# Density Self-Adaptive Hybrid Clustering Routing Protocol for Wireless Sensor Networks
## 3 The Design of DAHC Protocol
### The Adjustment of Cluster Density  
Cluster density adjustment is proposed for the distributed method, which may lead to uneven cluster density. The meaning of cluster density is the number of member nodes within a cluster. Table 1 shows the definition of some symbols used in the adjustment process. After the clusters are generated in the first round of an epoch, the CH will count the number of member nodes, and send the cluster density to the BS. When the BS receives all the cluster densities, the average value \(N_{0}\) will be calculated. Here, we set a range for cluster density. If it is within a reasonable range, the cluster will not need to be adjusted. The upper bound threshold \(T_{1}\) is the mean value of the cluster with density larger than \(N_{0}\), and the lower bound threshold \(T_{2}\) is set as the average value of the cluster with density less than \(N_{0}\). \(T_{1}\) and \(T_{2}\) are related to \(N_{0}\). After calculating the information, the BS will send it to all of the CHs, and then the CHs will transmit to the member nodes. Therefore, all the nodes in the network will know it. In the final stage of the cluster forming in a distributed way, the CH will judge the cluster density and make the appropriate adjustments. In a distributed method, each node maintains an information table, as shown in Table 2. In the table, the ID of the CH, the received signal strength indicator (RSSI), the cluster density, and the adjustment of the cluster are stored. After the election of CHs in a distributed way, the CHs and nodes will interact four times to complete the process of clustering as shown in Figure 2.  
1. Firstly, the CHs advertise to all nodes that they are CHs, and the nodes store the message to the information table, from strong to the weak, according to RSSI. At this point, only the ID and RSSI values are in the information table. 2. Secondly, the nodes select the CH with the strongest RSSI value to join, and send the join message. After all nodes join, the CH will count the cluster density and judge the adjustment circumstance. If the cluster density is in a reasonable range, the cluster will not be adjusted. If the cluster density is greater than \(T_{1}\) or less than \(T_{2}\), the cluster is adjusted, more or less, accordingly. \begin{table}
\begin{tabular}{c c} \hline \hline
**Symbol** & **Description** \\ \hline \(N_{0}\) & The average cluster density of the whole network. \\ \(T_{1}\) & The upper bound threshold of the cluster density. \\ \(T_{2}\) & The lower bound threshold of the cluster density. \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Notations. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**The ID of the CH** & **RSSI** & **Cluster Density** & **Adjustment** \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Information table. RSSI: the received signal strength indicator; CH: a cluster head  
Figure 2: The interactions between the CH (cluster head) and the member node. Thirdly, the CH sends the cluster density information and adjustment situation to all nodes within the communication range. The nodes will store the related information to the table. * Finally, the node will fill out the information table and provide feedback to the CH of the cluster it joins. After the four interactions, the CHs are aware of some local information and the adjustment of neighboring clusters. If the cluster density is too much, the CH will find the situation that the adjacent clusters have too few members. If so, the cluster will transfer some nodes to the neighboring clusters. Before the removal of the nodes, the CH will give a rejection list for the adjacent cluster heads. The nodes in the list can communicate with the adjacent CH, in accordance with RSSI, from the strong to the weak. In addition, the RSSI values in the list must be greater than \(-87\) dBm. The critical value is the conclusion obtained from the experimental results of the literature [16]. When the RSSI value is greater than \(-87\) dBm, the packet reception rate is above \(85\%\).