## 5 Simulation Study
Consequently, the \(C_{\rho_{\Psi}}\) of SUTCH is lower with the same transmitting power. On the other hand, with the decrease of \(\theta_{Q}\), the power allocated to each selected subchannel is bound to be reduced, which will lead to the deterioration in the \(C_{\rho_{\Psi}}\) of the SUTCH. Compared comprehensively, the \(C_{\rho_{\Psi}}\) of the SUTCH with \(\rho_{1}\) has the lowest value, since it just ignores any a priori knowledge of subchannel's status. However, under different conditions, the performance of the \(\rho_{ss}\) and \(\rho_{ps}\) are different. When the ratio of \(M/N\) is small, the best subchannel selection policy is \(\rho_{ss}\). However, if the ratio of \(M/N\) is large, the best subchannel selection policy is \(\rho_{ps}\). In the fourth simulation, as mentioned above, in Equation (49), the BER of SUCCH is derived. Therefore, Monte Carlo Simulation is used to prove its rationality. The simulation parameters are shown in Table 1. Suppose \(\sigma_{PU}^{2}=\sigma_{\text{SUTCH}}^{2}\). In Figure 9, the Simulation BER is calculated by Monte Carlo Simulation Experiment, while the Theoretical BER is calculated by Equation (49). As depicted in Figure 9, the simulation BER follows the Theoretical BER very closely. As mentioned in Section 4, the trade-off problem between the reliability of the SUCCH and the efficiency of the SUTCH is discussed. Here, suppose the arrival rate of the authorized PUs accessing to the subchannels follows a Poisson distribution. Simulation parameters are shown in Table 2. Suppose \(\lambda_{m}^{j}\) represents the arrival rate of the PUs in accessible subchannels. In the fifth simulation, the achieved spectral efficiency, achieved data traffic and unused data traffic are used to compare the accessible performance of the three different selection policies. Here, achieved spectral efficiency represents the proportion between data traffic and unused data traffic. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline \(N\) & 40 \\ Number of active PUs and SUs & [1, 40] \\ \(G_{\text{SUCCH}}\) & 2048 \\ Loading factor \(\Gamma\) & [1/160, 1/200,..., 1/400] \\ Random test times for each \(\Gamma\) & 750,000 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Simulation parameters. Figure 9: Theoretical and simulation BER versus different \(\Gamma\). Data traffic is the total amount of unit data traffic when the SUTCH has successfully accessed to the idle subchannel, while unused data traffic is the achievable amount of unit data traffic during the time cost in establishing the connection. In Figures 10-12, the different performances of the three strategies are shown in detail. Random strategy has the worst accessible performance, because it simply chooses the loading factor \(\Gamma\) randomly without proper accessible strategies. Meanwhile, the accessible performance of MDP Cross is better than that of Statistical Mean. Furthermore, the fluctuation of performance curve of MDP Cross is lower than that of Statistical Mean. It is due to the fact that, in the simulation, suppose \(\lambda_{m}^{j}\), \(j=1,2,\ldots,6\in[80,160]\) the state parameters of the accessible subchannel are changing very fast, therefore, it is a quick-changing subchannel environment. In the quick-changing subchannel environment, the history state information of subchannel environment is changing very fast. However, Statistical Mean will use a lot of history information, so the fast-changing of history information will make a bad influence on choosing the optimal allocation strategy of \(\Gamma\). Therefore, the accessible strategy of MDP Cross fits better in the quick-changing subchannel environment.