Node Selection Technique for Distributed
Beamforming in Green Cognitive Radio
Networks
August 8,2012
N.M.Tessema
Node Selection Technique for Distributed
Beamforming in Green Cognitive Radio
Networks
A
THESIS
submitted in partial fulfillment of the
requirements for the degree of
MASTER OF SCIENCE
in
ELECTRICAL ENGINEERING
by
N.M.Tessema
born in Dessie, Ethiopia
MTS-R Research Group
Department of TELECOMMUNICATIONS
EEMCS, Delft University of Technology
Delft, the Netherlands
www.ewi.tudelft.nl
ii
c
All
rights reserved 2012 N.M.Tessema.
Node Selection Technique for Distributed
Beamforming in Green Cognitive Radio
Networks
Author:
N.M.Tessema
Student id:
4117700
Email:
[email protected]
Abstract
The wide deployment of wireless sensor nodes for varieties of applications calls the need for
distributed beamforming as a cooperative scheme to efficiently use spectrum, to improve communication range and to save precious battery power during transmission. Given that there are a large
set of cooperative cognitive radio users, ensuring the minimal energy is consumed while keeping
the interference received by primary users below a given regulatory limit is crucial to maintain the
green aspect of Cognitive Radio Sensor Network. The major research question is how to develop
an efficient node selection method that allows to keep the energy consumption at the minimum and
while keeping the interference regulations of primary users. In this thesis, an efficient node selection
method which allows maintaining the Green aspect of the network is proposed. The node selection
method is used to save significant amount of energy per single transmission. Furthermore, the impact of ambiguous location information in distributed beamforming is investigated. The statistical
characterization of the phase error at the beamforming nodes is studied. A simple solution that leads
to minimize the degradative impact of location ambiguity is given.
DELFT UNIVERSITY OF TECHNOLOGY
DEPARTMENT OF
TELLECOMMUNICATIONS
The undersigned hereby certify that they have read and recommend to the Faculty of Electrical
Engineering, Mathematics and Computer Science for acceptance of a thesis entitled Node Selection
Technique for Distributed Beamforming in Green Cognitive Radio Networks by N.M.Tessema in
partial fulfillment of the requirements for the degree of Master of Science.
Chairman:
Prof.Dr O.Yarovyi
Supervisor:
Dr H.Nikookar
Mentor:
X.Lian
Comittee Member:
Dr E.Onur
Dated : Aug 8, 2012
iii
Acknowledgement
First of all, my heartfelt thanks goes to my supervisor Dr H.Nikookar for his continued assistance, guidance and encouragement. He always encouraged me to keep on progressing and with his constructive
comments on my work. It was quite a pleasure to work with you Dr Nikookar. Next, I would like to
thank my mentor Ms Xiaouha Lian for guiding me through every step and answering all my questions
and doubts. I would not have completed this thesis work without her guidance and support. I would
also like to thank Prof. Dr O.Yarovy for reading through my thesis work and his constructive comment
in shaping out my thesis at the begining. I would like to thank Dr E.Onur for going through my thesis
work and participating in the thesis comitteee. I also want to thank EEMCS Faculty African Scholarship
program for financing my study at Tudelft for 2 years. My list would not be complete without thanking
all my friends in Delft who helped me enjoy my stay during the program. Last but not least, I would like
to thank my father Merawi Tessema and my mother Almaz Bekele who continuously provided me with
their unconditional love. Their encouragement and motivation on my education is a great aspiration to
me. I would like to dedicate this thesis work for them.
N.M.Tessema
Delft, the Netherlands
Aug 8, 2012
v
Contents
Acknowledgement
v
Contents
vii
List of Figures
ix
List of Tables
xiii
List of Abbreviations
1
2
3
xv
Introduction
1
1.1
Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1
1.2
Problem Statement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2
1.3
Main Contributions of the Thesis
. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2
1.4
Related Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3
Background Concepts
5
2.1
Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5
2.2
Cognitive Radio Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6
2.3
Beamforming Approach for Cognitive Radio Networks . . . . . . . . . . . . . . . . . .
9
2.4
Transmit Distributed Beamforming . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
9
2.5
Distributed Transmit Beamforming for Cognitive Radio Sensor Networks . . . . . . . . 17
2.6
Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
Clustering for Distributed Beamforming in Cognitive Radio Networks
3.1
27
Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
vii
C ONTENTS
4
5
6
3.2
Concept of Clustering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
3.3
Clustering Node Selection Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
3.4
Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
Close to Optimal Node Selection for Green Cognitive Radio Sensor Networks
55
4.1
Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
4.2
System Model and Protocol . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
4.3
Minimizing Energy Consumption . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
4.4
Minimizing Interference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
4.5
Clustering Node Selection Method for Green Communication . . . . . . . . . . . . . . 63
4.6
Performance Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
4.7
Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
Location Ambiguity and Phase Error in WSN
67
5.1
Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
5.2
Location error ambiguity at the beamforming nodes . . . . . . . . . . . . . . . . . . . . 68
5.3
Investigating the effect of location uncertainty on distributed beamforming . . . . . . . 71
5.4
Analysis of Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
5.5
Modeling of Initial Phase Error at the beamforming nodes . . . . . . . . . . . . . . . . 79
5.6
Performance of Clustering node selection method in the presence of location error . . . . 84
5.7
Comparative Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
5.8
Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
Conclusions and Recommendations
91
6.1
Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
6.2
Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
6.3
Recommendations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
Bibliography
95
A Publications
99
viii
List of Figures
2.1
Cognitive cycle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7
2.2
Distributed Transmit Beamforming . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.3
System Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.4
beam pattern comparision for random realization of the nodes location . . . . . . . . . . . . 13
2.5
Average Beam pattern . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.6
CDF of the beam pattern . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.7
CRSN Network Architecture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.8
Approximate null steering beamformer with 20 nodes
2.9
Approximate null steering beamfromer with 200 nodes . . . . . . . . . . . . . . . . . . . . 20
. . . . . . . . . . . . . . . . . . . . 20
2.10 Null pointing using PODB distributed beamformer . . . . . . . . . . . . . . . . . . . . . . 21
2.11 Side lobe control via node selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.12 Caption for LOF . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
3.1
Clustering process example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
3.2
points i and j in cartesian coordinate system . . . . . . . . . . . . . . . . . . . . . . . . . . 30
3.3
Clustering Procedures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
3.4
System Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
3.5
Wrapping the phase of the node for clustering . . . . . . . . . . . . . . . . . . . . . . . . . 35
3.6
Phase difference between the nodes scaled as euclidean distance . . . . . . . . . . . . . . . 36
3.7
Selection of Clustering Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
3.8
Inter and intra cluster Proximity measure
3.9
Steps of k-means clustering algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
. . . . . . . . . . . . . . . . . . . . . . . . . . . 38
3.10 Clustering nodes using k-means clustering Algorithm . . . . . . . . . . . . . . . . . . . . . 40
ix
L IST OF F IGURES
3.11 Clusters or phase groups formed using k-means clustering . . . . . . . . . . . . . . . . . . 41
3.12 Validity Measure in radians . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
3.13 Toplogy of clusters and selected nodes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
3.14 Clustering node selection basic steps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
3.15 Beam Pattern of 6 nodes, PU located at φ = 200 . . . . . . . . . . . . . . . . . . . . . . . . 45
3.16 CDF of Beam Pattern of 6 nodes, PU located at φ = 200 . . . . . . . . . . . . . . . . . . . . 45
3.17 Beam Pattern of 10 nodes, PU located at φ = −200 and φ = 200
. . . . . . . . . . . . . . . 46
3.18 CDF of Beam Pattern of 10 nodes, PU located at φ = −200 and φ = 200 . . . . . . . . . . . 47
3.19 Beam Pattern of 21 nodes, PU located at φ = −400 , φ = −200 and φ = 200 . . . . . . . . . . 47
3.20 CDF of Beam Pattern of 21 nodes, PU located at φ = −400 ,φ = −200 and φ = 200 . . . . . . 48
3.21 Two DCR and one PU . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
3.22 Beamforming of two main beams with 20 nodes . . . . . . . . . . . . . . . . . . . . . . . . 49
3.23 Beamforming with 6 nodes for a node density of 4 nodes per meter square . . . . . . . . . . 50
3.24 SLL at the direction of PU for increasing value of node density . . . . . . . . . . . . . . . . 50
3.25 Beamforming with 6 nodes when PU is located at 4 degree . . . . . . . . . . . . . . . . . . 51
3.26 Beamforming with 6 nodes with broadened sidelobes . . . . . . . . . . . . . . . . . . . . . 51
3.27 Beamforming with 6 nodes at f=900MHZ and 2GHZ . . . . . . . . . . . . . . . . . . . . . 52
3.28 Comparision of clustering node selection for different values of R̃ . . . . . . . . . . . . . . 53
4.1
System Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
4.2
System Protocol . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
4.3
Over all energy consumption and Interference Vs the number of nodes . . . . . . . . . . . . 61
4.4
CDF comparision with and without clustering at 900 MHZ . . . . . . . . . . . . . . . . . . 62
4.5
Clustering node selection for Close to optimal number of nodes . . . . . . . . . . . . . . . . 64
4.6
Interference power and energy comparision with and without clustering method at 900 MHZ
5.1
Caption for LOF . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
5.2
Simulation Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
5.3
Beampattern Comparision Case 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
5.4
Average Phase Error in degrees at each node case 1 . . . . . . . . . . . . . . . . . . . . . . 72
5.5
Comparision of the beampattern Case 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
5.6
Average phase error at each node Case 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
5.7
Comparision of the beampattern Case 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
x
64
5.8
Average phase error at each node Case 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
5.9
Comparision of the beampattern Case 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
5.10 Average phase error at each node Case 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
5.11 Average Phase Error, Beampattern comparision Case5 . . . . . . . . . . . . . . . . . . . . . 75
5.12 Comparision of the beampattern for 10,20 and 50 nodes . . . . . . . . . . . . . . . . . . . . 76
5.13 Average phase error at each node when 10,20 and 50 nodes are used in beamforming . . . . 76
5.14 Comparision CDF of the sidelobe level with average 500 and without error . . . . . . . . . . 77
5.15 Comparision CDF of the sidelobe level with average 700 and without error . . . . . . . . . . 77
5.16 Rayleigh component of the phase error
. . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
5.17 Gaussian component of the phase error . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
5.18 Uniform Component of the phase error . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
5.19 Total phase error . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
5.20 Rayleigh component of the phase error . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
5.21 Total phase error . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
5.22 shape of total phase error at different nodes . . . . . . . . . . . . . . . . . . . . . . . . . . 82
5.23 Beamforming gain with and without averaging of the phase error CASE I . . . . . . . . . . 83
5.24 Beamforming gain with and without averaging of the phase error CASE II . . . . . . . . . . 83
5.25 Beamforming gain with and without averaging of the phase error CASE III . . . . . . . . . 84
5.26 location error at the CH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
5.27 Comparision of clustering method with and without phase error . . . . . . . . . . . . . . . . 85
5.28 Phase error at each beamforming node . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
5.29 Clustering method with and without phase error . . . . . . . . . . . . . . . . . . . . . . . . 86
5.30 Clustering Method with and without averaging . . . . . . . . . . . . . . . . . . . . . . . . 87
5.31 Phase error from Gaussian location error distribution . . . . . . . . . . . . . . . . . . . . . 88
5.32 Comparision main beam with different location error distributions . . . . . . . . . . . . . . 89
xi
List of Tables
3.1
Comparision of Clustering methdology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
4.1
Simulation parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
4.2
Number of Nodes used by Clustering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
5.1
Mainbeam degradation summary Case 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
5.2
Mainbeam degradation summary Case 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
5.3
Mainbeam degradation summary Case 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
xiii
List of Abbreviations
BER
Bit Error Rate
CH
Cluster Head
CLARA
Clustering for Large Applications
CR
Cognitive Radio
CRSN
Cognitive Radio Sensor Network
DB
Distributed Beamforming
DCR
Distant Cognitive Radio user
GPS
Global Positioning System
OFDM
Orthogonal Frequency Division Multiplexing
PCA
Principal Component Analysis
PU
Primary Users
RF
Radio Frequency
SNR
Signal to Noise Ratio
WSN
Wireless Sensor Network
xv
Chapter 1
Introduction
1.1
Motivation
Global energy consumption is currently one of the major concerns faced by governments worldwide,
because of its significant environmental footprint and the eventual exhaustion. Given the world wide
growth of wireless sensor communication for several applications, there is associated high demand for
consistent energy supply. Furthermore, with the increasing demand for high data rate services, Cognitive
radio access is a key in minimizing the spectral congestion leading to the emergence of Cognitive Radio
Sensor Networks. For monitoring and survelliance applications, the networks are usually deployed in
an unattended environments where periodic battery replacement is unlikely. As a result, power outage is
the most likely outcome without adoption of any energy reduction mechanism. Power outage will result
in node failure which would otherwise gather useful information. This is where green communication
comes to riscue in Cognitive Radio Sensor Networks.
Green communication is a paradigm shift of the technical approaches of communication in an effort
to create an energy-efficient network.Therefore, the adopted communication schemes of such networks
should be energy efficient. Distributed beamforming is a promising technology that can be used in this
regard in which the devices cooperate to steer a beam toward the receiver with prior cooperation among
themselves for synchronization and information exchange purposes.
The use node selection method prior to beamforming is an influential tool in achieving significant
energy conservation of these networks by appropriately choosing the number of nodes that can form the
communication link with the receiver. In cognitive radio sensor network, it is also critical to choose the
nodes so that the interference regulation of primary users is not violated. This is the main motivation
in developing a node selection technique for beamforming that maintains greenness in cognitive radio
sensor networks while fulfilling the requirements of primary users.
1
1. I NTRODUCTION
1.2
Problem Statement
The research points of this thesis work revolves in the following two major points:
• Investigating the use of a node selection method in distributed beamforming for the realization of
Green cognitive radio sensor network that allows energy reduction and at the same time conform
to regulatory requirement of primary users. As such it is required to develop an effective node
selection method that allows to select nodes which optimize the total energy consumption for a
green communication. The optimization would lead to a tradeoff analysis between decreasing the
energy consumption with the minimum number of nodes necessary to direct enough power to the
receiver. It is also necessary that the method to be developed is computationally simple for easy
deployment in Cognitive Radio Sensor Networks.
• The localization methods of the wireless sensor nodes are not free from error. That means the
location information of the sensor devices contains ambiguity term. Therefore, it is critical to
investigate the impact of location ambiguity of the sensor devices on distributed beamforming. It
is also required to use a location error model that actually represents the practical location error at
the sensor devices.
Accordingly, the first part of the thesis work deals with development of such an effective node
selection method that fullfills the above mentioned criteria.
In the second part of the thesis, a detailed study of the impact of location error on distributed beamforming is presented.
1.3
Main Contributions of the Thesis
Chapter 3
In chapter 3, a node selection techinique based on Clustering concept is proposed. The technique allows
to select small number of nodes for beamforming that are able to minimize interference in the direction
of primary user through sidelobe reductions. The obtained sidelobe reductions using clustering method
does not require any phase or amplitude adjustments at the nodes. The simplicity of the technique
conforms with limited computational capacity in wireless sensor networks. The use of small number of
nodes by the proposed method facilitiates the adoption of green communication in cognitive radio sensor
networks. The sidelobe reduction obtained from the node selection technique proves to be effective
2
Related Work
in high density wireless sensor network where several number of nodes are deployed in large sensor
network for applications such as earthquake monitoring.
Chapter 4
In chapter 4,the node selection techinique proposed in chapter 3 is used to demonstrate green communication by quantifiying the energy reduction obtained per single transmission in the order of Joules.
Chapter 5
In chapter 5, the impact of location ambiguity is investigated based on GPS Rayleigh distributed location error. The degradative impacts of the resulting phase error on the beampatten is discussed. The
performance of the proposed node selection method in the presence of location ambigiuty is investigated. Statistical characterization of the phase error at the beamforming nodes is studied given Rayleigh
distributed location error. The result obtained showed that the total phase error at the nodes is a mixture
distribution of Gaussian,Rayleigh and Uniform distributions. A simple solution based on averaging is
proposed which allows the beamforming nodes to remove significant amount of the phase error.
1.4
Related Work
A technique for sidelobe reduction based on node selection is given in [1] which is used to reduce
sidelobe level. The proposed technique uses a feedback channel from unintended receivers in order to
monitor the level of the received interference power. Randomly selected nodes are used for beamforming
in several number of trials before a reduced sidelobe levels is obtained. The results obtained are good in
minimizing interference to unintended receivers. However, this technique proves to be difficult in cognitive radio sensor networks because of the requirement for a separate feedback channel from primary
users in each trial. Besides, the total number of trials required for a given amount of sidelobe reduction
is high from a practical context. Furthermore, large number of nodes are used to achieve the desired
sidelobe reduction, making it energy inefficient. Therefore, there is a need for simpler node selection
technique that allows green communication with smaller number of nodes while keeping interference
below the limit.
Another related work with regard to the impact of location ambiguity on distributed beamforming
is given in [2] where the location error is modeled using uniform distribution. The authors have given
3
1. I NTRODUCTION
the closed form expression for the mainbeam degradation as a function of location ambiguity. However,
taking uniform distribution as location error of the nodes is not realistically practical. Therefore, statistical characterization of the phase error at the beamforming nodes based on a realistic location error
distribution is a necessary missing segment.
4
Chapter 2
Background Concepts
2.1
Overview
The proliferation of wireless technology and the advancement in power and size efficient computing has
allowed the use of small sensor devices to be employed in remote areas for different applications such as
disaster management, combat field reconnaissance, border protection and surveillance [3]. The devices
in such applications are usually deployed in large numbers in unattended environments to sense or gather
useful information. For a variety of reasons the devices are deployed at random locations without prior
knowledge of the topology of the network.
Related with their small physical size, these devices are provided with low memory, very low data
rates, low bandwidth processing, and limited energy supply i.e. they possess very small low powered
batteries and small omni-directional antennas. Since it is unlikely that these devices are periodically
monitored for battery replacement, efficient power consumption of these devices is critical.
However, the sensor devices need to report the gathered information back to a base station also
known as a sink node which is usually located in range of kilometers away from the sensor network. A
single device cannot sustain to form a communication link with the sink node out of its battery power
supply. Furthermore, there is no way that each device can focus its transmit signal in the direction of
the sink since they have only omni- directional antennas. Obviously, there is limitation in each device
in terms of required transmit power and directivity. This is where DB(distributed beamforming) comes
into picture.
The individual sensor devices are used as virtual antenna elements which cooperatively send the
same transmit signal simultaneously to improve range, directivity and SNR. For the same value of the
range,and receive SNR(signal to noise ratio) the distributed beamforming technique can be used decrease the overall transmit power. Distributed beamforming gives a double benefit in cognitive radio
5
2. BACKGROUND C ONCEPTS
sensor networks. The improved directivity of distributed beamforming technique not only allows to to
boost power in the desired direction but also is used minimize the transmit power in all other undesired
directions.
Efficient use of distributed beamforming as a technique however, requires a number of practical
things that need to be taken into consideration. Among this,monitoring the number of nodes to be used
in distributed beamforming for over all energy reduction is critical . This ensures to maintain the “green”
aspect of the network. Furthermore, the impacts of unavoidable location errors and phase errors on the
distributed beamforming needs to be investigated.
In this chapter, the concepts of distributed beamforming in cognitive sensor network and the asscoiated practical aspects will be discussed in detail.
2.2
Cognitive Radio Networks
The spread of wireless communication technology has allowed the use of diverse and high data rate
applications which add convenience and flexibility to everyday life. However, this situation has also
resulted in congestion and scarcity of the electromagnetic spectrum.
The traditional approach followed toward managing the frequency spectrum had also added a burden
toward the spectral congestion. This is because, the body of the government that is responsible for
managing the spectral band dedicates a certain frequency band to a specific user which is known as
PU(primary users). Often times, the assigned spectral band is not occupied by the PU 100 % of the time
while there is still the need to access a frequency spectrum by other group of users. Surprisingly, some
of the allocated bands are rarely used [4]. The electromagnetic spectrum is thus under-utilized.
One of the major approaches followed took advantage of the under-utilization of the spectrum by
looking for any spectral band which is not used at a particular time and a certain frequency band also
known as spectral hole. This new concept, introduced by Jhon Mitola, is called Cognitive Radio which
is a wireless communication system where the secondary users (cognitive radio users) which don’t have
legal use of the spectral band look for spectral holes to access spectral band [4]. By doing so, cognitive
radio improves the utilization of the radio spectrum.
A very explanatory statement is given by Haykin [4] defining cognitive radio as “ intelligent wireless
communication system that is aware of its surrounding environment(i.e. outside world ) and uses the
methodology of understanding by-building to learn from the environment and adapt its internal state
to statistical variations in the incoming RF stimuli by making the corresponding changes in certain
6
Cognitive Radio Networks
Figure 2.1: Cognitive cycle
operating parameters e.g. transmit power, carrier frequency and modulation strategy, with two prior
objectives in mind [4]:
• Highly reliable communications whenever and wherever needed
• Efficient utilization of the radio spectrum ”
Cognitive radio users can form a network among themselves which is called CR(Cognitive Radio)Network.
CR networks are allowed to access the spectrum only if they are not interfering with the PU who have
licensed access to the spectrum. Therefore, to understand the major procedures taken by CR networks
to access RF spectrum is explained in the next section.
2.2.1
Cognitive Cycle
In order not to violate the spectrum regulation and at the same time maximize the spectrum utilization,
there are a set of important cognitive functionalities which are performed in a cycle called cognitive cycle [4]. Radio-scene analysis, channel identification, and Transmit power control and Dynamic spectrum
management are tasks that constitute the cognitive cycle.
The following three set of procedures are done sequentially in a cognitive cycle as shown in Fig 3.4.
The first two tasks are done at the receiver while the third one is done at the transmitter.
Radio scene analysis/Spectrum Estimation: This cognitive task uses radio spectrum measurement
to identify spectral holes. Interference temprature is a widely used technique in spectrum hole detection.
Interference temprature is introduced by FCC in 2003 to quantify and measure interference in a given
spectrum band at a particular location. Interference temperature shows the level of occupancy of a
spectral band. The value of this function is used as criteria to detect spectral holes .
7
2. BACKGROUND C ONCEPTS
In order to determine the spectral holes, a large number of sensor nodes are used to scan/ sniff the
radio environment to account for spatial variation of the interference temperature. The radio environment is sensed by measuring the level of incoming RF(Radio Frequency) stimuli. Accordingly, the RF
spectrum being sensed can fall into one of spaces based on the level of interference present.
• Black Spaces :- Such bands are occupied by high powered interferers
• Grey Spaces:- partially occupied by low-powered interferers
• White Spaces: - free of any RF interference, except for thermal noise, noise from lightening, etc.
White and Grey spaces are desirable because the interference temperature in these spaces is acceptably
lower. Since the RF stimuli are non-stationary in space and time, interference temperature estimation
involves both spatial and temporal characteristic of the signal. Therefore, related with spatial-temporal
variation of RF stumuli ,the spectral hole detection is quantified through a Detection Statistics, a parameter which shows how long a RF spectrum stays in a white space [4]. Other methods of radio scene
analysis are feature detection,matched filter and energy detection methods. The advantage of Interference Temprature based spectrum sensing over the other methods is it is an FCC recommended method
that guarantees not to exceed interference temprature limit set by PU.
Channel Identification: This involves the identification of a specific channel to be used with in
the detected spectral hole for CR transmission.The interference temprature measurement is used in the
identification of a channel. If the power(interference temprature) detected with radio scene analysis for
a specfic frequency band is above the noise floor, the channel may be identified as occupied, other wise
it can be used for CR transmission. A cooperative algorithm for channel identification based on interference temprature is proposed in[5].
Transmit Power Control and Dynamic Spectral Management: Transmit power control and dynamic spectrum management are functionalites done at the CR transmitter based on the feedback obtained from radio scene analysis. The radio scene analysis measurements such as noise floor statistics,
trafic statistics and the detected spectral holes which change over frequency and time are used to adjust
transmit power and operational frequency band. Transmit power control function involves selecting the
transmit power levels of N CR users to jointly maximize their data-transmission rates, subject to the
constraint of not exceeding interference temperature. Dynamic spectral management is a modulation
strategy that adapts to the time varying conditions of the radio environment. Bandwidth and carrier
8
Beamforming Approach for Cognitive Radio Networks
frequency are dynamically modified according to channel condition. In case OFDM(Orthogonal Frequency division multiplexing), dynamic spectrum management may involve varying the number of bits
per channel based on the SNR.
2.3
Beamforming Approach for Cognitive Radio Networks
In cognitive radio environment, it is of prime importance to monitor transmitted power toward PU. It
is essential that power transmitted toward PU does not exceed interference temprature limit set by PU
themselves. The beamforming techniques are employed as an approach to minimize the transmitted
power in the direction of PU. As such, several beamforming solutions for CR networks have been proposed in the condition that each CR device is equipped with multiple antennas and the power transmitted
toward PU is minimized through null formation. Transmit power of CR users is preserved by focusing
the energy in the direction of the receiver. Therefore, beamforming methods are used to reduce interference to PU from CR transmission. Due to reciprocity, CR receivers will be able to filter out interference
from unwanted transmitter. Spatial variation of the RF stimuli which in this case is PU transmission is
accounted by adaptive beamforming.
A solution that allows maximizing SNR at CR receiver and under a transmit power constraint toward
PU is given in a probablistic context in [6]. The given beamforming solutions are provided considering
limited (Channel State Information) CSI and an upper limit on the transmit power at CR transmitters.
As a result,improved (Bit Error Rate)BER at the receiver is obtained while minimizing the interference
toward CR receiver.
Two adaptive beamforming solutions are given in [7] which indicated OFDM as a proper modulation
technique for CR. The first beamformer the authors proposed is based on spectrum masking concept
which is explained in [8]. This means subcarriers which lie in the same frequency range as PU are given
zero beamforming weight or deactivated. In that way, the the beamforming scheme allowed to supress
interference while maximizing the power toward PU. The second beamforming solution given is based
on spatial filtering concept. This was done by steering nulls in the direction of PU. This allows the PU
and CR to coexist simultaneously.
2.4
Transmit Distributed Beamforming
Transmit Distributed beamforming is a cooperative scheme where sensor devices arrange their transmissions in such a way that there will be coherent addition of the signal from each node at the receiver. As
9
2. BACKGROUND C ONCEPTS
such, distributed beamforming provides with efficient and cost effective means of long distance transmission to a far field receiver or base station by emulating a phased array antenna system.
The term distributed in distributed beamforming has two meanings associated with it [9]. First, it
implies that the beamforming nodes are not physically attached together rather distributed in a certain
area in contrast to the traditional antenna array system. Secondly, it implies that the distributed beamformer itself is distributed among the nodes as each node calculates its own beamforming weight with
no need for a central processing unit. Each sensor device serves as a virtual antenna element. The virtual
antenna array achieves the same beamforming gain in the main lobe enhancement, side lobe reduction,
null pointing etc as a traditional phased array antenna system.
Since distributed beamforming needs some kind of collaboration between the beam forming nodes
it is also known as Collaborative Beamforming. Prior to beamforming, the nodes share the transmit
signal information and synchronization information. Usually in collaborative networks a single node is
selected that is responsible to share information among the nodes. This node is referred to as CH(Cluster
Head)[1].
It is critical to ensure that there is frequency, time, and phase synchronization among the nodes so
that there will be coherent addition of the signals from all nodes. The nodes account for spatial separation
among themselves by applying initial phase that compensates for the phase shift due to propagation of
the signal toward the receiver.
From synchronized transmission of the signal from several nodes as well as initial phase adjustments
at the beamforming nodes, the transmit power is focused in the direction of the intended receiver. As a
result, distributed beamforming brings power gain that is a function of the number of nodes participating
in beamforming. Depending on the design objectives that distributed beamforming is used for, the
power gains of distributed beamforming can be translated into dramatic increases to range,rate or energy
efficiency [10]. Since less energy is scattered in an unintended direction distributed beamforming allows
interference reduction and increased security. Therefore,the distributed beamformer can be used to
control the power in the direction of PU so that interference is minimized.
2.4.1
System Model
Distributed beamforming is performed by virtual antenna array systems which are actually sensor nodes
distributed randomly in a circular disk of radius R. As the devices are separate instruments, they have
their own independent location given in polar coordinate system (rk , ψk ), where ψk ∈ (−π, π). The
location of the beamforming nodes is chosen to follow a uniform distribution in a circular disk where rk
10
Transmit Distributed Beamforming
Figure 2.2: Distributed Transmit Beamforming
Figure 2.3: System Model
follows a distribution fr k (r) = 2 Rr2 and ψk follows a distribution fψ k (ψk ) =
1
2π .
The receiver is located
in the same plane as the distributed beamformer at the far-field given by coordinate (A, φ0 ). A total of N
beamforming nodes participate in beamforming. Each node is equipped with a single isotropic antenna
and has its own location information (rk , ψk ), the direction of intended receiver φ0 and direction of PU
φP . The destination is located at the far field location (A, φ0 ) and the distance from each node to the
q
destination is given by dk (φ) = A2 + rk2 − 2rk A cos(φ − ψk )
2.4.2
Transmit DB Analysis
The transmit DB analysis given in this section is done by taking the following assumptions into account:
• The separation between any two nodes is large enough to ignore mutual coupling among the
nodes.
• Perfect frequency, phase, time synchronization of the transmission from different nodes
11
2. BACKGROUND C ONCEPTS
• All sensor nodes transmit identical energy, equal pathloss apply to all nodes.
• Any reflection, scattering, shadowing and multipath channel effects are ignored.
• Since the destination is located at the far field, the condition (A rk ) holds true. Then the far
field approximation of the distance from each node as given in [2] is written as :
dk (φ) ≈ A − rk cos(φ − ψk )
When N nodes participate in beamforming, each node transmits a signal. At the receiver, the signal
from each node is phase shifted due to propagation distance dk (φ0 ). In order to compensate for the phase
shift due to propagation toward intended receiver, each node applies an initial phase given in equation 2.1
Ψk = −
2π
dk (φ0 )
λ
(2.1)
As a result, the construction addition of the signal from N cooperative nodes brings the focusing of
the power or steering of the beam in the direction of the receiver with an array factor F(φ, r, ψ). The
array factor obtained is written as :
F(φ, r, ψ) =
1 N jΨk j 2π dk (φ)
∑e e λ
N k=1
(2.2)
The beam pattern or the power gain of the distributed beamformer is written as follows
P(φ, r, ψ) = F(φ, r, ψ) ∗ F ∗ (φ, r, ψ) = |F(φ, r, ψ)|2 ,
=
=
1 N N j(Ψk + 2π dk (φ)) − j(Ψl + 2π dl (φ))
λ
λ
e
,
∑ ∑e
N 2 k=1
l=1
N
2π
2π
1
1 N
+ 2 ∑ e j(Ψk + λ dk (φ)) ∑ e− j(Ψl + λ dl (φ))
N N k=1
l=1,l6=k
(2.3)
The expression given by equation 2.3 gives beam pattern of the distributed array. The value of
the beampattern direction at any direction φ indicates the relative power gain in that direction. Due to
random location of the beamforming nodes, the beampattern of distributed beamformer takes statistical
behaviour. Related with randomness of the nodes location,the sidelobe level of the beam pattern shows
12
Transmit Distributed Beamforming
Figure 2.4: beam pattern comparision for random realization of the nodes location
the random behaviour eventhough the mainbeam remains unchanged. The dependancy of the sidelobe
level of the beampattern on location of the nodes is shown in Fig 2.4. Therefore, the average beampattern
is used to characterize the beamforming gain. The average beampattern is found as the expectation of
the beampattern with respect to statistical variables r and ψ as shown below:
Pav (φ) = Er,ψ [P(φ, r, ψ)],
The closed form of the above expression is given in terms of first order Bessel function in [2] as shown
in equation 2.4,
φ
1
1 J1(4πR̃ sin( 2 )) 2
Pav (φ) = + (1 − )|
|
N
N
2πR̃ sin( φ )
(2.4)
2
where R̃ is the radius of the circular disk R normalised with the wavelength λ. The first term of equation 2.4 represents the sidelobe level of the beam pattern. For directions which are far from the main
lobe, the average beampattern asymptotically approaches
1
N.
This means, as the number of nodes in-
creases, the sidelobe level becomes smaller and smaller. The second term gives the contribution of the
main lobe [2]. The authors also derived a closed form expression for nth sidelobe peak which is given
2
3
in equation 2.5. It is observed from the equation that incremental expression (1 − N1 ) π1 [ π(n−
1 ] is an
4
increasing function of N. As such, the first sidelobe peaks gets larger for increasing value of N which
13
2. BACKGROUND C ONCEPTS
Figure 2.5: Average Beam pattern
can be verified from Fig 2.4.2.
Pav (φnpeak ) ≈
2.4.3
1
1 1
2
]3
+ (1 − ) [
N
N π π(n − 41 )
(2.5)
Average Directivity
The directivity of a distributed beamformer can be quantified how much of the radiated energy is focused
to the intended receiver. The closed form expression of the average directivity as given in [2] is shown
in equation 2.6.
D̃av =
N
1 + (N − 1)2 F3 ( 12 , 32 ; 1, 2, 3; −(4πR̃)2 )
(2.6)
where 2 F3 ( 12 , 32 ; 1, 2, 3; −(4πR̃)2 ) is a generalised hypergeometeric function. As 4πR̃ goes to ∞ the hypergeometric function converges to 0 and as a result maximal directivity of N is obtained. This can be
done by increasing the normalized radius R̃ while keeping the number of nodes N the same. It can be
generalised that maximum directivity value of N is obtained by distributing N nodes as sparse from each
other as possible. Unlike, traditional phased array system, where the antenna elements must lie close
enough together to be part of a single physical structure, distributed beamforming nodes can be located
14
Transmit Distributed Beamforming
Figure 2.6: CDF of the beam pattern
as sparesly as desired to maximize directivity. This makes distributed beamforming more attractive.
2.4.4
CDF of the beampattern
The power gain given by equation 2.3 gives the instantenous realization of the beampattern of the distributed beamformer. Although the gain in the direction of intended receiver remains the same all the
time, the power gain in all other directions is stochastic and is dependant on the location of the nodes as
shown in Fig 2.4. Therefore, the use of Cumulative Distribution Function(CDF) is invaluable to quantify
the instantenous power gain in the side lobe level. Fig 2.6 shows the CDF when 20 and 100 nodes are
used for beamforming at a direction different φ 6= φ0 . It is can be seen that from the figure, by using
more nodes lower sidelobe levels are obtained as it is apparent from CDF comparision.
2.4.5
Merits of Distributed Beamforming
As discussed in section 2.4.2, a distributed beamformer brings power gain in the direction of the intended receiver. This gain can be used for different purposes depending on the design objective for which
distributed beamforming is used. The power gain can be used to extend communication range,rate and
improved energy effciency as will be discussed in the following.
15
2. BACKGROUND C ONCEPTS
Extending Communication Range
By keeping the same level power PR at the receiver, power gain of distributed beamforming can be used
to obtain extended communication coverage range. From Frijs equation, we have :
PR = Pt Gt Gr
λ2
16π2 d 2
(2.7)
Where, Gt and Gr are gains of the transmitter and receiver and Pt is the total transmit power. When
N nodes cooperate in distributed beamforming power gain of Gt = N is obtained. As a result, keeping
the other factors constant the communication range will increase by a factor of N in comparision to what
is reachable by a single node.
Increased Capacity
If the communication range is kept the same, a group of N nodes can be used to increase the SNR
at the receiver by a factor of N because the received power is increased by N. From the well known
relation of SNR and system capacity i.e. B log2 (1 + Γ), an increased system capacity can be taken as a
merit of distributed beamforming, where B is the bandwidth used for communication and Γ is the SNR.
Consequently, the rate of the system is increased for the same value of bandwidth. Alternatively, the
increase in the SNR can be used to counteract the impacts of large scale fading.
Improved Energy Efficiency
The power gain of distributed beamforming can also be employed for decreasing the power consumption
or energy efficiency that is used to communicate to a receiver. If the communication range d and the
SNR at the receiver Γ are kept constant, the obtained power gain can be used to decrease transmit power
of each node, and hence the total transmit power as well. If a single node can form a communication
link with the receiver, by using N nodes, the obtained power gain N allows to decrease the total transmit
power by a factor of N. This can be easily shown by fixing Equivalent isotropically radiated power
(EIRP) Pt Gt constant for the same value of SNR at the receiver.
16
Distributed Transmit Beamforming for Cognitive Radio Sensor Networks
2.5
Distributed Transmit Beamforming for Cognitive Radio Sensor
Networks
The importance of beamforming approach in cognitive radio networks is discussed in section 2.3 in
allowing the coexistence of CR with PU in the same spectral band in which each CR user posses multiple
antenna array. However, when the individual cognitive users are sensor nodes, each CR user alone
can not perform beamforming because it only posses a single omnidirectional antenna. In this case,
distributed beamforming takes over the task of spatial filtering by which a group of cognitive sensor
nodes are used direct the transmission to an intended receiver while keeping the power transmitted in
the direction of PU as minimum as possible.
2.5.1
Cognitive Radio Sensor Networks
The increased spectrum utilization obtained by cognitive radios is a promising technology in wireless
sensor networks where there is a need for increased communication quality. Therefore, the merging of
cognitive radio technology with wireless sensor networks have led to emergence of CRSN (Cognitive
Radio Sensor Networks) [11]. A good descriptive definition of CRSN in the same paper defining CRSN
as “ a distributed network of wireless cognitive radio sensor nodes, which sense an event signal and
collaboratively communicate their readings dynamically over available spectrum bands to ultimately
satisfy the application-specific requirements. ”
CRSN are advantageous in that they adapt their transmissions to reduce power consumption. Cognitive radio capable sensor nodes may be able to change their operating parameters to adapt to channel
conditions.This also allows to avoid the extra energy consumption due to packet losses and retransmissions. This capability can be used to increase transmission efficiency, and hence, help reduce power
used for transmission and reception [11].
CRSN networks may be deployed in various applications. Some of the major applications are [11] :
Indoor Sensing Applications : The use of CRSN becomes an invaluable solution to the overcrowding
of indoor communication around ISM band. Conventional sensing applications operating around this
band may have conflicting transmission with Wi-Fi, Microwave and other indoor transmissions. CRSN
allows coexistence with other indoor wireless systems
Multimedia and Real-time surveliance applications: Different multimedia application such as video and
audio and Real-time surveillance applications such as target detection and tracking require minimum
channel access and communication delay. In crowded spectral environment of traditional WSN(wireless
17
2. BACKGROUND C ONCEPTS
Figure 2.7: CRSN Network Architecture
sensor network), this requirement of realtime applications may not be fullfilled. In CRSN, spectrum
access is maximized through simultaenous coexistence of CRSN with the PU or licensed users of the
band. Typical real-time sensing applications are military surveliance, where CRSN nodes could be
deployed to maximise the potential of spectrum access and realiablity [11].
CRSN Architecture
A typical CRSN network comprises a group of cognitive sensor nodes which are distributed in an area.
The network architecture of CRSN may be adhoc or cluster based [11]. As opposed to adhoc network
topololgy, cluster based network topology allows the presence of common communication channel for
exchange of control information such as spectrum sensing data, transmit signal information etc. This
leads to effective spectrum management because of no hidden terminal problem in cluster based CRSN.
The increasing communication overhead in cluster based CRSN can be counteracted by keeping the
number of nodes in a single cluster as small as possible. In a cluster based CRSN, a single node, is
selected as CH for coordinating cooperative communication among the nodes. The methdology for
selecting CH in different network toplogies is given in [12].
All the analysis given in this thesis work will be on cluster based CRSN. A cognitive node(CR
receiver) which serves as a sink is located at the far field. It is also assumed that this node has a
continious supply of energy that allows it to receive signal all the time. Further more, one or more of PU
are located around the CR receiver.
18
Distributed Transmit Beamforming for Cognitive Radio Sensor Networks
2.5.2
Distributed beamforming for interference minimization in CRSN
Omnidirectional antennas transmit equal power in all direction. In contrast,beamforming allows to focus
the transmit signal from each CR user toward the receiver. This leads to transmit less power to other
directions. In CRSN, it is regulatory requirement for the CR users to control the power transmitted in
the direction of PU. The PU users usually give a maximum value of interference that can be tolerated
from CR transmission which is measured using interference temprature metric.
Interference Temeprature
Interference temprature serves as a measure of interference in a particular frequency band. It gives an
idea of the level of occupancy of RF spectral band. Interference temprature IT is measured interms of
the received interfering power in a given bandwidth and it is mathematically defined as :
Pr = KIT B
(2.8)
where K is the Boltzmann’s constant and B is the bandwidth in hertz. Interference temprature limit IT,L
gives the maximum amount of interference for a given frequency band in a particular location. In CR
network context, this would mean regulating the power recieved at PU from CR transmission so that
Interference temprature limit is not exceeded. Therefore, interference temprature limit is the maximum
interference temprature that is tolerated by PU from CR transmission without degradaing quality of
service(Qos).
Thus,from equation 2.8 it is seen that for a given value of interference temprature limit IT L , there
is a maximum tolerable power received at PU. For PU which are located in the far field as shown in the
system model in Fig 2.2, the maximum transmit power that can be tolerated can be calculated from the
maximum received power obtained from equation 2.8.
In distributed beamforming, the sidelobe power level(relative power gain of the beamformer ) is
inversely proportional to the number of nodes. Therefore, increasing the number of nodes can be used
as a mechanism to decrease interference to PU. Furthermore, null formation and sidelobe reduction
methods serve as effective means of interference minimization methods.
Null Pointing
Null formation allows to reduce power received at PU by using amplitude and phase adjustments at
the beamforming nodes. In order to reduce system complexity due to information exchange the beam19
2. BACKGROUND C ONCEPTS
Figure 2.8: Approximate null steering
beamformer with 20 nodes
Figure 2.9: Approximate null steering beamfromer
with 200 nodes
forming weights are calculated in a distributed way at each beamforming node. Furthermore, each
beamforming node has only the knowledge its own location information and is non-aware of the other
nodes location. This means the complete array geometry is not known by each node. Therefore, the
closed form solution for the null steering beamformer is not available due to incomplete array geometry
information at each node. However, an approximate solution is available when the number of nodes
grows very large. Such types of null steering beamformer are available in litrature.
The authors in [13] have shown the use of the approximate null steering beamformer where each
node applies both amplitude and phase adjustments using the approximated values. The results obtained
have shown to reduce the first side lobe peak as shown in figures 2.8 and 2.9. A first sidelobe peak
reduction of 1dB is obtained when 20 nodes are used. The power minimization grows to 6.6dB when
200 nodes are used.
A new way of power minimization in the direction of PU for CR networks in a distributed way is
given in [14]. The solution provided allows a consistent energy consumption because equal beamforming magnitiude applied at each node. Besides, a technique of broadening nulls is also provided that
allowed to decrease the first sidelobe peak by around 4dB as shown in Fig 2.10.
The advantage of the above mentioned methods is that the way of calculating weights is distributed
without requiring exchange of location information among the nodes. However,significant power minimization requires a large number of nodes to be involved in distributed beamforming. With small
number of nodes, significant power reductions cannot be obtained.
20
Distributed Transmit Beamforming for Cognitive Radio Sensor Networks
Figure 2.10: Null pointing using PODB distributed beamformer
Side Lobe Control
Another approach for interference minimization for distributed beamforming is given in [1] . The authors
provided a protocol that allows selecting the nodes for beamforming that requires a feedback channel
from unintended receiver. The method initially takes random combination of nodes. The unintended receivers give a feedback if the power received is above a given threshold or not. The random combination
of nodes are used in a repeated number of trials until the power received at the unintended receiver is
below the desired threshold level.
This method seems to be computationally intensive as it requires multiple trials before convergence.
The beampattern shown in Fig 2.11 required 512 trials of the protocol before side lobe reductions are
obtained. It is difficult to realize this method in cognitive radio environment because, getting a feedback
channel from every PU is not practically feasible.
2.5.3
Practical Considerations for Distributed Beamforming in CRSN
Although distributed beamforming is a promising tehnology for long distance communication in CRSN,
there are a number of practical issues that must be addressed for its deployment. Therefore, study and
research into this practical issues is essential for facilitating the realization of distributed beamforming
as a technique. In this section,the two major practical issues are discussed one by one as given below:
21
2. BACKGROUND C ONCEPTS
Figure 2.11: Side lobe control via node selection
Green Communication
The issue of global warming has activated the need to adapt communication strategies that allow reduced
energy consumption for maintaining ’greenness’.When it comes to cognitive radios, using beamforming
for a better directivity is a strategy that improves energy efficiency. The green aspect of communication
is directly related with the number of nodes used in communication. Finding, the optimal number of
nodes for minimum energy consumption is critical.
Often times, wireless sensor nodes are deployed in large numbers. Distributed Beamforming gain
increases with increasing number of nodes. But it is not necessary for all nodes to participate in the
beamforming process for a given application. It may not be necessary in terms of the required transmit
signal power for more than a certain number of nodes to participate in the beamforming, i.e. a given
subset of the sensor network can accomplish the required beamforming performance [9].
Besides, there is practical challenge in terms of information sharing when the number of nodes increases. Prior to beamforming, the same transmit signal information must be shared among the beam
forming nodes. The more number of nodes are used, the more energy is consumed in sharing information.Therefore, the extra nodes, if involved in beamforming will consume extra energy and extra over
22
Distributed Transmit Beamforming for Cognitive Radio Sensor Networks
head in the pre-transmission phase.
Furthermore, it is indicated in [9] that adding more number of nodes than the optimal number may
not add more to the beamforming gain. That means there is a law of diminishing returns where increasing
the number of nodes no longer continues to improve the beamforming gain. Therefore, there is trade-off
between the number of nodes and power efficiency. By finding the optimum number of nodes which
consume minimum energy, at the same time fulfill the power gain requirement happens to be one of the
research questions in distributed beamforming for CRSN addressed in this thesis.
Coping localization uncertainties and associated phase errors
Location information plays a critical role in many wireless sensor applications. Localization tasks in
wireless sensor networks is done through GPS localization or localization algorithms. Due to multipath
environments,noise, interference etc there is an associated error with the obtained location information.
Distributed beamforming is based on initial phases adjustments at each beamforming node. The
initial phase calculation involves the use of location information as explained in section 2.4.2. Therefore, there is an initial phase error associated with location error uncertainities. As a result, the accuracy
of the obtained location information at the individual sensor nodes may not be enough to allow inphase(coherent) addition of the signal at the receiver. Especially, when operating at higher frequencies,
the location errors produce very large phase errors. This agains brings a very significant degradation of
the beamforming performance [2].
The major sources of location error in WSN are known to be [15]
• Localization Algorithms
• GPS
In next sections, brief introduction in two these localization methods and how this error is introduced
in the localization process will be covered
Localization Algorithms
In distributed sensor network, the location discovery is done at the individual nodes with the use of localization algorithms. Location discovery algorithms mainly involve the following two major procedures:
• Distance/angle measurements between any two nodes
• Combination of the distance or angle measurements
23
2. BACKGROUND C ONCEPTS
Distance or angle measurements serve as a major input in the location discovery processes and are usually based on one of the following techniques:
Received Signal Strength Indicator based ranging
The signal strength received is used to estimate the distance between any two nodes based on prior
knowledge of the transmit signal power. This technique is simple but is highly prone to error in consideration harsh propagation channel conditions.
Time difference of arrival indicator
The propagation time is translated into distance measurements based on the known speed of the signal
which is applied to RF, acoustic, infrared and ultrasound signals. The limitations of this method are
non-line of sight of conditions, environmental conditions such as humidity and temperature which affect
the speed of the signals.
Angle-of-Arrival (AoA)
The estimate of AOA of signals is used to estimate the location of the nodes.
Once the distance and angle measurements are complete, then, combination of the distance of location and angle measurement of different nodes is done to estimate the location of each node. The use of
the combination of radio and acoustic signals is most preferably used in distance estimates because the
difference in the speed of these two signals allows using radio signal for synchronization and acoustic
signal for distance measurement. The most widely techniques for combining distances are given below:
Hyperbolic trilateration: This method uses the intersection of three localization sources to determine
the position of a node.
Triangulation: the law of sines and cosines is used to estimate the location of a node using the angle
estimates from three different nodes.
Maximum Likelihood (ML) estimation: This method uses the principle of maximum likelihood to estimate the location of the nodes using distance measurements from a known localization source.
However, the distance measurements done in the first step are prone to different sources of error including obstacles, interference and multipath effects. Inaddition, the above mentioned ranging methods
have their own typical error with different distributions. The authors in [15] have shown the predictability of RSSI based ranging location error and have shown that location errors of such algorithms are
within 20cm of the true location of the nodes. Furthermore, the distance combination techniques which
involve solving a series nonlinear and linear equation are again prone to error. This brings uncertainty
in the location estimate of the nodes.
24
Summary
Figure 2.12: GPS measurement error distribution 1
GPS
GPS except for being an absolute global positioning system is similar to location discovery algorithm
run locally at the nodes in that it involves the same set of procedures. It involves distance measurement
and combination of distance measurements from satellites which is prone to error due to the same reason
mentioned in the last section. Therefore, the location estimates obtained from GPS contain ambiguity.
Several articles have been published characterizing the location ambiguity of GPS. Therefore,GPS location estimates are one source of location ambiguity in distributed wireless sensor nodes.
Characterization of location ambiguity, with well known models is very important in addressing the
practical issues of distributed beamforming. This will further allow to characterize the phase error at the
beamforming nodes. A GPS location error model with a Rayleigh distribution is given by [16].
2.6
Summary
In this chapter, the basic concepts behind distributed beamforming for cognitive sensor networks is
explained. The two major practical considerations of distributed beamformings i.e the importance of
maintaining ’green’ communication is emphasized and the degradative impact of location ambiguity is
explained. This mentioned issues are research questions of this thesis work. Specifically, a practical
technique for achieving green communication in CRSN through node selection will be developed.
1 Hemmes
et.al
25
Chapter 3
Clustering for Distributed Beamforming
in Cognitive Radio Networks
3.1
Overview
In this chapter, the concept of clustering is used to develop a new node selection method that allows side
lobe reduction in the direction of PU. The first part of the chapter deals with the theoretical concept of
clustering. Different clustering methodologies are discussed, k-means clustering algorithm is explained
in detail and its being used in the proposed node selection method is justified and compared with the
other clustering algorithms. In the second part of the chapter, the methodology of the proposed node
selection method is explained and simulation results are included.
3.2
Concept of Clustering
Clustering is an unsupervised grouping process that identifies an inherent structure with in a dataset by
classifying data into different groups called clusters [17]. Clustering is done with no prior information
about the intrinsic grouping and all the grouping is data driven, thus it is unsupervised process. This
means no training data is used in the clustering process. The main goal of clustering is to determine the
intrinsic grouping in a dataset. The intrinsic grouping with in a dataset is done by defining some criteria
to be used for clustering. As a result, objects in the same cluster are more similar to each other than
objects in different clusters according to some defined criteria. A typical grouping of data points with
clustering in x-y coordinate system is shown in Fig 4.1. The points are clustered into three different
groups based on the location of the points in the x-y coordinate system. It could be seen from the figure
that points which are very close to each other belong to the same cluster. In this example, the euclidean
distance between the points is taken as measure of criterion in clustering.
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3. C LUSTERING FOR D ISTRIBUTED B EAMFORMING IN C OGNITIVE R ADIO N ETWORKS
Figure 3.1: Clustering process example
It is logical to look into what constitutes a good clustering. The criteria to be chosen are expected
to provide the best grouping with in the dataset. Therefore, the choice of these criteria determines how
good the clustering result would be for a specific application. This depends on the application that
clustering is to be utilized. Accordingly, the criterion that best fits a data set for a good clustering is
determined by the user according to the application requirement.
Clustering is used in different applications including finding representative for homogenous groups
(data reduction), finding useful and suitable groupings (data classes) or finding unusual data objects
(outlier detection). In this chapter, the technique of clustering is employed to find suitable groupings of
nodes in the proposed node selection method.
3.2.1
Components of Clustering
Clustering as a widely used data anaylsis tool, has a standard set of procedures which comprise the
clustering process. These major procedures are identified as componenets of clustering[18]. In this
section, these procedures are explained sequentially in the following subsections.
Feature representation
The feature is a representative data of the set of objects to be clustered. Thus, feature is used as clustering
criteria in clustering process. Features are written as matrices composed of multidimensional vectors
called feature vectors. Thus, feature representation is the construction of data matrix to be used in
clustering.
The available number of features may be too large to give acceptable clustering result. Therefore,
reducing the number of features is important for a good clustering result. This can be done in one of two
ways, feature selection and feature extraction. Feature selection involves selection of the most effective
data set as a clustering criteria for a given application from a range of larger data set. Feature extraction is
28
Concept of Clustering
a method of compactly representing the original dataset with a smaller dataset by making transformation
on the original dataset. As opposed to selection of some of the features in feature selection, in feature
extraction all of the features are used to create the smaller extracted version of the data set. One widely
known dimensionality reduction techinique is PCA(principal component analysis)[19]. PCA uses the
eigen values of the feature vectors to identify the most important features. It uses the eigen value
decomposition of the feature set to select the first few features with larger most eigen values.
Afterwards, the selected or extracted features are used as an input in the clustering process.
Definition of feature proximity
The next important procedure in clustering is definition the proxmity measure. It is a way of telling how
different two data points i and j are for a number of feature vectors in the dataset. The measure thus
quantifies the order of simmilarity between two data points[18]. The obtained degree of simmilarity
between the data points is used by the clustering algorithms to classify the objects in different clusters.
The most common measures of proximity are Euclidean, City block, Cosine, Correlation, Mahalanobis,
Hamming and Bergman divergence. A brief explanation of these proximity measures is given below in
reference of two points shown in Fig 4.2.
• Euclidean
Square euclidean space scales the proximity measure between any two data points as the euclidean
1
distance d between the points, where d = (ix − jx )2 + (iy − jy )2 2 .
• City Block
This is merely the absolute value of the distance between any two points d = ki − jk. It is also
referrred to as Manhattan distance.
• Cosine: This proximity measure considers each data point as a vector and measures the angle α
between these points. Then,the cosine of the angle cos α is taken as a measure of proxmity as can
be seen from Fig 4.2.
• Correlation The correlation between the points is used as a measure of proxmity between points.
This method is suited for feature vectors that have larger variance between the elements.
• Hamming
This measure of proximity is suited for binary data for a binary matrix, representing the state of
various objects.
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Figure 3.2: points i and j in cartesian coordinate system
• Mahalanobis
This is simmilar to euclidean distance measure. The major difference is the covariance matrix of
the feature vectors is used in distance calculation as shown below:
T
1
d = k (ix − jx ))2 Σ−1 ( iy − jy )2 k 2
This is relevant when the feature is a multidimensional set. The proximity measure is normalized
with the covariance matrix of the features. This helps one feature vector not to dominate the other
feature vector. One drawback of this method is it is computationally intensive as it involves the
computation of the covariance matrix.
• Bergman
Bergman divergence is a combination of euclidean and cosine similarity measures
It is very important to identify the appropriate proximity measure suitable to the data domain for a proper
clustering result.
Data Preparation
The selected features or clustering criteria may have attributes that will degrade clustering tendency
or negatively impact the clustering result. Therefore, it is important to perform the necessary data
preparation. The preparation may involve scaling or transformation of the data set so that good clustering
result will be obtained[18].
Clustering
Clustering or grouping process involves the use of an appropriate clustering algorithm. Several clustering
algorithms have been developed so far. Generally, according to the unique way clusters are grouped,
clustering can be done in one of the following approaches [18]:
30
Concept of Clustering
• Hard vs Fuzzy Clustering :
Hard clustering assigns each data point to a single cluster. In this type of clustering, an object can
belong to only one cluster.A cost function is calculated to evaluate the clustering result. Different
algorithms of this category follow different approach to form the clusters. In general , clusters
formed by such algorithms are exclusive in nature. For a data set with N objects, K clusters are
formed where K ≤ N to optimize the distance between clusters. They run multiple iterations in
order to end up with the correct result. A typical algorithm of such kind is k-means clustering
algorithm .
On the other hand, fuzzy clustering assigns degrees of membership to each data point where each
point belongs to one or more clusters. Such clustering methods are well suited for a datasets with
uncertainty or imprecision of varying degrees which is modeled in fuzziness. Such data sets are
called fuzzy sets and the objects in the set have degree of member ship to the set they belong
to which is represented using membership functions. Therefore, in this type of clustering, an
object is grouped in more than one cluster with different degrees of membership. There is vague
or fuzzy boundary between different clusters. Typical example of an algorithm of this type is
fuzzy c-means clustering algorithm. The fuzzy-c means is an equivalent counterpart of k-means
algorithm for fuzzy data set.
• Probablistic vs Determinstic Clustering:
Probablistic clustering algorithms use bayesian classification approach to determine the probability that an object is classified under a single cluster. The fundamental assumption of these
methods is that the data set is a sample drawn from mixture model of several probability distributions. Objects under a single distribution are grouped under a single cluster and each cluster can
be associated with the distribution parameters such as mean or variance. Probabilistic clustering
uses the log likelihood function as a cost function in calculating the probability of assigning an
object under a single cluster [17]. Deterministic clustering however, as its name implies uses no
concept of probablity is associated in grouping the objects under a single cluster.
• Hierarchical vs Flat:
In hierarchical type of clustering, every object or point makes a single cluster and these clusters
are hierarchically merged in series of steps based on a property the clusters share. The hierarchy
can be formed from bottom to top as in agglomerative clustering methods or from top to bottom
as in divisive clustering methods. The drawback of hierarchical clustering methods is scalability.
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Figure 3.3: Clustering Procedures
The time and computational complexity is on the order of O(N 2 ), where N is the number of
total objects to be clustered. It also follows a greedy approach in that they can never undo what
was done previously i.e. the clusters will not be restructured in order to favor the final result of
clustering.
In flat clustering algorithms however, all clusters lie in the same level in the sense that each cluster
is not a subset of any other cluster. Besides, these clustering algorithm run a series of iterations to
make an online batch update to clusters formed until the good clustering results are formed.
Validity Measures
Once clustering is done, cluster validation or measuring the goodness of clustering algorithms is important in order to increase the benefit obtained from clustering methods [17]. After clustering is done, it is
the part of the clustering process to validate the accuracy of clustering results. This is usually measured
interms of the proximity of the cluster members to each other. Cluster validation techniques therefore,
measure how well cluster members are simmilar based on the preferred clustering criteria. Therefore,
goodness of the number of clusters selected can be evaluated by the validity measures.
In most clustering algorithms, the number of clusters is set as a user parameter. However, this
affects the clustering result as user chosen number may not result in the best or optimal clustering. Thus,
clustering validation techinques also serve as a feedback in determining the number of clusters to be
used as shown in Fig 3.3. Clustering can be redone for a different value of cluster number if the current
value of cluster number is not acceptable by the validity measure test.
3.2.2
Interpretation of results
As the main goal of clustering is to provide a practical information from the dataset, the interpretation
of the results is done in the specific field of expertise clustering is applied to. The knowledege extracted
32
Clustering Node Selection Method
from interpertation of results is used to solve problem faced in a specific field.
The above standard procedures of clustering process are summarised in Fig 3.3. These set of procedures are employed in the next section to develop a new node selection method.
3.3
Clustering Node Selection Method
In this section, the concept of clustering is applied to be used in the proposed node selection method.
The node selection is done by a node selected as a Cluster Head(CH). We use clustering process to serve
as informative input to node selection for distributed beamforming. As indicated in the last chapter,
green communication in cognitive radio network requires the use of less number of nodes while minimzing interference power to PU. Therefore, a node selection method that fullfills this criteria is of prime
importance. In the sections, the clustering methodologies are studied more closely with respect to their
relevance to our goal.
In developing the new method, we compare the different clustering methdolgies and study their
nature. In addition, we study the relevance of any of this algorithms to be used in node selection methods.The formal steps of clustering presented in the last section are applied and a specific clustering
algorithm, k-means clustering algorithm is chosen and used in the proposed node selection method.
The use of clustering for our application concerns selection of nodes to be used in beamforming that
allow communication with CR receiver with less number of nodes as possible. We want to choose nodes
so that the power transmitted in the direction of PU is minimized.The power minimization is achieved
by selecting nodes with destructive carrier phases. Clustering is used as an invaluable tool to identify
these nodes.
3.3.1
System Model
N Cognitive radio nodes are uniformly distributed in a circular area of radius R, and azimuth angle
ranging between −π and π as shown in 3.4. The intended CR receiver and the PU are located at far field
region at φ0 and at φ p respectively, where φ p ∈ (−π, π) and φ = φ0 with out loss of generality. Each
node has its own location information (rk , ψk ) , the direction of intended receiver φ0 and the direction
of PU φ p , all given in a polar coordinate system. Node Selection is done by the CH which has location
information of all the nodes and the direction of PU. The intended receiver is located at the far field
region (A, φ0 ) which validates the assumption (A R) and the far field distance from each node A in
any arbitrary direction φ is denoted by dk (φ, ψk ).
33
3. C LUSTERING FOR D ISTRIBUTED B EAMFORMING IN C OGNITIVE R ADIO N ETWORKS
Figure 3.4: System Model
3.3.2
Feature Representation
In choosing the feature to be used in clustering, we have taken into consideration our application requirement. It is required that the power transmitted in the direction of PU is minimized while keeping
the main beam at maximum. The unique characterstic of the nodes that must be used with the direct
connection with the power gain of the beampattern is the phase of the nodes. Therefore, the carrier phase
of the nodes is used as a feature to uniquely identify each node in the clustering process.
More specfically, the carrier phase in the direction of PU Ωkp = Ψk + 2π
λ dk (φ p , ψk ), where Ψk =
− 2π
λ dk is the initial phase applied at each node. Ωkp when used as a feature or clustering criterion leads
to controlling the power transmitted in the driection of PU.
The phase Ωkp is chosen as a clustering criterion because it solely determines the array factor gain
at a direction φ p as shown in equation 4.1.
F (φ p , ψk ) =
1 N j(Ψk + 2π dk (φ p ,ψk ))
λ
∑e
N k=1
(3.1)
The relation of the power gain of the distributed beamformer is related to the carrier phase of the signal
from each node as shown in equation 4.2 :
P (φ p , ψk ) = |F (φ p , ψk )|2
(3.2)
When a single PU direction is taken into consideration in the clustering process,the feature to be
used in the clustering process can be an N dimensional vector,where N is the total number of nodes
available.When there are multiple PU directions, the feature set will be a matrix Ω with dimension
[N, P] , where P is the total number of PU directions considered in the clustering process.
34
Clustering Node Selection Method
Figure 3.5: Wrapping the phase of the node for clustering
3.3.3
Data Preparation
It is shown that the matrix Ω is selected to be the feature vector to be used in clustering. In this section
the selected feature is prepared to give a meaningfull clustering result. The entries of the matrix is
represented by Ωk, j where k = 1, ..., N and j = 1, ..., P. Since these entries are phase values at the
direction of PU, they can take on any real number. However, only the values of the entries ranging
between −π and π give unique representation of the values of the entries. Therefore, in this data
preparation stage the phase values are wrapped between −π and π. It can be seen from Fig 3.5 that the
carrier phase of the node at a specific direction of the nodes is limited in the given range −π and π after
phase wrapping. This prepares the feature set for a phase grouping in the specified range to be used in
clustering proccess.
3.3.4
Definition of Proxmity Measures
Square euclidean distance is chosen as a measure of proximity for the selected feature set. Euclidean distance calculation allows accurate spatial representation of “distance” which is actually phase difference
between the nodes. Therefore, the euclidean distance d represents the phase difference of the signals
between any two nodes ∆Ωi,k as shown in Fig 3.6. Minimizing the sum of squared euclidean distance d 2
where d 2 = ∆Ωi,k 2 = kΩi − Ωk k2 is equivalent to least squares, or minimum variance, estimation methods which leads to faster convergence. The subscripts i and k range from 1 to N. Therefore, the use of
square euclidean distance makes the clustering process computationally faster and simpler as compared
to the use of other proxmity measures such as manhattan distance.
35
3. C LUSTERING FOR D ISTRIBUTED B EAMFORMING IN C OGNITIVE R ADIO N ETWORKS
Figure 3.6: Phase difference between the nodes scaled as euclidean distance
3.3.5
Selection of Clustering Algorithm
The choice of clustering algorithm is directly related to the nature of clustering to be done. It is therefore
important to formulate the structure of the clusters that need to be formed which leads to identifiying the
correct clustering algorithm. Therefore the following features are expected to be selected.
• For our problem at hand, we want a unique identification of each node by its phase at the far field.
It is then necessary to choose partition/exclusive based clustering method. In that way, a single
node will belong to a single cluster or phase group.
• Since the clustering algorithm is going to be run on wireless sensor devices, it must be simple and
fast algorithm with less memory requirement .
k-means algorithm is a popular such clustering algorithm based on Lyold’s method that satisfies the
above mentioned characterstics. Being a partition based clustering algorithms, its best performance interms several features is indicated in Table 5.1. Therefore, k-means is selected as a clustering algorithm
to be used in this node selection method due to its features listed below [20]:
• It is a simple algorithm and with scalability and complexity
The simplicity of kmeans allows it to be deployed in wireless sensor nodes with computational
limitations.
36
Clustering Node Selection Method
Table 3.1: Comparision of Clustering methdology
Methodology
Partitioning
Hierarchical
Probablistic
Comput.Complexity
O(N 2 )
O(N 2 )
O(N)
Time.Complexity
O(Nkl)
O(N 2 )
O(N + K)
Scalablity
large
small
large
Noise robustness
robust
not robust
robust
Space.Complexity
O(K + N)
O(N 2 )
O(N + K)
Figure 3.7: Selection of Clustering Algorithms
• It is converges fast compared to other clustering algorithms
It converges in small number of iterations. The use of sum of square distances even leads to faster
convergence
• It based on partitioning based exclusive clustering algorithm
This means a single node belongs to a single cluster only, unlike other clustering methods such
as fuzzy c-means and hierarchical clustering where a single node may belong to more than one
cluster
• It is also known to be robust to noise in the underlying data[20]
Therefore, k-means is selected for the its best features as opposed to other partition based algorithm
which are shown in the Fig 3.7.
3.3.6
Clustering/ Grouping with k-means clustering Algorithm
In this stage, the selected clustering algorithm is used to group the nodes into clusters. k-means algorithm takes the number of clusters K, the type measure of simmilarity squared euclidean distance and
the prepared data matrix Ω as an input. k-means algorithm does the clustering or grouping with the
37
3. C LUSTERING FOR D ISTRIBUTED B EAMFORMING IN C OGNITIVE R ADIO N ETWORKS
Figure 3.8: Inter and intra cluster Proximity measure
following set of operations listed below.
1. For a given input data Ω, it defines a set of arbitrarly assigned K center points represented as
centroids (Ωc,a ) where a = 1, ..., K. At the beginning, the centroid points are taken randomly. The initial
set of clusters are formed around this centroids based on the proxmity of the nodes to these centroids.
The proxmity measures are given by squared euclidean distance between a node and a centroid. Here,
we define two types of distances, intra-cluster distance d12a,k that defines the square euclidean distance
between cluster a and node k as given in equation 5.3, where k = 1, ...N. The inter-cluster distance d22a,b
defines the square euclidean distance between any two centroids Ωc,a and Ωc,b given by equation 5.8,
where a = 1, ..., K , b = 1, ..., K and a 6= b. The inter-cluster distance measures the proximity between two
clusters and intra-cluster is the distance between a node and a centroid. These distances are illustrated
in Fig 3.8. The cluster formation at this step is done by calculating the intra-cluster distance of each
node to every centroid and a node is grouped under the cluster for which the intra-cluster distance is the
minimum.
d12a,k = |Ωc,a − Ωk |2
(3.3)
d22a,b = |Ωc,a − Ωc,b |2
(3.4)
2. In every next iteration of the algorithm , a new set of centroids are calculated by taking the mean
38
Clustering Node Selection Method
of the data points formed under each cluster in the previous step as given by the expression :
(Ωc,a ) =
1
nc,a
∑Nk=1,k∈a Ωk
where nc,a is the number of elements in the cluster a.
Then, this newly calculated centroids are used to reform new set of clusters. Each node is regrouped
under the newly calculated cluster centorid to which its intra-cluster distance is the minimum and becomes the member of that cluster. Therefore, in every iteration, k-means algorithm minimizes the sum
of squared distances of each point from the centroid(intra-cluster distances). By doing that, the intercluster distance are also maximized. This step is repeated for a number of iterations by minimizing the
summation of the intra cluster distances for all clusters given by the following expression:
D
E
argmin ∑Ka=1 ∑Nk=1,k∈a d12a,k
The value of the above expression is monitored in every step of iteration before convergence.
3. k-means algorithm converges, when the current iteration stops to produce no better result than the
previous iteration. This means convergence is reached when the sum of intra-cluster distance no longer
decreases.
The algorithm’s operation are summarized in Fig 3.9.
After convergence, k-means provides us with K clusters. In our application K clusters formed represent K phase groups because clustering is done by using phase as a criteria. This means the nodes in
the same cluster have simmilar phase values at the specfic direction of PU. Alternatively, the nodes in a
single cluster form a single phase group as depicted in Fig 3.10. This was verified by clustering a group
of 200 nodes into 6 clusters at the direction of PU located at direction φ = 100 . It could be seen that each
cluster formed makes a phase group approximately 1.05 radians wide as shown in Fig 3.11.
3.3.7
Validity measures
Running validity measure after clustering allows to determine how good clustering results are. The
closeness of the elements in a single cluster is used as a measure of the goodness of the clustering result.
This measure uses the original method used by k-means algorithm to form the cluster. Therefore, here
we use the intra-cluster distance as an argument to measure the quality of clustering. Minimization
of summation of intra-cluster distance minimizes the variance with in a cluster. This means nodes in
39
3. C LUSTERING FOR D ISTRIBUTED B EAMFORMING IN C OGNITIVE R ADIO N ETWORKS
Figure 3.9: Steps of k-means clustering algorithm
Figure 3.10: Clustering nodes using k-means clustering Algorithm
40
Clustering Node Selection Method
Figure 3.11: Clusters or phase groups formed using k-means clustering
a single cluster are getting simillar in phase. The smaller value of this arguments indicates nodes are
closely clustered to the centroid and clustering results are good.
By monitoring, the value of the validity measure argmin N1 ∑Ka=1 ∑Nk=1,k∈a d12a,k , it is possible to tell
how good clustering results are. N is the total number of elements involved in clustering. The magnitude
of this argument can also provide a feedback on the validity of the number of clusters K formed. This
is because, good clustering result is dependant on the number of clusters formed for a given dataset. If
the validation measure obtained is unacceptable, clustering is done again for a different value of cluster
number.
The relation between validation measure and the number of clusters is evaluated for different number
of clusters as shown in Fig 3.12. It is seen from the figure that for K = 6, the validation measure is 0.09
which is acceptably small. Thus, it can be said that good clustering results are obtained. With higher
values of validation number, however the inter-cluster distance will get smaller at the same time. When
the inter-cluster distance decreases, it requires more nodes to get the same amount of power minimzation.
Therefore, working at smaller values of cluster number K is preferrable. This makes it necessary to work
with cluster numbers that keeps the validation number below 0.1.
3.3.8
Interpretation of Results
Clustering results from the previous section show that the clusters formed consist of nodes with simmilar
phase values. It is also evident that different clusters are very different from each other which is the
result of k-means algorithmic approach. Therefore, selecting nodes from different clusters allows to
select nodes with different phase values at specific direction.
41
3. C LUSTERING FOR D ISTRIBUTED B EAMFORMING IN C OGNITIVE R ADIO N ETWORKS
Figure 3.12: Validity Measure in radians
From the principle of superposition, selecting nodes with a destructive phase at a specific direction
allows to minimize the power in that direction i.e. argmin [P(φ p , ψ)]. The minimzation of the power
transmitted in the direction of PU is related with two principal factors. The first is the distance between
any two clusters which is actually the phase difference between any two clusters. This directly determines how much the signal from any two nodes are out of phase from each other. The second is the
number of selected nodes used inbeamforming.
When 5 clusters are generated, the cluster centers are 1.05 radian out of phase from each other.
Therefore, the signal generated from nodes selected belonging to the clusters are 1.05 radians out of
phase from each other. From the principle of superposition, the sum of the signals from these five
nodes. The composite signal decreased in amplitude by a factor of 10. This is equivalent around 20 dB
reduction in the power gain. This provides theortical basis in using clustering based on phase for node
selection in distributed beamforming in cognitive radio networks where interference minimzation is of
prime importance.
3.3.9
Using Clustering for node selection
Clustering node selection method first starts by computing the number of nodes to be selected. This
can be done with regard certain aspects of the network. In this thesis work, the number of nodes to be
selected takes into account the total energy consumption and interference minimization of the network
42
Clustering Node Selection Method
Figure 3.13: Toplogy of clusters and selected nodes
into account which will be covered in chapter 4. In this chapter, we assume the number of nodes to be
selected N0 is known in advance taking the mentioned issues into account.
Once the number of nodes to be selected is decided, clustering node groups the nodes into N0 groups
or clusters using the procedures discussed in the last section. Then, N0 will be selected by picking a
single node from every cluster. The node selected from each cluster is chosen to be the one closer to
the centroid. By doing that distance(phase difference) between the selected nodes will become larger.
This allows the selected nodes to be out of phase in larger degrees. This maximizes the destructive
additive effect of the beam pattern in the chosen direction. As a result,clustering node selection allows
the minimization of the power gain of distributed beamformer.
The procedures of clustering node selection method is summarized in Fig 3.14. The topology of 200
nodes grouped into 6 clusters is shown in Fig 3.13. The node belonging to each clusters are given in
different shape for the sake of separation.
In the next section, the use of the selected nodes to form a beam pattern that minimizes interference
on PU will be covered in detail.
Simulation Results
In this section, the use of the proposed node selection method to select nodes is demonstrated. The
selected nodes are then used for beamforming. A group of 400 nodes is distributed in a circular disk
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3. C LUSTERING FOR D ISTRIBUTED B EAMFORMING IN C OGNITIVE R ADIO N ETWORKS
Figure 3.14: Clustering node selection basic steps
of radius R = 32 meters. The working frequency is VHF at 160MHZ. Further more, beam pattern will
be used to minimize interference in the direction of PU only through the use of node selection with out
requiring any phase adjustment. The average beam pattern is generated when the selected nodes are
used for beamforming with different number of PU considered in the simulation scenario. The CDF of
the beam pattern is also generated using Monte Carlo simulation of 1000 iterations. Both the average
beam pattern and the CDF plot showed that interference minimzation with smaller number of nodes is
achieved using the proposed node selection method.
CASE I - Single PU direction
First the simulation is done by considering a single direction of PU at φ p = 200 . The number of nodes
to be selected is N0 = 6, and therefore K = 6 clusters are formed. The clustering criteria was taken to
be the carrier phase at φ p = 200 which is a vector of size [400,1]. The validation result obtained is 0.09
which means acceptable clustering results are obtained. Then, single node is selected from each cluster.
The selected nodes are then used for beamforming. The average beam pattern of 6 nodes was generated
with sharp main beam pointing in the direction the intended CR receiver as shown in Fig 3.15. It can be
seen from the figure the sidelobe level in the direction of PU is reduced down to -26.13 dBs. Fig 3.16
44
Clustering Node Selection Method
Figure 3.15: Beam Pattern of 6 nodes, PU located at φ = 200
Figure 3.16: CDF of Beam Pattern of 6 nodes, PU located at φ = 200
shows CDF of the beam pattern. The cdf plot shows the power gain at the direction of PU is less than
-20dB for close to 100 % of the time. The improvement in the interference minimization of clustering
method can be observed from CDF comparision shown in Fig 3.16.
CASE II - Multiple PU directions
In this subsection, it is assumed that more than one PU direction are known to exist at the far field.
Therefore, Clustering node selection takes into account all the direction of the PU in selecting the beamforming nodes. When multiple PU are considered in the clustering process, the clustering criteria is
45
3. C LUSTERING FOR D ISTRIBUTED B EAMFORMING IN C OGNITIVE R ADIO N ETWORKS
Figure 3.17: Beam Pattern of 10 nodes, PU located at φ = −200 and φ = 200
matrix of dimension [N, P] where N is the total number of nodes and P is the number of PU directions.
From the simulation results, it is observed that the introduction of more than one PU created the
need to use more number of nodes in the clustering process. This is because, when more number of
PU directions are considered, the inter-cluster distance at each direction gets smaller. The reduction
in inter-cluster distance brings the reduction in the obtained phase difference or phase offset between
clusters. This further means that the selected nodes will have smaller phase difference from each other
at those directions thus, requiring more number of nodes for the same level power minimzation.
Two PU:
We next considered two PU directions located at φ p = 200 and φ p = −200 in the clustering process. The
feature vector(clustering criteria) selected is the carrier phase is a matrix of size [400,2] in the two PU
directions. The number of nodes to be selected is N0 = 10 and the number of clusters is then k = 10 .
Afterwards, Clustering is done with 10 clusters and 10 nodes were selected accordingly. The validation
measure which is intra-cluster distance is found to be 0.033. This value is acceptably small.It is seen
that beamforming with 10 nodes gave around -23dB sidelobe level in the average beam pattern as shown
in the Fig 3.17. This is equivalent to sidelobe reduction of 13 dBs.
The CDF of the beam pattern is shown in Fig 3.18. It is observed from the figure that the power gain of
the beam pattern at both at φ p = 200 and φ p = −200 is kept at -18dB for close to 100 % of the time. This
indicates that clustering node selection method allowed significant reduction in the power transmitted
when there are two PU.
46
Clustering Node Selection Method
Figure 3.18: CDF of Beam Pattern of 10 nodes, PU located at φ = −200 and φ = 200
Figure 3.19: Beam Pattern of 21 nodes, PU located at φ = −400 , φ = −200 and φ = 200
47
3. C LUSTERING FOR D ISTRIBUTED B EAMFORMING IN C OGNITIVE R ADIO N ETWORKS
Figure 3.20: CDF of Beam Pattern of 21 nodes, PU located at φ = −400 ,φ = −200 and φ = 200
Three PU:
Clustering node selection method was used to minimize interference in the direction three PU located at
φ p = 200 , φ p = −200 and φ p = −400 . The feature vector(clustering criteria) selected is the carrier phase
in the those directions which is a matrix of size [400,3]. The number of nodes to be selected is N0 = 21
and the number of clusters is then k = 21. Afterwards, Clustering is done with 21 clusters from which
21 nodes were selected. The validation measure which is intra-cluster to inter-cluster ratio is found to
be 0.009. This value is acceptably small.
The selected 21 nodes are then used for beamforming. By generating the average beam pattern, it
is observed that the power transmitted at the direction of PU was reduced down to -23 dBs. This is
equivalent to around 10dB reduction in the average beam pattern as shown in the Fig 3.19. The CDF
of the beam pattern is shown in Fig 3.20. It is observed from this figure that the power gain at both
directions φ p = 200 , φ p = −200 and φ p = −400 is minimized.
CASE III Two DCR directions
In this section, two directions of DCR are considered in beamforming. This is done by dividing the
nodes into two groups(subclusters) so that each group of nodes directs the beam to each DCR. The
nodes in these subclusters apply separate initial phases to the known destinations. The nodes shown in
48
Clustering Node Selection Method
Figure 3.21: Two DCR and one PU
Figure 3.22: Beamforming of two main beams with
20 nodes
green belong to the first group and are used to steer the beam in the direction φ0,1 by applying intial
phase Ψ1 =
2π
λ
∗ dk (φ0,1 , ψk ). Similarly the nodes shown in blue belong to the second group and are used
to steer a beam to the direction φ0,2 by applying initial phase Ψ2 =
2π
λ
∗ dk (φ0,2 , ψk ). It is seen from the
figure that the main beam is steered at 00 and 300 . Furthermore, clustering node selection method is
used to reduce the sidelobe level in the given direction of PU.
CASE IV Impact of node density
In this section, the impact of increasing node density in the obtained sidelobe reduction by clustering
node selection method is studied.In the simulation, the number of nodes used for beamforming was kept
the same while increasing the number of nodes distributed in the same area of circle R = 32 meters.
It is observed from simulation results that larger sidelobe reductions are obtained with increasing node
density as shown in figures 3.23 and 3.24. As a result the sidelobe level in the direction of PU will be
lower. This is because, the more nodes are available, more phase values are available for clustering for
the same value of cluster number K. This allows to get smaller intra-cluster distances for sufficiently
large inter-cluster distances. This makes good clustering result to be obtained. As a result, larger side
lobe reductions are obtained.
CASE V When PU is close to DCR
In some beamforming scenarios ,it may be possible that a PU may lie in close proximity with Distant
Cognitive User (DCR). In this case it may be important to reduce the sidelobe level close to the main
49
3. C LUSTERING FOR D ISTRIBUTED B EAMFORMING IN C OGNITIVE R ADIO N ETWORKS
Figure 3.23: Beamforming with 6 nodes for a node
density of 4 nodes per meter square
Figure 3.24: SLL at the direction of PU for increasing value of node density
beam. For our working frequency of 160MHZ, the first minima of the mainlobe lies at −20 and 20 at
around -7dB level. By using clustering node selection the first minima was reduced down to −26dB at
40 as shown in Fig 3.21. In this way the power transmitted at PU close to DCR is minimized.
CASE VI When PU cover a range of spatial directions
The sidelobe reduction pointed at a single direction of PU may not be enough when PU users are spatially
distributed close to each other. It may be necessary to broaden the sidelobe reductions obtained to cover
a range of directions. In this case, clustering method can be used to reduce interference by broadening
the sidelobe level. Broadening of the sidelobe level is done by using multidirectional clustering and the
result obtained is shown in Fig 3.26.
CASE VII Clustering method at higher operational frequency
The change of operational does not affect the performance of clustering node selection method. This
is because the clustering criteria is uniformly distributed between −π and π regardless of operational
frequency when sufficiently large nodes are involved in the clustering process. This was verified by
using clustering node selection at other operational frequencies. The performance of clustering method
at higher frequencies f=900MHZ and f=2 GHZ is also verfied by selecting 6 nodes. Acceptable sidelobe
reduction of more than 19dBs is obtained as shown in Fig 3.27.
50
Clustering Node Selection Method
Figure 3.25: Beamforming with 6 nodes when PU is located at 4 degree
Figure 3.26: Beamforming with 6 nodes with broadened sidelobes
51
3. C LUSTERING FOR D ISTRIBUTED B EAMFORMING IN C OGNITIVE R ADIO N ETWORKS
Figure 3.27: Beamforming with 6 nodes at f=900MHZ and 2GHZ
CASE VIII Clustering method at for different values of R̃
The performance of clustering for different values of R̃ was investigated by varying the radius of the disk
while keeping the wavelength λ constant. Results obtained show that the same sidelobe reduction was
obtained for values of R̃ = 8, 17 and 20. The comparision results are shown in 3.28
In summary, it can be concluded that significant interference minimization can be obtained through
the proposed node selection method with out requiring any phase adjustments at the beamforming nodes.
The results obtained are very important taking into consideration that there is no need to apply beamforming weights to produce the obtained power reductions in the directions of PU. The sidelobe reductions obtained were large for high density distribution of the sensor nodes. Therefore, the node selection
method is more suited to low power high density sensor networks which serve in earth quake monitoring
applications or any other application that requires dense node distributions.
3.4
Summary
In this chapter a new node selection method based on clustering technique is proposed. And the results
presented in the chapter are summarised as follows:
52
Summary
Figure 3.28: Comparision of clustering node selection for different values of R̃
• Clustering node selection method is shown to significantly reduce the sidelobe level in the direction of PU. The results obtained are very important taking into consideration that there is no need
to apply beamforming weights.
• The use of subclusters which individually apply separate initial phases are used to direct multiple
beams in different directions. The selected nodes from these subclusters are used together to
reduce the sidelobe level.
• Sidelobe reductions obtained leads to interference minimization with small number of nodes with
out requiring any phase adjustments at the beamforming nodes.The use of small number of nodes
through node selection helps in decreasing the overall energy consumption of the network which
will be covered the next chapter.
• Increasing node density increases sidelobe reduction obtained from clustering node selection
method. The sidelobe reductions obtained are large for high density distribution of the sensor
nodes. This indicates that clustering is more suited to low powered high density sensor networks
which for instance serve in earth quake monitoring applications or any other application that re53
3. C LUSTERING FOR D ISTRIBUTED B EAMFORMING IN C OGNITIVE R ADIO N ETWORKS
quires dense node distributions.
• Clustering node selection method is also used to broaden sidelobe reductions which can be used
when the direction of PU is uncertain or when PU cover a range of spatial directions.
• The performance of clustering node selection method proves to be independant of operational
frequency and normalized radius R̃.
• Comparative analysis of this work with a similar work , i.e. sidelobe reduction via node selection given in [1] implies that clustering node selection is a simpler and efficient interms of radio
resource consumption and the number of nodes used in beamforming.
54
Chapter 4
Close to Optimal Node Selection for Green
Cognitive Radio Sensor Networks
4.1
Overview
Establishing green communicaton is given great emphasis as a crucial aspect of wireless networks. For
beamforming applications, maintaining the greeness of the network is directly related with optimizing
the total energy consumption with the number of nodes used for beamforming. The power consumption
of the network rises with the number of nodes. As large number of nodes are used, the more energy is
consumed. Therefore, selecting the optimal number of nodes for beamforming considerably enhances
the greenness of the network.
In CRSN, the number of nodes used in distributed beamforming should be large in order to have less
sidelobe level and thus transmit less power in the sidelobe region therefore be able to reduce interference
to PU as explained in chapter 2. Therefore, due to interference minimization, energy consumed in
distributed beamforming is non-optimal as more nodes are used for sidelobe reduction. The issue of
interference minimization brings non-optimality in the energy consumption of the network. The major
challenge is how to select the nodes used for beamforming from the stand point of interference on
primary users and over all energy consumption of the network.
In this chapter, the proposed node selection method in chapter 3 is applied to select a close to
optimal number of nodes for beamforming application in cognitive radio networks. Operating close to
optimality allowed the conservation of energy per transmission which is quantified in order of Joules
while keeping interference below the limit. It is further assumed that CR transmission is the single
source of interference power at PU and other sources of interference are not taken into account. The
energy reduction obtained through clustering method are demonstrated.
55
4. C LOSE TO O PTIMAL N ODE S ELECTION FOR G REEN C OGNITIVE R ADIO S ENSOR N ETWORKS
Figure 4.1: System Model
4.2
4.2.1
System Model and Protocol
System Model
A set of beam forming nodes are distributed in a circular area of radius R = 32m as shown in Fig 4.1.
One node is located in 3.21 square meter. The Cluster Head(CH) is located at the center of a circle and is
responsible for node selection, coordinating the pre-transmission information exchange and localization
activities. All the other nodes lie within the communication range of the CH and transmission rate of
the nodes is given by W0 . The beamforming nodes have a total transmit power gain of Gt = N in the
direction of the receiver. The beamforming nodes have a gain of unity in other directions. The far field
CR receiver has omni-directional antenna i.e.Gr = 1 and is located at a distance d which is given in km.
The CH calculates the numbers of nodes to every known CR destination through a method explained
in this chapter in a framework that allows maintaining the greenness of the network. Furthermore,
multipath and shadowing effects are ignored.
4.2.2
System Protocol
It is assumed that a system of protocols shown in Fig 4.2 is employed by the nodes in order to facilitate
the beamforming process. As such, a single transmission to a far field receiver with a distributed beamformer involves two major phases. The pre-transmission phase, is a process of coordination among the
beamforming nodes which allows the exchange of transmit signal information among the nodes. The
second phase referred to as the transmission phase is the stage where the selected nodes transmit the
signal to a far field receiver. The system protocol employed by the group of sensor nodes is briefly
presented below:
56
System Model and Protocol
Figure 4.2: System Protocol
Step1: The CH computes the number of nodes N to be used for beamforming for the given destination
and sends out participation request to other N − 1 number of nodes. Extra N − 1 nodes are required
because the CH itself is also involved in beamforming.
Step2: N − 1 nodes reply their request by sending a positive message back to the CH
Step3: The CH sends out the transmit signal message to the remaining N − 1 nodes
Step4: All N nodes send out the transmit signal simultaneously, amounting to a total of N transmissions
In this chapter, the number of nodes to be used for green cognitive radio networks is proposed from
the stand point of :
• Minimizing the energy consumption of the network
• Minimizing interference on PU
The optimal number of nodes N0 is calculated to minimize the total energy consumption of the network.
For a cognitive radio sensor network(CRSN), the number of nodes to be used in beamforming should be
large enough to reduce power transmitted in the sidelobe region so that interference power received at
57
4. C LOSE TO O PTIMAL N ODE S ELECTION FOR G REEN C OGNITIVE R ADIO S ENSOR N ETWORKS
PU is below the interference temprature limit.The interference temprature limit set by PU is known by
the CH.
In order not to exceed the interference temprature limit at the PU receiver, the power transmitted in
the direction of PU by the beamforming nodes should not exceed a given maximum power level which
can be derived from the interference temprature limit. The power transmitted in the direction of PU can
be suppressed through sidelobe reduction. Again, for a reduced side lobe level, the number of nodes
needs to be increased above the optimum value.
Therefore, the number of nodes to be used in DB for CR is not optimal but non-optimal considering
the interference minimization into account. This is because extra energy is spent when more nodes are
used to reduce interference in the direction of PU. In the following two sections, the relation between
the number of nodes,energy and interference minimization aspects of wireless cognitive network is
discussed in detail.
4.3
Minimizing Energy Consumption
In distributed beamforming, wireless sensor nodes minimize the energy spent in the transmit signal
power per node by cooperatively transmitting the same signal simultaneously so that the signal from
each node is added constructively at the receiver. Thus, the gain of the distributed array increases with
the number of nodes as indicated in Chapter 2. The power gain of the distributed beamformer in the
direction of the receiver can be used to decrease the total transmit power for a fixed
other words, if N nodes can direct a beam to the receiver at
Eb
N0 ,
Eb
N0
at the receiver.In
any extra M nodes participating in
beamforming can be used to decrease the total transmit power by a factor
N
N+M .
This can be easily
shown by fixing the expression Pt Gt . Thus, by using more nodes in beamforming the total transmit
power can be decreased. This leads to minimizing the total energy consumption of the network during
the transmission phase.
However, prior to transmission (pre − transmission) the beamforming nodes have to share information in a coordinated way so that all nodes can transmit the same signal at the receiver. The information
exchange during pre-transmission phase creates increasing overhead in terms of energy consumption as
the number of nodes increases. This means that the more number of nodes are used in beamforming, the
coordination overhead increases which is directly related to the energy consumption of the network. The
energy consumption during the pre-transmission phase increases with increasing number of nodes. In
58
Minimizing Energy Consumption
contrast, the energy consumption during transmission phase decreases with increasing number of nodes
due to reduction in the total transmit power. Therefore, it is critical to choose the number of nodes so as
to optimize the total energy consumption of the network i.e. the energy spent during the two transmission phases. Optimizing the number of nodes for the total energy consumption allows minimum energy
to maintain greenness.
In order to minimize the total energy consumption of the network, it is necessary to formulate the
relation between the total energy consumption and the number of nodes used in beamforming. The total
energy is quantified using the framework provided in [21] for a single hop transmission which is adapted
here to a transmission scheme in which CH is reachable by every node while taking the following points
into consideration:
• The number of nodes is optimized for fixed bit energy per noise power spectral density ratio
Eb
N0
at
CR receiver.
• Every node transmits at a fixed rate W0 bits/sec, S1 symbols long during pre-transmission phase
and S2 symbols long during transmission phase
• The nodes use a transmit power level P1 during the pre-transmission phase and P2 during signal
transmission to a far field receiver. In minimizing the total energy consumption, the total transmit
power during the two phases P1 + P2 is minimized.
• A node consumes power level a Watts when its transmitter is activated and b Watts when its
receiver is activated during reception of a signal
• The distributed network of N nodes uses a total transmit power Pt during transmission phase
• CH transmission is received by every node in the network and vice versa.
Thus for a fixed
Eb
N0
at the CR receiver, the following relation holds considering free space pathloss model
:
Eb
Pt Gt Gr
=
N0 KTW0 L0
c
4πd f
2
(4.1)
where c- is the speed of light, K is Boltzmann constant, f is frequency in Hz, and T is the receivers
effective temperature in degree Kelvin. Gt and Gr are the gain of the distributed network and far field
receiver respectively and L0 is the system loss.
59
4. C LOSE TO O PTIMAL N ODE S ELECTION FOR G REEN C OGNITIVE R ADIO S ENSOR N ETWORKS
For a distributed network of N nodes, the transmit beamforming power gain in the direction of the
receiver is Gt = N, then equation 4.1 can be rewritten as follows:
1 Eb KTW0 L0
Pt =
N N0 Gr
4πd f
c
2
(4.2)
Thus, the transmit power per node P2 is equally divided between the nodes which is :
P2 =
1 Eb KTW0 L0
N 2 N0 Gr
4πd f
c
2
(4.3)
The energy consumption of the network per transmission for a distributed beamformer of N nodes is
quantified below in Joules. Steps 1-3 are parts of the pre-transmission phase and Step 4, is the transmission phase
Step1: (N − 1)
a+b+P1
W0
S1
1
S1
Step2: (N − 1) a+b+P
W0
1
S2
Step3:(N − 1) a+b+P
W
0
2
Step4:(N) a+P
S2
W0
The total energy consumption of the network during a single transmission is the sum of the energy spent
during pre-transmission and transmission phase and is written in the following way:
a S2 Eb
4πd f 2 KT L0
a + b + P1
a + b + P1
−
(2S1 + S2 ))+NS2 +
(2S1 + S2 )
E = N(
W0
W0 N N0
c
Gr
W0
(4.4)
The minimization of equation 4.4 allows to determine the optimal number of nodes N0 . The energy terms
in the above equation which increase linearly with N is the energy spent during the pre-transmission
phase and the term which decrease inversely with N is the energy spent during the transmission phase.
The constant term with a negative sign represents the energy saved because the CH participated in the
beamforming process without consuming pre-transmission energy. Therefore, the relation between the
number of nodes used in beamforming N and the overall energy consumption is a convex line. There
exists a single minima which represents the energy consumed when optimal number of nodes are used.
Table 4.1: Simulation parameters
Eb
N0
50
60
a(µ w)
100
b(µw)
100
S1
2500kbit
S2
1Kbit
L0
20
P1
10mw
f
900MHz
d
7km
W0
500kbit/sec
T(kelvin)
600
Minimizing Interference
Figure 4.3: Over all energy consumption and Interference Vs the number of nodes
The simulation parameters that are used in the optimal number calculation are given in Table 4.1.
Eb
N0
and L0 values are given in linear values. It can be seen from Fig 4.3 the optimal number of nodes
is 5 which consume the minimum energy i.e.0.55 Joules per transmission. It is important to monitor the
interference power transmitted in the direction of PU when the optimal number of nodes are used for
beamforming. The issue of interference minimization in CR networks is covered in the next section.
4.4
Minimizing Interference
In this section, we show how interference minimization brings energy non-optimality in CRSN.
For a given interference temprature limit IT,L of PU as defined in chapter 2 , distributed beamforming
in CRSN should make sure that the interference generated should never exceed the limit. For a given
IT,L , in order to keep the interference power below the limit, there is a level of the sidelobe power level
P0 that must not be exceeded. Here in this section we evaluated the level of interference based on the
percentage of the time the sidelobe power level exceeded the given level P0 .
We scaled the interference generated according to the percentage of the time that the side lobe power
level in the direction of PU exceeded the maximum transmit power limit P0 . If the side lobe power level
in the direction of PU is greater than P0 for I0 % of the time, we denote the interference level as I0 %.
61
4. C LOSE TO O PTIMAL N ODE S ELECTION FOR G REEN C OGNITIVE R ADIO S ENSOR N ETWORKS
Figure 4.4: CDF comparision with and without clustering at 900 MHZ
Accordingly, by using only optimal number, i.e. N ∗ = 5 nodes, the interference level produces
significant interference(as large as 70%) for values of P0 = −15dB Watt. The use of more number of
nodes brings reduced sidelobe level and hence lessens the interference toward PU. Therefore, in order
not to exceed the interference temperature limit of PU it becomes compelling to pay a price by using
more number of nodes i.e. non-optimal number N1 . This makes the task of interference minimization
energy demanding as more energy is consumed through the use of more number of nodes. It is seen in
Fig 4.3 that interference level in % decreases with the number of nodes. The interference level reaches
close to 0 % when N1 = 50 nodes are used. This was verified by monitoring the level of interference
generated in the direction of PU according to the cumulative distributed function(CDF) of the beam
pattern. The CDF was generated using Monte Carlo simulation of 1000 iterations. Energy consumed by
50 nodes calculated using equation 4.4 is 3.2 Joules per transmission, and thus is non-optimal.
Now we have shown the energy non-optimality of interference minimzation in CRSN networks. In
the next section, we show the use of clustering node selection method as an effective solution in avoiding
this energy non-optimality by allowing operating near to optimal number while minimizing interference
on PU. By doing that the energy consumption per transmission of the network will be reduced. This
further promotes Green communication in CRSN.
62
Clustering Node Selection Method for Green Communication
4.5
4.5.1
Clustering Node Selection Method for Green Communication
Methodology
Clustering Node Selection method selects nodes which minimize the energy consumption as well as
minimize interference in the direction of primary users by operating close to optimal number of nodes.
The term close to optimality is used here, because the number of nodes used in clustering method is
dependant on the interference temprature limit IT L . Depending on the value of IT L , it may be necessary
to use extra few nodes more than the optimal value. Nonetheless, the inherent destructive addition of
the far field phases of the selected nodes in the direction of PU guarantees us to operate close to optimal
number of nodes.
The methodology of minimizing interference and energy using clustering node selection method
starts by calculating the optimal number of nodes N0 as described in section 4.3 by solving equation 4.4.
The optimal number of nodes are selected using clustering node selection method. The CH then monitors
the interference level in the direction of PU by calculating the CDF of the beam pattern. If the level side
lobe power level generated is below P0 for almost 100% of the time, then the optimal numbers of nodes
are selected and are used for beamforming. Otherwise, the number of nodes is increased by one until the
side lobe power level is below the maximum allowed transmit power P0 . The steps of clustering node
selection method are summarized in Fig 4.5.
By making sure that the power transmitted in the direction of PU is below the interference temprature limit, then the selected nodes are used for beamforming. The number of nodes N0 used by clustering method is considerably less than the non-optimal number of nodes N1 required without clustering
method. Therefore, through the inherent sidelobe reduction obtained by clustering method, it is possible
to save N1 − N0 nodes from being involved in clustering process. This allows energy conservation which
is quanitified in the order of Joules.
The issue of interference minimization required to increase the number of nodes to 50 without clustering method as shown in Fig 4.3 so as to keep interference below the limit. Clustering node selection
method can minimize interference power using M = 6 nodes. The CDF comparison is shown in Fig 4.4
when 6 nodes are used for beamforming. Through comparison of the CDF of the beampattern with and
without clustering, we can verify that minimization of interference is achieved using clustering method.
Without clustering method, it can be seen from the figure that the sidelobe level of the beampattern is
less than P0 = −15dB for less than 30 % of the time. This means the sidelobe level exceeds the given
limit for more than 70% of the time which creates significant interference toward PU. This can be alter63
4. C LOSE TO O PTIMAL N ODE S ELECTION FOR G REEN C OGNITIVE R ADIO S ENSOR N ETWORKS
Figure 4.5: Clustering node selection for Close to optimal number of nodes
Figure 4.6: Interference power and energy comparision with and without clustering method at 900 MHZ
64
Performance Evaluation
natively verified from the sidelobe reduction of more than 18dB obtained using 6 nodes in the average
beam pattern as shown in Fig 3.27 of Chapter 3 at 900 MHz.
The side lobe power level of 6 nodes using clustering method is less than P0 = −15dB for close to
100% of the time. Hence, clustering node selection method can avoid interference with 6 nodes which
is close to the optimal number 5.
In the following, we demonstrate the green aspect of clustering node selection method which saves
significant amount of energy per single transmission.
Accordingly, the energy consumption of 6 nodes selected using clustering method is 0.57 Joules per
transmission. Without clustering it was necessary to use 50 nodes which consume a total of 3.2 Joules
per transmission. Therefore, with clustering method 44 nodes have been saved from participating in
beamforming. This translates into energy conservation of 2.65 Joules per single transmission as can be
seen from Fig 4.6. Thus , the green aspect of clustering method is demonstrated.
4.6
Performance Evaluation
The performance of clustering node selection method toward optimality was verified by simulating a
number of scenarios giving a range of optimal number nodes for different values of inter-node transmit
power level P1 . The number of nodes used by clustering node selection method in each of the scenarios
is evaluated and is presented in Table 4.2. It can be observed that clustering can use the optimal number
of nodes to keep the interference below the limit for values of P0 = −15 dB in almost all of the cases
except the first one. The performance evaluations were done at f = 900MHZ for decreasing value of the
internode transmit power P1 shown in Table 4.2.
Table 4.2: Number of Nodes used by Clustering
Optimal Number of Nodes
Number of Nodes selected using Clustering
Inter-node transmit power level P1 in mW
5
6
40
6
6
12
8
8
8
9
9
6
11
11
4
16
16
2
In this chapter, the application of clustering node selection method in enhancing the greenness of
the network was demonstrated. A close to optimal node selection allowed energy conservation per single
transmission. The energy conservation obtained using clustering method allows CRSN to sustain their
65
4. C LOSE TO O PTIMAL N ODE S ELECTION FOR G REEN C OGNITIVE R ADIO S ENSOR N ETWORKS
power supply for a longer period of time as a result making the network “ green”.
4.7
Summary
In this chapter the use of Clustering node selection for green communication under interference power
constraint of PU is demonstrated. Minimizing the total energy consumption of the network per transmission is critical for maintaining the greenness of CRSN. Optimizing the energy consumption provides the
optimal number of nodes in WSN. However, for the CR, the non-optimality of the energy consumption
is inevitable due to extra strict requirement of power transmitted toward PU. Clustering node selection
solves the problem by allowing beamforming with close to optimal number of nodes to be selected while
keeping the interference to PU below the interference temperature limit. In doing so, the total transmit
energy consumed is minimized and at the same time the total transmit power P1 + P2 is minimized.
66
Chapter 5
Location Ambiguity and Phase Error in
WSN
5.1
Overview
Location information of wireless sensor devices is critical for wide varieties of applications. A group of
sensor nodes used for distributed beamforming use their location information to calculate initial phase
to focus the beam to the receiver. However, the ambiguity in the location information of these nodes
brings a corresponding phase error. The resulting phase error is known to produce a degradation on the
quality of the beam formed.
The impact of phase error on distributed beamforming gain is investigated by few authors in litrature.
The authors in [2] have modeled radial location error δr = Uni f [−rmax , rmax ] and angular location error
δψ = Uni f [−ψmax , ψmax ] to follow uniform distribution. The main beam degradation due to location
ambiguity is expressed in terms of hyper geometric functions. They have indicated that the maximum
location angle ambiguity that keeps the main beam degradation at 3dB is ψmax =
λ
2R .
This indicates that
as frequency increases the maximum location error that can be tolerated becomes very small. They also
have studied the impact of phase error at the beamforming nodes. They indicated the relation between
node density and degradation of the main beam. They showed that nodes which are distributed sparsely
are less sensitive to phase error.
However, the study done so far is based on modelling the location error with Uniform approximation. Nonetheless, the location ambiguities do not follow Uniform distribution in a practical context.
Therefore,extensive study on the impacts of location error ambiguity on distributed beamforming based
on practical location error model which happens in real life is not available. Besides, statistical characterization of phase error distribution is not available. In this chapter, a detailed study of the impact of
67
5. L OCATION A MBIGUITY AND P HASE E RROR IN WSN
location ambiguity based on GPS location error distribution is given.
The statistical distribution of the resulting phase error is investigated given the known distribution
of location ambiguity based on GPS localization error. Accurate modeling of the phase error allows to
understand ways of combating the impacts of phase error happening at each node and further improving
the beamforming performance. The obtained phase error distribution leads to adopting a solution based
on averaging. The results obtained show that severe impacts of phase error can be counteracted through
averaging. In addition, the performance of Clustering Node Selection method presented in chapter 3 is
investigated in the presence of location errors.
5.2
Location error ambiguity at the beamforming nodes
Location discovery in wireless sensor nodes is done by the sensor nodes. The sensor nodes discover
their location through a global positioning system or with the use of localization algorithms which are
run on the sensor nodes themselves as explained in Chapter 2. In either case, the location information
the nodes discover is always prone to error. This adds uncertainty to the location information the nodes
acquire.
Many network tasks of WSN are dependent on location information and distributed beamforming is
no exception in this. The distributed beamforming nodes apply an initial phase to steer the beam in the
direction of intended receiver. The uncertainty in the location information of the beamforming nodes
deteriorates the quality of the beam formed. Therefore, it is critical to study the statistical properties of
location error in order understand and model location error. The knowledge of location error model is
further used to stastically analyse the phase error at each beamforming node.
5.2.1
Modeling of Location Errors
Localization algorithms in WSN are extensively studied in literature.The authors in [22] have indicated
that localization algorithms follow a family of Rician distribution . It is indicated in [23] that location
error obtained from GPS follows Rayleigh distribution. The analysis given in the paper showed that X
and Y components of GPS location error follow Gaussian distribution and the resultant location error
is Rayleigh distributed. The modelling results of GPS location error approximated with Rayleigh distribution are shown in Fig5.1. In this chapter, we use the location error model provided in [23] for the
analysis of the phase error in subsequent sections.
1 Zandbergen2008
68
Location error ambiguity at the beamforming nodes
Figure 5.1: Modelling of Rayleigh location error 1
69
5. L OCATION A MBIGUITY AND P HASE E RROR IN WSN
5.2.2
Phase Error at the Beamforming Nodes
In distributed beamforming, the beamforming nodes with location (rk , ψk ) steer the beam toward the
intended CR receiver located at the far field in the direction φ0 by applying initial phase given by the
following expression:
Ψk =
2π
rk cos(φ0 − ψk )
λ
(5.1)
When there is location error uncertainty, the initial phases applied at each node contain error which is
given by the following equation:
Ψ∗k =
2π
(rk + δrk ) cos(φ0 − ψk − δψk )
λ
(5.2)
Therefore, the phase error at each node can be written as:
∆Ψk = Ψ∗k − Ψk
(5.3)
As a result, the distributed beamformer of N nodes will have an array factor given by the following
expression:
1 N j(Ψ∗k + 2π dk (φ))
λ
∑e
N k=1
(5.4)
1 N j(Ψk +∆Ψk + 2π dk (φ))
λ
∑e
N k=1
(5.5)
2π
1 N
∑ D(φ, ψk )e j(Ψk + λ dk (φ))
N k=1
(5.6)
F ∗ (φ|r, ψ, δψ, δr) =
F ∗ (φ|r, ψ, δψ, δr) =
F ∗ (φ|r, ψ, δψ, δr) =
where dk (φ) is the far field distance of each node at the direction φ. This means the constructive addition
of signals at the intended receiver is degraded by location uncertainty which is quantified at each node
by the degradation factor. The degradation factor D(φ0 , ψk ) in the direction of intended receiver φ0 at
each node will degrade the gain of the main beam toward to the intended receiver.
The beampattern obtained then is written as :
P(φ|r, ψ, δr, δψ) =
70
N
N
2π
1
∗
j(Ψk + 2π
λ dk (φ)) )
[N
(D(φ,
ψ
)D
(φ,
ψ
))+
D(φ,
ψ
)e
D∗ (φ, ψl )e− j(Ψl + λ dl (φ)) ]
k
k
k
∑
∑
2
N
k=1
l=1,l6=k
Investigating the effect of location uncertainty on distributed beamforming
Figure 5.2: Simulation Model
Since |D(φ, ψk )D∗ (φ, ψk )|, is 1, the beam pattern with location ambiguity is written as:
P(φ|r, ψ, δr, δψ) =
5.3
N
2π
2π
1
1 N
+ 2 [ ∑ D(φ, ψk )e j(Ψk + λ dk (φ)) ) ∑ D∗ (φ, ψl )e− j(Ψl + λ dl (φ)) ]
N N k=1
l=1,l6=k
(5.7)
Investigating the effect of location uncertainty on distributed
beamforming
In this section, the impact of phase error caused by location uncertainty of the nodes on distributed
beamforming gain is studied. Majorly, Rayleigh distribution of the location error is studied. Initially,
small location errors are applied and incrementally the location error values are increased. The resulting
impacts of the phase error on the mainbeam and the sidelobe level is studied in detail.
SIMULATION RESULTS
The effect of location error in (δrk , δφk ) is observed by using N = 50 nodes, which are distributed in
a circular radius of R = 10m, and transmit signal has wave length λ = 0.6m. The radial location error
δrk follows Rayleigh distribution based on the simulation model shown in Fig 5.2. The angular location
estimate δψk follows uniform distribution δψk = Uni f [−Ψmax , Ψmax ]. Working at higher frequency
f = 500MHZ is chosen where the impact of location ambiguity is severe. The obtained beam pattern
71
5. L OCATION A MBIGUITY AND P HASE E RROR IN WSN
Table 5.1: Mainbeam degradation summary Case 1
Location Uncertainity
values
Rayl(0.05) only
Uni f [−0.50 , 0.50 ] only
Rayl(0.05),Uni f [−0.50 , 0.50 ]
Mainbeam
degradation in (dBs)
−1.21
−0.29
−1.47
Change in first
sidelobe peak (dBs)
+0.99
−0.95
0
Absolute value of
Average phase error(degrees)
23 − 25
0.2
23 − 25
and the absolute value of the average phase error are used to evaluate impact of location ambiguity in
the subsequent sections.
A. Main Beam Degradation
CASE1:
At first small location error is introduced where δrk = Rayl(0.05) and δψk = Uni f [−0.50 , 0.50 ]
and the resulting degradation in the main beam is observed as shown in Fig 5.3. The average phase error
at each node due to location ambiguity is also plotted in Fig 5.4. It is seen from the figure that the absolute value of the average phase error at each node is limited in the range [22.850 , 25.50 ] for the given
values location error. These results are summarised in Table 5.1.
It is further observed that the major phase error is brought by the radial location ambiguity, not by
angular location ambiguity. This is because the impact of angular location ambiguity is down scaled
by sine and cosine in the phase error term given by equation 5.8, thus making the resulting phase error
relatively insignificant.
∆Ψk =
2π
rk [cos(φ0 − ψk ) cos(δψk − 1) + sin(φ0 − ψk ) sin(δψk )]
λ
Figure 5.3: Beampattern Comparision
Case 1
(5.8)
Figure 5.4: Average Phase Error in degrees at each
node case 1
CASE 2: Next the location error estimates are increased to Rayl(0.1) and Uni f [−10 , 10 ] and the impact of increase in the location error values is observed in the beam pattern degradation. It is seen in
72
Investigating the effect of location uncertainty on distributed beamforming
figures 5.5 and 5.6 that the phase error stays in the range [200 , 250 ] when there is only location error δψ
bringing main beam degradation of 1.16 dB. When there is only a radial location error Rayl(0.1), the resulting average phase error ranges between [450 , 500 ] which brings 4.6dB degradation in the main beam .
The simultaneous error in location (δrk , δψk ) brought a total degradation 6.133dB on the mainbeam with
average phase error at the beamforming nodes ranging between [550 , 570 ]. Table 5.2 summarizes the
main beam degradation values in dB for the given values of location error. Furthermore, it is to be noted
that the average phase error values at the beamforming nodes doubled when location error is doubled
from (Rayl(0.05),Uni f [−0.50 , 0.50 ]) to (Rayl(0.1),Uni f [−10 , 10 ]) as can be observed by comparing
Fig 5.4 and Fig 5.6
Figure 5.5: Comparision of the beampattern Case 2
CASE 3:
Figure 5.6: Average phase error at each node Case
2
The location error is highly increased with Rayl(0.15) where the Rayleigh parameter B =
0.25λ. Simulation results showed that phase error values range between [690 − 720 ]. The main beam
degradation increases down to -10dB. Furthermore, the first sidelobe peaks are very large (increased by
3dB). The first sidelobe peaks have comparatively similar gain as the mainbeam. Thus, the beam formed
is no longer usable when location error greater than 25% of wavelength which is 0.6m in our case as
shown in figures 5.7 and 5.8.
Table 5.2: Mainbeam degradation summary Case 2
Location
Uncertainity
values
Rayl(0.1) only
Uni f [−10 , 10 ] only
Rayl(0.1),Uni f [−10 , 10 ]
Mainbeam
degradation
(dBs)
−4.59
−1.16
−6.133
Change in first
sidelobe peak
(dBs)
+2.05
−1.82
+ 0.33
Change in
HPBW
(degrees)
−0.16
+0.4
+0.13
Absolute value of average
phase error
(degrees)
45 − 50
20 − 25
55 − 57
73
5. L OCATION A MBIGUITY AND P HASE E RROR IN WSN
Figure 5.7: Comparision of the beampattern Case 3
Figure 5.8: Average phase error at each node Case
3
CASE 4: The angular location error δψk is increased to Uni f [−30 , 30 ] and the average phase error
values ranging between [570 , 690 ] was observed as shown in Fig 5.10. The main beam degradation is
-8dB. Furthermore, the HPBW is (increased by 6 degrees).It can be seen from Fig 5.9 that the beam is
no longer usuable because of its very small directivity and very small gain.
Figure 5.9: Comparision of the beampattern Case 4
Figure 5.10: Average phase error at each node Case
4
CASE 5: The impact of the main beam degradation may be acceptable to only below 3dBs for most
beamforming applications. Therefore it is important to investigate the value of the location ambiguties
that keep the beam at -3dB line. Simulation results indicated that the main beam degradation is kept
below 3 dB for values of location error [Rayl(0.05),Uni f (−1.250 , 1.250 )]. The resulting phase error
ranges between [380 , 420 ].
74
Investigating the effect of location uncertainty on distributed beamforming
Figure 5.11: Average Phase Error, Beampattern comparision Case5
Table 5.3: Mainbeam degradation summary Case 2
Location
Uncertainity
values
Rayl(0.05) only
Uni f [−0.50 , 0.50 ] only
Rayl(0.05),Uni f [−0.50 , 0.50 ]
Rayl(0.1) only
Uni f [−10 , 10 ] only
Rayl(0.05),Uni f [−1.250 , 1.250 ]
Rayl(0.1),Uni f [−10 , 10 ]
Rayl(0.15) only
Uni f [−30 , 30 ] only
Mainbeam
degradation
(dBs)
−1.21
−0.29
−1.47
−4.59
−1.16
−3
−6.133
−10
−8
Change in first
sidelobe peak
(dBs)
+0.99
−0.95
0
+2.05
−1.82
+ 1.83
+ 0.33
+3
−3
Change in
HPBW
(degrees)
0
0
0
−0.16
+0.4
+0.03
+0.13
−0.36
+6
Absolute value of
average phase error
(degrees)
23 − 25
0.2
23 − 25
45 − 50
55 − 57
38 − 42
23 − 25
67 − 72
57 − 69
The summary of the impact of location ambiguity on the beam pattern investigated so far is summarized
in Table 5.3. It can be shown that the maximum location error for which the beam formed is no longer
usable is δr = Rayleigh(0.15) and δψ = Uni f (−30 , 30 )].
B. Location Error and Number of Nodes used for Beamforming
In this section, the mainbeam degradation when different number of nodes are used for beamforming
is investigated. In the simulation 10, 20 and 50 nodes with the same location error distribution, i.e.
[Rayl(0.05),Uni f (−1.250 , 1.250 )] were used as shown in figures 5.12 and 5.13. The main beam degradation increased when more number of nodes are used. It is to be noted that the average phase error
per node is the same in all the three cases because the same value of location error. However,when
less number of nodes are used in beamforming ,less main beam degradation is observed with the same
75
5. L OCATION A MBIGUITY AND P HASE E RROR IN WSN
average phase error per node. This justifies the use of selecting small number of nodes for beamforming
in situations where there is location ambiguity.
Figure 5.12: Comparision of the beampattern for 10,20 and 50 nodes
Figure 5.13: Average phase error at each node when
10,20 and 50 nodes are used in beamforming
CDF of the Beam Pattern:
The simulation results from previous sections show that the average side lobe level does not show any
change as a result of phase error at the beamforming nodes. It can be seen that the average sidelobe level
which is represented by the first term of equation 5.7 is independant of the degradation factor D(φ, ψk ).
This is because no initial phase adjustment is done in the directions other than φ = φ0 to begin with.
This means the initial phase error due to location error at the beamforming nodes does not affect average
power gain in the sidelobe region other than those directions at φ = φ0 ±50 . Further looking into the CDF
plot of location error ambiguity (Rayl(0.5),Uni f [−0.50 , 0.50 ]) and (Rayl(0.1),Uni f [−10 , 10 ]) shown in
figures 5.14 and 5.15 confirms this observation. The CDF with and without error has no difference as can
be observed from the figure. The CDF of the sidelobe level was generated using Monte Carlo simulation
of 1000 iterations.
5.4
Analysis of Results
From simulation results on the effect of location error on the main beam and sidelobe of the distributed
beam former the following conclusions can be drawn:
76
Analysis of Results
Figure 5.14: Comparision CDF of the
sidelobe level with average 500 and without error
Figure 5.15: Comparision CDF of the sidelobe level
with average 700 and without error
1. The radial location error δrk produces a corresponding phase error given by:
2π
δrk cos(φ0 − ψk )
λ
(5.9)
and has the following impacts:
• Main beam degradation
The constructive addition of carrier phases is no longer guaranteed because of the phase error
which brings a degradation factor given in equation 5.6.
• Increment in the first side lobe peak
This diminishes directivity of the beam pattern because severe increase in the first side lobe
peak creates loss of the power gain in the direction of intended receiver. This increment in the
first sidelobe peak happens because with the additional phase term of radial location ambiguity
2π
λ δrk cos(φ0 − ψk )
, which is periodic in nature with stochastic amplitude
2π
λ δrk .
This periodic
phase error creates additional term in the average beam pattern 1 F2 , a hyper geometric function
whose maxima coincides with the first sidelobe peak of the beam pattern. Thus, this increases the
first side lobe peak. The increase in δrk brings more increase in the first side lobe peak.
• Decrement of the Half Power Beam Width
The half power beam width decreases with increase in the radial location of a node, but the change
in HPBW is insignificant in comparison to main beam degradation. The maximum increment in
HPBW is less than 0.50 , for average phase error values of 700 .
77
5. L OCATION A MBIGUITY AND P HASE E RROR IN WSN
2. The angular location error δψk produces a corresponding phase error given by equation 5.10
and has the following impacts.
2π
rk [cos(φ0 − ψk )(cos(δψk ) − 1) + sin(φ0 − ψk ) sin(δψk )]
λ
(5.10)
• Main beam degradation
The constructive addition of carrier phases is no longer guaranteed because of the phase error
which brings a degradation factor given in equation 5.6. However, it takes larger value of the
angular location error δψk for a significant value of phase error and hence main beam degradation.
This is because the angular location error term δψk is downscaled by sine and cosine terms in the
phase error term as given by equation 5.10.
• Decrement of the first sidelobe peak
The first sidelobe peak decreases because the phase error due to δψk is uniformly distributed
creating a cancellation effect on the beam pattern. This can be justified by the periodic phase error
whose amplitude is constant whereas the sine and cosine terms create a destructive effect with one
of its minima coinciding with the first side lobe peak of the beam pattern, thus decreasing the first
side lobe peak.
• Increase of the half power beam width
The half power beam width increases with increasing angular location error. The simultaneous
effect of the radial and angular location error creates very small increase in HPBW.
3. For the same location error distribution, the use of more number of nodes brings more degradation of
the main beam. This is because the more number of nodes are used, the more phase error is introduced.
Therefore, the use of less number of nodes is beneficial from the perspective of counteracting the impacts of location ambiguity.
4. Doubling of the location ambiguity produced doubling of the average phase error at the beamforming
nodes.
5. The change in HPBW at the working frequency of 500 MHz requires a large location error compared
to working at lower frequencies.
6. The effect of the location error on the side lobe level of the beam pattern is insignificant. This was
verified through CDF plots and the average sidelobe region of the beampattern.
78
Modeling of Initial Phase Error at the beamforming nodes
7. The major impact of location ambiguity is the main beam degradation. This further results in reduction of the power gain and directivity.
5.5
Modeling of Initial Phase Error at the beamforming nodes
Understanding the statistical properties of the phase error at each beamforming nodes as a result of location ambiguity is very important. Building a statistical model for the phase error at the beamforming
nodes allows to devise startegies that allow to reduce the the initial phase error at each node and reduce
the degradation of the beam.
In this section, we study the statistical model of the initial phase error using Matlab distribution
R
fitting tool . The location error values with distribution [Rayleigh(0.1),Uni f (−10 , 10 )] at each node is
taken in the model fitting. The model fitting is repeated for verification purpose for location error values
[Rayl(0.125),Uni f (−1.50 , 1.50 )]. The data for analysis is taken by generating location error values
10000 times for a single location(rk , ψk ) values of node k.
The initial phase without location error at each node is written as:
Ψk =
2π
(rk ) cos(φ0 − ψk )
λ
(5.11)
In the presence of location of error the initial phase at each node is :
Ψ∗k =
2π
λ (rk + δrk ) cos(φ0 − (ψk + δψk ))
2π
rk [cos(φ0 − ψk ) cos(δψk ) + sin(φ0 − ψk ) sin(δψk )]+
λ
2π
δrk [cos(φ0 − ψk ) cos(δψk ) + sin(φ0 − ψk ) sin(δψk )]
λ
(5.12)
2π
2π
δrk [cos(φ0 − ψk ) cos(δψk )] + δrk [sin(φ0 − ψk ) sin(δψk )]+
λ
λ
2π
rk [cos(φ0 − ψk )(cos(δψk ) − 1) + sin(φ0 − ψk ) sin(δψk )]
λ
(5.13)
Ψ∗k =
∆Ψk = Ψ∗k − Ψk
∆Ψk =
It is seen from equation 5.13 that the phase error at the nodes consists of three terms. The first
given by
2π
λ δrk [cos(φ0 − ψk ) cos(δψk )]
is well approximated by Rayleigh distribution. This is because
79
5. L OCATION A MBIGUITY AND P HASE E RROR IN WSN
δrk is Rayleigh distributed and cos(δψk ) which is a term close to 1 for small values of δψk in the range
[−60 , 60 ]. This also verified by fitting the distribution of this term in matlab distribution fitting tool as
seen in Fig 5.16.It is seen from this Fig 5.16 that the first term constitutes the Rayleigh component of
the total phase error.
Figure 5.16: Rayleigh component of the
phase error
Figure 5.17: Gaussian component of the phase error
Studying the second term of the phase error given by
2π
λ δrk [sin(φ0 − ψk ) sin(δψk )]
shows that it is
a zero mean Gaussian proccess. This is because, δrk is Rayleigh distributed and sin(δψk ) which is
equivalent to δψk for small values of δψk is uniformly distributed between [−ψmax , ψmax ]. Therefore,
the term
2π
λ δrk [sin(φ0 − ψk ) sin(δψk )]
is well approximated by a Gaussian process with zero mean. This
was again verified, through matlab distribution fitting tool which is shown in Fig 5.17.
Looking into the the third term of the phase error which is given by
2π
λ rk [cos(φ0 − ψk )(cos(δψk ) −
1) + sin(φ0 − ψk ) sin(δψk )], it is seen that distribution for this term can be approximated with uniform
distribution of zero mean.
Figure 5.18: Uniform Component of the
phase error
80
Figure 5.19: Total phase error
Modeling of Initial Phase Error at the beamforming nodes
The distribution of the phase error given by equation 5.13 is the sum of the three components of the
phase errors. Furthermore, the last two components of the phase errors are well approximated by zero
mean Gaussian and Uniform distributions. It is therefore evident that the mean of the total phase error
is equal to the mean of the Rayleigh component of the phase error. This is because the Gaussian and
Uniform components of the phase are zero-mean processes. The total phase error which is the mixture
distribution of the three components is shown in Fig 5.19.
The statistical characterstics of the phase error is also investigated for a larger values of location error
given by [Rayl(0.125),Uni f (−1.50 , 1.50 )]. Simulation results showed the same statistical characterstic
of the phase error distribution is obtained. The only difference is the mean value of the phase error
has increased in comparision to the previous case as a result of the increase in the values of location
error as shown in figures 5.20 and 5.21. Therefore, it can be generalised that for a Rayleigh distributed
Figure 5.20: Rayleigh component of the
phase error
Figure 5.21: Total phase error
location error which is a widely used location error model for GPS, the resulting phase error follows a
distribution which is a mixture of Gaussian,Rayleigh and Uniform distributions.
In studying the distribution of the total phase error, it is seen that the shape of the distribution is determined by the magnitude the three different components of the phase error. If the Gaussian component
of the phase error has high magnitude ,then the error is Gaussian dominated, therefore, it will have a
shape closer to Gaussian distribution as can be seen from Fig 5.21. The same holds true to the shape
of the phase error distribution when the other components of the phase error dominate. In some of the
cases depending on the combination of the different errors, the total phase error may have a completely
different shape. The different shapes of the total phase error are shown in Fig 5.22
It is shown previously that the mean of Rayleigh component of the phase error and the total phase er81
5. L OCATION A MBIGUITY AND P HASE E RROR IN WSN
Figure 5.22: shape of total phase error at different nodes
ror are equal. This allows the beamforming nodes to remove the Gaussian and the Uniformly distributed
components of the phase error by simple averaging since these components are zero mean processes.This
is done in the following way.
The nodes generate multiple samples of the initial phase values through new GPS measurements
each time. Then the calculated initial phases are used as samples to be used for averaging. After,
averaging, a significant portion of the phase error is removed. This allows to decrease the mainbeam
degradation. This is demonstrated when different location error values are applied at the beamforming
nodes in cases I,II and III. The number of samples taken for averaging is 500.
CASE I- By introducing location error values given by (Rayl(0.1),Uni f [−10 , 10 ]) at the beamforming nodes, the use of averaging in decreasing the phase error is investigated. It can be seen from the
figure that the main beam degradation has improved from −6.144 dB to −3.97 dB, showing an overall
improvement of 2.17 dB in the main beam gain. In addition the first sidelobe peak values also decreased
by 1dB as can be seen in the Fig 5.23.
CASE II - The principle of averaging out of the phase error is also investigated for a larger value of
the phase error by introducing location error values given by (Rayl(0.1),Uni f [−1.50 , 1.50 ]). Through
averaging the main beam level was improved from −10.76dB to −7.63 dB. This is 3dB improvement of
the main beam. Besides, the first sidelobe level peak is also reduced by almost 2dB as shown in Fig 5.24.
CASE III - Finally, the use of simple averaging in removing the larger part of the phase error is
demonstrated by introducing location error values at the nodes given by (Rayl(0.125),Uni f [−30 , 30 ]).
Without the use of averaging, the beam degradation is so severe (17 dB) that no beam is pointed in the
direction of the reciever as shown in Fig 5.25. However, by averaging the phase error values,the main
82
Modeling of Initial Phase Error at the beamforming nodes
Figure 5.23: Beamforming gain with and without averaging of the phase error CASE I
Figure 5.24: Beamforming gain with and without averaging of the phase error CASE II
83
5. L OCATION A MBIGUITY AND P HASE E RROR IN WSN
Figure 5.25: Beamforming gain with and without averaging of the phase error CASE III
beam is improved pointed with more than 8 dB increment.
From the simulation results shown in cases I,II and II, it can be concluded that the averaging of the
phase error helps in removing most portion of the phase error and this brings improvement of the main
beam. Improvement of the first sidelobe peak is also obtained. The use of simple averaging is shown to
highly improve the beamforming performance, while remaining to be a very simple solution suitable for
wireless sensor devices.
5.6
Performance of Clustering node selection method in the presence of
location error
Clustering node selection method uses the far field phase of the nodes Ωk = − 2π
λ dk (φ p )+Ψk as criteria to
classify the nodes under different groups as discussed in chapter 3. The CH has the location information
of the beamforming nodes which it uses to calculate the farfield phase of each node. However, this
information is prone to ambiguity as mentioned at the beginning of this chapter. Therefore,grouping or
clustering nodes based on their phases has uncertainity associated with it. This means a node which is
grouped under a single cluster may not belong to the same cluster had the correct location information
been used in calculating the phase values. Furthermore, after node selection, additional phase error is
introduced at the beamforming nodes when the selected nodes are used for beamforming. Beamforming
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Performance of Clustering node selection method in the presence of location error
using Clustering node selection method thus incurres two sources of phase error ,i.e. at CH and the
beamforming nodes.
Therefore, in this section we study the two phase errors, i.e. the phase error at the CH and the phase
error at the beamforming nodes are studied separately. Finally, the effect of the simultaneous effect of
the two phase error are investigated.
5.6.1
Location Error at the CH
Figure 5.26: location error at the CH
Figure 5.27: Comparision of clustering method with
and without phase error
The CH calculates the far field phase Ω∗k at the direction of primary user when location term errors
δrk and δψk are introduced. Therefore, the phase error at CH is ∆Ω = Ω∗k − Ωk .
The accuracy of clustering method depends on the number of clusters which determines the phase
span of a single cluster. If there are N0 clusters, the phase span for a single cluster will be approximately
2π
N0 .
Clustering method selects a single node at the center of the cluster or the phase span. Therefore,
a selected node ends up in the wrong cluster only if the phase error at CH is greater than
means clustering method is robust to maximum phase error values less than
π
N0
π
N0 .
This
at the CH. This is also
verified by using 6 nodes for beamforming where phase error values less than 30 degree brought no
degradation in the clustering method performance. The maximum sidelobe reduction is obtained, as
long as the phase error of each node is kept under 300 . When location error values is increased to
(Rayl(0.05),Uni f [−0.50 , 0.50 ]), the average phase error values is 250 where as the instantaneous phase
error values calculated at the CH ranges upto 700 . This means some of the nodes end up in the wrong
cluster. As a result,some of the nodes selected have phase values that do not contribute to the sidelobe
reduction of clustering method.The beamforming comparision for clustering method with and without
phase error is shown in Fig 5.27 for values of location error (Rayl(0.05),Uni f [−0.50 , 0.50 ]).
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5. L OCATION A MBIGUITY AND P HASE E RROR IN WSN
5.6.2
Location Error at the beamforming nodes
The location information error at the beamforming nodes brings error in the initial phase term calculated
at each node given by:
Ψ∗k =
2π
λ
(rk + δrk ) cos(φ0 − ψk − δψk )
The above initial phase term contains error and has two impacts:
• Some of the nodes do not belong to the cluster or phase group they are classified under. This
affects the level of side lobe reduction obtained as explained in the last section, which is improved
by selecting the nodes which belong to the center of cluster.
• The beamforming gain is degraded, i.e. the level of main beam is reduced. Clustering method
minimizes this problem by selecting the nodes which are very close to the centroid.
When location error values given by (Rayl(0.05),Uni f [−0.50 , 0.50 ]) are applied ,the average phase error
values at the nodes range between 200 − 250 and acceptable performance is obtained as demonstrated in
Fig 5.29.
Figure 5.28: Phase error at each beamforming node
5.6.3
Figure 5.29: Clustering method with and without
phase error
Location Error at both beamforming nodes and CH
In this section,we consider the two phase errors at CH and the beamforming nodes simultaneously and
see their impact on clustering node selection method. The phase error introduced at CH and beamforming nodes brings main beam degradation as well as degradation of clustering result to become severe.
This means the sidelobe reductions obtained are lost because the CH can no longer identify the nodes
86
Performance of Clustering node selection method in the presence of location error
Figure 5.30: Clustering Method with and without averaging
based on their phases because of the phase error. This was verified by running the simulation for location error values applied both at the CH and the beamforming nodes (Rayl(0.05),Uni f [−20 , 20 ]) which
brings average phase error values [450 , 550 ]. The resulting degradation of the main beam is −4.57dB
and the sidelobe reduction is almost lost. However, the use of averaging is used to recover the mainbeam
degradation and the sidelobe reductions of clustering method as shown in Fig 5.30.
In conclusion, the performance of clustering node selection method in the presence of location error
can be summarized as follows:
Clustering node selection method is robust to maximum phase error values of
π
N0
at each node where N0
is the number of clusters. With the use of 6 nodes, up to a maximum of 30 degrees of phase error can be
tolerated without affecting the performance of clustering method.Since small number of nodes are used
in clustering, the main beam degradation is considerably small. For a larger values of the phase error
above 300 , the use of simple averaging at the beamforming nodes and the CH allows to improve the
performance of clustering method.
87
5. L OCATION A MBIGUITY AND P HASE E RROR IN WSN
Figure 5.31: Phase error from Gaussian location error distribution
5.7
Comparative Analysis
In this section, comparative analysis of beamdegradation is given with regard to the distribution of the
location error. In this chapter, Rayleigh distributed location error of GPS is employed. The comparision
is done with Gaussian and Uniform distributions of location error.
A typical condition where Gaussian location error happens is wireless sensor network localization using simple localization methods such as dead reckoning [24]. The degradation of the mainbeam due
to location error from Gaussian distribution is very simmilar with the results obtained from Rayleigh
distributed location error.
Looking into the resulting phase error distribution different results are obtained. With zero-mean
Gaussian location error at the beamforming nodes,the phase error is approximated through zero mean
Gaussian process as can be seen from the Fig 5.31.The total phase error shown on Fig 5.31 shows a
very good fitness to Gaussian distribution. This means most of the phase error can be removed through
averaging.
The impacts of location error models on the beamforming performance is investigated. It can be seen
from Fig 5.32 that for the same value of location error 1/6λ, the main beam degradation with different
location error models that follow Uniform,Gaussian and Rayleigh distributions is different. Therefore,
88
Summary
Figure 5.32: Comparision main beam with different location error distributions
modeling of location error with accurate distribution is important in revealing the actual degradation of
the beam.
5.8
Summary
From phase error analysis provided in this chapter the following key points are summarised:
• The knowledge of location error models is essential in determining the distribution of the phase
error at the beamforming nodes
• Rayleigh distribution which charactersizes GPS location error is used in this chapter to model
location error
• Location uncertainities in the beamforming nodes resulted in initial phase errors at the nodes.
Consequently, the degradation of the main beam becomes severe when the Rayleigh parameter of
the location error reaches 25% of the wavelength.
• The first sidelobe peak also shows increase as a result of location error uncertainity
89
5. L OCATION A MBIGUITY AND P HASE E RROR IN WSN
• At working frequency of 500MHZ,the average value of the phase error at the nodes that keep the
main beam degradation at 3dB is between [380 , 420 ]
• For the same value of Rλ , increasing the number of nodes increased the main beam degradation.
The smaller the number of nodes, the better robustness towards location error is obtained.
• No significant change of the average sidelobe level is observed due to location error uncertainities
• The resulting error in the initial phase of each node is shown to follow a mixture of Gaussian,
Uniform and Rayleigh distribution. Futhermore, the Uniform and Gaussian component of the
phase error are zero mean Gaussian proccesses.
• The use of simple averaging gives good results in removing the Uniform and Gaussian component
of the phase error, thus improves the quality of the beam formed.
• Comparative results of phase error distribution for Gaussian distribution of location errors show
that the phase error is zero mean Gaussian process. This makes averaging as an effective means
of removing phase error.
• The use of simple averaging both at the CH and the beamforming nodes is employed to give
acceptable performance of clustering method in the presence of location errors.
• Averaging proves to be a practical simple solution in distributed beamforming in the presence of
location ambiguities.
90
Chapter 6
Conclusions and Recommendations
6.1
Contributions
Chapter 3
In chapter 3, a node selection techinique based on Clustering concept is proposed. The technique allows
to select small number of nodes for beamforming that are able to minimize interference in the direction
of primary user through sidelobe reductions. The obtained sidelobe reductions using clustering method
does not require any phase or amplitude adjustments at the nodes. The simplicity of the technique
conforms with limited computational capacity in wireless sensor networks. The use of small number of
nodes by the proposed method facilitiates the adoption of green communication in cognitive radio sensor
networks. The sidelobe reduction obtained from the node selection technique proves to be effective
in high density wireless sensor network where several number of nodes are deployed in large sensor
network for applications such as earthquake monitoring.
Chapter 4
In chapter 4,the node selection techinique proposed in chapter 3 is used to demonstrate green communication by quantifiying the energy reduction obtained per single transmission in the order of Joules.
Chapter 5
In chapter 5, the impact of location ambiguity is investigated based on GPS Rayleigh distributed location error. The degradative impacts of the resulting phase error on the beampatten is discussed. The
performance of the proposed node selection method in the presence of location ambigiuty is investigated. Statistical characterization of the phase error at the beamforming nodes is studied given Rayleigh
91
6. C ONCLUSIONS AND R ECOMMENDATIONS
distributed location error. The result obtained showed that the total phase error at the nodes is a mixture
distribution of Gaussian,Rayleigh and Uniform distributions. A simple solution based on averaging is
proposed which allows the beamforming nodes to remove significant amount of the phase error.
6.2
Conclusions
In this thesis work, the use of node selection technique is shown to address green communication for
cognitive radio sensor networks and the following conclusions can be drawn:
• Optimizing the number of nodes for energy conservation is essential in order to maintain green
communication in wireless sensor networks. Interference minimization however brings suboptimality of energy. The proposed node selection method is used to avoid this energy suboptimality.
Clustering node selection method brings this energy minimization through sidelobe reductions.
The best sidelobe reduction of clustering method is obtained when the nodes are selected from
high density networks which may be employed in earthquake monitoring applications. The simplicity of the proposed node selection technique makes it preferrable for sensor networks where
computational capacity is limited. It is also shown that the technique effectively works in different operational frequencies. The technique equally performs independant of the operational
frequency.
• The energy conservation obtained per single transmission using clustering node selection method
is demonstrated. This enables the sustainablity of energy consumption of the network and attaining of green radio communications.
Looking into the degradative impacts of location ambiguity of individual sensor nodes based on Rayleigh
distributed location error, the following conclusion can be drawn:
• The main impacts location ambiguity is decrement in the main beam gain. Large location error
values totally prevent the formation of the beam to the receiver.
• The use of smaller number of nodes resulted in less degradation of the mainbeam. This also justifies the use of small number of nodes through node selection in order to reduce the degradative
impact of location ambigiuity on distributed beamforming. Given that the location ambiguity of
the nodes is Rayleigh distributed, the resulting phase error is shown to be a mixture distribution
92
Recommendations
of Rayleigh, Gaussian and Uniform distributions. Furthermore, the Gaussian and Uniform components of the phase error are shown to be zero mean processes. Steming from this fact, a simple
solution based on averaging is used to remove significant portion of the phase error.
• The robustness of clustering node selection method is also investigated. It was shown that clustering node selection method is robust to maximum phase error values of
π
K
where K is the total
number of clusters. By grouping the nodes into smaller number of clusters, the robustness to phase
error values can be maximised. For larger values of the phase error, simple averaging is used to
improve the performance of clustering node selection method.
6.3
Recommendations
With regard to the work done in this thesis, the following research directions are suggested.
• In this thesis, no channel conditions are taken into consideration in the analysis. Looking into
multipath effects and shadowing effects will take distributed beamforming one step further into
practical deployment.
• In this thesis, node selection is used for transmit distributed beamforming without consideration
of relay network. The use of relay network can be employed in cognitive radio sensor networks
when the direction of PU and CR receiver is the same. The relay network can be used to redirect
the mainbeam to an intended CR receiver while the transmitting network can be used to minimize
interference in that direction through sidelobe reduction. This analysis requires to consider the
channel condition between the transmitting and relaying network.
• A single CH is considered in the system model of this thesis work. Considering the use of more
than one CH in the node selection process might help in the situation of single point of failure.
Considering this scenario in the presence of location ambiguity, is a good extension of this thesis
work.
• In this thesis, the use of simple averaging is proposed as a solution to remove a significant portion
of the phase error at the beamforming nodes. However, a predictive modelling of the phase error at
the nodes may be employed to predict the actual phase error. Studying how predictive modelling
can be used to counteract phase error can be taken as an extension of this work.
93
6. C ONCLUSIONS AND R ECOMMENDATIONS
• In this thesis we have used GPS location error distribution to model location error. Studying the
impacts of other distributions of location error of different localization algorithms used by nodes
is also recommended.
94
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Appendix A
Publications
• N.M.Tessema, X.Lian, H.Nikookar, “Beamforming with Efficient Node Selection Techniques for
Green Cognitive Radio Networks”, EuMiWeek, 2012.
• N.M.Tessema, X.Lian, H.Nikookar, “Distributed Beamforming with Close to Optimal Number of
Nodes for Green Wireless Sensor Networks ”, IEEE Online Conference on Green Communications, 2012
99