base station positioning, nodes' localization and

Base Station Positioning, Nodes’ Localization and

Clustering Algorithms for Wireless Sensor Networks

A Thesis submitted

in Partial Fulfilment of the Requirements

for the Degree of

DOCTOR OF PHILOSOPHY

by

RAJIV KUMAR TRIPATHI

(Y7104097)

DEPARTMENT OF ELECTRICAL ENGINEERING

INDIAN INSTITUTE OF TECHNOLOGY KANPUR

October, 2012

Base Station Positioning, Nodes’ Localization and

Clustering Algorithms for Wireless Sensor Networks

A Thesis Submitted

in Partial Fulfilment of the Requirements

for the Degree of

DOCTOR OF PHILOSOPHY

by

RAJIV KUMAR TRIPATHI

(Y7104097)

to the

DEPARTMENT OF ELECTRICAL ENGINEERING

INDIAN INSTITUTE OF TECHNOLOGY KANPUR

October, 2012

Synopsis

Name of the Student : Rajiv Kumar Tripathi

Roll Number : Y7104097

Degree for which submitted : Ph.D.

Department : Electrical Engineering

Thesis Title : Base Station Positioning, Nodes’ Localizationand Clustering Algorithms forWireless Sensor Network

Thesis Supervisors : Dr. Yatindra Nath SinghDr. Nishchal Kumar Verma

Month and year of submission : October, 2012

Wireless sensor networks have found hundreds of applications to simplify the man-

agement of complex problems. Energy conservation in wireless sensor nodes is prime

concern to engineers in most of its applications. This becomes important as increase in

the network life time depends mainly on minimizing the energy consumption in sensor

nodes. Thus conserving and balancing the energy consumption is of utmost importance.

Main challenge in a wireless sensor network is to design algorithms with minimum en-

ergy expenditure. LEACH [1, 2] was one of the clustering/routing protocols for two

tiered wireless sensor networks which minimizes the energy consumption. This thesis

has expanded on the LEACH protocol to improve the wireless sensor network perfor-

mance.

SYNOPSIS iii

The main objective of the thesis is to investigate the mechanisms to conserve and

balance the energy consumption in two tiered wireless sensor networks. In this thesis,

the problems related to above aspect have been investigated.

The first issue is where to place base station in a wireless sensor network. The

base station position have been geometrically optimized to maximize the life of sensor

network in [3-6]. The energy minimization also depend on path loss along with the

position of deployed sensor nodes. In this thesis, we have considered path loss as well

as geometrical parameters for defining new optimal base station location. An algorithm

to estimate the sub-optimal base station position has also been proposed.

The second problem is anchor free localization in a single hop wireless sensor

network. Anchor free localization is important for localizing all the wireless nodes

without using GPS [7-11]. Average of distances is used for the first time to localize the

reference nodes in a wireless sensor network in this thesis.

Clustering techniques are important to save energy in a wireless sensor network

[12-22]. Two different clustering techniques have been proposed to minimize as well as

to balance the energy consumption among the nodes. Also the problem of identifying

bottleneck nodes have been investigated to conserve the energy in a WSN.

The thesis has been organized in the following six chapters.

Chapter 1 is the introduction to the wireless sensor networks. This chapter dis-

cusses the architecture of the wireless sensor networks and basics like sensors, base

station, radio model and the energy consumption model. This thesis is built around

the LEACH routing protocol. LEACH and its derivative Fixed-LEACH routing algo-

rithm have been discussed in detail as the background of work reported in this thesis.

SYNOPSIS iv

Chapter 2 discusses optimal location of base station in two tired wireless sensor

network. The geometry as well as path loss between the sensor nodes and the base

station have been considered. Weighted centroid method to find sub-optimal position

of base station has been proposed This method has been used in many localization

algorithms in literature. We have proposed new weights for computing the sub-optimal

location.

In chapter 3, anchor free localization algorithm for single hop wireless sensor net-

work has been proposed using internode distances. Merits and demerits of existing

anchor free localization techniques have also been discussed. Simulation results have

been presented to show that our method is better than the existing algorithms.

In chapter 4, We have proposed two methods for balancing energy consumption in

a WSN. In first one, new cluster head selection algorithm have been proposed based on

LEACH. The proposed algorithm achieved more balanced energy consumption among

sensor nodes. As this algorithm is based on number of supported node in previous

round, it is named as N-LEACH. Simulation results show significant improvement in

lifetime of sensor nodes compared to LEACH clustering.

In second method, we have proposed use of variable duty cycle of sensor nodes for

balancing energy consumption depending on distance of a sensor node and sink. The

nodes which are located near the sink consume lower energy compared to the farther

ones due to the smaller transmission distance. With same information transfer rates,

there will be uneven energy consumption in sensor nodes and farther nodes will die

earlier than the nodes closer to the sink. We propose transmission with reduced duty

cycle for farther nodes compare to nodes nearer to sink. We have presented a mechanism

to enforce equal energy consumption using variable duty cycle for all nodes participating

SYNOPSIS v

in a wireless sensor network. We have evaluated performance of proposed algorithm and

compared it with existing algorithms and found it better in terms of lifetime, average

energy consumption and balanced energy consumption for all the nodes.

Chapter 5 discusses the localized detection of bottleneck nodes in a wireless sensor

network. Criticality of bottleneck nodes has also been defined using partitioning in the

network. Different category bottleneck nodes can be found in a wireless sensor network.

Here the network is assumed to have four sink in each direction at the corners of network

as a root nodes, which use flooding for bottleneck nodes detection.

In chapter 6, the major conclusions of the work reported in the thesis have been

presented, and problems for further investigations have been suggested.

Dedicated to

Bhavya, Aadya

Ashutosh, Ajitesh

Acknowledgements

The wisest mind has something yet to learn.

— George Santayana

I feel immense pleasure in expressing my profound sense of gratitude to my thesis

supervisors Dr. Yatindra Nath Singh and Dr. Nishchal Kumar Verma under whose

supervision and inspiring guidance, I had privilege to carry out my research work. I

am indebted to them for their constant and ungrudging encouragement, valuable sug-

gestions and ingenious ideas. Words won’t be sufficient to quantify there immense

knowledge and understanding of the subject. They showed me different ways to ap-

proach a research problem and the need to be persistent to accomplish any goal. I am

also grateful to all the other faculty members for their support and encouragement.

I immensely express my heartiest thanks to my friends Rajiv, Anurag, Ashutosh,

Sandeep, Sanjeev, Amit, Arun and Ruchir for their support and help. I have spent some

of the craziest and most memorable moments with them. I would like to acknowledge

my lab coordinator Mr Vijay who helped me many times for software related problems.

Acknowledgements viii

I would also like to acknowledge my friend Rajiv Srivastava whose valuable sug-

gestions and discussions, helped me in my work. I wish to express my deep gratitude

to all of my the teachers whose consistent help and encouragement boosted my moral

and confidence.

I would also like to thanks to my friends Deepak Sharma, Pankaj Dumka, Amiya

Sahoo, Rishika Chauhan from Jaypee University of Engineering and Technology for

their support during my PhD.

Though it is beyond the scope of any acknowledgement for all that I have received

from my parents Mr. Bhanu Shanker Tripathi and Mrs. Maya Rani Tripathi, by the way

of inspiration, patience and encouragement at all times but most conspicuously during

this period, yet I make an effort to express my heartfelt and affectionate gratitude to

them. May God guide me to the wishes of my parents so that they feel the joy of having

lived a contained life in my conduct to them. I also want to express my deep gratitude

to my brothers Sanjeev Tripathi and Vikas Tripathi and my bhabhi Sarita Tripathi

who helped me by giving time to complete my thesis. Finally I want to thank my wife

Dr. Aparna Tripathi, who supported me in every step of my life and encouragement to

pursue PhD from this reputed institute, IIT Kanpur.

(Rajiv Kumar Tripathi )

Acronyms and Abbreviations

ABC Assumption Based CoordinatesACK AcknowledgementAFL Anchor Free LocalizationAoA Angle of ArrivalAPTEEN Adaptive Threshold sensitive Energy Efficient Sensor Network ProtocolBS Base StationCH Cluster HeadGPS Global Positioning SystemGER Global Energy RatioKPS Knowledge-based Positioning SystemLEACH Low-Energy Adaptive Clustering HierarchyMDS Multi Dimensional ScalingMEMS Micro Electro Mechanical SystemsMSPA Matrix transform-based Self Positioning AlgorithmNLOS Non Line of Sightnon-CH Non Cluster HeadPDM Proximity Distance MappingPEGASIS Power Efficient Gathering in Sensor Information SystemsQoS Quality of ServiceRSSI Received Signal Strength IndicatorRx ReceiverRF Radio FrequencySPA Self Positioning AlgorithmTEEN Threshold sensitive Energy Efficient Sensor Network ProtocolTDoA Time Difference of ArrivalTDMA Time Division Multiple AccessToA Time-of-ArrivalTx TransmiterVDC Variable Duty CycleWSN Wireless Sensor Network

List of Symbols

M Length of side of square wireless sensor network topologyL Total number of transmitted bitsF Location where sum of distance power 4 is minimized from all the nodesP Location of proposed pointC Location of centroid of distributed nodesd Distance between two nodesEelec Energy used for transmission and reception of electronicsEamp(L, d) Energy used by amplifier to transmit L bits at distance dETx(L, d) Energy used to transmit L bits at distance dERx Energy used to receive L bitsEDA Energy used for data aggregationECH Energy of a Cluster HeadEnon−CH Energy of a normal nodeECluster Energy dissipated in a clusterERound Energy dissipated by all the nodes during one RoundETotal Energy dissipated by all the nodes during one Epochεfs Free space loss constant measured in J/bit/m2

εmp Multi-path loss constant measured in J/bit/m4

n Total number of nodes in WSN topologyk Number of clusters in WSN topologynk

Average number of nodes per cluster in WSN topologykopt Optimum number of cluster in WSN topologyd0 Constant threshold distance for swapping amplification modelα Path loss constantDTR Distance between transmitter and receiverVs Velocity of acoustic signalVRF Velocity of radio frequency signalTn Constant threshold for cluster head selectionG Eligibility constant for cluster head selectionr Current round during simulation

List of Symbols xi

Dave Average distance among all nodes

Dc Normalized distance of all the nodes from the centroid of distributed nodesDiC Distance of ith node from the centroid of distributed nodes

ˆDhave Normalized average distance among all nodes when hop count is usedfor distance measurement

Ebs Energy for transmitting data to base stationEC Total energy of all the nodes if base station is placed at centroidEO Total energy of all the nodes if base station is placed at optimal pointEd2 Amplification energy consumption when all nodes suffer only free space lossEd4 Amplification energy consumption when all nodes suffer only multipath lossEd2,4 Amplification energy consumption when some nodes suffer free space and

remaining nodes multipath lossEMEC Total energy of all the nodes if base station is placed at center of minimum

enclosing circle

Contents

List of Figures xv

List of Tables xx

1 Introduction 1

1.1 Wireless Sensor Network . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.1.1 Sensor Nodes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.1.2 Base Station . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.1.3 Radio Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

1.1.4 Energy Consumption Model . . . . . . . . . . . . . . . . . . . . . 6

1.2 Research Issues and Literature Survey . . . . . . . . . . . . . . . . . . . 8

1.2.1 Deployment Strategy . . . . . . . . . . . . . . . . . . . . . . . . . 9

1.2.2 Localization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

1.2.3 Routing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

1.3 Thesis Organization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

2 Placement of Base Station in a Wireless Sensor Network 28

CONTENTS xiii

2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

2.2 Related Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

2.3 Problem Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

2.4 Algorithm for Base Station Location . . . . . . . . . . . . . . . . . . . . 34

2.4.1 Optimal location of base station - An example . . . . . . . . . . . 37

2.5 Simulation And Results . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

2.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

3 Anchor Free Localization Technique for Singlehop Wireless Sensor

Network 49

3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

3.2 Related Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

3.3 Challenges with Localization Techniques . . . . . . . . . . . . . . . . . . 52

3.3.1 Localization using Hop Count . . . . . . . . . . . . . . . . . . . . 52

3.3.2 Accumulation of Localization Error . . . . . . . . . . . . . . . . . 55

3.4 Metric for Proposed Algorithm . . . . . . . . . . . . . . . . . . . . . . . 56

3.5 Algorithm for Singlehop Localization . . . . . . . . . . . . . . . . . . . . 57

3.6 Simulation & Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

3.7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

4 Balancing Energy Consumption in a Wireless Sensor Network 64

4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64

CONTENTS xiv

4.2 Related Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

4.3 Method 1: N-LEACH, a Balanced Cost Cluster-Heads Selection Algorithm 68

4.4 Proposed Cluster Head Selection Algorithm . . . . . . . . . . . . . . . . 70

4.5 Method 2: Balancing Energy Consumption using Variable Duty Cycle

(VDC) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

4.6 VDC Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

4.7 Simulation and Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75

4.8 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80

5 Localized Detection of Bottleneck Nodes and Quantification of Criti-

cality in a Wireless Sensor Networks 81

5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81

5.2 Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84

5.3 Simulation Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86

5.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88

6 Conclusions and Future Works 89

6.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89

6.2 Suggestions for future works . . . . . . . . . . . . . . . . . . . . . . . . . 91

Bibliography 92

List of Publications 106

Appendix A 108

Appendix B 110

Appendix C 117

List of Figures

1.1 Wireless Sensor Network as Subset of Wireless Network. . . . . . . . . . 1

1.2 A Wireless Sensor Network . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.3 Block diagram of Sensor Node . . . . . . . . . . . . . . . . . . . . . . . . 3

1.4 A Sensor Node . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

1.5 A Base Station Node . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

1.6 Radio Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

1.7 Clustering in WSN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

1.8 RSSI vs Distance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

1.9 TDoA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

1.10 Hyperbolic Tri-lateration . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

1.11 Triangulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

1.12 Tn for One Epoch Time in Different Rounds . . . . . . . . . . . . . . . . 22

1.13 Frequency of Cluster Heads in LEACH . . . . . . . . . . . . . . . . . . . 23

1.14 Distribution of Cluster Heads in LEACH . . . . . . . . . . . . . . . . . . 23

1.15 Frequency of Cluster Heads in Fixed-LEACH . . . . . . . . . . . . . . . 24

LIST OF FIGURES xvii

1.16 Distribution of Cluster Heads in Fixed-LAECH . . . . . . . . . . . . . . 24

2.1 A Wireless Sensor Network topology . . . . . . . . . . . . . . . . . . . . 33

2.2 Weights calculation for Algorithm . . . . . . . . . . . . . . . . . . . . . . 35

2.3 Distances from Centroid of distributed nodes . . . . . . . . . . . . . . . . 38

2.4 Distances from Theoretical Optimal Position of base station . . . . . . . 38

2.5 Distances from Proposed Point as base station . . . . . . . . . . . . . . . 39

2.6 Distances from center of minimum enclosing circle as base station . . . . 39

2.7 Average percentage reduction in amplifier energy for proposed point com-

pared to centroid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

2.8 Average percentage reduction in amplifier energy when negative values

are clipped to zero . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

2.9 Average percentage reduction in amplifier energy for proposed point com-

pared to centroid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

2.10 Average percentage reduction in amplifier energy when negative values

are clipped to zero . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

2.11 Average percentage reduction in amplifier energy for minimum enclosing

circle compared to centroid . . . . . . . . . . . . . . . . . . . . . . . . . . 45

2.12 Average percentage reduction in amplifier energy for minimum enclosing

circle compared to centroid . . . . . . . . . . . . . . . . . . . . . . . . . . 45

3.1 Localization of a node in AFL . . . . . . . . . . . . . . . . . . . . . . . . 53

3.2 Nodes are localized integral multiples of maximum radio range R . . . . . 53

3.3 Localization using Hop Count . . . . . . . . . . . . . . . . . . . . . . . . 54

LIST OF FIGURES xviii

3.4 Relation between Dc and ˆDave . . . . . . . . . . . . . . . . . . . . . . . . 57

3.5 Estimation of Reference node 1 . . . . . . . . . . . . . . . . . . . . . . . 59





3.10 Localization for node j . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

3.11 Localization Problem for non rectangular sensor field . . . . . . . . . . . 60

3.12 GER vs size of topology for constant number of nodes . . . . . . . . . . . 61

3.13 GER vs number of nodes for constant size of topology . . . . . . . . . . . 61

3.14 Average localization error vs number of nodes for constant size of topology 62

3.15 Average localization error vs size of topology for constant number of nodes 62

4.1 Balanced Energy Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . 67

4.2 LEACH Algorithm Flowchart . . . . . . . . . . . . . . . . . . . . . . . . 71

4.3 Proposed Algorithm Flowchart . . . . . . . . . . . . . . . . . . . . . . . . 72

4.4 A Wireless Sensor Network topology . . . . . . . . . . . . . . . . . . . . 74

4.5 Number of Alive Nodes vs Time (in number of rounds) . . . . . . . . . . 76

4.6 Standard Deviation of residual energy for all the nodes at each epoch . . 77

4.7 Cumulative Distribution Function of mean energy lost in one epoch . . . 79

4.8 Probability Density Function of mean energy lost in one epoch . . . . . . 79

LIST OF FIGURES xix

5.1 Example of Bottleneck Node . . . . . . . . . . . . . . . . . . . . . . . . . 82

5.2 Undesirable Energy Histogram . . . . . . . . . . . . . . . . . . . . . . . . 83

5.3 Desirable Energy Histogram . . . . . . . . . . . . . . . . . . . . . . . . . 83

5.4 Root Nodes Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

5.5 Bottleneck Nodes Detection . . . . . . . . . . . . . . . . . . . . . . . . . 87

B-1 Geometric Median (x, y) . . . . . . . . . . . . . . . . . . . . . . . . . . . 110

B-2 Geometric medians for two points . . . . . . . . . . . . . . . . . . . . . . 112

B-3 Geometric medians for three points . . . . . . . . . . . . . . . . . . . . . 113

B-4 Geometric medians for four points . . . . . . . . . . . . . . . . . . . . . . 113

B-5 Geometric medians for five points . . . . . . . . . . . . . . . . . . . . . . 114

B-6 Geometric medians for Six points case 1 . . . . . . . . . . . . . . . . . . 115

B-7 Geometric medians for Six points case 2 . . . . . . . . . . . . . . . . . . 115

C-1 Point A (x,y) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117

C-2 Point A when only two point are in field i.e. n=2. . . . . . . . . . . . . 118

C-3 Point A when only three point are in field i.e. n=3. . . . . . . . . . . . 118

List of Tables

1.1 Radio Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

1.2 Different deployment technique . . . . . . . . . . . . . . . . . . . . . . . 12

1.3 Different localization technique . . . . . . . . . . . . . . . . . . . . . . . 20

1.4 Different Routing Techniques . . . . . . . . . . . . . . . . . . . . . . . . 26

2.1 Excess energy used by different methods compared to the optimal location 40

2.2 Nodes’ ratio when centroid as center . . . . . . . . . . . . . . . . . . . . 46

2.3 Nodes’ ratio when proposed point as center . . . . . . . . . . . . . . . . . 46

2.4 Distance in meter between centroid and point P . . . . . . . . . . . . . . 47

3.1 Average Actual Distance vs Average Distance due to number of hops . . 55

4.1 Average Lifetime of nodes in number of rounds . . . . . . . . . . . . . . . 77

5.1 % of Bottleneck Nodes . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

B-1 Geometric medians for different cases . . . . . . . . . . . . . . . . . . . . 116

Chapter 1

Introduction

1.1 Wireless Sensor Network

A Wireless Sensor Networks (WSNs) form a subset of Ad-hoc networks as shown in

Fig.1.1. Wireless sensor networks have many restrictions compared to Ad-Hoc net-

works in terms of its sensor nodes’ capability of memory storage, processing and the

available energy source. Wireless sensor networks are generally assumed to be energy

restrained because sensor nodes operate with small capacity DC source or may be placed

such that replacement of its energy source is not possible. Even though sensor networks

are a subset of ad hoc networks, the protocols designed for ad hoc networks cannot be

used as it is due to the reasons cited in [23].

Figure 1.1: Wireless Sensor Network as Subset of Wireless Network.

1.1 Wireless Sensor Network 2

1) The number of nodes in a sensor network is very large compared to ad-hoc networks.

Thus sensor networks require different and more scalable solutions.

2) In comparison to ad-hoc networks, sensor nodes have limited power supply and

recharging of power is impractical considering the large number of nodes and the en-

vironment in which they are deployed. Therefore energy consumption in WSN is an

important metric to be considered.

A WSN (see Fig.1.2) consists of spatially distributed autonomous sensors nodes to

cooperatively monitor physical or environmental conditions. The nodes communicate

wirelessly and often self-organize after being deployed in an ad-hoc fashion. A WSN

may consist of hundreds or even thousands of nodes. Source nodes transmit their data

to destination nodes through intermediate nodes. This destination node is connected to

a central gateway, also known as base station. Central gateway provides a connection

to the wired world where the data can be collected, processed, and analyzed.

Figure 1.2: A Wireless Sensor Network

The WSN consist of two main components:

1. Sensor Nodes, and

2. Base Station (Central Gateway).


1.1.1 Sensor Nodes

Sensors nodes are typically built of few sensors and a mote unit as shown in Fig.1.3.

A Sensor is a device which senses the information and pass it on to mote. Sensors

are typically used to measure the changes in physical environmental parameters like

temperature, pressure, humidity, sound, vibration and changes in the health parameter

of person e.g. blood pressure and heartbeat. MEMS based sensor have found good

use in sensor nodes. A mote consists of processor, memory, battery, A/D converter

for connecting to a sensor and a radio transceiver for forming an ad hoc network. A

mote and sensor together form a Sensor Node. A sensor network is a wireless ad-hoc

network of sensor nodes. Each sensor node can support a multi-hop routing algorithm

and function as forwarder for relaying data packets to a base station.

Figure 1.3: Block diagram of Sensor Node

1.1.2 Base Station

A base station links the sensor network to another network. It consists of a processor,

radio board, antenna and USB interface board. It is preprogrammed with low-power

mesh networking software for communication with wireless sensor nodes. Deployment

of the base station in a wireless sensor network is very important as all the sensor nodes

handover their data to the base station for processing and decision making. Energy


conservation, coverage of sensor nodes and reliability issues are taken care of during

deployment of base station in sensor network. Generally base stations are assumed

static in nature but in some scenarios they are assumed to be mobile to collect the

data from sensor nodes. The Crossbow sensor node and base station [24] are shown in

Fig.1.4 and Fig.1.5 respectively.

Figure 1.4: A Sensor Node Figure 1.5: A Base Station Node

1.1.3 Radio Model

We have assumed the same radio model which has been used in earlier works [2, 25].

For the radio hardware, the transmitter dissipates energy to run the transmitter radio

electronics and power amplifier, and the receiver dissipates energy to run the receive

radio electronics as shown in Fig.1.6.

For the scenarios described in this thesis, both the free space (d2 power loss) and the

multi path fading (d4 power loss) channel models were used depending on the distance

between the transmitter and the receiver. If the distance is less than a threshold, the

free space (fs) model is used; otherwise, the multi path (mp) model is used.


Figure 1.6: Radio Model

In the radio model of Tx amplifier, we use α = 2 for free space and α = 4 for

multipath model. Thus if a node transmits L number of bits, the energy used in

transmission will be

ETX(L, d) =Eelec.L+ Eamp(L, d), (1.1.1)

ETX(L, d) ={L.Eelec+L.εfs.d

2 if d<d0L.Eelec+L.εmp.d4 if d≥d0 . (1.1.2)

Here threshold

d0 =

√εfsεmp

. (1.1.3)

To receive L message bits, the radio spends energy

ERX(L) =Eelec.L. (1.1.4)


The parameters shown in Table 1.1 are used to evaluate the energy consumption in

a wireless sensor network.

Table 1.1: Radio ParametersDescription Symbol ValueEnergy consumed by the amplifier totransmit at a shorter distance

εfs 10pJ/bit/m2

Energy consumed by the amplifier totransmit at a longer distance

εmp 0.0013pJ/bit/m4

Energy consumed in electronic circuitto transmit or receive the signal

Eelec 50nJ/bit

Data aggregation energy EDA 5nJ/bit

1.1.4 Energy Consumption Model

Before discussing the energy consumption model, understanding of cluster is important.

Clustering (see Fig.1.7) is a process of grouping nodes using an algorithm to perform

certain tasks efficiently as per the requirements. Clustering can also be used to divide

the topology into sub-regions based on certain criteria e.g. whole area should be covered,

minimum energy consumption, maximum lifetime, etc..

Figure 1.7: Clustering in WSN


In a wireless sensor network, cluster heads are selected from all the nodes. Each node

chooses the nearest cluster head for forwarding packets to Base station. All the nodes

attached to cluster head, form the cluster. Let there be n nodes uniformly distributed

in an M ×M area and k clusters in topology. There will be on an average nk

nodes per

cluster. Out of these, there will be one cluster head node and remaining (nk− 1) non

cluster head nodes. Energy consumption for a cluster is derived further.

The energy consumption Enon−CH for a single non-cluster head node is only for

transmission of L bits to cluster head.

Enon−CH =L.Eelec + Eamp(L, d). (1.1.5)

ECH for a particular Cluster Head node is due to reception of data from all non-Cluster

Head node of that cluster, data aggregation and transmission of aggregated data to

base station.

ECH =(n

k− 1).L.Eelec +

n

k.L.EDA + ETX(L, d). (1.1.6)

Where EDA is energy used by Cluster Head for data aggregation. Now the energy

consumption in a cluster is given by

ECluster =ECH + (n

k− 1)Enon−CH . (1.1.7)

More detailed energy consumption model will depend on specific problem in a wireless

sensor network. We shall be looking at these details later in thesis.

1.2 Research Issues and Literature Survey 8

1.2 Research Issues and Literature Survey

Wireless sensor networks are quite different from general wireless networks due to var-

ious constraints and highly application specific nature of WSNs. Consequently, WSNs

pose different research challenges. In wireless communication system, the models for

signal strength drop over a distance are well developed. Effects of signal reflection, scat-

tering and fading are well understood. In an actual WSN, cost and other application

specific issues affect the communication properties of the system. For example, radio

communication in WSN is of low power and short range compared to any other wireless

communication network. The system performance characteristics vary considerably in

WSN even though the same basic principles of wireless communication network are

used in WSN. The size, power, cost and their tradeoffs are fundamental constraints

in WSNs. Considering the basic differences with the wireless communication systems,

many issues have been identified and investigated. Major issues affecting the design

and performance of a wireless sensor network are the following:

1) Deployment strategy

2) Localization

3) Clustering for hierarchal routing

4) Coverage efficacy

5) Efficient medium access control

6) Efficient database centric design

7) Quality of service implementation

8) Acceptable security

We have restrained ourselves to the study of first three issues. This thesis concentrate

mainly on deployment strategy, localization and clustering for hierarchal routing.


1.2.1 Deployment Strategy

The deployment strategy depend mainly on the type of sensors and the application.

The following deployments strategies are generally used in WSNs.

Random deployment: Random deployment is the most practical way of placing the

sensor nodes. For a dynamic sensor network, where there is no a-priori knowledge of

optimal placement, random deployment is a natural option.

Incremental deployment: The incremental placement strategy is a centralized, one-

at-a-time approach to place the sensors. The implementation makes use of information

gathered through the previously deployed nodes to determine the ideal deployment

location of the next sensor node. This can be calculated at base station.

Computational geometry approach: The computational geometry approach is the

simplest method for sensor deployment. In this approach, the target sensing region is

constructed by a set of grids or polygons thus deciding the node placement.

Movement-assisted deployment: In certain scenarios, deployment scheme is prone

to deviate from the plan, because the actual landing positions cannot be controlled

due to the existence of wind and obstacles. For industrial use, where the detection

of some part of a machine is required, or in a wildlife sanctuary, one may use mobile

sensor nodes, which can move to the desired places to provide the required coverage. In

movement-assisted deployment, initially random deployment is performed. Thereafter

re-deployment of the mobile sensor nodes is performed with incremental optimization.

The WSN consists of sensor nodes and a base station. So researchers can solve two

different problems of deployment. In this thesis, the literature survey for deployment is

divided in two parts. In the first part, sensor nodes’ deployment is discussed. Thereafter

the literature survey on base station deployment have been done.


Sensor node deployment problems have been studied in terms of energy conservation

by Howard et al. [26] in 2002 and Heo et al. [27] in 2003. Dhillon et al. [28] optimized

the number of sensors in 2004. Also in the same year, Zou et al. [29] proposed virtual

force algorithm (VFA) as a sensor deployment strategy to enhance the coverage after

an initial random placement of sensors. One of the successful application of the com-

putational geometry in WSNs deployment problem is the Voronoi diagram approach

investigated by Wang et al. [30] in 2004. In 2005, Lin et al. [31] proposed near-optimal

sensor placement algorithm to achieve complete coverage. Liu et al. [32] proposed

power aware sensor node deployment in 2006. Poe et al. [33] studied deployment of

sensor nodes while considering area coverage, energy consumption, and worst-case de-

lay of the WSNs in 2009. Park et al. [34] achieved optimum sensor nodes deployment

using Fuzzy C-means algorithm in 2011. The research in last decade for sensor node

deployment have indicated it to be a application specific problem. Most of the research

approaches are geometrical and also optimize the number of sensor nodes in general.

Some of the famous research projects are as follows: Redwoods project [35], which

sought to observe the microclimate variations surrounding Redwood trees in a coastal

forest. Volcano monitoring using acoustic sensors to detect the seismic activity and

record high-frequency measurements [36], and ZebraNet project to gather position data

of zebras in their natural environment in Kenya [37].

Presently main issues in sensor node deployment are-

1) Sensor nodes deployment to maximize the coverage in the network. Detection of

coverage holes, repositioning of sensor nodes to repair coverage holes,

2) Deployment to achieve minimal energy consumption configuration,

3) Deployment of sensor nodes for a large scale WSN to minimize the event sensing

delays.


As in this thesis, investigation in the base station deployment problem has been

presented so the literature survey on base station deployment is important. There

are several proposed algorithms available in the literature for optimal location of base

station in a WSN. Though the Fermat point is very old problem for optimal facility

location but when the optimal location depends on several parameters other than only

distance, new methods have been evolved. Pan et al. (2003, 2005) [3, 4] provided

algorithms for locating a single base station using an upper bound and a lower bound

initially. Bogdanov et al. (2004) [38] optimized the positions of base stations in a data

collecting sensor network to minimize the power consumed by the sensors. Efrat et al.

(2004) [39] used approximation schemes for optimally locating a base station. Wong

et al. (2006) [40] proposed novel binary integer programming formulation of the base

station placement problem. Akkaya et al. (2007) [5] showed that dynamic positioning

of the BS is an effective means for boosting the network dependability. Basheer et

al. [41] proposed delaunay refinement based sub optimal receiver placement technique

which reduces the dilution of localization accuracy. This method solve two problems

of wireless sensor network simultaneously, one is base station positioning and other,

minimization of localization error. Recently Paul et al. (2010) [6] also proposed a new

optimal location of base station using geometrical approach for maximum lifetime of

the sensor network. Most of the algorithms use power minimization between nodes and

base station. In this thesis also, power consumption minimization has been considered

along with the geometry as well as the path loss exponent of the medium. The issues

for investigation in base station deployment are the following.

1) Deployment of base station to maximize network lifetime,

2) Dynamic and multiple base station positioning,

3) Base station deployment for minimal energy consumption.

Literature survey summary is shown in Table 1.2.


Table 1.2: Different deployment technique

Technique Algorithm Deployment Method

Sensor node Deployment Howard et al. [26] Deployment of a mobile nodes inan unknown environment.

Heo et al. [27] Deployment of mobile sensornodes in the region of interest.

Dhillon et al. [28] Probabilistic optimization ofnumber of sensors.

Zou et al. [29] Virtual force algorithm as a sen-sor deployment strategy.

Wang et al. [30] Deployment problem using theVoronoi diagram approach .

Lin et al. [31] Near-optimal deployment toachieve complete coverage.

Liu et al. [32] Power-aware sensor node deploy-ment.

Poe et al. [33] Considering coverage, energy con-sumption, and delay.

Park et al. [34] Nodes deployment using Fuzzy C-means algorithm.

Base Station Deployment Pan et al. [3, 4] Minimum Enclosing Circle withlower and upper bound.

Bogdanov et al. [38] Minimizing power consumptionof sensor nodes.

Efrat et al. [39] Approximation schemes for locat-ing a base station.

Wong et al. [40] Binary integer programming forbase station placement.

Akkaya et al. [5] Dynamic positioning of base sta-tion to increase network lifetime.

Basheer et al. [41] Receiver placement using delau-nay refinement by reducing local-ization error.

Paul et al. [6] Using geometrical approach formaximum lifetime.


1.2.2 Localization

Localization of sensor nodes in WSNs, has been and still is quite a vital area of research.

Localization is a method to determine the accurate physical position of sensor nodes.

Wireless sensor networks are used in the different environments to perform various

monitoring tasks such as search, rescue, disaster relief, target tracking. In many such

tasks, node localization is important to the application. Existing localization algorithms

basically consists of two basic phases-

(1) Distance (or angle) estimation, and

(2) Distance (or angle) combining.

1.2.2.1 Distance (or angle) estimation

We determine distance or angle between nodes in phase 1 using following methods.

Received Signal Strength Indicator (RSSI): This techniques measure the received

power of the signal at the receiver. If the transmit power is known, effective propagation

loss can be calculated. Theoretical and empirical models can be used to translate this

loss into a distance estimate. This method has been used mainly for RF signals. Using

popular Friis’ equation [42], the detected signal strength PRx is given by

PRx =PTx .GTx .GRx .(λ

4πd)2. (1.2.8)

It shall be noted that PRx decreases quadratically with the distance d from the sender.

The sensor nodes convert the received signal strength to received signal strength indi-

cator (RSSI). It is ratio of the received power to the reference power (PRef ).

RSSI =10.log(PRxPRef

). (1.2.9)


Figure 1.8: RSSI vs Distance

Typically, the reference power represents an absolute value of PRef = 1mW and

RSSI is represented in dBm. When 2.4 GHz signal is transmitted with PTx = 50W ,

RSSI (in dBm) as a function of the distance is shown in Fig.1.8. RSSI is the prime

candidate for range measurements due to its simplicity. Given a known transmission

power and a good model of the wireless channel, the distance between transmitter and

receiver can be estimated based on the received power. Unfortunately, the accuracy

of these RSSI range measurements is highly sensitive to multi-path fading, non-line of

sight (NLOS) scenarios, and other sources of interference, which may result in large

errors. These errors can propagate through all subsequent triangulation computations,

leading to useless information.

Angle-of-Arrival (AoA): Nodes estimate the angle at which signals are received and

use simple geometric relationships to calculate node positions. Localizations in AoA can

be solved using triangulation. AoA localization is susceptible to measurement noise and

few additional problems. This technique require knowledge of reference direction. Thus

AoA approaches require costly antenna arrays on each node. Usually such antennas are

not affordable in cheap sensor nodes.


Time Difference of Arrival (TDoA): The propagation time can be directly

translated into distance, based on the known signal propagation speed. These methods

can be applied to many different signals, such as RF, acoustic, infrared and ultrasound.

The short transmit ranges of 1 to 10 m result in unacceptably high synchronization

demands of 3 psec per cm resolution, when TDoA techniques are employed.

For example, RF and acoustic signal have different speed, and if transmitted simul-

taneously by transmitter at known time, will be received by receiver at time T1 and

T2 respectively, due to the difference in their speed as shown in Fig.1.9. Thus time

difference is delay ∆T = (T1 − T2). Let the distance between transmitter and receiver

be DTR, and velocity of acoustic and RF signal be Vs and VRF respectively. DTR is

given by

DTR =∆T × Vs(1− Vs

VRF). (1.2.10)

As Vs << VRF ,

DTR =∆T × Vs. (1.2.11)

Figure 1.9: TDoA


1.2.2.2 Distance (or angle) combining

In phase 2, phase 1 data is used to determine (X,Y) coordinates of all the nodes. The

most common methods for phase 2 are the following.

Hyperbolic Tri-lateration: This process uses distances or absolute measurements

of time-of-flight from three or more sites. As shown in Fig.1.10.

Figure 1.10: Hyperbolic Tri-lateration

Equation of Spheres are

a2=x2+y2+z2,b2=(x−d)2+y2+z2, and

c2=(x−i)2+(y−j)2+z2 .

(1.2.12)

Solving, we get

x =a2 − b2 + d2

2d, (1.2.13)

y =a2 − c2 + i2 + j2

2j− i

j.x, and (1.2.14)

z =±√a2 − x2 − y2. (1.2.15)


Thus using proper assumptions Hyperbolic Tri-lateration can be used to solve localiza-

tion problems.

Triangulation: This process uses at least one distance estimate and two measured

angles. The angle measurement may be done with receiver antenna diversity or phase

comparison. As shown in Fig.1.11, Sine theorem, i.e.

Figure 1.11: Triangulation

a

sinA=

b

sinB=

c

sinC(1.2.16)

and Cosine theorem, i.e.

c2=a2+b2−2ab.CosC

b2=a2+c2−2bc.CosB

a2=b2+c2−2bc.CosA

(1.2.17)

can be used. But these methods require at least two references for localization of

unknown nodes. Geometry of the references nodes and configuration of network nodes,

decide accuracy in localization through triangulation. Localization also depend on

accuracy of the range measurements in phase 1.

Initially Harter et. al developed a small device called Bat for localization of various

objects in 1999. Bats consist of a radio transceiver, controlling logic and an ultrasonic

transducer. Objects to be localized were tagged with bats. The location of these bats

were tracked by the system to build a location database of these objects [43].


The literature survey for localization can be divided into two parts. In first part, the

anchor based localization is discussed and in second part, anchor free localization.

Anchor based localization: Priyantha et al. [44] at MIT developed a hardware plat-

form known as Cricket. The sensor nodes localization is done using inter node ranges

in that hardware. Doherty et al. [45] in 2001, developed semidefinite program based on

connectivity and pairwise angles between nodes for localization. In 2002, Savvides et al.

[46] derive the Cramer-Rao lower bound (CRLB) for network localization, expressing

the expected error characteristics for an ideal algorithm, and compared it to the actual

error in an algorithm based on multilateration. In a well known work APS (Ad Hoc

Positioning System), Niculescu et al. [47] proposed two localization algorithms using

angle of arrival in 2003.In same year, He et al. [48] proposed APIT (Approximate PIT)

localization using neighbor information. Meertens et al. [49] (2004) have shown that

how sensor nodes in a WSN can construct, align and reconcile a spatial map of its own

position and those of other, nearby nodes based on inter-node distance information,

thus providing a global coordinate system. Peng et al. [50] (2006) focused on localiza-

tion techniques based on angle of arrival information between neighboring nodes and

proposed a new localization and orientation scheme that considers beacon information

multiple hops away. Cheng et al. [51] (2007) proposed an algorithm which uses two

different localization techniques, multidimensional scaling and proximity distance map-

ping (PDM), in a phased approach. The phased approach has comparable complexity

to PDM but less than MDS. Huang et al. [52] (2008) used Monte Carlo sampling steps

in the context of the localization using a single beacon for various types of observations

such as ranging, Angle of Arrival (AoA) and connectivity. Basheer et al. [53] (2011)

proposed localization technique using constrained simulated annealing with tunnelling

transformation to solve non-tractable posterior distribution.


Anchor free localization: Initially, Bulusu et al. [7] (2000) gave the anchor free

localization algorithm for the wireless sensor networks. In 2001 Capkun et al. [8] (2001)

proposed the self positioning algorithm (SPA). They used distances between the nodes

to build a relative coordinate system. In the same year Savarese et al. [9] proposed

the Assumption Based Coordinates (ABC) algorithm. It determines the locations of

the unknown nodes, one at a time. Priyantha et al. [10] (2003) proposed Anchor

Free Localization (AFL) using hop count. The key idea in AFL is fold-freedom, where

nodes first configure into a topology that resembles a scaled and unfolded version of the

true configuration, and then run a force-based relaxation procedure. Moses et al. [11]

(2003) used a calibration signal for measuring time-of-arrival and direction-of-arrival

of sensor nodes in anchor free localization. Moore et al. [54] (2004) localized nodes

in a sensor network with noisy distance measurements, using no beacons or anchors.

Fang et al. [55] (2005) had proposed Knowledge based Positioning System (KPS). The

nodes are deployed as one group at a time centered around a group coordinates. The

nodes in a group gets distributed around center as per source distribution function. In

this scheme, each sensor first finds out the number of its neighbors from each group.

Using node degree in a group, nodes estimate a location based on the principle that

the estimated location should maximize the probability of the observation. Basheer et

al. [56] (2009) introduced a new parameter R-factor, which enhances the localization

accuracy.Wang et al. [57] (2010) developed a standardized clustering-based approach

for the local coordinate system formation. Wang et al. [58] (2010) considered residual

energy, node degree and principles of triangle inequality to heuristically build clusters,

then fuse the clusters into one cluster. Basheer et al. [59] (2011) used cross correlation

of shadow fading noise and copulas to improve localization accuracy. The related work

for localization is summarized in the Table 1.3.


Table 1.3: Different localization technique

Technique Algorithm Localization Method

Anchor Based Localization Priyantha et al. [44] Localization using time differenceof arrival (TDoA).

Doherty et al. [45] Semidefinite program based local-ization.

Savvides et al. [46] Localization using collaborativemultilateration.

APS [47] Localization using angle of arrival.APIT[48] Approximate PIT Test using neigh-

bor information.Meertens et al. [49] Localization using inter node dis-

tance.Peng et al. [50] Localization using angle of arrival.Cheng et al. [51] Localization using MDS and prox-

imity distance mapping.Huang et al. [52] Localization using Monte Carlo

method.Basheer et al. [53] Localization using stochastic tun-

nelling.Anchor Free Localization Bulusu et al. [7] GPS-less low cost outdoor localiza-

tion.ABC [9] Assumption Based Coordi-

nates (Solved geometrically).SPA [8] Localization using distances be-

tween the nodes.AFL [10] Anchor Free Localization using hop

count.Moses et al.[11] Localization using time-of-arrival

and direction-of-arrival.Moore et al. [54] Localization using robust quadri-

laterals.KPS [55] Knowledge-based Positioning Sys-

tem.Basheer et al. [56] Localization using receive error fac-

tor and diversity.MSPA [57] Matrix transform-based Self Posi-

tioning Algorithm.Wang et al. [58] Cluster based localization using

residual energy and node degree.Basheer et al. [59] Localization using cross correlation

of shadow fading noise and copulas.


1.2.3 Routing

Routing in the WSNs is challenging due to the inherent characteristics that distinguish

these networks from the other wireless networks like ad hoc networks or cellular net-

works. It is not possible to use a global addressing scheme for the deployment of a

relatively large number of sensor nodes. Thus, traditional IP-based protocols may not

be applicable to WSNs. Sensor nodes are tightly constrained in terms of energy, pro-

cessing, and storage capacities. Thus, they require careful resource management. In

most of the application scenarios, nodes in WSNs are generally stationary after deploy-

ment except for a few mobile nodes. Nodes in other traditional wireless networks are

free to move, which results in unpredictable and frequent topological changes. Routing

protocols in the WSNs mainly depend on the application and the network architecture

of the sensor networks.

Routing in the WSNs can be classified into two broad categories:

(1) Network structure based routing, and

(2) Protocol operation based routing.

Network structure based routing: Flat addressing based routing, hierarchical based

routing, and location based routing can be used depending on the network structure.

In flat addressing based routing, all nodes are typically assigned equal roles or function-

ality. In hierarchical routing, nodes will play different roles defining the hierarchy in

the network. In location-based routing, sensor nodes’ positions are exploited to route

the data in the network.

Protocol operation based routing: Protocol operation based routing can be clas-

sified into multipath based, query based, negotiation based, QoS based, or coherent

routing technique.


Hierarchical routing is based on network structure. It is also known as cluster-

based routing, and is a well-known technique with special advantages related to energy

efficient communication. As this thesis is based on LEACH routing, the literature

survey focusses only different hierarchical routing protocols.

Low Energy Adaptive Clustering Hierarchy (LEACH): In LEACH [1] topol-

ogy is divided in to clusters. Few nodes are selected as cluster heads and other nodes

use these cluster heads as routers to the sink. All the data processing are performed at

cluster head. Cluster heads change randomly over time in order to balance the energy

consumption in nodes. A node becomes a cluster head for the current round if the

chosen random number is less than the following threshold,

Tn =

{ p

1−p.(rmod 1p )

if n in G

0 otherwise (1.2.18)

Here p is the desired percentage of cluster heads (In [2], p is 5% of number of nodes

for maximum lifetime), r is current round, and G is a number, which decides eligibility

to become cluster head and form a set of nodes that have not been cluster heads in

current epoch. Fig.1.12 shows the value of Tn for p = 0.1 and 10 rounds in one epoch.

Figure 1.12: Tn for One Epoch Time in Different Rounds


LEACH was the first protocol which tried achieving the balance in energy consump-

tion among nodes. There were also with some shortcomings in LEACH,

(1) Residual energy of nodes was not considered during cluster head selection.

(2) Probability function for becoming a cluster head was based on the assumption that

all nodes have same initial energy, which is not true in case of heterogeneous networks.

(3) Number of cluster head nodes are not fixed in LEACH due to stochastic selection

depending on probability rule.

Every round in LEACH will have the different cluster numbers as shown in Fig.1.13.

We have chosen p = 0.05 in 100 nodes topology, 5 nodes become cluster head with

highest frequency. After every epoch, every node again becomes eligible to be a cluster

head as all the nodes have become cluster head once in earlier epoch. Fig.1.14 shows

the number of cluster heads in various rounds in different epochs.

Figure 1.13: Frequency of Cluster Heads inLEACH

Figure 1.14: Distribution of Cluster Headsin LEACH

In real situations, sensor nodes drain out non uniform amount of energy due to

different distances between sensor nodes and sink and different transmission rates. In

heterogeneous network there may be two or more groups of nodes which have different

initial energy. If nodes have different amount of energy, then the nodes with more

energy should be cluster heads more often than the nodes with less energy, to ensure


that all nodes die approximately at the same time.

Fixed-LEACH is one of the solutions to this problem. The number of cluster heads

are fixed in Fixed-LEACH as shown in Fig.1.15 and the frequency remain fixed as shown

in Fig.1.16. But as the nodes choose its nearest cluster head, the number of supported

nodes may be different for each cluster head. This leads the uneven energy dissipation

among nodes. In this thesis, we have proposed a better solution compared to Fixed-

LEACH, which provide more balanced energy consumption in a WSN.

Figure 1.15: Frequency of Cluster Heads inFixed-LEACH

Figure 1.16: Distribution of Cluster Headsin Fixed-LAECH

We can also reduce the energy consumption in LEACH algorithm using compression

scheme for data aggregation in wireless sensor network. Such a scheme was proposed

by Kasirajan et al. [60] (2010). More than 50% of energy was saved with low overhead

and less than 5% of distortion.

Other Hierarchical Protocols: After LEACH, several algorithms have been de-

rived to form the energy efficient wireless sensor network while balancing remaining

energy level among the nodes. LEACH inspired many hierarchical protocols such as

Power-Efficient Gathering in Sensor Information System (PEGASIS) [14], Threshold

sensitive Energy Efficient sensor Network protocol (TEEN) [12] and Hybrid Energy

Efficient Distributed clustering (HEED) [15] etc..


Manjeshwar et al. [12, 13] (2001,2002) had proposed two hierarchical routing proto-

cols, TEEN and APTEEN; these protocols are designed for time-critical applications

using TDMA schedule. Lindsey et al. [14, 17] (2002) proposed PEGASIS, an enhanced

protocol over LEACH to extend network lifetime by using only one node in a chain to

transmit to the sink instead of multiple nodes. Younis et al. [15, 16] (2004) proposed

a Hybrid Energy-Efficient Distributed Clustering (HEED). They assumed availability

of multiple power levels in sensor nodes. Ye et al. [18] (2005) proposed the algorithm

EECS, which elects cluster heads with more residual energy through local radio com-

munication while achieving good cluster head distribution. Hansen et al. [19] (2006)

have shown that using a minimum separation distance between cluster heads improves

energy efficiency, measured by the number of messages received at the base station

per unit energy consumed. Junping et al. [20] (2008) improved LEACH and proposed

TB-LEACH. In this algorithm, competition for cluster heads no longer depends on a

random number as in LEACH. Nodes which have the shortest time interval for each

node’s random time interval will win the competition and become cluster heads en-

sure that the partition of cluster is balance and uniform. Kumar et al. [21] (2009)

proposed energy efficient heterogeneous clustered scheme for wireless sensor networks.

They improved lifetime and performance of the network using weighted probability of

the election of cluster heads. Otgonchimeg et al. [22] (2009) proposed Energy Efficient

Clustering algorithm for Event-Driven (EECED) wireless sensor networks. This algo-

rithm aimed at prolonging the lifetime of a sensor network by balancing energy usage

of the nodes. EECED makes higher chances to be selected as cluster head for the nodes

with more residual energy. Said et al. [61] (2010) proposed Improved and Balanced

LEACH (IB-LEACH) to decrease probability of failure of nodes and to prolong the time

interval before the death of the first node. The related work for hierarchical routing is

summarized in the Table 1.4.


Table 1.4: Different Routing Techniques

Algorithm Clustering Rule

LEACH [1] Random probabilistic clustering.LEACH-C [2] Centralized clustering algorithm to produce better clusters.LEACH-F [2] Clustering with fixed number of clusters.TEEN [12] Total number of transmissions are reduced by allowing the

nodes to transmit only when the sensed value less than athreshold value.

APTEEN [13] New TDMA schedule is introduced to avoid collisions of close-by nodes which fall in the same cluster. As these nodes sensesimilar data and try to send their data simultaneously.

PEGASIS[14, 17]

Each node communicates only with a close neighbor and takesturns in transmitting to the base station, thus reducing theamount of energy spent per round.

HEED [15, 16] Cluster heads are selected periodically according to a hybrid ofthe node residual energy and node proximity to its neighborsor node degree.

EECS [18] Clustering based on residual energy through local radio com-munication while achieving better cluster head distribution.

Hansen et al.[19]

Clustering for large sensor networks using a minimum sepa-ration distance.

TB-LEACH[20] Nodes which have the shortest time intervals from randomlyselected time interval by nodes will win the competition andbecome cluster heads to ensure that the partition of cluster isbalanced and uniform.

EEHC [21] Cluster head selection based on weighted election probabilitiesaccording to the residual energy in each node. Heterogeneoustopology is assumed.

EECED [22] Nodes with more residual energy have more chances to beselected as cluster head.

IB-LEACH [61] Clustering using characteristic parameters of heterogeneity.MMCR [62] Multi-interface multi-channel routing for enhancing capacity

of wireless sensor network.

1.3 Thesis Organization 27

1.3 Thesis Organization

Objective of the work done in this thesis is to improve the conservation of energy and

balancing the energy consumption of sensor nodes, which leads to improvement in the

lifetime of a sensor network. The anchor free localization of sensor nodes in wireless

sensor networks have also been investigated.

This thesis is organized in the following structure. Chapter 2, discuses the base sta-

tion positioning based on multipath loss and a mathematical model have been presented

to analyze the base station positioning performance in terms of total energy used from

different points. In chapter 3, anchor free localization technique is discussed. In chapter

4, modifications have been proposed in the LEACH algorithm, to improve its perfor-

mance in terms of lifetime and balancing the energy consumption in nodes along with

variable duty cycle algorithm for balancing energy consumption among sensor nodes. In

chapter 5, bottleneck nodes have been defined and detected along with their criticality.

Chapter 6, concludes the thesis.

Chapter 2

Placement of Base Station in aWireless Sensor Network

2.1 Introduction

Base station location is an important factor in a wireless sensor network as it affects

its lifetime. In this chapter, the question of “Where should the base station be placed

in two tiered wireless sensor network field ?”1 has been investigated. The objective is

to minimize the overall energy consumption in a wireless sensor network. A heuristic

algorithm has been proposed to find such a base station location. Considering some

nodes to be far enough to use a different path loss model for their signals to the base

station, our proposed algorithm considers two categories of nodes and hence two differ-

ent path loss models based on their distance from the base station. The results show

that the new algorithm provides a better base station location than earlier methods.

The overall energy consumption is quite close to the optimal solution.

1Rajiv Kr. Tripathi, Yatindra Nath Singh and Nishchal Kr. Verma, “Two tiered wireless sensornetworks - Base station optimal positioning case study,” Published in IET Journal Wireless SensorSystem, Vol.2, Issue.4 December 2012, pp. 351-360..

2.2 Related Work 29

2.2 Related Work

In the literature so far, many heuristic algorithms have been proposed to find sub-

optimal solutions [39] of optimum base station positioning in two tiered wireless sensor

network. Although these heuristics are shown to be effective, their algorithms depend on

the topology and are based on structural metrics. Akkaya et al. [5] discussed a different

method for finding the optimal position of a base station. Pan et al. [3] considered only

free space loss and found that minimum enclosing circle gives the maximum lifetime for

a sensor network.

The optimal location of a base station can be analyzed with respect to minimum

energy expenditure or maximum lifetime of a sensor network. Even though both seems

to have the same objectives but this is not true. Pan proved in his paper that the

center of a minimum enclosing circle, is the optimal location for the n-of-n lifetime.

n-of-n lifetime means the time after which the first node dies or time upto when n out

of n nodes remain alive. The minimum enclosing circle is equivalent to minimizing the

maximum distance between the base station and any sensor node in the network, i.e.,

(x0, y0) =arg min(x,y)

(max∀i∈N

√(x− xi)2 + (y − yi)2

). (2.2.1)

Here (x0, y0) is the center of the minimum enclosing circle. This approach is also

known as the minmax algorithm for the optimum base station location [63], which

provides maximum lifetime for a static single base station in a two tiered WSN. Recently

Paul et al. [6] proposed an optimal location of base station by combining multi-hop

inter-cluster routing with single-hop intra-cluster routing where the death of the first

sensor node indicates the end of network lifetime. Paul used the center of minimum

enclosing circle as the optimal location of the base station.

2.2 Related Work 30

We prove that the overall energy consumption is minimized at the centroid of the

nodes in Appendix A, when path loss exponent α is 2. In this method, average energy

expenditure is minimized but first nodes may die earlier compared to minmax approach,

as energy consumption in the sensor nodes, is rather uneven. For example, it may

happen that most of the nodes are close to the base station, while a few nodes are

far from it. Therefore, these far off sensors use more energy than nearer ones and

hence deplete their energy at a faster rate and die sooner. This approach in known as

minimum average or minavg [63].

Vass et al. [63] has also shown that maximum relative energy is a better approach as

compared to minimum average or minmax approach. This approach uses current status

of the sensor nodes, thus being more effective for a short period of time. But in the long

run, minavg approach is a better choice. Lin et al. [31] minimized the total distance

from sensor nodes to the base station to reduce the number of data relays, and placed

the base station in an area with a high density of sensor nodes. This is the point where∑ni=1wi.di is minimized. Here di is the distance between sensor i and base station and

wi is sensor’s density in the vicinity of sensor i.

Son et al. [64] proposed that Fermat point is the best point for positioning the base

station. He used hexagonal topology for showing lifetime optimization. Power aware

base station positioning was proposed in [38]. It was proved that the choice of position

of base station depends on the data rate or equivalently, the power efficiency of the

network.

We have used a weighted centroid method for finding the optimal base station loca-

tion. This method has also been recently used for localization algorithms in the wireless

sensor networks [65-70].

2.3 Problem Formulation 31

2.3 Problem Formulation

The energy consumption in network for one round is the sum of energy dissipated by

all the clusters.

ERound =k∑j=1

ECluster(j). (2.3.2)

Now using equation (1.1.7) from energy consumption model,

ERound =L.(2n− k).Eelec + n.L.EDA +k∑i=1

Eamp(L, dbs(i)) +n∑i=1

Eamp(L, dch(i)).

(2.3.3)

As signals from all the nodes are assumed to suffer free space loss in reaching to respec-

tive cluster head, and following [2],

n∑i=1

Eamp(L, dch(i)) =L.(n− k).εfs.M2

2πk. (2.3.4)

Here, M is the length of the square field used for WSN deployment. There are three

different cases depending on distance between cluster head node and the base station.

Case 1: When all the nodes in a sensor network are near to the base station, such

that there is free space loss for the transmission from all nodes to base station. Then

ERound is given by

ERound =L

[(2n− k).Eelec + n.EDA + (n− k).εfs.

M2

2πk+ εfs

k∑j=1

d2j

]. (2.3.5)

Here dj is the distance between cluster head and the base station. After nk

rounds when

every node has become cluster head once, total energy spent is given by

Etotal =L.n

k


M2

2πk

]+ L.εfs

n∑j=1

d2j . (2.3.6)


Case 2: When base station is far away from all the nodes, that is multipath loss exists

for transmission from nodes to base station. Then Etotal spent in nk

rounds is given by

Etotal =E1 + L.εmp

n∑j=1

d4j , (2.3.7)

where

E1 =L.n

k


M2

2πk

]. (2.3.8)

Case 3: When some nodes are near and some nodes are far away from the base station

then Etotal is given by

Etotal =E1 + L.εfs

p∑i=1

(d2i ) + L.εmp

q∑j=1

d4j . (2.3.9)

Here node i and node j are from different sets, and p number of nodes are nearer to base

station and q number of nodes are farther from base station (di<d0 ⇒ nearer nodes

and dj ≥ d0⇒ farther nodes). Since E1 is same in all the three cases, we use second

and third term in equation (2.3.9) for further investigation.

For Case 1, Energy for transmitting data to base station Ebs in each nk

rounds is

Ebs =L.εfs

n∑j=1

d2j . (2.3.10)

For Case 2,

Ebs =L.εmp

n∑j=1

d4j . (2.3.11)

For Case 3,

Ebs =L.εfs

p∑i=1

d2i + L.εmp

q∑j=1

d4j . (2.3.12)

We need to find optimal location for the base station, which minimizes Ebs.


Figure 2.1: A Wireless Sensor Network topology

Let n sensor nodes be uniformly distributed in a rectangular field at (x1, y1), (x2, y2),

..., (xn, yn) respectively, and base station be deployed at (x, y) as shown in Fig.2.1.

The Euclidean distance between the base station and the nodes are d1, d2, d3, ..., dn

respectively. Here di is

di =√

(x− xi)2 + (y − yi)2. (2.3.13)

Case 1 (di < d0 ;∀ i): Let d2 be the sum of squares of all the Euclidean distances. As

all the nodes will have only free space loss, energy consumption in amplification, Ed2 in

the sensor network will be sum of amplifier energy consumption of the all the nodes.

Ed2 =L.εfs.(d21 + d2

2 + d23 + ....+ d2

n) (2.3.14)

Sum of square of all the Euclidean distances, d2 will be minimum at the centroid of

nodes [93, 95, 96]. Thus amplification energy consumption Ed2 will also be minimum if

base station is placed at the centroid.

Case 2 (di ≥ d0 ;∀ i): When all the nodes are far away from the base station and will

have only multi-path loss. Then we need to minimize

Ed4 =L.εmp.(d41 + d4

2 + d43 + ....+ d4

n), (2.3.15)

for optimal base station location.

2.4 Algorithm for Base Station Location 34

Ed4 will be minimum at a point, say F ; we can determine point F only by heuristic

search methods. This point F converge to the centroid of nodes when all the nodes are

placed symmetrically.

Case 3 (Some nodes with di < d0 and remaining nodes with di ≥ d0): When

few node are near and other remaining nodes are far away from the base station then

we have to minimize the following equation.

Ed2,4 =L.εfs.(d21 + ..+ d2

p) + L.εmp.(d41 + ..+ d4

q). (2.3.16)

Where p+ q = n and p, q ≥ 1.

Now minimizing Ed2,4 will depend on which type of nodes are dominating in energy

expenditure, nearby nodes or farther nodes. If nearby nodes are dominating i.e. p >> q,

then centroid of p nodes will be the optimal position. If q ≥ p, then farther nodes will

decide the optimal location for the base station and then centroid of q nodes (if q

nodes are symmetrically placed) will be the optimal position. When both type of nodes

are equally dominating, the optimal location of the base station can be found by the

proposed algorithm.

2.4 Algorithm for Base Station Location

Problem: To find the location of base station where Ed2,4 is minimized.

Step 1: Find centroid (Cx, Cy) of the nodes distributed in the field. This is the point,

where Ed2 is minimized, and is given by

Cx =

∑ni=1 xin

, (2.4.17)

and

Cy =

∑ni=1 yin

. (2.4.18)


Step 2: Find the nodes which are at less than d0 distance from the centroid.

Step 3: Weights are calculated using centroid for all the nodes as

wi =

{1 if diC<d0diC

2

d02 if diC≥d0

(2.4.19)

Here diC is the distance between ith node and the Centroid. The justification for above

mentioned weights is as follows.

Calculation of weights for proposed algorithm: We take weight w as 1 for the

nodes which are at less than d0 distance from the centroid, and something else for other

nodes which are at equal or higher distance than d0 from the centroid. As the proposed

point will be weighted average of all points, the weights w for all the node will be 1,

when all the nodes are closer than d0 from centroid. Thus proposed point P is same as

centroid. The proposed point will be different only when some nodes are farther than

d0 distance from centroid.

Let us have a square field with length of side ‘M ’. We assume that M = d0/√

2.

In this case wherever we place our base station, only free space loss will be suffered by

transmission from all the nodes inside the field (see Fig.2.2).

Figure 2.2: Weights calculation for Algorithm


We have taken three nodes at (x1, y1), (x2, y2) and (x3, y3) in the field, then the base

station location P (Px, Py) is given by proposed point will be P (Px, Py) as all the nodes

can suffer only free space loss

Px =x1 + x2 + x3

3, (2.4.20)

and

Py =y1 + y2 + y3

3. (2.4.21)

But when side M > d0/√

2 and let the base station is at centroid of nodes. Then two

nodes will suffer free space loss and third node will suffer multipath loss. If weight to

(x3, y3) is w and for other nodes it is 1, then proposed point P (Px, Py) is given by

Px =x1 + x2 + w.x3

2 + w, (2.4.22)

and

Py =y1 + y2 + w.y3

2 + w. (2.4.23)

In equation 2.4.22 and 2.4.23, assume w is very large say ∞, then Px will become x3

and Py will be y3. If w is very small say 0, then Px will become x1+x2

2and Py will be

y1+y22

. Thus, we need to make these weights more than 1 so that proposed point shifts

towards nodes, which are having multipath loss.

Weights must increase with distance from the centroid for shifting proposed point

towards nodes which are having multipath loss. Using w as diC2

d02 provide us good results

as w is always greater than 1 and proportional to the distance and thus with amplifier

energy also.

w =εmp.d

4iC

εfs.d2iC

=εmp.d

2iC

εfs=

(diC)2

(d0)2. (2.4.24)


Step 4: Determine the weighted average of nodes’ positions as proposed optimal po-

sition (xp, yp) for the base station.

xp =

∑ni=1wi.xi∑ni=1wi

, (2.4.25)

and

yp =

∑ni=1wi.yi∑ni=1wi

. (2.4.26)

This is a heuristic algorithm which provides an approximate solution. For more accurate

solution (theoretical optimal point), we can place our base station in such a way that

the distance from all the nodes which are at less than d0 from the centroid, may increase

up to the maximum of d0 while reducing the distance from the remaining nodes which

are at greater than d0 distance from centroid. We have cited an example which give

more insight into the algorithm and thus justify it.

2.4.1 Optimal location of base station - An example

Let us consider three points in a 150×150 square area plane, at positions (0, 150),(0, 0)

and (150, 150). The centroid for these points turns out to be at (50, 100). The distances

from the centroid to points 1, 2 and 3 (see Fig.2.3) are d1C , d2C & d3C respectively. Here,

d1C = 70.7107 and d2C = d3C = 111.8034.

Thus amplifier energy in J/bit-node for three nodes at centroid is

EC =(εfs.d21C + εmp.d

42C + εmp.d

43C)/3 = 1.5208× 10−7 J/bit− node (2.4.27)

We have assumed the values of εmp=1.3×10−15J/bit/m4 as multipath loss constant and

εfs=10−11J/bit/m2 as free space loss constant in this example. This gives us d0 = 87.7m.


Figure 2.3: Distances from Centroid ofdistributed nodes

Figure 2.4: Distances from TheoreticalOptimal Position of base station

Now we calculate the theoretical optimal position (see Fig.2.4), by placing base

station at d0 from point 1 along the perpendicular bisector of line joining points 2 and

3. This point is ( d0√2,150- d0√

2). It will have d1O, d2O and d3O distances from points 1,

2 and 3 respectively. Now d1O = 87.7000 and d2O = d3O = 107.6444. The amplifier

energy in J/bit-node for three nodes at the optimal point O is

EO =(εmp.d41O + εmp.d

42O + εmp.d

43O)/3 = 1.4200× 10−7 J/bit− node (2.4.28)

The proposed base station location P using weighted average is given by

xp =0 + 0 +

d23Cd20.150

1 +d22Cd20

+d23Cd20

=57.35, (2.4.29)

and

yp =150 + 0 +

d23Cd20.150

1 +d22Cd20

+d23Cd20

=92.65. (2.4.30)

This point (57.35, 92.65) will have d1p, d2p & d3p as distances from points 1, 2 and 3

(see Fig.2.5). Now d1p = 81.1051 and d2p = d3p = 108.9635. Thus amplifier energy in

J/bit-node for the three nodes with base station at point P , is

EP =(εfs.d21p + εmp.d

42p + εmp.d

43p)/3 = 1.4410× 10−7 J/bit− node (2.4.31)


Figure 2.5: Distances from ProposedPoint as base station

Figure 2.6: Distances from center of min-imum enclosing circle as base station

We also calculated the amplifier energy by considering center of minimum enclosing

circle as base station location (see Fig.2.6). The center for minimum enclosing circle

comes out to be (75, 75). This will have d1M , d2M and d3M distances from points 1, 2

and 3 respectively. These distances are d1M = d2M = d3M = 106.066. The amplifier

energy EMEC in J/bit-node for three nodes at this point is

EMEC =(εmp.d41M + εmp.d

42M + εmp.d

43M)/3 = 1.6453× 10−7 J/bit− node. (2.4.32)

From these results, we see that the proposed point leads to,

EP − EOEO

× 100 =1.47%, (2.4.33)

more energy consumption compared to optimal location of base station.

While using centroid energy consumption exceeds by

EC − EOEO

× 100 =7.10% (2.4.34)

with respect to optimal point.


If we consider center of minimum enclosing circle as base station location then dif-

ference in amplifier energy between optimal location and center of minimum enclosing

circle is

EMEC − EOEO

× 100 =15.86%. (2.4.35)

Using Lin’s weighted method [31], the base station deployment comes at (0, 150) and

the distance from node 1 and node 3 is now 150 and from node 2 is zero. so the amplifier

energy in J/bit-node for the three nodes at this point will be EL.

EL =(εmp.d41 + 0 + εmp.d

43)/3 = 4.38× 10−7 J/bit− node. (2.4.36)

where d1 = d3 = 150 and d2 = 0 and compare to optimal position the amount of excess

energy is given by

EL − EOEO

× 100 =208.45%. (2.4.37)

Comparison of existing algorithms with our algorithm is shown in Table 2.1. This shows

that how much excess energy is used in these methods [31, 3, 63] and proposed method

compared to optimal location.

Table 2.1: Excess energy used by different methods compared to the optimal locationMethod Excess Energy Used

Weighted position by Lin [31] 208.45%Minimum enclosing circle or minmax [3] 15.87%

Centroid or minavg [63] 07.10%Proposed weighted position 01.47%

2.5 Simulation And Results 41

2.5 Simulation And Results

Example in previous section shows a comparison of different techniques to find optimal

location of base station. Merely citing an example do not provide the novelty of work.

Thus in this section, generic results are shown to prove the validity of our hypothesis.

We have calculated the average amplification energy in J/bit-node, Ec, of all the

nodes, for the base station at centroid is

EC =Ek∑n

i=1 dαiC

n. (2.5.38)

Average amplification energy in J/bit-node, Ep, for base station at the proposed point

is given by

EP =Ek∑n

i=1 dαiP

n. (2.5.39)

Average amplification energy in J/bit-node, EMEC , for base station at the center of

minimum enclosing circle is given by

EMEC =Ek∑n

i=1 dαiM

n. (2.5.40)

Here E2 and E4 are εfs and εmp respectively. For nodes having diC or diP or diM< d0,

α = 2, and for all others, α = 4.

The percentage reduction in average amplification energy with base station at pro-

posed point (say P) compared to base station at centroid is given by

Percentage Reduction =EC − EPEC

.100%. (2.5.41)

The percentage reduction in average amplification energy with base station at center of

minimum enclosing circle compared to base station at centroid is given by

Percentage Reduction =EC − EMEC

EC.100%. (2.5.42)


Simulation was performed for 1000 different random sensor placements. Corresponding

Ec, Ep and percentage reduction have been evaluated. Average of this percentage

reduction is taken and plotted for different number of nodes (5 to 200 in step of 10)

distributed in different size field (square region with side length 30 meter to 500 meter

in steps of 10 meter).

In Fig.2.7, we have shown average percentage reduction by placing base station at

proposed point compared to centroid of distributed nodes. This has been done for

different number of nodes and length of side of square field. We see that for the area

with side less than 150 meter almost all the nodes suffer free space loss (as the size of

topology is small, farthest node from the centroid of nodes will have distance less than

d0) so point P converges to centroid and the percentage reduction become zero in this

area (as all the weights become 1). The reduction peaks when number of nodes ranges

from 5 to 50 and length of square field between 160 meter to 270 meter (this is region

where both types of nodes are existing, nodes which suffer free space loss as well as the

multipath loss. As some nodes will have distance less than d0 and rest will have greater

than d0 from the centroid of distributed nodes). It can be observed that the percentage

reduction is significantly large in this region and varies from 0 to 4.85%. For side length

of more than 300 meter and for 5 number of nodes the average percentage reduction

becomes negative as the weights are high in magnitude comparison to the side less than

300 meter of topology weights. But for the higher number of nodes because of average

process the higher weights are not dominating. Thus the average percentage reduction

is near to zero in this case.


Figure 2.7: Average percentage reduction in amplifier energy for proposed point com-pared to centroid

Figure 2.8: Average percentage reduction in amplifier energy when negative values areclipped to zero

Fig.2.8 shows the results when only the positive average percentage reduction has

been considered. The results for negative reduction are clipped to zero to emphasize

positive reduction results in the figure. This gives the region where our algorithm will

be best fit. The ignored values corresponds to large field with few nodes or small field

with large number of nodes, which is not of much interest.


Figure 2.9: Average percentage reduction in amplifier energy for proposed point com-pared to centroid

Figure 2.10: Average percentage reduction in amplifier energy when negative values areclipped to zero


Fig.2.11 shows the improvement w.r.t. centroid when center of the minimum enclos-

ing circle is considered as the base station location. This shows that it is never better

than centroid for given distribution. Fig.2.9, Fig.2.10 and Fig.2.11 present the three

dimensional figures for the results shown in Fig.2.7, Fig.2.8 and Fig.2.12 respectively.

Figure 2.11: Average percentage reduction in amplifier energy for minimum enclosingcircle compared to centroid

Figure 2.12: Average percentage reduction in amplifier energy for minimum enclosingcircle compared to centroid


We have used Table 2.2 and 2.3 to validate the results shown in Fig.2.7 and Fig.2.8.

We have calculated ratio of number of nodes (Nd2) lying inside the circle of radius d0 to

the ones outside the circle (Nd4) with center being the centroid and then the proposed

point respectively in Table 2.2 and 2.3. This node ratio is given by

Node Ratio =Nd2

Nd4

. (2.5.43)

As we increase number of nodes for a constant length of square side usually this ratio

decreases. This shows that number of nodes who suffer multipath loss increases with

node density. Table 2.2 and 2.3 verify the same because as we increase the number of

node for a constant size of topology and vice versa, gain in amplifier energy at proposed

point reduces. This is because the point F is dominated by number of nodes with

multipath loss.

Table 2.2: Nodes’ ratio when centroid as centerLength of square side Number of Nodes

⇓ 30 50 70 90 110180m 3.90 3.49 3.27 3.22 3.14200m 2.01 1.79 1.70 1.66 1.64220m 1.22 1.14 1.07 1.06 1.05240m 0.89 0.80 0.77 0.76 0.76260m 0.66 0.61 0.59 0.58 0.57

Table 2.3: Nodes’ ratio when proposed point as centerLength of square side Number of Nodes

⇓ 30 50 70 90 110180m 3.75 3.42 3.23 3.17 3.11200m 1.85 1.69 1.62 1.60 1.59220m 1.09 1.07 1.03 1.02 1.02240m 0.78 0.75 0.73 0.73 0.73260m 0.59 0.57 0.56 0.55 0.55

Results in Table 2.2 and 2.3 verify the results of Fig.2.7, Fig.2.8, Fig.2.9 and Fig.2.10.

2.6 Conclusions 47

Table 2.4 shows the distance between the centroid and the proposed point. In this

table, for a fixed field size, as we increase the number of nodes this distance decreases.

Table 2.4 also verify our results that as we increase the node density for a smaller

constant size of topology the proposed point and centroid of nodes comes closer to each

other. Also the gain in amplifier energy at proposed point reduces as the centroid of

nodes dominates. For smaller size of topology, proposed point merge with centroid so

the distance become zero for smaller topology. As we increase the size of topology the

distance between the proposed point and centroid increase this shows that centroid is

less dominating as we increase the size of topology.

Table 2.4: Distance in meter between centroid and point PLength of square side Number of Nodes

⇓ 10 50 90 130 17030m 0 0 0 0 0180m 3.8 2.3 1.8 1.6 1.4330m 21.3 11.4 8.7 7.2 6.7480m 34.6 17.6 13.0 11.6 10.3

2.6 Conclusions

Lifetime maximization and overall energy consumption minimization are two different

problems in a wireless sensor network. The optimal point for the maximum lifetime of

a sensor network is the center of the minimum enclosing circle of all nodes. If all the

nodes have free space path loss (α = 2) then the energy consumption is minimized when

the base station is placed at centroid. If all the nodes suffer only multipath loss (α = 4)

then the optimal base station location will be point F . For the case when both type

of nodes (some with free space path loss and some with multipath loss) are there in a

sensor network, we have proposed a new location of the base station for minimization of

2.6 Conclusions 48

energy consumption. This point is centroid of weighted position of the deployed nodes.

These weights are dependent on the path loss. Our proposed point provides a sub-

optimal solution. Results show that the proposed point provides a better performance

compared to centroid as well as center of minimum enclosing circle for sensor nodes.

These results can be used for deployment of a base station in two tiered wireless sensor

networks.

Chapter 3

Anchor Free Localization Techniquefor Singlehop Wireless SensorNetwork

3.1 Introduction

Most of the applications of wireless sensor network are associated with position infor-

mation. Generally GPS devices are not used in large scale sensor network due to the

cost and poor availability of GPS signals due the environmental problems. It is very

important to acquire the nodes position without GPS. As in most of the applications

sensor nodes are directly connected to the base station. We have proposed an anchor

free localization algorithm for singlehop wireless sensor network. The proposed algo-

rithm is based on internode distances. Average of the internode distances is used as

main metric to localize the reference node in the proposed algorithm.

3.2 Related Work 50

3.2 Related Work

Capkun [8] proposed first Self Positioning Algorithm (SPA) for Ad-Hoc wireless net-

works. After that, Anchor Free Localization (AFL) [10], Assumption Based Coordinates

(ABC) [9], Knowledge-based Positioning System (KPS) [55], GPS-less low cost outdoor

localization [7], Matrix transform-based Self Positioning Algorithm (MSPA) [57], Mobile

Geographic Distributed Localization (MGDL) [71], Ad Hoc Positioning System (APS)

[47] were proposed.

In SPA [8] algorithm, every node establishes its local coordinate system by setting

itself as the origin. Two other nodes are randomly chosen such that the three nodes

do not lie on the same line to minimize triangulation error and can communicate with

each other. If from a node the distance to each of the three nodes can be estimated

then it can be localized.

Anchor Free Localization (AFL) [10] algorithm has two phases. First phase is a

heuristic that produces a layout which looks similar to the original layout. In second

phase, nodes locally correct and balance the optimal solution by adopting the opti-

mization algorithm to ensure that the energy in new location is less than that in the

original location. In AFL, localization is dependent on communication range of nodes

and gives good result only when average connectivity of network is more than seven.

Localization error may increase due to unavailability of direct path between nodes and

results into an estimate which is multiple of communication radius R, depending on

number of hops.

3.2 Related Work 51

Assumption Based Coordinates (ABC) [9] uses cooperative ranging approach for

localization. This algorithm localizes one unknown node at a time by making assump-

tions, compensating the errors through corrections and use of redundant calculations as

more and more information becomes available. In ABC accumulation of errors increases

with number of beacon-free node.

Knowledge-based Positioning System (KPS) [55] algorithm is based on pre-configured

knowledge of probability distribution of configuration. This algorithm uses two main

concepts which are configuration point and the probability distribution function. Con-

figuration point is the location of the determined point which is in the node group, when

deploying the nodes. The probability distribution function is obeyed by each group’s

nodes after the sensor nodes’ configuration.

Bulusu [7] in his paper on GPS-less low cost outdoor localization, used overlapping

region of nodes to localizes new nodes considering some reference nodes which are

already localized. Nodes localized themselves to the centroid of their reference points

and localization error depend on separation distance between two adjacent reference

nodes and the transmission range of these reference points.

Wang [57] developed a clustering-based approach for the local coordinate system for-

mation wherein a multiplication factor is introduced to regulate the number of master

and slave nodes and the degree of connectivity among master nodes. Using homoge-

neous coordinates, Wang derived a transformation matrix between the two Cartesian

coordinate systems to efficiently merge them into a global coordinate system.

APS [47] and Peng et al. [50] used Angle Of Arrival (AoA) capability of the nodes

to derive position information. Moses et al. [11] used time of arrival and direction of

arrival to localize nodes for anchor free localization.

3.3 Challenges with Localization Techniques 52

3.3 Challenges with Localization Techniques

In SPA algorithm, communication cost and convergence time increases exponentially

with the number of nodes. Thus, SPA algorithm is not useful for energy constrained

WSN. ABC algorithm can be realized easily, but the localization accuracy is poor.

KPS require deployment knowledge which is generally not available with sensor nodes.

GPS-less low cost outdoor localization also depend on communication range and sepa-

ration of reference nodes. AFL algorithm is fully distributed, only requires a relatively

small number of communications and simple calculations, and has good scalability and

robustness. Apart from these, following problems are generally faced by this algorithm.

3.3.1 Localization using Hop Count

There are two problems with use of hop count as a measurement of distance [72].

1. Distance measurements are always integral multiples of maximum radio

range R : In AFL localization, five reference nodes n0, n1, n2, n3 and n4 are found

in phase 1 as shown in Fig.3.1. Node n0 lies in the center of topology. For a node nj,

hop-counts h0,j, h1,j, h2,j, h3,j and h4,j from n0, n1, n2, n3 and n4 respectively, are used

for localization. Localization is expressed in polar coordinates as (ρj, θj)

ρj =h0,j ×R; (3.3.1)

here R is maximum radio range.

θj =arctan

(h1,j − h2,j

h3,j − h4,j

). (3.3.2)


Figure 3.1: Localization of a node in AFL

As we see in Fig.3.2, node A and B lie within one hop transmission from center node,

thus in AFL localization ρA = ρB = R as h0,A = h0,B = 1. Similarly for node C and

node D, ρC = ρD = 2R as h0,C = h0,D = 2. Thus nodes are localized with resolution of

maximum radio range R. This inaccuracy corresponds to a total error of about 0.5R

per measurement, which can be too high for some applications.

Figure 3.2: Nodes are localized integral multiples of maximum radio range R

Nagpal [73] had shown that even better hop count distance estimates can be com-

puted by averaging distances with neighbors, which can reduce hop count error down

to 0.2R. But for multihop scenario, it can accumulate to high localization error. As

average connectivity increases, the probability of nodes lying along the straight-line

path increases rapidly this happens till average connectivity of 15 nodes, there after

any further increase in sensor density has diminishing returns. Thus algorithms using

hop count techniques work properly with average connectivity in the range of 7 to 15.


Thus many different nodes will be assigned same ρj in AFL localization. If R is

increased then more number of nodes will have same ρj and if decreased then problem

of unavailability of direct edges increases, This is discussed in next subsection.

2. Problem of unavailability of direct edges : As we see in Fig.3.3. Node A

and B are not in direct communication range as actual distance between A and B, i.e.

dAB >R. Similarly node A and node C are not in direct communication range due to

obstacle in between these nodes. Here hA,B = 3 and hA,C = 4, thus algorithm using

hop count localization will localize node B at 3R distance and node C at 4R distance

away from the node A respectively.

Figure 3.3: Localization using Hop Count

Such cases will be very frequently observed in a sensor network with low density

of sensor nodes. Thus unavailability of direct edges may lead to substantially high

localization errors. Only in case of node D, the hop distance measurement will be

correct as hA,D = 4 as the node D is approximately 4R away from node A.

For different value of communication range, the connectivity varies and thus average

distance due to number of hops. Actual average distance between nodes remains con-

stant as topology is fixed. Error between actual average distance and hopcount average

distance is

%Error =(Dhave −Dave).100

Dave

, (3.3.3)


We have calculated actual average distance, Dave, between 40 nodes randomly dis-

tributed in a 100× 100 m2 field and then average distance in terms of number of hops,

Dhave, between nodes by choosing different communication range from 30m to 50m

with step of 5m. Results are shown in Table 3.1.

Table 3.1: Average Actual Distance vs Average Distance due to number of hopsMax. RadioRange(m)

AverageConnectivity

Dave(m) Dhave (m) % Error

30 9.40 946.6 1395.7 47.4435 12.20 946.6 1383.3 46.1340 14.75 946.6 1429.0 50.9545 17.75 946.6 1431.0 51.1650 21.20 946.6 1445.0 52.64

The average of this percentage error comes out to be 49.66%. Thus one can conclude

that merely using hop counts will give an error of approximately 50% for localization

in any algorithm irrespective of average connectivity for the nodes.

3.3.2 Accumulation of Localization Error

In the present techniques which are used for anchor free localization, first the reference

nodes are detected, and then all other nodes are localized with the help of these reference

nodes. For multihop scenario, the nodes are localized in tiered fashion. First tier nodes

which are nearest to reference nodes, are localized first with some localization error.

Then second tier of nodes are localized using the first tier nodes as a reference nodes.

So localization error of first tier nodes is directly added to second tier of nodes. Thus

localization error accumulates as we localize higher tier nodes. This is the serious

problem with ABC algorithm [9], where the average estimated position error reaches as

much as 60%.

3.4 Metric for Proposed Algorithm 56

3.4 Metric for Proposed Algorithm

Let n sensor nodes be randomly distributed in a topology at (x1, y1), (x2, y2), (x3, y3),...

and (xn, yn). Let distances between node i and other nodes be di1, di2, ....din. Here dij

is defined as

dij =√

(xi − xj)2 + (yi − yj)2 (3.4.4)

The average distance of a node (Dave) among distributed nodes is having nearly similar

estimation to the distance from that node to the centroid of nodes (Dc). As we do have

position information to calculate the centroid, we use Dave for localization. This Dave

for ith node among n distributed nodes is defined as [93, 95, 96].

(Dave)i =

∑nj=1 dij

n− 1for ∀ j; j 6= i (3.4.5)

Normalized Dave can be obtained by dividing maximum Dave among all nodes to Dave

to particular node. ˆDave is given by:

ˆDave =Dave

(Dave)max(3.4.6)

We have plotted ˆDave and Dc (Normalized distance of all the nodes from the centroid

of distributed nodes) for 20 distributed nodes in 100 × 100 square meter topology as

shown in Fig.3.4. This shows that as we increase the distance from the centroid of a

node the Dave increase similarly. As we proposed anchor free localization so we have to

localize reference nodes first then other nodes. We used this Dave to localize reference

nodes. Thus using only internode distance we can localize reference nodes.

3.5 Algorithm for Singlehop Localization 57

Figure 3.4: Relation between Dc and ˆDave

3.5 Algorithm for Singlehop Localization

Let n sensor nodes are randomly distributed in a topology.

Step 1 : Every node broadcast a hello message with its id using TDMA scheduling.

Each node calculates (n-1) distances (dij) using RSSI from all other nodes. Further

every node calculates average of all the distance estimates. Thus, Dave for ith node is

calculated using equation (3.4.5).

Step 2 : Every node will broadcast this Dave and the node having highest Dave is

the farthest node from the centroid and will lie at the corner of topology as shown in

Fig.3.5. This node will be first reference node for the system.

Step 3 : Farthest node from the first reference node will be second reference node

as shown in Fig.3.6. This node will always lie in opposite corner of node 1.


Step 4 : Now node 2 will send data of all distances d2j to node 1. Node 1 finds

(d1j + d2j) ∀ j; j 6= 1, 2. The node which has highest value of this sum will be the node

farthest from 1 & 2 nodes. This node will also lie in the corner of topology, shown as

node 3 in Fig.3.7. This node will be third reference node for the system.

Step 5 : Now node 3 find the farthest node from it and this will be fourth refer-

ence node. This node will lie in opposite corner of node 3 as shown in Fig.3.8.

Step 6: Node having minimum Dave will have minimum distance from the centroid.

This node will be the fifth reference node for our protocol. This node will lie at the

center of topology as shown in Fig.3.9 and act as origin for localization.

Thus, we have calculated five reference positions. Now we localize rest of nodes as

follows. Origin is assigned to reference node 5. With respect this node, we calculate

angle of different nodes for localization. Reference node 1 is considered on positive

x axis, and reference node 2 considered near to negative x axis. Reference node 3 is

considered near to positive y axis, and reference node 4 is considered near to negative

y axis.

Thus node j can be localized in the topology by estimating θ as shown in Fig.3.10.

cos(θ) =d2

51 + d25j − d2

1j

2.d51.d5j

(3.5.7)

Thus node j is localized in topology depending on in which quadrant the node is lying.

For example if the node j is lying in 1st quadrant then coordinate for node j is given by

x =d5j.cosθ, (3.5.8)

and

y =d5j.sinθ. (3.5.9)


Figure 3.5: Estimation of Refer-ence node 1





Figure 3.10: Localization fornode j

3.6 Simulation & Results 60

Figure 3.11: Localization Problem for non rectangular sensor field

This method will give incorrect results when the field in which sensor nodes are

distributed is non rectangular e.g. as shown in Fig.3.11. Here the reference nodes are

not diagonally away so will give high triangulation error which lead to wrong estimation

of position of sensor nodes in this sensor field. One need to build additional algorithms

to split such fields into multiple rectangular fields and use this algorithm in them.

3.6 Simulation & Results

We have used the average percentage error of the calculated distances compared to the

true distance between neighbors, as well as Global Energy Ratio (GER) which capture

the true behavior of auto-localization algorithms [10]. The global energy ratio is the

root-mean-square normalized error value of the node-to-node distances and is given by

GER =

√∑i, j: i<j e

2ij

N(N−1)2

(3.6.10)

Normalized error eij is given by

eij =dij − dijdij

(3.6.11)

Here the error eij is the difference between the true distance dij and the estimated

distance from the algorithms, dij.


This measure captures both the edge length errors and the structural error of the

graph, because it has contributions from both nodes that are neighbors as well as nodes

that are not. GER metric also captures the errors in the final configuration due to

erroneous range estimates.

Fig.3.12 shows the graph between GER and number of nodes for different Size of

topology. In the proposed algorithm simulation, we have taken square fields of lengths

100m to 400m with step of 100 and number of nodes varied from 100 to 250 with step

of 50.

Fig.3.13 shows the graph between GER and Size of topology for different communica-

tion range of nodes. GER remains nearly constant. This shows that GER is independent

of size of topology in a wireless sensor network.

Figure 3.12: GER vs size of topology forconstant number of nodes

Figure 3.13: GER vs number of nodes forconstant size of topology


Figure 3.14: Average localization errorvs number of nodes for constant size oftopology

Figure 3.15: Average localization error vssize of topology for constant number ofnodes

We also have used the same metric as used in [72, 45], for localization error estimation

for proposed algorithm.

Error =1

n

n∑i=1

||ei − li||. (3.6.12)

where n is the number of sensors, li denotes the real location of the ith node and ei

denotes the location estimate of the ith sensor where i = 1, ..., n.

We have used same parameters as in GER calculations. Average localization error

for different number of nodes in proposed algorithm is shown in Fig.3.14. Average

localization error decreases with number of nodes.

Fig.3.15 shows the graph between Average localization error and Size of topology

for different communication range of sensor nodes. Average localization error increases

with size of topology. As GER is independent of size of topology average localization

error gives better performance for localization error.

3.7 Conclusions 63

3.7 Conclusions

In this chapter we proposed anchor free localization techniques for singlehop wireless

sensor network using internode distance only. Proposed algorithm is very simple and

effective in terms of average localization error. GER results shows that localization

error decreases with increases in number of nodes. Here we are able to localize the

sensor nodes with average localization error less than 6% error in all topologies. The

proposed new metric Dave is able to perform localization in anchor free scenario.

Chapter 4

Balancing Energy Consumption in aWireless Sensor Network

4.1 Introduction

Balancing energy consumption is an important issue. This leads to maximum lifetime

of a sensor network. Energy consumption in a node depends on many factors such

as distance from the sink (base station), number of nodes supported by a node when

it is a cluster head and duty cycle of transmission by the nodes. Depending on these

parameters, some sensor nodes spend higher amount of energy compared to other nodes.

This leads to the uneven energy consumption, which reduces the time after which the

first node dies in the sensor network. By adjusting these parameters, we can force the

balanced energy consumption among sensor nodes thereby increasing its lifetime. This

thesis pertains to wireless sensor network which is a highly distributed system with very

limited computing capacity and only locally observed information at each node. The

clustering methods which have been given mostly in literature refer to algorithms and

methods when all information is known to the executor of algorithm and he then forms

the clusters based on various parameters. We have not looked into these algorithm

4.2 Related Work 65

as these are impractical for wireless sensor networks. In WSN, we will usually prefer

extremely simple algorithms which can be executed at the sensor nodes considering only

the local observations. In such a scenario, no node have complete picture of the cluster

formation. LEACH was first logical mechanism and later only variation of this basic

mechanisms were invented by various researchers for improving the performance. We

have presented the comparison with most of such algorithms. In this chapter, we have

proposed two methods for balancing energy consumption in a wireless sensor network.

4.2 Related Work

There are two main category of sensor network depending on routing of data to sink.

One is multi-hop and another is single-hop. In a multi-hop wireless sensor network

energy hole is a common problem. Some nodes are used frequently to hand over the

data to base station as all the forwarded data come through these nodes only. We

need to take care of all such nodes which are closer to base station to avoid energy hole

problem. This problem is solved by different researcher with different methods. Haenggi

(2003) [74] proposed four methods to solve the energy hole problem. In first method,

he proposed that distance between nodes must be decreased as the nodes are moving

towards base station. This ensure large data can be transmitted to a lower distance with

equal amount of energy. But this assumes that nodes are spread in an ordered fashion

in the sensor field. In the second method, he proposed balanced data compression to

achieve effectively one packet handing by each node. In third method, he showed data

can be directly handed over to base station rather than forwarding to next node if base

station is within its communication range. In his last method, he used equalization of

the end-to-end reliability method to balance energy consumption in a wireless sensor

4.2 Related Work 66

network. Olariu et al. (2006) [75] developed the theoretical model of the uneven energy

depletion phenomenon in sink based wireless sensor networks. Powell et al. (2007) [76]

computed the optimal parameters for probabilistic data propagation in wireless sensor

network and proved that these parameters maximize the networks lifetime in centralized

manner. Bouabdallah et al. (2009) [77] showed that significant amount of energy can

be saved by sending data through multiple paths, instead of a single path. Zhang H. et

al. (2009) [78] proposed energy-balanced data gathering (EBDG) protocol for solving

energy hole problem. Zhang X. et al. (2011) [79] solved this problem by deploying

nodes non uniformly in a wireless sensor network. The density of nodes is increased

towards the direction of base station.

But in most of the applications only one tiered or two tiered sensor network is used.

Single hop or two tiered scenario is different compared to multi-hop scenario, thus energy

consumption also will be different. Two tiered architecture of sensor network itself is a

solution to energy hole problem in a wireless sensor network. For example, in LEACH

if a node is selected as cluster head again and again then its energy will deplete first.

Such a scenario we need different protocols to balance the energy consumption. Many

researchers have tried to balance energy consumption in two tiered sensor network. In

LEACH, cluster head selection among sensor nodes is done randomly and two tiered

sensor network topology is used. Although LEACH algorithm avoids energy hole prob-

lem but cluster heads deplete their energy much faster compared to other nodes. This

is main cause of unbalanced energy consumption in LEACH. Hybrid Energy-Efficient

Distributed Clustering (HEED) proposed by Younis et al. (2004) [15, 16] is another

well-known clustering based routing algorithm in two tiered wireless sensor network. In

this work relationship between residual energy and reference energy is used for cluster

head selection. Zytoune et al. (2009) [80] worked on balancing energy consumption in

4.2 Related Work 67

two tiered wireless sensor network. Their probabilistic cluster head selection depends

on the position of a node. They divided sensor field in sub-regions (N1, N2, N3, and

N4 as shown in Fig.4.1) and depending on distance (d1, d2, d3, and d4) between these

sub-regions and the base station probability of all nodes (p1, p2, p3, and p4) are decided.

Figure 4.1: Balanced Energy Algorithm

Zytoune et al. used stochastic cluster head selection algorithm by a modifying the

probability of each node to become cluster head based on its required energy to transmit

to the base station. Zytoune et al. also solved this problem for two tiered wireless sensor

networks.

Thus due to relevance of two tiered wireless sensor networks, We have discussed

problem of balancing energy in two tired wireless sensor network in this thesis. We

have proposed two methods for energy balancing. The first one is for small area sensor

network, where the eligibility of cluster head is decided by number of nodes supported

in last round. In second one, we have varied duty cycle of a node depending on the

distance from a node to base station. This work is similar to Zytoune et al. balanced

energy consumption algorithm.


4.3 Method 1: N-LEACH, a Balanced Cost Cluster-

Heads Selection Algorithm

In LEACH algorithm [1], load on individual cluster head nodes increases (decreases)

depending on more (less) than optimum number of nodes supported by it. As only the

number of cluster heads are fixed and the remaining nodes choose the nearest cluster-

head node for data transmission, the number of supported nodes for each cluster head

vary quite a bit. This leads to uneven load distribution among nodes in a Wireless

Sensor Network (WSN). We propose a new cluster head selection method, N-LEACH,

based on number of supported nodes in earlier rounds.1

Problem Statement: Any node become cluster head once in a epoch and rest round

it behave like normal nodes. When a node i becomes a cluster head and it supports Ni

nodes for data transmission, the energy consumption is

ECH =L.Ni.(ERX + EDA) + ETX−amp(L, ditobs) (4.3.1)

As there are nk

nodes in a cluster. So node i will behave as a normal node for (nk− 1)

rounds in each epoch. Thus energy spent by node i as non cluster-head node is

Enon−CH =(n

k− 1).ETX−amp(L, ditoch) (4.3.2)

Energy consumption for node i in one epoch is sum of equations (4.3.1) and (4.3.2).

Ei =(n

k− 1).ETX−amp(L, ditoch) + L.Ni.(ERX + EDA) + ETX−amp(L, ditobs) (4.3.3)

Similarly for jth node energy consumption in one epoch is

Ej =(n

k− 1).ETX−amp(L, djtoch) + L.Nj.(ERX + EDA) + ETX−amp(L, djtobs) (4.3.4)

1Rajiv Kr. Tripathi, Yatindra Nath Singh and Nischal Kr. Verma, “N-LEACH, a balancedcost cluster-heads selection algorithm for Wireless Sensor Network,” Proceeding of IEEE NationalConference on Communications, NCC 2012 , Vol.1, No.1, IIT Kharagpur, India, Feb. 2012, pp.1-5.


In a small area network energy consumed in transmission of data from non cluster head

nodes to cluster heads is nearly same as energy consumed in transmission from cluster

head nodes to base station. It is with the assumption that base station is located at

the centroid of the deployed sensor nodes. So ETX−amp is approximately same for both

the nodes either for transmission from normal node to cluster head or for transmission

from cluster head node to base station.

Thus for a small area network

ETX−amp(L, ditoch) ≈ ETX−amp(L, djtoch), (4.3.5)

and

ETX−amp(L, ditobs) ≈ ETX−amp(L, djtobs). (4.3.6)

If Ni is much larger than Nj then energy consumed in receiving and data aggregation

play more important role compared to transmission of data.

Ei − Ej ∼=L. (Ni −Nj) . (ERX + EDA). (4.3.7)

So here main difference between nodes’ energy consumption is due to reception and

data aggregation only.

If the optimum number of clusters are k then the average number of supported nodes

by a cluster head are nk

for a particular round. The optimum number of cluster head

for a two tiered wireless sensor network is defined by Heinzelman et al. [2]

k =

√n√2π·√εfsεmp· M

d2toBS

(4.3.8)

Where n is the total number of nodes, M is length of side of square topology and dtoBS

is the average distance of different cluster heads to base station.

4.4 Proposed Cluster Head Selection Algorithm 70

The cluster number in some round may become less than k or in some round greater

than k. If the cluster head nodes support more than nk

nodes, then it spends more

energy which it should have been spending in nk

number of rounds. If cluster heads are

more than k, then cluster head nodes support less than nk

nodes. Thus cluster heads

spend less energy compared to others nodes in nk

number of rounds.

The different cluster numbers [84] in WSNs along with random choice of cluster

heads will make the node numbers in every cluster different and leading to uneven

energy dissipation for all nodes in each round. Therefore, we propose a new technique

which leads to dissipation of approximately 1 epoch energy on an average in each round.

4.4 Proposed Cluster Head Selection Algorithm

Step 1: In the first round of data transmission G is set to be −1 for all nodes.

Step 2: Operation for the epoch is performed after every nk

rounds. The value of G is

reduced by one for all the nodes which are having G ≥ 0 at the end of each epoch.

Step 3: All the nodes which are having G < 0 are eligible to become cluster head.

Step 4: The nodes will become cluster-head by randomly choosing a threshold Tn

between 0 and 1 using equation (1.2.18).

Step 5: If a node becomes a cluster head, it supports N number of nodes. If this N is

greater than Nave = nk, then this node is going to loose higher amount of energy, and if

N is less than Nave, then this node is going to save some energy compared to other nodes

which have already become cluster heads or will become cluster head within remaining

rounds in same epoch.


We add(kn

)*N to G when a node become cluster head. Thus value of G become

proportional to N, if a node support large number of nodes then this will loose its

eligibility criterion for next few nk

rounds as this will not become eligible unless G ≤ 0.

If it supports lesser than Nave nodes then it remains eligible to become cluster head

again. Thus a node can spend only Nave energy in every nk

rounds. The LEACH and the

proposed algorithm are shown in the Fig.4.2 and Fig.4.3 respectively as the flowcharts.

Figure 4.2: LEACH Algorithm Flowchart


Figure 4.3: Proposed Algorithm Flowchart

4.5 Method 2: Balancing Energy Consumption using Variable Duty Cycle (VDC) 73

4.5 Method 2: Balancing Energy Consumption us-

ing Variable Duty Cycle (VDC)

A sensor node consumes energy for event sensing, coding, modulation, transmission,

reception and aggregation of data. Data transmission has highest share in total energy

consumption [81, 82]. The required transmission power of a wireless radio is propor-

tional to square or an even higher order exponent of distance in the presence of obstacles.

Thus the distance is main factor responsible for energy consumption in a wireless sensor

network. As some nodes are nearer to sink they loose lesser energy compared to distant

nodes. This leads to an unbalanced energy consumption among sensor nodes. In this

subsection, we have proposed the use of variable duty cycle of sensor nodes for balancing

the energy consumption depending on distance of a sensor node from the base station.

4.6 VDC Algorithm

Zytoune et al. [83],[25] analyzed that sensor nodes drain out non-uniform energy due

to different distances between sensor nodes and base station. Thus nodes will have

different amount of residual energy depending on distance from the base station. One

of the solutions is that the nodes with more energy should be cluster heads more often

than the nodes with less energy. This ensures that all nodes die approximately at the

same time. Zytoune et al. used probability of cluster head selection as a function of

distance of the node from the base station to solve this problem.

Problem Statement: Let there be two nodes, node i and node j, and Ei and Ej are

the energy required to send one bit from respective nodes to base station as shown in

Fig.4.4. Node i will consume less energy compare to node j which is farther compared

4.6 VDC Algorithm 74

to node i, from the base station.

Figure 4.4: A Wireless Sensor Network topology

If we fix duty cycle for node i, Di, duty cycle for node j for equal average energy

consumption per cycle will be

Dj =Ei.Di

Ej. (4.6.9)

Here the duty cycle means, periodicity of transmission of data for a node. If transmission

cycle period is Ti then Di = 1Ti

. Thus EiTi

=EjTj

.

Every node can communicate with base station and vice versa. Base station will

inform all nodes how far it is from the nearest node and each node will estimate its own

distance from base station (Thus energy which need to be transmitted per bit to base

station). Thus all nodes can set their duty cycle Dj using equation (4.6.9). Let di be the

distance of the nearest node from the base station. Total number of bits transmitted

by node i in one cycle be Ni. It will consume least energy for transmitting data packets

to base station and has highest probability to die in the last. We take this nearest node

as reference; other nodes who want to have same energy consumption must transmit

lesser number of bits compared to this reference node.

We can achieve this adjustment by reducing duty cycle of the nodes. Here assumption

is that each node transmits same number of bits per cycle. Thus Nj=Ni,∀ j. Thus nodes

4.7 Simulation and Results 75

differ in periodicity of transmission (duty cycle).

Energy used to transmit Ni bits from reference node to base station is

ETX(Ni, di) ={Ni.Eelec+Ni.εfs.d

2i if di<d0

Ni.Eelec+Ni.εmp.d4i if di≥d0

. (4.6.10)

Now for any node j, the energy used for transmission is

ETX(Nj, dj) ={Nj .Eelec+Nj .εfs.d

2j if dj<d0

Nj .Eelec+Nj .εmp.d4j if dj≥d0

. (4.6.11)

We can determine the duty cycle for node j using equation (4.6.9), (4.6.10) and (4.6.11)

with assumption that nearest node to base station will have free space loss:

Dj =

ETX+εfs.di

2

ETX+εfs.dj2 .Di if dj<d0

ETX+εfs.d2i

ETX+εmp.d4j

.Di if dj≥d0. (4.6.12)

Thus we can achieve the balanced energy consumption in the sensor network by adjust-

ing the duty cycle of all sensor nodes using equation (4.6.12).

4.7 Simulation and Results

We have used same simulation parameters for both the methods. These parameters are

as follows: 100 nodes were randomly deployed in 100× 100 m2 area. The initial power

of all nodes is considered to be 0.5 J. Data packet size is assumed L = 20000bits/packet.

Base station is assumed to be at centroid of nodes. We carry out a comparison among

the LEACH, Fixed-LEACH and the proposed methods in this simulation.

The simulation is performed for 50 different random topologies in all the algorithms.

The averaged results are shown and analyzed for their effectiveness. Duty cycle for


nodes in LEACH, Fixed-LEACH and in node nearest to base station in the proposed

method 2 (VDC) has been fixed to 50%. Other nodes in proposed algorithm will have

duty cycle less that 50% depending on the distance from the base station.

Fig.4.5 shows percentage of node alive in the topology with time. LEACH and Fixed-

LEACH nodes die earlier compared to proposed method 1 and 2. Thus showing that

N-LEACH and VDC performs better than LEACH and Fixed-LEACH. In method 1

algorithm curve is above than that for LEACH until around 50% nodes are dead and As

N-LEACH utilizes the nodes energy evenly. This balancing results in sudden reduction

of alive nodes in the end. In method 2, curve is much above than LEACH and Fixed-

LEACH for all the time as VDC algorithm utilizes less amount of energy compared to

LEACH and Fixed-LEACH. It may be noted that channel capacity has been sacrificed

for far off nodes.

Figure 4.5: Number of Alive Nodes vs Time (in number of rounds)


Table 4.1 shows the number of rounds after which 1st and 50% node are dead in

the network for 50 different topologies for all the protocols. Lifetime for N-LEACH

and VDC is more than 12.21% and 12.3% higher compared to LEACH and 5.1% and

6.1% higher compared to Fixed-LEACH for first node death respectively. Lifetime for

VDC is more than 19% higher compared to LEACH and 18.2% higher compared to

Fixed-LEACH for 50% node death.

Table 4.1: Average Lifetime of nodes in number of rounds% of dead node Algorithm

⇓ LEACH Fixed-LEACH Method 1 Method 21 156 167 175 17850 241 246 243 301

We have calculated average energy consumption of all the nodes after every epoch.

Using this we have calculated residual energy of all the nodes at the end of each epoch.

Then standard deviation of residual energy after every epoch is plotted in Fig.4.6, The

method of calculating standard deviation of residual energy was earlier used by Shin

[85]. Results show that the variation in balance energy after every epoch in the sensor

network is always less for the proposed algorithms as compared to LEACH as well as

Fixed-LEACH protocol.

Figure 4.6: Standard Deviation of residual energy for all the nodes at each epoch


We have also estimated cumulative distribution function and probability density

function of nodes for their mean energy lost in one epoch. We have used Gaussian kernel

density estimator [99] defined for given N independent realizations χN ≡ {X1, ..., XN}.

This method is used to estimate probability density function f of an unknown contin-

uous probability density function f on X. f is defined as

f(x; t) =1

N

N∑i=1

φ(x,Xi; t), x ∈ <, (4.7.13)

where

φ(x,Xi; t) =1√2πt

e−(x−Xi)

2

2t(4.7.14)

is a Gaussian p.d.f. (kernel) with location Xi and scale√t. The scale is usually referred

to as the bandwidth.

Fig.4.7 is the cumulative distribution function of mean energy lost in one epoch for

all the nodes for LEACH, Fixed-LEACH, N-LEACH and VDC respectively. This figure

shows that the energy spend by sensor nodes in N-LEACH and VDC is having lower

spread compared to LEACH and Fixed-LEACH. Mean of energy lost in N-LEACH is

centered near around LEACH and Fixed-LEACH, but in VDC mean of energy lost is

much lesser compared to all other algorithms.

Fig.4.8 is the estimated probability density function of mean energy lost in one epoch

for all the nodes for LEACH, Fixed-LEACH and N-LEACH respectively. This figure

also shows that in N-LEACH and VDC expenditure of node is having lower spread and

closer to the mean energy of all nodes. It implies more balanced energy consumption

in proposed protocols compared to LEACH and Fixed-LEACH.


Figure 4.7: Cumulative Distribution Function of mean energy lost in one epoch

Figure 4.8: Probability Density Function of mean energy lost in one epoch

4.8 Conclusions 80

4.8 Conclusions

In method 1 the lifetime of the network increases significantly without introducing new

parameters or assumptions regarding sensor nodes capabilities and data overheads for

routing. We have shown results for different topologies. This shows that proposed

cluster head selection method is robust against topology changes also. This algorithm

can also be used for dynamic wireless sensor networks.

In method 2 the nodes which are located near the sink consume lower energy com-

pared to the farther ones, due to the smaller transmission distance. With same infor-

mation transfer rates, there will be asymmetric energy consumption in sensor nodes

and farther nodes will die earlier than the nodes closer to the sink. If farther nodes

transmit with reduced duty cycle compared to nodes nearer to sink a more balanced

energy consumption can be achieved. We have presented a mechanism to enforce equal

energy consumption using variable duty cycle for all nodes participating in a wireless

sensor network. We have evaluated performance of proposed algorithm and compared

it with existing algorithms and found it to be better as increases lifetime almost by

10%, reduces average energy consumption and balacne the energy consumption in all

the nodes.

Chapter 5

Localized Detection of BottleneckNodes and Quantification ofCriticality in a Wireless SensorNetworks

5.1 Introduction

In a WSN, sensor nodes work without knowledge of their position in the network. If

we look at multihop scenario, after random deployment of nodes, some of the nodes

are in critical positions as they connect one group of sensor nodes to another. If these

nodes are removed from the network it may lead to partitioning of network. Most of the

routing protocols identify a node as a bottleneck node depending upon residual energy

of the node. The nodes would have consumed considerable amount of energy before

they could have been identified as bottleneck nodes. We propose an alternative method

to detect the bottleneck nodes in the network just after their deployment.1

1Rajiv Kr Tripathi, and Shakya, R. and Verma, N.K. and Singh, Y.N., “Localized detection ofbottleneck nodes and quantification of criticality in a wireless sensor networks,” Engineering (SIBIR-CON), 2010 IEEE Region 8 International Conference on , vol.1, no.1, pp.326-328, 11-15 July 2010.

5.1 Introduction 82

Energy consumption is not uniform for all the nodes hence nodes must conserve more

energy if it is more critical in the network. A node is more critical, if its removal leads

to the large increase in probability of partitioning of the network. As the nodes need

to be low cost, they are assumed to be not having the GPS capability for localization.

The consequence is that the nodes are not aware of their exact position in the network.

Thus we can not use localization methods to identify the bottleneck nodes in a sensor

network. Here we propose a simple method based on local information for detection of

bottleneck nodes with their criticality.

Figure 5.1: Example of Bottleneck Node

Bottleneck nodes (as shown in Fig.5.1) are such nodes that have to be shared by

multiple paths because of low density in its vicinity. These nodes are located at such

positions in the network, that they are used quite frequently to forward the packets

from one part of network to other, consuming more energy compared to other nodes

in the network. Removal of these nodes will cause partitioning of network most of the

time.

The objective of this chapter to study the algorithm using local information to iden-

tify bottleneck nodes as well as their criticality rating. The criticality level thus should

affect the nodes contribution in the forwarding packets. Conventionally, when we iden-

tify criticality based on residual energy, we assumed that probability of network parti-

tioning due to removal of a node is same for all the nodes.

5.1 Introduction 83

The researcher working on energy efficient routing algorithms, maximization of life of

sensor network and efficient distributed topology, have designed routing protocols and

topology distributions, which reduces traffic load on critical nodes for extending the

lifetime of a sensor network. Ritter and Winter [86] have discussed partition detection

for a mobile ad-hoc network by identifying critical nodes.

Figure 5.2: Undesirable Energy Histogram Figure 5.3: Desirable Energy Histogram

Xiao and Dai [88] had tried to balance the nodes’ energy consumption for increasing

the life of a sensor network and shown that the nodes which lie in the central part

of topology consumes more energy compared to other nodes. The energy used by all

the nodes in the a sensor network with and without criticality of nodes is compared by

Schurgers and Srivastava [87] (Fig.5.2 and 5.3). It is evident from these, that there exist

such bottleneck nodes. Fig.5.2 presents a typical energy consumption histogram at a

certain point in time. Some nodes have rarely been used as they have less neighbors

and hence less packet for forwarding; while others have almost completely drained their

energy as they had large number of neighbors and were being used frequently to forward

data packets. Our aim is to find these nodes who will potentially completely drain their

energy much sooner compared to other nodes in a topology. The histogram in Fig.5.3 is

more desirable than the one in Fig.5.2, although the total energy consumption is same

in both, during observation period.

5.2 Algorithm 84

Jorgic [89] introduced several localized definitions of critical nodes and critical links.

They are based only on topological and positional information. In our study, the nodes

are not mobile and the topology of the network is static. There are no base stations in

the network. So any node can transmit data to any node as it expected to happen in

an self configured distributed sensor network.

5.2 Algorithm

Nodes are divided into two types- root nodes which initiates the flooding in the network,

and the others who forward root nodes’ unique signal throughout the network. Root

nodes have to be chosen carefully to ensure that most of the area in the network is

monitored. Their key property is that they have a relatively small amount of neighbors

compared to the nodes which are not root nodes. The reason for this kind of selection

is that with a relatively low neighbor count, root nodes are most likely at the border

of the network topology. The number of neighbors, a node has, allows us to select the

most appropriate root nodes. In other words, it allows us to identify border nodes. So

after deploying nodes, we start with the metric- neighbor count within certain radius

of transmission of all the nodes. The critical node detection in a topology is performed

in two steps.

Step 1: Finding root nodes: There is a reset timer in each node. If timer expires,

the node level is made∞ to identify the node, which has not got any flood packet, as an

isolated node. Each node also has Tx timer; after every transmission, it is reset. Upon

expiry of Tx, of the flooding transmission is done. The Tx timer should have value less

than the reset timers. Just after deployment, each nodes will send a PING broadcast

message. All nodes which are inside communication range of radius R will receive it

5.2 Algorithm 85

and respond with the ACK message. Each node will also store transmitting node’s

entry as neighbor in their database. Neighbors count will be the criterion to decide

if a node is a root node or not. Each node sends the neighbors’ count to each of its

neighbors. Thus each node knows its neighbors and their neighbors count. Any node

which has only one neighbor identify itself as a root node. The root node if identified

send flooding packet to all the neighbors which in turn further propagate it. If all the

nodes are having more than one neighbors, then there will not be any root node so far.

If time out happens and no flooding packets are seen, each node will reset its Tx timer.

Then nodes increase the threshold number of neighbors for deciding if it is a root node

or not. One important thing which must be taken care of that is the communication

range must be chosen at its largest possible value for estimating the neighbors count.

By doing this, the chances to select a root node at border will be maximum. For a high

density sensor network, these nodes will surely lie at the border of the topology. One

point must be taken care of, that the two root nodes must not lie in the each other

communication range directly to avoid false detection of bottleneck node.

Step 2: Detection of critical nodes : Let n nodes decide to become root nodes

throughout the topology. These nodes start flooding with its own level set at zero. The

neighboring nodes who receive flooding request from zero level will assign level one to

themselves and further propagate the flooding packet. Nodes give next higher level to

their neighbors and so on. All root nodes will generate different flooding packets. Each

node rebroadcast the received flooding packet only if it is makes the current node a

higher level node. If it is making it of same level or lower, then it is discarded. Once

a node accepts a request for level change while it has already been assigned a higher

level from a different root node, it is considered critical node. If a critical node receives

flooding packet at same level from third root node, then it is more critical node as this

5.3 Simulation Setup 86

node connects three root nodes. Thus criticalness of a node will depend on number of

different flood packets received from different root nodes. Thus the each node knows

its criticalness before the actual transmission of data. For this step the communication

radius must be optimum to save energy and no isolated nodes should be there in the

topology.

5.3 Simulation Setup

In the simulation, sensor nodes were randomly distributed within an area of 1000 ×

1000 m2. Each sensor is given an initial level 0 and a unique node ID. We have taken

160 nodes with communication radius 185m in our simulation. We have chosen root

nodes at the corners of the rectangular area. In a topology, where most of the time,

the traffic moves across the network, the nodes can use this information to detect their

criticality and so enhance the life time of sensor network by taking appropriate routing

decisions.

Each root node sets its level to zero. Root nodes start flooding with unique source

id. The neighbors of root nodes are assigned level one with unique ID of corresponding

root nodes. When two different root nodes’ signals come at a node it will consider itself

as bottleneck node of category-1. If any of these category-1 bottleneck nodes gets a

flood signal from the third root node this will be category-2 bottleneck node. As there

are n root nodes so at most bottleneck nodes will be of category-(n−1) criticality which

are connected to all n root nodes. These will be most important nodes as they may be

used to forward packet to whole topology of the network.

5.3 Simulation Setup 87

Figure 5.4: Root Nodes Selection Figure 5.5: Bottleneck Nodes Detection

Here simulation is performed for 150 different topologies. The following table shows

the percentage of bottleneck nodes in a topology. These bottleneck nodes must be

treated differently than the other ordinary nodes for different applications. As we have

taken 4 root nodes so there are 3 category of bottleneck nodes. Among them, category-3

are the most critical bottleneck nodes.

In Fig.5.4 the red color circle nodes shows the random deployment of the nodes in

the topology and root node selection is shown, the blue circles are the root nodes. In

Fig.5.5 the blue star nodes are category-1 bottleneck nodes and magenta color nodes

are category-2 and most critical bottleneck node i.e. category-3 is shown by green color.

Table 5.1: % of Bottleneck NodesCategory Category (1) Category (2) Category (3)

% of Bottleneck Nodes 19.308% 3.533% 1.512%

Table 5.1 shows the percentage of bottleneck nodes in the WSN. Bottleneck node

of Category-1 comes out be nearly 20% of the total sensor nodes. So nearly 25% total

nodes are bottleneck of all categories in a WSN. So rest 75% nodes can be used more

compared to these bottleneck nodes for data transmission in a WSN.

5.4 Conclusions 88

5.4 Conclusions

There exists nearly 25% bottleneck node in a sensor network. Detection of these nodes

may be performed based on residual energy or localized detection method. Localized

detection of bottleneck nodes is apriori that means we can detect bottleneck nodes in a

sensor network just after deployments of nodes. But if we use residual energy method

which is posteriori method that means after using sensor network for a sufficient time,

we check residual energy of nodes. Then after we can detect the bottleneck nodes in a

sensor network. Thus Localized detection is better as the criticality of nodes is defined

before energy consumption start. Thus the load distribution on sensor nodes can be

managed depending of its criticality.

Chapter 6

Conclusions and Future Works

6.1 Conclusions

The conclusions of the work presented in the thesis are as follows.

The Optimal location of base station can be obtained such that either the transmis-

sion energy expenditure is minimum or lifetime of the sensor network is maximum. If

all nodes suffer only free space transmission loss to base station then centroid of nodes

is the optimal position for base station deployment. If all nodes suffer only multipath

transmission loss to base station then point F (as discussed in thesis, point F is the

point, which minimizes∑n

i=1 d4i , where di is the distance from the point F to node i)

is the optimal position for base station deployment. If some nodes suffer free space

loss and remaining nodes, multipath loss to base station, then point O (as discussed

in thesis) is the optimal position for base station deployment. This location can not

be calculated by any method. It can be guessed only for certain situations. We have

suggested a method to find base station location quite closer to the optimal point. Our

method can be used in any topology in general.

1. Conclusions 90

For the case when lifetime of the network is to be maximized, placing the base station

at the center of minimum enclosing circle is the choice. This is with the assumption

that lifetime is defined as time after which first node die due to energy depletion.

The second issue investigated by us is Anchor free localization. It can be performed

by either using average distance between nodes or using hop count as distance mea-

surement. Using average distance is very simple and in single hop localization, approx-

imately 6% localization error occurs for the rectangular sensor field.

We also observe that localization error of approximately 50% is introduced when

using hop counts as distance measurement in any localization algorithm. It may be

noted that nodes are localized in integral multiples of maximum communication radio

range R, in hop count based metric.

We have also looked at how to balance the energy consumption and thereby increase

the lifetime of the sensor network. Energy consumption is mainly due to reception and

data aggregation for a smaller size sensor network.Thus energy consumption mainly

depend on number of nodes supported by the cluster head node. Consequently, number

of supported nodes is an important factor for balancing energy consumption in WSN.

We have exposed the mechanism to decide candidacy of a node to become cluster head

node depending on number of nodes supported in the past.

Energy consumption among sensor nodes in a WSN can also be balanced using

variable duty cycle transmission. This is a viable technique when energy consumption is

mainly due to data transmission over longer distance in sensor networks. This technique

is for large sized sensor networks. In this method, length of transmission duty cycle

of sensor nodes is proportional to distance between sensor nodes and base station to

achieve balanced energy consumption.

6.2 Suggestions for future works 91

In a wireless sensor network some nodes need to work more as they are used frequently

to forword the data for all the nodes. These are bootleneck neck nodes.In a WSN, nearly

25% such nodes exits. Bottleneck nodes consumes more energy compared to other nodes

in the network. Thus identification and conserving energy specifically in these nodes is

more important.

6.2 Suggestions for future works

This thesis mainly concentrate on the conserving and balancing energy in a wireless

sensor network. We have investigated only few of the problems. Some of the problems

can be further explored are as follows. Algorithms for placing more than one base station

can be explored depending on communication parameters. More accurate methods can

be developed for anchor free localization in WSN. Models for identification of bottleneck

nodes and resulting life time enhancement techniques. Further, we fed at the end of this

study that overheads needed to implement any method should be as low as possible and

low enough to made it viable. Further if random access MAC (medium access control)

is used, there will be random delay and energy overhead which gets added. The impact

of these need more investigations along with new methods to minimize this delay and

to improve throughput per unit energy consumed.

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List of Publications

Published Papers:

1. Rajiv Kr Tripathi, Y. N. Singh and Nischal K. Verma, “Clustering Algorithm

for Non Uniformly Distributed Nodes in a Wireless Sensor Network,”In IET Jour-

nal of Electronics Letter, Vol.49, No.4, February 2013, pp. 299-300.

2. Rajiv Kr Tripathi, Y. N. Singh and Nischal K. Verma, “Two tiered wireless

sensor networks - Base station optimal positioning case study,” In IET Journal

of Wireless Sensor System, Vol.2, No.4, December 2012, pp. 351-360.

3. Rajiv Kr Tripathi, Y. N. Singh and Nischal K. Verma, “N-LEACH, a Balanced

Cost Cluster-Heads Selection Algorithm for Wireless Sensor Network,”Proceeding

of IEEE National Conference on Communications, NCC 2012 , Vol.1, No.1, IIT

Kharagpur, India, Feb. 2012, pp.1-5.

4. Rajiv Kr Tripathi, Rajeev Shakya, Nischal K. Verma and Y. N. Singh, “Local-

ized Detection of Bottleneck Nodes and Quantification of Criticality in a Wire-

less Sensor Networks,” Proceeding of IEEE Region 8 SIBIRCON-2010, Irkutsk

Listvyanka, Russia, pp. 326–328.

LIST OF PUBLICATIONS 107

Communicated Papers:

1. Rajiv Kr Tripathi, SatishKrishna Dulli, Y. N. Singh and Nischal K. Verma,

“Analysis of Weights for optimal positioning of base station in a wireless sensor

network,” In IET Journal Electronics Letter, February 2013.

Appendix A 108

Appendix A - Optimal location of base station when all nodes suffer only

free space loss

Let d2 be the sum of square of all the Euclidean distances as all the nodes have only

free space loss.

d2 =d21 + d2

2 + d23 + ....+ d2

n. (A-1)

From equations (2.3.13) and (A-1),

d2 =n∑i=1

[(x− xi)2 + (y − yi)2

]. (A-2)

d2 =n∑i=1

[x2 + x2

i − 2xxi + y2 + y2i − 2yyi

]. (A-3)

Expanding the summation.

d2 =n(x2 + y2) +n∑i=1

(x2i + y2

i )− 2xn∑i=1

xi − 2yn∑i=1

yi. (A-4)

now let

C1 =n∑i=1

xi, (A-5)

C2 =n∑i=1

yi, (A-6)

and

C3 =n∑i=1

(x2i + y2

i ). (A-7)

Now equation (A-4) becomes,

d2 =n(x2 + y2)− 2xC1 − 2yC2 + C3. (A-8)

Taking ∂(d2)∂x

and ∂(d2)∂y

for finding maxima and minima.

∂(d2)

∂x=2nx− 2C1 = 0. (A-9)

Appendix A 109

⇒ x =C1

n. (A-10)

∂(d2)

∂y=2ny − 2C2 = 0. (A-11)

⇒ y =C2

n. (A-12)

As ∂2d2

∂x2 and ∂2d2

∂y2both are positive for all values x and y, equation (A-10) and (A-12)

provide minima of equation (A-1).

∂2d2

∂x2=∂2d2

∂y2=2n. (A-13)

Thus sum of square of distances from n points is minimized at the centroid of given

points.

Appendix B 110

Appendix B -Contribution in 2D Geometry-Revealing Line of symmetry

The Center of mass, which converges in to Centroid for uniformly distributed mass

of some objects lies in the line of symmetry [90, 91]. It has been proved [92] that it is

impossible to find the exact location of geometric medians other than the centroid. But

after observing many different cases, we have concluded that other geometric medians

also lies on same line. We consider the cases where many points are distributed in a

two dimension plane. Within this if symmetry exists, we will have at least one line of

symmetry. We will investigate the positioning of various geometric medians in context

of line of symmetry.

Figure B-1: Geometric Median (x, y)

The geometric median of a discrete set of sample points in a Euclidean space is the

point minimizing the sum of distances to the sample points [100]. For n points (x1, y1),

(x2, y2), (x3, y3),...(xn, yn) (as shown in Fig.B-1) distributed in 2-Dimensional plane the

kth geometric median Mk is the point (x, y) which minimizes.

n∑j=1

(dj)k (B-1)

Here dj is given by

dj =√

(x− xj)2 + (y − yj)2. (B-2)

Appendix B 111

For k = 1, this become optimal facility location, also known as Fermat-Weber point or

1-median or M1. It is the (x, y) such that M1 is minimized.

M1 =(d1 + d2 + d3 + ...+ dn−1 + dn) (B-3)

Computing the optimal facility location is a challenge as it has been shown that no

explicit formula exist for finding the optimal facility location. Only numerical approxi-

mations to the solution of this problem are possible.

For k = 2, this is known as centroid (Cx, Cy) or center of mass, defined similarly to

the geometric median as minimizing the sum M2 of the squares of the distances to each

sample [80-83].

M2 =d21 + d2

2 + d23 + ...+ d2

n−1 + d2n. (B-4)

This location can be find by

Cx =

∑ni=1 xin

(B-5)

Cy =

∑ni=1 yin

(B-6)

Similarly we can define higher order geometric medians (kth median) as point which

minimizes

Mk =dk1 + dk3 + dk3 + ...+ dkn−1 + dkn. (B-7)

Similar to 1-median, there is no explicit formula to determine the location of these

higher order medians. Pierre de Fermat posed Fermat Problem in the early 1600.

But it was not studied or applied substantially until the twentieth century and still

it need to further work for more results. In the latest development in 2003, Bose

et al. [97] described more sophisticated geometric optimization procedures for finding

Appendix B 112

approximately optimal solutions to this problem and in 2008, Nie, Parrilo and Sturmfels

[98] showed that the problem can also be represented as a semidefinite program. Here

we have shown that these medians lie on the line of symmetry with some interesting

observations.

Examples: We have calculated the geometric medians using MATLAB in the fol-

lowing examples.

Example 1: There are two points P1 and P2 having line of symmetry at center of

both point and perpendicular to the plane of the points (see Fig.B-2). All medians M1,

M2,...Mn coincide each other and lie on point of intersection of line of symmetry and

the line joining the points.

Figure B-2: Geometric medians for two points

Example 2: Three points P1, P2 and P3 lie on the vertices of right angle isosceles

triangle. All medians M1, M2,...Mn lie on the line from right angle vertices to center

of line joining to other two points. This is the line of symmetry for three points. Mn

median for large value of n, will lie on the center of line joining to other two points.

Fermat point i.e. point M1 for right angle isosceles triangle will lie at 0.1726× L from

the right angle vertices on the line of symmetry (see Fig.B-3). Where L is the equal

sides of the triangle.

Example 3: Four points P1, P2, P3 and P4 (see Fig.B-4) lie on the vertices of square

of side L. All medians M1, M2,...Mn coincide to each other where two lines of symmetry

cut each other i.e. at the center of the square.

Appendix B 113

Figure B-3: Geometric medians for three points

Figure B-4: Geometric medians for four points

Appendix B 114

Example 4: Out of Five points, four points P1, P2, P3 and P4 lie on the vertices of

square of side L and one point P5 on the line of symmetry (see Fig.B-5). All medians

M1, M2,...Mn distributed on the line joining point P5 to center of square. Mn median

for large value of n, will lie on the center of the square.

Figure B-5: Geometric medians for five points

Example 5: For six point we have discussed two example where by keeping M2

constant by moving two points inwards for case 1 and outwards for case 2. In case

1 the geometric medians contract from both side towards M2 that M1 and Mn both

approaches to M2. In case 2 the geometric medians diverge from both side from M2

that M1 and Mn both move away from M2.

Case 1: Six points out of these, four points P1, P2, P3 and P4 lie on the vertices of

square of side L and points P5 and P6 lie on the one side of square and moving towards

center of points P1 and P3 (see Fig.B-6). All medians M1, M2,...Mn distributed from

center line of P1 and P3 to center of P1, P2, P3 and P4. Mn median for large value of n,

will lie on the center of P1, P2, P3 and P4.

Appendix B 115

Figure B-6: Geometric medians for Six points case 1

Figure B-7: Geometric medians for Six points case 2

Appendix B 116

Case 2: Six points out of these, four points P1, P2, P3 and P4 lie on the vertices of

square of side L and points P5 and P6 lie on the one side of square and moving away

from points P1 and P3 (see Fig.B-7). All medians M1, M2,...Mn distributed from center

line of P1 and P3 to center of P1, P2, P3 and P4. Mn median for large value of n, will

lie on the center of line joining points P1 and P3.

Table B-1: Geometric medians for different casesM1 M2 M3 M100

Two Points (75.0, 0.0) (75.0, 0.0) (75.0, 0.0) (75.0, 0.0)Three Points (31.7, 118.2) (50.0, 100.0) (55.3, 94.7) (72.8, 77.2)Four Points (75.0, 75.0) (75.0, 75.0) (75.0, 75.0) (75.0, 75.0)Five Points (28.1, 75.0) (45.0, 75.0) (50.4, 75.0) (50.3, 75.0)

Six Points Case 1 (14.2, 75.0) (50.0, 75.0) (62.4, 75.0) (75.0, 75.0)Six Points Case 2 (60.9, 75.0) (50.0, 75.0) (31.3, 75.0) (0.0, 75.0)

Observations: Results shown in Table B-1 verifies the examples discussed above

and strengthen the observations. Though there is no explicit proof of geometric median

except median-2, through analysis and observation we have found the following facts

which are useful in designing optimal location facility.

(1) For the kth median, when value of k is very large, standard deviation of array

D = [d1, d2, d3, ...dn−1, dn] is minimized at the geometric median. We have discussed

this problem in Appendix C. Although literature regarding this could not be found.

(2) Fermat point i.e. point M1 for right angle isosceles triangle will lie at 0.1726× L

from the right angle vertices on the line of symmetry (see Fig.B-3). Where L is the

length of sides of the triangle.

Future Work: Though these observations lead to some interesting results for symmet-

rically placed points in a plane but further research is recommended for those interested

on geometric medians localization for randomly distributed n points when axis of sym-

metry may or may not exit.

Appendix C 117

Appendix C -Open Problem

Let n points be randomly selected inside finite bounded area at (x1, y1), (x2, y2), (x3, y3)

.....(xn, yn) and a point A (x, y) be inside that area (As shown in Fig.C-1).

Figure C-1: Point A (x,y)

Distances between point A and nodes are d1, d2, d3, ....dn. The di is defined in equa-

tion (2.3.13). Let D be array of distances from point A to all the points.

D = [d1 d2 d3 ... dn−1 dn]

Problem statement: What value of (x, y) inside finite bounded area minimizes the

standard deviation of array D.

Example 1: See in Fig.C-2, where we have chosen only two point i.e. n=2. Here

choice of point A is trivial that is midpoint of two point.

Standard deviation σ for n = 2 is given by

σ =

√(d1 − d1+d2

2

)2+(d2 − d1+d2

2

)22

. (C-1)

Appendix C 118

Figure C-2: Point A when only two point are in field i.e. n=2.

So for d1 =d2 = (d1+d2)2⇒ σ = 0.

Thus standard deviation is minimized at midpoint of these two point. And Point A is(x1+x2

2, y1+y2

2

).

Example 2: Now we see for n = 3, The best choice is circumcenter (see Fig.C-3) of

three point.

σ =

√√√√(d1 −∑3i=1 di3

)2

+(d2 −

∑3i=1 di3

)2

+(d3 −

∑3i=1 di3

)2

3. (C-2)

Where d1 =d2 =d3⇒ σ = 0

Figure C-3: Point A when only three point are in field i.e. n=3.

Now for n = 4 and more points as no circumcenter is possible in general, so now

standard deviation will not be zero. Because all the nodes can’t have equal distances

Appendix C 119

from any point. Standard deviation will be minimized at some point with some nonzero

value and given by

σ =

√√√√(d1 −∑4i=1 di4

)2

+(d2 −

∑4i=1 di4

)2

+ ...+(d4 −

∑4i=1 di4

)2

4. (C-3)

which can be simplified as,

σ =

√(4.d1 −

∑4i=1 di

)2+(4.d2 −

∑4i=1 di

)2+ ...+

(4.d4 −

∑4i=1 di

)264

(C-4)

σ =1

4√

4

√√√√16.d21 +

(4∑i=1

di

)2

− 8.d1.4∑i=1

di + ...+ 16.d24 +

(4∑i=1

di

)2

− 8.d4.4∑i=1

di.

(C-5)

Adding similar terms,

σ =

√√√√1

4.

4∑i=1

di2 − 1

16.

(4∑i=1

di

)2

.. (C-6)

Similarly for n = 5, this becomes

σ =

√√√√1

5.

5∑i=1

di2 − 1

25.

(5∑i=1

di

)2

, (C-7)

and in general for n nodes, this becomes

σ =

√√√√ 1

n.

n∑i=1

di2 − 1

n2.

(n∑i=1

di

)2

. (C-8)

From the equation (C-8) if we check for n = 2 and n = 3 in both cases σ will become

zero. The problem is to find the point A(x, y) such that standard deviation of array D

(equation (C-8)) is minimized.

base station positioning, nodes' localization and

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