## 1 Introduction  
Satellite communications are part of the global telecommunications infrastructure, offering crucial services such as remote area connectivity, disaster response, and vital communication channels [1, 2]. Satellites enable extensive coverage due to their strategic placement, proving indispensable for transmitting signals across vast distances. Specifically, geostationary orbit (GEO) satellites are essential in this framework because their fixed position relative to the Earth makes them perfect for applications requiring constant and consistent coverage over broad areas, such as TV broadcasting, meteorological services, and emergency communication systems [3]. The increasing trend towards the development and deployment of multi-orbital systems consists of a combination of satellite placement on Low Earth Orbit (LEO), Medium Earth Orbit (MEO), and GEO to achieve global connectivity, low latency, and operational redundancies. These systems combine the strengths of each orbit type: extensive coverage from GEO satellites, the lower latency and higher user density of LEO satellites, and the balance between the two offered by the MEO satellites. Advanced technologies currently under development include dynamic inter-satellite routing and integration with terrestrial networks for increased efficiency and adaptability in several applications, such as emergency communications, rural connectivity, and IoT services [4]. The diversity of modulation techniques employed in these systems is a critical component, with each method bringing specific characteristics that impact the efficiency and reliability of communications. These modulation techniques vary from traditional types like Phase Shift Keying (PSK), Differential Phase Shift Keying (DPSK), and Frequency Modulation (FM) to more advanced, spectrum-efficient methods such as Quadrature Amplitude Modulation (QAM) and Orthogonal Frequency-Division Multiplexing (OFDM) [5; 6]. These advanced techniques are crucial for enhancing transmission rates and minimizing transmission errors. Unlike classic ground-to-satellite links, these multi-orbit systems involve inter-satellite communications, which require efficient methods for managing transmissions between satellites in different orbits, each with its own propagation characteristics and signal delays. The handover between satellites is one challenge, as the transition of connections must be smooth to avoid data loss, especially in LEO and MEO networks, where satellites are in continuous motion relative to ground stations. In addition, dynamic interference management becomes essential, given that multi-orbital networks must operate in a complex environment, where multiple signals can affect link quality. In this context, it is essential to analyze the performance of modulation schemes used in these dynamic environments and how they can be optimized to improve transmission reliability and efficiency. The calculation of the link budget is fundamental for the efficient design and functioning of satellite communication systems [7; 8]. This procedure enables engineers to assess and refine system performance by analyzing signal loss due to various factors, including rain attenuation, space loss, and interference. This evaluation ensures that there is adequate margin to compensate for unexpected variations in the communication channel, thereby preserving service quality. The margin of the satellite system is calculated based on a detailed analysis of the factors contributing to losses and the probability of variations of these factors. The evaluation and adjustment of the margin is part of the satellite system optimization process, especially in multi-orbital systems, where transitions between satellites in different orbits require maintaining a stable connection to avoid interruptions in essential services [9]. Most of the existing studies in the literature focus on the static link budget, but the sensitivity to different types of modulations and dynamic conditions in multi-orbit networks is not sufficiently explored [2; 9].