## 6 Numerical and Simulation Results
Furthermore, the asymptotic results at the high average SNR region and the numerical results by using the mixed \(\alpha\)-\(\mu\) model also show similar behaviors as those in Figure 3. These results demonstrate the parameters \(\alpha\) and \(L\) can provide the diversity gain, as shown in (64). In Figure 6, based on (42) and (43), we obtain the ASEP of MPSK for the MRC system in the i.n.i.d. and correlated cases. It is clear that the ASEP of MPSK degrades with the increase in the correlation coefficients (\(\rho=\rho_{N}=\rho_{G}=0\) and \(0.5\)) and/or the order of modulation (\(M=2\), \(4\), \(8\), and \(16\)). Figure 4: Outage probability of various communication systems as a function of the average SNR (\(\overline{\gamma}\)) over i.i.d. and correlated \(\alpha\)-\(\mu\)/IGA fading channels with \(n=5\), \(\mu=2\), and \(\gamma_{th}=5\) dB. Figure 5: ABEP of DPSK for various communication systems as a function of the average SNR (\(\overline{\gamma}\)) over i.i.d. \(\alpha\)-\(\mu\)/IGA fading channels with \(n=5\) and \(\mu=2\). Figure 3: Outage probability of various communication systems as a function of the average SNR over i.i.d. \(\alpha\)-\(\mu\)/IGA fading channels with \(n=5\), \(\mu=2\), and \(\gamma_{th}=5\) dB. Figure 7 plots the average channel capacity per unit bandwidth of various communication systems versus the average SNR (\(\overline{\gamma}\)) over several different communication conditions. It is evident that the average capacity improves with the growth of the value of \(\alpha\), \(\mu\), \(n\), \(L\), and/or \(\overline{\gamma}\), respectively. However, the increase in \(\rho\) (\(\rho=\rho_{N}=\rho_{G}\)) leads to the reduction in the average capacity. Interestingly, the growing trends of average capacity become slight when the value of \(n\) gets larger (\(n=5\)-\(50\)) and/or when the value of \(\rho\) gets smaller (\(\rho=0.5\to 0\)). These results suggest these parameters have less impact on the average capacity than other parameters (\(\alpha\), \(\mu\), \(L\), and/or \(\overline{\gamma}\)). More importantly, the approximated analysis using (49) and the mixed \(\alpha\)-\(\mu\) model matches well with the exact numerical results. Moreover, Figure 8 shows the EC of various communication systems as a function of the average SNR (\(\overline{\gamma}\)) over several different communication conditions with \(n=5\) and \(\mu=2\). It can be seen from Figure 8 that the EC gets larger with the increase in the value of \(\alpha\), \(L\), and/or \(\overline{\gamma}\), respectively. On the other hand, the EC gets smaller when the value of A and/or \(\rho\) (\(\rho=\rho_{N}=\rho_{G}\)) grows, where the parameter A has a dominating impact on the EC. In addition, the approximated results by using (57) and the mixed \(\alpha\)-\(\mu\) model show good agreements with the exact numerical results. Figure 6: ASEP of MPSK for the MRC system as a function of the average SNR (\(\overline{\gamma}\)) over i.n.i.d. and correlated \(\alpha\)-\(\mu\)/IGA fading channels with \(n=5\) and \(\mu=2\). Figure 7: Average channel capacity per unit bandwidth of various communication systems as a function of the average SNR (\(\overline{\gamma}\)) over different \(\alpha\)-\(\mu\)/IGA fading channels.