## 5 Simulation Study  
In this section, the achievable spectrum efficiencies with different subchannel selection policies are compared. Here, the spectrum sharing load factor is \(\theta_{Q}=-30\) dB and the number of subchannels is \(N=40\). The mean values of random variables \(g_{ps}^{j},g_{ss}^{j}\) are denoted by \(\lambda_{ps},\lambda_{ss}\), respectively. The achieved spectrum efficiency is defined as follows:  
\[C_{\rho_{\psi}}=C_{M}^{\rho_{\psi}}/M\Delta f \tag{58}\]  
Here, in order to facilitate the comparison, \(C_{\rho_{1}}\) is defined as the achieved spectrum efficiency with uniform subchannel selection, \(C_{\rho_{ss}}\) is defined as the achieved spectrum efficiency with the SU-SU-based selection policy, \(C_{\rho_{ps}}\) is defined as the achieved spectrum efficiency with the SU-PU-based selection policy. In the first simulation, suppose the interference threshold is a constant and \(\lambda_{ps}=\lambda_{ss}\), and the \(C_{\rho_{\psi}}\) is analyzed by increasing \(M\), which is depicted in Figure 6.  
As depicted in Figure 6, \(C_{\rho_{1}}\) is lower than that of \(C_{\rho_{ss}}\) and \(C_{\rho_{ps}}\), therefore, it indicates that \(\rho_{1}\) has a poorer performance compared to \(\rho_{ss}\) and \(\rho_{ps}\). For \(M=1\), the gap between \(C_{\rho_{1}}\) and \(C_{\rho_{ss}}\) is large. However, with the increase of \(M\), the gap is reduced. This result is reasonable because the tap is related to the \(M/N\) ratio, and the larger \(M/N\), the lower the tap is. The reason is that for a larger \(M/N\), the set of \(M\) subchannels accessible by \(C_{\rho_{1}}\) and \(C_{\rho_{ss}}\) probably has a large overlap. With the increase of \(M\), the rate of decrease of \(\rho_{ps}\) is reduced with the slowest rate. This is mainly due to the fact that the total interference threshold of the receivers of the PUs is a constant. At the same time, \(\rho_{ps}\) selects these subchannels with the lower \(g_{ps}^{j}\), which enables the SUs transmitters to send the maximum transmitting power, without generating high interference on the receivers of the  
Figure 6: Achieved spectral efficiency of the SUTCH with three selection policies with \(M\). Pus and satisfying the constraint of the interference threshold of the PUs. According to Figure 6, for a large number of accessible subchannels with constant interference constraint, \(\rho_{ps}\) achieves a better performance. In the second simulation, the influence of the number of subchannels \(N\) is analyzed. Suppose \(M=1\), \(\lambda_{ps}=\lambda_{ss}\), the \(C_{\rho_{\mathcal{P}}}\) is analyzed by increasing \(N\). The result is depicted in Figure 7.  
As seen in Figure 7, for all the different subchannel selection policies, the \(C_{\rho_{\mathcal{P}}}\) increases with the increase of \(N\). This is because that the probability of selecting proper subchannels for SUTCH is increasing with \(N\). Furthermore, it is interesting to find that the gap between these three selection policies also increases with the increase of \(N\) and \(\rho_{ss}\) outperforms the others in this simulation. In the third simulation, both the influences of \(g_{ps}\) and \(g_{ss}\) are evaluated. Suppose \(N=40\), \(M=1\). The \(C_{\rho_{\mathcal{P}}}\) is analyzed with \(\lambda_{ps}/\lambda_{ss}\) for different \(\theta_{Q}\) values. The simulation result is depicted in Figure 8.  
Figure 8: Achieved spectral efficiency of the SUTCH under three selection policies with \(\lambda_{ps}/\lambda_{ss}\). Figure 7: Achieved spectral efficiency of the SUTCH under three selection policies with \(N\). As depicted in Figure 8, it is clearly observed that the \(C_{\rho_{\Psi}}\) of the SUTCH decreases with the increase of \(\lambda_{ps}/\lambda_{ss}\). Meantime, the \(C_{\rho_{\Psi}}\) of the SUTCH decreases with the decrease of \(\theta_{Q}\). This is due to the fact that with the increase of \(\lambda_{ps}/\lambda_{ss}\), the attenuation of \(g_{ps}\) is decreased while that of \(g_{ss}\) is increased.