## 3 System Architecture
### FSO Channel Modeling  
Atmospheric attenuation and fluctuations in signal amplitude and phase--often referred to as intensity scintillation--play a major role in free-space optical (FSO) communication. Multiple statistical models, such as the Log-normal, K, Negative exponential, Gamma-Gamma, and Log-normal Rician distributions, are utilized to describe optical turbulence [45]. Among these, the Gamma-Gamma model is extensively used due to its effectiveness in capturing a wide range of turbulence effects and related attenuation [6]. The FSO link in the proposed system is modeled using the Gamma-Gamma distribution, which accurately represents the effects of atmospheric turbulence on signal propagation. This distribution accounts for intensity fluctuations due to refractive index variations, leading to signal fading and degradation in free-space optical links. The normalized light intensity \(I\) is characterized by the probability density function (PDF) presented in [46]:  
\[P(I)=\frac{2(\alpha\beta)^{\frac{\alpha+\beta}{2}}}{\Gamma(\alpha)\Gamma( \beta)}\,l^{\frac{\alpha+\beta}{2}-1}\,K_{\alpha-\beta}\Big{(}2\sqrt{\alpha \beta I}\Big{)}, \tag{1}\]  
where \(\alpha\) and \(\beta\) are determined by:  
\[\alpha=\exp\Bigg{(}\frac{0.49\,\sigma_{R}^{2}}{\big{(}1+1.11\sigma_{R}^{\frac{ 12}{2}}\big{)}^{\frac{5}{6}}}\Bigg{)}-1,\quad\beta=\exp\Bigg{(}\frac{0.51\, \sigma_{R}^{2}}{\big{(}1+0.69\,\sigma_{R}^{\frac{12}{2}}\big{)}^{\frac{5}{6}}} \Bigg{)}-1.\]  
Here, \(\alpha\) and \(\beta\) signify the effective numbers of small- and large-scale turbulence cells, respectively. In these expressions, \(\Gamma(\cdot)\) is the Gamma function, and \(K_{\alpha-\beta}(\cdot)\) denotes a modified Bessel function of the second kind. The variance of intensity fluctuations, \(\sigma_{R}^{2}\), quantifies the level of atmospheric turbulence and is given by:  
\[\sigma_{R}^{2}=1.23C_{n}^{2}k^{\frac{2}{2}}z^{\frac{11}{6}} \tag{2}\]  
where \(C_{n}^{2}\) is the refractive index structure parameter that typically varies between \(10^{-13}\,\mathrm{m}^{\frac{-2}{3}}\) (strong turbulence) and \(10^{-17}\,\mathrm{m}^{\frac{-2}{3}}\) (weak turbulence), \(k=\frac{2\pi}{\lambda}\) is the optical wavenumber, and \(z\) is the free-space optical (FSO) link distance. A quasi-static--or frozen--channel assumption is applied to analyze how the channel evolves over time, assuming the fading remains stable within each frame of symbols (coherence time) and updates from one frame to the next. The impact of turbulence across different regimes, from weak to strong, can be characterized using the Rytov variance. Scintillation causes fluctuations in received signal intensity, affecting system performance. The integration of LDPC decoding plays a crucial role in mitigating these effects, significantly improving signal integrity and data reliability. The optical power loss in the FSO channel is influenced by multiple factors, including geometric losses, atmospheric absorption, and scattering effects. The received power, \(P_{r}\), at the destination can be expressed as:  
\[P_{r}=P_{t}\times e^{-\alpha L}\times h_{t} \tag{3}\]  
where \(P_{t}\) is the transmitted optical power, \(\alpha\) is the atmospheric attenuation coefficient, \(L\) is the FSO link distance, and \(h_{t}\) is the turbulence-induced fading factor modeled using the Gamma-Gamma distribution. The FSO link is affected by atmospheric turbulence, which causes fluctuations in received power due to refractive index variations. The Gamma-Gamma model is widely used to characterize the probability density function (PDF) of intensity fluctuations in strong turbulence conditions. However, beyond turbulence, other impairments, such as pointing errors, beam divergence, and aperture averaging, also play a crucial role in system performance. Pointing errors arise due to mechanical misalignment or atmospheric disturbances, leading to beam displacement at the receiver and significant power loss. The severity of pointing errors increases over long distances, contributing to additional outage probability.