# Neural Network SNR Prediction for Improved Spectral Efficiency in Land Mobile Satellite Networks
## 4 Results and Discussion
### Single Channel Spectral Efficiency
The visual representations of the obtained spectral efficiencies are shown in Figures 5-7, indicating clearly how the trends of spectral efficiencies behave for different shadowing, \(f_{Dm}\) and SNR conditions. NN2 is consistently better than the OI, with NN also being better in most cases. For an SNR of 0 dB, the improvement seems negligible, but as the SNR increases, the difference between spectral efficiency becomes more prominent. The shapes of the presented curves also change based on the amount of shadowing. It can be seen in Figure 5 that the spectral efficiency rises mostly linearly with the SNR for most of the light shadowing conditions, regardless of the algorithm, but the trends become more curved as the \(f_{Dm}\) increases. For average shadowing, the trends seem more curved, and for heavy shadowing, almost no curve looks linear. This conclusion also stands for all algorithms, meaning that regardless of the achieved improvement, the relationship between SNR and spectral efficiency has a different trend based on the type of channel that is observed. Observing the results from Figure 8, it can be seen more clearly that NN2 has a consistently better performance than OI and almost always a better performance than NN. The improvement in spectral efficiency that the NN2 provides is not drastic in comparison to OI or NN, as can be seen, but it is consistent. This clearly indicates the importance of considering different scenarios, as developing complex algorithms can provide limited improvement in certain ones. The consistency shows that the proposed method is conceptually good, but for practical applications, it is important to weigh the benefits of the spectral efficiency improvement against the complexity of integrating complex models into a system. When comparing NN2 and NN, it is important to note that, as opposed to the simple SNR prediction, NN2 has better performance. This is due to the introduced margin and the need for a transmission error rate no greater than 0.01. Since there are many MODCODs considered for communication, their operations thresholds are not that far apart. Hence, if the neural networks predict an SNR value that is much higher than the operation point of the best possible MODCOD, no data will be transmitted, and a transmission error will occur. This is why the NN2 approach of underestimating values is useful because it is less likely to make such mistakes, so the determined margin ensuring a low error rate will not be as high and will not bring down the spectral efficiency improvements as much as it will for NN. Figure 10: The achieved spectral efficiency improvement in % compared to the OI, on the test set for various scenarios under heavy shadowing conditions using a single channel. Scenarios where the transmission error is \(<\)0.01 are shown in blue, and scenarios where the transmission error is \(>\)0.01 are shown in red. In terms of achieving a transmission error rate no greater than 0.01 for light shadowing specifically, Figure 8 recapitulates that for an expected SNR of 0 dB, it is not possible, and no approach achieves this, but it is also shown that for the SNR of 3 dB and an \(f_{Dm}\) of 5 Hz, none of the algorithms could obtain a transmission error rate lower than 0.01. This channel does not fall under the category of difficult or unpredictable, as there is light shadowing, and the \(f_{Dm}\) is quite small. However, since the SNR is not high, it is always possible that the SNR values happen to be distributed in such a way that the outage probability is higher than 0.01, which is exactly what happened in this case. This stands in line with the results obtained for average and heavy shadowing, as for both, there was an error rate higher than 0.01 for all scenarios where the expected SNR was equal to 3 dB. One more interesting occurrence is that for an \(f_{Dm}\) of 100 Hz and an expected SNR of 3 dB, the NN did not achieve an error rate lower than 0.01, while NN2 and OI did.