# Free Space Optical Communication: An Enabling Backhaul Technology for 6G Non-Terrestrial Networks
## 2 Fundamentals of FSO Signal Transmission
### Atmospheric Attenuation
While the horizontal link distance in a terrestrial FSO link may span a considerable length, the vertical distance experienced by an airborne link is constrained by the thickness of the fog. It can be also noted that the link between the ground and the airborne node may take the form of a slant link. In such cases, the propagation distance through the fog exceeds its thickness, which ranges from just a few meters above the ground to several hundred meters high, depending on the specific atmospheric conditions and the type of fog. The vertical extent of fog is influenced by factors such as temperature, humidity, wind, and local topography. \begin{table}
\begin{tabular}{l l l} \hline
**Models** & **Wavelength** & **Visibility** \\ \hline Kruse Model & 785 and 1550 & 0 m to more than 50 km \\ \hline Kim Model & 785 and 1550 & 0 m to more than 50 km \\ \hline Al-Naboulsi & 400- to 1500 & 50 m to 1000 m \\ \hline \end{tabular}
\end{table} 
Table 4: Models for fog extinction coefficients. In summary, the propagation distance through fog is influenced by both thickness and the elevation angle. In Figure 6, we present the attenuation losses associated with fog based on Equation (5), considering a propagation distance up to 10 km. The extinction coefficient is calculated using [PERSON]'s model, considering visibility values of \(V=1\) km and \(V=4\) km. It is observed that fog has a significant impact. For example, at a wavelength of \(\lambda=1550\) nm and visibility of \(V=4\) km, the attenuation losses are recorded as 1.54 dB, 7.69 dB, and 15.39 dB for distances of 1 km, 5 km, and 10 km, respectively. These values further increase for \(\lambda=785\) nm and reach 3 dB, 14.99 dB, and 29.97 dB for the same distances. The difference in attenuation loss as a result of wavelength can be written using Equation (5) as \(10\log_{10}(\exp([\gamma(\lambda_{1})-\gamma(\lambda_{2})]\ z_{\text{km}}))=[ \gamma(\lambda_{1})-\gamma(\lambda_{2})]\ z_{\text{km}}/\ln 10\). For example, consider \(\lambda_{1}=1550\) nm and \(\lambda_{2}=850\) nm. Attenuation coefficients are calculated using [PERSON]'s model as \(\gamma(\lambda_{1})=2.330\) dB/km and \(\gamma(\lambda_{2})\)= 3.147 dB/km, assuming a visibility of \(V=1\) km. The difference in attenuation loss is then calculated as 17.73 dB and 35.46 dB, respectively, at propagation distances of 5 km and 10 km (See Figure 6a). To model the effect of rain, various empirical models have been proposed in the literature, including the Japan Model [87], France model [87], Widespread rain model [85], and Orographic rain/drizzle model [85]. In each of these models, the rain extinction coefficient is represented as \(\gamma=aR^{b}\), where \(R\) stands for the rate of rainfall in millimeters  
Figure 5: Attenuation loss versus transmission distance for clear weather conditions (\(V=50\) km). Figure 6: Attenuation loss versus transmission distance for foggy weather conditions with visibilities of (**a**) \(V=1\) km, (**b**) \(V=4\) km. per hour (mm/h) (1 mm rainfall indicates that this area is filled with water of height 1 mm. In other words, 1 mm of rain is 1 L per square meter. ), and \(a\) and \(b\) are model parameters obtained through data fitting from experimental results (see Table 5). These experiments were conducted in various geographical locations. It is evident that the values of \(a\) and \(b\) differ between locations, owing to variations in rain characteristics, such as droplet size, which can vary across different areas of the Earth. In Figure 7, we investigate the impact of rain-induced signal losses on vertical/slant links, which are constrained by both the cloud's altitude and the elevation angle of the beam. It is important to note that the cloud bottom is positioned a few hundred meters above the sea surface. Hence, the results presented in the figure are based on propagation distances of up to 500 m. Although the rain rate can potentially reach 50 mm/h, it typically remains below 10 mm/h in most geographical locations [88].