# An Improved Energy-Efficient Routing Protocol for Wireless Sensor Networks
## 3 Proposed Scheme  
### LEACH Protocol  
The LEACH protocol plays an important role in the field of WSNs [26; 27]. In the CH election phase, the CH of every cluster compresses the data collected from the member nodes and then sends them to the sink node [9]. The mechanism of selecting the CH is determined by the threshold value \(T(n)\) and the rand function. The SN generates a random number \(M(0\leq M<1)\). If it is satisfied with \(M\leq T(n)\), the node is elected as the head node of the cluster for the current round. The limit value \(T(n)\) is calculated as follows:  
\[T(n)=\begin{cases}\frac{p}{1-p*(r*\text{ mod }(1/p))},&n\in G,\\ 0,&\text{otherwise},\end{cases} \tag{4}\]  
where \(p\) is the ratio of the total number of CHs to SNs and represents the probability of each node becoming CH during round 0 [4], \(r\) is the current number of rounds, \(G\) is the set of the nodes that will not be elected as a CH in a recent \(1/p\) round, and \(\text{mod}(\cdot)\) denotes the modulus operator. The power amplifier energy consumption to total energy consumption ratio versus the distance is shown  
Figure 2: Radio energy dissipation model.  
in Figure 3. The power amplifier energy consumption to total energy consumption ratio can be calculated by:  
\[ratio=\left\{\begin{array}{l}\frac{m\ast e_{fs}sd^{2}}{m\ast E_{calc}+m\ast e_{fs }sd^{2}},d\leq d_{0},\\ \frac{m\ast e_{up}sd^{4}}{m\ast E_{calc}+m\ast e_{up}sd^{2}},d>d_{0}.\end{array}\right. \tag{5}\]  
The LEACH protocol adopts the concept of clustering and periodic data collection, which can reduce the data transmission between the nodes and the BS. Therefore, this protocol can not only reduce the energy loss, but also can extend the network lifetime. In addition, the CH uses the method of data aggregation, which can reduce correlated data locally. This method can also optimize the amount of data in the network and reduce energy consumption. Moreover, the time division multiple access (TDMA) schedule used by LEACH allows the member nodes to go into sleep mode, and this mechanism holds back the collision between clusters and extends the sensors' battery life [28; 29; 30].  
However, the density of nodes is not considered in the traditional LEACH protocol when selecting the CH. The placement of nodes and the expected number of CHs per round are considered when assigning CHs. Therefore, this protocol cannot ensure the uniform distribution of the CHs [31]. Additionally, the LEACH protocol does not consider the residual energy of nodes and the average energy of all nodes when selecting the CH. This will lead to a node with a lower energy being chosen as the CH. Thus, this protocol leads to the quick exhaustion of the node energy [31]. Finally, the CH communicates directly with the BS by adopting a single hop communication mode. If the BS is far from some of the CH nodes, about 80% of the energy consumption of the node comes from the power loss of the long-distance data transmission [4]. Under the free space channel model, the power amplifier energy consumption to total energy consumption ratio is about 80% when \(d\approx 141\) m. In addition, under the multipath fading channel model, the power amplifier energy consumption to total energy consumption ratio is about 80% when \(d\approx 112\) m. Therefore, looking towards real applications, it is necessary to develop an energy-efficient protocol to decrease the energy loss of the WSN.