## 3 Performance Analysis
### Outage Probability  
The OP is a common metric for measuring the reliability of a wireless communication system. The OP is defined as the probability of the received SNR \(\gamma\) being smaller than a given threshold \(\gamma_{\text{th}}\). Therefore, the OP can be expressed as  
\[P_{\text{out}}(\gamma_{\text{th}}) =\Pr(\gamma\leq\gamma_{\text{th}})\] \[=\Pr(\max\{\gamma_{1},\gamma_{2},\ldots,\gamma_{M}\}\leq\gamma_{ \text{th}})\] \[=\prod_{m=1}^{M}F_{\gamma_{m}}(\gamma_{\text{th}}) \tag{15}\]  
where \(F_{\gamma_{m}}(\cdot)\) represents the CDF of \(\gamma_{m}\). Note that the last equality holds because the \(M\) paths are independent of each other. According to (5), \(F_{\gamma_{m}}(\gamma_{\text{th}})\) can be expressed as  
\[F_{\gamma_{m}}(\gamma_{\text{th}})=1-\big{[}1-F_{\gamma_{m,1}}(\gamma_{\text{ th}})\big{]}\big{[}1-F_{\gamma_{m,2}}(\gamma_{\text{th}})\big{]} \tag{16}\]  
where \(F_{\gamma_{m,1}}(\cdot)\) and \(F_{\gamma_{m,2}}(\cdot)\) represent the CDFs of \(\gamma_{m,1}\) and \(\gamma_{m,2}\), respectively. According to (2), (14), and (9.31.5) in [24], \(F_{\gamma_{m,1}}(\gamma_{\text{th}})\) can be further written as  
\[F_{\gamma_{m,1}}(\gamma_{\text{th}}) =F_{h_{m,1}}(h_{\text{th}})\] \[=\exp\left(-\frac{\theta_{\text{FoV},m,1}^{2}}{2\sigma_{\text{o}}^ {2}}\right)+\left[1-\exp\left(-\frac{\theta_{\text{FoV},m,1}^{2}}{2\sigma_{ \text{o}}^{2}}\right)\right]\frac{\zeta_{m,1}^{2}}{\Gamma(\alpha_{m,1})\Gamma (\beta_{m,1})}\] \[\times G_{2,4}^{3,1}\bigg{[}\frac{\alpha_{m,1}\beta_{m,1}}{A_{m,1}h_{m,1}^{1}}\sqrt{\frac{\gamma_{\text{th}}\sigma_{\text{c}}^{2}}{2T^{2}P_{ \text{t}}^{2}}} \begin{array}{c}1,\zeta_{m,1}^{2}+1\\ \zeta_{m,1}^{2},\alpha_{m,1},\beta_{m,1},0\end{array} \right] \tag{17}\]  
where \(h_{\text{th}}=\sqrt{\gamma_{\text{th}}\sigma_{\text{f}}^{2}/\big{(}2T^{2}P_{ \text{t}}^{2}\big{)}}\) is the corresponding threshold of the channel gain. Similarly, the expression of \(F_{\gamma_{m,2}}(\gamma_{\text{th}})\) can be obtained as  
\[F_{\gamma_{m,2}}(\gamma_{\text{th}}) =\exp\left(-\frac{\theta_{\text{FoV},m,2}^{2}}{2\sigma_{\text{o} }^{2}}\right)+\left[1-\exp\left(-\frac{\theta_{\text{FoV},m,2}^{2}}{2\sigma_{ \text{o}}^{2}}\right)\right]\frac{\zeta_{m,2}^{2}}{\Gamma(\alpha_{m,2})\Gamma (\beta_{m,2})}\] \[\times G_{2,4}^{3,1}\bigg{[}\frac{\alpha_{m,2}\beta_{m,2}}{A_{m,2}h_{m,1}^{1}}\sqrt{\frac{\gamma_{\text{th}}\sigma_{\text{d}}^{2}}{2T^{2}P_{ \text{o}}^{2}}} \begin{array}{c}1,\zeta_{m,2}^{2}+1\\ \zeta_{m,2}^{2},\alpha_{m,2},\beta_{m,2},0\end{array} \right] \tag{18}\]Substituting (17) and (18) into (16), we can obtain the following expression of \(F_{\gamma_{m}}(\gamma_{\rm th})\):  
\[F_{\gamma_{m}}(\gamma_{\rm th}) = 1-\left\{\left[1-\exp\left(-\frac{\theta_{\rm FoV,m,1}^{2}}{2 \sigma_{0}^{2}}\right)\right]\left[1-\frac{\zeta_{m,1}^{2}}{\Gamma(\alpha_{m,1} )\Gamma(\beta_{m,1})}\right.\right. \tag{19}\] \[\times G_{2,4}^{3,1}\Bigg{[}\frac{\alpha_{m,1}\beta_{m,1}}{A_{m,1 }h_{m,1}^{4}}\sqrt{\frac{\gamma_{\rm th}\sigma_{r}^{2}}{2T^{2}P_{\rm t}^{2}}} \Bigg{[} \begin{array}{c}1,\zeta_{m,1}^{2}+1\\ \zeta_{m,1}^{2},\alpha_{m,1},\beta_{m,1},0\end{array} \Bigg{]}\Bigg{]}\Bigg{\}}\] \[\times\left\{\left[1-\exp\left(-\frac{\theta_{\rm FoV,m,2}^{2}}{2 \sigma_{0}^{2}}\right)\right]\left[1-\frac{\zeta_{m,2}^{2}}{\Gamma(\alpha_{m, 2})\Gamma(\beta_{m,2})}\right.\right.\] \[\left.\left.\times G_{2,4}^{3,1}\Bigg{[}\frac{\alpha_{m,2}\beta_{ m,2}}{A_{m,2}h_{m,2}^{4}}\sqrt{\frac{\gamma_{\rm th}\sigma_{\rm d}^{2}}{2T^{2}P_{ \rm o}^{2}}}\Bigg{[} \begin{array}{c}1,\zeta_{m,2}^{2}+1\\ \zeta_{m,2}^{2},\alpha_{m,2},\beta_{m,2},0\end{array}