## 2 Materials and Methods
### Calculations
The analytical calculations of the extinction coefficient for different weather conditions for 1.55 \(\upmu\)m and 4.0 \(\upmu\)m wavelengths were performed using the PcModwin 6.0 software (Ontar, North Andover, MA, USA) (Table 2). The first wavelength corresponds to the operation spectrum of now available commercial OWC systems, and the second one to the spectral region of ICL emission. For rain, the same beam attenuation is noticed for the considered wavelengths, and there are also no significant differences for very low visibility (below 500 m). However, if the visibility is increased, the propagation conditions of light improve again for longer wavelengths. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \(\lambda\) & & & & **Aerosol Model \({}^{*}\), Vis [km]** & & & & \\ \hline \multirow{4}{*}{\(1.5\)\(\upmu\)m} & \multirow{2}{*}{\(A\)} & \(C\) & \(C\) & \(T\) & \(M\) & \(D\) & \(F\) & \(R\) & \(H\) \\  & & 23 km & 5 km & 5 km & 23 km & 23 km & 0.5 km & 12.5 & 2 \\ \cline{1-1}  & & 23 km & 5 km & 23 km & 23 km & 0.5 km & 12.5 & 2 \\ \cline{1-1}  & & 23 km & 0.24 & 0.40 & 0.43 & 0.31 & 0.22 & 8.92 & 2.08 & 0.86 \\ \cline{1-1}  & & 23 km & 0.05 & 0.06 & 0.13 & 0.15 & 0.12 & 0.07 & 10.58 & 1.88 & 0.65 \\ \hline \hline \end{tabular} \({}^{*}\)A—only absorption, C—country, \(T\)—town, \(M\)—maritime, \(D\)—desert, \(F\)—fog, \(R\)—rain, \(H\)—haze.  
\end{table} 
Table 2: The extinction coefficient \(\gamma\) [km\({}^{-1}\)] of two wavelengths \(\lambda\) and for different weather conditions from PcModwin 6.0. Figure 1: Spectra of atmospheric transmittance. Noise in OWC systems is mainly generated in the receiver. There are different sources of noise in both photodetector and readout electronics (amplifiers). Its detectivity usually describes the detector noise [30]:  
\[D^{*}=\frac{A_{d}\sqrt{\Delta f}}{NEP}, \tag{4}\]  
where \(A_{d}\) is the active detector surface, \(\Delta f\) is the bandwidth, and \(NEP\) is the noise equivalent power. The total output noise power is equal to:  
\[P_{t}=P_{n}K+P_{a}, \tag{5}\]  
where \(P_{n}\) is the input noise power (photodetector noise), \(K\) is the amplifier gain, and \(P_{a}\) is the amplifier noise. There is observed dynamic progress in infrared photodetectors technology allows to obtain very high detectivity [31]. Nowadays, the optimization of readout electronics also ensures ultra-low noise levels below the photodetector one [32]. Optical link performances are very often modified by air turbulence [33]. This phenomenon is based on a random variation of the refractive index generated by optical cells (eddies) of different sizes formed during fluctuations of temperature and pressure in the atmosphere. Due to the described phenomena, the propagating beam is disturbed, and random changes of the received signal are observed. As a result, the effects of beam wandering, beam spreading, or scintillation can be registered. Simplifying, it causes random changes in signal-to-noise power ratio (SNR). This effect is described by the scintillation index corresponding to the normalized fluctuation of the signal [34]:  
\[\sigma_{\mathrm{I}}^{2}=\frac{\left\langle\mathrm{I}^{2}\right\rangle-\left\langle \mathrm{I}\right\rangle^{2}}{\left\langle\mathrm{I}\right\rangle^{2}}, \tag{6}\]  
where I is the light intensity on the detector surface, and \(\left\langle\mathrm{I}\right\rangle\) is its mean value. The signal variance is determined by a refractive index structure parameter (\(C_{\mathrm{n}}^{2}\)--index), link range, and a light wavelength. The \(C_{\mathrm{n}}^{2}\) parameter defines the level of turbulence. Theoretically, the operation in longer wavelengths allows obtaining better transmission during a moderate level of turbulence. For strong turbulence, the same attenuation for OWC wavelengths is observed. The effects of scintillation influence are challenging to predict, considering the complex dependence on temperature and pressure distribution, humidity, altitude, surface character, and more.