## 4 Evaluation
### Simulation Setup of NB-IoT Signal  
This paper evaluates the BLER and Throughput of the following three forward link architectures for transmitting NB-IoT over satellite when the feeder link is optical:  
1. Case 1: NB-IoT detect-and-forward (See Section 2.2.1). 2. Case 2: NB-IoT decode-and-forward (See Section 2.2.2). 3. Case 3: NB-IoT encapsulated in DVB-S2(X) frames. (See Section 2.2.3). In all cases, the NB-IoT frame length is set to \(N=1032\) bits. The pulse-shaping filter for NB-IoT and DVB-S2(X) waveforms is assumed to be Square-Root Raised-Cosine (SRRC) with roll-off factor \(\rho=0.15\). The overlapping factors that have been considered in the simulations to implement the time-packing signaling are \(\delta=0\), 15, 25 and 40%. Note that when \(\delta=0\%\) (i.e., no overlapping), the symbol time is equal to the _Nyquist_ symbol time. The modulation scheme used in the optical feeder links is 4-PAM, in order to make it compatible with the Intensity Modulation/Direct Detection approach. On the contrary, the access link uses QPSK, which is one of the modulation schemes considered for the downlink in the NB-IoT standard. So, in both optical feeder and radio access links, the number of modulation states is \(M=4\) and the number of bits per modulated symbol is \(N_{b}=2\). In order to make fair comparisons, all the relaying satellite architectures under analysis use the same data rate. In particular, the BLER and throughput of the different satellite relaying strategies have been tested with nine possible code rates, namely: Three _low_ code rates that are more robust than the mother code rate of the convolutional encoding (i.e., 0.2222, 0.259 and 0.3), three _medium_ code rates that provide similar error correction capabilities than the mother code rate (i.e., 0.4444, 0.5319 and 0.6), and three _high_ code rates that are the least robust (i.e., 0.6386, 0.7678 and 0.854). For the first and second use cases, these code rates correspond to the code rate of the NB-IoT waveform. However, for the third case, these code rates represent the joint code rate of the DVB-S2(X) and NB-IoT  
Figure 8: Cumulative distribution function of the power loss that turbulence-induced beam wander and scintillation introduces in the uplink direction of the optical feeder link in case of an untracked collimated beam with \(\lambda=1.55\,\upmu\)m, \(W_{0}=10\,\mathrm{cm}\), \(\zeta=52.61\,\mathrm{deg}\), \(A_{0}=1.7\times 10^{-14}\,\mathrm{m}^{-2/3}\). The ground station site is assumed next to Madrid (\(h_{0}=864\,\mathrm{m}\)) and the position of the GEO satellite is assumed at 19.2\({}^{\circ}\) East (\(H=36\),000 km). Wind speeds: \(v=10\,\mathrm{m/s}\) (solid red line), \(v=21\,\mathrm{m/s}\) (dashed green line), and \(v=30\,\mathrm{m/s}\) (dashed-dotted line). waveforms. This joint code rate is defined as the product between the code rates of the DVB-S2(X) and NB-IoT signals as  
\[R_{c,\text{case 3}}=R_{c,\text{tot}}\times R_{c,\text{dvb}}. \tag{33}\]  
In (33), the code rates of NB-IoT and DVB-S2(X) have been selected such that the their joint code rate \(R_{c,\text{case 3}}\) is equal to the code rates of NB-IoT for the first and second cases. Thus, three code rates (i.e., low, medium and high) have been considered for each waveform (i.e., NB-IoT and DVB-S2(X)), which enable to obtain the nine code rates for cases 1 and 2. Specifically, the code rates of the DVB-S2(X) and NB-IoT standards that have been used are: \(R_{c,\text{dvb}}=0.66667\), 0.8 and 0.9 [33] and \(R_{c,\text{tot}}=0.3333\), 0.66667 and 0.96, respectively. Thus, we obtain nine possible combinations of the code rates, which are values that are similar to the ones used in the three relaying architectures (see Table 3 for more details). Therefore, after obtaining a similar code rate for the three cases under study, the architecture that provides the best in terms of BLER and throughput is determined for the different SNR working regimes in the optical feeder link (uplink) and radio access link (downlink), respectively.