## 4 Simulation Results and Analysis
That is because the PS factor is fixed and the cooperative relay is chosen randomly while the proposed scheme has the optimal TS factor, the optimal cooperative relay and the optimal power allocation. Figure 5 shows the information rate of our proposed scheme under four different cases. The fix TS factor is set as \(\alpha_{F}=0.5\). Case 1 is the proposed algorithm that has the optimal relay, the optimal power allocation and the optimal TS factor, which is called O-PA&O-RS&O-TS. The optimal relay, the optimal power allocation and the fixed TS factor is called O-PA&O-RS&F-TS as case 2. Case 3 is the optimal relay, the equal power allocation \(P_{S1}=P_{S2}=P_{T}^{\max}/2\) and the fixed TS factor, which is called E-PA&O-RS&F-TS. Case 4 is the random relay, the equal power allocation and the fixed TS factor, which is called E-PA&R-RS&F-TS. From Figure 5, we note that the optimal relay selection has a great impact on the information rate by comparing case 3 and case 4. However, the information rate of case 2 and case 3 are very similar, for the system only allocates power to two source nodes, and the channels are distributed and independent. As shown in Figure 5, case 4 has the worst performance in four algorithms. The performance of case 2 and case 3 are improved compared with case 4, while the proposed algorithm has the best performance. The information rate of the proposed scheme is about 1.4 bps/HZ higher than case 2 and case 3 when SNR = 20 dB. Figure 6 displays the information rate versus SNR by comparing the proposed scheme, joint power allocation and relay selection in [20] and the traditional equal power allocation (EPA) scheme. From reference [20], the optimal values of \(P_{S1}\), \(P_{S2}\) and \(P_{R_{i}}\) can be obtained as  
\[P_{S1}=\frac{P_{T}^{\max}\sqrt{1+P_{T}^{\max}{|{g_{i}}|}^{2}}}{2\sqrt{1+P_{T}^ {\max}{|{h_{i}}|}^{2}}+2\sqrt{1+P_{T}^{\max}{|{g_{i}}|}^{2}}} \tag{30}\]  
\[P_{S2}=\frac{P_{T}^{\max}\sqrt{1+P_{T}^{\max}{|{h_{i}}|}^{2}}}{2\sqrt{1+P_{T}^ {\max}{|{h_{i}}|}^{2}}+2\sqrt{1+P_{T}^{\max}{|{g_{i}}|}^{2}}} \tag{31}\]  
\[P_{R_{i}}=P_{T}^{\max}/2 \tag{32}\]  
Figure 4: The proposed scheme versus the PS scheme. With the optimal power allocation solution found, selecting the relay node with maximum SNR as cooperative relay. The traditional EPA scheme is defined as \(P_{\mathrm{S1}}=P_{\mathrm{S2}}=P_{R_{i}}=P_{T}^{\mathrm{max}}/3\) and the relay selection is random. From Figure 6, it can be seen that the proposed scheme has better performance than the other two schemes. And compared with the other two schemes, the relay node can harvest energy through wireless-powered, which solve the power constraint of relay nodes. As shown in Figure 7, the number of relay nodes in the relay set has an impact on the information rate. The proposed algorithm has the lowest information rate when \(R=10\). As the number of relays increases, the information rate increases. When the number of relays reaches 100, the information rate can reach 3.49 bps/HZ. The improvement of the information rate can reach 0.1 bps/HZ when the relay numbers from 10 to 50. However, the improvement of the information rate is only about 0.02 bps/HZ when the relay numbers from 50 to 100, which indicates that excessive candidate relays do not significantly improve the information rate. In future research, we can expand the optimal number of candidate relays in this study. Figure 5: Performance of TS scheme in different power allocation and relay selection methods. Figure 6: Performance comparison between the proposed scheme and the conventional scheme.