## 4 Evaluation
### Simulation Results
When comparing time-packing versus no-time-packing, results show that time-packing signaling provided a better throughput, and the gain was depended on the \(E_{\text{b}}/N_{0}\) of the access link. Figure 12 shows the throughput for each code rate and overlapping factor for Case 2 (Decode-and-forward with NB-IoT). From this figure, it is possible to observe that the regeneration of the NB-IoT signal in the satellite permits to use also medium code rates (i.e., \(R_{\text{c,iot}}=0.4444\)) with overlapping factor \(\delta=0\) and \(15\%\). Therefore, it means that the largest throughput is not obtained with the largest possible overlapping factor (i.e., \(\delta=40\%\)) and low code rates (i.e., \(R_{\text{c,iot}}=0.3\)) as in the previous case, but with a low-to-moderate overlapping factor (i.e., \(\delta=15\%\)) and a medium code rate (i.e., \(R_{\text{c,iot}}=0.4444\)). Figure 11: End-to-end throughput versus \(E_{\text{b}}/N_{0}\) in the access link for a NB-IoT frame (\(\text{SNR}_{\text{fl}}=15\,\text{dB}\)). 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), \(0.8628\) (magenta diamond). Solid (dashed-) lines with (un)filled markers: \(\text{BLER}\leq 10^{-2}\) requirement (not)fulfilled. Wind speed: \(v=21\) m/s. Diameter of telescope aperture: \(W_{0}=10\,\text{cm}\). Similarly, Figure 13 shows the throughput for each code rate and overlapping factor for Case 3 (Decode-and-forward with NB-IoT and DVB-S2(X)). Results of this figure show that the best code rate to use in the optical feeder link is \(R_{c,\text{dvb}}=0.6666\). For the NB-IoT system, in contrast, the best option is \(R_{c,\text{tot}}=0.3333\) when the \(E_{\text{b}}/N_{0}\) in the access link varies between \(-1\) and \(5\,\text{dB}\), \(R_{c,\text{tot}}=0.6666\) when the \(E_{\text{b}}/N_{0}\) in the access link grows from \(5\) to \(9\,\text{dB}\), and finally \(R_{c,\text{tot}}=0.96\) for \(E_{\text{b}}/N_{0}\) values beyond \(9\,\text{dB}\) in the access link. Figure 12: End-to-end throughput versus \(E_{\text{b}}/N_{0}\) in the access link for a NB-IoT frame in a regenerative satellite (Decode-and-Forward with NB-IoT) (\(\text{SNR}_{\text{fl}}=15\,\text{dB}\)). 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). Solid (dashed-) lines with (un)filled markers: \(\text{BLER}\leq 10^{-2}\) requirement (not) fulfilled. Wind speed: \(v=21\) m/s. Diameter of telescope aperture: \(W_{0}=10\,\text{cm}\). Figure 14a-c show the envelope of the throughput for Cases 1-3 and the different overlapping factors under study. From these figures, it is possible to observe that for Cases 1 and 3, the larger is the overlapping factor, the higher is the maximum throughput that is achieved when \(\delta=40\%\). On the contrary, for Case 2, the maximum throughput is achieved when the overlapping factor is \(\delta=15\%\). Figure 14d shows the percentage gain in throughput of the time-packed versus no-time-packed signalling. From this subfigure, it is possible observe that for when the access link \(E_{\mathrm{b}}/N_{0}\) is between \(-2\) and \(5\,\mathrm{dB}\), the percentage gain of Case 1 is in the order of \(50\%\). For other values of \(E_{\mathrm{b}}/N_{0}\), this gain falls down to about \(10\%\). For Case 2, the percentage gain on the throughput envelope of time-packed schemes is larger than \(40\%\) when the \(E_{\mathrm{b}}/N_{0}\) varies between \(-4\) and \(1\,\mathrm{dB}\). However, for values of \(E_{\mathrm{b}}/N_{0}\) larger than \(1\,\mathrm{dB}\) in the access link, this gain in the throughput envelope reduces to about \(20\%\). For Case 3, we have that for an \(E_{\mathrm{b}}/N_{0}\) larger than \(0\,\mathrm{dB}\), the minimum gain in the throughput envelope is \(40\%\).