Clustering for Lifetime Enhancement in Wireless Sensor Networks

Abstract

Wireless sensor networks face challenges such as energy consumption, scalability, security vulnerabilities, and communication range limitations, impacting their overall performance and reliability. To resolve these problems, energy-efficient protocols and adaptive sleep modes are implemented in wireless sensor networks (WSNs). Actually, LEACH clustering is widely regarded as one of the primary strategies to extend the lifetime of WSNs. However, clustering does not always guarantee optimal performance. In this paper, we demonstrate that clustering effectiveness is contingent on specific conditions related to several key parameters, including cluster density and the distance of nodes from the base station. Our research presents a mathematically validated analysis, supported by simulation results, that illustrates how clustering can enhance WSN performance, particularly in terms of network lifetime, throughput, and the timing of the first, middle, and last node deaths. Our findings indicate that LEACH is inefficient when nodes are within 80 m of the base station. Furthermore, clusters’ densities are related directly to the distance to the base station. Specifically, for distances less than 80 m, nodes should send their data individually; for distances between 83 and 123 m, a cluster density of two is most effective; and for distances between 123 and 149 m, the optimal density increases to three nodes.

1. Introduction

In wireless sensor networks (WSNs), clustering is a popular method to improve network lifetime because it can reduce energy consumption from multiple aspects [1,2]. This structure partitions the network nodes into clusters, designating a unique node as cluster head (CH) periodically for each cluster, while all other remaining nodes are denoted as cluster members (CMs). The clustering approach helps considerably extend the entire lifetime of WSNs [3,4].

Based on the hypothesis that clustering is a better way to prolong a WSN’s lifetime [5], researchers consider a cluster protocol with a higher density and a short distance to the Base Station (BS). This strategy adopts a high level of initial energy as the most effective clusters [6,7], which must have the maximum chance to enhance WSNs’ lifetime. Furthermore, recent studies have worked on developing more efficient criteria to ensure the selection of the most suitable cluster heads (CHs) in the WSN and have used optimization techniques to merge criteria to create new ones.

In 2023, a new study developed three main CH criteria: residual energy, node centrality, and number of neighbors merged utilizing fuzzy optimization [8]. To ensure the selection of the short paths to transport packets, they used reinforcement learning combined with a genetic algorithm-based routing protocol. Later, reference [9] introduced the TEECH fuzzy-based protocol, which suggests that an ideal CH is one with a high level of remaining energy, a maximum number of neighbor nodes, and very close to its BS. In the reference [10], a new strategy of sink mobility was introduced, based on SMEOR routing in energy harvesting. Using residual energy to select a suitable CH is undiscussable. This is because the level of energy defines in one way or another the lifetime of a node. However, the load charge also defines the amount of energy used in each operation that consumes energy. For WSNs, as modeled in LEACH [11], which is a one-hop cluster-based protocol, the fundamental operations are resumed in the sending, receiving, and aggregating packets. Furthermore, LEACH limits this architecture in a WSN composed of 100 nodes distributed in an area of 100 m × 100 m, with a BS located in the center. To LEACH, an optimal cluster is one with 10 nodes that uses a random manner to select CHs.

Clustering is now the foundation of the majority of solutions developed to address routing and lifespan issues in WSNs. However, these methods are not always optimal, as their effectiveness depends on the network’s design and topology, particularly in cluster-based structures. It is not always true that clustering is the most effective strategy for increasing the lifespan of WSNs.

In this paper, we aim to evaluate the correctness of the hypothesis that “clustering is a better approach to prolong WSNs’ lifetimes”. Based on a mathematical study and proven by simulation results, our findings demonstrate that this hypothesis is not entirely correct. Furthermore, we prove that cluster density is related directly to nodes and their distance to the BS.

2. Related Work

Clustering is the main approach used to enhance WSN performance. It begins with the LEACH protocol [11], which is still considered the foundation of many routing protocols, especially those focused on extending network lifespan. LEACH organizes the WSN into multiple clusters, each composed of several nodes that connect directly to one another. It employs a random-based CH selection process. CHs define their neighbors within a range of 20 m. These neighbors then send the data they collect directly to their CHs. Afterward, the CHs aggregate the data and send them in a single hop towards the BS.

This section aims to present the most recent and high-quality work on cluster-based and LEACH successor protocols.

In 2021, another study presented an improved version of the LEACH protocol [12]. This protocol aims to extend the WSN’s lifetime by considering the clusters’ density. They consider that clusters of different densities unbalance the workload of cluster leaders, leading to exhaustion of their energy. They reduce the number of nodes by minimizing the scope of cluster leader selection in dense areas. CHs are selected based on their equivalent densities and residual energy. In addition, the data collected can be sent in one or more hops, depending on what is optimal.

To avoid the hotspot problem, the authors of reference [13] focus on selecting nodes close to the base station with a high energy level. They proposed the fuzzy-based EE-LEACH protocol. EE-LEACH uses the nodes’ residual energy, density, and distance from the base station to rank them. The best-ranked nodes are then used as CHs. In this way, they ensure that nearby nodes with a large amount of energy are selected and that nodes with less energy are neighbors and remain alive for their lifetime. Random selection of CHs could give nodes with difficult conditions the opportunity to be CHs. To solve this problem, the authors of [14] proposed an energy-aware CH selection algorithm. They take into account the residual energy, position, and centrality of the nodes. They adjust the range according to the dense areas of the nodes, where the clusters can be very dense to obtain fair cluster densities without affecting the connectivity of the nodes.

Extending the lifetime and conserving energy in WSNs is a major research challenge due to the small, non-replaceable batteries of the sensors. In [15], the NM-LEACH protocol is introduced to prolong the lifespan of sensor nodes. It considers nodes’ residual energy and their distance to the BS. This protocol also improves network stability. It selects an even distribution of CHs by choosing nodes with greater residual energy and shorter distances to the BS.

In 2021, Suleiman and Hamdane focus on node centrality [16]. They developed a distance-based adaptive low-energy clustering method. It elects adaptive CHs with the lowest possible centrality. In this way, the distance between nodes in the same cluster must be smaller, which reduces energy consumption. They also take into account residual energy, which indicates whether a node is capable of being a CH or of conserving its energy and does not affect the lifetime of the WSN.

The limited energy of wireless sensors is always a major challenge. IoT networks suffer from this, which affects their lifetime. To address this challenge, Sennan et al. [17] propose the Energy-Aware Cluster-based Routing LEACH (EACR-LEACH) protocol for IoT networks. It uses residual energy, the number of neighbors, the distance to the sink, and the number of nodes acting as CHs. The latter is defined as the number of times a node has been a CH to control the random selection of CHs and make nodes fair in their CH load and conserve their energy.

For IoT networks, the routing of data takes up a large proportion of the batteries. IoT devices manage many smart applications and must meet the needs of the applications. To obtain optimal paths that conserve device energy, Shafiq et al. [18] propose the Robust Cluster-Based Routing Protocol (RCBRP). It aims to optimize routing paths and conserve node energy, thus providing a longer network lifetime. RCBRP has two main algorithms: a cluster-based energy efficiency algorithm and another to obtain the distances and amount of energy required. In this way, they ensure balanced path loads on the network devices and achieve a more functional period.

In 2023, Suresh et al. developed energy-efficient cluster routing protocols [19]. This is a Honey Badger-based algorithm that selects CHs using a chance value. The chances of the nodes take into account their distance from the base station, their residual energy, the proximity of neighboring nodes, their degrees, and their centrality. Then, a Fuzzy Firebug Swarm optimization algorithm is used to give the optimal path between the CHs and their BS.

Later in 2022, Taha et al. proposed a Fuzzy Independent Circular Zones Protocol called FICZP [20]. It selects the cluster head based on the lifetime of neighbors and the remaining energy of the nodes as the most essential parameters, and a second parameter considers the lifetime as a member, which takes into account the average energy consumed in transmitting packets from the nodes to their neighbors. Then, a fuzzy system combines them and gives a cost value for each linked node, allowing the optimal path to the base station to be selected.

In 2024, Wang presented fuzzy logic-based clustering and quantum annealing algorithm-based routing to enhance WSNs’ lifespans [21]. They suggested using the residual energy, the number of neighbors, the distance to the BS, and the nodes’ centrality emphasized in a fuzzy inference system to obtain suitable CHs. Also, they implemented an energy threshold to neglect nodes with insufficient levels of energy, which gives more chances to nodes that are highly preferred and have a long lifetime period.

To address the challenge of selecting the optimal cluster head (CH), Alghamdi presented a new clustering model based on a novel hybrid algorithm combining the dragonfly and firefly algorithms. The model optimizes CH selection based on nodes’ energy, delay, distance, and security [22].

Finally, Vipul Narayan and A. K. Daniel proposed a new Region-Based Cluster Head Selection (RBCHS) protocol [23]. It optimizes energy in heterogeneous sensor networks. RBCHS divides the network area into multiple zones. It uses static clustering to ensure area coverage. It employs a hybrid routing scheme for data transmission to the BS. RBCHS selects CHs based on their minimum distance to the BS, their residual energy (RE), and their number of neighboring nodes.

To summarize, the assumption that “clustering improves network lifetime and conserves energy” is always used to develop the most efficient routing protocols in WSN and IoT networks. Moreover, most of the parameters, such as node residual energy, number of neighbors, centrality, and distance to the BS, are often chosen to select CHs and control node lifetime. Clustering is the main approach used to enhance WSN performance. It begins with the LEACH protocol [11], which is still considered the foundation of many routing protocols, especially those focused on extending network lifespan. LEACH organizes the WSN into multiple clusters, each composed of several nodes that connect directly to one another. It employs a random-based CH selection process. CHs define their neighbors within a range of 20 m. These neighbors then send the data they collect directly to their CHs. Afterward, the CHs aggregate the data and send them in a single hop towards the BS.

Most of the work in the domain of enhancing WSN lifetime involves cluster-based protocols. This section aims to present the most recent and high-quality work on cluster-based and LEACH successor protocols.

In 2021, another study presented an improved version of the LEACH protocol [12]. This protocol aims to extend the WSN’s lifetime by considering the clusters’ density. They consider that clusters of different densities unbalance the workload of cluster leaders, leading to exhaustion of their energy. They reduce the number of nodes by minimizing the scope of cluster leader selection in dense areas. CHs are selected based on their equivalent densities and residual energy. In addition, the data collected can be sent in one or more hops, depending on what is optimal.

To avoid the hotspot problem, the authors of reference [13] focus on selecting nodes close to the base station with a high energy level. They proposed the fuzzy-based EE-LEACH protocol. EE-LEACH uses the nodes’ residual energy, density, and distance from the base station to rank them. The best-ranked nodes are then used as CHs. In this way, they ensure that nearby nodes with a large amount of energy are selected and that nodes with less energy are neighbors and remain alive for their lifetime. Random selection of CHs could give nodes with difficult conditions the opportunity to be CHs. To solve this problem, the authors of [14] proposed an energy-aware CH selection algorithm. They take into account the residual energy, position, and centrality of the nodes. They adjust the range according to the dense areas of the nodes, where the clusters can be very dense to obtain fair cluster densities without affecting the connectivity of the nodes.

Extending the lifetime and conserving energy in WSNs is a major research challenge due to the small, non-replaceable batteries of the sensors. Extending the lifetime and conserving energy in WSNs is a major research challenge due to the small, non-replaceable batteries of the sensors. In [15], the NM-LEACH protocol is introduced to prolong the lifespan of sensor nodes. It considers nodes’ residual energy and their distance to the BS. This protocol also improves network stability. It selects an even distribution of CHs by choosing nodes with greater residual energy and shorter distances to the BS.

In 2021, Suleiman and Hamdane focus on node centrality [16]. They developed a distance-based adaptive low-energy clustering method. It elects adaptive CHs with the lowest possible centrality. In this way, the distance between nodes in the same cluster must be smaller, which reduces energy consumption. They also take into account residual energy, which indicates whether a node is capable of being a CH or of conserving its energy and does not affect the lifetime of the WSN.

The limited energy of wireless sensors is always a major challenge. IoT networks suffer from this, which affects their lifetime. To address this challenge, Sennan et al. [17] propose the Energy-Aware Cluster-based Routing LEACH (EACR-LEACH) protocol for IoT networks. It uses residual energy, the number of neighbors, the distance to the sink, and the number of nodes acting as CHs. The latter is defined as the number of times a node has been a CH to control the random selection of CHs and make nodes fair in their CH load and conserve their energy.

For IoT networks, the routing of data takes up a large proportion of the batteries. IoT devices manage many smart applications and must meet the needs of the applications. To obtain optimal paths that conserve device energy, Shafiq et al. [18] proposed the Robust Cluster-Based Routing Protocol (RCBRP). It aims to optimize routing paths and conserve node energy, thus providing a longer network lifetime. RCBRP has two main algorithms: a cluster-based energy efficiency algorithm and another to obtain the distances and amount of energy required. In this way, they ensure balanced path loads on the network devices and achieve a more functional period.

In 2023, Suresh et al. developed energy-efficient cluster routing protocols [19]. This is a Honey Badger-based algorithm that selects CHs using a chance value. The chances of the nodes take into account their distance from the base station, their residual energy, the proximity of neighboring nodes, their degrees, and their centrality. Then, a Fuzzy Firebug Swarm optimization algorithm is used to give the optimal path between the CHs and their BS.

Later in 2022, Taha et al. proposed a Fuzzy Independent Circular Zones Protocol called FICZP [20]. It selects the cluster head based on the lifetime of neighbors and the remaining energy of the nodes as the most essential parameters, and a second parameter considers the lifetime as a member, which takes into account the average energy consumed in transmitting packets from the nodes to their neighbors. Then, a fuzzy system combines them and gives a cost value for each linked node, allowing the optimal path to the base station to be selected.

In 2024, Wang presented fuzzy logic-based clustering and quantum annealing algorithm-based routing to enhance WSNs’ lifespan [21]. They suggested using the residual energy, the number of neighbors, the distance to the BS, and the nodes’ centrality emphasized in a fuzzy inference system to obtain suitable CHs. Also, they implemented an energy threshold to neglect nodes with insufficient levels of energy, which gives more chances to nodes that are highly preferred and have a long lifetime period.

To address the challenge of selecting the optimal cluster head (CH), Alghamdi presented a new clustering model based on a novel hybrid algorithm combining the dragonfly and firefly algorithms. The model optimizes CH selection based on nodes’ energy, delay, distance, and security [22].

Finally, Vipul Narayan and A. K. Daniel proposed a new Region-Based Cluster Head Selection (RBCHS) protocol [23]. It optimizes energy in heterogeneous sensor networks. RBCHS divides the network area into multiple zones. It uses static clustering to ensure area coverage. It employs a hybrid routing scheme for data transmission to the BS. RBCHS selects CHs based on their minimum distance to the BS, their residual energy (RE), and their number of neighboring nodes.

Table 1. Comparisons between our proposed approach and the literature.

Protocol	Cluster-Based	CH Selection Criteria	Routing Strategy	Key Contribution/Feature
LEACH [11]	Yes	Random selection	Single-hop to BS	Foundational protocol, random CH selection
Improved LEACH [12]	Yes	Residual energy, density	Single/multi-hop	Balanced CH workload withdensity awareness
EE-LEACH [13]	Yes	Residual energy, density, distance to BS (fuzzy logic)	Not specified	Avoids hotspot, fuzzy logic-based ranking
Energy-aware LEACH [14]	Yes	Residual energy, position centrality	Not specified	Adaptive CH range based on density
NM-LEACH [15]	Yes	Residual energy, distance to BS	Not specified	Even CH distribution, improved stability
Adaptive low energy [16]	Yes	Centrality, residual energy	Not specified	Minimizes intra-cluster distance
EACR-LEACH [17]	Yes	Residual energy, number of neighbors, CH load history	Not specified	Controls fairness in CH load
RCBRP [18]	Yes	Residual energy, distance, energy cost	Clustered routing	Optimized path for energy balance
Honey Badger-based [19]	Yes	Distance, residual energy, neighbors’ degree, centrality	Fuzzy swarm optimization	Hybrid metaheuristic CH selection
FICZP [20]	Yes	Lifetime of neighbors, residual energy, member lifetime	Fuzzy system	Energy-aware fuzzy zone-based clustering
Fuzzy-quantum annealing [21]	Yes	Residual energy, number of neighbors, distance, centrality	Quantum routing	Energy thresholding, hybrid IA
Dragonfly–firefly hybrid [22]	Yes	Energy, delay, distance, security	Hybrid metaheuristic	Focus on secure and efficient CHs
RBCHS [23]	Yes	Distance to BS, residual energy, number of neighbors	Static clusters + hybrid routing	Heterogeneous networks, zoned CH selection
Our approach	Yes	Distance to BS, a controlled density	Static topology, adaptive and zone-based, optimal strategy changes with distance from BS	Mathematically validated, proved that clustering is not always optimal;

provides a comprehensive overview of existing approaches.

The assumption that “clustering improves network lifetime and conserves energy” is always used to develop the most efficient routing protocols in WSN and IoT networks. Moreover, most of the parameters, such as node residual energy, number of neighbors, centrality, and distance to the BS, are often chosen to select CHs and control node lifetime.

3. Advanced Clustering Approach

A cluster is a set of sensor nodes, one chosen periodically as the cluster head (CH), and the rest of them considered as members. The CH was almost chosen based on different criteria. In the literature, researchers have used multiple metrics, such as the distance, the number of members, and the remaining energy. At this point, we should mention that the type of routing protocol represents the main aim in the selection of these criteria. Therefore, we are obliged to choose the category of protocols this study focuses on. Mainly, clustering is used to optimize the energy consumed in the communication between nodes to fulfill the WSN application’s needs. The communication process consumes a significant part of the nodes’ energy. Therefore, minimizing the consumed energy in this main process leads to prolonging the WSN performance, especially its lifetime.

Our purpose is to study the different parameters of clustering and which give the best performance. We start with the hypothesis that clustering is more efficient to prolong network lifetime. At the end of this section, we conclude with the best ways to use clustering for developing more efficient routing protocols for WSNs.

This section is partitioned as follows: the first subsection is for selecting the real parameters that affect clustering efficiency, followed by the rest of the subsections that discuss each parameter’s effect individually.

3.1. Parameters That Affect Clustering Efficiency

According to the literature, there exist many parameters that affect the clustering performance. However, the starting point is the LEACH energy model, which is the root of them all. It resumes the main communication operations in a WSN. Therefore, we start by analyzing this model, then we discuss other parameters that have been used by researchers in order to enhance their routing protocol’s performance.

3.2. Parameters Considered in the LEACH Energy Model

In this part, we give the leach energy model and extract the main parameters that affect the clustering method. The leach energy model is represented by Equations (1)–(4). Equation (1) represents the process of sending a packet towards either a sink or a neighbor node. Equation (2) is the reception equation. It gives the energy consumed when receiving a packet from a neighbor node. Equation (3) is the aggregation equation, which gives the amount of energy consumed in the aggregation of received packets by a cluster head from its member nodes. The aggregation operation is specified for cluster heads that are responsible for the collection of all packets from their members, aggregating them into one packet that should be sent towards the base station in the case of one-hop communication or towards a neighbor cluster head in the case of multi-hop communication. Equation (4) is used to identify the use of two forms of Equation (1).

$$E_{Tx}=\left\{\begin{array}{c}L.E_{elec}+L.{\epsilon }_{fs}.d^2,ifd<d_0\\ L.E_{elec}+L.{\epsilon }_{mp}.d^4,ifd\ge d_0\end{array}\right.$$

(1)

$$E_{Rx}\left(n_p\right)=n_p.L.E_{elec}$$

(2)

$$E_{DA}\left(n_p\right)={(n}_p+1)L.E_a$$

(3)

$$d_0=\sqrt{{\displaystyle \frac{{\epsilon }_{fs}}{{\epsilon }_{mp}}}}$$

(4)

where:

$E_{Tx}:$ denotes the energy consumed in the transmission process.

$E_{Rx}:$ represents the energy consumed in the reception process.

$E_{DA}:$ is the energy consumed in the data aggregation process.

$d_0:$ is the distance condition value applied to the two equations to obtain the consumed energy in Equation (1).

The other parameters are given in

Table 2. LEACH energy model parameters.

Parameter	Value
$L$	Packet length (4000 bits).
$E_{elec}$	Energy dissipated to run the transmitter or receiver circuitry (50 nJ/bit).
${\epsilon }_{fs}$	Transmitter amplifier, energy-free space model (10 pJ/bit/m2).
${\epsilon }_{mp}$	Transmitter amplifier, energy multipath model (0.0013 pJ/bit/m4).
$d$	Distance (m).
$d_0$	Approximately $87.7\mathrm{m}$.
$n_p$	Number of packets.

:

Based on these equations, it is obvious that the main considered variable is the distance for the transmission equation. However, the reception and the aggregation equations are linear functions, and their main variable is the number of packets either received or aggregated, respectively. The leach protocol uses clustering as the main approach to reduce the consumed energy, and it utilizes one-hop communication either in the inner cluster (i.e., between a CH and its members) or between CHs and the WSN’s BS. For the leach, this is the best approach to obtain better WSN performances.

This study starts by checking the correctness of these hypotheses. The two fundamental questions we have to answer are, is clustering efficient for all times, or do some variations need to be fixed to obtain better performance? And, is one-hop communication the preferable method to transfer packets either between CMs and their CH or between CHs and their BS?

3.3. Clustering Efficiency: Analysis Study

Clustering divides the WSN into several sets, either equal or unequal. The number of nodes that construct a cluster represents its density. Therefore, cluster density is a fundamental parameter that affects the clustering efficiency. According to Leach, the optimal density of a cluster in a WSN composed of 100 nodes distributed in an area of 100 m × 100 m is 10 (one is a cluster head, and the remaining nine nodes are cluster members).

To check the efficiency of the cluster density, firstly, we should extract the equation that represents a cluster’s consumed energy, which is the sum of the energy consumed by the CH and the CMs. Equations (5)–(7) give the energy by consumed a cluster head, by members, and their sum, which represents the energy consumed by a cluster, respectively.

$$E_{CH}\left({CH}_{d2BS},M\right)=E_{Tx}\left({CH}_{d2BS}\right)+E_{Rx}\left(M\right)+E_{DA}(M+1)$$

(5)

$$E_{CM}=\sum _{i=1}^n{E}_{Tx}{\left({CH}_{d2CH}\right(i))}_{CH}$$

(6)

$$E_C=E_{CH}+E_{CM}$$

(7)

where:

$E_{CH}\left({CH}_{d2BS},M\right)$ is the consumed energy by a CHdistant from the BS by $d2BS$ with M member nodes.

$E_{CM}$ represents the consumed energy of a node as a member in a cluster with a density of $n$ nodes with ${CH}_{d2CH}\left(i\right)$ as the distance to each node in the cluster where it is a CH.

$E_C$ is the total consumed energy by a cluster.

Our aim is to reach a conclusion that helps any researcher in the field know how to deal with the clustering approach to develop more efficient routing protocols. According to the literature, the standard network used to simulate WSNs is a WSN composed of 100 nodes distributed randomly in a 100 m × 100 m area, where the BS position is in the center of it, as shown in Figure 1. Therefore, based on this topology, the min distance to the BS could be farther than 0 m and less than the Euclidean distance between the BS (50, 50) and the furthest point in the area, which are the four vertices’ points (i.e., (0, 0), (0, 100), (100, 0), and (100, 100)). This distance equals 70.7107 m.

The second parameter is the number of nodes (i.e., the cluster’s density). To name a cluster, we need at least two nodes, one as CH and one as CM. However, a cluster’s density could surpass the optimal value considered by Leach (i.e., 10 nodes). In that case, we determined that the max number of members should be double this value, which is 20 nodes.

The third parameter is the distance between a CM and their CH. It is farther than 0 m and limited by a range of 20 m. To this point, we fixed the ranges of the three essential parameters in a clustering approach based on the LEACH hypothesis, which is clustering with one-hop communication either within a cluster or between a CH and its BS, which is efficient to prolong a WSN’s performance.

Now, to check this hypothesis, we compare it against the basic manner, which is nodes sending their packets directly towards the BS. To perform this comparison in the right way, we must utilize the same conditions. Our main performance parameters are the consumed energy/node lifetime, node throughput, first, half, and last dead nodes.

It is obvious that defining the same conditions means considering the three parameters for the clustering approach; we need a cluster where all nodes should be in the range of the rest of the nodes (i.e., they represent a complete graph). However, in the basic manner, we have a number of nodes distributed randomly in the area sending their collected packets individually. Therefore, firstly, we obtain a cluster where all nodes are completely connected, then we simulate them in the two different manners. In this case, the max distance between any two nodes should be equal to or less than 20. Therefore, a node could not be a distance of more than 10 m from the center of a circle that surrounds the cluster’s nodes, as shown in Figure 2.

Also, the second parameter is the distance between the CH and the BS, which varies from one node to another, which gives a variation of each node to be CH. Therefore, the nodes take turns as the CH for each round of simulation. In this part, we have two cases: each round, a new node takes its chance randomly but cannot take another chance until all nodes perform their role as CH because they all have the same number of members/neighbors. Then, the second case considers the variation in the distance to the BS because nodes differ in their sending distance, which makes them consume different amounts of energy. This causes distant nodes to use up their batteries before closer ones.

In the first case, we have 10 nodes, each of which takes one often turns. The CH’s role and the rest of the nine roles are managed by the CM. Equation (8) represents the energy consumed by a node for each ten rounds (i.e., one turn as CH and nine of them as CMs). However, Equation (9) gives the formula of the cluster nodes sending their packets individually.

$$E\left(d_{2BS},d_{2CH},10rounds\right)=E_{CH}(d_{2BS})+\sum _{i=1}^{i=9}{E}_{CM}\left({d_{2CH}}_i\right)$$

(8)

where:

$E$ represents the energy consumed by a node in ten rounds, one as CH and nine as CMs.

$E_{CH}$ defines the consumed energy of a node as CH.

$E_{CM}$ defines the consumed energy of a node as CM.

$d_{2BS}$ is the distance between the CH node and the BS.

$d_{2CH}$ is the distance between the CM node and the current round’s ith CH.

$$E_n\left(d_{2BS},10rounds\right)=10.E_{Tx}\left(d_{2BS}\right)$$

(9)

where:

$E_n$ represents the energy consumed by a node in ten rounds, sending its data individually to the BS.

Figure 3 represents the consumed energy using either clustering or nodes sending their data individually. It is obvious that if nodes send their collected data individually, it is significantly better than collaborating in a cluster, at least for the range of 1 to 141 m distance to the BS. This leads us to the next question: What is the efficiency of using clustering to minimize consumed energy and, in other words, to prolong the WSN lifetime? Could it be that when each node sends its data individually, there is a significant difference in the times when the first, middle, and last nodes die?

Additionally, the clustering approach may result in the highest FDN value compared to individual data transmission, which could be beneficial for our WSN. This is especially important considering that the WSN lifetime is typically defined by the death of the first node.

To calculate the lifetime of a node within a cluster, we must first determine the number of neighboring nodes and the average distance between a node and its neighbors. Based on the LEACH protocol, the optimal cluster density is ten nodes—one CH and nine CMs. The average distance, considering the energy consumed by nodes to send a packet within a range of 1 to 20 m, is approximately 14 m. Figure 3 shows the cluster’s lifetime for nodes with an initial energy of 0.5 joules using two different approaches. The distance to the BS remains within the range of 1 to 141 m.

According to Figure 4, we can conclude that clustering alone is not the most efficient method throughout the entire operation to minimize energy consumption and extend the lifetime of a WSN. Clustering is effective for nodes located at distances greater than approximately 75 m, as indicated in the graphs in Figure 3. Additionally, the distance between nodes has a relatively minor impact on the WSN’s lifetime. The three graphs show variations in performance only during the first 50 rounds, which is minimal compared to the significant impact of the distance to the BS.

Up to this point, we have not tested the impact of cluster density. In other words, when using clustering, the optimal cluster density is not always achieved. It is possible to work with clusters that have either lower or higher densities. Our reference remains the optimal cluster density proposed by the authors of the LEACH protocol, which serves as the foundation for over 22,100 research papers in the field.

To understand the effect of the number of neighbors on a node’s lifetime, we first calculate the energy required to serve a neighbor. This includes the energy needed to receive a packet and aggregate it, either with the packet from the CH or with packets from all the nodes in the cluster. Equation (10) represents the energy required when a new node joins the cluster.

$$E_j=E_{Rx}+E_{DA}$$

(10)

where:

$E_j$ represents the energy consumed by a CH for each neighbor that joins its cluster.

To assess the impact of the number of neighbors on the lifetime of a CH, we first consider that the role of the CH varies based on the CH selection process. In this study, we assume that the CH role is distributed equally among nodes, meaning each node has an equal chance of becoming a CH depending on the cluster’s density. For example, if a cluster consists of 10 nodes, each node should ideally serve as a CH once and as a CM nine times. Consequently, the energy consumed by a node within a cluster is represented by Equation (11):

$$E_{CH}\left(d_{2BS},N_n\right)={\displaystyle \frac{1}{(N_n+1)}}{E}_{Tx}\left(d_{2BS}\right)+(N_n).E_{Rx}+(N_n+1).E_{DA}$$

(11)

where:

$E_{CH}$ is the energy consumed by a node as a CH.

$N_n$ is the number of neighbors.

Equation (12) illustrates the percentage impact of a CH serving a single neighboring node.

$$P\left(E_j,E_{CH}\right)=100{\displaystyle \frac{E_j}{E_{CH}(d_{2BS},N_n)}}$$

(12)

where:

$P$ represents the percentage of energy consumed by a CH when serving a new neighboring node.

Figure 5 illustrates the proportion of energy consumed for receiving and aggregating packets from one, two, and three neighbors relative to the total energy consumed by a CH at varying distances from its BS, ranging from 1 to 141 m (depicted by the blue graph). The red graph represents the proportion of energy consumed for transmitting packets relative to the total energy consumed by the CH over the same distance range. The selected number of neighbors for this comparison—1, 2, and 3—was intentional for the purpose of the analysis.

From Figure 5, we can conclude that the energy required to receive and aggregate a packet remains high until the distance is approximately 83 m when the cluster consists of only two nodes. For a cluster density of three nodes, this high energy consumption persists until a distance of 123 m. When the cluster density increases to four nodes, the high-energy portion extends beyond the diameter of the area (141 m), reaching approximately 149 m. This is why we chose cluster sizes of 1, 2, and 3 nodes—because once the node serves three neighbors, the energy consumption remains higher until the distance exceeds the diameter of the area. What happens if the cluster density exceeds three nodes? This implies that using a clustering approach in a standard area of 100 m by 100 m with a base station (BS) located in the center is not advisable. The maximum distance to the BS is 70.71 m, which is less than 83 m. In other words, even when using clusters composed of just two nodes, a distance larger than 83 m is needed. However, in a topology where the BS is located at one of the vertices of the area, with the farthest point being 141.42 m away, the optimal choice is to use clusters with a maximum density of three nodes. In summary, as the cluster density increases, the required distance becomes greater.

Figure 6 presents the energy consumption for receiving and aggregating packets, similar to Figure 5, but with different numbers of neighbors. In this scenario, we selected a cluster density of 10 nodes (one cluster head (CH) and nine cluster members (CMs)), as preferred by LEACH, which hypothetically represents the optimal cluster size. Additionally, we examined a cluster with double the density of LEACH’s optimal cluster, chosen because most clusters in the area should not exceed this density except in rare cases. Finally, we tested the entire WSN with a density of 100 nodes as a single cluster to determine the maximum distance that covers this density.

Based on this figure, a cluster head (CH) with nine cluster members (CMs) consumes more energy serving its members than it does sending a packet to the base station (BS) until the distance is less than 250 m. If the CH serves nineteen CMs, this distance increases to 358 m. Although it is unrealistic to have all nodes in a WSN within one cluster due to the limited neighbor selection range of 20 m, this scenario is considered for estimation purposes to demonstrate the impact of density. According to the third subplot, for a cluster composed of 100 nodes, the energy consumed in receiving and aggregating packets remains highest as long as the distance is less than 810 m.

In summary, this section analyzed the efficiency of using the clustering approach to determine whether clustering enhances WSN lifetime, as hypothesized. By comparing the lifetime of a node in a cluster with that of a node sending packets individually, we found that individual sending is preferable when the distance is less than 75 m (see Figure 3).

Next, we examined the energy consumed within a cluster, specifically the energy used by the cluster head (CH) in receiving, aggregating, and transmitting the aggregated packet to the base station (BS). For each cluster member (CM), the CH expends energy in receiving and aggregating the packet, with the minimum being the energy used by a CH serving a cluster composed of two nodes. In such a case, the energy consumed in serving a CM is greater than the energy required to transmit a packet to the BS as long as the distance is less than 83 m. This distance is greater than the farthest point in a WSN distributed over an area of 100 m × 100 m with a BS located at the center (50, 50). As the cluster density increases, this critical distance also increases. In a scenario where the BS is located at a vertex of the area and the farthest distance is 141.42 m, we found that a cluster with a density of four nodes (one CH and three members) is inefficient, as it requires a distance of at least 149 m to be effective.

Furthermore, testing the optimal LEACH cluster (one CH and nine CMs) revealed that it requires a distance greater than 250 m to be more efficient than individual sending. We also considered a scenario with double the density of the LEACH optimal cluster, representing common cases where a cluster might reach a density of 20 nodes, though this is rare. The results indicate that such a cluster is inefficient unless the distance exceeds 358 m. We even tested an unrealistic scenario where all WSN nodes are gathered in a single cluster, which is impossible due to the limited neighbor range of 20 m. However, in this case, clustering would only be more efficient than individual sending if the distance exceeds 810 m.

In conclusion, clustering is efficient for nodes that are at least 75 m away from the BS. The efficiency of clustering is directly related to both the distance to the BS and the density of the cluster.

4. Simulation Results

In this section, our primary focus is on validating the results from the previous section (Clustering Study). We examined two scenarios: the first involved a WSN composed of 100 nodes distributed within a 100 m × 100 m area, with the base station (BS) located at the center (50, 50). The second scenario differed only in the base station’s location, which was at (100, 100). Our main goal was to verify the findings in the previous section by comparing the individual transmission approach with the clustering approach.

4.1. First Scenario: The Base Station (BS) Is Located at the Center of the Area (50, 50)

Figure 7 illustrates the WSN topology for this scenario.

According to our study, the most effective approach for this topology is where all nodes transmit their data individually. This approach results in a longer network lifetime compared to the clustering-based approach with cluster sizes of 2 and 3. Figure 8 and Figure 9 illustrate these topologies, respectively.

The three topologies illustrate the WSN construction and node distribution, including individual nodes, pairs, and trios. The WSN’s performance is evaluated based on five parameters: lifetime, throughput (packets sent to the BS), First Dead Node (FDN), Middle Dead Node (MDN), and Last Dead Node (LDN). Figure 10 depicts the lifetime of each topology, with the graphs representing the lifetime for individual nodes, Cluster-2, and Cluster-3, respectively.

As discussed in Section 5, the individual transmission approach yields the highest lifetime, followed by the cluster with the lowest density. Specifically, the topology with clusters of two nodes (Cluster-2) performs better in terms of lifetime than the topology with clusters of three nodes (Cluster-3), and so on. Figure 11 shows the throughput for each of the three topologies, while

Table 3. FDN, MDN, LDN for individual nodes, Cluster-2, and Cluster-3 topologies.

Topology	FDN	MDN	LDN
Individual	1340	1912	2496
Cluster-2	1229	1361	1541
Cluster-3	816	1118	1137

provides the values for the remaining three parameters: FDN, MDN, and LDN. The individual topology consistently outperforms the clustering-based topologies, with the cluster with the lowest density performing better than those with higher densities.

To summarize, in a WSN composed of 100 nodes distributed within a 100 m × 100 m area with a base station located at the center (50, 50), the individual transmission approach for sending packets to the base station outperforms cluster-based topologies across all criteria (lifetime, throughput, FDN, MDN, and LDN).

4.2. Second Scenario: The Base Station (BS) Is Located at the Center of the Area (100, 100)

In this scenario, we first replicate the tests from the initial scenario, where nodes either transmit data individually or are grouped into clusters of two or three. We then conduct additional tests, incorporating our study’s findings on the relationship between distance from the base station (BS) and node performance. Specifically, individual transmission is more effective for nodes located less than 83 m from the BS, clusters of two nodes are better for nodes between 83 and 123 m from the BS, and clusters of three nodes are most effective for nodes between 123 and 149 m, which includes the area’s diameter of 141 m, representing the maximum distance within the area.

Figure 12, Figure 13 and Figure 14 show the topologies for individual nodes, clusters of two nodes, and clusters of three nodes, respectively.

The lifetime and throughput for these topologies are shown in Figure 15 and Figure 16, respectively.

Table 4. FDN, MDN, LDN for individual nodes, Cluster-2, and Cluster-3 topologies.

Topology	FDN	MDN	LDN
Individual	302	1056	2477
Cluster-2	477	1084	2477
Cluster-3	264	1121	2187

provides the values for the FDN, MDN, and LDN parameters.

According to the results shown in Figure 9 and Figure 10, a cluster with a density of 2 nodes is the most effective for prolonging lifetime, indicating better conservation of node energy. This is followed by the individual topology, then the Cluster-3 topology. However, in terms of throughput, the individual topology outperforms the others, followed by Cluster-2 and then Cluster-3. This is because individual nodes send packets to the base station more frequently than when they are part of pairs or trios.

Regarding the FDN, which defines the network’s lifetime (Figure 15 and Figure 16), Cluster-2 performs the best, lasting 477 rounds before the first node dies. This is followed by the individual topology with 302 rounds, and finally, Cluster-3 with 264 rounds. Note that there are other definitions of network lifetime, such as until the last node dies or until the application can no longer function.

For MDN, the results show that Cluster-3 performs the best, followed by Cluster-2 with 1084 rounds, and then the individual-based topology with 1056 rounds. Finally, for LDN, both the Cluster-2 and individual topologies have the same value, lasting 2477 rounds, while the Cluster-3 topology achieves 2187 rounds.

The conclusion drawn from the simulation highlights that different distances yield optimal efficiency for each topology. For distances less than 83 m, the individual node topology is more efficient. For distances between 83 and 123 m, the cluster with a density of two nodes performs better, and for distances between 123 and 141 m, the cluster with three nodes is more effective. However, the overall simulation results indicate that the Cluster-2 topology outperforms the others, followed by the individual node topology, with the Cluster-3 topology being the least effective.

In the following simulations, we implement the findings from our study. First, we use a topology divided into two zones: nodes within 83 m transmit individually, while nodes farther than 83 m transmit in pairs. For the final topology, we divide the WSN into three zones: the first for nodes within 83 m, the second for nodes between 83 and 123 m, and the third for nodes beyond 123 m.

Figure 17, Figure 18 and Figure 19 illustrate different scenarios: In the first scenario, all nodes transmit their data individually. In the second scenario, nodes within 83 m transmit individually, while more distant nodes operate in pairs. In the final scenario, nodes within 83 m still transmit individually, nodes between 83 and 123 m transmit in pairs, and nodes beyond 123 m transmit in trios.

Figure 20 and Figure 21 display the lifetime and throughput for these topologies.

Table 5. FDN, MDN, LDN for individual nodes, Cluster-2, and Cluster-3 topologies.

Topology	FDN	MDN	LDN
Individual	330	1142	2495
Cluster-2	510	1113	2495
Cluster-3	628	1140	2495

presents the values for the FDN, MDN, and LDN parameters.

Figure 21 demonstrates that partitioning the WSN according to our study improves its performance. The individual node topology is the weakest, but when the WSN is divided into two zones (Figure 18), its lifetime increases significantly. Adding a third zone for nodes beyond 123 m, organized into trios, further enhances the lifetime (Figure 21). According to Table 3, the FDN, which represents the lifetime, improves from 330 rounds for the individual topology to 510 and 628 rounds for the Cluster-2 and Cluster-3 topologies, respectively.

However, as mentioned earlier, throughput represents the number of packets sent to the BS. It is related to the number of individual nodes, pairs, and trios in the WSN and their lifetimes. Considering the number of individuals, pairs, and trios in the WSN, it is clear that the individual topology has the highest value, followed by pairs and trios. However, lifetime also plays a crucial role, which explains why Cluster-3 has a higher throughput value than Cluster-2 (see Figure 15). The individual topology does not show a significant difference compared to the other topologies. This can be explained by the short area, where individual nodes dominate, and the lack of long distances that would otherwise challenge this topology. Ultimately, these values vary depending on the distance to the BS and the area dimensions.

5. Conclusions

Currently, most of the solutions presented and developed to solve the routing and lifetime problems of wireless sensor networks are based on clustering. However, these techniques are not always optimized according to the topology and architecture of the network as well as its evolution and dynamics. The hypothesis that clustering is the best approach for extending the lifetime of WSNs is not always correct. In this paper, we demonstrated that for a 100 × 100 m topology with 100 nodes and a BS located at the center (50, 50), it is more effective for nodes to send their data individually. However, for a topology with the same characteristics but with the BS located at (100, 100), our findings suggest that the area should be divided into three zones for optimal performance. In the first zone, where nodes are within 83 m of the BS, nodes should send data individually. For nodes located between 83 and 123 m from the BS, nodes should collaborate in pairs. Finally, in the third zone, clusters of three nodes are more efficient where they are beyond 123 m from the BS. These findings demonstrate that clustering is not always the best method for enhancing WSN lifetime. Also, the assumption that dense clusters are always better should be applied considering the distance to the BS.

As future work, we aim to complete this study for the Internet of Things, where thousands of nodes are distributed in a large area.