arXiv:2411.01977v2 Announce Type: replace Abstract: In the realm of digital communication, understanding and mitigating the probability of error is crucial, particularly in Rayleigh fading channels where signal impairments are common. This paper presents a unified approach to derive the probability of error formulations for two-users NOMA systems operating in Rayleigh fading channels. The methodologies and findings outlined in this study are essential for IoT applications in construction and civil engineering. Specifically, the derived error probability formulations can be employed to enhance the reliability and efficiency of IoT-based monitoring systems in these sectors. By optimizing communication protocols, the proposed approach ensures accurate data transmission, thereby facilitating real-time monitoring and decision-making processes in construction sites and civil infrastructure projects.