# Neural Network SNR Prediction for Improved Spectral Efficiency in Land Mobile Satellite Networks
## 4 Results and Discussion
### Double Channel Spectral Efficiency  
The final evaluation step is the one where the performance of the proposed method is evaluated for two communication channels. Here, only the NN2 and OI are compared for an easier overview of the results, especially considering that the NN2 approach has provided better results for the single channel spectral efficiency improvement. Figure 11 shows the results for light shadowing, Figure 12 for average shadowing and Figure 13 for heavy shadowing. Figure 11: The achieved spectral efficiencies on the test set for various scenarios under light shadowing conditions using two channels, comparing OI and NN2. The color of each square represents a relative improvement of the achieved spectral efficiency calculated as \((M_{i}^{\mathrm{NN2}}-M_{i}^{\mathrm{OI}})\,/\,M_{i}^{\mathrm{OI}}\). Figure 11 shows how the combination of two channels can influence the performance of the proposed system. Each larger square represents a scenario where the channels \(f_{Dm}\) s are fixed (e.g., second row, third column, \(f_{Dm}1\) = 25 Hz, \(f_{Dm}2\) = 50 Hz), while the smaller squares correspond to various combinations of expected SNR. The type of square, such as red outline, regular outline and hatched, corresponds to the range of transmission errors for that scenario, and the color scale corresponds to the relative improvement in spectral efficiency. The relative improvement is above 0 for all scenarios, i.e., there are no scenarios where the OI outperformed the NN2. Secondly, the red squares outline the scenarios in which the desired transmission error rate was achieved, i.e., it was under 0.001. It can be seen that for a low \(f_{Dm}\), it is always achievable, but as the \(f_{Dm}\) rises, this becomes more difficult, and for the \(f_{Dm}\) = 100 Hz, regardless of SNR, the proposed method achieved a transmission error rate lower than 0.01 but not lower than 0.001. On the other hand, it can be seen that the relative improvement of spectral efficiency provided by the NN2 is much more prominent for the scenarios with a higher \(f_{Dm}\) (as seen in dark blue) as opposed to the ones for lower \(f_{Dm}\) (seen in white or light blue). This shows that depending on the scenario, different goals can be achieved and that the final goal has to be considered through the design of the algorithm since the most straightforward solution (such as NN) might not provide the best results. Overall, scenarios where lower errors are obtainable present ones where SNR is easier to predict; hence, OI initially had good performance, which is why the relative improvement offered by the NN2 is not as high as for some other scenarios. Figure 12 shows how the increase in shadowing affects the performance of the system. When compared to the light shadowing conditions, many of the results are in darker blue, showing a greater relative improvement than the one achieved for light shadowing. Secondly, it can be seen that aside from a couple of scenarios of both channels having an \(f_{Dm}\) of 25 Hz, an error rate lower than 0.001 could not be achieved if one of the channels does not have an \(f_{Dm}\) of 5 Hz. Thirdly, it can be seen that for some scenarios of higher \(f_{Dm}\)s and lower expected SNRs, not even an error rate of 0.01 could be achieved. This is due to the unavoidable error rate, in the same manner as it was present for single channel evaluation. The results shown in Figure 13 show several outcomes that could be considered expected and several ones that provide new information. Firstly, the scenarios where the unavoidable error is above 0.01 are more prominent, as can be seen for lower expected SNR scenarios where multiple fields are hatched. Secondly, there are more scenarios where the transmission error could be lower than 0.001 for higher \(f_{Dm}\)s when compared to the average shadowing. This might seem unexpected as more frequent and more heavy shadowing is not a favorable condition.