# Free Space Optical Communication: An Enabling Backhaul Technology for 6G Non-Terrestrial Networks
## 2 Fundamentals of FSO Signal Transmission
### Turbulence-Induced Fading for Airborne Nodes  
Turbulence refers to the irregular and random motion of air caused by various factors such as wind, temperature variations, and atmospheric pressure changes. This motion leads to fluctuations in the refractive index of air. When an optical beam propagates through a turbulent medium, it experiences distortion and scattering due to random fluctuations in the refractive index. The effects of turbulence can be particularly pronounced in long link distances. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Model Name** & \(k\) & \(a\) \\ \hline Japan & 1.58 & 0.63 \\ \hline France & 1.076 & 0.67 \\ \hline Widespread rain & 0.25 & 0.63 \\ \hline Orographic rain/drizzle & 1.20 & 0.33 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Rain model parameters. As demonstrated in Figure 8, there are two primary effects of turbulence on optical beam propagation. The foremost effect is scintillation, which refers to the rapid and random fluctuations in the received intensity known as fading. In addition to scintillation, turbulence also introduces beam wandering and beam broadening. Beam wander refers to the lateral displacement of the beam center caused by the turbulent motion of the air. As the beam propagates through the turbulent atmosphere, it may shift its position in a random manner. On the other hand, beam broadening refers to the spreading of the beam's spatial profile due to the scattering and diffusion caused by turbulence. This results in a larger receiver beam size (i.e., additional geometrical loss). Figure 7: Rain attenuation for propagation distances of (a) 100 m, (b) 300 m, and (c) 500 m.  
The refractive index structure parameter \(C_{n}^{2}\) is a measure of the strength of the fluctuations in the refractive index. In order to model accurate turbulence in vertical/slant FSO links for airborne nodes, it is important to know how the refractive index structure constant (\(C_{n}^{2}\)) changes with altitude. The atmosphere is not uniform with respect to altitude but has variations in both temperature and pressure. However, the change in temperature with altitude decreases as we move away from the Earth's surface. Accordingly, different models for \(C_{n}^{2}\) have been presented based on experimental measurements carried out at different geographical locations, different months, and/or different times in the day, to represent how the refractive index structure constant changes with altitude and time [66, 89, 90, 91, 92, 93, 94, 95, 96]. It can be seen from these models that the turbulence is more dominant in the first 2 km close to the Earth's surface, decreases with altitude, and almost vanishes before reaching an altitude of 10 km. Among the available models of the refractive index structure constant, the SLC model [95,96] is applicable for both day and night conditions, covering altitudes up to 20 km. According to this model, the refractive index as a function of altitude (\(h\)) is given by  
\[C_{n}^{2}(h)=\left\{\begin{array}{ll}\left\{ \begin{array}{ll}1.70\times 10^{-14 }&,0\,\mathrm{m}\leq h<18.5\,\mathrm{m}\\ 3.13\times 10^{-13}h^{-0.99836}&,18.5\,\mathrm{m}\leq h<243\,\mathrm{m}\\ 1.30\times 10^{-15}&,240\,\mathrm{m}\leq h<880\,\mathrm{m}\\ 8.87\times 10^{-7}h^{-3}&,880\,\mathrm{m}\leq h<7216\,\mathrm{m}\\ 2.00\times 10^{-16}h^{-0.5}&,7216\,\mathrm{m}\leq h<20000\,\mathrm{m}\\ 8.40\times 10^{-15}&,0\,\mathrm{m}\leq h<18.5\,\mathrm{m}\\ 2.87\times 10^{-12}h^{-2}&,18.5\,\mathrm{m}\leq h<107\,\mathrm{m}\\ 2.5\times 10^{-16}&,107\,\mathrm{m}\leq h<1525\,\mathrm{m}\\ 8.87\times 10^{-7}h^{-3}&,1525\,\mathrm{m}\leq h<7216\,\mathrm{m}\\ 2.00\times 10^{-16}h^{-0.5}&,7216\,\mathrm{m}\leq h<20000\,\mathrm{m}\\ \end{array}