## 3 Challenges in FSO Communication
### FSO System and Channel Models
#### 3.2.1 FSO System Model  
In this section, we analyze a practical FSO link that employs IM/DD with On-Off Keying (OOK) modulation. The data are encoded onto the instantaneous intensity of an optical beam at the Tx. It is assumed that the optical power emitted from the transmit aperture into free space is affected by factors such as misalignment fading (PE), fading induced by AT, and background or ambient noise before it reaches the receive aperture. These factors lead to variations in signal intensity. As a result, the received electrical signal \(r\) at the receive aperture can be modeled as follows [3; 89; 90; 91]:  
\[r=\eta_{e}lx+n, \tag{1}\]  
where \(\eta_{e}\) denotes the effective photoelectric conversion ratio of the Rx, \(x\in\{0,1\}\) represents the transmitted information bit, \(n\) represents the additive white Gaussian noise (AWGN) with zero mean and variance \(\sigma_{n}^{2}=N_{0}/2\), \(N_{0}\) denotes the one-sided noise power spectral density in watts/Hz, and the term \(h=h_{t}h_{\mathrm{a}}h_{\mathrm{p}}\) signifies the irradiance affecting the channel state, which is a product of the deterministic path loss \(h_{\ell}\), the random attenuation due to AT-induced fading \(h_{\mathrm{a}}\), and the random attenuation caused by geometric spread and PE \(h_{\mathrm{p}}\). Both \(h_{\mathrm{a}}\) and \(h_{\mathrm{p}}\) are random variables characterized by their respective PDFs, \(f_{h_{\mathrm{a}}}(h_{\mathrm{a}})\) and \(f_{h_{\mathrm{p}}}(h_{\mathrm{p}})\). Noise Model  
The noise performance of a Rx is influenced by the type of photodetector employed, specifically whether a PIN photodetector or an APD is used. It is important to recognize that each of these photodetectors contributes to the overall noise in distinct ways. In this subsection, we delve into the different noise models associated with both PIN and APD photodetectors, providing a comprehensive review of their respective noise characteristics and how they impact the Rx performance. If an APD Rx is employed, the overall noise contribution is understood to consist of three primary components: thermal noise, shot noise, and dark current. However, assuming the dark current is insignificant, the noise generated by the APD Rx, denoted as \(n\), can be represented as the sum of the thermal noise, \(i_{Th}\), and the shot noise, \(i_{Sh}\). Therefore, the equation representing the APD Rx noise is [92; 93]  
\[n=i_{Th}+i_{Sh}, \tag{2}\]  
where \(i_{Sh}\) and \(i_{Th}\) represent the shot noise and thermal noise, respectively. The thermal noise \(i_{Th}\) is characterized as a zero-mean stationary Gaussian random process, with its variance defined by [92; 93]  
\[\sigma_{Th}^{2}=4k_{B}\frac{T}{R_{L}}F_{n}\Delta f, \tag{3}\]  
where \(k_{B}\) represents the Boltzmann constant, \(T\) denotes the absolute temperature in degrees Kelvin, \(R_{L}\) represents the APD load resistance, \(F_{n}\) represents the amplifier noise figure, and \(\Delta f=R_{b}/2\) denotes the symbol effective noise bandwidth that is associated with the bit rate \(R_{b}\). Shot noise is influenced by the APD Rx and can be modeled similarly to thermal noise using a zero-mean stationary Gaussian random process. The variance in shot noise can be described as  
\[\sigma_{Sh}^{2}=2q_{e}\bar{g}^{2}F_{A}\Re hP_{t}m\Delta f, \tag{4}\]  
where \(q_{e}\) is the electron charge, \(m\) is the modulation index, \(P_{t}\) represents the transmitted optical power, \(\Re\) and \(\bar{g}\) are the APD responsivity and average gain, respectively, and \(F_{A}\) represents the excess noise factor of the APD, which is defined by  
\[F_{A}=k_{A}\bar{g}+(1-k_{A})\left(2-\frac{1}{\bar{g}}\right), \tag{5}\]  
where \(k_{A}\) represents the ionization factor. Utilizing the characteristics of Gaussian random variables, the total APD noise can be modeled as a stationary random process with a mean of zero.