## 3 Calculation Results  
For MDI-QKD protocol, we chose vacuum + weak decoy states in the same scheme as [11]. For satellite-based links, it includes Down-link and Up-link and PDT is different through different links. However, both of them have the same simulation method. In this paper we only show Down-link.  
By using PDT and Equation (2), Figure 2 is gotten. It only cares about the relationship between the average transmittance and the operation of the satellite visually, which is useful to the following researches. From Figure 2, the average transmittance is up to the max when the satellite is closed and nearly vertical to the ground and decreases with increasing height and angle.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Night** & **Condition 1** & **Condition 2** \\ \hline \(C_{n}^{2}\) & \(1.12\times 10^{-6}\) m\({}^{-2/3}\) & \(5.50\times 10^{-6}\) m\({}^{-2/3}\) \\ \(n_{0}\) & 0.61 m\({}^{3}\) & 3.00 m\({}^{3}\) \\ \hline
**Day** & **Condition 1** & **Condition 2** \\ \hline \(C_{n}^{2}\) & \(1.64\times 10^{-6}\) m\({}^{-2/3}\) & \(8.00\times 10^{-6}\) m\({}^{-2/3}\) \\ \(n_{0}\) & 0.01 m\({}^{3}\) & 0.05 m\({}^{3}\) \\ \hline \hline \end{tabular}
\end{table}
Table 2: List of practical parameters of weather conditions [10].  
Figure 2: The convexity of average transmittance with the orbit’s height and the angle from zenith changing in condition 1.  
Considering that the height of satellite and the angle from zenith and the weather conditions, we simulate and get Figures 3 and 4. \(\lambda\) is the signal light's wavelength. It helps to study general optical communication window in satellite-based links. \(L_{A}\) is the length of optical-fiber-based links and also the distance between [PERSON] and [PERSON] on the ground.  
As we can see, by the longitudinal comparison, due to the weather such as the light and so on, the average key rate is higher in the same condition during the day than that at night.; by the horizontal comparison, in different weather conditions, it changes little during the day, but changes a lot at night.  
Figure 3 shows that the large tolerance of general optical communication window. Changing the wavelength of signal light has little effect on the average key rate. In Figure 4, we can find that the ground loss has large effect on the average key rate. When \(L_{A}=100\) km, the lowest average key rate is almost as low as \(10^{-9}\). Besides, when the satellite operates between (\(500\) km, \(0^{\circ}\)) and (\(700\) km, \(45^{\circ}\)), the average key rate is relatively stable. The average key rate decreases fast when the satellite's height and angle from zenith exceed (\(700\) km, \(45^{\circ}\)). It almost reaches \(0\) at (\(1500\) km, \(75^{\circ}\)), which means that it can hardly communicate with MDI-QKD when the satellite is too high and almost parallels to the ground.  
From the two figures, what we should be noticed is the large effect of the loss of optical-fiber-based links on the ground. However, it also can cover a general city. The large tolerance of general optical communication window helps combine optical-fiber-based links with satellite-based links.  
Figure 3: The secret key rates of the MDI-QKD protocol in two different weather conditions, as functions of the angle from zenith and the orbit’s height, are reported at signal light’s wavelength \(\lambda=850\) nm, \(1310\) nm, \(1550\) nm respectively. \(L_{A}\) is fixed at \(50\) km.