## 1 Introduction  
The integration of 5G terrestrial networks with satellite systems presents a transformative opportunity to achieve seamless, ubiquitous connectivity on a global scale, particularly for the rapidly expanding Internet of Things (IoT) in smart cities [1; 2; 3]. As 5G technology continues to evolve, its promise of ultra-low latency, high data rates, and massive device connectivity can extend to areas traditionally underserved by terrestrial networks through the incorporation of satellite communication systems [4; 5]. This 5G-satellite integrated network framework is poised to play a crucial role in enabling reliable communication in remote and rural areas, enhancing connectivity for critical applications such as autonomous vehicles, remote sensing, and global IoT networks [6; 7]. The convergence of 5G and satellite systems introduces a new paradigm in communication infrastructure, merging the high-capacity, low-latency characteristics of 5G with the extensive coverage provided by satellite networks. This hybrid approach addresses the limitations of terrestrial-only networks, enabling continuous connectivity across challenging environments, including densely populated urban areas and isolated rural regions. For IoT applications in smart cities, this integration enables consistent, high-quality data exchange across a vast number of connected devices, essential for efficient urban management, environmental monitoring, and public safety [3; 8]. Research in 5G-satellite convergence has gained considerable traction, focusing on the potential and challenges of integrating terrestrial and satellite networks for diverse applications. [PERSON] et al. [9] highlight the technical challenges of integrating low-Earth-orbit (LEO) satellite networks with 5G, addressing issues such as handover mechanisms, interference management, and quality-of-service (QoS) maintenance. [PERSON] et al. [8] also discuss the architecture of integrated 5G-satellite networks, emphasizing the need for efficient resource allocation and interference coordination mechanisms to maintain reliable connectivity in high-density IoT deployments. Existing studies have also addressed the unique propagation challenges posed by these networks, given the differing altitudes and coverage zones of terrestrial and satellite systems. [PERSON] et al. [10] explore propagation characteristics specific to high-frequency bands in 5G and satellite communication, analysing how atmospheric absorption, scattering, and reflection impact signal quality. Their findings underline the importance of accounting for environmental factors, especially in dense urban settings where building interference and multipath effects are prevalent. [PERSON] et al. [11] propose adaptive modulation and coding techniques to mitigate propagation losses in hybrid networks, emphasizing the role of environment-specific models in ensuring robust performance. A critical aspect of ensuring seamless connectivity in 5G-satellite integrated networks is the accurate modelling of signal propagation. The two-ray model has been widely used due to its simplicity and effectiveness in capturing the interaction between direct and reflected signals in terrestrial communication environments [12; 13; 14]. The model, which considers both line-of-sight (LOS) and ground-reflected paths, is well suited for urban areas with significant ground infrastructure [12]. In the context of 5G-satellite convergence, however, using the two-ray model presents additional complexities due to varied altitudes and satellite signal paths. [PERSON] et al. [9] suggest that while the two-ray model is beneficial for understanding ground-based reflections in 5G-satellite integrated networks, it requires further adaptation to account for factors such as signal delay, Doppler shift, and the Earth's curvature. Recent works by [PERSON] et al. [15] propose modified versions of the two-ray model, incorporating satellite-specific propagation characteristics, thereby improving predictive accuracy in 5G-satellite integrated networks.