## 2 System and Channel Model
### FSO Sublink  
Considering the Malaga atmospheric turbulence model and pointing errors, the PDF of instantaneous SNR \(\gamma^{FSO}\) at the output of the FSO sublink is [39]:  
\[f_{\gamma^{FSO}}(\gamma^{FSO})=\frac{\xi^{2}A}{2^{\prime}\gamma^{FSO}}\sum_{k= 1}^{\beta}b_{k}\Omega_{1,3}^{3,0}\left(B\left(\frac{\gamma^{FSO}}{\mu^{FSO, \prime}}\right)^{\frac{1}{\gamma}}\left|\begin{array}{c}1+\xi^{2}\\ \xi^{2},\alpha,k\end{array}\right.\right) \tag{1}\]  
where \(G_{\cdot,\cdot}^{\cdot,\cdot}(\cdot)\) is the Meijer-G function, and \(\xi\) is the ratio of the equivalent beam radius of the receiver plane to the jitter standard deviation of the receiver plane, which represents the degree of deviation of the beam from the boresight. For example, the greater the value of \(xi\), the smaller the deviation of the beam from the boresight. \(A=\frac{2a^{\alpha/2}}{\xi^{1+\alpha/2}\Gamma(\alpha)}\left(\frac{\beta\beta} {\beta\beta+\Omega\gamma}\right)^{\beta+\frac{\alpha}{2}}\), \(B=\frac{\xi^{2}\alpha\beta(\beta+\Omega\gamma)}{(\xi^{2}+1)(\beta\beta+\Omega \gamma)}\), \(a_{k}=\left(\begin{array}{c}\beta-1\\ k-1\end{array}\right)\frac{(\beta\beta+\Omega\gamma)^{1-\frac{k}{2}}}{(k-1)^{ \alpha}}\left(\frac{\Omega\gamma}{\xi}\right)^{k-1}\left(\frac{\alpha}{\beta }\right)^{k/2}\), \(b_{k}=a_{k}[\alpha\beta/(\beta\beta+\Omega\gamma)]^{-(\alpha+k)/2}\), \(k\) is a summation variable and \(\Gamma(\cdot)\) is the Gamma function. \(\alpha\) is a positive parameter, which is related to the effective number of large-scale vortices in the scattering process, and \(\beta\) is the value of the fading parameter. \(g=2b_{0}(1-\rho)\) represents the average power of the independent scattering component received by the off-axis eddies path, \(2b_{0}\) is the average power of the total scattering component, \(\rho\in[0,1]\) represents the scattering power value  
Figure 1: Hybrid FSO/RF system model with RF or FSO link eavesdropping.  
coupled with the line of sight component, \(\Omega^{\prime}\) is the average power of mutual coupling components. \(\mu^{FSO,r}\) represents the average SNR of the FSO sub-link, \(r\) is the parameter that defines the detection technology, that is, \(r=1\) represents heterodyne detection (HD) and \(r=2\) represents direct detection (DD). When \(r=1\), \(\mu^{FSO,1}\)=\(\mu_{HD}\)=\(\overline{\tau}^{FSO}\). When \(r=2\), \(\mu^{FSO,2}\)=\(\mu_{DD}=\frac{\alpha_{0}^{2}\left(\zeta^{2}+1\right)^{-2}\left(\zeta^{2}+2 \right)\left(\zeta+\Omega^{\prime}\right)}{\left(\alpha+1\right)\left[2g\left( \zeta+2\Omega^{\prime}\right)+\Omega^{2}\left(1+\frac{1}{\beta}\right)\right]} \mu^{FSO,1}\).  
By applying the integral identity \(F_{\gamma^{FSO}}\left(\gamma^{FSO}\right)=\int_{0}^{\gamma^{FSO}}f_{\gamma^{FSO }}(t)dt\) to (1), the CDF of \(\gamma^{FSO}\) can be obtained as:  
\[F_{\gamma^{FSO}}(\gamma^{FSO})=D\sum_{k=1}^{\beta}c_{k}G_{r+1,3r+1}^{3r,1}\! \left(E\frac{\gamma^{FSO}}{\mu^{FSO,r}}\left|\begin{array}{c}1,\kappa_{1}\\ \kappa_{2},0\end{array}\right.\right) \tag{2}\]  
where \(D=\xi^{2}A/\left[2^{r}(2\pi)^{r-1}\right]\), \(c_{k}=b_{k}\kappa^{\alpha+k-1}\), \(E=B^{r}/r^{2r}\), \(\kappa_{1}=(\xi^{2}+1)/r,\ldots,(\xi^{2}+r)/r\) (includes \(r\) items), \(\kappa_{2}=\xi^{2}/r,\ldots,(\xi^{2}+r-1)/r,\alpha/r,\ldots,(\alpha+r-1)/r,k/r,\ldots\), \((k+r-1)/r\) (includes \(3r\) items) to simplify the expression. It is worth noting that the Malaga distribution has unified most of the existing uniform and isotropic turbulence mathematical models in Table 1 of [40], such as the Gamma-Gamma distribution, Lognormal distribution, K distribution, and so on.