## 5 Experimental Results and Analysis
### Different Forms of Energy in CFSFDP-E  
CFSFDP-E considers the residual energy, while the energy can have many forms that make the nodes with high residual energy more likely to become CHs than those with lower residual energy. In order to get a better performance of balancing energy consumption, we make some improvements on CFSFDP-E. Set \(E_{f}\) to describe different forms of energy. The trends of curves \(E_{f}=(1/\log E)^{x}\) or \(E_{f}=E^{y}\) can adjust the proportion of energy appropriately. Because when the expression of \(\gamma\) is  
Figure 4: Energy consumption of LEACH and CFSFDP-E.  
Figure 3: Network lifetime comparison of LEACH, CFSFDP and CFSFDP-E.  
changed from Equation (11) to \(\gamma_{i}(r)=\rho_{i}(r)[1/\log E_{i}(r)]^{x}\delta_{i}(r)\) or \(\gamma_{i}(r)=\rho_{i}(r)[E_{i}(r)]^{y}\delta_{i}(r)\), the impact of residual energy will be increased so that the possibility of nodes with high residual energy to be selected as cluster heads will increase. In following experiments, Table 6 shows the results of different values of \(x,y\) for different forms of energy. From the result, we can observe that when the form of energy is \(E^{y}\), the FND is 978 as \(y=3\), which is more than 150 rounds longer than that of \(y=1\). And when the form of energy is \(\left(1/\log E\right)^{6}\), the FND, HND and LND is very close to each other which means the energy consumption of all nodes is in a state of equilibrium. In addition, it is obvious that the performance of FND is better as the order increases for both forms of energy. The reason for this result is that when the order of energy increases, the impact of energy will hold the dominate position, while the influence of local density and distance will be less and less. In order to balance the impact of local density, distance and energy, it is indispensable to normalize these three elements. We set \(\gamma^{\prime}\) as the \(\gamma\) after normalization. \(\gamma^{\prime}\) in the \(r\) round for node \(i\) can be calculated as follows:  
\[ \begin{array}{ll}\gamma^{\prime}_{i}(r)&=\rho^{\prime}_{i}(r)E^{\prime}_{i} (r)\delta^{\prime}_{i}(r)\\ &=\frac{\rho_{i}(r)-\rho_{\min}(r)}{\rho_{\max}(r)-\rho_{\min}(r)}\cdot\frac{E _{i}(r)-E_{\min}(r)}{E_{\max}(r)-E_{\min}(r)}\cdot\frac{\delta_{i}(r)-\delta_{ \min}(r)}{\delta_{\max}(r)-\delta_{\min}(r)}\;i\in I\end{array}  \tag{15}\]  
where \(\rho^{\prime}_{i}(r),E^{\prime}_{i}(r),\delta^{\prime}_{i}(r)\) represent the local density, residual energy and distance of each node after normalization in the \(r\) round, respectively:  
\[\left\{ \begin{array}{ll}\rho_{\min}(r)=\min[\rho_{i}(r)],\;i\in I\\ \rho_{\max}(r)=\max[\rho_{i}(r)],\;i\in I\\ E_{\min}(r)=\min[E_{i}(r)],\;i\in I\\ E_{\max}(r)=\max[E_{i}(r)],\;i\in I\\ \delta_{\min}(r)=\min[\delta_{i}(r)],\;i\in I\\ \delta_{\max}(r)=\max[\delta_{i}(r)],\;i\in I\end{array} \right. \tag{16}\]  
In the first round, the initial energy of all nodes is the same. Therefore, we do not normalize the energy and the value of \(\gamma_{i}\) is still calculated by Equation (5) for each node in this round. Table 7 is the result of different forms of energy after normalization. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**FORM OF ENERGY** & \(\backslash\) & **FND** & **HND** & **LND (90\%)** \\ \hline \multirow{2}{*}{\(E_{f}=E^{y}\)} & \(y=1\) & 822 & 1009 & 1036 \\  & \(y=2\) & 980 & 1000 & 1006 \\  & \(y=3\) & 978 & 1001 & 1005 \\ \hline \multirow{2}{*}{\(E_{f}=\left(1/\log E\right)^{x}\)} & \(x=2\) & 873 & 1006 & 1068 \\  & \(x=4\) & 965 & 1005 & 1023 \\  & \(x=6\) & 991 & 1014 & 1021 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Network lifetime with different forms of energy.