## 5 Our Proposed Scheme  
While LEACH is an interesting routing protocol for WSNs it suffers from a number of weaknesses that affect its performance. Such weaknesses are due to a number of factors related to its operation, as highlighted below.  
* Ignoring the residual energy of sensor nodes when selecting the CH in next rounds. Therefore, if a sensor node with low residual energy is chosen as the CH, then it dies quickly. Hence, the robustness of the network is affected and its lifetime degrades.
* The CHs located at the boundary of the clusters would dissipate more energy and thus decrease the overall performance of the network.
* CHs located far away from the BS consume more energy for transmitting data compared to CHs closer to the BS. This can compromise the network life time.  
To overcome these issues and improve the performance of LEACH, a new variant named LEACH enhanced with probabilistic cluster head selection (LEACH-PRO) is proposed. LEACH-PRO introduces a probabilistic mechanism in which CHs selection is made based on two metrics: The maximum residual energy and the minimum distance to BS. LEACH-PRO has similar design logic as LEACH since both protocols operate in rounds. Each round completes its operations in two phases; setup phase and steady state phase. The main difference lies in the CH selection process and the fact that sensors located at the border of the sensing field are excluded from participating in the CH selection process if they satisfy the conditions set in Equation (9). LEACH-PRO detailed operational steps are illustrated in Figure 3. We assume a static deployment of sensor nodes in the sensing field with the coordinates of each node determined a priori as \((x_{i},y_{i})\) to easily identify borderline nodes. Each node generates a random number and saves it in its memory. However, nodes at the borderline must be selected as CM only and excluded from the CH selection process.  
It is worth noting that several other parameters could be determining for keeping a cluster active for a maximum duration. Among these parameters, there is the number of clusters in the network as well as the update frequency of the cluster head selection. These factors are discussed in several papers in the literature such as [30; 31]. While in this paper we focused on clusters with constant load, our proposed algorithm is compatible with several strategies in the literature, such as those discussed in [32], which are based on a dynamic determination of the number of clusters.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Protocol** & \begin{tabular}{c} **Communication** \\ **Pattern** \\ \end{tabular} & \begin{tabular}{c} **Mobility** \\ **Assumption** \\ \end{tabular} & \begin{tabular}{c} **Scalability** \\ **Scalability** \\ \end{tabular} & \
\begin{tabular}{c} **Clustering** \\ **Approach** \\ \end{tabular} &
\begin{tabular}{c} **Energy** \\ **Efficiency** \\ \end{tabular} & **Overhead** \\ \hline LEACH & Single-Hop & Stationary nodes & Low & Distributed & Moderate & High \\ A-LEACH & Chain-Based & Stationary nodes & Low & Distributed & High & Low \\ LEACH-EE & Multi-Hop & Stationary nodes & Very High & Distributed & High & High \\ LEACH-M & Multi-Hop & Mobile nodes & High & Distributed & Low & High \\ LEACH-F & Single-Hop & Stationary nodes & Low & Centralized & High & High \\ LEACH-DE & Single-Hop & Stationary nodes & Low & Distributed & High & High \\ IB-LEACH & Single Hop & Stationary nodes & Low & Distributed & High & High \\ LEACH-PRO & Single-Hop & Stationary nodes & High & Distributed & High & Moderate \\ \hline \hline \end{tabular}
\end{table}
Table 3: Comparison of various extensions of LEACH protocol.