## 6 Numerical Results and Discussions
These systems achieve the same performance with the PSC as \(\gamma_{th}=\gamma_{\tau}\). Figure 4: Outage probability values of dual-branch SSC systems as functions of the average SNR (\(\overline{\gamma}_{1}\)) first branch over n.i.n.i.d. Fisher–Snedecor \(\mathcal{F}\) fading channels, where \(\overline{\gamma}_{th}=\gamma_{\tau}=3\) dB. Figure 5: Outage probability values of different switched diversity systems as functions of the outage threshold (\(\gamma_{th}\) ) over Fisher–Snedecor \(\mathcal{F}\) fading channels with \(m=2\), \(n=5\), \(\overline{\gamma}_{1}=10\) dB, and \(\gamma_{\tau}=3\) dB. Based on (35) and (68), Figure 6 plots the ABEP of DPSK for the dual-branch SSC receiver as a function of the average SNR of the first branch (\(\overline{\gamma}_{1}\)) over i.n.i.d. Fisher-Snedecor \(\mathcal{F}\) fading channels with \(\gamma_{\tau}\) = 5 dB. For the sake of comparison, a moderate fading case (\(m_{1}\) = 1.2, \(m_{2}\) = 1.5, \(n_{1}\) = 5, \(n_{2}\) = 6, \(\overline{\gamma}_{1}\) = \(\overline{\gamma}_{2}\)) is also assumed as a benchmark (black curve). As expected, it can be observed from Figure 6 that similar results are drawn as those in Figure 4.  
By using (49), (58) and (68), Figure 7 depicts the comparison of ABEP values of DPSK for the SEC, the SECps, and the multibranch PSC as functions of the average SNR of the first branch (\(\overline{\gamma}_{1}\)) over i.i.d. Fisher-Snedecor \(\mathcal{F}\) fading channels with \(m\) = 2, \(n\) = 5, and \(\gamma_{\tau}\) = 6 dB. We can see from Figure 7 that the ABEP of SEC with four branches outperforms that of the dual-branch SEC (which is equivalent to the dual-branch SSC [3]), while the ABEP of SECps is improved compared with the SEC in the low and middle SNR regions. This is because the SECps provides the same behaviors as the PSC in the low SNR region. However, the ABEP values of the SEC and the SECps gradually tend toward the same performance in the high SNR region. This can be explained by the fact that the switched diversity systems prefer to remain in one branch and no branch switching occurs when two or more branches have a higher SNR, which is adequate to provide the desired performance, than the switching threshold SNR. In Figure 8, we demonstrate the ABEP values of DPSK for SSC, SEC, and SECps as functions of the switching threshold (\(\gamma_{\tau}\)) over Fisher-Snedecor \(\mathcal{F}\) fading channels, where \(m\) = 2, \(n\) = 5, and \(\overline{\gamma}_{1}\) = 10 dB. It can be observed from Figure 8 that the ABEP values of the SSC and SEC are optimal when a certain optimal switching threshold is determined. As an example, the optimum value of the ABEP of DPSK for the SSC system in the i.i.d. case is Pe(\(E\)) = 0.005798, while the optimal switching threshold is \(\gamma_{\tau}^{*}\)\(\approx\) 5 dB (i.i.d.-opt, red star). This optimal value is the same as the ABEP of PSC. Interestingly, the optimal ABEP of the SSC becomes larger and the optimal \(\gamma_{\tau}^{*}\) becomes smaller when the correlation coefficient increases. Furthermore, when \(\gamma_{\tau}\) becomes very small or is large enough that \(\overline{\gamma}_{1}\) = 10 dB, the ABEP values of the SSC and the SEC gradually approach that of the no-diversity case (\(\rho_{G}\) = \(\rho_{N}\) = 1). These results show that all the branches are unavailable when \(\gamma_{\tau}\) is higher, while all of the branches are acceptable when \(\gamma_{\tau}\) becomes smaller, meaning the diversity system is likely to choose one branch and no longer provides diversity gain. The performance of the SECps gradually improves from SEC to PSC when \(\gamma_{\tau}\) grows, and no optimal threshold exists. This is because no branch is acceptable and the SECps has  
Figure 6: ABEP of DPSK for the dual-branch SSC as a function of the average SNR of the first branch (\(\overline{\gamma}_{1}\)) over i.n.i.d. Fisher-Snedecor \(\mathcal{F}\) fading channels with \(\gamma_{\tau}\) = 5 dB. to choose the branch with the largest SNR.