## 6 Numerical Results and Discussions  
Capitalizing on the aforementioned derived analytical expressions, various numerical and simulation results under different Fisher-Snedecr \(\mathcal{F}\) fading scenarios are presented and discussed in this section. In the simulations, we adopted the simulation approaches described in [29; 38]. All of the simulation results show a good agreement with the numerical analysis and validate the accuracy of our derivations. In the theoretical analysis, a Python code provided in [52] was applied to evaluate the bivariate Meijer G-function and multivariate Fox's H-function in Section 5. For certain analytical expressions, including the sum of the two-fold infinite series, the required minimum numbers of truncated terms are provided in Tables 1-4 in [38] for different cases in order to meet the given target accuracy, while for the sum of the four-fold infinite series in the n.i.n.i.d. case, an example for the convergence rate of the infinite sum by using (15) and (25) at the sixth significant figure is as follows: \(k_{min}=l_{min}=30\), \(l_{min}=j_{min}=20\), as \(m_{1}=1\), \(m_{2}=2\), \(n_{1}=5\), \(n_{2}=6\), \(\rho_{N}=\rho_{G}=0.5\), \(\gamma_{\tau}=\gamma_{th}=3\) dB. Furthermore, we consider comparisons and discussions regarding the impacts of the correlation coefficients and the optimum threshold on the performance of the switched diversity systems, because the impacts of the multipath parameters and the shadowing parameters on the performance were widely discussed in [34; 38]. In Figure 1, we show a comparison of the normalized average output SNR values of SCC (\(\overline{\gamma}_{SCC}/\overline{\gamma}\)), PSC (\(\overline{\gamma}_{SC}/\overline{\gamma}\)), SEC (\(\overline{\gamma}_{SEC}/\overline{\gamma}\)), and SECps (\(\overline{\gamma}_{SECps}/\overline{\gamma}\)) as functions of the multipath fading parameter (\(m\)) over Fisher-Snedecor \(\mathcal{F}\) and Nakagami-\(m\) (\(n\rightarrow\infty\), Equations (18), (28), (82) and (84) in [53]) fading channels when \(\overline{\gamma}\) = 5 dB and \(\gamma_{\tau}\) = 5 dB. It can be seen from Figure 1 that the average SNR gain decreases gradually as \(m\) increases for various fading scenarios. Especially for the smaller values of \(m\), this gain degrades quite rapidly. When one parameter varies and other parameters are fixed for comparison purposes, we find that: (_i_) the average SNR gain of the i.i.d. case (\(\rho_{N}=0\) and/or \(\rho_{G}=0\)) is higher than that of the n.i.i.d. case (\(\rho_{N}=0.5\) or \(\rho_{G}=0.5\)); (_ii_) the average SNR gain over Nakagami-\(m\) (\(n\rightarrow\infty\)) fading channels is smaller than that over Fisher-Snedecor \(\mathcal{F}\) (\(n=5\)) fading channels; (_iii_) the average SNR gain of the PSC outperforms that of the SCC. Furthermore, it is clear that the average SNR gains of the SEC and the SECps (\(L=3\)) become larger by comparing them with the dual-branch SSC, while the average SNR gain of the SECps outperforms that of the SEC. It is interesting to note that the average SNR gain of the SSC system in the n.i.i.d. case achieves the maximum value as \(\gamma_{\tau}=5\) dB by comparing it with \(\gamma_{\tau}=8\) dB (dot line) and \(\gamma_{\tau}=2\) dB (dash line). This is because \(\gamma_{\tau}=5\) dB approaches the optimum switching threshold \(\gamma_{\tau}^{*}\approx 5.56\) dB when \(\overline{\gamma}=5\) dB, where \(\gamma_{\tau}^{*}\) can be calculated with the help of the numerical analysis of (61). Based on (67), Figure 2 illustrates the AoF values of switched diversity systems as functions of the multipath fading parameter (\(m\)) for various correlation conditions over Fisher-Snedecor \(\mathcal{F}\) fading channels, where \(n=5\), \(\overline{\gamma}=5\) dB, and \(\gamma_{\tau}=5\) dB. As expected, it can be observed that the values of the AoF show similar behaviors as the average SNR gain values in Figure 1 as \(m\) increases. On the contrary, the AoF increases with the increase of the correlation coefficients ( \(\rho_{G}=\rho_{N}=0\), 0.5, 0.7, 0.9, 1).