## 4 Evaluation
### Simulation Results  
The results provided in this section evaluate the BLER and throughput of the three aforementioned NB-IoT satellite relaying architectures in the following aspects:  
1. Evaluation of the end-to-end BLER and throughput when the \(E_{\mathrm{b}}/N_{0}\) of the feeder link varies from 2 to 22 dB in steps of 1 dB (see Figure 9), the SNR of the access link is 20 dB, the wind speed is 21 m/s, and the NB-IoT code rates are \(R_{\mathrm{c,tot}}=0.3333\), 0.66667, and 0.95556. There is no time-packing (\(\delta=0\%\)) and configuration is Case 1 (Detect-and-Forward NB-IoT). The throughput of Figure 9 is the \(\mathrm{THR}\big{(}0,R_{\mathrm{c,tot}}\big{)}\) of (34);
2. Evaluation of the end-to-end BLER and throughput when the \(E_{\mathrm{b}}/N_{0}\) of the access link varies from \(-8\) to 12 dB in steps of 1 dB (see Figure 10), the SNR of the feeder link is 15, 20, and 25 dB, the wind speed is \(v=10\), 21, and 30 m/s, and the NB-IoT code rates are \(R_{\mathrm{c,tot}}=0.3333\), 0.66667 and 0.95556. There is no time-packing (\(\delta=0\%\)) and the tested configuration is Case 1 (Detect-and-Forward NB-IoT). The throughput of Figure 10 is \(\mathrm{THR}\big{(}0,R_{\mathrm{c,tot}}\big{)}\) of (34);
3. Evaluation of the throughput for Case 1 (see Figure 11): Detect-and-Forward NB-IoT when the SNR of the feeder link is 15 dB, the \(E_{\mathrm{b}}/N_{0}\) of the access varies from \(-8\) to 12 dB, and the code rates of the NB-IoT and overlapping factors are as defined in Section 4.2. The throughput of Figure 11 corresponds to \(\mathrm{THR}\big{(}\delta,R_{\mathrm{c,tot}}\big{)}\) of (34);
4. Evaluation of the throughput for Case 2 (see Figure 12): Decode-and-Forward NB-IoT when the SNR of the feeder link is 15 dB, the SNR of the access varies from 0 to 20 dB, and the code rates of the NB-IoT and overlapping factors are as defined in Section 4.2. The throughput of Figure 12 corresponds to \(\mathrm{THR}\big{(}\delta,R_{\mathrm{c,tot}}\big{)}\) of (34);
5. Evaluation of the throughput for Case 3 (see Figure 13): Detect-and-Forward NB-IoT encapsulated in DVB-S2(X) frames when the SNR of the feeder link is 15 dB, the SNR of the access varies from 0 to 20 dB, and the code rates of the DVB-S2(X) and NB-IoT and overlapping factors are defined as in Section 4.2. The throughput of Figure 13 corresponds to \(\mathrm{THR}\big{(}\delta,R_{\mathrm{c,tot}}\big{)}\) of (34);
6. Evaluation of the envelope of the throughput when the overlapping factor \(\delta\) remains constant for all cases under study (see Figure 14a-c) when the SNR of the feeder link is 15 dB, the SNR of the access varies from 0 to 20 dB, and the code rates of the DVB-S2(X)/NB-IoT frames and the overlapping factors are defined in Section 4.2. The throughput of these figures corresponds to \(\mathrm{THR}(\delta)^{*}\) of (35);
7. Evaluation of the gain in throughput of time-packing signaling with respect to no-time-packing, as shown in Figure 14d. The SNR of feeder link is 15 dB, the SNR of the access varies from 0 to 20 dB. This gain is denoted as \(G_{\mathrm{thr}}(\%)\) and is computed following (38);
8. Comparison among the envelope of the throughput for all cases under study (see Figure 15a-d) in terms of the overlapping factor \(\delta\), when the SNR of feeder link is 15 dB, the SNR of the access link varies from 0 to 20 dB, and the code rates of the DVB-S2(X)/NB-IoT frames and overlapping factors are defined as in Section 4.2. The throughput of these figures corresponds to \(\mathrm{THR}(\delta)^{*}\) of (35);
9. Comparison of the envelope of the throughput for all cases under study (see Figure 16a) when the SNR of the feeder link is 15 dB, the SNR of the access link varies from 0 to 20 dB. The throughput plotted in this figure is denoted as \(\mathrm{THR}_{\mathrm{case}\,q}\) and is computed according to (37);
10. Comparison of the gain in throughput offered by Cases 2 and 3 with respect to Case 1 (see Figure 16b) when the SNR of the feeder link is 15 dB, the SNR of the access link varies from 0 to 20 dB.