## 4 Numerical Results  
In this section, numerical computer simulations are provided to verify the theoretical analysis and show the impacts of key parameters on the system performance. In what follows, we set \(P_{1}=P_{2}=\mu P_{r}\), \(\delta_{1}^{2}=\delta_{2}^{2}=\delta_{r}^{2}\), \(\overline{\lambda}_{1i}=\overline{\lambda}_{2i}=\overline{\gamma}\), \(R_{s}=20\) bit/s/Hz, and \(M=3\); Furthermore, we assume that the \(S_{1}\)-R and \(S_{2}\)-R link have the same impairment level in Figures 2-8, which means that \(k_{1}=k_{2}=k_{3}=k\). The parameters for the shadowed-Rician fading channel are located Table 1.  
Figures 2 and 3 plot the OP of the system versus different \(\overline{\gamma}\) for AF and DF protocols, respectively. From both figures, we first observe that the simulation results are tight across the analytical results versus the entire SNRs, which justify the correctness of the analytical results. Secondly, we can see that the OP of the system will be fixed when the system is under HIs and the SNR is high enough. Thirdly, we also get that the system will have lower OP when the HIs level is larger. Finally, we derive that the OP between AF and DF protocol is different at the same SNR where the OP of AF is lower than that of DF protocol, which implies the advantages of AF protocol in this paper. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Shadowing** & \(\mathbf{m_{1i}}\) & \(\mathbf{b_{1i}}\) & \(\mathbf{\Omega_{1i}}\) \\ \hline Frequent heavy shadowing (FHS) & 1 & 0.063 & 0.0007 \\ Average shadowing (AS) & 5 & 0.251 & 0.279 \\ Infrequent light shadowing (ILS) & 10 & 0.158 & 1.29 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Channel Parameters. Figures 4 and 5 show that the OP of the system versus different \(x_{0}\) for AF and DF protocols, respectively. According to the different forward protocols, the predefined threshold \(x_{0}\) ranges from 0 dB to 30 dB and 16 dB, respectively. The outage threshold will have a bound when the system is suffering HIs, which has been proved by (24) and (31). When the threshold is larger than the bound, the OP will be always 1. From both figures, we also know that the threshold bound of system is just the function of the HIs level. The larger impairments level is, the larger threshold bound would be obtained. Besides, the bound of DF protocol is lower than that of AF protocol, which is the character of the forward protocol in HIs environment. Figure 3: OP of the system for DF protocol versus different \(\overline{\gamma}\). Figure 2: OP of the system for AF protocol versus different \(\overline{\gamma}\). Figure 6 depicts OP of the system versus different \(\overline{\gamma}\) for different \(N\). It indicates that when more terrestrial relays are employed with the system, the system performance will be enhanced. The increasing of the terrestrial relay number will bring a great performance gain to the system. Figure 4: OP of the system for AF protocol versus different \(x_{0}\): FHS. Figure 5: OP of the system for DF protocol versus different \(x_{0}\): AS. Figures 7 and 8 illustrate the throughput of the system for both AF and DF protocols, respectively. From both figures, we observe that the throughput is lower than that of the target rate \(R_{s}\) for the reason that the system suffers HIs. The results from both figures also suggest that the system will have better performance when the level of the HIs is larger. They also depict that the system will have worse performance when the channel is under heavy shadowed-Rician fading. In addition, we know that the impact of HIs on DF protocol is larger than that of AF protocol in the considered network, which is the character of the considered HIs system. Figure 6: OP of the system versus \(N=2\) and \(N=4\): FHS. Figure 7: Throughput of the system for AF protocol versus different \(\overline{\gamma}\): AS. Figure 9 plots the OP of the system for AF and DF protocols versus different HIs level in AS. In this figure, we assume that \(k_{1}+k_{2}+k_{3}=2.7\)[37].