## 2 Materials and Methods
Margin is used to compensate for uncertainties or unexpected variations in propagation conditions or equipment performance [21]. It can be defined as the difference between the received \(\frac{E_{b}}{N_{o}}\) and the required \(\frac{E_{b}}{N_{o}}\), providing a back-up measure against unexpected link damage, as in Equation (16). \[EIRP[dBW]=P_{TxHPA}[dBW]-OBO_{TxHPA}[dB]-L_{TxFeder}[dB]-L_{TxOther}[dB]+G_{Tx}[ dBi]-L_{Radome}[dB] \tag{1}\]7The estimation of the \(\frac{E_{b}}{N_{o}}\) ratio is closely related to the type of coding used in the system: convolutional, block, Turbo, etc. [21; 22; 23]. Each kind of coding introduces a specific performance regarding noise and error tolerance that influences the minimum threshold required to ensure the reliability of the transmission. The type of coding determines the system design directly; therefore, it gives an idea of how robust the link would be under high-noise or interfering conditions. It is an important factor toward the optimization of the overall performance of the satellite communication network. In this paper we examine the impact of different error correction codes on link margin and overall system performance in multi-orbit satellite communication networks. For the ground-to-GEO link, convolutional coding is applied. This coding method improves the system's bit error rate performance by introducing redundancy, allowing for better error correction. In LEO-MEO inter-satellite links, where dynamic channel variations are more pronounced due to satellite motion, Low-Density Parity-Check (LDPC) codes are used. These codes provide superior noise resilience compared to convolutional codes, making them suitable for rapidly changing propagation environments. For MEO-GEO links, which experience fewer rapid signal variations but require robust error correction against burst errors, Reed-Solomon (RS) codes are implemented. Finally, in LEO-GEO communications, where severe channel variations occur, extended Golay codes are used. These codes, with their large minimum distance between codewords, are highly effective in mitigating errors. From the perspective of modulation types, we analyzed four modulation schemes commonly used in satellite communications: PSK, DPSK, QAM, and OFDM. PSK encodes data by varying the phase of the carrier signal, offering good noise resilience, with lower-order schemes like BPSK and QPSK being widely used for their robustness in satellite links. DPSK improves on PSK by encoding information in the phase difference between consecutive symbols, eliminating the need for precise phase synchronization, which is beneficial in dynamic satellite environments. QAM combines phase and amplitude variations to increase spectral efficiency, making it ideal for high data rate applications, although it requires a higher signal-to-noise ratio (SNR) to maintain performance. OFDM utilizes multiple orthogonal subcarriers to enhance resistance against multipath fading and Doppler shifts, making it well-suited for dynamic multi-orbit satellite networks where signal conditions fluctuate. As we can see, we have a lot of elements that are quantified in determining the link budget and system performance. Next, we propose to determine the margin for different types of modulations used in multi-orbit satellite communication systems.