  With growing popularity, LoRa networks are pivotally enabling Long Range
connectivity to low-cost and power-constrained user equipments (UEs). Due to
its wide coverage area, a critical issue is to effectively allocate wireless
resources to support potentially massive UEs in the cell while resolving the
prominent near-far fairness problem for cell-edge UEs, which is challenging to
address due to the lack of tractable analytical model for the LoRa network and
its practical requirement for low-complexity and low-overhead design. To
achieve massive connectivity with fairness, we investigate the problem of
maximizing the minimum throughput of all UEs in the LoRa network, by jointly
designing high-level policies of spreading factor (SF) allocation, power
control, and duty cycle adjustment based only on average channel statistics and
spatial UE distribution. By leveraging on the Poisson rain model along with
tailored modifications to our considered LoRa network, we are able to account
for channel fading, aggregate interference and accurate packet overlapping, and
still obtain a tractable and yet accurate closed-form formula for the packet
success probability and hence throughput. We further propose an iterative
balancing (IB) method to allocate the SFs in the cell such that the overall
max-min throughput can be achieved within the considered time period and cell
area. Numerical results show that the proposed scheme with optimized design
greatly alleviates the near-far fairness issue, and significantly improves the
cell-edge throughput.
