# Neural Network SNR Prediction for Improved Spectral Efficiency in Land Mobile Satellite Networks
## 3 A Novel Channel State Prediction and MODCOD Selection Strategy
### MODCOD Selection Evaluation  
After the initial evaluation that shows the ability of the algorithms to perform SNR predictions, the next step was to evaluate the algorithms in terms of spectral efficiency. For spectral efficiency evaluation, all operation points of the DVB-S2X protocol [11] (short-frame communication) were used. For the considered MODCODs, the spectral efficiencies (\(M_{i}\)) and the SNR thresholds (\(T(M_{i})\)), minimal SNR value needed to operate with the efficiency, are listed in Table 3. Based on the algorithms' predicted SNR, the system takes the highest possible MODCOD that could be successfully used with that predicted SNR.  
The first level of evaluation was performed for each channel separately. So, the evaluation for each ML algorithm was performed for 90 different channels. To ensure the evaluations relate to practical use cases, margins were determined on the training set so that the transmission error on the training set is lower than 0.01 where possible or lower than 0.001+unavoidable error (samples where the SNR is lower than the lowest operation threshold). This margin was extracted for each algorithm and scenario separately (simple search with a resolution of 0.5 dB) and was then applied to the predictions on the appropriate test set. In this way, all algorithms have a comparatively fixed error rate, and the performances in terms of spectral efficiency could be adequately performed. The determined error rate threshold of 0.01 was selected as the highest possible error rate that might be considered usable for transmission, and further evaluation was performed on two channels as it is considered that combining two channels would create a scenario where, at least in theory, a lower error rate could be obtained.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**MODCOD** & \(M_{i}\) **[b/s/Hz]** & \(T(M_{i})\) **[dB]** \\ \hline BPSK-S 1/5 & 0.1 & \(-\)9.9 \\ BPSK-S 11/45 & 0.12 & \(-\)8.3 \\ BPSK 1/5 & 0.2 & \(-\)6.1 \\ BPSK 4/15 & 0.27 & \(-\)4.9 \\ BPSK 1/3 & 0.33 & \(-\)3.72 \\ QPSK 11/45 & 0.49 & \(-\)2.5 \\ QPSK 4/15 & 0.53 & \(-\)2.24 \\ QPSK 14/45 & 0.62 & \(-\)1.46 \\ QPSK 7/15 & 0.93 & 0.6 \\ QPSK 8/15 & 1.07 & 1.45 \\ QPSK 32/45 & 1.42 & 3.66 \\
8 PSK 8/15 & 1.60 & 4.71 \\
8 PSK 26/45 & 1.73 & 5.52 \\
16 APSK 7/15 & 1.87 & 5.99 \\
16 APSK 8/15 & 2.13 & 6.93 \\
16 APSK 26/45 & 2.31 & 7.66 \\
16 APSK 3/5 & 2.40 & 8.1 \\
16 APSK 32/45 & 2.84 & 9.81 \\
32 APSK 2/3 & 3.33 & 11.41 \\
32 APSK 32/45 & 3.56 & 12.18 \\ \hline \hline \end{tabular}
\end{table}
Table 3: MODCODs, the spectral efficiencies (\(M_{i}\)) and the SNR thresholds (\(T(M_{i})\)).  
The final step of the evaluation was performed using two channels, where each combination of channels within the same level of shadowing is considered. This was performed for Ol and NN2 to provide an easier comparison since NN2 has been shown to have better performance in terms of spectral efficiency than all other algorithms. For this evaluation, a greedy selection was performed by the algorithms, i.e., for each point in time, the channel with the higher predicted SNR was selected. This creates a single array of SNR prediction values for the final algorithm predictions. The true labels were selected based on the labels for the channel that was selected for that corresponding point in time. The same principle for margin estimation was performed, extracting the margin on the training set and then applying it to the test set for OI and NN2 separately. The resolution for the search was also 0.5 dB, but the goal transmission error was 0.001 since two channels would often allow for a lower transmission error. Of course, if the transmission error of 0.001 was unattainable, the margin would be determined to reach the unavoidable error +0.0001 on the training set. The comparison between the NN2 and OI is performed by showing a relative improvement in spectral efficiency from the NN2 algorithm, calculated as \(\left(M_{i}^{NN2}-M_{i}^{OI}\right)/M_{i}^{OI}\).