# A Novel Adaptive Cluster Based Routing Protocol for Energy-Harvesting Wireless Sensor Networks
## 2 Adaptive Hierarchical-Clustering-Based Routing Protocol for EH-WSNs
### HCEH-UC Routing Algorithm
\begin{table}
\begin{tabular}{c c} \hline \hline
**Mode** & **Energy-Consumption** \\ \hline transmission/reception mode & \(50(\mathrm{nl}\cdot\mathrm{bit}^{-1})\) \\ free-space information amplification (\(\epsilon_{\mathrm{fs}}\)) & \(10(\mathrm{p}\cdot\mathrm{bit}^{-1}\cdot\mathrm{m}^{-2})\) \\ multipath-fading information amplification (\(\epsilon_{\mathrm{mp}}\)) & \(0.0013(\mathrm{p}\cdot\mathrm{bit}^{-1}\cdot\mathrm{m}^{-4})\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The energy consumption in radio transmission and reception mode. \(B\), the total amount of transmission data to the base station in one cycle for this cluster is \(k_{B_{S}}\) bit, the distance between the cluster head node and the base station is \(d_{Bs}\), the \(q\)th node in the cluster need to transfer to the cluster head node \(s\) in each cycle is \(k_{gs}\) bit, and the distance between \(q\) and \(s\) is \(d_{gs}\). In the network shown in Figure 1, the energy consumption \(E_{\text{Bs}}\) of the cluster head node \(s\) in one cycle includes the energy consumption \(E_{Rx}\) of receiving the data from the nodes, the energy consumption \(E_{Df}\) of data fusion, and the energy consumption \(E_{Tx}\) when sending the data package to the base station \(B\), which can be described as (6):  
\[ \begin{split} E_{\text{Bs}}&=E_{Rx}(k_{\text{Bs}})+ E_{Df}(k_{\text{Bs}})+E_{Tx}(k_{\text{Bs}},d_{\text{Bs}})\\ &=\text{E}_{\text{elec}}*k_{\text{Bs}_{s}}+E_{DA}*k_{\text{Bs}_{s }}+E_{Tx-dlec}(k_{\text{Bs}_{s}})+E_{Tx-amp}(k_{\text{Bs}_{s}},d)\end{split}  \tag{6}\]  
where \(E_{DA}\) represents the energy consumption constant for data fusion. Assume the node \(q\) transmits \(k_{gs}\) bit data to the cluster head node \(s\) in one data transmission cycle:  
\[\sum_{q=1}^{Q}k_{qs}=k_{\text{Bs}}. \tag{7}\]  
Thus, the energy consumption \(E_{gs}\) of the \(q\)th node to transfer these data can be described as (8):  
\[E_{gs}=E_{Tx-dlec}(k_{qs})+E_{Tx-amp}(k_{gs},d),q\
eq s. \tag{8}\]  
When the battery capacity of the cluster head node is insufficient to support the routine operation, the exhausted cluster head node should alter into the sleep node to collect the energy. The sleep node can barely implement the data delivery mission. Therefore, aiming towards uninterruptible target coverage with energy harvesting (UC-EH), the appropriate node would be selected as the new cluster head node based on the location information and status of the remaining nodes in the cluster. Assume that the \(E_{estimation}\) represents the energy consumption of data delivery for different nodes:  
\[E_{estimation}(s)=E_{\text{Bs}}+\sum_{q=1}^{Q}E_{gs},q\
eq s \tag{9}\]  
where the \(E_{estimation}(s)\) includes the energy required \(E_{gs}\) for nodes to transmit data to the cluster head \(s\) and the energy required \(E_{Bs}\) for the cluster head node to transmit data to the  
Figure 1: Topology of wireless sensor network. base station. Assume that the remaining node energy can be represented by \(E_{rest}\), and the \(\rho\) is adopted to represent the probability of being selected as a cluster head for the \(q\)th. \[\rho(q)=\left\{ \begin{array}{cc}1-\frac{E_{existing}(q)}{E_{rest}(q)},q\in G\\ 0\quad,q\
otin G\end{array} \right. \tag{10}\]  
where \(G\) represents the set of unselected nodes in the current data-transmission cycle. The \(E_{estimation}\) would increase along with the increase in the distance from nodes to the cluster head node and the cluster head to the base station. The energy required for data delivery of the successor cluster head should be small and the energy remaining in the successor cluster head should be sufficient, which means that the node with the largest probability \(\rho\) becomes the successor CH. The node clusters formed by the proposed clustering algorithm would be evenly distributed in the target detection area, and the distance between the nodes in the cluster is much smaller than the distance to the base station. Therefore, the energy consumption of the cluster head node is much larger than that of the other nodes.