# Combined Fusion Rules in Cognitive Radio Networks Using Different Threshold Strategies
## 6 Simulation Results  
MATLAB simulation environment is employed to simulate different scenarios to investigate the detection performance of different fusion schemes versus factors, such as number of sensing samples, \(M\), fusion rule parameter, \(K\), and the number of users per cluster, \(S\). The simulation parameters are \begin{table}
\begin{tabular}{c c c} \hline \hline
**Fusion Scheme** & **Number of Bits at the Cluster Level** & **Number of Bits at the FC Level** \\ \hline One-bit hard & \((S-1)C\) & \(C\) \\ \hline Two-bit softened hard & \(2(S-1)C\) & \(C\) \\ \hline Simple combined & \(2(S-1)D_{1}+(S-1)(C-D_{1})\) & \(C\) \\ \hline Modified combined & \(2(S-1)D_{3}+(S-1)D_{4}\) & \(D_{2}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Reporting overhead analysis for four different fusion schemes. selected as \(M=10\), \(\bar{Q}_{fc}=\)0.05, \(S=4\) CRs, \(C=5\) clusters, \(L=2\), \(\alpha=3\), \(\delta=1\), \(P\left(H_{0}\right)=P\left(H_{1}\right)=0.5\), \(Q_{D}=0.5\), \(P_{s}=0.1\) mW and \(P_{r}=0.5\) mW. For simplicity, it is assumed that there are five clusters with the same number of CRs. Moreover, it is assumed that all clusters experience Rayleigh fading channel. It is worth mentioning that the values of the two-bit softened hard scheme (i.e., \(\beta_{1}\) and \(\beta_{2}\)) are determined off line using exhaustive search and are stored in a look up table to reduce the computational complexity. A comparison in a total probability of detection considering a different number of sensing samples between the four fusion schemes, namely, one-bit, two-bit, simple combined, and modified combined schemes, under Rayleigh fading channel is demonstrated in Figure 4. The figure shows that the modified combined algorithm outperforms the three other fusion schemes, since this algorithm ignores the clusters with low probability of detection. Moreover, it is noticed that the simple combined fusion algorithm only outperforms the one-bit fusion scheme, the improvement comes due to converting the fusion rule of some cluster from one-bit to two-bit fusion scheme [24]. For further comparisons, the impact of varying the number of CRs in each cluster on the total probability of detection with different values of fusion rule parameter \(K\) attained by the schemes is considered. Figure 5 provides a comparison between the four fusion schemes in terms of probability of detection considering the impact of selecting different values of fusion rule factor, \(K\). The figure also shows the superiority of the modified combined algorithm over the three other schemes. It also shows that the detection performance improves as the number of CRs increases which increases the spatial diversity. Figure 6 investigates the impact of increasing the number of users, i.e., CRs, in a cluster on the total probability of detection for the four above-mentioned schemes and the weighted fusion algorithm [16]. The figure shows that the modified combined algorithm outperforms the weighted fusion algorithm as the number of CRs in a cluster increases, this is because the modified combined algorithm ignores the unreliable clusters which have probability of detection less the eligibility threshold, i.e., \(Q_{dc(i)}<Q_{D}\), while the weighted fusion algorithm includes all clusters with their weights which reduces the total probability of detection. Figure 4: A comparison in a total probability of detection for four fusion schemes vs. number of sensing samples. Figure 7 displays the consumed power of the four schemes in three cases. Case 1 represents a CRN with five clusters, each cluster with three CRs, case 2 represents a CRN with five clusters, each cluster has four CRs, while case 3 represents a CRN with five clusters, each cluster has five CRs. The figure reflects the energy efficiency of the modified combined scheme, where modified combined scheme consumes less power compared to the two-bit scheme in all three cases.