On the Spectral Efficiency of LoRa Networks: Performance Analysis, Trends and Optimal Points of Operation

In the present paper a closed-form framework is derived for the analysis and optimization of the coverage probability (Pcov) and of the area spectral efficiency (ASE) in long-range (LoRa) networks. The proposed framework exploits stochastic geometry tools to associate the Pcov and the ASE to the end device (ED) transmit power and to the ED density. The analysis reveals the trends of the Pcov and of the ASE curves, with respect to both of the two parameters, while the robustness of the framework holds even at the asymptotic cases. Building upon the derived framework, the analysis demonstrates that no joint global optimum exists that jointly maximizes the Pcov over both parameters, suggesting that the optimization of the Pcov must be performed separately, for the two key network parameters considered. As opposed to that, the analysis demonstrates that a set of global optima exists that jointly maximize the ASE over both parameters, and these global maxima are subsequently derived in closed form. Thus, the derived framework fully characterizes the performance of LoRa networks, while defining in closed form the optimal points of operation that can be proven of significant value, for the transceiver and network design, of practical LoRa networks.