# Neural Network SNR Prediction for Improved Spectral Efficiency in Land Mobile Satellite Networks
## 4 Results and Discussion  
### SNR Prediction  
The initial testing results present the MSE between the predictions and labels on the test set for various channels and for the five observed algorithms. The OI is considered a baseline algorithm as it is simple to implement and is often used in the literature, while the ML models were expected to offer improvement. In terms of MSE performance (as well as spectral efficiency), the implemented LR and SVM performed the same or worse than the regular NN, so for an easier comparison, only the results of the NN are presented in this and further sections as it will be a good representative of the best performing simple ML algorithms. The MSE values for all observed scenarios are shown in Table 4, while Figures 2-4 show the same metric visually for light shadowing, average shadowing and heavy shadowing, respectively. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & & \multicolumn{4}{c}{**MSE [dB\({}^{2}\)]**} \\ \hline
**SNR [dB]** & \(f_{Dm}\) **= 5 Hz** & \(f_{Dm}\) **= 25 Hz** & \(f_{Dm}\) **= 50 Hz** & \(f_{Dm}\) **= 75 Hz** & \(f_{Dm}\) **= 100 Hz** \\ \hline \multicolumn{6}{c}{Light shadowing} \\ \hline  
\hline \hline \end{tabular}
\end{table} 
Table 4: The MSE [dB\({}^{2}\)] achieved on the test set for various scenarios, OI/NN/NN2. When observing the values from Table 4, it can be concluded that based on different scenarios, the MSE can have quite a large range of values, from 0.2 dB\({}^{2}\) to 38.2 dB\({}^{2}\) for the outdated information. The vast range of these values shows that based on different channel characteristics, different expectations for SNR prediction quality should be present. The ranges of MSE for NN and NN2 have the same minimum value as the OI, and this value is so low that it can be concluded that the implementation of additional algorithms  
Figure 4: The achieved MSE for SNR prediction on the test set for various scenarios under heavy shadowing conditions. Figure 3: The achieved MSE for SNR prediction on the test set for various scenarios under average shadowing conditions. Figure 2: The achieved MSE for SNR prediction on the test set for various scenarios under light shadowing conditions. outside of OI can be completely redundant in certain scenarios, e.g., \(f_{Dm}=5\) and higher expected SNR values. On the other hand, the maximum MSE for NN is quite lower than the maximum value for outdated information, amounting to 18.5 dB\({}^{2}\), which is less than half of the maximum value of the OI and almost half of the OI MSE value for that respective scenario. Notably, the NN2 has a consistently higher MSE than the NN but also provides an improvement when compared to the OI. This is to be expected as the loss function of the NN2 is not made to optimize for the MSE or exact prediction; rather, it is created to force the network to rarely overestimate the SNR value. For pure SNR prediction, this is impractical, but it will later be shown that this has benefits when observing practical applications and spectral efficiency. The results shown in Figures 2-4 intuitively show the overall trends of the MSE in terms of various algorithms and channel scenarios. Notably, it can be observed that for all algorithms, the MSE is higher when the \(f_{Dm}\) parameter rises. This is expected as the higher values of \(f_{Dm}\) correspond to channels that have less predictable changes, and both OI and neural networks have difficulties performing when more rapid SNR changes are present. It is also evident that for a very low \(f_{Dm}\), regardless of SNR, the algorithm performs quite similarly. As presented in Table 4, improvements exist in most scenarios, but they are so minor that the development of special algorithms for the prediction of SNR can be considered redundant. On the other hand, for high \(f_{Dm}\) values, the improvements that the neural networks provide become more evident. It is interesting to note that the discrepancy between the performance of NN and NN2 also increases with the increase in \(f_{Dm}\), regardless of shadowing conditions.