# Stable Throughput Analysis of Heterogeneous Hybrid FSO/RF Networks with Cognitive Radio Capability
## 6 Numerical Results  
In the simulation, the FSO link and RF parameter values are computed as follows [31]:\[\alpha = \left(e^{\frac{0.48\lambda^{2}}{(1+0.18\delta^{2}+0.5\xi^{2}1/5)/76}} \right)^{-1}, \tag{46}\] \[\beta = \left(e^{\frac{0.542(1+0.60\delta^{2}12/5)-5/6}{(1+0.8\delta^{2}+0. \delta^{2}2\xi^{2}1/5)^{5/6}}}\right)^{-1},\] (47) \[\xi = \sqrt{0.5c_{n}^{2}k^{7/6}z^{11/6}},\] (48) \[k = 2\pi/\lambda_{f_{0}}, \tag{49}\]  
where \(\xi\) and \(z\) are the waver number of RF links and the distance between the FSO transmitter and the receiver. We assume a point receiver, i.e., \(D<<z\), leading to \(d=0\)[32]. The average SNR of FSO is given by [33; 34]  
\[\gamma_{f_{0}}^{\text{HY}}=\frac{\eta\frac{P_{f_{0}}^{\text{HY}}P_{LO,f_{0}} ^{\text{HY}}}{\sigma_{f_{0}}^{\text{HY}}}}{\sigma_{f_{0}}^{\text{HY}}}, \tag{50}\]  
where \(\eta\), \(P_{f_{0}}^{\text{HY}}\sigma_{f_{0}}^{\text{HY}}\), and \(P_{LO,f_{0}}^{\text{HY}}=\alpha_{l}z\) are the responsivity of the FSO receiver, transmit power of the FSO transmitter, noise variance at the FSO receiver, and an attenuation factor by distance, respectively. The values of FSO parameters used in the simulation are summarized in Table 1[34; 35; 36]. For the desired channel \(h_{i}^{j}\), we assumed the channel power \(\sigma_{i}^{j}\) for \(\text{CN}(0,\sigma_{i}^{j})\) as  
\[\sigma_{i}^{j}=\frac{G_{\text{T}}G_{R}}{P_{PL,RF}P_{oxy}}, \tag{51}\]  
where \(G_{T}\), \(G_{R}\), \(P_{PL,RF}\), \(P_{oxy}\) is the transmit and receive antenna gains, pathloss, and an attenuation factor for oxygen. The pathloss and attenuation factor for oxygen is given by [36]  
\[P_{PL,RF}=20\log_{10}(4\pi zf_{RF}),\hskip 36.135 ptP_{oxy}=\alpha_{oxy}z. \tag{52}\]  
For the interfering channel \(g_{i}^{j}\), we assumed the channel power \(\hat{\sigma}_{i}^{j}\) for \(\text{CN}(0,\hat{\sigma}_{i}^{j})\) as  
\[\hat{\sigma}_{i}^{j}=\frac{G_{T}G_{R}}{P_{PL,RF}^{\text{HY}}P_{oxy}^{\text{HY }}}, \tag{53}\] \begin{table}
\begin{tabular}{c c c} \hline \hline
**FSO Parameter** & **Symbol** & **Value** \\ \hline Wavelength & \(\lambda_{f_{0}}\) & 1550 nm \\ \hline Photo detector diameter & \(D\) & 0.2 m \\ \hline Transmit power & \(P_{f_{0}}^{\text{HY}}\) & 20 dBm \\ \hline Responsivity & \(\eta\) & 0.5 \\ \hline Noise variance & \(\sigma_{f_{0}}^{\text{HY}}\) & \(5\times 10^{-12}\) \\ \hline Clear air & \(c_{n}^{2}\) & \(5\times 10^{-14}\) \\  & \(\alpha_{l}\) & 0.43 dB/Km \\ \hline Haze & \(C_{n}^{2}\) & \(1.7\times 10^{-14}\) \\  & \(\alpha_{l}\) & 4.2 dB/Km \\ \hline Moderate rain & \(C_{n}^{2}\) & \(5\times 10^{-15}\) \\  & \(\alpha_{l}\) & 5.8 dB/Km \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Simulation parameters for FSO systems. where \(P^{I}_{PL,RF}\), \(P^{I}_{oxy}\) is the pathloss and the attenuation factor for oxygen between interfering links, which is given by  
\[P^{I}_{PL,RF}=20\log_{10}(4\pi z^{I}f_{RF}),\qquad\qquad P^{I}_{oxy}=\alpha_{oxy }z^{I}, \tag{54}\]  
where \(z^{I}\) is the distance between interfering links. The value of the RF parameters used in the simulation is summarized in Table 2[36]. Figure 4 illustrates the stable regions for the SAS when the distance is set to \(z=z^{I}=3000\) m. In this scenario, we have \(s_{f_{1},\texttt{R}0}=s_{f_{2},\texttt{R}0}=s_{f_{1},\texttt{M}yr}=s_{f_{2}, \texttt{M}yr}=0.6581\), and \(s^{I}_{f_{1},\texttt{R}0}=s^{I}_{f_{2},\texttt{R}0}=s^{I}_{f_{1},\texttt{M}yr}= s^{I}_{f_{2},\texttt{H}yr}=0.2389\); while \(s_{f_{0},\texttt{H}yr}\) takes on the values of 1, 0.7308, and 0, respectively. Under clear air conditions, a hybrid FSO/RF pair can effectively transmit signals through the FSO link, leaving the \(f_{2}\) channel idle. Consequently, the RF pair remains unaffected by the hybrid FSO/RF pair, resulting in no change in the performance related to \(\lambda_{\texttt{R}0}\). In hazy conditions, the cooperative case achieves a higher \(\lambda_{\texttt{R}0}\) compared to the reference case (REF) when \(\lambda_{\texttt{H}yr}\) is between 0 and 0.875.