## 4 Brief Overview of EOICHD Protocol  
In this section section, a clustering protocol termed as EOICHD, a cluster-based routing protocol, is proposed to address the drawbacks of LEACH protocol in [27]. This protocol is similar to LEACH protocol, and it operates in rounds. In each round, nodes (also termed as normal nodes) sense information and send the sensed information to respective CHs, and further data are transmitted to BS. Each round comprises a CH setup phase and a data transmission phase. The EOICHD protocol ensures selecting the nodes that have considerable larger residual energy as CH nodes. It also ensures that the selected CHs are separated by certain predetermined distance. CH selection is carried out based on two crucial parameters such as residual energy and inter-cluster head distance. As per EOICHD, a node is considered a candidate CH if its residual energy is greater than the rest of the nodes' average residual energy. Let there be \(m\) nodes in the network, and every node has a transmission range \(R\). Let \(n\) be an arbitrary node participating in the CH selection process. It will be selected as CH if its residual energy \(e_{n}\) is greater than average residual energy of the entire network as per the condition (3). \[e_{n}\geq\left(\frac{1}{(m-1)}\times\sum_{k=1}^{m}e_{k}\ (where,k\
eq n)\right) \tag{3}\]  
To better understand the condition (3), two cases of node distribution are considered as shown in Figures 2 and 3. Let there a be set of nodes \(\{n_{0},n_{1},n_{2},n_{3},n_{4},n_{5}\}\), and assume residual energy of each node is represented by \(\{e_{n_{0}},e_{n_{1}},e_{n_{2}},e_{n_{3}},e_{n_{4}},e_{n_{5}}\}\). Table 1 shows the residual energy of each node per case. The average residual energy of the network \(e_{n}\) for case 1 and case 2 is 1.53 and 1.75, respectively. Based on the observations, it is quite obvious that the nodes with a residual energy more than the average residual energy are suitable candidates to be selected as CH. In case 1, \(\{n_{0},n_{2},n_{5}\}\) have their residual energy greater than the average remaining energy of the network, i.e., 1.53. Hence, \(\{n_{0},n_{2},n_{5}\}\) are ideal candidate CH nodes with reference to remaining energy. Similarly, in case 2, \(\{n_{0},n_{5}\}\) have residual energy greater than the average remaining energy of the network, i.e., 1.75. Hence, \(\{n_{0},n_{5}\}\) are ideal candidate CH nodes with reference to remaining energy. The strategy of choosing a node based on the residual energy ensures that the nodes with high residual energy are preferred as CH over low-residual-energy nodes. Based on the example scenarios as described in Figures 2 and 3, the condition mentioned is very much needed while choosing CH. Figure 1: Radio Model. Reprinted with permission from [16]. Copyright 2000 IEEE. Another criterion for selecting the CH nodes is estimation of inter cluster head distance \((d_{opt})\). For a given wireless sensor network, \(d_{opt}\) has to be estimated before network begins \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \multicolumn{2}{c}{**Case 1**} & \multicolumn{2}{c}{**Case 2**} \\ \cline{2-5}
**Node ID** & \begin{tabular}{c} **Remaining** \\ **Energy of Node** \\ **(\(e_{n_{i}}\))** \\ \end{tabular} & \begin{tabular}{c} **Remarks** \\ **Energy of Node** \\ **(\(e_{n_{i}}\))** \\ \end{tabular} & \
\begin{tabular}{c} **Remaining** \\ **Energy of Node** \\ **(\(e_{n_{i}}\))** \\ \end{tabular} &
\begin{tabular}{c} **Remarks** \\ **Energy of Node** \\ **(\(e_{n_{i}}\))** \\ \end{tabular} \\ \hline \(n_{0}\) & 2.5 & Candidate CH & 4 & Candidate CH \\ \(n_{1}\) & 1.5 & – & 1.5 & – \\ \(n_{2}\) & 1.8 & Candidate CH & 1.6 & – \\ \(n_{3}\) & 1 & – & 1 & – \\ \(n_{4}\) & 0.5 & – & 0.5 & – \\ \(n_{5}\) & 1.9 & Candidate CH & 1.9 & Candidate CH \\ \cline{2-5} \(-\) & _1.53_ & Average energy & _1.75_ & Average energy \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Remaining energy of nodes in Case-1 and Case-2. Figure 3: Case2: Nodes \(\{n_{0},n_{5}\}\) are candidate cluster head nodes.