## 3 SWIPT-Based Multi-Hop Uneven Clustering Routing Protocol Design for RF EH-CRSNs
### Complexity Analysis of ES-MUCRP
\begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **Values** \\ \hline Network radius (\(R\)) & 150 m \\ Total number of CRSN nodes (\(K\)) & 450 \\ Quantity of PUs (\(m\)) & 50 \\ Channel occupancy rate of PUs (\(p_{c}\)) & 0.8 \\ Number of authorized channels (C) & 5 \\ Length of control packets (\(L_{1}\)) & 100 bits \\ Length of data packets (\(L_{2}\)) & 1024 bits \\ Weight factor for adjusting the impact of energy state function (\(\alpha\)) & 10 \\ Energy expended on data aggregation (\(E_{DA}\)) & 5 nJ/bit/packet \\ Energy consumption of electronic circuitry (\(E_{elec}\)) & 50 nJ/bit \\ Energy utilized for channel switching (\(E_{switch}\)) & 10 nJ \\ Power amplifier coefficient under free-space path loss model (\(E_{fs}\)) & 10 pJ/bit/m\({}^{2}\) \\ Duration of EH (\(t_{1}\)) & 0.2 s \\ Conversion efficiency of linear EH (\(\eta\)) & 0.8 \\ Maximum transmission range of CRSN nodes (\(R_{t}\)) & 50 m \\ Interference protection range of PUs & 20 m \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Simulation parameter settings. Figure 2: Comparison of the number of surviving nodes across various protocols. Figure 4: Comparison of the total energy consumption per round across various protocols. Figure 3: Comparison of the total control overhead per round across various protocols. \begin{table}
\begin{tabular}{c c} \hline \hline
**Protocols** & **The Number of Rounds until the First Node Death** \\ \hline CogLEACH & 3469 \\ DSAC & 203 \\ WCM & 478 \\ NSAC & 415 \\ IMOCRP & 5588 \\ Fuzzy C-means & 4220 \\ S-MUCRP & 893 \\ E-MUCRP & 989 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Specific comparison results of the number of surviving nodes. In ES-MUCRP protocol, the overall control overhead incurred during the CHs selection and cluster construction is more than triple but less than four times the count of non-first-ring active nodes. Specifically, CRSN nodes in the first ring become independent CHs directly, eliminating the need for broadcasting CHs selection weights and thus avoiding the associated control overhead. Furthermore, during the CHs selection process, CRSN nodes beyond the first ring broadcast information such as available channels, their locations, and CHs selection weights to their neighbors. Neighboring nodes determine their potential to become CHs based on the received information. Nodes that qualify as CHs then disseminate CHs announcement messages, prompting ordinary nodes that receive these announcements to broadcast their withdrawal from the CHs competition. During cluster formation, nodes not designated as CHs apply to join clusters by sending out join requests. 2. WCM protocol incurs a total control overhead for CHs selection and cluster formation that is roughly four times the count of active nodes: all CRSN nodes broadcast their spectrum sensing results and CHs weights on CCC to select CHs; neighboring nodes that receive this information decide if they are eligible to become CHs, with qualifying nodes broadcasting CHs announcements, and other nodes broadcasting their withdrawal from CHs competition; nodes not designated as CHs apply to join the CH with the greatest weight and shared available channels, after which the CH communicates the cluster details to the sink. In DSAC protocol, each CRSN node starts as a CH and merges with adjacent clusters based on the common available channels and cluster distances until they reach the optimal number derived from theoretical calculations. This involves substantial control information exchanges between CMs and CHs, as well as among neighboring CHs, resulting in considerable energy expenditure. In NSAC protocol, all CRSN nodes calculate their own weight based on the remaining energy and channel quality and continuously update and broadcast their weight information, and the node with the highest weight in the vicinity becomes a CH, with neighboring nodes joining to become CMs. Unclustered nodes repeat this until clustering is completed.