## 2 Related Researches
### LEACH Protocol  
LEACH (low-energy adaptive clustering hierarchy) is a representative protocol based on cluster-based routing. The LEACH protocol consists of a set-up phase and a steady-state phase. In the setup phase, CHs are selected randomly by the stochastic threshold, and then clusters are configured. CHs from the nodes are selected by Equation (1) and the values are between 0 and 1 [28; 29; 30; 31].  
\[T(n)=\left\{\begin{array}{cc}\frac{p}{1-p\left(mnd\frac{1}{p}\right)}&if\;n \in G\\ 0&otherwise\end{array}\right. \tag{1}\]  
where \(p\) is the selection probability of the cluster head, \(r\) is the current round, and \(G\) is the set of nodes that were not elected as the cluster head until the previous round. The value of Equation (1) shall be between 0 and 1. Each node generates a random number value between 0 and 1 and is compared to Equation (1); then a node with a random number value less than the result of Equation (1) is elected as the CH. After CHs are selected, clusters are formed as follows. The selected CHs broadcast advertising messages, including their own data, to surrounding nodes. Nodes that receive advertising messages from CHs form a cluster by sending a join-request message to join the CH which is transmitting with the highest signal power; nodes can read the RSSI (received signal strength index). When all clusters' configurations are completed, CH creates the time division multiple access (TDMA) schedule that tells each node the time to transmit, depending on the number of member nodes.  
At the steady-state stage, nodes in the cluster transmit data according to the TDMA schedule assigned by its CH selected during the setup phase and return to the sleep mode to save the power. After all nodes send data to the CH, the CH completes the steady-state phase by merging the data received from all nodes to the BS in a CDMA (code division multiple access) manner. The cycle that has been completed from these setup phase to the steady-state phase is called one round.  
Figure 3 shows one round of flow-chart of LEACH; the left part is for CH selection, and the right part for cluster configuration. The dotted line is the radio communications of CH's broadcasting, TDMA scheduling, and nodes' messages.  
The LEACH protocol has the advantage of increasing network energy efficiency by electing all nodes as cluster heads evenly, improving the problem of a certain node becoming a cluster head continuously in an existing clustering-based protocol, and distributing equally the energy consumption of the network. However, by using only an equation probabilistically when selecting a CH, the network has the disadvantages of shortening the lifespan of the network due to problems such as the selection of nodes with insufficient remaining energy. To address this, a variety of protocols have been proposed that modify the equation.  
In the case of Equation (1) used to select CHs in the LEACH, the residual energy of the nodes is not taken into account. Therefore, even if the remaining energy of the actual node is low, it can be elected as a CH. To improve this, [PERSON] proposed a threshold Equation (2) which was modified as follows.  
\[T(n)=T(n)\times\frac{E_{current}}{E_{max}} \tag{2}\]  
In Equation (2), \(E_{max}\) is the initial energy as the maximum energy of the node and \(E_{max}\) means the remaining energy of the node at specific round. The threshold equation's value is multiplied by the percentage of remaining energy in each node. This lowers the probability of being selected as the CH, as shown in Table 1.  
To make the nodes which have less remaining energy not induce CHs results in increased network lifetime. In addition, a number of variations of LEACH have been studied to improve the performances of energy issues.