1 Introduction

Sensor networks are static ad hoc networks built with tiny, lightweight, and movable detection stations built with multiple sensor nodes. All sensor nodes have four components: a transducer or sensor device, a microcomputer or low-capacity processor, a transceiver or low-range wireless transmitter–receiver, and an energy source. There are three domains in WSNs. The first domain is called the device domain, in which a large number of sensors are deployed. The sensors sense some physical parameter (e.g., temp, pressure, humidity, etc.) and send this sensory information to the application domain containing a back-end server. All the sensory inputs are stored in the back-end server for several different applications. All this information exchange between the device domain and the application domain takes place with the network domain's help, which lies in between the device and application domain. There has a static base station inside the network area of the WSNs [1,2,3,4]. Since all the sensors have minimal power, sensor networks' network lifetime can only be improvised with innovative technology.

The current technology has completed with it, enabling the equipping of smaller powered devices, which can be fitted with programmable computing, to sense various parameters and capacity to communicate wirelessly. Furthermore, these wireless sensors come at a low cost that enables many of them in the network. It has resulted in highly reliable and more accurate data with extensive system coverage [5].

WSNs have expanded pronounced popularity because of their applicability in a wide range of applications. WSNs were initially designed for applications in any situation. But nowadays, they have some additional application areas comprising health & hospitals [6], traffic management [7], military, tracking, transport, industry [8], environment, pollution monitoring [9] and control, and so on. Its limited source environment has always been an issue. Heterogeneous networks have earned a great deal of evaluation due to their resource limitations.

WSNs are most frequently created with a group of sensor nodes in disjoint sets called a cluster. Clustering for WSNs provides the scalability of the network, the sharing of resources, and the efficient use of restricted resources to ensure an energy-saving and stability attributes for network topology.

Through the clustering scheme, lower communication overheads and adequate resource allocations are achieved, decreasing energy consumption and lowering the sensor node interference.

There will be large size clusters competing in the network area with a small number of groups. Also, tiny size clusters will exhaust that cluster head containing the transmission of higher message volume originating from that cluster. When the CHs receive a high message volume from the cluster member, a lot of energy is spent per round. According to this statement, after a few rounds, CH will be dead.

Protocols for such networks should be formulated to make efficient use of the sensor nodes' limited power. Aggregation of data can abolish the redundancy of data and decrease communication load [10]. Hierarchical mechanisms or clustering are particularly useful in increasing the network's scalability and reducing the extensively oppressed data latency.

A lot of work came up later on the routing protocols like ' power-aware’ for WSNs. Optimal routes are selected according to the energy of each node throughout the road in such protocols. Longer routes with more energy-consuming nodes are preferred than the shorter route nodes through helping to prevent “hot spots” within the network. At Low Energy Adaptive Clustering Hierarchy (LEACH), the CHs are placed randomly rotated to attain the same objective [11, 12].

Some protocols, such as SEP, are based on the heterogeneous network for the WSNs. SEP protocol can prolong the stability of heterogeneous two-level networks consisting of dual-sensor nodes depending upon their original energy, such as normal & advanced nodes. The SEP protocol works similar to the LEACH protocol. Still, in SEP protocol, the rotating probability of CH and the likelihood of selection are directly linked to the node's original energy. Figure 1 highlights the heterogeneous model for wireless sensor networks. It shows the resources, impact, and behavior exhibited by the heterogeneous network.

Fig. 1
figure 1

Heterogeneous system for WSN

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In this work, we investigate a clustering algorithm based on heterogeneous protocols for WSNs that are energy efficient. A novel and improved approach is proposed for prolonging the duration that the network lives for and decreasing the energy consumed. The proposed work decreases the sensor node energy consumption, improves the network lifetime, and decreases the data transmission. The main contribution of our work in this paper is as follows:

  • To enhance the energy efficiency, we propose two innovative routing methods of the WSNs. We use the heterogonous network of the WSNs. Here two different types of plans are used for node distribution. (1) A random spread of the heterogeneous sensor nodes over a region M × M m2 area. (2) The location of heterogeneous sensor nodes is determined by the 2D elliptical Gaussian distribution method.

  • The clustering threshold method is employed during CH selection and formation. CH selection is made from both advance and normal nodes. The proposed method balances the cluster distribution in the WSNs.

  • The clustering method is essential to be repetitive in every round. The dynamic threshold is used for cluster head selection. It may conclude a fair number of CHs and make it reasonable for each cluster member to be clustered.

  • The same simulation environment and parameters are considered to verify our proposed ADV-LEACH1 and ADV-LEACH2 method outperforms over the existing protocols (LEACH [10, 13], SEP [13, 14], and Modified-LEACH [13, 15]) in WSNs.

The rest of the paper is organized as follows: A literature overview is given in Section 2 covering the system model with lots of old and newly proposed work. Section 3 discusses the network model with the node distribution layout of the current method and energy model. The proposed ADV-LEACH1 and ADV-LEACH2 method of clustering is mentioned in Sect. 4. Section 5 demonstrates the performance evaluation of the proposed approach via simulation results and analysis compared with existing protocols. Section 6 concludes the paper.

2 Related Work

The priority of a WSN is to decrease various nodes’ level of consumed energy and extend the WSN's life cycle. To enhance the sensor node energy according to the advantages of static clustering through overhead reduction, various hop methods in data transmission and creating multiple sectors in the total area so that minimizing the energy consumed by cluster head (CH) can be achieved [16]. In the CH selection method, the residual energy belonging to each node is considered. The range of CH is extended to increase energy consumption by various network nodes [17].

The CHs having more residual energy are selected in [18] because of the energy state of the nodes and through energy utilization by a combination of a single hop with multiple hop mode, balancing of energy intake amongst the nodes, and the BS.

Using the LEACH algorithm calculated the value of CHs that are consuming the lowest energy. Further, the authors optimized the network lifetime with the clustering algorithm called K-means. In this way, the authors can improve the network lifetime [19].

Additionally, the amount of energy being consumed is reduced. A higher life cycle is achieved by introducing parameters like energy, distance, and density to modify the CH and its performance [15].

An energy routing protocol depends on efficient data collection, and optimal selection of CHs has been designed by the authors in [20]. This protocol extends the network's lifetime. However, the time delay produced by multiple tasks still affects. It always works by choosing the sensor nodes with a higher residual power without taking other factors into account, as the nodes' position could be positioned far from BS.

The authors in [20] have proposed a LEACH-B protocol. The first choice of CH is based on the original LEACH. The CH amount modification is accomplished based on all residual energies available from all nodes as the second selection commences. The amount of CHs in each round is thus set and almost optimal. The remaining energy consumption increases the network lifetime as compared to LEACH during the simulation.

Authors in [21] propose a suitable communication technique. Through the simulation, the authors find that the consumption of total energy is minimized when no cooperation is done. However, the overhead traffic is more in the nodes' case in groups (clusters) per round.

The authors propose [22] the SEP protocol, an optimized leach algorithm in a heterogeneous network for a network lifetime improvement. However, the unstable CHs’ level of consuming energy and sensor nodes would reduce the lifespan that added the sensor node energy to CH election to minimize the CH’s level of consuming energy and decrease the energy consumption of the cluster nodes by indirect intermediate node transmission. The enhanced SEP protocol performs well to balance energy consumption to improve the LEACH protocol’s lifespan.

The authors in [23] present many challenges related to the quality of WSNs. The consumption of energy is considered to be the warm study area out of these challenges. The maximum of WSN-energy is employed for data transmissions among the sensor nodes or to a BS. Several routing protocols are now in place to promote data dissemination in the WSNs. A new approach has been proposed to break the whole WSN down into multiple levels. Every single node will act on its status and position accordingly. Besides, both techniques were developed, one dynamic and one static, to route the data among both of them. Simulation results show that the modified techniques extend lifetime, enhance reliability, and increase network bandwidth compared to the LEACH, enhanced DMHT-LEACH (EDMHT-LEACH), and improved MHT-LEACH (EMHT-LEACH) protocols.

The author in [24] proposes an energy-efficient disseminated clustering approach. Based on the LEACH protocol, the LEACH-extended Message-Passing (LEACH-XMP) proposal significantly enhances the cluster forming method that is crucial to WSN processes. Unlike the existing methods, a practical nonlinear energy consumption model is considered, rendering extremely nonlinear and difficult clustering optimization. An advanced message-passing method is presented for this purpose to improve an efficient disseminated approach. This suggested methodology's core advantages can be ascertained: the natural tendency nature of a disseminated approach and computational traffic on every node. It is, therefore, useful for empirical distribution. However, within a few iterations, the proposed method converges quickly to an obvious solution. The simulation results certify that the future LEACH-XMP maximizes the network's lifespan considerably over the existing techniques.

The authors in [25] present the newly proposed LEACH (IEE-LEACH) improved energy-efficient protocol that considers residual network energy and node energy. To attain optimum performance, when it comes to the energy being consumed reduction in sensor nodes, the suggested IEE-LEACH accounts for maximum CH numbers and forbids cluster formation of nodes nearest to the BS. Also, the modified IEE-LEACH approach employs a different clustering threshold for the choice of CHs between sensor nodes and further uses single-hop, multi-hop, and hybrid communications to increase energy efficiency within the network. This hypothesized result shows that the proposed protocol significantly lowers the amount of energy being consumed by WSNs in contrast with some current routing protocols.

The authors in [26] develop a functional utility mechanism that can efficiently manage power transmission, residual energy, network connectivity, and a topology game control system. According to this, the non-cooperative game theory gets closely examined. The hypothetical investigation demonstrates a topology game system as a latent game capable of converging into a Nash equilibrium. A topology game control approach, EFTCG, that is efficient in its energy use and tolerant to faults is enhanced to build an adaptive system topology.

The authors in [27] introduced WMSNs, capable of gathering multimedia actions, i.e., traffic accidents and wildlife monitoring. The multimedia applications generate very high network traffic due to this higher rate of consuming energy. Energy is the primary resource in WMSN. It requires a flawless manner of routing that efficiently handles the dynamic topology while simultaneously extending the network lifetime. The authors propose an algorithm for routing that combines active cluster formation, selection of CHs, and multipath communication of the data, routing to decrease the energy consumption and overhead. According to the genetic algorithm (GA), the primary method uses a meta-heuristic optimization to dynamically select the best path with a lesser distance and less energy consumption based on a cost function.

Significant research has been conducted for the improvement in CH selection and cluster formulation reduction. A good clustering algorithm reduces energy consumption as well as improves the network lifetime of the WSNs. FBECS [28] improves stability and can provide high residual energy. However, the enhancing of the network lifetime by this approach is not sufficient. The model is sensitive to noise and outliers. The AVL tree clustering model in [29] would increase the network lifetime and save maximum energy consumption. However, the model does not apply to network security. Improved ABC [30] reduces the delay and can send more packets. NEAHC [31] maximizes the number of alive nodes and also increases the distribution of packets. Yet, the model requires more time to run. MOEA [32] reduces energy consumption, and the model makes the inter-cluster communication more efficient. However, optimal transmission energy is required for the model. K-means approach [33] absorbs less energy and improves the network lifetime. However, it is complex to estimate K-value, and it also has less success with the global cluster. The authors in [34] and [35] implement an advanced approach to optimize energy, security, and reduced delay. In [36, 37], the author presents the route determination approaches for a mobile sink in 3D WSNs and a survey based on machine learning for WSN. Various evolutionary and optimization-based clustering approaches [38, 39] have been introduced to maximize the network lifetime, but all these algorithms are complex and time-consuming compared to threshold approaches. However, the current clustering model is not successful.

The proposed clustering algorithms are designed based on the threshold approach for improving the network lifetime and energy efficiency in WSNs. Both these clustering algorithms are easy to compute and having much lesser complexity. Thus, the overall time complexity is O(nk), where O(n) time is required to calculate the threshold probability for all the nodes to become the CHs and O(k) time is required for allocating n nodes to k CHs. Another threshold-based clustering approach has been recently recommended in [40] with time complexity of O(mn2), which is shown to be improved over a small target area and higher initial energy.

3 Network Model

Some assumptions are considered for design the network model, which are mentioned as follows: Use of nodes in WSNs defines a fundamental matter that must be considered. It can affect network operations in various means such as security, routing, or energy. The node deployment technique also involves the life span of the WSN. Sensor nodes located at one hop away to sink require receiving and retransmitting packet data to different nodes. Due to the higher consumption of energy in these nodes, these problems persist in the entire network. Thus, to overcome these problems, assuming a heterogeneous system, the sensor nodes are distributed to give normal and advanced nodes as per the energy level. Advanced nodes characteristically show elevated energy consumption as compared to the normal nodes. Here we assume the sensor nodes of heterogeneous networks are deployed in the M × M area. All the sensor nodes are static as they are deployed in the target area and cover it completely. The BS is also fixed and positioned inside and outside of the target area. The advanced and normal sensor nodes are initially provisioned with the same amount of energy, respectively.

Phase-1 Heterogeneous sensor node is randomly deployed over a region M × M m2 area. The location coordinate of the BS is (50, 50) and (50, 150). Packet data of size 4000 bits then get transmitted to the CH originating from the nodes. We simulate our MATLAB version 2015b to test this algorithm and evaluate its performance [14, 41,42,43,44].

Phase-2 The location of heterogeneous sensor nodes is restricted by the 2D elliptical Gaussian distribution method. From the Gaussian distribution, energy is balanced, and network lifetime increases as these two elements are moderately affected by the standard deviation factor [13, 45]. The Gaussian distribution [13] of the network is given in Eq. (1):

$$ f\left( {x,y} \right) = \frac{1}{{2\pi \sigma_{x} \sigma_{y} }}\exp - \left( {\frac{{\left( {a - x_{0} } \right)^{2} }}{{2\sigma_{x}^{2} }} - \frac{{\left( {a - y_{0} } \right)^{2} }}{{2\sigma_{y}^{2} }}} \right) $$
(1)

where \(\left({x}_{o},{y}_{o}\right):\) represent the initial location points of each sensor node. \(\sigma_{x} \;{\text{and}}\;\sigma_{y}\) are the standard deviations for x and y dimension, correspondingly.

Every sensor node has its unique ID as well as the location. The value of xo and yo will be equal to 0. Here sensor nodes have a 0.5 J or 1 J amount of the initial energy and are called the normal and advanced nodes as the batteries of nodes are not rechargeable, so the nodes become dead when the battery's energy is spent.

3.1 Energy Radio Model

Here, the simple model that describes radio-energy dissipation is used in [46,47,48,49]. The radio power model extends two ways to simulate energy consumption to transfer a k-bit information to a measured ranged: free-space mode (\(\in\)fs d2) and multipath fading \(( \in md^{4} )\). It depends on the transmission distance, which will be used in the model, as mentioned in Fig. 1. (d), representing displacement between the transmitting components to the receiving one, was evaluated. The radio-energy model for both models is discussed below (Fig. 2).

$$ \begin{aligned} E_{TX} (k,d) & = E_{{TX - {\text{elec}}}} (k) + E_{{TX - {\text{amp}}}} (k,d) \\ & = \left\{ {\begin{array}{*{20}l} {E_{{{\text{elec}}}} *k + \in_{f} *k*d^{2} ,} \hfill & {d < d_{o} } \hfill \\ {E_{{{\text{elec}}}} *k + \in_{m} *k*d^{4} ,} \hfill & {d > d_{o} } \hfill \\ \end{array} } \right. \\ E_{RX} (k) & = E_{{{\text{elec}}}} *k \\ \end{aligned} $$
(2)
$$ E_{Rx} \left( k \right) = E_{{{\text{elec}}}} *k $$
(3)

where \({E}_{TX}\) is the actual energy consumption for the packet transmission. \({E}_{\mathrm{elec}}\) is electronic energy. \({E}_{RX}\) is the critical use of energy for obtaining packets. \({d}_{0}\) is the square root of the multipath fading dividing by free space.

Fig. 2
figure 2

Radio-energy model

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4 Clustering Approach

Clustering is an essential part of a hierarchy based protocol capable of increasing the network lifetime, determined by the CH selection and clustering formulation approach. WSN clustering can decrease energy consumption because the energy transmission depends on the sender to the receiver. LEACH protocol problems are based on three particular issues. The first issue operates with CH's bad choice. The second issue is arranged inside each cluster by the unequal distribution of nodes. The third issue is the formalized transmission of information (stable state phase). Each node continuously transmits the information within the cluster. Based on these three issues, important data information is dropped. This drop occurs due to elevated energy consumption. Based on this, the lifetime of the network is decreased. Two methods are suggested in this document to solve the LEACH as mentioned earlier and SEP protocol issues in WSN.

The proposed approaches aim to diminish energy amounts consumed by distributed nodes in given areas. The CH selection approach improves according to the CH threshold T(n) to select the best CH node.

4.1 Leach

LEACH is used in the network of the microsensor application [10, 46]. Here both the techniques of cluster-based routing with energy efficiency and media accesses are combined. The LEACH protocol is to save the sensor's energy hence enhancing the network’s lifetime. During the setup phase, CH is randomly selected at the starting of every round after deploying the sensor nodes. Each of the sensor nodes elects varying numbers between 0 and 1. Should any of these numbers be less than the limit value or cluster threshold value (T(n)), that node is then selected for CH at the current round. The threshold (T(n)) is designed based on Eq. (4).

$$ T\left( n \right) = \left[ {\begin{array}{*{20}l} {\frac{P}{{1 - P*\left( {r \bmod \left( \frac{1}{P} \right)} \right)}},} \hfill & {{\text{if}}\, n \in G} \hfill \\ {0,} \hfill & {{\text{otherwise}}} \hfill \\ \end{array} } \right. $$
(4)

Given n represents the number of sensor nodes. p the chance to select the CH. r the current round. G configuration of sensor nodes that haven’t been chosen for CH in 1/p rounds.

Steps of LEACH involvement:

  1. a)

    Advertisement phase In this first step, the eligible node is issued a notification for becoming its member to other nodes cluster. Based upon the Received Signal Strength (RSS), the offer is accepted by the node.

  2. b)

    Cluster setup phase Here, nodes will respond only to chosen CHs.

  3. c)

    Schedule creation here, CH gets a reply from the sensor nodes. It must make a TDMA system and send it back to its clustering members to intimate them. After that, the information can be passed on to it.

  4. d)

    Data transmission In this phase, the information collected by every sensor node will be delivered to the CH during their period. The data transmission is done during a specific period, as energy consumption is reduced; the radio of clustering members will be switched off.

Despite the preservation of energy at sensor nodes and subsequently minimizing the routing table size, it is not free from limitations [50]. They are:

  • The nodes' remaining energy shall not be deliberated when a random selection of CH is made.

  • While increasing the network's dimension, the CH, positioned a higher distance removed from BS, that CH’s spent the higher energy. The performance of LEACH is acceptable, provided there is a small network size.

Following are the restrictions of Time division multiple access or TDMA [13]:

  • Even if there are no recent data available, each CH transmits the data to the allocated slot in its time (non-scalable nature).

  • Specific clusters may have higher sensor node volumes than other clusters that affect the frequency of data transmission with BS. The sensor nodes in the smaller cluster spend energy faster than those sensor nodes that have their place in the more significant cluster.

  • Random numbers between the values 0 and 1 are generated in sensor nodes. Nodes that have a lesser number than the threshold are termed to be CH. This implies that CH production is not constrained by any means.

  • The node's energy efficiency is affected by the CH’s number.

  • There is an assumption in LEACH that every sensor contains enough data transmissions with the BS. Therefore, energy consumption depends on the distance from BS as more from BS; there will be more energy consumption.

  • Furthermore, LEACH assumed that all the nodes were homogeneous in the network, which is not realistic for most applications. Therefore, for further improvement, heterogeneous systems are used.

  • Enhanced security is required in LEACH as data privacy among various sensor nodes is not preserved.

4.2 SEP

The SEP [14, 22, 51,52,53] algorithm is a heterogeneous WSN routing protocol. The SEP protocol characterizes a dual-level HWSNs approach designed for featuring normal as well as advanced nodes. The advanced node’s battery has higher original energy in contrast with normal nodes. The SEP protocol is distributed into two parts: the setup and the phase where data is transmitted.

This way, the election chances of CH in every round can be directly connected with the initial energy that the sensor node possesses. Need to determine each node, according to the threshold probability formula, becomes a CH or not.

The probability formula of CH selection is the same as the LEACH protocol given in Eq. (4). All the nodes have different probabilities based on energy levels. In the SEP protocol, the sensor nodes are categorized into normal and advanced nodes, and their chance is, respectively, design. The total energy changes in the system, suppose \({E}_{\mathrm{in}}\) to be original energy contained by normal sensor nodes while \({E}_{\mathrm{in}}*\left(1+\alpha \right)\) would be advanced node energy. The network cumulative energy hikes by a \(\left(1+\alpha *m\right)\) factor. The first enhancement of the previous LEACH is to increase energy proportional to the increased time of the WSN network. To enhance the system performance, a new modified probability design which is equal to \(P/\left(1 + \alpha *m\right)\) According to this system, the more the energy, i.e., α *m times and almost α* m, the more the nodes with similar energy as the normal nodes. Two different probabilities are designed for normal and advanced node separately. With the normal node becoming a CH, the probability \({P}_{\mathrm{nrm}}/\left(1 + \alpha *m\right)\) per rounds and the advanced node also turns to a CH, the probability \({P}_{\mathrm{adv}}(1+\alpha )/\left(1 + \alpha \cdot m\right)\) per rounds.

4.3 Modified-LEACH

According to the existing studies explained in the related work, the clustering approach of SEP [21] is enhanced through the excess energy contained by sensor nodes and the distance (d)among CH and sensor nodes. To redesign the threshold (T(n)) formula for the clustering process, consider the sensor nodes' mean energy and distance. Within an enhanced algorithm, multipath fading & free-space model is implemented [15, 54]

As the algorithm starts working, the sensor nodes are divided into high and low energy nodes. After that, consider only the remaining energy together with the sensor nodes' distance for the selection of the new CH.

As CH selection has been made, CH nodes start the communication and data transmission. The multipath and free-space model is utilized to compare sensor node distance and transmission distance for a practical choice of energy transmission.

In [14, 55], sensor nodes are distributed into normal and advanced sensor nodes, α is a part that signifies the higher energy level than normal nodes, and m denotes the ratio of advanced sensor nodes. Padv and Pnrm indicate the probability of advanced and normal nodes that are selected to the CH, respectively,

$$ P_{{{\text{nrm}}}} = \frac{P}{1 + \alpha * m} $$
(5)
$$ P_{{{\text{adv}}}} = \frac{{P *\left( {1 + \alpha } \right)}}{1 + \alpha * m} $$
(6)

For the reduction in energy consumption, consider two parameters, energy and distance of the nodes. The combination of current energy and initial energy factor and the current sensor node's distance is used to design a new probability formula. The maximum value of the distance from the nodes to BS is used to generate an improved formula T(n) of the cluster head election. The primary purpose of developing a new formula is to reduce the number of CH nodes dead because of less energy. Equations (5) and (6) are used to deploy the WSN nodes. The new formula of T(n) is given below for standard and advanced sensor nodes [15].

For normal nodes:

$$ T\left( n \right)_{{{\text{nrm}}}} = \left[ {\begin{array}{*{20}l} {\frac{{P_{{{\text{bnrm}}}} *\left( {u\left( {\frac{{E_{{{\text{current}}}} }}{{E_{{{\text{start}}}} }}} \right) + v\left( {\frac{{d_{{{\text{current}}}} }}{{d_{{{\text{max}}}} }}} \right)} \right)}}{{1 - P_{{{\text{nrm}}}} *\left( {{\text{rmod}}\left( {\frac{1}{{P_{{{\text{nrm}}}} }}} \right)} \right)}},} \hfill & { n \in G} \hfill \\ {0,} \hfill & {\text{ otherwise}} \hfill \\ \end{array} } \right. $$
(7)

For advanced nodes:

$$ T\left( n \right)_{{{\text{adv}}}} = \left[ {\begin{array}{*{20}l} {\frac{{P_{{{\text{badv}}}} *\left( {u\left( {\frac{{E_{{{\text{current}}}} }}{{E_{{{\text{start}}}} }}} \right) + v\left( {\frac{{d_{{{\text{current}}}} }}{{d_{{{\text{max}}}} }}} \right)} \right)}}{{1 - P_{{{\text{adv}}}} *\left( {{\text{rmod}}\left( {\frac{1}{{P_{{{\text{adv}}}} }}} \right)} \right)}},} \hfill & {n \in G} \hfill \\ {0,} \hfill & { {\text{otherwise}}} \hfill \\ \end{array} } \right. $$
(8)

According to Eqs. (7) and (8), \({P}_{\mathrm{bnrm}}\)= b ∗ \({P}_{\mathrm{nrm}}\), \({P}_{\mathrm{badv}}\) = a∗\({P}_{\mathrm{adv}}\) is the weight of \({P}_{\mathrm{nrm}}, {P}_{\mathrm{adv}}\), respectively. b is a proportional parameter according to network size. \({E}_{\mathrm{current}}\) is the current sensor node energy. \({E}_{\mathrm{start}}\) is the original energy of the sensor nodes. \({D}_{\mathrm{current}}\) is the present sensor node distance. \({D}_{\mathrm{max}}\) is the highest distance among the BS sensor nodes. u, v are the ratio coefficient. Its value varies from 0 to 1 and u + v = 1.

4.4 MODIFICATION: Proposed Method -1 (ADV-LEACH1)

The proposed method-1 is intended to create a node deployment scenario and energy allocation among nodes based on past research [15, 55].

In this method, we consider the set of commonly used parameters for enhancing the clustering approaches, which is inappropriate in the existing protocol. The enhancement is carried out on the Modified-LEACH method. The distance between the sensor nodes to the BS should be lesser to become the CHs so that the energy consumption of the CH node will be less and less number of CH will be dead. The new formula designed for clustering with add-on the distance from sensor nodes to BS (\({d}_{basestation}\)). Sensor node distance is minimized from BS for the reduction in energy consumption in Eqs. (9 & 10), respectively, for normal &advanced nodes.

For normal nodes:

$$ T\left( n \right)_{{{\text{mnrm}}}} = \left[ {\begin{array}{*{20}l} {\frac{{P_{{{\text{bnrm}}}} *(u\left( {u\left( {\frac{{E_{{{\text{current}}}} }}{{E_{{{\text{start}}}} }}} \right) + \left( {\frac{{d_{{{\text{current}}}} }}{{d_{{{\text{max}}}} }}} \right) + \left( {\frac{1}{{d_{{{\text{basestation}}}} }}} \right)} \right)}}{{1 - P_{{{\text{nrm}}}} *\left( {{\text{rmod}}\left( {\frac{1}{{P_{{{\text{nrm}}}} }}} \right)} \right)}},} \hfill & { n \in G} \hfill \\ {0, } \hfill & {{\text{otherwise}}} \hfill \\ \end{array} } \right. $$
(9)

For advanced nodes:

$$ T\left( n \right)_{{{\text{madv}}}} = \left[ {\begin{array}{*{20}l} {\frac{{P_{{{\text{badv}}}} *(u\left( {u\left( {\frac{{E_{{{\text{current}}}} }}{{E_{{{\text{start}}}} }}} \right) + \left( {\frac{{d_{current} }}{{d_{{{\text{max}}}} }}} \right) + \left( {\frac{1}{{d_{{{\text{basestation}}}} }}} \right)} \right)}}{{1 - P_{{{\text{adv}}}} *\left( {{\text{rmod}}\left( {\frac{1}{{P_{{{\text{adv}}}} }}} \right)} \right)}},} \hfill & { n \in G} \hfill \\ {0, } \hfill & {{\text{otherwise}}} \hfill \\ \end{array} } \right. $$
(10)
figure a

4.5 MODIFICATION: Proposed Method -2(ADV-LEACH2)

The proposed method-2 is used in a phase-2 network model. Node deployment and energy distribution among the nodes are designed through the use of the 2D elliptical Gaussian distribution function [13, 45].

The clustering method is modified by considering such parameters. These parameters are the remaining energy, the many time's nodes being selected as a CH, the distance among CH to BS together with average energy (\({E}_{\mathrm{avg}})\) of sensor nodes per round.

Another parameter that can enhance the network lifetime is the remaining energy of the sensor nodes. \(T{\left(n\right)}_{\mathrm{mnrm}}\) and \(T{\left(n\right)}_{\mathrm{madv}}\) is the multiplication of the factor that is designed by residual energy and initial energy of the sensor nodes within that current round given in Eqs. (11 & 12), respectively, for normal and advanced nodes.

Our simulations demonstrate this modification of the CH threshold (\(T\left( n \right)_{{{\text{nrm1}}}} \;\& \; T\left( n \right)_{{{\text{adv1}}}}\)), which can improve the lifetime of the nodes.

$$ T\left( n \right)_{{{\text{nrm1}}}} = \left\{ {\begin{array}{*{20}l} {T\left( n \right)_{{{\text{mnrm}}}} \times \frac{{E_{{{\text{re}}}} }}{{E_{{{\text{in}}}} }}} \hfill & {{\text{if}}\;n \in G} \hfill \\ 0 \hfill & {{\text{elsewhere}}} \hfill \\ \end{array} } \right. $$
(11)
$$ T\left( n \right)_{{{\text{adv1}}}} = \left\{ {\begin{array}{*{20}l} {T\left( n \right)_{{{\text{madv}}}} \times \frac{{E_{{{\text{re}}}} }}{{E_{{{\text{in}}}} }}} \hfill & {{\text{if}}\;n \in G} \hfill \\ 0 \hfill & {{\text{elsewhere}}} \hfill \\ \end{array} } \right. $$
(12)

In Eqs. (11) & (12), \({E}_{\mathrm{re}}\) is the sensor node remaining power per round. \({E}_{\mathrm{in}}\) is the original energy of the sensor nodes.

This change has an essential drawback. The network will stop after individual rounds because the value of the threshold is significantly less. So now it is necessary to fix this by extending \({T(n)}_{\mathrm{nrm}1}\) and \({T(n)}_{\mathrm{adv}1}\) by an average energy \(({E}_{\mathrm{avg}})\) parameter which increases the CH threshold (\(T\left( n \right){\text{nrm}}_{2 } \;\& \; T\left( n \right){\text{adv}}_{2}\)) for all sensor nodes to approve which information is transferred till the nodes are not dead. The sensor nodes have more incredible residual energy as compared to other nodes in the network; that node has a very high opportunity of selecting the CH node. After all the corrections, the improved threshold \(T\left( n \right){\text{nrm}}_{2}\) and \(T\left( n \right){\text{adv}}_{2}\) are given in Eqs. (13 & 14).

$$ T\left( n \right){\text{nrm}}_{2} = \left\{ {\begin{array}{*{20}l} {T\left( n \right){\text{nrm}}_{1} \times \left( {E_{{{\text{avg}}}} } \right)} \hfill & {{\text{if}}\;n \in G} \hfill \\ 0 \hfill & {{\text{elsewhere}}} \hfill \\ \end{array} } \right. $$
(13)
$$ T\left( n \right){\text{adv}}_{2} = \left\{ {\begin{array}{*{20}l} {T\left( n \right){\text{adv}}_{1} \times \left( {E_{{{\text{avg}}}} } \right)} \hfill & {{\text{if}}\;n \in G} \hfill \\ 0 \hfill & {{\text{elsewhere}}} \hfill \\ \end{array} } \right. $$
(14)

Another factor is the distance that impacts on CH limit. The greater the distance between the nodes, BS consumed more energy for data transmission. The new CH threshold formula is provided in Eq. (15) & (16).

$$ T\left( n \right)_{{{\text{fnrm}}}} = \left\{ {\begin{array}{*{20}c} {T\left( n \right){\text{nrm}}_{2} \times \left( {\frac{1}{{{\text{dtobs}}_{{{\text{av}}}} }} + \frac{1}{{{\text{dtobs}}_{n} }}} \right)} \\ 0 \\ \end{array} } \right.\begin{array}{*{20}c} {{\text{if}}\;n \in G} \\ {{\text{elsewhere}}} \\ \end{array} $$
(15)
$$ T\left( n \right)_{{{\text{fadv}}}} = \left\{ {\begin{array}{*{20}l} {T\left( n \right){\text{adv}}_{2} \times \left( {\frac{1}{{{\text{dtobs}}_{{{\text{av}}}} }} + \frac{1}{{{\text{dtobs}}_{n} }}} \right)} \hfill & {{\text{if}}\;n \in G} \hfill \\ 0 \hfill & {{\text{elsewhere}}} \hfill \\ \end{array} } \right. $$
(16)

In Eqs. (15) & (16), \({\mathrm{dtobs}}_{\mathrm{av}}\) is equal to the average distance between nodes to BS.\({\mathrm{dtobs}}_{n}\) is equal to the distance among the node to BS.

During network setup, some assumptions are considered for a new formula of the CH threshold. The procedure is designed for both normal and advanced nodes.

  • Each sensor node will produce a random number of 0 to 1.

  • Calculate the value from the above final threshold formula \({T(n)}_{\mathrm{fadv}}\) & \({T(n)}_{\mathrm{fnrm}}\) for advanced and normal nodes.

  • If the chosen random number is lower as compared to \({T(n)}_{\mathrm{fadv}}\) & \({T(n)}_{\mathrm{fnrm}}\) value, then that node will become CH for that round.

This CH threshold (\((T\left( n \right)_{{{\text{fadv}}}} \;\& \; T\left( n \right)_{{{\text{fnrm}}}} )\) formula approves only for those nodes which have higher energy and less distance to BS. That node will have the opportunity to choose the CH per round. It also ensures that the node transfers the data to BS until it dies. As the energy level is low and the distance among the sensor nodes to BS is larger than the node, it has a meager chance to become a CH (Fig. 3).

Fig. 3
figure 3

Flow chart of proposed study

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figure b

4.6 Algorithm Illustration

For a deep understanding of the proposed ADV-LEACH1 and ADV-LEACH2 algorithm, we illustrate in this section. In this example, we consider a random and 2D elliptical Gaussian distribution node deployment for a heterogeneous network with normal and advanced nodes.

Initially, we deploy the 30 sensor nodes randomly along with BS positioned at (50, 50) and (50, 150), respectively, as shown in Fig. 4.We apply the ADV-LEACH1approach on the network by assigning all the sensor nodes inside the target area. We determine the threshold probability value by Eqs. (9) & (10) based on advance and normal sensor node, respectively. The higher threshold probability nodes (Table 1) are cluster heads as compared to the random threshold, as shown in Fig. 5. In our example, nodes {1, 2, 3, 4, 6, 11, 16, 19} and {1, 2, 3, 5, 6, 13, 28} are the cluster heads with BS positioned at (50, 50) and (50, 150) respectively. All the CHs join the closed sensor node in the network to make a complete cluster, as shown in Fig. 6. After the clustering process is complete, data transmission between CH to BS and cluster member to CH begins. We repeat the same step to generate new CH and clusters in every round until all the sensor nodes will die.

Fig. 4
figure 4

Layout of the 30 sensor node deployment randomly with BS positioned at (50, 50) and (50, 150), respectively. Blue and yellow color circle shows the normal and advance node. Red color star is representing the BS

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Table 1 Node probability in randomly deployed heterogonous network
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Fig. 5
figure 5

Layout of the cluster head from the 30 sensor node. Blue and yellow color triangle shows the normal and advance cluster head. Red color star is representing the BS

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Fig. 6
figure 6

Layout of the complete randomly deploy heterogeneous network with normal node (blue color circle), advance node (yellow color circle), cluster head in triangle shape blue as normal and yellow as advance with BS positioned at (50, 50) and (50, 150), respectively

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Now 30 sensor nodes by 2D elliptical Gaussian distribution are deployed along with BS positioned at (50, 50) and (50, 150), respectively, as shown in Fig. 7. We apply the ADV-LEACH2 algorithm to determine the threshold probability value by Eqs. (15) & (16) based on advanced and normal sensor nodes, respectively. The higher threshold probability nodes (Table 2) are cluster heads as compared to the random threshold shown in Fig. 8. In our example, nodes {1, 2, 3, 4, 5, 6} and {1, 2, 3, 4, 5, 6} are the cluster heads with BS positioned at (50, 50) and (50, 150), respectively. An optimum number of CHs are determined using the current clustering approach in Fig. 9. We repeat the same step to generate new CH and clusters in every round until all the sensor nodes will die.

Fig. 7
figure 7

Layout of the 30 sensor node 2D elliptical Gaussian distribution deployment with BS positioned at (50, 50) and (50, 150), respectively. Blue and yellow color circle shows the normal and advance node. Red color star is representing the BS

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Table 2 Node probability in 2D elliptical Gaussian distribution deployed heterogonous network
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Fig. 8
figure 8

Layout of the cluster head from the 30 sensor node. Blue and yellow color triangle shows the normal and advance cluster head. Red color star is representing the BS

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Fig. 9
figure 9

Layout of the complete 2D elliptical Gaussian distribution deploy heterogeneous network with normal node (blue color circle), advance node (yellow color circle), cluster head in triangle shape blue as normal and yellow as advance with BS positioned at (50, 50) and (50, 150), respectively

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5 Simulation Results and Analysis

Here heterogeneous network is used with normal and advanced nodes. Two techniques are used for node deployment, which has already been described in the above section. Random node deployment and 2D elliptical Gaussian distribution are executed. The proposed methods are simulated using MATLAB 2015b. All the algorithm functions and programs were written in Dev C/C++ and MATLAB. MATLAB GUI installed and ran on the Windows 10 operation system; 8 GB RAM has been used for analysis. The WSN scenario is created with 200 sensor nodes being deployed in (100 × 100) m2area. The BS is positioned at (50, 50) and (50,150), respectively, inside and outside of the network. The layout of a heterogeneous network with BS placed inside and outside of the network is shown in Figs. 10 and 11, respectively. The original energy is 0.5 J for ordinary and 1 J for advanced sensor nodes. The initial parameters are mentioned in Table 3. When the node energy is zero or less than zero, the node is assumed to be dead. The dead node can never become a CH or cluster member, as shown in Fig. 12.

Fig. 10
figure 10

Heterogeneous network with BS positioned at (50, 50) center of the network

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Fig. 11
figure 11

Heterogeneous network with BS positioned at (50, 150) outside of the network

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Table 3 Initial parameter
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Fig. 12
figure 12

Heterogeneous network after few rounds with BS positioned at (50, 50) center

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We use various performance metrics listed as follows to assess the performance of the proposed method.

Number of alive nodes (\({N}_{\mathrm{alive}}\)) number of nodes still alives after finishing every round or during the round. When the energy of a node is more than zero, that node is counted as an alive node.

Number of dead nodes (\({N}_{\mathrm{dead}}\)) Number of nodes has their energy less than or equal to zero, those nodes are counted as dead nodes in every round (Table 4).

Table 4 List of symbols and abbreviations
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Network lifetime The network lifetime is measured as the number of rounds until the last node dies (LND). The network’s lifetime is calculated based on three metrics, the first node die (FND), half nodes die (HND), and the last node dies (LND).

Several cluster heads (CHs) Several CHS significantly affect the energy efficiency of WSNs. If the number of CHs increases, the energies consumed will be different due to the large numbers of the aggregation processes performed by these CH nodes. On the other hand, when the numbers of CH nodes are reduced, the resources are also heavily consumed due to the vast amount of data aggregated by each CH node. Each CH needs to communicate with BS to provide the bulk aggregated data. As a consequence, these CHs will be dead sooner.

Energy imbalance factor (EIF) We evaluate the characteristics of the proposed algorithm's energy balance. This is expressed as a standard deviation (SD) of energy consumption of the nodes and given by Eq. (17).

$$\mathrm{EIF}= \frac{1}{n}\sqrt{\sum_{i=1}^{n}{({E}_{\mathrm{avg}}- {E}_{\mathrm{con}} (i))}^{2}}$$
(17)

where n is the total alive sensor nodes, \({E}_{\mathrm{avg}}\) is the average residual energy consumption, and \({E}_{con}\) is the consumed energy by the node i in every round.

Remaining energy The average remaining energy of the sensor nodes is measured after the data transmission in every round. That node energy works as the original energy of the sensor node for the next round.

The standard deviation of cluster size The standard deviation (SD) of the cluster size \({(\sigma }_{\mathrm{SD}})\) is used to measure the load in the clusters, and the following Eqn defines it. (18).

$${\sigma }_{SD}=\sqrt{\frac{\sum_{i=1}^{m}{({M}_{i}\,-\,\stackrel{-}{M})}^{2}}{m}}$$
(18)

Here, m is the number of clusters, \({M}_{i}\) is the number of cluster i, and \(\stackrel{-}{M}\) is the average number of members in all the clusters.

Number of packets received The total packet received is the summation of the total received packet by cluster head and base station per round and given by Eq. (19).

$$ {\text{Total}}\;{\text{Packet}}\;{\text{Received}} = \mathop \sum \limits_{i = 1}^{r} {\text{Pkt}}\_{\text{recv}}_{{{\text{CH}}}} + \mathop \sum \limits_{i = 1}^{r} {\text{Pkt}}\_{\text{recv}}_{{{\text{BS}}}} $$
(19)

Average Throughput (\({Thr}_{Avg}\)) The proportion of packets received (\({N\_Pkt}_{recv}\)) by a BS from the cluster head for a round (r) needs to get the last packet by BS is measured in bytes per rounds, where \({Packet}_{size}\) is the packet size in bits. It can be represented numerically as per Eq. (20).

$${Thr}_{Avg}=\frac{{N\_Pkt}_{recv}\times {Packet}_{size}}{r}$$
(20)

The simulation results generated by MATLAB in 2500 rounds are compared with LEACH, Modified-LEACH, SEP, ADV-LEACH1, and ADV-LEACH2 protocols. The proposed approaches are compared with the existing protocols based on five performance parameters.

5.1 Number of alive (\({{\varvec{N}}}_{{\varvec{a}}{\varvec{l}}{\varvec{i}}{\varvec{v}}{\varvec{e}}}\)) sensor nodes

The number of alive nodes versus rounds is depicted in Fig. 13a. The simulation results reveal that this newly suggested technique improves the network's lifetime. The ADV-LEACH2 & ADV-LEACH1 show the number of alive sensor nodes is high compared to LEACH, Modified-LEACH, and SEP protocols.

Fig. 13
figure 13

a Number of Alive nodes based on the number of rounds, b number of dead nodes based on the number of rounds

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5.2 Number of Dead (\({{\varvec{N}}}_{\mathbf{d}\mathbf{e}\mathbf{a}\mathbf{d}}\)) Sensor Node Analysis

Figure 13b illustrates performance contrasts between the approaches based on the number of dead nodes per round. The systems are simulated for 200 sensor nodes. The rate of dead sensor nodes for ADV-LEACH2 and ADV-LEACH1 is much lesser than LEACH, Modified-LEACH, and SEP.

One can quickly notice a higher survival rate of nodes for both the proposed approaches (ADV-LEACH1 & ADV-LEACH2) than the LEACH, SEP, and Modified-LEACH approach of common nodes. It may decrease the death ratio of nodes up to 80% compared to SEP and Modified-LEACH and up to 20% compared to LEACH. In the advanced nodes, the proposed approach (ADV-LEACH2) is better than SEP & Modified-LEACH system; it still reduces the node death rate and improves the network's lifetime significantly. Figure 14(a-b) & Table 5 represent the overall death rate (%) versus algorithms for every sensor node, with a fixed count of rounds (1500 rounds) for all the algorithms. Here 200 sensor nodes have been considered for the present scenario. 22% of sensor nodes are dead in the case of the proposed algorithm (ADV-LEACH2) compared to other algorithms in 1500 rounds. It has a significantly less dead ratio as compared to different algorithms. Table 2 clearly shows the performance of the mentioned algorithms in terms of the network lifetime and dead balance.

Fig. 14
figure 14

a Number of dead node of the normal and advanced node, b dead node ratio versus number of algorithms comparison

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Table 5 Comparative analysis
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Figure 15 compares the ADV-LEACH1, ADV-LEACH2, Modified-LEACH, LEACH, and SEP in terms of death rate versus BS location. In this scenario, the BS is moving from one point to other points. Such a result performs the core function, knowing the effect on network lifetime based on BS's position change from (50, 50) to (50, 150). It can be noted from the figure that ADV-LEACH2 has a lesser death node ratio than all the other approaches, i.e., ADV-LEACH1, LEACH, Modified-LEACH, and SEP based on clustering. The ADV-LEACH2 takes care of low residual energy CHs by assigning fewer sensor nodes.

Fig. 15
figure 15

Dead node ratio for various algorithms based on the BS location

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5.3 Network Lifetime

This simulation demonstrates the network lifetime of proposed (ADV-LEACH2 and ADV-LEACH1) approaches compared to the other existing protocols. The main contribution of the present clustering algorithm is to increase the network lifetime according to LND metrics. As shown in Fig. 16, ADV-LEACH1 & ADV-LEACH2 outperform LEACH, Modified-LEACH, and SEP in the LND metrics. The network lifetime based on LND 2872, 2552, 2501, 2461, and 2401 belongs to ADV-LEACH2, ADV-LEACH1, SEP, Modified-LEACH, and LEACH, respectively, as shown in Table 5. Therefore, ADV-LEACH1 and ADV-LEACH2 are energy-efficient and capable of prolonging the network lifetime approaches.

Fig. 16
figure 16

Network lifetime versus number

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5.4 Comparison of the Number of Cluster Heads

Several CHs have a significant impact on the energies of the sensor node. The stability of the number of CHs around an optimal number is essential to balance energy consumption in the next round. Figure 17 shows the number of CHs versus rounds compared to LEACH, Modified-LEACH, SEP, ADV-LEACH1, and ADV-LEACH2. The simulations show that the proposed algorithm having the optimal number of CHs is around 15 for 200 nodes to achieve better network performance. The currently proposed algorithm is designed for the modification in CHs selection and cluster formulation, which increases the energy efficiency per round. Figure 17 shows the number of CH among four different approaches in 100 rounds. ADV-LEACH2 in few rounds accomplishes stability of an optimum number of CHs equal to 15 due to node distribution around the BS by Gaussian distribution, and all the sensor nodes are divided into clusters based on the CHs work over its cluster members. When a network has a high CH in the system, it is directly indicating the imbalance and higher energy consumption.

Fig. 17
figure 17

Number of cluster heads based on the number of rounds

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5.5 Comparison of Energy Imbalance Factor (EIF)

Eqn evaluates the energy imbalance factor. (17). Figure 18a shows the EIF of the 200 sensor nodes with BS at the target areas' center. It is easy to observe that the proposed approach's energy consumption (ADV-LEACH1 and ADV-LEACH2) is more balanced compared to other algorithms, including LEACH, Modified-LEACH, and SEP.

Fig. 18
figure 18

a Energy imbalance factor versus rounds, b average remaining energy based on the number of rounds

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5.6 Comparison of Remaining Energy

In Fig. 18b, the clusters' remaining energy for each round is indicated for every wireless sensor network approach. The remaining energy per round of ADV-LEACH1 & ADV-LEACH2 is much more than the other three algorithms because of the reason that ADV-LEACH1 & ADV-LEACH2 are using the dynamic clusters. Therefore, the advertisement messages decrease, and a lesser number of cluster members participate in the communication. Also, most importantly, such statements are spread out inside the area of a cluster. In LEACH, the broadcast messages are disseminated for that whole network, but in SEP and Modified-LEACH, such details/msgs0 are transmitted in a cluster area range. As such, all remaining energy for clustering in LEACH is less as compared to SEP and Modified-LEACH. The remaining energy for clustering is higher in Modified-LEACH as compared to SEP due to the higher members of the cluster that results in to increase in the advertisement messages’ quantity. Figure 18 shows that both the proposed approaches accomplish less energy consumption as compared to other existing techniques.

5.7 Comparison of Standard Deviation (SD) of Cluster Size

The SDs of cluster size are shown in Fig. 19. The proposed algorithm is compared with LEACH, Modified-LEACH, and SEP and has the smallest SD of cluster size since the formed clusters using the proposed approach in ADV-LEACH1 and ADV-LEACH2 have a balanced cluster members distribution. The smallest SD in ADV-LEACH2 means that all the groups' cluster members are nearly the same, and there is no over-loaded cluster with a large number of members.

Fig. 19
figure 19

Standard deviation of cluster size versus number of nodes

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The cluster head is selected by a combination of threshold probability in the LEACH and Modified-LEACH and SEP, but the broadcast messages are transmitted within the cluster radius. It leads to the single-node cluster formation and increases as the number of nodes increases. SD also increases. In ADV-LEACH2, the number of single-node clusters is zero because of modified CHs selection probability based on a different energy and distance combination. Every sensor node gets at least one broadcast message.

5.8 Evaluation of Number of Packets Received

Figure 20a shows the total number of packets received versus the number of rounds. The total received packet is a combination of the received packet at the CHs and BS. At the starting up to the 500th round, all five algorithms show nearly equal values. After the 500th round, LEACH delivers significantly fewer messages to the CHs/BS than other approaches. The total received statements by the CHs/BS in the network using ADV-LEACH2 are much higher than LEACH, Modified-LEACH, and SEP. ADV-LEACH2 packet delivery slowly increases, which is due to setting the closer distance from the BS. The distance to the CHs or BS does not exceed the maximum distance because its nodes save energy.

Fig. 20
figure 20

a Total packet received versus rounds, b average throughput based on the number of rounds

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5.9 Comparison of Average Throughput

According to Eq. (20), the higher total packet received at the BS is proportional to the higher throughput of the average throughput. Figure 20(b) shows the average throughput comparison of all five algorithms versus the number of rounds. The proposed algorithm offers higher data delivery at the BS as compared to other algorithms over the number of rounds.

6 Conclusions

In this paper, an energy-efficient method to improve the cluster heads selection and nodes distribution has been proposed. Two separate approaches have been proposed for the nodes deployment and CHs selection of the WSNs. The first approach aims to choose the suitable CHs node for every cluster per round in the heterogeneous WSNs system. This process is done by improving the CHs selection threshold. When the sensor nodes are far from the BS and CHs, those sensor nodes will not communicate. The second approach worked on this drawback to resolve this issue. The second approach aimed to escape some sensor nodes distant from the BS and CHs by designing a new nodes distribution method, such as Gaussian distribution. In this approach, the sensor node's heterogeneous deployment has been rescheduled by balancing the nodes to cover almost the same distance. The simulation outcomes from the suggested techniques have been contrasted to other existing routing approaches within the context of energy consumption, the lifetime of the network, and alive or dead nodes per round. Both the proposed techniques have reduced energy consumption during the transmission of data. As a result, the network lifetime has increased in contrast with different existing approaches.

So, we can conclude that the proposed work is best suited for creating a real-time WSNs system. In the future, we will extend this work in terms of security as well as privacy concepts. We will also attempt to simulate this paradigm to a real-world network.