## 4 Simulation Results
### OP of the Secondary Network  
This sub-section studies the OP of the secondary network with \(N_{\text{T}}=N_{\text{R}}=2\). As presented in Figures 2 and 3, \(P_{\text{PT}}\) should be higher than \(-1\) (dB) so that the secondary transmitters are allowed to use the licensed band. In Figure 4, we present the OP at the secondary sources as a function of \(P_{\text{PT}}\) in dB with different values of the number of relays (\(M\)), and with \(x_{\text{R}}=0.3\). At first, we can see that the simulation results verify the correction of the expressions of \(\text{OP}_{\text{SS}_{1}}\) and \(\text{OP}_{\text{SS}_{2}}\) derived in Section 3. Then, we can see that \(\text{OP}_{\text{SS}_{2}}\) is lower than \(\text{OP}_{\text{SS}_{1}}\) because the datum \(x_{1}\) has not yet been decoded by \(\text{SR}_{b}\) at the first time slot. It is also seen from Figure 4 that the OP of \(\text{SS}_{1}\) and \(\text{SS}_{2}\) is lower with the increase in the number of relays (\(M\)). However, as observed in \(\text{OP}_{\text{SS}_{2}}\), with \(M=3\) and \(M=8\), \(\text{OP}_{\text{SS}_{2}}\) only changes slightly. Finally, we can observe that \(\text{OP}_{\text{SS}_{1}}\) and \(\text{OP}_{\text{SS}_{2}}\) decrease with the increase in \(P_{\text{PT}}\). However, both \(\text{OP}_{\text{SS}_{1}}\) and \(\text{OP}_{\text{SS}_{2}}\) rapidly converged to saturation values as \(P_{\text{PT}}\) is sufficiently high. Moreover, the saturation values do not depend on \(P_{\text{PT}}\), which means that the diversity order is equal to zero. To explain the saturation points in Figure 4, we first rewrite the SINRs given in (10), (12), and (18) at a high \(P_{\text{PT}}\) regime as follows:  
\[\psi_{\text{SR}_{b},x_{1}}\overset{P_{\text{PT}}\rightarrow+\infty}{\approx }\frac{P_{\text{SS}_{1}}g_{\text{SS}_{1}\text{SR}_{b}}}{P_{\text{SS}_{2}}g_{ \text{SS}_{2}\text{SR}_{b}}+P_{\text{PT}}g_{\text{PT}\text{T}\text{SR}_{b}}},\psi_{\text{SR}_{b},x_{2}}\overset{P_{\text{PT}}\rightarrow+\infty}{\approx }\frac{P_{\text{SS}_{2}}g_{\text{SS}_{2}\text{SR}_{b}}}{P_{\text{PT}}g_{ \text{PT}\text{SR}_{b}}}, \tag{57}\]  
\[\varphi_{\text{SS}_{1}}\overset{P_{\text{PT}}\rightarrow+\infty}{\approx} \frac{P_{\text{SR}_{b}}g_{\text{SR}_{b}\text{SS}_{1}}}{P_{\text{PT}}g_{  
From (35), (57), and (58), we can see that SINRs \(\psi_{\text{SR}_{\text{P}},\
u_{1}}\), \(\psi_{\text{SR}_{\text{P}},\
u_{2}}\), \(\varphi_{\text{SS}_{1}}\), and \(\varphi_{\text{SS}_{2}}\) at high \(P_{\text{PT}}\) values do not depend on \(P_{\text{PT}}\), and this is the reason why \(\text{OP}_{\text{SS}_{1}}\) and \(\text{OP}_{\text{SS}_{2}}\) converge to the saturation values. Figure 5 presents \(\text{OP}_{\text{SS}_{1}}\) and \(\text{OP}_{\text{SS}_{2}}\) as functions of the number of relays (\(M\)) with different positions of the secondary relays and with \(P_{\text{PT}}=10\) (dB). As seen from Figure 5, \(\text{OP}_{\text{SS}_{1}}\) and \(\text{OP}_{\text{SS}_{2}}\) are lower with the increase in \(M\). However, when \(M\) is high enough, \(\text{OP}_{\text{SS}_{1}}\) and \(\text{OP}_{\text{SS}_{2}}\) converge to saturation values. For example, when \(x_{\text{R}}=0.4\), \(\text{OP}_{\text{SS}_{2}}\big{(}\text{OP}_{\text{SS}_{1}}\big{)}\) converges to the constants as \(M\geq 2\) (\(M\geq 6\)). Figure 5 also illustrates that, as \(M\) increases, the performance gap between \(\text{OP}_{\text{SS}_{1}}\) and \(\text{OP}_{\text{SS}_{2}}\) is smaller. Therefore, an increasing \(M\) also provides the performance fairness between \(\text{SS}_{1}\) and \(\text{SS}_{2}\). Finally, it can be observed that position of the secondary relays significantly affects \(\text{OP}_{\text{SS}_{1}}\) and \(\text{OP}_{\text{SS}_{2}}\). As seen from Figure 5, \(\text{OP}_{\text{SS}_{1}}\) and \(\text{OP}_{\text{SS}_{2}}\) with \(x_{\text{R}}=0.2\) are much lower than those with \(x_{\text{R}}=0.4\).