## 5 Calculation of Outage Probability Using (5)
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Sr. no.** & **Fading Channel** & **CDF Evaluated at and from \(\gamma_{th}\)** \\ \hline \multicolumn{3}{c}{Small-scale multipath scattering propagation models} \\ \hline
1 & Rayleigh [5] & \(1-\exp\left(\frac{-\gamma_{th}}{\hat{\gamma}}\right)\) \\ \hline
2 & \(\eta-\lambda-\mu\)[10] & \(\begin{bmatrix}1-\left(\frac{2\sqrt{\pi}(1+\lambda^{2})}{p^{2}}\right)^{2p} \frac{\sqrt{\pi}}{\gamma(\mu)^{2}\delta\lambda-\delta\gamma}\\ \sum_{j=0}^{\infty}\frac{1}{j!\Gamma(\alpha+j+j)}\left(\frac{d}{\beta}\right) \left(\Gamma(2(\mu+j))-\Gamma\left(2(\mu+j),\frac{\gamma_{th}}{\hat{\gamma}} \right)\right)\end{bmatrix}\) \\ \hline
3 & \(\alpha-\lambda-\mu\)[11] & \(\begin{bmatrix}\frac{\sqrt{\pi}(1-\lambda^{2})^{p}}{2^{p}-\Gamma(p)}\sum_{j=0} ^{\infty}\frac{(\frac{j}{2})^{2j}}{j!\Gamma(j+\alpha+\beta)}\\ \left(\Gamma(2(\mu+j))-\Gamma(\mu+2j,j)\right)\end{bmatrix}\) \\ \hline
4 & [PERSON] [7] & \(1-\frac{\Gamma\left(m,\frac{m}{\hat{\gamma}}\gamma_{th}\right)}{\Gamma(m)}\) \\ \hline
5 & [PERSON] [8] & \(1-\exp\left(-\frac{2\sqrt{\pi}}{\hat{\gamma}}\Gamma\left(1+\frac{2}{c}\right) ^{\frac{5}{2}}\right)\) \\ \hline
6 & [PERSON] [9] & \(1-\left[Q\left(\alpha(\alpha)\sqrt{\frac{2\alpha}{\hat{\gamma}}},\beta(\alpha) \sqrt{\frac{2\alpha}{\hat{\gamma}}}\right)\right.\) \\ & & \(-Q\left(\beta(\alpha)\sqrt{\frac{2\alpha}{\hat{\gamma}}},\alpha(\alpha)\sqrt{ \frac{2\alpha}{\hat{\gamma}}}\right)\right]\) \\ \hline \multicolumn{3}{c}{Composite Multipath-Shadowing-LOS propagation (composite small- and large-scale fading)} \\ \hline
7 &
\begin{tabular}{c} Generalized \\ Gamma [4] \\ \end{tabular} & \(1-\frac{\Gamma\left(m\beta^{p}\gamma_{th}^{p}\right)}{\Gamma(m)}\) \\ \hline
8 & Generalized K [14] & \(1-\left[\pi c\kappa c\left(\pi\right)\left(\frac{(2\gamma_{th})^{p}\gamma_{ th}(\pi-\lambda+1+\pi\gamma_{th})}{\Gamma(\mu)\Gamma+\alpha(1+\pi)\gamma_{th}}\right) \right.\) \\ & & \(-\frac{(2\gamma_{th})^{p}\gamma_{th}(\pi_{th}(\pi_{th}+\lambda+1\pi_{th})}{ \Gamma(\mu)\Gamma+\alpha(1+\pi)\gamma_{th}})\right]\) \\ \hline \multicolumn{3}{c}{Composite multipath scattering and shadowing propagation with an LOS component} \\ \hline
9 & FTR [15] & \(\left(\frac{m+k}{\sqrt{(m+k)^{2}-k\Delta^{2}}}\right)^{m-1-2q}\gamma_{th}\phi_{ 2}^{(1)}\left(1+2q-m,m-q-0.5;\frac{m(1+k)}{(m+k)\gamma}\gamma_{th}\right)\) \\ & & \(-\frac{m(1+k)}{(m+k(1+\Delta))\gamma}\gamma_{th},-\frac{m(1+k)}{(m+k(1-\Delta)) \gamma}\gamma_{th},-\frac{1+k}{\gamma}\gamma_{th}\right)\bigg{]}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: CDF expressions of some popular fading channels. Scenario 3: In scenario 3, the links between S-R and R-D take the Weibull PDF and the Rayleigh PDF, respectively, representing a special case of both Rayleigh-generalized gamma fading and Nakagami-m-Weibull fading scenarios. This scenario is used to model multipath fading in both links, in which one link, represented by Rayleigh fading, is subjected to intense scattering with no line of sight of transmission and the other link, represented by Weibull fading, experiences fading that varies from worse to better than Rayleigh fading. Utilizing the CDF expressions from Table 2 in (5), the outage probability for scenario 3 can be calculated as  
\[p_{out}(\gamma_{th})=1-\exp\left(\frac{-\gamma_{th}}{\tilde{\gamma}}\right)\exp \left(-\frac{\gamma_{th}}{\tilde{\gamma}}\Gamma\left(1+\frac{2}{c}\right)^{ \frac{\delta}{2}}\right) \tag{8}\]  
Scenario 4: In scenario 4, the links take the Nakagami-m PDF and Nakagami-q PDF. Nakagami-q is a fading distribution which models short-term signal variations that span from one-sided Gaussian to Rayleigh fading. Such fading is usually observed on satellite links due to strong ionosphere scintillation. This scenario, therefore, models a system that experiences short-term signal variations in both links but one link is always subjected to signal variations that are worse than Rayleigh fading, as the case of satellite links suffering from ionosphere scintillation.