## 3 SWIPT-Based Multi-Hop Uneven Clustering Routing Protocol Design for RF EH-CRSNs
### Network Model
#### 3.2.4 Data Transmission Stage  
After the completion of cluster formation and route establishment, nodes enter the data transmission stage. However, frequent data transmission and relay will result in substantial energy depletion of CRSN nodes. To prevent CRSN nodes from dying prematurely due to insufficient energy, which would lead to data transmission failures, and to avoid the energy waste caused by excessive activations of the SWIPT mechanism, ES-MUCRP protocol has incorporated an energy status control mechanism that manages node states during data transfer. Specifically, this mechanism divides the state \(S_{j}\) of CRSN node \(j\) into three categories according to its residual energy \(E_{res}(j)\): the dead state \(S_{death}\), the sleep state \(S_{sleep}\), and the active state \(S_{active}\). When \(E_{res}(j)\) falls below \(E_{death}\), the node is energy-depleted and in the dead state \(S_{death}\), unable to perform any functions and losing its environmental monitoring capabilities. When \(E_{res}(j)\) is higher than or equal to \(E_{death}\) but below the dormancy threshold \(E_{dormancy}(j)\), to prevent energy exhaustion, the node enters the sleep state \(S_{sleep}\), only engaging in linear EH and not participating in data transmission, relay, or similar operations. When \(E_{dormancy}(j)\leq E_{res}(j)\leq E_{max}\), the node has sufficient residual energy and is in the active state \(S_{active}\), capable of conducting energy-intensive operations. The dormancy threshold \(E_{dormancy}(j)\) for CH \(j\) consists of the energy consumed in the control information exchange, reception, aggregation, and forwarding of intra-cluster data, as well as assistance in relaying data from outer layers per round, as shown in Equation (11). \[ \begin{array}{ll}E_{dormancy}(j)&=3L_{1}\times\left(E_{ellec}+E_{fs}\times R_{r( j)}^{2}\right)+3L_{1}\times E_{ellec}\times\left(N_{r(j)}-1\right)+\left(N_{r(j)}-1\right) \\ &\times E_{ellec}\times L_{2}+N_{r(j)}\times E_{DA}\times L_{2}+L_{2}\times \left(E_{ellec}+E_{fs}\times d_{CH(j)-route(r(j)+1)}^{2}\right)\\ &+\frac{\sum\limits_{k=j}^{5}N_{CH}(k)\times\left(2E_{ellec}+E_{fs}\times \mathcal{E}_{dr(j(j))-cnt(r(j)-1)}\right)\times L_{2}}{N_{CH}(r(j))}\end{array}  \tag{11}\]  
where \(d_{CH(j)\to route(r(j)+1)}\) signifies the Euclidean distance between CH \(j\) and its next-hop relay; \(N_{CH}(r(j))\) quantifies the CHs in the same ring as CH \(j\); and \(\sum\limits_{k=r(j)+1}^{2}N_{CH}(k)/N_{CH}(r(j))\) is the quantity of data packets from outer rings that CH \(j\) aids in relaying. The dormancy threshold \(E_{dormancy}(k)\) for CM \(k\) comprises the energy required for control information exchange and for data delivery to the CH per round, as presented in Equation (12):  
\[ \begin{array}{ll}E_{dormancy}(k)=\\ 3L_{1}\times\left(E_{ellec}+E_{fs}\times R_{r(k)}^{2}\right)+2L_{1}\times E_{ ellec}\times\left(N_{r(k)}-1\right)+2L_{1}\times E_{ellec}+L_{2}\times\left(E_{ ellec}+E_{fs}\times d_{CM(k)\to CH}^{2}\right)\end{array} , \tag{12}\]  
where \(R_{r(k)}\) is the cluster radius size of the layer where CM \(k\) is located; and \(d_{CM(k)\to CH}\) is the Euclidean distance from CM \(k\) to its CH. Utilizing the aforementioned energy status control mechanism to identify the node's status, nodes in the active state carry out data transmission. Data transmission encompasses both intra-cluster and inter-cluster data transfers, detailed as follows:  
1. The intra-cluster data transmission process is specifically depicted in Figure 1. It determines whether node \(j\) is a CH or a CM, and CHs that have CMs schedule time division multiple access (TDMA) time slots for their CMs, who receive the schedule information and decide whether to transfer energy to the CH through SWIPT while transmitting data based on their energy levels. Figure 1: Flowchart of the intra-cluster data transmission process in ES-MUCRP. Based on \(E_{intra}(j)\), as shown in Equation (4), and the residual energy \(E_{res}(j)\), it is determined whether to employ SWIPT technology.