## 3 Challenges in Terahertz-Based FSO Communication
### Signal Distortion  
In THz communication, signal degradation is caused by turbulence and scattering in the air, and significantly degrades the signal [64; 65]. These distortions are quantified using metrics such as the scintillation index (S\({}_{\text{I}}\)), a measure of the intensity of fluctuations caused by turbulence:  
\[\text{S}_{\text{I}}=\frac{\left\langle\text{I}^{2}\right\rangle-\left\langle \text{I}_{\text{int}}\right\rangle^{2}}{\left\langle\text{I}_{\text{int}} \right\rangle^{2}} \tag{11}\]  
where \(\left\langle\text{I}_{\text{int}}\right\rangle\): the average signal intensity. \(\left\langle\text{I}^{2}\right\rangle\): The mean square signal intensity. Higher S\({}_{\text{I}}\) values correspond to more substantial turbulence, which leads to increased signal degradation. Atmospheric turbulence can also be described using the Kolmogorov turbulence model [22; 38], which relates the refractive index structure parameter (C\({}_{\text{n}}^{2}\)) to the turbulence strength:  
\[\Phi_{\text{n}}(\text{k})=0.033\text{C}_{\text{n}}^{2}\text{k}^{-11/3} \tag{12}\]  
where \(\Phi_{\text{n}}(\text{k})\): the power spectral density of refractive index fluctuations. C\({}_{\text{n}}^{2}\): the refractive index structure parameter (m\({}^{-2/3}\)). k: the wavenumber (m\({}^{-1}\)). Additionally, signal distortion due to scattering can be modeled using the Mie scattering equation for spherical particles:  
\[\text{Q}_{\text{s}}=\frac{2}{\text{x}^{2}}\sum_{n=1}^{\infty}(2n+1)\left( \left|\text{a}_{\text{n}}\right|^{2}+\left|\text{b}_{\text{n}}\right|^{2}\right) \tag{13}\]  
where Q\({}_{\text{s}}\): the scattering efficiency. \(\text{x}=\frac{2\pi\text{T}}{\Lambda}\): the size parameter (ratio of particle size r to wavelength \(\lambda\)). \(\text{a}_{\text{n}},\text{b}_{\text{n}}\): the scattering coefficients for spherical harmonics. These equations provide a mathematical framework to understand and quantify the impact of turbulence and scattering on THz communication. The mitigation strategies for these impacts include the following: \begin{table}
\begin{tabular}{l l l l l l l} \hline \hline
**Parameter** & **Device Type** & **Value/Range** & **Challenge** & **Cause** & **Solution** & **Citation** \\ \hline \multirow{4}{*}{Output Power} & Quantum & \multirow{2}{*}{\begin{tabular}{} \end{tabular} } & Low & High & \multirow{2}{*}{\begin{tabular}{} \end{tabular} } & Novel gain media & \multirow{2}{*}{[61]} \\  & Cascade Lasers & & power output & & hold current & optimizations & \\ \hline \multirow{4}{*}{Output Power} & Photonic & \multirow{2}{*}{\(\sim\)100 \(\mu\)W} & Low & Energy loss in & Enhanced & \multirow{2}{*}{[62]} \\  & Mixers & & conversion & photonizing & phase-matching & \\  & & efficiency & process & techniques & \\ \hline \multirow{4}{*}{\begin{tabular}{} \end{tabular} } & Free-Electron & \multirow{2}{*}{\begin{tabular}{} \end{tabular} } & \multirow{2}{*}{\begin{tabular}{} \end{tabular} } & \multirow{2}{*}{\begin{tabular}{} \end{tabular} } & Large-scale & \multirow{2}{*}{\begin{tabular}{} \end{tabular} } \\  & Lasers (FELs) & & & & & \\ \cline{1-1} \cline{4-7}  & & & & & & \\ \hline \multirow{4}{*}{\begin{tabular}{} \end{tabular} } & \multirow{2}{*}{\begin{tabular}{} \end{tabular} } & Limited to & Limited & \multirow{2}{*}{\begin{tabular}{} \end{tabular} } & \multirow{2}{*}{\begin{tabular}{} \end{tabular} } & High-speed & \multirow{2}{*}{[63]} \\  & Modulation & & GHz-range & & & & \\ \cline{1-1} \cline{4-7}  & & & & & & & \\ \cline{1-1} \cline{4-7}  & & & & & & & \\ \hline \multirow{4}{*}{\begin{tabular}{} \end{tabular} } & External & \multirow{2}{*}{\begin{tabular}{} \end{tabular} } & Extends to & Complexity & \multirow{2}{*}{\
\begin{tabular}{} \end{tabular} } & \multirow{2}{*}{
\begin{tabular}{} \end{tabular} } & Low-loss & \multirow{2}{*}{[63]} \\  & Modulation & & & & & \\ \cline{1-1} \cline{4-7}  & & & & & & \\ \cline{1-1} \cline{4-7}  & Modulation & & & & & & \\ \hline \hline \end{tabular}
\end{table}