An Energy-Balancing Unequal Clustering Algorithm for Multi hop Routing in WSN

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An Energy-Balancing Unequal Clustering Algorithm for Multi-hop

Routing in WSN

Sheima Hassan Elamin Hamed January 2013

This thesis is presented as part of

Degree of Master of Science in Electrical Engineering

Blekinge Institute of Technology School of Engineering

Department of Electrical Engineering Supervisor: Professor Wlodek Kulesza

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Abstract

Energy saving is a critical issue in Wireless Sensor Networks as they have limited amount of energy and no rechargeable batteries. Clustering plays an effective role in utilization and saving of the limited energy resources of the deployed sensor nodes, where nodes are grouped into clusters and one node, called the cluster head is responsible for collecting data from other nodes, aggregates them and sends them to the BS, where data can be retrieved later. In multi-hop communication, the cluster head farthest away from the BS routes its data over several hops until they reach the BS. A network portioning problem arises when the nodes that are very close to the BS burdened with heavy relay traffic load and therefore die much faster than others.

In this research we introduced a new unequal size clustering algorithm that balances the energy consumption among all clusters, where each cluster will have an optimal number of nodes, clusters that are close to the BS will have few number of nodes to be able to save energy for inter cluster communication compared to the ones that are far from the BS, that have large number of nodes. This optimal clustering algorithm helps to balance energy and prolong the life time of nodes. Simulation results show that our unequal clustering mechanism balances the energy consumption well among all nodes and it achieves an obvious improvement on the network lifetime

Key words:

Multi-hop routing, Energy balancing, Linear optimization, Network lifetime, Unequal clustering, Wireless Sensor Networks

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List of figures

Figure 1: Network illustration of single hop and Multi-hop routing in WSN. ... 17

Figure 2: Diagram shows the first order radio model equations. ... 18

Figure 3 Flow chart illustrating the Gradient Descent minimization algorithm ... 21

Figure 4: Illustration of geometry of three cluster network ... 26

Figure 5: Flowchart of the proposed optimal clustering algorithm ... 27

Figure 6: Random deployment of 250 nodes in a circle section area, ... 30

Figure 7: Initial equal radius cluster formation of the network (M=3, Rmax=150m, θ=π/6 rad, N=250). ... 32

Figure 8: New optimal clusters formation (M=3, Rmax=150m, θ=π/6 rad, N=250). ... 32

Figure 9: Life time of the network after applying the equal clustering (M=3, Rmax=150m, θ=π/6 rad, N=250). ... 33

Figure 10: Life time of the network after applying the proposed clustering algorithm (M=3, Rmax=150m, θ=π/6 rad, N=250). ... 33

Figure 11: Initial equal radius cluster formation of the network (M=3, Rmax=150m, θ=π/6 rad, N=100). ... 35

Figure 12: New optimal clusters formation (M=3, Rmax=150m, θ=π/6 rad, N=100)... 35

Figure 13: Life time of the network after applying the equal clustering (M=3, Rmax=150m, θ=π/6 rad, N=100). ... 36

Figure 14: Life time of the network after applying the optimal clustering (M=3, Rmax=150m, θ=π/6 rad, N=100). ... 36

Figure 15: Initial equal radius cluster formation of the network (M=3, Rmax =150m, θ=π/6 rad, N=500). ... 37

Figure 16: New optimal clusters formation (M=3, Rmax =150m, θ=π/6 rad, N=500). ... 37

Figure 17: Life time of the network after applying the equal clustering (M=3, Rmax =150m, θ=π/6 rad, N=500). ... 38

Figure 18: Life time of the network after applying the optimal clustering (M=3, Rmax =150m, θ=π/6 rad, N=500). ... 38

Figure 20: New optimal clusters formation (M=3, R=50m, θ=π/6, N=250). ... 40

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List of tables

Table I: Initial Simulation Parameters ... 30

Table II: Optimal radiuses of the new unequal cluster formation (M=3, R=150m, θ=π/6, N=250) ... 31

Table III: Optimal cluster radiuses for different network parameters (first scenario) ... 34

Table IV: Optimal cluster radiuses for different network parameters (second scenario) ... 39

Table V: Optimal cluster radiuses for different network parameters (third scenario) ... 44

Table VI: Optimal cluster radiuses for different network parameters (Fourth scenario, M=2) ... 49

Table VII: Optimal cluster radiuses for different network parameters (Fourth scenario, M=4) .. 49

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Glossary

Term Description

Base station (BS) An information processing center where all data that have been sensed by the sensor nodes are collected, processed and stored for later retrieval.

Cluster It is a group of nodes in a network that are grouped together to reduce energy consumption during data transmission.

Cluster Head (CH) It is a node responsible for collecting data from other nodes, aggregates them and sends them to the base station where they can be retrieved later.

Homogeneous It means that sensor nodes are having uniform structure and of the same or similar nature.

Inter-Cluster communication

Data reception and transmission between clusters.

Intra-Cluster communication

Data reception and transmission within one cluster.

Network Lifetime The lifetime of a network is the active time of the network until the first node runs out of energy.

Residual Energy Energy that remains in nodes’ batteries.

Rounds A round comprises of a set up phase (cluster organization, CH role rotation) and a steady state phase (data collection, data aggregation and data forwarding).

Wireless Sensor Network Large number of micro-sensors that communicate wirelessly and bring themselves together to form a network.

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Chapter One

Introduction and Review of Related Works

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1.1 Introduction

Rapid advances in Wireless Sensor Networks (WSNs) have enabled densely deployment of nodes. WSNs are an emerging technology that consists of large number of low cost, low power sensor nodes; a sensor node, an electronic device that is capable of detecting environmental conditions. Those sensor nodes can be deployed randomly to perform many applications such as monitoring physical events, for example environmental monitoring, battlefield surveillance, disaster relief, target tracking, etc.

and they work together to form a wireless network.

A typical node of a WSN is equipped with four components [19]: a sensor that performs the sensing of required events in a specific field, a radio transceiver that performs radio transmission and reception, a microcontroller: which is used for data processing and a battery that is a power unit providing energy for operation.

The limited energy given to each node, supplied from non-rechargeable batteries, with no form of recharging after deployment is one of the most crucial problems in WSN. Many routing protocols have been proposed for WSNs. Most of the hierarchical algorithms proposed for WSNs concentrate mainly on maximizing the lifetime of the network by trying to minimize the energy consumption [19].

Researchers agreed that clustering of nodes in wireless sensor networks is an effective program of energy conservation [20]. Clustering is defined as the grouping of similar objects or the process of finding a natural association among some specific objects or data [6]. In WSN it is used to minimize the number of nodes that take part in long distance data transmission to a BS, what leads to lowering of total energy consumption of the system [21].

Clustering reduces the amount of transmitted data by grouping similar nodes together and electing one node as a cluster head, where aggregation of data is performed to avoid redundancy and communication load caused by multiple adjacent nodes, then sending the aggregated data to the next cluster head or to the BS, where it is processed, stored and retrieved.

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10 In any clustering organization intra-cluster communication as well as inter-cluster communication can be single hop or multi-hop [1]. However, the hot spot and network partitioning arises when using multi-hop routing in inter-cluster communications.

Because the cluster heads close to the BS, are burdened with heavy relayed traffic that will make them die faster than other cluster heads, resulting in loss of coverage of sensing.

To effectively prolong the life time of network sensors, the network should be designed carefully to be energy efficient. Many of the previous clustering algorithms organize the network into equal size clusters; however, the problems of unbalanced energy consumption exist. We proposed an unequal size clustering algorithm that results in more uniform energy dissipation among cluster heads and prolongs the life time of the whole network.

This thesis consists of four chapters, Chapter One consists of an introduction to the WSN and a review of related works; the problem statement, research questions, and main contributions are also discussed. Chapter Two describes the network model and details of the proposed algorithm. The validation and simulation results of the proposed algorithm were shown in Chapter Three. Chapter Four concludes the report.

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1.2 Review of related work

During last few years many unequal clustering algorithms have been proposed for Wireless Sensor Networks as an efficient way for balancing the energy consumption and prolonging the lifetime of the networks. Here we mention some of the most relevant clustering algorithms.

Chengfa Li et al., proposed an energy efficient unequal clustering algorithm (EEUC), where several cluster heads are selected to compete for final cluster heading based on residual energy of each node [1]. EEUC calculates a competition radius (Rcomp) for each node, which is a function of its distance to the BS, where there are no two competitive nodes within the same competition radius. Node’s competition radius should decrease as its distance to the BS decreases; the result is that clusters closer to the BS are expected to have smaller cluster sizes. Voronoi diagram of sensor nodes is then constructed.

Heinemann et al. [20] described the LEACH protocol as a hierarchical self-organized cluster based approach for monitoring applications. The data collection area is randomly divided into clusters. LEACH uses Time Division Multiple Access scheme (TDMA), to transmit data from the sensor nodes to the CH. Then the CH aggregates the data and transmits them to the next CH or to the BS for processing. The cluster heads rotate randomly and a re-clustering is performed at the beginning of each round.

Gong et al. [2], suggested multi-hop routing protocol with unequal clustering (MRPUC). Nodes that have the largest residual energy are selected as CHs. After calculating the maximum distance between the nodes and the BS and using a predefined values for the maximum and minimum cluster radius, MRPUC calculates the cluster radiuses of all nodes. If the node’s distance to the nearest CH is less than its cluster radius, then the node will join that cluster.

Another clustering algorithm was discussed in [3]. The authors analyzed an approach called unequal clustering size (UCS) where the network is organized into clusters of different sizes, by controlling the number of nodes in every cluster with respect to the number of nodes in next cluster. Thus the position of the cluster head is determined a priori.

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12 Wei Li [8], proposed a geometric programming approach, he suggested an iterative method for solving the geometric programming by selecting the optimal location of cluster heads. The optimum mentioned in his proposal refers to minimizing energy consumption under certain constrains.

Tashtarian et al. [5] developed energy efficient level based and time based clustering algorithm that has the ability of forming unequal size clusters related to the lower and upper boundaries of each energy level. The network is divided into radial levels based on the energy saved in each cluster. This energy is defined as the difference between energy used by cluster head when using single hop and multi hop communication models. Based on this saved energy, some clusters expand their sizes to cover some extra nodes instead.

A Degree and Size based Clustering Approach (DASCA) is another distributed clustering strategy introduced by Venkataraman et al. [7]. It restricts the number of nodes in each cluster and limits the number of next hop neighbors of a node in a cluster for achieving load balance in the network. Clusters are formed based on energy spent to communicate with the farthest next hop neighbor and the total energy spent on each link of its next hop neighbors which are calculated in the first step of the algorithm.

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1.3 Problem statement, research questions and main contribution

Researches that have been done on the area of energy consumption in WSN show that about 70% of the energy is being consumed during the data transmission phase.

Therefore, the data transmission process should be optimized and an efficient data aggregation should take place to avoid redundancy caused by adjacent sensor nodes.

Network architectures, applications and deployment strategies have to be designed to maintain energy consumption and to prolong the life time of the network.

In general, each cluster head spends its energy on intra-cluster communication which increases proportionally with the number of nodes within a cluster, while other amount of the energy is spent on inter-cluster communication and it is a function of the expected amount of information relayed from further clusters. Hot spots and network partitioning are major problems that result from limited energy resources in WSN. In a multi hop routing when cluster heads cooperate with each other to forward their data to the BS, the cluster heads closer to the BS are burdened with heavy relay and tend to die early due to the continuous many-to-one traffic pattern.[1]

 The research question that arises in respect to the mentioned problem can be formulated as:

How to perform unequal clustering process in order to balance the energy consumption and to avoid those CHs closer to the BS die quicker than those which are far from the BS due to large intra-cluster communication?

 The hypothesis, that answers the research question is:

As a possible solution for this problem, we proposed to model the WSN field as a circle section where the position of nodes are located in polar coordinates system by radius and angle and to define cluster sizes by inner and utter boundaries and finally to calculate the unequal clusters’ size using an optimization algorithm balancing energy consumption between inter and intra cluster communication resulting in longer WSN life time.

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 The main contributions of this thesis are:

In this thesis we investigated energy balancing and network life time maximization. A new energy efficient clustering algorithm that balances the energy consumption among CHs of WSN by dividing the network into unequal size clusters was proposed, based on mathematical calculations; number of nodes in each cluster, the average distance between cluster members and their corresponding CHs and the distance between the adjacent CHs can be expressed as functions of clusters’ radiuses. The energy consumption will be optimized and the different clusters’ radiuses can be obtained.

Cluster head selection and rotation is then done based on the highest residual energy.

Simulation was performed in MATLAB, and for the validation of the proposed algorithm the simulation was ran for different network parameters and results were analyzed based on an analytical approach.

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Chapter Two

A novel algorithm of the unequal clustering

balancing energies for inter and intra cluster

communication

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2.1 Overview of clustering techniques

Clustering is the task of dividing objects into groups called clusters, those objects has to be similar in a way or another. In WSN, clustering techniques are applied to solve the challenges encountered in WSN as a result of constrained energy supplies, communication range and bandwidth capabilities. In large scale WSN, clustering is an effective technique for the purpose of improving the utilization of limited energy and prolonging the network lifetime. [19].

Communication within one cluster as well as communication between different clusters can take place as combination of single hop and multi- hop as illustrated in Figure 1.

In single hop communications, each sensor node can directly reaches the BS. While in multi- hop communications, nodes are forced to route their data over several hops until the data reaches the BS; due to the transmission range limitations. However, the single hop transmission from the CHs to the BS is not scalable because of limitation of the maximum transmission range.

However, both models face the unavoidable of unbalanced energy consumption among different sensor nodes, leading to hotspot and network partitions problems.

Clustering algorithms differ with respect to the metrics they use for cluster control such as energy, lifetime calculations, hops, distance from the cluster head and also the type of controls such as centralized or distributed [7].

In this chapter we will discuss some of the clustering strategies.

2.1.1 Hierarchical clustering (Connectivity based clustering)

Hierarchical clustering approach breaks the network into several clustered layers [15], data travels from a lower clustered layer to a higher clustered layer. Data is first aggregated but as it moves from one node to another it covers greater distances that helps the data to reach the BS faster, thus reducing travel time and latency [16]. A good example of the hierarchical clustering algorithms is Low Energy Adaptive Clustering Hierarchy (LEACH).

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2.1.2 Data centric clustering

Data centric clustering is designed to find shortest distance between pairs of nodes [13]; it aggregates data and sends it from different recourses to a destination using named data. Since assigning global identifiers to every sensor nodes in a WSN may not be feasible due to the huge number, nodes are addressed by their locations, proximity, or capability rather than a globally unique identifier. It has been shown that data-centric clustering offers an obvious performance gain over a wide range of operational

scenarios.

Figure 1: Network illustration of single hop and Multi-hop routing in WSN.

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2.2 Energy model of a wireless sensor

In all WSN organizations, the wireless communication element of a sensor node is responsible for the most of energy wastage activities. Energy cost of transmission and reception of data can be evaluated using a simple model for the radio hardware energy dissipation as illustrated in Figure 2 [20].

d

Transmit Electronics Transmit Amplifier

k-bit packet

Antenna

Receiver Electronics

Antenna

k-bit packet

Eelect * k Eamp * d²*k

E_elect * k

Figure 2: Diagram shows the first order radio model equations.

Depending on a distance d between the transmitter and receiver, the energy required transmitting and receiving a k –bit packet over the distance can be expressed as stated in the equations 2.1 and 2.2 respectively where both the free space and the multi-path fading channel models are used in the model:

( ) ( )

{

(2.1)

Likewise, the energy consumed to receive this message is shown in:

( ) (2.2)

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19 where:

- energy dissipated per bit at transmitter;

- energy dissipated per bit at receiver;

- amplification factor;

-cost of circuit energy when transmitting or receiving one bit of data;

- free space coefficient;

- multi path coefficient;

k - number of transmitted data bits;

d - distance between a sensor node and its respective cluster head or between a CH to another cluster head nearer to the BS or between CH and BS;

- distance threshold value [14] obtained by √

For scalability purpose, we assume that the intra-cluster transmission range must satisfy d < d0 and inter-cluster transmission range must satisfy the bound d ≥ d0. An error free communication and an ideal MAC layer [14] are also assumed so that transmission is perfect and there is no collision and retransmission.

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2.3 The proposed algorithm

The basic idea of the clustering technique is a situation where sensor nodes are clustered and one CH is selected in each cluster that aggregates and compresses data in order to save energy and thereby to prolong the lifetime of the WSN.

We proposed an energy efficient clustering algorithm that balances the energy consumption for intra and inter cluster communication. The algorithm organizes the network into unequal size clusters, where the clusters closer to the BS consist of a fewer number of nodes, to balance the energy used for the intra-cluster and inter-cluster communication.

To optimize sizes of clusters, an optimization algorithm called Gradient descent is used [22]. It is a first order optimization algorithm that finds a local minimizer of a function by taking steps proportional to the negative gradient of the function at the current point. It can also approach the local maximum of the function by taking steps proportional to the positive gradient of the function. The flow chart that illustrates the steps of the Gradient Descent algorithm is shown in Figure. 3.

Gradient descent is based on the observation that if the cost function F(x) (energy consumption in our case) is defined and differentiable, it starts with an initial point ( ) and generates a sequence of points according to an iterative procedure of a factor (α) as illustrated in Figure. The cost function F(x) decreases faster if one goes in the direction of the negative gradient of F(x) at a certain point (a set of radiuses in our study case).

Our goal is to determine the optimal clusters’ radiuses that minimize the total power consumption among all CHs:

{

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21 Figure 3 Flow chart illustrating the Gradient Descent minimization algorithm

2.3.1 Energy balancing layered model

After the random deployment of nodes, each of M clusters can have ( , , , … ) numbers of nodes. Since the sensor nodes are deployed with a uniform distribution, then the network density ρ is:

⁄ (2.3)

where N is the total number of nodes, S is the surface of deployment. According to our proposal, different clusters contain different number of nodes which can be defined as a product of the network density and the cluster surface:

(2.4)

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22 where is number of nodes in i-th cluster of surface. Then each of M clusters contains, N1 = ρ. S1, N2 = ρ. S2, N3 = ρ. S3 and NM = ρ. SM; S1 , S2 , S3 and SM are surfaces of each clusters respectively.

2.3.2 Multi-hop data transmission

All cluster nodes send the data gathered from sensing field to the CH. CH receives data from its cluster members, aggregates them then sends them to the CH closer to the BS or directly to the BS. Intra-cluster communication assumes single hop data transmission, while the inter-cluster communication implements multi-hop data transmission to avoid long distance data transmission that causes excessive energy depletion and CH’s premature death.

According to the radio hardware energy dissipation simple model (1), the total energy for forwarding k bits of data is the sum of energy spent by each of ( ) cluster members to transmit k bits to the CH and energy spent by CH to receive these data and then to transmit it to the next CH or to the BS.

The total energy consumed by the network in one round consists of three components: inner transmission energy used within each cluster, utter transmission energy applied for sending data between clusters and then the receive energy necessary for receiving data. The total energy can be described in equation 2.5:

∑ ( ) ( )

( ) (2.5)

We assume that:

-denotes the distance between cluster nodes in the i^thcluster and their corresponding CH.

-denotes the distance between CH of the i^th cluster and the CH of (i-1)^th cluster or the BS.

-denotes number of nodes in the i^th cluster.

– a number of bits transmitted in i^th cluster by each node, M – a number of clusters.

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23 Assuming that numbers of transmitted bits by each regular node are the same for each node then the total inner transmission energy of the WSN is:

∑ ( )

∑ ( )( )

(2.6)

Appling the same assumption we can define the total WSN utter transmission energy:

∑ ( )

∑[( )( )]

(2.7)

The total receiving energy used by all CHs is defined as:

∑ ( ) ∑ [( ) ∑

]

(2.8)

We can illustrate the method principles for a case study of M=3. Energy consumed by the CH3 of the furthermost cluster from the BS per transmission round when each node sends k bits is the energy consumed for receiving data from other non CH nodes plus the energy consumed for transmitting this data over a distance to the CH2.

( ) ( ) (2.9)

Energy consumed per each non-CH node in furthermost cluster i=1 is only the energy consumed to transmit data over an average distance to CH1:

( ) (2.10)

Thus, energy consumption per unit time of all nodes in cluster 1 is:

( ) (2.11)

Substituting (2.9) and (2.10) into (2.11) we get:

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24 ( ) ( ) ( )( )

( ) ( )

(2.12)

All CHs in other layers have to transmit data generated in their clusters as well as data originated from the farther layers. Therefore, the energy consumption per transmission round in cluster number 2 (i=2) is:

( ) ( )( ) ( )( )

( ) ( ) ( ) (2.13)

Likewise in the third cluster when i=1,

( ) ( )( ) ( )( ) ( )

( ) ( ) (

) (2.14)

The total energy spent by the whole network is the sum of energy consumed in all clusters and stated in equations (2.12), (2.13) and (2.14) that can be expressed as:.

(2.15)

For this clustering mechanism, the problem is formulated as energy minimization using Linear Optimization Programming techniques. Based on the geometric structure of the network; numbers of nodes, average distances between cluster members and CHs di and distances between contiguous CHs Di can all be expressed as functions of clusters’ radiuses (R1, R2 ,… Ri,… and Rmax).

We assume that the distance between cluster members and the CH (di)is taken as an average distance that is expressed mathematically as a half of the root mean square of the a half of the cluster width defined as (Ri-Ri-1) and a half of the distance between two points farthest from the cluster center. For a case of three cluster network of maximum radius Rmax and the angle , see Figure 4, the three average distances are:

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√(

) ( )

(2.16)

√(

) ( )

(2.17)

√( ) ( )

(2.18)

Average distances between contiguous CHs, are assumed to be equal to the distances between adjacent clusters’ centers. For a case of three cluster network of maximum radius Rmax and the angle , see Figure 4, it can be expressed as:

(2.19)

(2.20)

(2.21)

The number of cluster members can be computed as a product of network average density and the surface of each cluster. Accordingly for the case of three cluster network of maximum radius Rmax and the angle , it is:

(2.22)

(2.23)

(2.24)

and are the maximum radius and maximum angle that define the boundaries of area of deployment respectively.

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Figure 5 illustrates the proposed clustering algorithm that mainly consists of:

Formation of clusters based on optimal radiuses calculations. Selection of CHs in each cluster formed. Data aggregation phase which involves gathering of collected data by the cluster head from the sensor nodes within its cluster. Data transmission phase involves the transfer of all data from each cluster head to the next cluster head(s) and then to the BS. CH election and rotation is performed by taking into consideration the largest residual energy of nodes in the cluster.

R1

R₂

R_max



d1

d2

d3

D3

D2

D1

Figure 4: Illustration of geometry of three cluster network

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27 Figure 5: Flowchart of the proposed optimal clustering algorithm

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Chapter Three

Validation of the algorithm and simulation

results

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29 In Chapter 2, we described our proposed unequal clustering algorithm for improving the network lifetime. In this chapter, we used simulation tools to prove that the algorithm performs better in terms of energy balancing and therefore improving the lifetime of WSN.

We assume that a network consists of N nodes which are uniformly deployed in a circle section area defined by a maximum radius and a maximum angle of , see Figure 4. The proposed method has been validated for different combinations of network parameters: a number of clusters, a number of nodes, maximum radius and angle. The chosen numbers of nodes are: N = 100, N = 250 and N = 500 nodes.

Maximum radius took three values of 50m, 150m and 500m. And finally the chosen angle took three different values of: rad, rad and rad. The network has the following general characteristics:

1. All nodes are homogeneous and they have the same capabilities.

2. All nodes have the same initial energy (n).

3. The BS is placed at (0, 0); the origin of the area of deployment.

4. Nodes positions are defined by radius and angle ( and respectively).

5. Nodes are immobile after deployment.

6. A normal node transmits its data directly to its respective cluster head within a particular cluster.

7. Cluster heads use the multi-hop routing scheme to send their data to the next cluster head and then to the BS.

8. Nodes are uniformly randomly distributed.

3.1 Simulation Setup and Scenarios

We implemented the proposed algorithm on MATLAB. An example of 250 nodes randomly deployed in a circle section area, that has a maximum radius of 150 m, and maximum angel of rad with the BS being placed in the origin of the plane (0, 0) is shown in Figure 6. All nodes have an initial energy of 0.5J, Eelec set to 50 nJ/bit, 𝜖amp set to 100 pJ/bit/m², and the size of the sensor data packet was set to 4000 bit. Initial simulation parameters are listed in Table I. We apply the radio model (2.1) and (2.2) to calculate the energy consumption for 400 transmission rounds.

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30 Figure 6: Random deployment of 250 nodes in a circle section area,

Table I: Initial Simulation Parameters

Parameter Symbol Unit Value

Total number of nodes N - 250

Maximum radius meters 150

Maximum angel Radians ⁄

Initial energy of node (n) Joules 0.5

Data packet size k bits 4000

Energy circuitry cost at transmission and reception

Nano Joule per bit

50 nJ/bit

Free space coefficient Pico Jouleper bit per meter

square 10 pJ/bit/ m²

Multipath coefficient Pico Jouleper bit per meter

to power 4

0.0013 pJ/bit/ m⁴

Distance threshold [14] meters 87m

0 50 100 150

X axis Length in Metres

Y axis Length in Metres

Random Deployment of nodes

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3.2 Validation of the proposed method

To validate the proposed method we simulate the network model and estimate the lifetime for different scenarios. For illustration of the validation procedure Figure 7 and 8 shows the equal and optimal cluster formation respectively for three clusters where 250 nodes are deployed randomly over a circle section that has a maximum radius of 150 meter and a maximum angle of rad. The optimal cluster sizes are obtained from the optimal analysis and calculations discussed in chapter 2 and have the values listed in Table II. Cluster head selection and rotation is done based on largest residual energy.

Table II: Optimal radiuses of the new unequal cluster formation (M=3, R=150m, θ=π/6, N=250)

Rmax=150m, θ=π/6 rad, N=250, M=3

R1 (m) 14.55

R2 (m) 68.4

The network lifetime of the equal clustering and the unequal clustering for three clusters (M=3) are shown in Figure 9 and Figure 10 respectively. We observe that the first node dies after 145 rounds in the equal cluster formation and the network lifetime increases to 210 rounds in the proposed unequal clustering method. Unlike the equal cluster formation, the proposed multi-hop unequal clustering technique in which cluster hierarchy takes presence in cluster formation and highest residual energy for selection of next cluster head, we observed that this technique offers a longer life time for individual nodes and even the entire network.

As a result of the efficient clustering technique, considerable amount of energy is saved during both intra and inter cluster communication, where clusters far from the BS tend to spend their energy in intra cluster communication while collecting the data from a large number of nodes.

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32 Figure 7: Initial equal radius cluster formation of the network (M=3, Rmax=150m, θ=π/6 rad, N=250).

Figure 8: New optimal clusters formation (M=3, Rmax=150m, θ=π/6 rad, N=250).

0 50 100 150

X axis Length in metres

Y axis Length in metres

Equal Radius Cluster Formation

0 50 100 150

Optimal Cluster Formation

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33 Figure 9: Life time of the network after applying the equal clustering (M=3, Rmax=150m, θ=π/6 rad, N=250).

Figure 10: Life time of the network after applying the proposed clustering algorithm (M=3, Rmax=150m, θ=π/6 rad, N=250).

0 50 100 150 200 250 300 350 400

0 50 100 150 200 250

Graph Illustrating the Network Life Time

Number of Rounds Number of Nodes (Number of Alive Nodes for a Particular Round of Simulation)

0 50 100 150 200 250 300 350 400

0 50 100 150 200 250

Number of Rounds Number of Nodes (Number of Alive Nodes for a Particular Round of Simulation)

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3.3 Validation and simulation results for other scenarios

In this section we will show simulation results for different scenarios and different network parameters (Maximum radius, Maximum angle and number of nodes).

3.3.1 First scenario (variation of number of nodes)

With a change in network density by increasing the number of nodes N= 100 and N=500 nodes, we have got the clusters radiuses as listed in Table III:

Table III: Optimal cluster radiuses for different network parameters (first scenario) Rmax=150m, θ=π/6 rad,

N=100, M=3

Rmax=150m, θ=π/6 rad, N=500, M=3

R1(meters) 28.6 10.8

R2 (meters) 80.8 67.8

Figure 11 and 12 show the cluster formations for the equal radiuses and optimal radiuses respectively when a number of nodes N equal 100. The corresponding network lifetimes for those scenarios are shown in figure 13 and 14 respectively. In Figure 15 and 16 N increases to 500 nodes and their corresponding network lifetimes are compared in Figure 17 and 18. We observed that the proposed unequal size clustering method has shown better results for both scenarios; the first node dies after 138 rounds approximately in the equal clustering formation and the first node dies after 155 rounds in the optimal cluster formation for the case of N=100. While the network lifetime increases from 10 rounds in equal radius cluster formation to 25 rounds when we apply the proposed unequal clustering mechanism in the case when N=500.

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35 Figure 11: Initial equal radius cluster formation of the network (M=3, Rmax=150m, θ=π/6 rad, N=100).

Figure 12: New optimal clusters formation (M=3, Rmax=150m, θ=π/6 rad, N=100).

0 50 100 150

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36 Figure 13: Life time of the network after applying the equal clustering (M=3, Rmax=150m, θ=π/6 rad, N=100).

Figure 14: Life time of the network after applying the optimal clustering (M=3, Rmax=150m, θ=π/6 rad, N=100).

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Number of Rounds

Number of Alive Nodes

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Number of Rounds

(37)

37 Figure 15: Initial equal radius cluster formation of the network (M=3, Rmax =150m, θ=π/6 rad, N=500).

Figure 16: New optimal clusters formation (M=3, Rmax =150m, θ=π/6 rad, N=500).

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(38)

38 Figure 17: Life time of the network after applying the equal clustering (M=3, Rmax =150m, θ=π/6 rad, N=500).

Figure 18: Life time of the network after applying the optimal clustering (M=3, Rmax =150m, θ=π/6 rad, N=500).

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Number of Rounds

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Number of Rounds

(39)

39

3.3.2 Second scenario (variation of the maximum radius)

For further verification of our proposed method, we run the simulation for two other values of the maximum radius R= 50m and R= 500m. The equal cluster formation and the optimal cluster for R= 50m are shown in Figure 19 and Figure 20 respectively. Their corresponding network lifetimes are displayed in Figure 21 and Figure 22 respectively.

While Figure 23 and Figure 24 show the equal and optimal cluster formation for R=

500m. The network lifetimes for both scenarios shows remarkable improvement when we compare the equal clustering to our proposed algorithm due to the considerable amount of energy saved during the intra and inter cluster communications.

Table IV: Optimal cluster radiuses for different network parameters (second scenario) Rmax=50m, θ=π/6 rad,

N=250, M=3

Rmax=500m, θ=π/6 rad, N=250, M=3

R1 (m) 8.5 103.7

R2 (m) 22.6 290.4

(40)

Figure 20: New optimal clusters formation (M=3, R=50m, θ=π/6, N=250).

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Equal Raduis Clustering (R=50)

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(41)

Figure 22: Life time of the network after applying the equal clustering (M=3, Rmax =50m, θ=π/6 rad, N=250).

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Number of Rounds

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0 50 100 150 200 250

Number of Rounds

(42)

Figure 24: New optimal clusters formation (M=3, Rmax =500m, θ=π/6 rad, N=250).

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(43)

Figure 26: Life time of the network after applying the optimal clustering (M=3, Rmax =500m, θ=π/6 rad, N=250).

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0 50 100 150 200 250

Number of Rounds

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0 50 100 150 200 250

Number of Rounds

(44)

44

3.3.3 Third scenario (variation of the maximum angle)

Another scenario for the validation of the proposed algorithm is the variation of the maximum angle, two different values for were examined rad and rad.

Having the optimal cluster radiuses listed in Table V for both scenarios, the equal size clusters as shown in Figure 27 and Figure 31 and the optimal unequal clusters were constructed in Figure 28 and Figure 32. The network lifetimes for both equal and optimal clustering were displayed and compared. When the first node dies after 92 rounds in the equal radius clustering while the first node runs out of energy after 155 rounds in the case of our optimal unequal size clustering. When network lifetime increases from 83 rounds to 97 rounds which indicates that longer network lifetime is achieved.

Table V: Optimal cluster radiuses for different network parameters (third scenario)

Rmax=150m, θ=π/4 rad, N=250, M=3

Rmax=150m, θ=π/3 rad, N=250, M=3

R1 (m) 34.3 21.4

R2 (m) 81.5 73.9

An Energy-Balancing Unequal Clustering Algorithm for Multi hop Routing in WSN