# A Novel Connectivity-Based LEACH-MEEC Routing Protocol for Mobile Wireless Sensor Network
## Proposed Framework
### Energy Model  
In this paper, three levels of energy consumption model are considered for mobile sensor node, i.e., wireless radio antenna's transmission energy \(E_{Tran}\), receiver energy \(E_{Recv}\)[2,46] and mobility energy \(E_{mob}\). Equation (3) calculates transmission energy \(E_{Tran}\) to transmit \(s\) bit message over a specific distance \(d_{is}\). \[E_{Tran}(s,d_{is})=sE_{Tran\_dec}+sE_{Tran\_amp}d_{is}{}^{\varphi}, \tag{3}\]  
where \(E_{Tran\_dec}\) is a radio dissipation energy and \(E_{Tran\_amp}\) energy is transmission circuitry energy constant (their values are defined in simulation parametric Table 1). \(\varphi\) is a path loss exponent and it depends on \(d_{is}\), which is the distance between the transmitting and receiving nodes. The distance \(d_{is}\) is compared to distance \(d_{m}\). In Equation (4), \(d_{m}\) is calculated, where \(h_{r}\) and \(h_{t}\) are the height of antennas, SL is the loss of system, \(pi_{val}\) is known as Archimedes' constant (that is approximately equal to 3.14) and \(\lambda\) is wavelength of the signal. \[d_{m}=\frac{4 pi_{val}\sqrt{SL}h_{r}h_{t}}{\lambda} \tag{4}\] \begin{table}
\begin{tabular}{c c} \hline \hline
**Key** & **Value** \\ \hline Field area & 100 \(\times\) 100 m\({}^{2}\) \\ Number of MWSN & 100 \\ Primary energy of MWSN & 2 J \\ \(E_{Tran\_dec}\) & 50 nJ/bit \\ \(E_{Tran\_mp,miss}\) & 10 pJ/bit/m\({}^{2}\) \\ \(E_{Tran\_mp,ray}\) & 0.0013 pJ/bit/m\({}^{4}\) \\ One \(\omega\)dime & 10 s \\ \(d_{m}\) & 87 m \\ Maximum velocity & 1.5 m/s, 7.5 m/s \\ Simulation duration & 1000 s \\ Hop & 1-hop \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Simulation parameters. Figure 1: An example of Mobile LEACH routing protocol. If \(d_{is}<d_{m}\), then the free space model is ideal (\(\phi=2,E_{Trans\_amp}=friss\)). If \(d_{is}\)>\(d_{m}\), then the multipath model is selected (\(\phi=4,E_{Trans\_amp}=two\_ray\_amp=multipath\)). The receiver energy \(E_{Recv}(s)\) is defined as the energy requires to receive \(s\) bit message by receiving node. It requires \(sE_{Recv\_lec}\), which is the energy spent by electric circuit of antenna to receive \(s\) bit message, and \(E_{(idle+error)}\) idle nature of receiver and error term are assumed as constant value of energy loss (due to obstacle blocking line of sight between two sensor nodes). It is given as follows:  
\[E_{Recv}(s)=sE_{Recv\_lec}+E_{(idle+error)} \tag{5}\]  
The energy dissipation due to the mobility of sensor nodes is denoted by \(E_{Mob}\). A mobile sensor node movement between two points cost \(E_{Comp}(N_{i})\) computational energy and \(E_{mov}(N_{i})\) energy loss due to mobility for each round. It can be decomposed as follows. \[E_{Mob}(N_{i})=E_{Comp}(N_{i})+E_{mov}(N_{i}), \tag{6}\]  
\[E_{Comp}(N_{i})=\Delta Ic_{T_{m}}(N_{i})*\Delta Vt_{T_{m}}(N_{i})*T_{m}, \tag{7}\]  
where \(E_{Comp}(N_{i})\) is the dissipation of computational energy due to transmission of one bit in \(T_{m}\) seconds [47]. \(E_{mov}(N_{i})\) is the depletion of energy due to mobility of nodes in \(T_{m}\) seconds. \(\Delta Ic_{T_{m}}(N_{i})\) and \(\Delta Vt_{T_{m}}(N_{i})\) are given as follows:  
\[\Delta I_{T_{m}}(N_{i}) =I_{init}^{T_{m}}-I_{Cur}^{T_{m}+10} \tag{8}\] \[\Delta V_{T_{M}}(N_{i}) =V_{init}^{T_{m}}-V_{Cur}^{T_{m}+10} \tag{9}\]  
where \(T_{m}=\)\(0,10,20,30.....1000\), showing that each round consists of 10 s. Equations (7) and (8) show the change in current \(\Delta I_{T_{m}}(N_{i})\) and change in voltage \(\Delta V_{T_{M}}(N_{i})\) due to mobility after \(T_{m}\) seconds. \(I_{init}^{T_{m}}\) shows the initial value of current at \(T_{m}\) seconds and \(I_{Cur}^{T_{m}+10}\) shows the value of current after \((T_{m}+10)\) seconds. Similarly, \(V_{init}^{T_{m}}\) shows the value of voltage at \(T_{m}\) seconds and \(V_{Cur}^{T_{m}+10}\) shows the value of voltage after \((T_{m}+10)\) seconds. The energy consumption \(E_{mov}(N_{i})\) due to mobility can be rewritten as [48].