## 2 Materials and Methods
### Our Proposed Solution: A Combination of CR and MODCOD Techniques and Its Applications  
Our proposed solution combines the CR concept in the underlay paradigm and MODCOD technique, in the ACM mode, to mitigate FS interferences on low-orbit satellite downlinks. Calculation steps were developed in the cognitive paradigm for the operability of the exploitation technique. The following spectrum exploitation dimensions were considered: (i) power \(P\); (ii) frequency \(f_{c}\); (iii) modulation MOD; (iv) coding COD; and (vi) bandwidth \(BW\). The objective was to enable the satellite transmitter to improve the SINR (signal-to-interference plus noise ratio) at the receiver input. Through link budget simulations for distinct standardized DVB-S2X--MODCOD configurations, we performed the troubleshooting strategy applied to spectral coexistence and data throughput maximization by adapting the MODCOD functionality. The variation of \(m\) bits per symbol in APSK modulations combined with appropriate code rates produced the bandwidth values as a function of both the symbol rate and the required SINR. Considering that the specified BER is a function of SINR for each MODCOD adapted during each satellite pass over the ground station in the presence of interfering signals, the MODCOD selection depends on the interference-to-noise ratio (INR), which directly results from the measurement of \(E_{b}/(I_{0}+N_{0})\) performed by the receiving system. This adaptive technique is employed in the transmission channel of the WFI camera on the CBERS-4 and AMAZONIA-1 (AMZ-1) satellites, with a bit rate of 51.28 Mbps. Thus, the established MODCODs and their properties: designations, identifications (_ID_), spectral efficiencies (\(\eta_{tot}\)), the relationship between \(E_{b}/N_{0}\) and \(E_{S}/N_{0}\), and the effective bandwidth of the modulated carrier are shown in Table 2. For example, based on Table 2, we can evaluate that for the MODCOD scheme QPSK \(3/5\) (_ID_ = 8), the required \(E_{b}/N_{0}\) for the specified BER (\(10^{-7}\)) has a low value of \(E_{b}/N_{0}\) = 1.480 dB, which increases the link margin and allows for operating with higher INR values. Figure 5: Depiction of images from C-4 WFI (26 days INPE’s catalog). Source: adapted from DGI-INPE (2018): (**a**) complete set; (**b**) set with failures. In Figure 6, the results of Table 3 are graphically represented. We can see that as the interference power increases, the INR also increases, and the system should automatically select the appropriate MODCOD to support the current INR value while maintaining a constant bit rate transmission. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**MODCOD** & _ID_ & _float_ & \(E_{b}/N_{0}\) **(dB) Ideal Frame of 64,800 Bits** & \(E_{b}/N_{0}\) **(dB)** & **Symbol BW (MHz)** \\ \hline QPSK 1/3 & 9 & 0.656448 & \(-\)1.24 & 0.587996705 & 78.12 \\ QPSK 3/5 & 8 & 1.188304 & 2.23 & 1.480724410 & 43.15 \\ QPSK 5/6 & 7 & 1.654663 & 5.18 & 2.992904443 & 30.99 \\ QPSK 9/10 & 6 & 1.788612 & 6.42 & 3.894838598 & 28.67 \\ SPSK 3/4 & 5 & 2.2282142 & 7.91 & 4.430060434 & 23.01 \\ SPSK 5/6 & 4 & 2.478562 & 9.35 & 5.408002130 & 20.69 \\
8 PSK 9/10 & 3 & 2.679207 & 10.98 & 6.699937308 & 19.14 \\
16 APSK 5/6 & 2 & 3.300184 & 11.61 & 6.424618456 & 15.54 \\
32 APSK 8/9 & 1 & 4.397854 & 15.69 & 9.257591924 & 11.66 \\ \hline \hline \end{tabular} Note: given the system spectral efficiency \(\eta_{tot}\) = the ratio between the energy per information bit and single-sided noise power spectral density: \(E_{b}/N_{0}=E_{s}/N_{0}-10\text{log}_{10}(\eta_{tot})\).  
\end{table} 
Table 2: Adaptive MODCOD in DVB-S2X.