## 4 Evaluation
### Simulation Setup of the Optical Channel
Without loss of generalization, it is assumed that the ground station is placed next to the city of Madrid, Spain (i.e., Lat. 40.43\({}^{\circ}\) North, Long. 4.25\({}^{\circ}\) West, and altitude \(h_{0}=864\) m), with an expected system availability due to cloud-free line-of-sight conditions close to 99.8%. Similarly, the satellite is assumed to be placed in the GEO position of 19.2\({}^{\circ}\) East at an altitude of \(H=36\),000 km, giving as result a zenith angle \(\zeta=52.61\) deg. for the optical feeder link in the forward direction of communication. The nominal value of the refractive index near the ground level is \(A_{0}=1.7\times 10^{-14}\) m\({}^{-2/3}\), and the CDF is plotted for three different wind speeds (i.e., \(v=10,21\) and 30 m/s). Note that when \(v=21\) m/s, the refractive index model becomes the well-known H-V\({}_{5/7}\) model. Finally, an untracked collimated beam is assumed, with a beam radius of \(W_{0}=10\) cm at a wavelength of \(\lambda=1550\) nm. As expected, the stronger is the wind speed, the more variability is introduced in the instantaneous intensity of the received optical signal at the GEO satellite. For example, the 10-th percentile for the turbulence-induced power loss (i.e., power loss margin for a 90% link availability without coding) is equal to 2.4, 3.0 and 3.8 dB for a wind speed of 10, 21 and 30 m/s, respectively. These turbulence-induced power losses grow to 4.3, 5.4 and 7.0 dB when we study the 1-st percentile (i.e., power loss margin for a 99% link availability without coding) for the same three values of wind speeds (i.e., 10, 21 and 30 m/s, respectively). \begin{table}
\begin{tabular}{c c c c} \hline
**Symbol** & **Optical Link Parameter** & **Value** & **Unit** \\ \hline \(P_{\rm o,ld}\) & Optical power of LD (including EDFA booster) & 47.0 & dBm \\ \hline \(G_{\rm o,tx}\) & Optical gain of transmitter (ground telescope) & 110.9 & dBi \\ \hline \(G_{\rm o,rx}\) & Optical gain of receiver (satellite telescope) & 112.8 & dBi \\ \hline \(L_{\rm o,fsl}\) & Free space loss of optical link (\(\lambda~{}=~{}1550\) nm, \(H=~{}36\),000 km) & 289.8 & dB \\ \hline \(L_{\rm o,atm}\) & Atmospheric attenuation (absorption and scattering) & 0–10 & dB \\ \hline \(L_{\rm o,bsl}\) & Beam spreading loss due to scintillation & 1.6 & dB \\ \hline \(L_{\rm o,sys}\) & System losses in the optical feeder link & 4.5 & dB \\ \hline \(G_{\rm edfa}\) & Gain of the optical amplifier (EDFA) & 50.0 & dB \\ \hline \(\mu\) & Responsivity of photodetector (PIN diode) & 0.5 & A/W \\ \hline \(B_{\rm e}\) & Bandwidth of electrical filter (PD output) & 1.5 & GHz \\ \hline \(B_{\rm o}\) & Bandwidth of optical channel (\(\lambda~{}=~{}1550\) nm) & 12.5 & GHz \\ \hline \(\rho_{\rm ase}\) & PSD of amplified spontaneous emissions & \(2.0\times 10^{-19}\) & W/Hz \\ \hline \(\rho_{\rm{rin}}\) & PSD of RIN process (normalized) & \(-160\) & dBc/Hz \\ \hline \(\rho_{\rm{back}}\) & PSD of background noise at EDFA input & \(7.6\times 10^{-25}\) & W/Hz \\ \hline \(i_{\rm n}\) & Electrical noise current spectral density & \(1.0\times 10^{-11}\) & A \\ \hline \(i_{\rm dark}\) & Dark current at the PIN diode output & \(1.0\times 10^{-10}\) & A \\ \hline \end{tabular}
\end{table} 
Table 2: Parameters of the optical feeder link used in the NB-IoT satellite system and associated power budget.