A Finer ALOHA-Based Analytical Model for LR-FHSS Performance Evaluation

Long-Range Frequency-Hopping Spread-Spectrum (LR-FHSS), the latest LoRaWAN physical layer standard, was designed to enhance the uplink capacity of these networks, a prerequisite for direct-to-satellite Internet of Things deployments in areas lacking terrestrial infrastructures. As LR-FHSS still employs an unslotted ALOHA channel-access scheme, its network behavior can be accurately captured using the classical ALOHA model. This paper introduces the Multi-Class Multi-Channel ALOHA-based Model (<tex>$\text{MC}^{2} \text{AMB}$</tex>), a novel analytical model that accurately approximates packet delivery success ratios and other metrics, enabling comprehensive evaluation of LR-FHSS networks without requiring computationally expensive simulations. Simulation results demonstrate that <tex>$\text{MC}^{2} \text{AMB}$</tex> accurately estimates network performance across various density scenarios, outperforming state-of-the-art models in this regard. Furthermore, the model enables the to determine optimal values for key parameters by leveraging its derivatives, providing valuable insights for network optimization.