## 4 Discussion  
Each modulation scheme involves a balance between spectral efficiency and robustness to the noise. In the analysis performed, we considered different modulation orders, reaching up to 32 PSK, 16 DPSK, 128 QAM, and OFDM with 64 QAM subcarriers. Based on the results obtained in Figure 6, it can be seen that PSK modulation is a fairly robust modulation scheme to noise, especially at lower levels than PSK, such as BPSK or QPSK in earth-satellite links. These schemes have a simple coding factor and are more resistant to interference but sacrifice spectral efficiency because they transmit a limited number of bits per symbol. For satellite applications where signal reliability is important, such as communications in difficult atmospheric conditions (rain or gas attenuation), PSK is a good choice. DPSK modulation, although similar to PSK modulation, offers additional robustness because information is transmitted through the phase differences between consecutive symbols. This makes DPSK more robust to fading effects and other propagation problems, as proof, it offers the best link margin according to Figure 7. However, compared to PSK, the spectral efficiency may be reduced because more advanced coding schemes cannot be applied as efficiently. QAM modulation provides the highest spectral efficiency compared with the previous two schemes, allowing more bits to be transmitted per symbol. However, this efficiency comes at a price in terms of noise robustness. QAM is much more sensitive to channel degradations such as noise and interference and requires a higher Eb/No ratio to maintain an acceptable BER. OFDM has the advantage of a high spectral efficiency, its robustness to interference and Doppler effects is relevant in moving satellite communications, and it makes a suitable choice for systems that require a reliable and stable connection, even under difficult conditions. These trade-offs must be considered when designing a satellite communications system. For example, under ideal conditions, such as low-noise channels, OFDM and QAM may be preferable due to their higher transmission rate. For links subject to severe weather conditions or interference, PSK or DPSK might be better choices, as they provide more stable performance at the expense of lower spectral efficiency. In the case of multi-orbital scenarios, the differences between modulation schemes are influenced not only by the noise robustness or the error correction code but also by the dynamic variations of the propagation channel, such as Doppler effects and the rapid changes in the trajectory of LEO and MEO satellites. In the context of LEO-MEO communications, the Doppler effect is significant, and signal phase stability becomes essential. According to the results obtained in Figure 8, DPSK offers the highest link margin, which suggests that this modulation is more suitable for this type of link in combination  
Figure 14: Link margin vs. modulation scheme for Starlink connection: (**a**) Convolutional code; (**b**) LDPC code; (**c**) Reed-Solomon code; (**d**) Golay code. with hard convolutional codes. However, in conditions of stabilized channel and effective Doppler control, OFDM could be a better option due to its high spectral efficiency and good margin. For MEO-GEO links, OFDM becomes the preferred option under typical propagation channel conditions in combination with Reed-Solomon codes. If the amount of errors increases significantly from different methods, BDPSK would be the modulation that would ensure the highest performance, as shown in Figure 10. For typical LEO-GEO links, OFDM offers an advantage in terms of spectral efficiency and link margin. It can increase transmission performance and ensure a high transmission rate in combination with the Golay codes, as seen in Figure 12.  
To show the quantitative impact of the codes used, we refer to 16 DPSK modulation at BER \(1\times 10^{-6}\). The hard convolutional code offers a coding gain of 3.2 dB, directly improving the link margin.