RIS-assisted LoRa networks with diversity: Impact of hardware impairments and phase noise

This paper investigates the performance of downlink LoRa networks assisted by reconfigurable intelligent surfaces (RIS) and diversity techniques. We derive closed-form expressions for the coverage probability (Pcov) under four scenarios: phase noise at the RIS only, hardware impairments at both the gateway and end devices (EDs), the combined effect of both impairments, and an ideal benchmark case. The analysis is carried out within a unified framework that is valid for any number of RIS elements, providing key insights into the influence of hardware impairment levels, gateway transmit power, and the diversity order as the number of RIS elements grows large. The results reveal that coverage probability improves with transmit power but deteriorates under more severe hardware impairments, while the diversity order scales directly with the number of RIS elements. Monte Carlo simulations validate the analytical findings and confirm that the ideal scenario achieves the best performance, followed in order by the phase noise, hardware impairment, and combined impairment cases.