# _photonics_
## 4 Simulation Results
### Feasibility of LEO Satellite-to-Ground QKD in Daytime and Nighttime
#### 4.2.2 QKD under Different Background Noise Levels  
The detection of single-photon signals buried in the intent background noise stemming from the solar radiance could be practically a very challenging task. Therefore, specific techniques are required to alleviate the presence of noise photons in QKD links, such as narrow spectral filtering and short detector gate time opening at Bob station. Even in this case, the presence of solar daylight radiance still affects drastically the performance of the link. The values of the solar background radiance during the day depend on the position of the  
Figure 2: (**a**) Total downlink loss (dB) over distance (km) and over receiving telescope aperture (m). (**b**) Normalized secure key rate (SKR; bps/pulse) over link distance (km) and over receiving telescope aperture (m) under nighttime conditions.  
satellite relative to the sun azimuth as well as on the OGS's location. In addition, weather conditions such as cloud presence may further deteriorate the situation, enhancing the strength of the effect of solar radiance. Typical values for \(H_{rad}\) (\(\mathrm{watt/sr~{}m^{2}\upmu m}\)) at 1550 nm for clear sky daylight conditions may vary between 0.1 and 6 (\(\mathrm{watt/sr~{}m^{2}\upmu m}\)) [24; 52; 57]. In Figure 3, the effect of the solar radiance over the normalized secure key rate is presented. It can be observed that the background noise is a limiting factor not only in the distance reach, but also in the angle of view. This leads to a smaller view cone, which in turn reduces the satellite-OGS communication time.  
In Figure 3, it is evident that strong limitations are imposed on the key establishment due to background radiance in daylight. More specifically, under our assumptions (0.2 nm filter passband, 1 ns detector gate opening, and 100 \(\upmu\)rad FOV), the noise levels even for low solar radiance values are over the acceptable threshold, and therefore, no QKD link can be established. Further narrowing the quantum passband is a candidate solution, but state-of-the-art equipment with increased optical loss will be required. In general, it is uncertain if such a link could be operating under full daylight conditions [57].  
In nighttime, the main source of background radiance is the moonlight. In addition, the night sky and city lights can also generate an amount of noise photons in the detectors. Typical values nighttime radiance (\(H_{rad}\)) at 1550 nm may vary from \(1.5\times 10^{-5}\) (\(\mathrm{watt/sr~{}m^{2}\upmu m}\)) (moonless clear night) to \(1.5\times 10^{-3}\) (\(\mathrm{watt/sr~{}m^{2}\upmu m}\)) (full moon clear night) [24; 52; 57]. Even in the case of full moon, the background radiance corresponds to 10 kcps in the photon counter at most.  
In the next subsections, we assumed that the link is always interrupted during daylight, and therefore, communication is only established during nighttime. The nighttime solar radiance was set to an average value of \(1.5\times 10^{-4}\) (\(\mathrm{watt/sr~{}m^{2}\upmu m}\)) and was kept constant for the needs of the numerical study.