A New Closed-Form Expression of the Coverage Probability for Different QoS in LoRa Networks

Abstract

In this work, coverage probability (Pcov) and area spectral efficiency (ASE) of LoRa networks with multiple classes of quality-of-service (QoS) of end-devices (EDs) are investigated. In particular, an approximated but tractable mathematical framework is proposed to compute a recent definition of the Pcov. Based on the proposed framework, the closed-form expressions of both Pcov and ASE are provided. Moreover, the trends of both metrics are unveiled that respect to some key parameters such as the density of the EDs, the transmit power, and the spreading factor (SF). Our findings show that depending on networks parameters, the ASE is either a unimodal function or monotonically increasing as a function of EDs’ density. In addition, the optimal value of EDs’ density that maximizes the ASE are computed in closed-form expression too. Finally, Monte Carlo simulations are provided to verify the correctness of our framework.