## 4 Performance Analysis and Evaluation
### Convergence and Computational Complexity of the EESA-RLC Algorithm
We examined the performance of a single MN that learns and determines cumulative average rewards for each selected clusterhead in a total number episodes of \(E_{psd}=5000\), as shown in Figure 10. We also examined the influence of the two metric functions, _viz_ energy consumption and local decision accuracy, on the optimal cluster selection as shown in Figure 11.  
Figure 9: Comparison of computational complexity between EESA-RLC and other approaches. The cumulative average reward represents the average reward obtained for energy consumption and local decision accuracy during the learning process. Figure 10 shows cumulative average for the three clusterheads \(CH_{1},CH_{2},CH_{3}\) that are within the radio range of the MN without the remaining four clusterheads \(CH_{4},CH_{5},CH_{6},CH_{7}\) that have no direct link with the MN. The result indicates that clusterhead \(CH_{1}\) attracts the highest cumulative average reward of \(\tau_{Av}^{t}=0.65\), followed by clusterhead \(CH_{2}\) which attracts cumulative average reward of \(\tau_{Av}^{t}=0.4\), while clusterhead \(CH_{3}\) receives the lowest cumulative average reward of \(\tau_{Av}^{t}=0.12\). This indicates that the agent learns and adapts to the environment through exploration of the neighbouring clusterheads and exploitation of actions that attract favourable rewards to return clusterhead \(CH_{1}\) as the optimal clusterhead. Figure 11 shows the effect of energy dissipation and local decision accuracy on selecting a clusterhead during the learning phase and choosing the optimal clusterhead. The agent learns the energy and cooperative sensing costs for each of the neighboring clusterhead and then selects the most favorable clusterhead that satisfies the pairwise constraints and minimum energy dissip  
Figure 11: Average rewards for energy consumption and local decision. Figure 10: Average cumulative rewards for clusters. optimal clusterhead. The local decision accuracy indicates the success of individual MN's local decision about channels occupancy in respect to cooperative decision. In this context, local decisions are considered to be accurate when local decisions about a set of channels agree with the cooperative decisions irrespective whether the channels are available or not. Therefore, it can be deduced from the result, all the three clusterheads \(CH_{1}\), \(CH_{2}\) and \(CH_{3}\) have satisfied the pairwise constraint which requires at least one common available channel between the MN and the clusterhead but only clusterhead \(CH_{1}\) satisfied the minimum energy consumption requirement with the highest reward value \(rw_{E}^{t}=0.98\). This suggests that significant amount of energy can be saved when the MN selects \(CH_{1}\) as the optimal cluster as compared to \(CH_{3}\) which attracts zero reward \(rw_{E}^{t}=0\) for energy consumption. Therefore, it is extremely important to consider not only cooperative sensing success, but also energy consumption when choosing the optimal clusters. To evaluate the performance of our algorithm, we used GWSA [17] clustering as the benchmark for comparison, since it also considers spectrum-aware constraints in the network clustering and converges to optimal clusters. We first implemented the algorithms and obtained the optimal clustering through simulation, and then compared the performance of GWSA with our algorithm in terms of network energy minimization and spectrum sensing enhancement. Based on member nodes' distances to their respective clusterheads in each cluster and clusterheads' distances to the BS obtained from each of the clustering scheme, we determined Sum of Square Error (SSE) for the network, and computed network energy consumption and determined probability of detection for the two schemes as shown in Figures 12-14 respectively. Figure 12 compares the average SSE for different numbers of member nodes for the two clustering schemes. The SSE is a key component for determining the performance of clustering schemes in terms of network energy efficiency.