LAUSR

This letter uses stochastic geometry and queuing theory to study the scalability of long-range (LoRa) networks, accounting for duty cycling restrictions and imperfect spreading factor (SFs) orthogonality. The scalability is characterised by the joint boundaries of device density and traffic intensity per device. Novel cross-correlation factors are used to quantify imperfect SF-orthogonality. Our results show that a proper characterisation of LoRa orthogonality extends the scalability of the network. They also highlight that for low/medium densities decreasing the SF extends the spanned spectrum of sensing applications characterised by their traffic requirements (i.e., sensing rate). However, for high density $(>10^{4}$ nodes/Km $^{2}$ ), the Pareto frontiers converge to a stability limit governed by the SF allocation scheme and the predefined capture thresholds. The results further evince the importance of capturing threshold distribution among the SFs to mitigate the unfair latency.