# An Eccentricity Based Data Routing Protocol with Uniform Node Distribution in 3D WSN
## 4 Performance Evaluation  
### Simulation Setup  
The performance of EDR is evaluated with random and uniform node distribution in MATLAB 9.2.0.556344 (R2017a). It is assumed that all of the deployed nodes are constituted in such a way that there are always other nodes within their radio range \(R_{\rm s}\). The parameters used in the simulation are shown in Table 2.  
In the simulation, the transmitting and receiving costs are measured based on the first order radio dissipation model that has been described in [13]. In this model, the transmitter and receiver dissipate \(E_{\rm elec}\) to run the transmitter and receiver circuitry. To amplify the signal, amplifier dissipates \(E_{\rm amp}\) or \(E_{\rm fs}\). Equations (7) and (8) were used to calculate the energy in transmitting and receiving an \(L\)-bits message over a distance \(d\) between the transmitter and the receiver. To aggregate data, an RC node consumes energy defined by \(E_{\rm DA}\).  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline Sensor field & (200 \(\times\) 200 \(\times\) 200) m\({}^{3}\) \\ Sink position & (100, 100, 250) m \\ Number of sensor nodes: \(n\) & 120 \\ Subspace edge length: _SubSL_ & 100 m \\ Initial energy of a sensor node: \(Ei\) & 0.5 J \\ Threshold energy: \(T_{\rm E}\) & \(Ei/\alpha\) \(\left(\alpha=6\right)=0.08\) J \\ Weight factor: \(\beta\) & 0.5 \\ Data packet size: & \\ D\_Msg & 500 bits \\ \(AD\_Msg\) & 4000 bits \\ Control packet size & 256 bits \\ The transmitter or receiver circuitry: \(E_{\rm elec}\) & 50 nl/bit \\ Data aggregation cost: \(E_{\rm DA}\) & 5 nl/bit/report \\ Transmit amplifier cost: \(E_{\rm amp}\) (\(d>d_{0}\)) & 0.0013 pl/bit/m\({}^{2}\) \\ Transmit amplifier cost: \(E_{\rm fs}\) (\(d\leq d_{0}\)) & 10 pJ/bit/m\({}^{4}\) \\ Energy dissipation for sensing: \(E_{\rm sen}\) & 0 J/bit \\ Threshold distance: \(T_{\rm D}\) & 180 m \\ Maximum transmission range: \(R_{\rm max}\) & 346.41 m \\ Transmission range equal to a subspace diagonal length: \(R_{\rm s}\) & 173.20 m \\ Adjustable transmission range: \(R_{\rm min}\) & \(<\)\(R_{\rm s}\) \\ \hline \hline \end{tabular}
\end{table}
Table 2: Simulation parameters setting.  
Figure 1: An example of forwarding routing centroid (RC) node selection.  
\[E_{Tx}(L,d)=\left\{\begin{array}{ll}E_{elec}L+E_{fs}Ld^{2}&if\ d\leq d_{0}\\ E_{elec}L+E_{amp}Ld^{4}&if\ d>d_{0}\end{array}\right., \tag{7}\]  
where \(d_{0}\) is defined by \(d_{0}=\sqrt{\frac{E_{fs}}{E_{amp}}}\).  
\[E_{Rx}=\ E_{elec}L. \tag{8}\]  
The number of RC/CH nodes election in EDR and 3D EADC are fixed during each round that are prior defined based on the number of subspaces/competition regions of the CH nodes election, respectively. By contrast, the number of elected CH nodes in 3D LEACH differs from EDR and 3D EADC; it fluctuates randomly instead of the fixed numbers. The subspaces of EDR and the competition regions of 3D EADC contain an equal number of member nodes that is \((n=120)/(k=8)=15\).  
The EDR protocol is compared with 3D LEACH and 3D EADC in the same network field in terms of steady state and network lifetime. In the simulation, the parameters used for 3D LEACH and 3D EADC are: radio range \(R\) for the advertisement of the elected CH node to form a cluster that is equal to \(R_{\rm max}\), CH competition range \(R_{\rm c}\) is equal to \(R_{\rm s}\), the radio range \(r\) for broadcasting residual energy to neighborhood nodes is 100 m and the range \(R_{\rm r}\) for broadcasting route message is equal to \(2R_{\rm s}\), respectively. An average percentage of nodes to become the CHs in each round in 3D LEACH is \(p=0.1\).  
During the simulation, the CH nodes and the RC nodes were elected at a certain round in the protocols are shown in Figure 2. The figure shows that the number of elected CHs in 3D LEACH is random and the number of RCs/CHs is predefined in EDR and 3D EADC, respectively.  
Figure 2: _Cont._