## 2 System and Channel Model
### Atmospheric Turbulence Model  
Even in clear weather conditions, the atmospheric turbulence effect is observed. In fact, solar radiation absorbed by the Earth's surface makes the air around the Earth's surface warmer than that at higher altitudes. This layer of warmer air becomes less dense and rises to mix turbulently with the surrounding cooler air, causing the air temperature to fluctuate randomly. These random temperature variations lead to corresponding refractive index fluctuations and thus, inhomogeneities caused by turbulence can be considered as discrete cells, or eddies of different temperatures, acting like refractive prisms of different sizes and refractive indices. The interaction between THz propagating wavelengths and turbulent medium generates random phase and amplitude variations of the received signal, which results in the performance degradation of the link. Consequently, atmospheric turbulence is a very complex stochastic effect which hinders the propagation of the information-bearing beam and causes the so-called scintillation effect which results, in turn, in random temporal and spatial fluctuations of the received signal intensity, analogous to fading in RF systems [2; 20; 40; 61; 62]. Considering therefore that this effect brings about continuous and very rapid fluctuations on the intensity of the signal that arrives at the receiver's side, it should be mainly investigated through statistical methods and processes. The selection of the appropriate model is mainly determined by the strength of the turbulence effect along the propagation path. In this work, turbulence-induced scintillations are described by the Gamma-Gamma distribution model [21; 24; 26; 54; 57; 58; 63; 64], which has been widely used in the FSOs area and more recently in the THz regime [19; 40] as a very accurate model for weak-to-strong turbulent conditions. According to the well-known Gamma-Gamma turbulence model, which was first proposed in [65], the PDF of the positive random variable \(h_{a,n}\) is obtained as  
\[ \begin{array}{c}f_{h_{a,n}}(h_{a,n})\ =\ \frac{2(\alpha_{n}\beta_{n})\frac{ \alpha_{n}+\beta_{n}}{2}}{\Gamma(\alpha_{n})\Gamma(\beta_{n})}h_{a,n^{2}}^{ \frac{\alpha_{n}+\beta_{n}}{2}-1}\\ \times\ K_{\alpha_{n}-\beta_{n}}\big{(}2\sqrt{\alpha_{n}\beta_{n}h_{a,n}} \big{)},\end{array}  \tag{8}\]  
with \(\Gamma(. )\) representing the gamma function [66], Equation (8.310.1), \(K_{\
u}(. )\) denoting the \(\
u\)-th order modified Bessel function of the second kind [66], Equation (8.432.2), while the parameters \(\alpha_{n}\) and \(\beta_{n}\) can be directly related to the \(n\)-th turbulent channel along with the link's parameters, as described in [63]:  
\[ \begin{array}{c}\alpha_{n}=\left[exp\left(\frac{0.49\delta_{n}^{2}}{\left(1 +0.18d_{n}^{2}+0.56k_{n}^{\frac{12}{6}}\right)^{\frac{2}{6}}}\right)-1\right] ^{-1}\\ \beta_{n}=\left[exp\left(\frac{0.51k_{n}^{2}(1+0.69k_{n}^{12/5})^{-5/6}}{\left( 1+0.9d_{n}^{2}+0.62d_{n}^{2}\delta_{n}^{2(1/5)}\right)^{\frac{2}{6}}}\right)- 1\right]^{-1}\!,\end{array}  \tag{9}\]  
where \(d_{n}=0.5D_{n}\sqrt{2\pi\lambda_{n}^{-1}z_{n}^{-1}}\), with \(D_{n}\) standing for the receiver's aperture diameter and \(\lambda_{n}=c/f_{n}\) being the operational wavelength, while the parameter \(\delta^{2}\) denotes the Rytov variance for which the spherical wave propagation in a horizontal path is obtained as [67; 68]:  
\[\delta_{n}^{2}=0.5C_{n}^{2}k_{n}^{\frac{7}{6}}z_{n}^{\frac{11}{6}}, \tag{10}\]  
with \(k_{n}=2\pi/\lambda_{n}\) being the wavenumber and \(C_{n}^{2}\) representing the refractive index structure parameter which is proportional to the atmospheric turbulence strength [67; 68]. Consequently, the Rytov variance is a metric of turbulence-induced scintillations, while also it becomes evident from Equation (10) that atmospheric turbulence is a wavelength-dependent and especially a distance-dependent effect.