## 3 SWIPT-Based Multi-Hop Uneven Clustering Routing Protocol Design for RF EH-CRSNs
### Complexity Analysis of ES-MUCRP
Therefore, the number of nodes effectively collecting data in Fuzzy C-means is low. ES-MUCRP protocol is a multi-hop clustering routing protocol that enables data to be transmitted to the sink through multi-hop routing. It also selects relatively stable channels with the highest count of CMs for intra-cluster and inter-cluster data transmission, leading to infrequent channel reclaim by PUs. Additionally, the number of nodes effectively collecting data in ES-MUCRP protocol is higher than that in S-MUCRP protocol. In an effort to quantitatively assess the surveillance capabilities of the clustering routing protocols, the average number of nodes effectively gathering data for each protocol has been computed, and the results are illustrated in Figure 8. It is evident from Figure 8 that the gap in the average number of nodes effectively collecting data between ES-MUCRP and S-MUCRP protocols widens progressively after round 2588. Calculations reveal a 6.77% increase in the average number of nodes effectively collecting data for ES-MUCRP protocol compared to S-MUCRP protocol. According to Table 4, the duration of effective data collection under ES-MUCRP protocol is significantly extended, with an additional 5281 rounds over S-MUCRP protocol, primarily for the following reasons:  
Figure 7: Comparison of the number of nodes effectively gathering data across various protocols. 1. The EH mechanism effectively replenishes the nodes' residual energy, decelerating the death rate of the nodes. 2. After round 2588, the residual energy of some nodes and key relay nodes drops significantly. The energy status control mechanism and the inter-cluster SWIPT mechanism within ES-MUCRP protocol are activated, which equalize energy consumption across the network and effectively avoid premature deaths of nodes, thereby notably prolonging the duration of network monitoring. The proposed ES-MUCRP protocol can be applied in EH-CRSNs to supplement and balance the remaining energy among nodes, thereby enhancing network surveillance capabilities. For instance, it can be used in the industrial IoT mentioned in the Introduction Section, assisting in the collection and transmission of various environmental data to achieve industrial automation and intelligence. Its limitations can be summarized from the following two aspects:  
1. ES-MUCRP protocol is proposed on the assumption of perfect spectrum sensing in this paper, disregarding the potential for sensing errors. Although this assumption simplifies the design of the protocol, it might not align with the actual detection capabilities of CRSN nodes. 2. In EH-CRSNs, communication is restricted to direct links between transmitters and receivers, where substantial path loss due to large Euclidean distance can deplete the limited battery energy of nodes. Although ES-MUCRP can slow down the rate of energy depletion in nodes, it cannot inherently resolve the limitations imposed on network lifespan by finite battery capacity. \begin{table}
\begin{tabular}{c c} \hline \hline
**Protocols** & **The Duration of Effective Data Collection** \\ \hline CogLEACH & 7500 \\ DSAC & 1097 \\ WCM & 7500 \\ NSAC & 627 \\ IMOCRP & 7500 \\ Fuzzy C-means & 7500 \\ S-MUCRP & 2588 \\ ES-MUCRP & 7500 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Specific comparison results of the duration of effective data collection. Figure 8: Comparison of the average number of nodes effectively collecting data.