## 4 Evaluation
### Simulation Results
Though Case 3 provides the largest gain, the minimum \(E_{\mathrm{b}}/N_{0}\) in the access link to use time-packing is larger than in Cases 1 and 2. Figure 13: End-to-end throughput versus \(E_{\mathrm{b}}/N_{0}\) in the access link for a regenerative satellite that receives a NB-IoT frame encapsulated in a DVB-S2(X) satellite frame (\(\mathrm{SNR_{fl}}=15\,\mathrm{dB}\)). NB-IoT code rates: 1/3 (red), 2/3 (blue) and 0.96 (magenta). DVB-S2(X) code rates: 2/3 (squares), 0.8 (circles) and 0.9 (diamonds). Solid (dashed-) lines with (un)filled markers: \(\mathrm{BLER}\leq 10^{-2}\) requirement (not) fulfilled. Wind speed: \(v=21\,\mathrm{m/s}\). Diameter of telescope aperture: \(W_{0}=10\,\mathrm{cm}\). Figure 15 shows the envelope of the throughput for all cases in terms of the overlapping factor. From these figures, it is possible to observe that for Cases 1 and 3, the larger is the overlapping factor, the larger is the maximum throughput that is feasible when \(\delta=40\%\). On the contrary, for Case 2, the maximum throughput is achieved when \(\delta=15\%\)  
Figure 14: End-to-end throughput envelope (left and upper-right) and gain in the throughput envelope of time-packed versus no-time-packed (lower-right), represented as a function of the \(E_{\mathrm{b}}/N_{0}\) in the access link for Cases 1–3. Overlapping of \(\delta=0\%\) (solid red line), \(\delta=15\%\) (dotted blue line), \(\delta=25\%\) (dashed cyan line), and \(\delta=40\%\) (dashed-dotted magenta line). Figure 14d shows the gain in throughput of time-packed with respect to no-time-packed; here, Case 1 is represented with a continuous purple line, Case 2 is plotted with a dotted brown line, and Case 3 is shown with a dashed green line. Wind speed: \(v=21\,\mathrm{m}/\mathrm{s}\). Diameter of telescope aperture: \(W_{0}=10\,\mathrm{cm}\). Next, Figure 16 presents the envelope of the throughput for all cases (Figure 16a) and the percentage gain of Cases 2 and 3 with respect to Case 1 (Figure 16b). Studying Figure 16a, it is possible to conclude that Cases 2 and 3 have a better throughput than Case 1 in most cases. Thus, Case 1 is used as benchmark to assess the goodness of Cases 2 and 3. From this figure, it can also be noted that the regeneration of the NB-IoT signal enables to lower the minimum \(E_{\text{b}}/N_{0}\) to about 1.5 and 4 dB for Case 2 and Case 3, respectively. Regarding the gain in throughput for Cases 2 and 3 with respect to Case 1, for \(E_{\text{b}}/N_{0}\) values lower than \(-2\) dB, the best option is to use Case 2; for an \(E_{\text{b}}/N_{0}\) ranging between \(-2\) and 4 dB, both Cases 2 and 3 provide practically the same throughput. Finally, for \(E_{\text{b}}/N_{0}\) larger than 4 dB, the best strategy is to encapsulate the NB-IoT frames into the DVB-S2(X) ones (Case 3). Finally, Figures 17-19 show the BLER of the three relay cases under study. Figure 15: End-to-end envelope of throughput for all cases under study versus \(E_{\text{b}}/N_{0}\) in the access link. Case 1 (continuous red line), Case 2 (dotted blue line) and Case 3 (dashed magenta line). Wind speed: \(v=21\) m/s. Diameter of telescope aperture: \(W_{0}=10\) cm. Figure 16: End-to-end throughput envelope for all cases under study versus \(E_{\text{b}}/N_{0}\) in the access link. Case 1 (continuous red line), Case 2 (dotted blue line), and Case 3 (dashed magenta line) (left side). On the right, gain in the end-to-end throughput of Cases 2 (continuous red line) and 3 (dashed blue line) with respect to Case 1. Wind speed: \(v=21\,\text{m}/\text{s}\). Diameter of telescope aperture: \(W_{0}=10\,\text{cm}\). Figure 17: End-to-end BLER versus \(E_{\text{b}}/N_{0}\) in the access link for a NB-IoT frame transmitted over a non-regenerative satellite (Detect-and-Forward) (\(\text{SNR}_{\text{fl}}=15\,\text{dB}\)). NB-IoT code rates: 0.2222 (red square), 0.259 (red circle), 0.3 (red diamond), 0.444 (blue square), 0.5319 (blue circle), 0.6 (blue diamond), 0.6386 (magenta square), 0.7678 (magenta circle) and 0.8628 (magenta diamond).