## 3 System Model
### Energy Model  
The COA protocol transmits data using a standard channel model [31]. The energy consumption of the node was measured based on the amount of energy required to transmit a data packet from the participant to the sink node. Figure 2 depicts the COA energy consumption model.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**S.No**} & \multirow{2}{*}{**Authors**} & \multicolumn{2}{c}{**Proposed CH**} & \multirow{2}{*}{**Advantages**} & \multirow{2}{*}{**Limitations**} \\  & & **Selection** & & \\  & & **Optimization Techniques** & & \\ \hline
1 & [PERSON] et al. [24] & ARO & \
\begin{tabular}{c} Network lifetime and packet delivery \\ ratio are improved by 15\% and 5\% \\ \end{tabular} &
\begin{tabular}{c} It takes more time to form \\ clusters in the network \\ \end{tabular} \\ \hline
2 & [PERSON] et al. [25] & DA & \
\begin{tabular}{c} Minimized energy consumption by \\ 0.0014 J \\ \end{tabular} &
\begin{tabular}{c} It consumes more energy \\ during CH selection \\ \end{tabular} \\ \hline
3 & [PERSON] et al. [26] & SOA & \
\begin{tabular}{c} Improved throughput and network \\ lifetime by 6–10\% and 3–18\% \\ \end{tabular} &
\begin{tabular}{c} Sensor nodes deplete energy \\ early during CH \\ selection process \\ \end{tabular} \\ \hline
4 & [PERSON] et al. [27] & HSA-CSO & \
\begin{tabular}{c} Prolongs network lifetime and \\ minimizes energy consumption \\ \end{tabular} &
\begin{tabular}{c} Convergence takes time for \\ CH selection process \\ in network \\ \end{tabular} \\ \hline
5 & [PERSON] et al. [28] & PDU-SLno & \
\begin{tabular}{c} Increased network lifetime and \\ consumes less energy \\ \end{tabular} &
\begin{tabular}{c} Sensor nodes deplete energy \\ early during CH \\ selection process \\ \end{tabular} \\ \hline
6 & [PERSON] and [PERSON] [29] & SSA & Extended lifetime of sensor nodes & Takes more time to converge \\ \hline
7 & [PERSON] et al. [30] & EABC-FA & \
\begin{tabular}{c} Prolonged network lifespan by 23.21\% \\ and energy stability by 19.84\% and \\ reduced network delay 22.88\% \\ \end{tabular} &
\begin{tabular}{c} It takes more time to select \\ CH selection \\ \end{tabular} \\ \hline \hline \end{tabular}
\end{table}
Table 1: CH selection using optimization algorithms.  
In COA, distance 'p' between the nodes's' and 'r' is represented within the coverage area. It employs either a multipath channel fading model or the free space channel. The evaluation of the energy consumption for transmitting t bits of data from node's' to node 'r' is conducted as follows:  
\[E_{TX}(t,p)=tE_{elec}+m\mathrm{ep}(s,r)^{\alpha} \tag{1}\] \[=\left\{\begin{array}{l}t\times E_{elec}+t\varepsilon_{\mathrm{ ft}}\mathrm{p}(s,r)^{2}\text{ \ where }\mathrm{p}(s,r)<\mathrm{p}_{0}\\ tE_{elec}+t\varepsilon_{\mathrm{mp}}\mathrm{p}(s,r)^{4}\text{\ where }\mathrm{p}(s,r)\geq \mathrm{p}_{0}\end{array}\right.\]  
where \(t\varepsilon_{\mathrm{ft}}\mathrm{y}(s,r)^{2}\) or \(t\varepsilon_{\mathrm{mp}}\mathrm{y}(s,r)^{4}\) represents amplifier unit energy consumption.  
The distance threshold value \(\mathrm{p}_{0}\) is computed using Equation (2).  
\[\mathrm{p}_{0}=\sqrt{\frac{\varepsilon_{\mathrm{f}t}}{\varepsilon_{mp}}} \tag{2}\]  
Figure 1: COA network model.  
Figure 2: COA energy model.  
The energy expenditure by node 'r' in the reception of 'q' bits of data from node's' is expressed by Equation (3).  
\[E_{RX}(P)=PE_{elec} \tag{3}\]