Analysis and Optimization for Large-Scale LoRa Networks: Throughput Fairness and Scalability

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.