## 6 Numerical Results and Discussions
This is because the system performance degrades when the correlation coefficients become larger. For comparison purposes, the AoF values of the dual-branch PSC system, three-branch SEC, and SECps systems are also presented. It is evident that the AoF value of the PSC system has a lower value than that of SSC under the same correlation conditions, while the SECps system can provide better system performance than the SEC system. By using (26), (28) and (46), the OP values of SSC and SEC receivers are plotted in Figure 3 as functions of the average output SNR (\(\overline{\gamma}\)) first branch over \(\mathcal{F}\) composite fading conditions. It can be seen that the OP achieves optimum performance as \(\gamma_{th}=\gamma_{\tau}\) and shows the worst performance as \(\gamma_{th}>\gamma_{\tau}\), regardless of the fading conditions. This is because the OP of the SSC receiver can be viewed as that of the PSC system as \(\gamma_{th}=\gamma_{\tau}\) in [53]. As expected, the OP of the SEC with \(L=3\) can be improved by comparing it with the dual-branch SSC system. Figure 4 depicts the OP of the dual-branch SSC system as a function of the average SNR (\(\overline{\gamma}_{1}\)) of the first branch over n.i.n.i.d. Fisher-Snedecor \(\mathcal{F}\) fading channels with \(\overline{\gamma}_{th}\) = \(\gamma_{\tau}\) = 3 dB. For comparison, a moderate fading case (\(m_{1}\) = 1.2, \(m_{2}\) = 1.5, \(n_{1}\) = 5, \(n_{2}\) = 6, \(\rho_{G}\) = \(\rho_{N}\) = 0.5, \(\overline{\gamma}_{1}\) = \(\overline{\gamma}_{2}\)) is considered as a benchmark (black curve). As anticipated, it can be observed from Figure 4 that the OP is significantly improved when the multipath fading parameters (\(m\)) become larger and other parameters are fixed. On the other hand, when the correlation coefficients decrease, the shadowing parameters grow, or the average SNR of the second branch becomes larger than the one of the first branch, the OP is gradually raised. This is because the multipath fading parameters affect the curve slope of the OP, while the other parameters have an impact on the coding gain of the OP, where the coding gain is defined as the shifting degree of the OP curve to the left versus the SNR in a log-log scale. Figure 3: Outage probability values of dual-branch SSC and three-branch SEC systems as functions of the average SNR (\(\overline{\gamma}_{1}\)) first branch over Fisher–Snedecor \(\mathcal{F}\) fading channels, with different values of \(\overline{\gamma}_{th}\) and \(\gamma_{\tau}\) and with \(m\) = 2 and \(n\) = 5. Figure 2: Comparison of the AoF values of different switched diversity systems as functions of the multipath fading parameter (\(m\)) over Fisher–Snedecor \(\mathcal{F}\) fading channels, where \(n\) = 5, \(\overline{\gamma}\) = 5 dB, and \(\gamma_{\tau}\) = 5 dB. Figure 5 plots the comparison of the OP values of different switched diversity systems as functions of the outage threshold (\(\gamma_{th}\)) with \(m=2\), \(n=5\), \(\overline{\gamma}_{1}=10\) dB, and \(\gamma_{\tau}=3\) dB. It is clear that the OP of the SSC greatly deteriorates with the increase of the correlation coefficients (\(\rho_{G}=\rho_{N}=0\), 0.5, 0.7, 0.9, 1). These results demonstrate that the increase of the correlation coefficients leads to the worst received signals, while the OP of the SSC system tends toward that of a single branch (i.e., no diversity, \(\rho_{G}=\rho_{N}=1\)). Importantly, as \(\gamma_{th}\leq\gamma_{\tau}\), we can see from Figure 5 that the OP of the SEC significantly outperforms that of the SSC with the increase of the number of branches, while the OP of the SECs shows the same performance as that of the PSC; as \(\gamma_{th}>\gamma_{\tau}\), the OP of all the switched diversity systems shows the worst value. This may be explained by the fact that the increase of the outage threshold value degrades the system performance and results in no diversity gain. Therefore, the switched diversity systems can provide the diversity gain only when \(\gamma_{th}\leq\gamma_{\tau}\).