## 4 Performance Analysis and Evaluation
After extensive state-actions exploration and clusters exploitation during the learning phase, the EESA-RLC algorithm partitions the network into seven clusters \(\{cl_{1},cl_{2},cl_{3},cl_{4},cl_{5},cl_{6},cl_{7}\}\) which translate into seven different clusterheads \(\{CH_{1},CH_{2},CH_{3},CH_{4},CH_{5},CH_{6},CH_{7}\}\) as shown in Figure 6. The network consists of 250 uniformly distributed SUs and five PUs randomly deployed in the network. The SUs form seven clusterheads and 243 member nodes. During the learning phase, each member node considers only clusterheads that are within its radio range instead of all seven clusters and chooses the optimal cluster among its neighborhood clusters. The seven clusters which are the optimal number for the network as determined through simulation as shown in Figure 6, are indicated by dashed circles with the corresponding common available channels inscribed in the circle. To examine the effect of cluster size on the network energy consumption, we determined the energy consumed by both member nodes and their respective clusterheads for different cluster sizes through simulation, as shown in Figure 7. For a fixed number of nodes, when the number of clusters is too small (e.g., 3), each cluster would have a large number of member nodes that communicate with high transmission power. This increases the network energy consumption due to long intra-cluster distance communication between the member nodes and their clusterheads. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **Description** & **Value** \\ \hline \(N\) & Number of SUs cognitive radio sensor nodes & 250 \\ \hline \(n_{\pi}\) & Number of licensed channels & 5 \\ \hline \(\mathcal{M}\) & Number of primary users & 5 \\ \hline BS & Base Station Coordinate & 75,75 \\ \hline \(d_{i,j}\) & Maximum distances for & \(\leq 45\) m [45] \\  & intra-cluster transmission & \(\leq 150\) m [45] \\ \hline \(d_{j,g}\) & Maximum distance for & \(\leq 150\) m [45] \\  & inter-clusters transmission & \(\leq 150\) m [45] \\ \hline \(E_{psd}\) & Number of episodes & 5000 \\ \hline \(\alpha^{k}\) & Step Size for learning rate & \(a/(b+k)\), a = 1, b = 10 \\ \hline \(\gamma\) & Discounted factor & 0.9 \\ \hline \(pkt\) & Packet Size & 32 byte \\ \hline \(\mathrm{E_{n}^{mx}}\) & Initial Energy & 1250 mJ \\ \hline \(B_{W}\) & Channel Bandwidth & \(Ch_{1}\): 650 MHz \(Ch_{2}\): 600 MHz \(Ch_{3}\): 200 MHz \\  & & \(Ch_{4}\): 750 MHz \(Ch_{5}\): 50 MHz \\ \hline \(\varepsilon\) & Tradeoff between exploration and exploitation & 0.7 \\ \hline \(E_{sp}\) & Energy dissipation: signal samples processing & 150 nJ/bit [49] \\ \hline \(E_{ap}\) & Energy dissipation: data aggregation & 5 nJ/bit [45] \\ \hline \(E_{ec}\) & Electronics dissipation: & 50 nJ/bit [50] \\  & electronics circuit & \\ \hline \(E_{ss}\) & Energy dissipation: event sensing & 33.75 μJ/bit [45] \\ \hline \(E_{log}\) & Energy dissipation: data logging & 81.4 μJ/bit [45] \\ \hline \(E_{am}\) & Energy dissipation: amplifier, & \\  & intra-cluster & 7 pJ/bit/m\({}^{2}\)[45] \\ \hline \(E_{mp}\) & Energy dissipation: amplifier, & \\  & inter-cluster & 0.002 pJ/bit/m\({}^{4}\)[45] \\ \hline \(P_{ed}\) & Power consumption: tuning detector’s circuit & 40 mW [49] \\ \hline \(E_{dp}\) & Energy dissipation: data fusion & 0.187 μJ/bit [49] \\ \hline \(\eta\) & Power amplifier drain efficiency & 92.4\% [51] \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Value of parameters used in the simulation. Figure 6: Pairwise spectrum-aware clustering result. On the other hand, for large number of clusters (e.g., 15), the network energy consumption is relatively small, but inter-cluster communication consumes relatively high energy because of the excessive number of clusterheads which in reality consume much more energy than member nodes. Therefore, network energy consumption can be minimized by determining the optimal number of clusters that balances energy consumption for inter-cluster and intra-cluster communications.