# Combined Fusion Rules in Cognitive Radio Networks Using Different Threshold Strategies
## 6 Simulation Results
Furthermore, the figure shows that two-bit fusion rule always consumes more power compared to the three other schemes, since the two-bit scheme reports double the bits that required by the one-bit scheme. Moreover, it can be noticed that simple modified scheme outperforms two-bit scheme where it consumes less power when compared to two-bit scheme. Quantitatively, Figure 7 shows that the modified combined scheme can save about 32-34% of the power compared to two-bit softened hard scheme, while the simple combined scheme can save about 12-22% of the power compared to two-bit softened hard scheme in the three cases. From reporting overhead perspective, Table 2 compares the incurred reporting overheads for the four fusion schemes. The table shows that modified combined algorithm incurs less reporting overhead compared with simple combined and two-bit fusion schemes, since the modified combined  
Figure 5: Total probability of detection, \(Q_{d}\), for different fusion schemes vs. number of CRs in a cluster, where S. comb. refers to simple combined algorithm. Figure 6: The impact of increasing the number of users on the total probability of detection for different schemes considering half voting. algorithm considers only the eligible clusters to share in making final decision about the existence of the PU which significantly reduces the number of reporting bits transmitting over the reporting channel. Furthermore, the table shows that one-bit fusion scheme incur less number of reporting overhead than the modified combined fusion algorithm by about 9%, however, the latter fusion algorithm significantly outperforms the one-bit in the detection performance in terms of total probability of detection as shown in Figures 4 and 5. Moreover, the modified combined fusion algorithm incurs less reporting overhead between the CHs and the FC compared with the three other fusion schemes. Quantitatively, Table 2 shows that simple combined scheme and modified combined scheme can save 17% and 37% of the reporting compared with Two-bit scheme, respectively. Figure 8 compares the probability of detection, i.e., detection performance, for different values of SNR for one-bit, two-bit, simple combined, and adaptive combined schemes under Rayleigh fading channel when the maximum allowable probability of false alarm constraint of \(Q_{f}=\{0.05,0.005\}\). The figure shows that adaptive combined algorithm outperforms all other fusion schemes for the total SNR range under both values of constraints because the eligibility threshold is varying such that the total probability of detection would increase. Moreover, the figure ensures that \(Q_{d}\) increases as SNR increases as proven in [10]. For comprehensive comparisons, a weighted fusion algorithm [28] is considered to investigate the detection performance of all schemes mentioned in the previous cases. In the weighted fusion algorithm, each cluster is assigned with a weight value proportional to its SNR, the weight of the \(i\)-th cluster, \(w_{i}\) is provided as, \(w_{i}=\frac{\mathcal{I}_{i}}{max(\hat{\gamma})}\), where \(\hat{\gamma}_{i}\) is the average SNR over the \(i\)-th cluster, while \(max\) (\(\hat{\gamma}\)) is the largest average SNRs among all clusters in the systems. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Fusion Scheme**} & **Number of Bits at the Cluster Level** & **Number of Bits at the FC Level** & **Total Number of Bits** & **Total Reporting Overhead** \\ \hline One-bit & 15 & 5 & 20 & 20 B \\ \hline Two-bit & 30 & 5 & 35 & 35 B \\ \hline Simple combined & 24 & 5 & 29 & 29 B \\ \hline Modified combined & 18 & 4 & 22 & 22 B \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Reporting overhead analysis for five clusters, each with four CRs. Figure 7: Comparison in power consumed by different schemes. The comparison between all above-mentioned schemes involves obtaining the total probability of detection and the incurred total detection error rate as performance metrics which are displayed in Figure 9 and 10, respectively.