## 4 Simulation Results
### Source Specification/Requirement Analysis
#### 4.1.1 Emission Rate Analysis--LEO  
To begin with, a LEO satellite pass was simulated. For simplicity, we will assume an ideal LEO pass over the Helmos OGS in Greece (Latt: 37.98, Long: 22.20), meaning that the satellite reaches a maximum elevation angle of 90 degrees. For this ideal case, the satellite was visible (>20\({}^{\circ}\) elevation) for approximately 5 min and 30 s. For this first case study, a ground station at 500 m was simulated. In addition, a 1 m aperture telescope, with a 0.08 m secondary mirror and a 10 m focal length, was assumed for the receiver station. Figure 3 provides the end-to-end link loss (Y-right axis), as well as the expected normalized SKR (bps/pulse) (Y-left axis) over time, where different transmitted block sizes values were assumed. More tip-tilt correction was considered for the telescope-to-SMF coupling (corresponding to a value of \(\gamma\) = 0.28 in Equation (15)) while considering both (a) SNSPD and (b) SPAD detectors. Since the link loss was higher when SPADs were used as detection units, higher transmitted block sizes were required. Since future OGSs might  
\begin{table}
\begin{tabular}{c c c} \hline
**Symbol** & **Parameter** & **Value** \\ \hline \(\eta_{Bob}\) & Detector’s setup loss & 2 dB \\ \(C_{n}^{2}\) & Refractive index structure parameter & \(1.7\times 10^{-14}-1.7\times 10^{-13}\) m\({}^{-2/3}\) \\ \(H_{rad}\) & Background solar radiance & \(1.5\times 10^{-5}-1.5\times 10^{-1}\) W/m\({}^{2}\)sr \(\upmu\)m \\ \(P_{0}\) & Outage probability & 1\% \\ \(\Omega_{FOOT}\) & Receiver’s FOV & 100 urad \\ \(\lambda_{pass}\) & Filter’s spectral passband & 0.2 nm \\ \(\eta_{filter}\) & Filters efficiency & 0.7 \\ \(\mu\) & Mean signal photon/pulse & 0.7 \\ \(v\) & Mean decoy photon/pulse & 0.1 \\ \(\varepsilon_{s}\) & Smoothing parameter & \(9\times 10^{-11}\) \\ \(\varepsilon_{pe}\) & Parameter estimation & \(7.7\times 10^{-11}\) \\ \(\varepsilon_{cc}\) & Error correction parameter & \(8\times 10^{-11}\) \\ \(\eta_{SNSPD}\) & SNSPDs detection efficiency & 0.85 \\ \(DCR_{SNSPD}\) & SNSPDs dark count rate & 10 cps \\ \(\tau_{dead\_SNSPD}\) & Dead time SNSPD & 30 ns \\ \(\eta_{SPAD}\) & SPADs detection efficiency & 0.15 \\ \(DCR_{SPAD}\) & SPADs dark count rate & 300 cps \\ \(\tau_{dead\_SPAD}\) & Dead time SPAD & 20 us \\ \(\tau_{gate}\) & Effective gate time window & 1 ns \\ \(\varepsilon_{0}\) & Error probability for noise counts & 50\% \\ \hline \end{tabular}
\end{table}
Table 1: _Cont._be equipped with either detector type, a sufficient transmitted block size that can comply with these two detection systems seems to be about \(N_{trans}>10^{10}\) bits. To achieve this, the on-board source was required to provide an emission rate of approximately \(f_{rep}>40\) MHz, which is compatible with the typical achievable detection rates of both SPAD and SNSPD detectors. Considering the normalized calculated SKRs, as well as by assuming an emission rate of 40 MHz (which yields a maximum transmitted block size of \(10^{10}\) bits in the case of LEO, i.e., where the satellite is only visible for 300 s), an average SKR of 8 kbps and 800 bps were calculated for the case of SNSPD and SPAD detection, respectively, over a single LEO passage. It is important to note that, once again, the calculations above provide the minimum requirements for key distillation. These results can be enhanced if one considers state-of-the-art sources that can provide higher transmitted block sizes, larger receiver apertures, or a full-AO correction of the turbulent wavefront. The aforementioned parameters will be discussed in Section 5.