectively allocate wireless resources to support potentially massive UEs while resolving the prominent near-far fairness issue, which is challenging due to the lack of tractable analytical model and the practical requirement for low-complexity and low-overhead design. Leveraging on stochastic geometry, especially the Poisson rain model, we derive (semi-) closed-form formulas for the aggregate interference distribution, packet success probability and hence system throughput in both single-cell and multi-cell setups with frequency reuse, by accounting for channel fading, random UE distribution, partial packet overlapping, and/or multi-gateway packet reception. The analytical formulas require only average channel statistics and spatial UE distribution, which enable tractable network performance evaluation and incubate our proposed Iterative Balancing (IB) method that quickly yields high-level policies of joint spreading factor (SF) allocation, power control, and duty cycle adjustment for gauging the average max-min UE throughput or supported UE density with rate requirements. Numerical results validate the analytical formulas and the effectiveness of our proposed optimization scheme, which greatly alleviates the near-far fairness issue and reduces the spatial power consumption, while significantly improving the cell-edge throughput as well as the spatial (sum) throughput for the majority of UEs, by adapting to the UE/gateway densities.

翻译：洛拉网络在帮助长距离连接广域中低成本和受电力限制的用户设备方面起着关键作用,而一个关键问题是有效分配无线资源,以支持潜在的大规模电子设备,同时解决突出的近距离公平问题,因为缺乏可移植的分析模型以及低复杂度和低顶部设计的实际要求,这具有挑战性。利用随机网络性能测量,特别是波瓦松雨模型,我们得出(半)封闭式公式,用于集成干扰分布、包包成功概率以及因此在以频率再利用的单细胞和多细胞设置中的系统吞吐量,方法是核算频道疲软、随机UE分布、部分包重叠和/或多端包接收等突出的问题。分析公式只需要平均频道统计数据和低复杂度设计的实际要求,从而能够进行可移植的网络性能评估,并插入我们提议的循环平衡(IB)方法,以快速产生高水平的联合传播系数分配、权力控制以及义务周期调整的系统,从而通过最大分析性平流率,从而大大地调整我们的拟议最高和最高比率,从而降低平均平流率。