## Appendix A  
Based on (30), \(MGF_{\gamma_{SSC}}^{(\gamma_{1})}(s)\) can be written as:  
\[MGF_{\gamma_{mc}}^{(\gamma_{1})}(s)=\underbrace{\int_{0}^{\infty}\exp(-s\gamma )g_{\gamma_{1}}(\gamma)d\gamma}_{I_{A1}}+\underbrace{\int_{\gamma_{\tau}}^{ \infty}\exp(-s\gamma)f_{\gamma_{1}}(\gamma)d\gamma}_{I_{A2}}. \tag{11}\]  
To solve the first integral \(I_{A1}\) in (11), we insert (18a) into \(I_{A1}\) and use the identity in ([50], Equation (11)) to represent \(exp(-x)\) in terms of the Meijer G-function; with the aid of ([43], Equation (7.811.5)), \(I_{A1}\) can be derived as  
\[\begin{array}{ll}I_{A1}&=\sum\limits_{k=0}^{\infty}\sum\limits_{l=0}^{\infty }\sum\limits_{l=0}^{\infty}\sum\limits_{l=0}^{\infty}\frac{P_{l}^{k+l}P_{G}^{ \gamma_{l}+l}\sigma\Gamma(\lambda_{1})(m_{2}-m_{1}),(n_{2}-n_{1}),\alpha_{1}^ {m_{1}+1}\gamma_{\tau_{1}}+k}{\Gamma(m_{1})\Gamma(n_{1})\Gamma(m_{2}+k+l)(n_{2 }+l)(m_{1}+k)}\\ &\times G_{1,2}^{2,1}[s/\alpha_{2}\big{|}_{0,n_{2}+l+j}^{1-(m_{2}+k+i)}\big{|} _{2}F_{1}[\lambda_{1},m_{1}+k;1+m_{1}+k,-\alpha_{1}\gamma_{\tau}].\end{array} \tag{12}\]  
For the second integral \(I_{A2}\) in (11), we use the primary definition of the Meijer G-function defined in ([43], Equation (9.301)) to find the closed-form solution. Firstly, substituting (1) into \(I_{A2}\), \(I_{A2}\) can be rewritten as:  
\[\begin{array}{ll}I_{A2}&=\frac{\Lambda_{1}^{m_{1}}}{B(m_{1},n_{1})}\int_{0} ^{\infty}\frac{\gamma^{n_{1}-1}\exp(-s\gamma)}{(\Lambda_{1}\gamma+1)^{n_{1}+n _{1}}}d\gamma-\frac{\Lambda_{1}^{m_{1}}}{B(m_{1},n_{1})}\int_{0}^{\gamma_{ \tau}}\frac{\gamma^{n_{1}-1}\exp(-s\gamma)}{(\Lambda_{1}\gamma+To find the closed-form expression of \(I_{\Lambda 22}\), we represent \((1+x)^{a}\) in terms of the Meijer G-function defined in ([51], Equation (10)), then apply the primary definition of the Meijer G-function, whereby \(I_{\Lambda 22}\) can be rewritten as:  
\[\begin{array}{ll}I_{A22}&=\frac{\Lambda_{1}^{m_{1}}}{\Gamma(m_{1})\Gamma(m_{ 1})}\int_{0}^{\gamma_{\tau}}\gamma^{m_{1}-1}G  
By substituting (A12) into (A11) and employing the primary definition of the univariate Meijer G-function, the closed-form expression of \(\Psi_{1}\) can be yielded as:  
\[\Psi_{1}=\Gamma(0.5)G_{2,3}^{3,1}[g/\eta_{1}\big{|}_{0,n+l,0.5}^{1-(m+k),1}].\] (A13)  
Likewise, the closed-form expression of \(\Psi_{2}\) can be yielded as:  
\[\Psi_{2}=\Gamma(0.5)G_{2,3}^{3,1}[g/\Lambda_{2}\big{|}_{0,n,0.5}^{1-m,1}].\] (A14)  
Based on the definition of the bivariate Meijer G-function in ([45], Equation (13.1)), \(\Psi_{3}\) can be expanded as:  
\[\Psi_{3}=\bigg{(}\frac{1}{2\pi j}\bigg{)}^{2}\!\int_{L_{1}}\int_{L_{2}}\bigg{(} \int_{0}^{1}x^{t_{1}-0.5}(1-  
in terms of the multiple Mellin-Barnes-type contour integral defined in [44], after some mathematical manipulation, the closed-form expression of \(\Psi_{5}\) in (A18a) can be obtained as:  
\[\Psi_{5}=\frac{0.5^{0.5}}{\Gamma(0.5)}H_{1,1:2:1,1}^{0,1:2:1,1,1}[\frac{2g_{QAM} }{\eta_{1}},-0.5]_{(-0.5-1,1)}^{(0.5-1,1)}|_{(0.1),(n+l:1)}^{(1-(m+k):1)}|_{(0.1 )}^{(0.5,1)}]. \tag{21}\]  
Similarly, the closed-form expressions of \(\Psi_{6}\) and \(\Psi_{7}\) can be respectively obtained as:  
\[\Psi_{6}=\frac{0.5^{0.5}}{\Gamma(0.5)}H_{1,1:1,2:1,1}^{0,1:2:1,1,1}[\frac{2g_{ QAM}}{\Lambda_{2}},-0.5]_{(-0.5-1,1)}^{(0.5-1,1)}|_{(0.1),(n+1)}^{(1-m:1)}|_{(0.5 )}^{(0.5,1)}], \tag{22}\]  
\[\Psi_{7}=\frac{0.5^{0.5}}{\Gamma(0.5)}H_{2,2:0.1:1:1,1}^{0,2:1,1:1,1}[2g_{QAM} \gamma_{\tau},\gamma_{\tau}\Lambda_{2},-0.5]_{(-0.5-1,0.1),(-m:1,1,0)}^{(0.5-1, 1,0),(-m:1,1,0)}|_{0}-\left|\begin{smallmatrix}1-(m+n)\\ 0\end{smallmatrix}\right|_{0}^{0.5}]. \tag{23}\]  
Finally, by substituting (21), (22) and (23) into (A17), the analytical expression in (81) can be obtained.