device-to-device communications underlaying a cellular network

Faculty of Electrical Engineering, Mathematics and Computer Science

Department of Telecommunications

Wireless and Mobile Communications (WMC) Group

Device-to-Device Communications

Underlaying a Cellular Network

Marcos Meibergen(1282468)

Supervisors

Ir. A. Slingerland

Dr. A.C.C. Lo

Members

Prof. I.G.M.M. Niemegeers

Dr. I.E. Lager

January 2011

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Copyright © 2011, M. Meibergen

All rights reserved. No part of the material protected by this copyright may be re-

produced or utilized in any form or by any means, electronic or mechanical, including

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permission from the author and Delft University of Technology.

DELFT UNIVERSITY OF TECHNOLOGY

Abstract

Faculty of Electrical Engineering, Mathematics and Computer Science

Department of Telecommunications

Wireless and Mobile Communications (WMC) Group

Master of Science Thesis

by Marcos Meibergen

Mobile voice service is already considered a necessity by many, and mobile data, video,

and TV services are now becoming an essential part of consumers’ lives. The number

of mobile subscribers is growing rapidly and bandwidth demand due to data and video

services is increasing. There is a need for capacity to increase in order for mobile

broadband, data access, and video services to engage the end consumer. Device-to-device

(D2D) communications underlaying cellular networks entails the ability of a cellular

network to allow devices to communicate directly with each other in the operating

(licensed) spectrum of the cellular network. With the application of specific rules and

strategies, D2D communications offloads the mobile network and increases the spectral

efficiency.

In this thesis we developed a method for the application of D2D communication, con-

trolled by a cellular network. By deriving the theoretical upper bound on the interference

we have analytically derived equations describing the minimum distances to be main-

tained between simultaneously operating links, to achieve a given minimum SINR. We

devised a strategy to group and schedule links which fulfill these minimum requirements,

so that multiple links may operate simultaneously. We describe a power optimization

method to minimize the number of groups to further improve the efficiency of the occupa-

tion of resources. Finally we performed simulations for various D2D scenarios, including

a scenario representing a realistic urban environment, to illustrate the potential of this

grouping and scheduling strategy.

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Contents

Abstract ii

List of Figures v

List of Tables vii

Abbreviations viii

Preface 1

1 Introduction 2

1.1 Era of the Mobile Internet . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.2 Implications for Mobile Operators . . . . . . . . . . . . . . . . . . . . . . . . 3

1.3 D2D Communications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

1.4 Scope of the Research . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

1.5 Literature Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

1.6 Thesis Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2 Wireless Communication Systems 9

2.1 Cellular Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

2.1.1 Cellular Network Concept . . . . . . . . . . . . . . . . . . . . . . . . 9

2.1.2 Cells . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2.1.3 Channel Access . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

2.1.4 From 1G to 4G and beyond . . . . . . . . . . . . . . . . . . . . . . . 11

2.2 Wireless Local Area Networks . . . . . . . . . . . . . . . . . . . . . . . . . . 13

2.3 Ad-Hoc Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

2.4 Cognitive Radio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

3 D2D Links Distance Study 15

3.1 Basic Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

3.1.1 D2D Links versus Cellular Links . . . . . . . . . . . . . . . . . . . . 15

3.1.2 Elementary Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

3.2 Path Loss . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

3.3 Minimum Distance Between Two D2D Links . . . . . . . . . . . . . . . . . 23

3.4 Minimum Distance Between D2D Links in a Cell:A First Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

3.5 Minimum Distance Between D2D Links in a Cell:A Second Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

iii

Contents iv

3.6 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

4 Scheduling of D2D Links 35

4.1 Grouping D2D Links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

4.2 Assumptions and Considerations . . . . . . . . . . . . . . . . . . . . . . . . 37

4.2.1 Spectrum Sharing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

4.2.2 Multiplexing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

4.2.3 Signalling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

4.3 Grouping Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

4.3.1 Greedy Grouping Algorithm . . . . . . . . . . . . . . . . . . . . . . . 43

4.3.2 Fair Grouping Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . 46

4.4 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

5 Optimization with Power Control 49

5.1 Problem Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

5.2 Optimization Mathematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

5.3 Derivation of the System Equations . . . . . . . . . . . . . . . . . . . . . . . 51

5.4 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

6 Simulation Results 54

6.1 Topology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

6.2 Scenarios . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

6.3 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64

6.3.1 First Distance Model with Greedy Grouping Algorithm . . . . . . 64

6.3.2 Second Distance Model with Fair Grouping Algorithm . . . . . . . 73

6.3.3 Optimization with Power Control . . . . . . . . . . . . . . . . . . . 79

6.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82

7 Business Opportunities Enabled by D2D Communications 85

7.1 Augmented Reality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85

7.2 Social Networking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86

7.3 Mobile Commerce and Advertising . . . . . . . . . . . . . . . . . . . . . . . 88

8 Conclusions and Final Remarks 89

8.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89

8.2 Future Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92

A Simulation Results 94

B KPN Company Profile 105

Bibliography 106

List of Figures

1.1 3G+ Global Penetration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.2 Apple iPad . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

1.3 Mobile Data Traffic Growth . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2.1 Cell Shapes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2.2 Evolution of Cellular Communication . . . . . . . . . . . . . . . . . . . . . . 13

3.1 Cellular Link versus D2D Link . . . . . . . . . . . . . . . . . . . . . . . . . . 17

3.2 Mean D2D Link Distance in function of Cellular Link Distance . . . . . . 18

3.3 D2D Range Area of a Node Close- and Far from the BS . . . . . . . . . . 18

3.4 PDF for Distance Between Two Random Points in a Circle . . . . . . . . 19

3.5 Circular Cell with 50 nodes, interconnected via D2D- or via Cellular Links 20

3.6 Converging Property of Link Lengths and Relative Link Frequencies . . . 21

3.7 Relation Between D2D Link-Length and Distance Between Links . . . . . 23

3.8 Distance Between Two D2D Links Operating Simultaneously . . . . . . . 24

3.9 Model for Calculating Upper Bound on Interference . . . . . . . . . . . . . 26

3.10 Interfering Nodes Placed on Hexagons . . . . . . . . . . . . . . . . . . . . . 27

3.11 Model Simplification Comparison . . . . . . . . . . . . . . . . . . . . . . . . 29

3.12 Simplified model for calculating upper bound on interference . . . . . . . 29

3.13 Illustrative Explanation of dmargin . . . . . . . . . . . . . . . . . . . . . . . 32

4.1 Grouping of D2D Links With a Distance Criterium . . . . . . . . . . . . . 36

4.2 Grouping of D2D Links With a Distance Criterium Sidenote . . . . . . . . 37

4.3 Spectrum Sharing Strategies . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

4.4 Scheduling of D2D links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

4.5 Mapping of Links to a Graph . . . . . . . . . . . . . . . . . . . . . . . . . . 44

4.6 Example Of Links Grouped With Greedy Grouping Algorithm . . . . . . 45

4.7 Distribution of Links over Groups - Greedy Algorithm . . . . . . . . . . . 45

5.1 Interfering D2D links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

6.1 Examples of Cell Scenarios with Fixed D2D Link Lengths (500 Nodes) . 59

6.2 Examples of Cell Scenarios with Fixed D2D Link Lengths (100 Nodes) . 60

6.3 Examples of Cell Scenarios with Variable D2D Link Lengths . . . . . . . . 61

6.4 Examples of Cell Scenarios with Clusters (Cluster Radii: 100 meters) . . 62

6.5 Examples of Cell Scenarios with Small Clusters (Cluster Radii: 10 meters) 63

6.6 Number of Groups formed, Greedy Grouping - Scenario 1 . . . . . . . . . 70



v

List of Figures vi



6.11 Number of Groups formed, Fair Grouping - Scenario 1 . . . . . . . . . . . 76





6.16 Decrease of dmin with Power Control - Greedy Grouping Algorithm . . . 81

6.17 Decrease of dmargin with Power Control - Fair Grouping Algorithm . . . . 81

6.18 Example of our Realistic Cell Scenario . . . . . . . . . . . . . . . . . . . . . 82

7.1 Augmented Reality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

7.2 Bump Screenshots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88

8.1 Tin Can Telephone . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93

List of Tables

3.1 Links and Distances Simulation Results of a Circular Cell With 50 Nodes 20

3.2 Propagation Model Parameters . . . . . . . . . . . . . . . . . . . . . . . . . 30

6.1 All Scenarios . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

6.2 Total Aggregate Cell Throughput . . . . . . . . . . . . . . . . . . . . . . . . 68

6.3 Optimization with Greedy Grouping Algorithm . . . . . . . . . . . . . . . 80

6.4 Optimization with Fair Grouping Algorithm . . . . . . . . . . . . . . . . . 80

A.1 Greedy Grouping Simulation Results - Scenario 1 . . . . . . . . . . . . . . 95





A.6 Fair Grouping Simulation Results - Scenario 1 . . . . . . . . . . . . . . . . 100





vii

Abbreviations

3GPP 3rd Generation Partnership Project

AMPS Advanced Mobile Phone System

AR Augmented Reality

BS Base Station

CDMA Code Division Multiple Access

CSD Circuit-Switched Data

D2D Device-to-Device

EDGE Enhanced Data rates for GSM Evolution

ETSI European Telecommunications Standards Institute

EV-DO Evolution-Data Optimized

FDMA Frequency Division Multiple Access

FDD Frequency-Division Duplexing

GPRS General Packet Radio Service

GSM Global System for Mobile Communications

HSCSD High-Speed Circuit-Switched Data

HSDPA High Speed Downlink Packet Access

HSPA High Speed Packet Access

HSUPA High Speed Uplink Packet Access

IEEE Institute of Electrical and Electronics Engineers

IETF Internet Engineering Task Force

ITU International Telecommunication Union

LI Lawful Interception

LTE Long Term Evolution

M2M Machine-to-Machine

MS Mobile Station

viii

Abbreviations ix

QoS Quality of Service

RAN Radio Access Network

RBS Radio Base Station

SDM Space Division Multiplexing

SINR Signal-to-Noise plus Interference Ratio

TDD Time-Division Duplexing

TDMA Time Division Multiple Access

UMTS Universal Mobile Telecommunications System

WAP Wireless Access Protocol

Wi-Fi Wireless Fidelity

WLAN Wireless Local Area Network

WPAN Wireless Personal Area Network

Preface

This work is the master thesis of Marcos Meibergen, defended at the Delft University of

Technology, as partial fulfilment of obtaining the M.Sc. degree in Electrical Engineering.

This work has been done under the supervision of dr.ir. A. Lo and ir. A. Slingerland,

partly at KPN in The Hague and partly at the Delft University of Technology. In

Appendix B on page 105 a short company profile of KPN is given.

1

http://www.kpn.nl

http://home.tudelft.nl/en/

Chapter 1

Introduction

In spite of the economic downturn, the demand for mobile services increased worldwide

during the past few years. In this chapter the main drivers behind this growth are stated

and it is motivated why the growth of mobile traffic is expected to keep accelerating.

The implications for mobile operators are briefly discussed and therewith the motivation

for this research on device-to-device communication underlaying cellular networks is

provided.

1.1 Era of the Mobile Internet

The mobile Internet has been a long time coming. It found its beginnings around 1998

with the Wireless Access Protocol (mostly abbreviated as WAP), which was designed

to let small, handheld wireless devices connect to the Internet. In the Netherlands,

marketers hyped WAP at the time of its introduction, but in terms of speed, ease of

use, appearance and interoperability it did not meet the expectations1. This led to

the wide use of sardonic phrases such as “Worthless Application Protocol”, “Wait And

Pay” and so on [21]. Since the introduction of WAP a lot has happened, and after a

slow start, the mobile Internet is now finally booming. Increasingly more people want to

have access to the Internet anytime and anywhere with their mobile phones and laptops.

The drivers are adoption of 3G, social networking, video, VoIP, and impressive mobile

devices. Research group Ovum reports that global 3G penetration should pass the 20%

mark in 2010 and will continue to rise, as shown in figure (1.1). Facebook — the most

popular social networking website — has more than 400 million active users, of which

more than 25% access Facebook through their mobile devices [14]. Facebook also reports

that people that use Facebook on their mobile devices are twice more active on Facebook

1Interestingly, in contrast to Europe and the USA, WAP was a huge success in Japan.

2

http://www.ovumkc.com

http://www.facebook.com

Chapter 1. Introduction 3

than non-mobile users. Video on mobile is likely to grow just like it did on the desktop

and stimulate explosive growth of mobile data usage. An example is Youtube Mobile,

which is expected to grow much more the coming years. VoIP leader Skype already has

more registered users than any global carrier, while the network effects from Apple’s

iPhone are immense [16].

Figure 1.1: The expected rising trajectory of the global 3G+ penetration.

There are more devices other than the ones mentioned above, which are increasingly

being connected to the Internet wirelessly e.g. mp3 players, e-readers, digital photo

frames, car electronics, home entertainment etc.. New products like Apple’s recently

presented iPad, displayed in figure (1.2), will exploit even more extensively the possi-

bilities offered by a broadband mobile Internet connection. And finally, because of the

emergence of cheap wireless sensors, the amount of mobile machine-to-machine (M2M)

connections will continue to increase at accelerating rates. More objects are gaining

the ability to communicate, giving shape to the concept of “the Internet of things” [5].

All these developments indicate that we are in the early stages of an Era of the Mobile

Internet.

1.2 Implications for Mobile Operators

For the wireless service providers the increasing popularity of mobile communications is

great news. The expansion of wireless ubiquity will lead to an increase of consumers who

http://www.youtube.com/mobile

http://www.skype.com

http://www.apple.com/uk/iphone/

http://www.apple.com/uk/iphone/

http://www.apple.com/ipad/


Figure 1.2: Apple hopes to set a new standard for wireless personal devices with theiriPad, which is expected to generate large amounts of traffic for mobile operators.

access and rely on mobile networks. However, while the traffic load on mobile networks is

expected to grow exponentially during the coming years, the income is — unfortunately

— not necessarily directly coupled to this growth. The vast majority of mobile operators

charge a monthly fixed price for broadband mobile access to the Internet. This pricing

structure is commonly called “flat fee”. The price is regardless of the usage2. Hence as

costumers generate more traffic, the operator earns less money per bit. In [19] professor

Erik Fledderus argues that telcos will not be able to sustain this pricing structure for a

long time. This may seem obvious today, but not too long ago nobody was talking about

the demise of ‘all-you-can-eat’ mobile data plans. According to Cisco [11], mobile data

traffic will globally increase 39 times between 2009 and 2014, reaching 3.6 exabytes3

per month by 2014, as shown in figure (1.3). Meanwhile, consumer expectations will

continue to rise. To transport all bits, enough capacity must be available to prevent

congestion to occur. Significant network investments are urgently needed if operators

want to keep up with the demand. Telcos invest huge amounts of money in network

expansion, upgrades and deployment of new technologies.

The biggest cost challenge facing wireless service providers today is the backhaul network

[7]. This infrastructure is very expensive to maintain and difficult to scale. The surge

of data traffic is pushing many mobile networks to their capacity limit. More antennas

are required to accommodate all users and achieve acceptable signal coverage. Mobile

2However, most operators maintain the rights to apply a bandwidth cap in case of excess data usageby a user. Implementation of a bandwidth cap is sometimes termed a Fair Use Policy.

31 exabyte = 103 petabytes = 106 terabytes = 109 gigabytes

http://web.tue.nl/staff/nl/e.r.fledderus

http://www.cisco.com


Figure 1.3: Projected Mobile Data Traffic Growth.

operators are seeking innovative solutions to cope with the rising demand of mobile

traffic while minimizing operating costs. A good example of what has been brought up

as a solution to relieve some pressure of the mobile networks and to use the limited and

expensive spectrum more efficiently are the so-called femtocells. Femtocells are small

cellular base stations using broadband connections for backhaul, intended to extend

coverage and offload the mobile macro network in home and small office environments.

Analyst firm Berg Insight [15] estimates that the femtocell shipments will grow from 0.2

million units in 2009 to 12 million units worldwide in 2014.

1.3 D2D Communications

In order to solve the issues mentioned in the previous paragraph, to enhance the commu-

nication capacity and capabilities and to introduce new services, research is performed

on many subjects, e.g. antenna design, data compression, modulation techniques and so

on. A recent research topic is device-to-device (D2D) communications as an underlay to

cellular networks [17]. A D2D link is a direct connection between two communicating

devices, in spectrum managed by the cellular network. The goal of using D2D links

is to: (a) increase the spectral efficiency, (b) reduce the load on the network and (c)

introduce and facilitate new services.

As the number of communicating devices grows, the spectrum in which the signals are

present becomes crowded. In mobile access networks, if the backhaul and backbone

http://www.berginsight.com/


portions of the network are dimensioned properly, the limiting factor (the bottleneck)

is the air interface. The reason for this is that wired data transport can achieve much

higher bitrates compared to wireless data transport4. By allowing D2D communications

the spectral efficiency can be improved, increasing the capacity of the air interface.

The improvement is achieved because the transmission in a D2D session occurs using

one direct wireless link, while a ‘conventional’ cellular session uses two wireless links,

with the BS as relay. Hence the BS is released from its function to forward data. The

spectral efficiency is especially improved when multiple D2D links are able to operate

simultaneously, using the same resources. The spectral efficiency is also improved by

exploiting spatial diversity in an active way; devices in each others proximity have the

opportunity to communicate directly and thus possibly to transmit their data with a

lower signal power. As the data does not pass through the fixed network, the load on

the fixed network can be reduced for short range (peer-to-peer) communication.

As the name of this work suggests, the D2D communication occurs ‘under the umbrella’

of a cellular network. This means that the D2D sessions take place in the same fre-

quency band as the cellular communication. Therefore, the sessions take place under

the supervision of the cellular network. In practice this implies that the BS covering the

area in which the devices are present is in control, provisioning and managing the com-

munication links. This control functionality is indispensable if the D2D communication

takes place in the licensed frequency band, because the interference caused by D2D links

on the normal cellular communication must be contained. At no time D2D communica-

tion may interrupt cellular communication. Additionally, D2D links also interfere with

each other. These interference problems are the main challenge when facilitating D2D

communication as such.

1.4 Scope of the Research

The purpose of this thesis is to present a strategy for the application of D2D communica-

tion in a cellular network. The research consists of four parts: (a) We analytically derive

equations describing what the minimum distance between simultaneously operating links

should be to achieve a minimum required SINR at all receivers. For the derivation of

the equations we propose a method to find an upper bound on the interference between

D2D links. (b) We propose a method to use the derived equations in a practical way.

(c) The derived analytical equations give minimum distance requirements in the worst

case scenario. It is possible to relax this stringent minimum distance requirement while

still being able to achieve a given minimum SINR by using optimization mathematics.

4For example, the maximum theoretical download speed for LTE is 326 Mbps, while speeds of 100Gbps can be achieved using fibre-optics.


We describe the optimization problem and provide the system equations to find a possi-

ble solution. (d) We perform simulations with different scenarios to analyze the results

obtained with our D2D scheduling strategy.

1.5 Literature Review

D2D communication underlaying cellular communication systems has been under the

attention of scientific researchers for a short time and therefore is a quite new area to

be explored. Most research has been performed in Finland, at the Helsinki University

of Technology with the cooperation of Nokia Research Center.

In [17], the authors propose to facilitate local peer-to-peer communication by a D2D

radio that operates as an underlay network to an IMT-Advanced cellular network based

on Orthogonal Frequency Division Multiple Access (OFDMA) technology. A power con-

trol scheme for the D2D links is proposed that share uplink resources with a cellular

network. The power control scheme is evaluated in an indoor interference-limited sce-

nario. The results show that D2D communication can take place with a good D2D link

Signal-to-Noise Ratio (SINR). It is also shown that indoor D2D communication causes

negligible interference to outdoor cellular users in the downlink of a metropolitan area

network.

In [4], D2D communication in a single-cell environment is analyzed in which one cellular

user and two D2D users share the available radio resources. The analysis focuses on

optimizing the sum rate by power control for different modes of resource sharing. It is

shown that with optimized power control, significant improvements for the sum rate can

be achieved in the given scenario.

The relevant issues regarding the feasibility of D2D communications as an underlay to

the LTE-Advanced network are discussed in [9]. In this paper, solutions are sketched

in how the interference of D2D communications to the cellular network can be con-

trolled. Results are given for an indoor scenario and an outdoor scenario with many

eNBs distributed in a Manhattan grid5. The results demonstrate that underlay D2D

communications by reusing cellular resources is possible for both scenarios. It is seen

that LTE-Advanced, if any system, offers opportunities for D2D communications due to

its time-frequency flexibility in allocations.

5The Manhattan Grid Model is introduced in [10]. In this model, nodes move only on predefinedpaths, separated by square buildings.

http://www.tkk.fi/en/

http://www.tkk.fi/en/

http://research.nokia.com


In [8], it is illustrated how D2D communication can be established in an LTE-Advanced

network having an SAE (System Architecture Evolution) architecture. The main con-

tribution of this article is to draft the functionality and messaging required to set up a

D2D connection inside the SAE architecture, and also if the session setup takes place as

an application layer signaling to the Internet beyond the cellular network.

A resource allocation scheme for mitigating intra-cell interference is proposed in [18].

Again, the same indoor scenario is used as in the previously mentioned papers. System

simulations indicate large performance gains in this scenario.

1.6 Thesis Structure

In chapter 2 the wireless communication systems which are relevant for this research are

introduced and the technologies are compared with each other. Its principles are briefly

explained and the addition of D2D communication capabilities to cellular networks is

placed into context. In chapter 3 we introduce a basic model to illustrate the idea

of D2D communication in a cellular network, followed by the derivation of equations

describing the minimum distance to be maintained between simultaneaously operating

links in a worst case scenario to guarantee a required SINR. In chapter 4 we use two

grouping algorithms to group links which may simultaneously communicate, while still

satisfying the conditions derived in chapter 3. We also explain the scheduling method

to be used for the formed groups of links. In chapter 5 we show that when the minimum

distance requirement is relaxed, the minimum SINR can possibly still be achieved at

all the receivers by using coordinated power control. We derive system equations to

show that this a linear programming (LP) problem. In chapter 6 we have performed

simulations with various scenarios to show results obtained with the methods explained

through chapters 3-5. All simulations are performed with Matlab6. In chapter 7

new business opportunities enabled or facilitated by D2D communication for mobile

operators are discussed. We conclude this document with a summary of our conclusions

and suggestions for future studies involving this topic, given in chapter 8.

6Matlab stands for “Matrix Laboratory” and is a numerical computing environment and fourth-generation programming language. Developed by The MathWorks, Matlab allows matrix manipula-tions, plotting of functions and data, implementation of algorithms, creation of user interfaces, andinterfacing with programs written in other languages.

http://www.mathworks.nl/products/matlab/

Chapter 2

Wireless Communication Systems

Wireless communication is the transfer of information over a distance without the use of

wires. The distances may be short or long. In this chapter the fundamental properties of

some wireless communication technologies of interest are given. The goal of this chapter

is to explain the concept and evolution of cellular networks briefly and to position D2D

communication as proposed in this research in the contemporary wireless networking

landscape.

2.1 Cellular Networks

2.1.1 Cellular Network Concept

Cellular systems for mobile communications implement Space-Division Multiplexing

(SDM). Each transmitter, typically called a base station (BS), covers a certain area.

In general, a cell can be defined as the area covered by one sector, i.e. one antenna

system. Antenna systems are located at their base station1. One base station can have

many antenna systems, thus many cells. The base station has a radio connection with

the mobile station (MS), and this base station should be capable of communicating with

the mobile station within a certain coverage area. A mechanism is used that transfers

the connection of users from cell to cell, when the MS moves out of range of the original

BS and into the range of the next.

In cellular networks, mobile stations cannot communicate directly with each other. Com-

munications are always relayed via the base station(s) covering the area(s) in which the

mobile stations are located. To be able to accommodate enough mobile stations while

1The term to denote a base station in a GSM network is Base Transceiver Station (BTS) and in aUMTS network Node B. The exact functionality of the base station differs per cellular technology.

9

Chapter 2. Wireless Communication Systems 10

maintaining the call quality standards, the radio network should be able to offer sufficient

capacity and coverage.

2.1.2 Cells

The shape of a cell is often modeled as a regular hexagon (Figure 2.1(a)). By using the

hexagonal shape, cells can graphically be displayed next to each other without having

overlapping areas of coverage. The ideal shape of a cell, which represents the ideal

coverage of the power transmitted by the base station antenna, is a perfect circle (Figure

2.1(b)) with a fixed radius R. Cell radii can vary from tens of meters in buildings, and

hundreds of meters in cities, up to tens of kilometers in large open areas. In reality,

the shape of cells are never perfect hexagons or circles (Figure 2.1(c)), but depend on

the environment (buildings, mountains, valleys etc.), on weather conditions and in some

systems2 even on system load. Hence the real shape of a cell is not a fixed figure; it

fluctuates over time and depends on a multitude of parameters.

(a) Artificial (b) Ideal (c) Realistic

Figure 2.1: Cell Shapes

Cells can be classified as outdoor and indoor cells. Outdoor cells can be further classified

as macro-, micro- and pico-cells. Macro-cells are the original, wide area high power base

stations which cover large areas. In urban areas, a separate layer of micro-cells may

be installed to provide the capacity and in-building penetration needed, taking load off

the macrocellular network. For office buildings and shopping malls with extremely high

demand pico-cells are used, which are even smaller cell sites.

To ensure that the mutual interference between cells remains below a harmful level,

adjacent cells have to be separated. In GSM and LTE this is done by assigning different

frequencies to adjacent cells. It is up to the operator to decide how to divide the available

2While in conventional FDMA and TDMA systems, like GSM, each subscriber has the full transmis-sion power of the base station, in CDMA systems (like UMTS and CDMA2000), the output power ofthe base station is divided among all active subscribers. If there are more subscribers, the coverage areaof a BS in a CDMA system will become smaller. This mechanism is called cell breathing.


bandwith over the cells. In UMTS, cell separation is done by code division; base stations

are assigned different CDMA codes.

In cellular mobile communication, frequency spectrum is a precious, limited resource.

The frequency band used by a mobile operator is located in the licensed band. The

mobile operator wishes to utilise the available spectrum as efficiently as possible. Cel-

lular network planning and optimisation is a complex and time-consuming task. More

information on this matter can be found in [20].

2.1.3 Channel Access

The goal in the design of cellular systems is to be able to handle as many calls as possible

within a given bandwidth with some reliability. Up- and download is commonly sep-

arated with Frequency-Division Duplexing (FDD) or Time-Division Duplexing (TDD).

FDD means that the transmitter and receiver operate at different carrier frequencies.

In TDD different time-slots are assigned for the up- and downlink. There are several

different ways to allow simultaneous access to the channel by different users. The most

common multiple-access schemes are:

� Frequency Division Multiple Access (FDMA): The frequency band is divided into

smaller frequency bands, providing different frequency bands to different data-

streams. As mentioned above, FDMA is used for cell separation in GSM and

LTE.

� Time Division Multiple Access (TDMA): Allows several users to share the same

frequency channel by dividing the signal into different time slots. TDMA is used

for user-separation in a GSM cell.

� Code Division Multiple Access (CDMA): a scheme based on spread spectrum.

Used for both cell- and user-separation in UMTS.

The Medium Access Control (MAC) protocol regulates the channel access (i.e. assigns

frequency bands, time-slots and CDMA codes) and is responsible for the avoidance of

collisions.

2.1.4 From 1G to 4G and beyond

The concept of cellular telephony was invented in AT&T’s Bell Labs in the early 1970’s.

These first mobile systems are referred to as first generation or 1G and used analog-

technology. The analog systems used frequency division multiple access (FDMA). For


example, the AMPS system uses a 30 KHz wide carrier band for each mobile user chan-

nel. An improvement upon the AMPS system is Narrow AMPS (NAMPS) where each

carrier band is only 10 KHz wide so that three times as many mobile subscribers can

be supported. An add-on to the AMPS system is cellular digital packet data (CDPD).

CDPD enabled the transfer of packet data over analog channels with data speeds reach-

ing up to 19.2 kbps.

As the number of cellular subscribers grew, there was a need for increased network ca-

pacity. Digital systems were invented, including among others the European initiated

Global System for Mobile Communication (GSM) and the United States initiated Code

Division Multiple Access (CDMA)3. The 2G systems support basic data services with

limited capacity since a single voice channel is used for the data transmission. Further-

more, the mobile subscriber is charged, as for voice calls, on a connection-time basis.

An improvement to this scheme was made available in the form of High-Speed Circuit

Switched Data (HSCSD) where multiple bearer slots are made available to the same

call. To provide better support for data services, ETSI developed the General Packet

Radio Service (GPRS), a packet transmission system that overlays GSM. GPRS is a

2.5G wireless communication system, offering data transfer speeds of up to 80 kbps.

The mobile subscriber is charged for the amount of data transferred, not on a time basis

as done for voice calls.

The evolution toward third generation cellular systems (3G) was driven by the need

for higher capacity, faster data rates, and better quality-of-service (QoS). Through the

introduction of sophisticated methods of coding and transmitting data, Enhanced Data

rates for GSM Evolution (EDGE) was developed, delivering higher bit-rates. EDGE

is implemented as an enhancement for GSM/GPRS networks and can offer a bit-rates

up to 236.8 kbps. This means it can handle four times as much traffic as standard

GPRS. Although EDGE is part of ITU’s 3G definition, it is often considered a pre-3G

radio technology4. In Europe, the 3G standard is UMTS. UMTS is based on wideband

CDMA (W-CDMA) and is based on evolved GSM core networks and the radio access

technologies that they support. UMTS can be extended to improve the data rates with

High Speed Packet Access (HSPA), also referred to as 3.5G.

A 4G system is expected to provide an all-IP based mobile broadband solution to mo-

bile devices. Facilities such as ultra-broadband Internet access, IP telephony, gaming

services, and streamed multimedia may be provided to users. The pre-4G technology

3GPP Long Term Evolution (LTE) is often branded 4G, but the first LTE release does

not fully comply with the IMT-Advanced requirements. LTE Advanced (Long Term

3The 2G version of CDMA is referred to as cdmaOne.4EDGE is occasionally referred to as 2.75G, implying that is is faster than GPRS, but slower than

typical 3G networks.


Evolution Advanced) is a candidate for IMT-Advanced standard, formally submitted by

the 3GPP organization to ITU-T.

D2D functionality as described in this thesis must be considered an addition to a 4G�

cellular network. The spectrum of radio frequencies available for communication is

limited and a benefit of a mobile network with D2D capabilities would be its ability

to reuse radio frequencies. This reuse provides for increased network capacity as more

mobile subscribers can be supported. Other possible advantages of a cellular network

with D2D capabilities are described in paragraph 1.3.

Figure 2.2: Evolution of Cellular Communication.

2.2 Wireless Local Area Networks

There are many protocols and technologies for wireless communication within a certain

geographic area. Currently, Bluetooth and Wi-Fi are the most popular and widely used

ones, having many applications. Bluetooth and Wi-Fi both operate in the unlicensed

ISM (industrial, scientific and medical) frequency bands, meaning that no hard QoS

guarantees can be given because the interference is not controlled.

D2D communication offers an alternative in case hard QoS guarantees are necessary or

wished for, or when no Wi-Fi hotspots are accessible to- or within the range of a mobile

device. Because D2D communication is controlled by the BS and uses the licensed

frequency band, a reliable communication channel can be offered. D2D communication

has the advantage that the cellular network identifies the users, so that no manual


pairing mechanism is necessary to form links (as with Bluetooth) and no keys have to

be exchanged to make a connection (as with WiFi).

2.3 Ad-Hoc Networks

A wireless ad-hoc network is a decentralized, self-configuring wireless network. The

network is ad hoc because it does not rely on a preexisting infrastructure, such as

routers in wired networks or access points in managed (infrastructure) wireless networks.

Instead, each node participates in routing by forwarding data for other nodes, and

so the determination of which nodes forward data is made dynamically based on the

network connectivity. An ad-hoc multihop network could be constructed out of D2D

links underlaying a cellular network, provided that a cellular network is present. By

utilising the knowledge of the BS regarding the (estimated) position and activity of nodes

and the overall network load distribution, the performance of such ad-hoc networks could

be increased by routing data more efficiently.

2.4 Cognitive Radio

Cognitive radio is a paradigm for wireless communication in which either a network or a

wireless node changes its transmission or reception parameters to communicate efficiently

avoiding interference with licensed or unlicensed users. This alteration of parameters

is based on the active monitoring of several factors in the external and internal radio

environment, such as radio frequency spectrum, user behaviour and network state.

Most of the research work is currently focusing on Spectrum Sensing Cognitive Radio,

particularly in the TV bands. The essential problem of Spectrum Sensing Cognitive Ra-

dio is in designing high quality spectrum sensing devices and algorithms for exchanging

spectrum sensing data between nodes.

Our research in D2D communication and the research in cognitive radio share essen-

tially the same goal: to increase the spectral efficiency. In cognitive radio this is done

autonomously by every individual device, whereas with D2D communication as described

in this thesis, there is a central regulating autority (the base station), coordinating all

communication.

Chapter 3

D2D Links Distance Study

In the first paragraph of this chapter, an elementary analysis is performed based on the

basic principle of D2D communication in a cellular network, which is to communicate

directly instead of relaying signals through a Base Station (BS). This paragraph is

meant to give an indication of the benefits of D2D communication in a cellular network

and serves as an exploratory research on D2D communication in a cellular network.

Subsequently, we introduce a simple path loss model and introduce two analytical models

used for the derivation of our equations, which describe the minimum distance to be

maintained between simultaneously operating D2D links in a cell. We want to use the

minimum distance as an input for our link grouping algorithms described in chapter 4.

3.1 Basic Model

3.1.1 D2D Links versus Cellular Links

In cellular communication, the BS serves as a relay. The radio path of a cellular link

consists of two parts: the path from the transmitter to the base station and the path

from the base station to the receiver. A D2D link is a single direct path from transmitter

to receiver. When comparing the two links, we may not simply assume that the length

of a D2D link is equal to the summation of the two paths of a cellular link. The two

parts of the cellular link have to be taken into account separately. For example if the

battery life of the wireless devices is the parameter of interest, we want to compare the

transmitting power of a device when communicating via D2D versus cellular links. In

this case the path from the base station to the receiving device in a cellular link does

not have to be taken into account. The path from the transmitter to the base station

can be compared directly to the D2D path. For the overall cell performance in terms

15

Chapter 3. D2D Links Distance Study 16

of interference and capacity, both parts of the cellular link would have to be taken into

account.

In the elementary analysis, a comparison is made between D2D- and cellular links based

on the length of the links (i.e. the distance between the two communicating nodes).

We perform this comparison as follows: when node A needs to send data to node B, we

define a D2D link to be a direct path from A to B. The cellular link is the path from

A to the BS. In cellular communication, the BS then forwards the data to B. The up-

and downlink of the BS are assumed to be separated by means of a channel separation

technique (paragraph 2.1.3). Hence, a D2D link from A to B is compared to a cellular

link from A to BS, even though in cellular communication the BS still has to forward

the data to B. This is an important assumption for the following analysis. Because the

forwarding takes place in a different frequency band, time slot or with different CDMA

code, the link from BS to B can be considered separately.

3.1.2 Elementary Analysis

In a circular cell with radius R, we uniformly distribute N nodes over the area in the cell.

If N � ª, the average distance from a node to the base station (i.e. the center of the

circle) can be determined by weighthing all radii and dividing the sum of all weighted

radii by the sum of the weights:

E�R� � R R0 f�r�r drR R

0 f�r�dr , (3.1)

where f�r� is the weight function, identified with a distribution function of r:

f�r� � 2πr, 0 @ r @ R. (3.2)

This distribution function weights each radius according to the circumference of a ring

with that radius. Filling equation (3.2) in equation (3.1) gives:

E�R� � R R0 2πr2 dr

R R0 2πr dr

�

�23πr

3�R0�πr2�R0

�2R

3. (3.3)


The distance found in equation (3.3) is the average distance between randomly placed

nodes in a circular cell and the base station (Figure 3.1(a)). D2D links bypass the base

station and are formed directly between nodes within the cell (Figure 3.1(b)).

(a) Cellular Link (b) D2D Link

Figure 3.1: Cellular Link (a) versus D2D Link (b).

The computation of the average distance between two random points (nodes) in a circle

with radius R can be found in [2] and is given by:

E�radius� � 128R

45π�� 0.9054R� (3.4)

From equations (3.3) and (3.4) we learn that using D2D links is on average disadvan-

tageous compared to cellular links, for communications within a circular area with a

centrally placed BS. The purpose of D2D links is not to replace, but rather to comple-

ment cellular links. The average of the distances from a random node to all other nodes,

is a function of the position of that node relative to the center of the cell: nodes near to

the edge have a larger mean distance to other nodes compared to nodes located in the

center of the cell. This relation between the distance to the cell center and the mean

distance to all nodes is shown in figure (3.2). From this plot it can be seen that the mean

distance from a randomly placed node to another node in the circle is always larger than

the distance from that node to the cell center. However, the difference between the mean

distance to other nodes and distance to the cell center decreases as we move away from

the cell center. Also, the number of nodes to which a direct D2D link with a distance

shorter than the distance to the cell center can be estabilished increases, as we move

towards the edge of the cell. This is illustrated in figure (3.3). In other words: better

opportunities for D2D communications occur as we move away from the cell center.

The most simple and intuitive way to decide whether to use a cellular link or a D2D

link, is to choose the one with the shortest distance. This means that the maximum

D2D link distance equals the circle radius R, because if the distance of a D2D link is

larger than R, a cellular link will be chosen. The probability density function f�x� of

the distance x between two random points in a circle of radius R is given by [2]:


Figure 3.2: Mean D2D distance in function of the distance to the cell center.

(a) D2D close to the BS (b) D2D far from the BS

Figure 3.3: D2D range area of a node close to the BS (a), and further away from theBS (b); in (b) there are more D2D opportunities.

f�x� � 2x

πR2

¢¦¤2 cos�1 � x

2R� � x

R

¾1 �

x2

4R2

£§¥ , �0 B x B 2R�. (3.5)

In figure (3.4) this probability density function is plotted. The shaded area indicates

all distances for which x A R. By integrating this area, we find a lower bound on the

average fraction of nodes to which a D2D link will not be profitable:

S2R

Rf�x� � 0.413. (3.6)

It is possible to simulate the scenario in which every node is connected to the other

nodes via the shortest link. If the D2D link between a pair of nodes is shorter than

both the links from the two individual nodes to the center of the cell, we define this as a

duplex-D2D link. If the D2D link is only shorter than the distance from one of the two


Figure 3.4: Probability density function f�x� for distance x between two randompoints in a circle of radius R.

nodes to the center of the cell, we define this as a simplex-D2D link. The pseudo-code

for the link choice is as follows:

01: FOR all nodes j

02: FOR all nodes i except node j

03: IF distance(j � center) < distance(j � i) AND

04: distance(i � cell center) < distance(j � i)

05: THEN there’s a duplex-D2D link from node i to node j

06: ELSEIF distance(j � cell center) < distance(j � i)

07: THEN there’s a simplex-D2D link from node i to node j

08: ELSE there’s no D2D link from node i and j;

09: node i has a cellular link with the base station

10: END if

11: END inner for-loop

12: END outer for-loop

In figure (3.5) a cell is shown with 50 nodes with the links made based on the above

pseudo-code. The red links are duplex-D2D links, blue links are simplex-D2D links and

green links are normal cellular links. From this simulation, the number of every link

type and their corresponding average lengths have been calculated and listed in table

(3.1).


Figure 3.5: Circular cell with 50 nodes, interconnected via D2D- or via cellular links.

Link Type Number of Links Average Link Length

Duplex-D2D 249 0.366RSimplex-D2D 236 0.647R

Cellular 1716 0.605R

Total 2450 0.561R

Table 3.1: Link types and their corresponding average distances from a simulation ofa circular cell with 50 nodes.

Without D2D links, there would be 50 � 49 � 2450 cellular links from every node to the

BS. In cellular networks, a node always connects to the BS with the same cellular link,

independent of which node it is communicating to. Hence there are 50 cellular links,

each used multiple times. Our simulation with 50 nodes shows that if solely cellular links

are in place, the average length of these links is 0.641R. As expected, this value lies

close to the average length calculated with equation (3.3). With D2D links, the average

distance of the links is reduced with 0.641R�0.561R0.641R � 100% � 12,5%. Moreover, we see

that the D2D links account for 2450�17162450 � 100% � 29.9% of all links. Of all D2D links,

249�2249�2�236 � 100% � 67.9% are duplex-D2D links. From figure (3.5) it can be observed

that most duplex-D2D (red) links, are located in the outer half of the circle. The average

length of these duplex-D2D links, is significantly smaller than the average lengths of the

simplex-D2D and cellular links. The duplex-D2D links are the links which often bring

most advantage. In our simulation, the average length of the cellular links which are

replaced by duplex-D2D links is equal to 0.726R. Hence, the mean length of these links

decreased with 0.726R�0.366R0.726R � 100% � 49.6%.

The same simulation is executed to verify the properties of the average lengths and the


relative frequency of the three types of links, in function of the number of nodes in the

cell. From the results, shown in figure (3.6), it can be seen that the regarding values are

stable.

Figure 3.6: Converging property of (normalized) link lengths and (relative) link fre-quencies in function of the number of nodes in the cell.

In reality, the decision to switch a local communication session from cellular to D2D,

depends on the design of the system. If a system is, for example, designed specifically

to increase the battery lifetime of the mobile devices, the only parameter which will be

observed is the output power of the mobile device; if a transmitter can reduce its overall

transmit power by transmitting directly to its destination instead of via a BS, this will

be the trigger to use a D2D link. This might not be the case for both devices in the

link, with the consequence of having a non-symmetrical communication system.

Another parameter which might be of influence is the traffic type. For small, short and

infrequent data transmissions, it might not be beneficial to set-up a D2D link, while for

large and long data streams a possible D2D link would be appealing. Other influencial

parameters could be e.g. the cell load or latency of the data delivery. In the rest of our

analysis we assume that the BS has decided what D2D links are present, based on one

or more parameters as the ones described above.

If the D2D links are very close to each other, they might not be able to operate simulta-

neously, as they would cause too much interference on each other. However, if the D2D

links are separated by a large distance, interference might not be an issue, because of

the degradation of the signal power over the travelled distance. This propagation loss

can be modeled with path loss models. In the next paragraph we introduce the path

loss model that we will use to find by what distance wireless (D2D) links need to be


separated to be able to operate simultaneously while still achieving a given minimum

SINR.

3.2 Path Loss

Path loss is the reduction (attenuation) in power density of an electromagnetic wave as

it propagates through space. Path loss models describe the signal attenuation between

a transmit and a receive antenna as a function of the propagation distance and other

parameters. Path loss for a non-free space wireless environment, such as a path with

obstructions consisting of buildings and trees, can be difficult to model. Different models

have been developed to describe the propagation behavior in different conditions. Some

models include many details of the terrain profile to estimate the signal attenuation,

whereas others just consider carrier frequency and distance travelled by the signal.

Research on propagation models is an academic field of its own. For our research we have

chosen to use a log-distance path loss model. The log-distance path loss model is a radio

propagation model that predicts the path loss a signal encounters inside a building or in

densely populated areas over distance. This model is widely used in literature because

of its relative simplicity, while still providing a realistic description of the overall signal

degradation. With the chosen model, which is described in [22], we can calculate the

path loss for urban wireless environments as follows:

PLdB�d� � PLFSdB�d0� � 10n log10 � dd0� �XdB, (3.7)

where

PLFSdB�d0� � 20 log10 �4πd0f

c� . (3.8)

PLFSdB�d0� is the free space loss for a distance d0 that is close to the transmitter,

but in the far field1, and d A d0. n is the path loss exponent, and XdB is a zero-mean

Gaussian random variable representing the variations in the path loss caused by multiple

reflections.

To make a distinction between different types of links (e.g. indoor/outdoor, D2D/cellular),

it is possible to use different parameters for calculating the path loss depending on the

link type. Typically, d0 is taken to be 1 km for large urban mobile systems, 100 m

for microcell systems, and 1 m for indoor wireless systems. The path loss exponent n

1The far field (along with the near field and the transition zone) is a boundary region of the elec-tromagnetic radiation emitted by an antenna. Certain behavior characteristics of electromagnetic fieldsdominate at one distance from the radiating antenna, while a completely different behavior can dom-inate at another location. Therefore, defined boundary regions categorize behavior characteristics ofelectromagnetic fields as a function of distance from the radiating source.


would be 2 for the free-space case. When obstructions are present, n is larger than 2.

Usually it is in the range of 2 to 6 with a typical value being n � 4, which is for the 2-ray

ground-reflection case [6].

When the system parameters are fixed and the zero-mean Gaussian random variable

neglected, equation (3.7) can be written as a function of the distance d:

PLdB�d� � 10n log10�d� �C (3.9)

where C is a constant which depends on the chosen system parameters. We use this

path loss model in the rest of this work.

3.3 Minimum Distance Between Two D2D Links

In figure (3.7) the relation between the length of a D2D link and the distance between

D2D links is illustrated. In figure (3.7(a)), two D2D links are communicating over a

distance of dD2D,1 and are separated from each other by a distance of dlinks. In figure

(3.7(b)), the D2D link size is increased while the distance between the links remains the

same. In the first case a better SINR will be experienced at the receivers than the latter

case; to maintain the SINR at the same level, dlinks would have to be larger as well.

(a) Short D2D Links (b) Long D2D Links

Figure 3.7: Two D2D links of length dD2D,1 are separated from each other by adistance of dlinks (a). If the D2D link is larger, while the separation remains the same,

more interference will be experienced at the receivers in (b).

We now analyse the case in which two D2D links are operating simultaneously. In figure

(3.8), suppose node i and node j form a D2D link, where node i is receiving data from

node j. At the same time, node k is transmitting data to another node l. The SINR at

node i will be

SINRi �PRij

PRik �N, (3.10)


where PRij is the signal power received by node i from node j and PRik is the interference

power received by node i from the interfering node k. For now we assume that there is

no noise present. For simplicity reasons we proceed with notations in decibels. Hence

equation (3.10) becomes

SINRi,dB � PRij,dB � PRik,dB, (3.11)

where

PRij,dB � PTj,dB � PLdB�dij� (3.12)

and

PRik,dB � PTk,dB � PLdB�dik�, (3.13)

where PTj and PTk is the power transmitted by node j and node k respectively. PLdB�d�is the propagation loss of a signal travelling over a distance d. Therefore, in equation

(3.12) dij is the length of the D2D link and in equation (3.13) dik is the distance between

the receiver and the interferer. The propagation loss can be calculated using equation

(3.7). Using equations (3.12) and (3.13) in equation (3.11) gives

SINRi,dB � PTj,dB � PLdB�dij� � PTk,dB � PLdB�dik�. (3.14)

We assume that a D2D link has a maximum length of dD2Dmax and all devices have

Figure 3.8: Node j is transmitting a signal to node i. Node k is interfering node i. Toguarantee a minimum SINR at node i, the minimum distance min�dik� between node

i and k can be calculated.

a maximum transmit power PTmax . Suppose there is a minimum SINR requirement,

stating that SINRi,dB C φ (dB). If the interfering node k is too close to the receiving

node i, the SINR requirement will not be achievable, even if node j is transmitting

at full power, i.e. when PTj � PTmax . We are interested in determining the minimum


distance dmin between the receiving node i and the interfering node k, at which the SINR

requirement can still be fulfilled, i.e. �dik � dmin� � �φ B SINRi,dB�. Hence equation

(3.14) becomes

φ B SINRi,dB � PTmax,dB � PLdB�dij� � PTk,dB � PLdB�dmin�. (3.15)

In the worst case, the interferer is transmitting with full power, i.e. PTk � PTmax . In

this case, φ � SINRi,dB. Filling in these values in equation (3.15) gives

φ � PTmax,dB � PLdB�dij� � PTmax,dB � PLdB�dmin�� PLdB�dmin� � PLdB�dij�. (3.16)

Equation (3.9) can be used in equation (3.16) to calculate the path losses. This gives

φ � 10n log10�dmin� �C � �10n log10�dij� �C�. (3.17)

Cancelling out the constant C and rearranging gives us

dmin � �10φ

10n �dij . (3.18)

This is the relation we were looking for. We can generalize equation (3.18) for any D2D

link, by replacing dij by dD2D, the length of the D2D link. Thus

dmin�dD2D� � �10φ

10n �dD2D. (3.19)

Hence, when two links with node pairs i�j and k�l are operating at the same time, com-

municating independently from each other bidirectionally, the following always holds:

�min�dik, dil, djk, djl� C dmin�max�dij , dkl�� SINRm C φ�, (3.20)

where m can be any of the nodes �i, j, k, l� and dmin is calculated with equation (3.19).

In the next paragraph we will extend this analysis for the case in which there are more

than two D2D links operating simultaneously.

3.4 Minimum Distance Between D2D Links in a Cell:

A First Approach

In this paragraph, we explain the model which has been used to derive an equation

which describes a direct relation between the required minimum distance dmin between


all D2D links operating simultaneously and the maximum length dD2Dmax of a D2D link.

When all nodes are separated by at least dmin, a hexagonal grid is formed. This is shown

in figure (3.9). The worst case in terms of interference, is when the node in the center

of the cell (green node) is in receiving mode while all other nodes are interferers (red

nodes).

Figure 3.9: The green node is the receiver, while red nodes are transmitters. Allnodes fulfill the requirement of being at least dmin appart from each other.

We would like to know how many nodes interfere on the receiving node in the center.

This is equal to the number of nodes that fit in the cell minus the center node. As can

be observed from figure (3.9), the interfering nodes are placed in hexagons around the

receiver. The first three hexagons are shown in figure (3.10). On every hexagon, six

interferers are placed. Hence the number of interfering nodes in a cell depends on the

number of hexagons that fit in the cell. The length of the edges of a hexagon is equal


to the distance of a node on that hexagon to the center of the cell. Starting from the

smallest hexagon, the length vh of the edges of the hth hexagon is

vh �

¢¦¤h�1

2 dmin, if h is odd

h2

º3dmin, if h is even

(3.21)

We call the hth hexagon an odd or an even hexagon if h is odd or even respectively.

Figure 3.10: The model from figure (3.9) is shown above, with the first three hexagonson which the interferers around the center node are placed.

The number of hexagons that fit in a cell is a function of the radius r of the cell and

the minimum distance dmin between nodes. We can maximally fit rdmin

� odd hexagons

and rº3dmin

� even hexagons in a cell with radius r. Hence the maximum number of

interfering nodes according to the model illustrated in figure (3.9) is

N � 6 r

dmin� � 6 � rº

3dmin

� . (3.22)

When all interfering nodes transmit with the maximum power PTmax , an upper bound

on the interference received by the node in the center of the cell can be calculated and

is given by:

Imax �

A

Qi�1

PTmax

PL�dA,i� � B

Qi�1

PTmax

PL�dB,i� , (3.23)

where A and B are the total number of nodes on the odd and even hexagons respectively,

i.e.

A � 6 r

dmin� and B � 6 � rº

3dmin

�


and PL�d� is the path loss in function of the distance d travelled by the signal as

described in paragraph 3.2. As explained before, the distance from an interfering node

to the center of the cell is equal to the size of the vertices of the hexagon on which that

interfering node is placed. The distances used in equation (3.23) are given by:

dA,i � � i6�dmin and dB,i � � i

6�º3dmin. (3.24)

In figure (3.11) the interference power in dB is shown against values that dmin may take,

for the path loss exponent values of n � 2,4 and 6. The interference power is also plotted

for the case when only the interfering nodes closest to the receiver (i.e. the nodes on

the smallest hexagon) are active. As can be seen, the difference between all interfering

nodes being active compared to only the six nodes on the smallest hexagon, is small

(at most 0.8 dB for n = 4) for the system parameters shown in table (3.2). Hence, a

simplification is possible, when we ignore the interference from the nodes that are not

on the smallest hexagon ring2. We simplify equation (3.23) by only taking the first

hexagon ring of interfering nodes in account, i.e. A � 6 and B � 0. This simple model is

illustrated in figure (3.12). From equation (3.24) we get

dA,i � dmin, (3.25)

and by combining equations (3.23) and (3.25) we find

Imax�dmin� � 6

Qi�1

PTmax

PL�dmin� � 6PTmax

PL�dmin� , (3.26)

which in decibel notation is expressed as

Imax,dB�dmin� � 10 log10 �6PTmax

PL�dmin�� PTmax,dB � PLdB�dmin� � 10 log10�6�. (3.27)

2If the system parameters are chosen differently, the difference between the interference from allthe nodes or only from the six nodes on the smallest hexagon is possibly not negligible; signals withlower frequency propagate further, hence interference will increase. The system parameters used hereare representative for what the real parameters would be for a system where D2D communication isimplemented.


Figure 3.11: The blue line shows the inteference power received by the central receiverwhen all interfering nodes are present, the red line with only the nodes on the closesthexagon. Cell radius r � 1000 (meters), Tmax is taken to be the maximum output power

from a UMTS/3G mobile phone (Power class 4 mobiles) (125 mW).

Figure 3.12: The green node is the receiver, while red nodes are transmitters. Allnodes fulfill the requirement of being at least dmin appart from each other.


Parameter Value

XdB 0

d0 1 (m)

f 2 (GHz)

c 3 � 108 (m/s)

Table 3.2: Propagation Model Parameters.

For the calculation of the path loss, equation (3.9) is used with the parameter values

shown in table (3.2), thus

PLdB�d� � 10n log10�d� �C, (3.28)

where C � 38.5 dB. The SINR at the receiving node is

SINR �PR

IR �N, (3.29)

or in decibel notation

SINRdB � PR,dB � IR,dB �NdB, (3.30)

where PR is the received signal power, IR is the received interference power and N is the

noise. For now we take that N � 0. We assume that a D2D link has a maximum length

of dD2Dmax and the distance between all interfering nodes is at least dmin. Suppose there

is a minimum SINR requirement, stating that SINR C φ (dB). When the maximum

interference is experienced by the receiver (i.e. IR � Imax), we still want to achieve the

minimum SINR requirement. Thus

φ B SINRdB � PR,dB � Imax,dB. (3.31)

We want to find the dmin for which the SINR requirement can always be fulfilled, even

when the paired transmitter and receiver are separated by the maximum D2D link length

dD2Dmax . In this worst case SINR � φ and the transmitter transmits with maximum power

PTmax , so that the received signal power will be

PR,dB � PT,dB � PLdB�dD2D�� PTmax,dB � PLdB�dD2Dmax�. (3.32)

Using equations (3.31) and (3.32) we find that

φ � PTmax,dB � PLdB�dD2Dmax� � Imax,dB�dmin�. (3.33)


Rewriting gives

Imax,dB�dmin� � PTmax,dB � PLdB�dD2Dmax� � φ. (3.34)

Now equations (3.27) and (3.34) can be combined:

PTmax,dB � PLdB�dmin� � 10 log10�6� � PTmax,dB � PLdB�dD2Dmax� � φ. (3.35)

We can see that PTmax,dB cancels out. Rewriting equation (3.35) gives

PLdB�dmin� � φ � PLdB�dD2Dmax� � 10 log10�6�. (3.36)

We can now use equation (3.28) to find the path losses and fill these in equation (3.36):

10n log10�dmin� �C � φ � 10n log10�dD2Dmax� �C � 10 log10�6�. (3.37)

Cancelling out C and rewriting gives

dmin � �10�φ�10 log10�6�

10n��dD2Dmax , (3.38)

which is the relation we were looking for.

It must be noted that in the worst case, the required SINR might not be met at some

receiving nodes3. The reason for this, is the simplification we made to acquire equation

(3.27). However, in practice the worst case scenario is highly unlikely; the majority of

the nodes will not be transmitting at full power and the placement of the nodes will

not be as dense as in figure (3.9). Simulation results presented in chapter 6 show that

using dmin as a requirement yield SINRs at the receiving nodes which are far above the

required SINR φ.

In the next paragraph another method is introduced to find a minimum distance to be

maintained between active nodes from different links. Instead of assuming that all nodes

transmit with maximum power and are placed in a hexagonal grid, different assumptions

are made.

3.5 Minimum Distance Between D2D Links in a Cell:

A Second Approach

In the previous paragraph, we determined an upper bound on the interference, and

used it to calculate the minimum distance dmin between receiving nodes and interferers.

3The closer a node lies to the center of the cell, the more interference power it will receive accordingto the model shown in figure (3.9).


The upper bound was derived with the assumption that all interferers transmit with

maximum power PTmax and are placed on a hexagonal grid. In reality, D2D links are

not of equal length. If a power control mechanism is in place, transmitters involved in

D2D communication over a short distance will transmit less power than transmitters

involved in a D2D session over a large distance. In this paragraph we take this fact

into account with a different approach for the estimation of the interference that will

be experienced at the receivers and discuss a new way to define the ‘contention zone’ of

a D2D link. The goal of this is to find a less stringent requirement on the separation

between links while still guaranteeing a given SINR.

Figure 3.13: Illustrative explanation of dmargin; it is the distance between a interfererand a receiver minus the length of the D2D link of the interferer.

As illustrated in figure (3.13), we define a ‘margin-distance’ dmargin to be the distance

between an interferer and a receiver minus the length of the D2D link of the interferer.

Hence

dmargin � dik � dlk. (3.39)

We assume that we know the necessary signal power PRlk to be received by node l from

node k. Because we also assume omnidirectional antennas, the signal power density

coming from node k is equal anywhere on the border of a circle with radius dlk around

node k. The interference power PRik received by node i from node k is

PRik,dB � PRlk,dB � PL∆,dB�dlk, dmargin�, (3.40)


where PL∆,dB�dlk, dmargin� is the path loss of the signal travelling from point P to node

i. The path loss function as described in equation (3.9) is not linear, thus

PL∆,dB�dlk, dmargin� � PLdB�dlk � dmargin� � PLdB�dlk�� 10n log10�dlk � dmargin� � 10n log10�dlk�� 10n log10 �dlk � dmargin

dlk� . (3.41)

To achieve a given SINR requirement stating that SINR C φ, we need to limit the

interference. This is done by setting a minimum on dmargin. If the dmargin between

an interfering and a receiving node is too small, they may not operate simultaneously.

We want to find an expression for dmargin,min just like we did for dmin in the previous

paragraph. If there are L links active at the same time, there are L�1 interfering nodes

for every receiver. If we assume that all receiving nodes receive the same signal power

PR from their paired transmitter, analogous to the way we derived equation (3.40), the

maximum interference at a receiver is

Imax,dB � PR,dB � PL∆,dB�dD2Dmax , dmargin,min� � 10 log10�L � 1�� PR,dB � 10n log10 �dD2Dmax � dmargin,min

dD2Dmax

� � 10 log10�L � 1�, (3.42)

where dD2Dmax is the largest allowed D2D link length. The minimum SINR is

SINRmin,dB � PR,dB � Imax,dB, (3.43)

and is in the worst case equal to φ. Hence combining equations (3.42) and (3.43) gives

φ � 10n log10 �dD2Dmax � dmargin,min

dD2Dmax

� � 10 log10�L � 1�. (3.44)

Rearranging gives

dmargin,min � �10�φ�10 log10�L�1�

10n�� 1�dD2Dmax . (3.45)

We can apply the same method as in the previous section, to argue that it is acceptable

to limit the amount of interfering links to 6, so that Lmax � 7. It can be observed that

when there are only two interfering links, i.e. L � 2, equation (3.45) reduces to

dmargin,min � �10� φ10n

�� 1�dD2Dmax , (3.46)


so that the minimum distance between two links becomes

dmin � dD2Dmax � dmargin,min

� �10φ

10n �dD2Dmax , (3.47)

which is indeed the same equation as equation (3.19), where only two links where con-

sidered.

3.6 Chapter Summary

In this chapter we have performed an elementary analysis on the distances between two

random points in a circle and the distances between a random point in a circle to the

center of the cell, representing D2D and cellular links respectively. A comparison is

made in terms of the average link lengths in a cell when the choice of the BS to make

use of a D2D link instead of using cellular links relies solely on link lengths.

We have used a simple path loss model to derive an upper bound on the interference

coming from devices separated from each other by a distance of at least dmin. We

used this upper bound to analytically derive an equation with which we can find the

minimum separation requirement between nodes as a function of the path loss exponent,

the minimum SINR and the maximum D2D link length. To guarantee a minimum SINR

at every node without the need of adjusting the initial transmit powers, the dmin from

the derived equation can be used.

We also presented a second method to derive a minimum distance requirement, with the

use of a margin distance dmargin. With this second method we can take it into account

that not every link is of equal length and assuming power control on D2D links give

a less stringent distance requirement while still guaranteing a minimum SINR at every

node.

In the next chapter we give a purpose to the derived minimum distances in this chapter

by introducing the idea of grouping links.

Chapter 4

Scheduling of D2D Links

Many criteria can be used to measure the effectiveness of a communication system to see

if it is ideal or perfect. For digital wireless communication systems, the optimum system

might be defined as the system that minimizes the probability of bit error subject to

constraints on transmitted energy and channel bandwidth. Bit error probability and

signal bandwidth are of prime importance for the quality of a wireless communication

link.

As explained in chapter 2, wireless communication is susceptible to interference. In order

to limit the bit error rate and utilize the signal bandwidth as efficiently as possible,

we want to minimize the interference experienced by wirelessly communicating links.

In the previous chapter we derived equations describing the minimum distance to be

maintained between active nodes. When at least this minimum distance is maintained

between the simultaneously communicating nodes, the interference is limited and a given

SINR requirement can be guaranteed at the receiver.

In practice, D2D links can be set-up anywhere in an area. We obviously do not always

have the capability of changing the location of communicating nodes. Even if this

capability is available, it is not always desirable or possible to change the location of

a link, as the link is probably there for a reason. Hence the following question arises:

‘Why did we derive a spatial requirement in the previous chapter?’. The answer will

follow from this chapter.

In this chapter we introduce two algorithms which group links. First we explain the

concept of grouping. Then we elaborate on the assumptions made and the considerations

taken into account in the application of the algorithms. Finally we explain the grouping

algorithms.

35

Chapter 4. Scheduling 36

4.1 Grouping D2D Links

In the previous chapter we derived two equations, specifying the minimum distance

that must be maintained between links to guarantee a given SINR. Now we want to

form groups of links which all fulfill the calculated minimum distance requirement with

respect to each other so that all links in the same group may operate simultaneously

while achieving a minimum SINR.

Groups of links are formed by using a distance criterium; only links that are separated

from each other by a distance of at least ∆ meters may belong to the same group, so

that all links belonging to the same group are separated by at least ∆ meters. This is

illustrated in figure (4.1). In this figure three links are shown. Suppose that d @ ∆ @ 2d,

so that the distance between the nodes of link 1 and 2 is less than ∆. From the distance

criterium, it follows that link 1 and 2 may not belong to the same group. The same goes

for link 2 and 3. Link 1 and 3 however, are separated by a distance larger than ∆ and

can therefore be placed in the same group.

Figure 4.1: Grouping of D2D links with a distance criterium.

We may take ∆ � dmin, where dmin is the minimum distance criterium we derived in

equation (3.38). If we do so, then all links belonging to the same group fulfill the

minimum distance requirement. When all the links in a group – and only the links

of that group – operate simultaneously, the minimum SINR used to calculate dmin is

guaranteed for all links in that group.

Note that technically, it is only required that a distance of dmin is maintained between

receivers and interferers. It is possible that this is the case, while not all of nodes fulfill

the distance requirement. This is illustrated in figure (4.2(a)). Here, we see that the two

receivers are not separated by a distance of ∆ meters (still considering that d @ ∆ @ 2d).

But receivers do not interfere with each other, so this would not be harmful for the D2D

communication. However, as soon as the transmitter and receiver in one link change


roles, the links cannot belong to the same group any more. This is shown in figure

(4.2(b)).

In the rest of our research we assume that all D2D communication is bi-directional, hence

we require that all nodes fulfill the distance requirement (with the exception of the paired

nodes). We make this assumption because the data flowing between nodes in D2D links

are not symmetrical and are typically independent of each other (although one can think

of exceptions, where data being shared locally is correlated between devices that are not

communicating at that instance). If the D2D links are bi-directional, D2D links do not

have to wait for each other to change the direction in which they are communicating.

Also, no new groups need to be formed for the reverse direction, because the same groups

can be used. Hence less coordination from the BS is needed, reducing the complexity of

the system and the signalling overhead.

(a)

(b)

Figure 4.2: Not all nodes in the links fulfill the distance requirement, but technicallythe two D2D links shown in (a) could belong to the same group, because the interferersare distant enough from the receivers. However, this is not the case any more as soon

as the transmitter and receiver in one link change roles, as shown in (b).

4.2 Assumptions and Considerations

4.2.1 Spectrum Sharing

Most cellular systems, including the UMTS/WCDMA Frequency Division Duplexing

mode and the cdma2000 system, use Frequency-Division Duplexing (FDD) to separate


the up- from the downlink. In our discussion we assume this principle, but the same

conclusions would apply for TDD or another mechanism. The D2D communication has

to be accommodated next to the present cellular communication. This can be achieved

by sharing resources or allocating dedicated resources in either the up- or downlink, or

both. All possibilities are depicted in figure (4.3).

(a) Uplink Sharing (b) Downlink Sharing (c) Up- and Downlink Sharing

(d) Uplink Dedicated (e) Downlink Dedicated (f) Up- and Downlink Dedicated

Figure 4.3: Spectrum Sharing Strategies

The scenario in which the cellular uplink spectrum is shared with D2D communication

is shown in figure (4.3(a)). In the uplink spectrum, devices involved in a cellular com-

munication session transmit signals to the BS. Hence active D2D transmitters will cause

interference at the BS. D2D communication may only take place if the ongoing cellular

communication is not disturbed too much, i.e. a minimum required SINR ratio has to

be achieved at the BS. A similar analysis as the one performed in paragraph (3.4) can

be used to define which D2D links may be active without causing interference at the BS

above a certain level. However, by sharing the uplink spectrum, D2D links close to the

BS will less likely be allowed to exist, as these links cause more interference at the BS.

Moreover, D2D receivers will - to a lesser or greater extent - suffer from the interference

caused by the cellular transmissions.

In the scenario shown in figure (4.3(b)), the cellular downlink spectrum is shared with

D2D communication. In this case, the D2D links may not disturb the devices receiving

data from the BS. The BS will cause interference at the receiving D2D nodes, especially


when the BS is transmitting to a node near the edge of the cell while the D2D receiver

is located close to the BS.

The scenario shown in figure (4.3(c)) combines the first two options. This method

combines the challenges of the first two options, but also the advantages; more bandwidth

is available for D2D communication.

Sharing spectrum between cellular and D2D links is especially advantageous when short

cellular links are active, i.e. when devices near to the BS are communicating over a

cellular link with the BS. Then there may be some D2D links which fulfill the minimum

distance requirement with respect to that cellular link. However, with equation (3.3)

we have shown that the average distance to the center of a cell is equal to 2R3 . Hence,

almost the whole cell will be part of the contention zone on average, so that limited

resources can be reused by using one of the schemes shown in figures (4.3(a)-(c)).

With our particular grouping strategy, the minimum distance requirements derived in the

previous chapter are functions of (among other parameters) the maximum link length;

the larger the maximum link length, the larger the minimum distance requirement will

be. If the maximum length of a cellular link is assumed to be as large as the radius of

the cell, the minimum distance requirement will be very large if these links are included.

Because the BS is assumed to be located in the center of the cell, the whole cell will

belong to the contention area. The consequence is that no D2D links can be placed in

the same group with a cellular link, so that the efficiency is not increased by using a

scheme in which cellular and D2D links share spectrum.

The options shown in figures (4.3(d)-(f)) assume dedicated resources are allocated for

D2D communication. The advantage of allocating dedicated resources instead of shar-

ing resources with the cellular communication, is that the D2D communication does not

interfere with the cellular communication and vice versa, resulting in a less complex

system. The downside of these schemes is that the efficiency during the cellular commu-

nication sessions is not increased; the cellular link timeslots are still being used by only

one cellular link. However, as argued above, we do not expect to be able to achieve high

profits by sharing spectrum with cellular links.

In cellular communication, the up- and downlink bands are usually not utilized sym-

metrically; users tend to download more than to upload. Hence if the up- and downlink

bands are of equal width, we can expect to have more ‘space’ for D2D communication

in the uplink band. The advantage of using both the up- and downlink band is that we

have more available spectrum. The disadvantage of is that D2D devices will have to be

signalled to tune in to the correct band. The options shown in figures (4.3(d)-(f)) might


suggest that a fixed portion of the resources is reserved for D2D communications. How-

ever, the portion that is used for D2D communications can be determined dynamically,

so that no resources are wasted in case there are no D2D sessions.

4.2.2 Multiplexing

The separation of signals is more commonly referred to as multiplexing. Signals can be

separated from each other over time, frequency, code or space. The principle behind

the different possibilities of multiplexing are explained briefly in paragraph (2.1.3). In

the real world, every multiplexing method has its own limitations and disadvantages.

Ideally, all methods have the same performance; in the end the limited bandwidth simply

has to be divided over the number of users. It is beyond the scope of this research to go

into the details of multiplexing.

The algorithms presented in this chapter, group certain links such that all links in

a group can operate simultaneously using the same resources. The different groups

however, still need to be separated from each other. In theory this can be done by

means of any of the multiplexing methods mentioned before, i.e. by distributing CDMA

codes, by assigning different frequencies or by allocating individual time slots to every

group. For the discussion in our analysis we have chosen for the separation of groups in

a TDMA fashion, but the analysis also applies to FDMA and CDMA if the details of

multiplexing1 are not taken into account. There are many factors which play a roll in

the choice of the optimal multiplexing technique (e.g. the limited amount of resources,

energy consumption, QoS requirements, etc.).

In our analysis we assume that all cellular communication uses TDMA with Frequency

Division Duplexing (FDD) to separate the up- from the downlink. This is depicted

with more detail in figure (4.4), in which there are n mobile devices active in cellular

communications and M groups with D2D sessions. A group contains one or more active

D2D links. In this figure only one timeslot in the up- and one in the downlink is shown

for D2D signalling. This is merely for illustrative purposes; in a real scenario more

signalling time slots may be used. The signalling occurs between the BS and the devices

and therefore is seen as cellular communication.

1With details we mean for example the guard intervals between time slots, guardband betweenadjacent frequency channels and the non-perfect orthogonality between CDMA codes.


We assume that all nodes want to be able to both transmit and receive data indepen-

dently of other D2D links. Bi-directional communication is usually the case in commu-

nication sessions2. The mutual independence makes the D2D communication flexible;

large data transfers can occur simultaneously with short bi-directional exchange of data,

without one having to wait for another. Another advantage is that less coordination is

required from the BS (i.e. less signalling by the BS).

Figure 4.4: In the figure dedicated slots are allocated for D2D communication, bothin the uplink as in the downlink frequency bands.

4.2.3 Signalling

All wireless communication in the licensed spectrum has to be coordinated by the BS

covering the area. The coordination is done through signalling. A protocol is necessary

to specify how the signalling occurs. Devices eligible for D2D communication have to be

informed on which frequency band and timeslot they are allowed to communicate. The

initial signalling between the BS and the D2D ‘candidates’ can occur via the timeslots

designated for cellular communication. As explained before, in D2D sessions there are

no specified slots for up- and downlink. Hence after a D2D session has been set-up, the

involved devices need to signal each other as well, to coordinate and negotiate the up-

and download times. Pre-defined preambles can be used to specify the start and the end

of messages. A mechanism to acknoledge the correct reception of data is also necessary.

2Depending on the protocol, even in a session where only one device in a link wishes to share data,the receiver of the data often will have to acknoledge that the data has arrived. Hence at instances thereceiver also serves as transmitter and vice versa. However, there are networks where the communicationis only one-way, like some sensor networks.


To monitor the quality of a link, devices may signal (amongst other QoS parameters)

their SINR level. A power control mechanism can then be used to regulate the transmit

power3.

The BS decides in which group a D2D link is placed and in what timeslot a group

operates, as shown in figure (4.4). Over time, new D2D links are created while some

existing D2D links are terminated. For optimization reasons, the BS may want to

change the group of active D2D sessions. Signalling timeslots in which all devices in a

D2D session listen to the BS can be used to receive coordination commands from the

BS. The commands are then broadcasted by the BS in one or more signalling timeslot

as such. In figure (4.4) one BS broadcasting timeslot is illustrated (blue timeslot).

Finally, the devices in a D2D session have to inform the BS when the communication

is terminated. Depending on the traffic pattern, strategies can be developed to, for

example, agree upon a time to live of a certain link. Another possibility is to periodically

send a message to the BS to stay updated on the status of the link. This transmission of

this periodical message has to be in agreement with the BS, so that one or more timeslots

for cellular communication is reserved. By doing so, the ongoing cellular communication

is not disturbed.

The signalling overhead depends on the dynamics of the cell, i.e. the traffic that is

flowing and the mobility of nodes. In a static scenario, where nodes do not change

their positions frequently and communication sessions are set-up for a longer period,

the signalling overhead is limited. In a very dynamic scenario, a signalling protocol is

required which prevents too much signalling traffic.

Signalling (protocols) is a topic of its own and is beyond the scope of this thesis. We

assume that it is possible and that the signalling overhead is limited.

4.3 Grouping Algorithms

We assume that the BS is responsible for the set-up and allocation of time slots for

D2D links. In our analysis we also assume that the position of the nodes is known to

the BS and that nodes are stationary. In reality, the position of devices may not be

known exactly at every moment, but there are many possibilities to approximate the

position of a device. For example, UMTS supports location based services, standardised

by 3GPP in [1]. 3GPP specification also describes location based service reliability,

priority, security, privacy and other related aspects. Another possibility is to use the

3A maximum transmit power, defined by the BS, must be known by all the devices participating ina D2D session and may not be exceeded.


location of known fixed points in the network to determine the location of other devices

relative to these points. Other possibilities may include the use of Global Positioning

System (GPS), requiring the devices to signal their position to the BS.

As explained earlier in this chapter and as depicted in figure (4.4) every group has its own

time slot. We want to minimize the number of necessary time slots in order maximize

the capacity of the cell in terms of time slots. Hence we want to create as few groups as

possible, i.e. we want to maximize the number of links in every group.

This problem can be formulated as the graph coloring problem in graph theory. Graph

coloring in its simplest form, is a way of coloring the vertices of a graph such that no

two adjacent vertices share the same color. Much research has been performed in this

area. A nice overview comparing the performance of the most commonly known coloring

algorithms can be found in [3].

To use graph coloring theory for our link grouping problem, we can make a graph out

of a set of D2D links, where every link is represented by a vertex. If links do not fulfill

the distance requirement with respect to each other, an edge is drawn between the two

vertices representing the links. This is illustrated in figure (4.5) for the set of links shown

in figure (4.1). Link 2 does not fulfill the distance requirement with both link 1 and 3,

hence an edge is drawn between the vertices representing these links. Now it is easy to

see that the links 1 and 3 can be colored with the same color, as they are not adjacent.

The colour of a vertex in a graph can be seen as the group that the link belongs to.

In graph theory, the smallest number of colours needed to color all vertices in a graph

is called the chromatic number. Calculating the chromatic number of a graph is an

NP-complete problem4 [23].

4.3.1 Greedy Grouping Algorithm

We have written and implemented an algorithm similar to the classic Welsh-Powell

greedy coloring algorithm [24] in Matlab. The Welsh-Powell algorithm is known for its

simplicity and speed. Yet the error margin is acceptable [3]. Out of a set of links a

graph is drawn as explained in the previous paragraph. To draw the graph edges, the

distance criterium ∆ must be given as input. From the graph we construct an adjacency

matrix. This matrix is used in the greedy grouping algorithm. The pseudo-code for the

algorithm is as follows:

4An NP-complete problem is a problem which is both NP (verifiable in nondeterministic polynomialtime) and NP-hard (any NP-problem can be translated into this problem).


Figure 4.5: The links shown in figure (4.1) are mapped to the graph shown above,where every vertex represents a D2D link. An edge between vertices is present if thelinks represented by the vertices do not fullfil the distance requirement with respect to

each other.

01: Make a list of all the vertices, by decreasing degree

02: Create a first group and place the first vertex in this group

03: WHILE not all vertices are placed in a group

04: Try to place the next vertex in an existing group,

starting at the first group, then the second group, etc.

05: If not possible, create a new group for the vertex

06: END while

As an example, we can show what groups are formed out of ten links with a link length

of 300 meters, randomly placed in a cell with a radius of 1000 meters. From equation

(3.38) we calculate that for a target SINR of 6 dBs and path exponent n � 4, the

distance requirement dmin � 663.2 meters. The links are shown in figure (4.6). Every

color represents a group, so that links of the same color belong to the same group. The

figure shows that five groups are created to accommodate all ten links. Note that we

can not guarantee that the result achieved by the greedy grouping algorithm is the most

optimal one.

The histogram in figure (4.7) shows how many links are placed in every group. It can

be seen that the number of members in a group is not equally divided; the first group

accommodates three links, while the second, third and fourth group acommodate two

links per group. The last group is created for only one link. From the algorithm, it

is expected that the first groups usually contain more members compared to the last

groups. This is because we specified in the algorithm to try to place links in a group

which is as low numbered as possible.


Figure 4.6: ten links grouped with the greedy grouping algorithm. Links of the samecolor belong to the same group.

Figure 4.7: Histogram showing the number of links per group resulting from thegreedy grouping algorithm of the links shown in figure (4.6). The bar colors correspond

with the group colors shown in figure (4.6).


The unequal distribution may seem unfair, because links in a crowded group will experi-

ence more interference than links in a less filled group. Nonetheless, the greedy grouping

algorithm is well suited to be used with our first distance model described in paragraph

(3.4). Then the distance criterium ∆ is given by equation (3.38), i.e. ∆ � dmin. With

our first distance model, a minimum SINR is guaranteed if the corresponding minimum

distance requirement is fulfilled, which is always the case with the links in groups formed

with the greedy grouping algorithm.

For our second distance model (described in paragraph (3.5)), the greedy grouping

algorithm is not suited. In the next paragraph we explain why this is the case and

introduce a new grouping algorithm, based on an adapted version of our greedy grouping

algorithm.

4.3.2 Fair Grouping Algorithm

When using our second distance model described in paragraph (3.5), the unequal distri-

bution of links over groups created with the greedy grouping algorithm form an issue.

The reason for this, is that in our second distance model we assume that we know in

advance the number of interfering links L � 1. With the greedy grouping algorithm we

cannot predict how many interfering links there will be in every group, until we have

created the groups. To create groups, the distance requirement must be given. But with

our second distance model, the distance requirement can only be created knowing L,

because L is required as input in equation (3.45) to calculate dmargin,min.

To be able to use our second distance model, we want the distribution of links over the

groups to become more or less equal, so that we can estimate L as follows:

L � �Lt

M� , (4.1)

where Lt is the total number of links in the cell and M the number of groups. To

achieve this, we introduce an adapted version of the greedy grouping algorithm, that

tries to minimize the number of groups, but distributes the links over the groups as

fairly as possible as well. This algorithm is referred to as the fair grouping algorithm.

The pseudo-code for the algorithm is as follows:


01: Make a list of all the vertices, by decreasing degree

02: Create a first group and place the first vertex in this group

03: WHILE not all vertices are placed in a group

04: Check in which of the existing groups the vertex can join

05: Select the group with the least members

05: If not possible, create a new group for the vertex

06: END while

However, we do still have a problem. The minimum distance criterium dmargin,min

is used by the fair grouping algorithm to create M groups. But for the calculation

of dmargin,min, we need to know the number of groups M to estimate the number of

interfering links L with equation (4.1). To solve this problem, we need to perform some

iterations with the fair grouping algorithm to acquire a final result.

For the first iteration, we need an initial estimation L0 of L. We take L0 � Lt, where Lt

is the total number of links in the cell. This would be the case if all links were placed

in just one group, hence M0 � 1. In this case the interference is maximal; all links are

active simultaneously, hence every receiver will suffer from the interference coming from

Lt � 1 transmitters. dmargin,min can then be calculated with L0 and is used to form

M1 groups with the fair grouping algorithm. We can then verify if the true number of

interfering nodes with this group formation, L1, coincide with the estimated number of

interfering nodes, L0. We do this i iterations, until Li � Li�1.

In chapter 3 paragraph 3.4, we have shown that not all interfering links interfere equally

with each other; transmitters far away contribute less to the interference level than the

ones located nearby. The true number of interfering nodes can therefore be estimated

by only taking the nearest nodes to the receiver into account. From our simulations,

presented in chapter 6, we learn that usually around four iterations are needed to reach

the point where the estimated number of interferers is equal to the actual number of

interferers. In chapter 6 we also show for several scenarios how the fair grouping al-

gorithm (in combination with the second distance model) performs compared to the

greedy grouping algorithm (in combination with the first distance model) in terms of

the number of created groups and the minimum SINR level achieved in every group

formation.


4.4 Chapter Summary

In this chapter we gave a purpose to the equations we had derived earlier in chapter

3, by introducing the idea of grouping links. To guarantee a given minimum SINR,

only the links which are separated by a calculated minimum distance dmin may operate

simultaneously.

We applied graph theory to form groups of links in a way that all links belonging to

the same group fulfill a given minimum distance requirement with respect to each other.

Links in the same group can be allocated the same resources, while still achieving a

minimum SINR requirement at all times, as explained in chapter 3.

Our aim is to use as few groups as possible. We explained how we used the well known

Welsh-Powell algorithm for the grouping of links in combination with our first distance

model and adapted this algorithm so it could be used with our second distance model.

Different spectrum sharing strategies are possible to accommodate the D2D groups. We

argued that for our grouping method the best suited strategy is to allocate dedicated

resources (timeslots) for the D2D sessions in both the up- and the downlink frequency

bands.

Chapter 5

Optimization with Power Control

5.1 Problem Description

When D2D links operate simultaneously, they cause interference to each other. In

chapter 3 we described two methods that give us a minimum distance requirement for

simultaneously active links. In the first method we assumed a worst case scenario where

all transmitters transmit with maximum power. In the second scenario we assumed

perfect power control, where the transmitters can regulate their transmit power such

that a given signal power is achieved at the receivers. If the minimum distance require-

ments are all met, the achieved SINR will never fall below the minimum required SINR.

However, it may be desirable to relax the minimum distance requirements in order to

be able to put more links in the same group. By doing this, time-slots are cleared for

cellular links or for more D2D groups.

When the minimum distance requirement is reduced, it is possible that the required

minimum SINR is not achievable any more at all the receivers. When at some link the

minimum SINR is not obtained, by use of a power control mechanism, the transmitter

in the link can increase the transmit power in order to achieve the minimum SINR.

While that individual link will get a higher SINR, the other links will suffer more from

the interference caused by the transmitter in that link, because of the higher transmit

power. Hence by trying to meet the SINR requirement for one link, other links might no

longer meet their SINR requirements any more. As a reaction, other transmitters might

start increasing their transmit power too, trying to counteract the higher interference.

It is evident that this can lead to a situation in which all transmitters transmit with

maximum power with the consequence of causing a high interference level in the cell such

that the minimum SINR is not achievable at any receiver. The uncoordinated increase

of transmit power is not a good approach to this problem.

49

Chapter 5. Optimization with Power Control 50

In this chapter we try to find a solution by using optimization. In mathematics and

computer science, an optimization problem is the problem of finding the best solution

from all feasible solutions. In our case, we would like to minimize the transmit power

while still achieving a given minimum SINR at all the receivers.

5.2 Optimization Mathematics

We have derived system equations describing our problem and found a solution by using

optimization mathematics. The optimization problem is implemented in Matlab util-

ising medium-scale linear programming1. Linear programming (LP) is a mathematical

method for determining a way to achieve the best outcome (such as maximum profit or

lowest cost) in a given mathematical model for some list of requirements represented as

linear relationships2.

Linear programs are problems that can be expressed in canonical form, like:

maximize c�x

subject to Ax B b,

where x represents the vector of variables (to be determined), c and b are vectors of

(known) coefficients and A is a (known) matrix of coefficients. The expression to be

maximized or minimized is called the objective function (c�x in this case). The details

of optimization mathematics is beyond the scope of our research.

With our Matlab implementation, it is possible to give a minimum SINR as input. The

algorithm will try to find a solution for which all receiving nodes achieve the minimum

SINR, by adjusting the transmit powers. The solution also minimizes the sum of the

transmit powers. The transmit power has a lower bound which is determined by the

sensitivity of the receivers, and an upper bound determined by legal restrictions on

maximum transmit power of mobile devices. The existence of a solution depends on the

SINR requirement and on the separation between the links dmin; the higher the SINR

requirement and the smaller the distance dmin, the lower the probability of finding a

solution.

1The method used in the Matlab Optimization Toolbox functions is an active set strategy (also knownas a projection method) similar to that of Gill et al., described in [12] and [13]. It has been modified forboth Linear Programming (LP) and Quadratic Programming (QP) problems.

2More formally, linear programming is a technique for the optimization of a linear objective function,subject to linear equality and linear inequality constraints. Given a polytope and a real-valued affinefunction defined on this polytope, a linear programming method will find a point on the polytope wherethis function has the smallest (or largest) value if such point exists, by searching through the polytopevertices.


5.3 Derivation of the System Equations

By using a simple example with three simultaneously operating links, we can derive our

system equations to describe our problem as a linear program. After doing so, we can

expand our system equations for L links. The three links are shown in figure (5.1).

Every link i has a transmitter Ti (red vertices) and a receiver Ri (green vertices). The

attenuation factor of a signal travelling from Ti to Ri is given by αi, so that

PRi � PTiαi, (5.1)

where PRi is the signal power received by Ri and PTi is the signal power transmitted by

Ti. The attenuation factor of a signal travelling from Ti to Rj is given by βij , so that

IRj ,Ti � PTiβij , (5.2)

where IRj ,Ti is the interference power received by Rj and transmitted by Ti. The relation

between the attenuation factor and path loss, introduced in paragraph 3.2, is:

attenuation factor �1

path loss. (5.3)

Figure 5.1: Three simultaneously active D2D links. In the figure, green nodes arereceiving data and red nodes are transmitting data.

We shall now derive the system equations for the three links shown in figure (5.1). After

doing so, the step to extend the equations for L links is straightforward. The SINRs


experienced at the receivers of three simultaneously operating links are given by

SINRR1 �PR1

IR1,T2 � IR1,T3 �N�

PT1α1

PT2β21 � PT3β31 �NC φ, (5.4)

SINRR2 �PR2

IR2,T1 � IR2,T3 �N�

PT2α2

PT1β12 � PT3β32 �NC φ, (5.5)

SINRR3 �PR3

IR3,T1 � IR3,T2 �N�

PT3α3

PT1β13 � PT2β23 �NC φ. (5.6)

We can rewrite equations (5.4) to (5.6) as follows:

PT1α1 � φPT2β21 � φPT3β31 C φN, (5.7)

PT2α2 � φPT1β12 � φPT3β32 C φN, (5.8)

PT3α3 � φPT1β13 � φPT2β23 C φN. (5.9)

Equations (5.7) to (5.9) can then be rewritten as a matrix equation:

��α1 �φβ21 �φβ31

�φβ12 α2 �φβ32

�φβ13 �φβ23 α3

��PT1

PT2

PT3

�� C

��φN

φN

φN

�� . (5.10)

By changing signs we can get equation (5.10) in the form of Ax @ b:

��α1 φβ21 φβ31

φβ12 �α2 φβ32

φβ13 φβ23 �α3

��PT1

PT2

PT3

�� @

��φN

�φN

�φN

�� . (5.11)

We can generalize equation (5.11) and extend it for L links:

��

�α1 φβ21 φβ31 � φβL1

φβ12 �α2 φβ32 � φβL2

φβ13 φβ23 �α3 � φβL3

� � � � �

φβ1L φβ2L φβ3L � �αL

��

��

PT1

PT2

PT3

�

PTL

��@

��

�φN

�φN

�φN

�

�φN

��. (5.12)

We now have expressed our problem as a linear program. If the attenuation factors are

known and a minimum SINR requirement φ is given, the coefficients of matrix A can

be calculated. For the construction of the vector b, the noise level must be estimated.

Matlab has a built-in functionality which is able to solve this optimization problem. We

have performed simulations and implemented this functionality in order to find out if

for a certain group-set, a solution exists. The simulation set-up and results can be found

in chapter 6, paragraph 6.3.3.


5.4 Chapter Summary

The minimum distance requirements derived in chapter 3 are based on worst case sce-

narios. In this chapter we explained the consequences of reducing the minimum distance

requirement, viz. that the SINR at one or more receivers might fall below the minimum

SINR requirement. We also explained that if this is the case, it might still be possible

to achieve the required minimum SINR at all the receivers, by adjusting the transmit

powers of the transmitters with coordinated power control. We showed that this prob-

lem is of a linear program type and derived the system equations. With these equations

it is possible to find out if a solution exists for which the SINR requirement is fulfilled

at all the receivers, while the sum of transmit powers is minimized.

Chapter 6

Simulation Results

In this chapter we present our simulation results. By varying the parameters of our

topology, we have the ability to populate a cell in many ways. D2D communication

is implemented with the two grouping algorithms described in (4.3.1) and (4.3.2), each

with its own minimum distance model described in 3.4 and 3.5 respectively. To learn

more about the grouping performance we simulate different scenarios with varying node

densities, D2D link lengths and clustering parameters. The results of the different sce-

narios and both methods are then compared. We show that the fair grouping algorithm

performs much better than its greedy variant when the link lengths vary strongly. Fi-

nally, the optimization with power control as described in chapter 5 is implemented and

simulated with a realistic urban scenario to discover how much additional gain can be

achieved by relaxing the minimum distance requirements.

This chapter is organized as follows: we start by introducing the topology possibilities

offered by our Matlab model. Then we introduce the different scenarios which have been

simulated. In paragraph 6.3 all simulation results are presented and examined, starting

with the greedy grouping algorithm, followed by the fair grouping algorithm and the

power optimization results. We end with a summary of our findings. The numerical

results of the simulations can be found in appendix A on page 94.

6.1 Topology

In this research, an important parameter is the position of devices and their wish to

exchange information locally. Hence our focus is on the placement of devices (commonly

referred to as nodes) in a certain area. The area is taken to be a circular cell with radius

R. This circular-cell approximation is commonly used to approximate the real shape

54

Chapter 6. Simulation Results 55

of a cell (see paragraph 2.1.2). Nodes can be distributed uniformly in the cell and in

clusters. For our initial analysis, a uniform distribution of nodes is used. However, it

is very unlikely that nodes are distributed uniformly over a cell. As mentioned before,

D2D communication underlaying a cellular network is specifically beneficial for locally

communicating devices. That is why a more realistic scenario is modeled by distributing

clustered nodes. Clusters are formed by communicating devices that are in each other’s

vicinity.

In a cell, K circular clusters can be created. We want to have the ability of varying the

cluster properties in order to perform simulations with cells containing different cluster

types. The cluster radii RCk can be the same for all clusters (i.e. ¦k � RCk � RC), or vary

around RC with a standard deviation σC. One can specify the number of nodes present

in a cluster with radius RC. These nodes are distributed uniformly within a cluster.

Clusters are distributed uniformly within the cell. Clusters do not overlap.

Additionally to nodes, D2D links can be distributed within a cell or a cluster. In fact,

this is the same as the distribution of nodes as described above, with the difference that

pairs of nodes are distributed. A pair of nodes form a D2D link. Hence we have control

of the size of the D2D links, for simulation purposes. If L links are generated, the D2D

link lengths dD2D,l can be the same for all links (i.e. ¦l � dD2D,l � dD2D), or dD2D,l can be

randomly assigned a value where ¦l � dD2Dmin B dD2D,l B dD2Dmax . To distribute L links, L

nodes are distributed uniformly over the cell or cluster. Then a circle is placed around

every node and depending on the D2D link length another node is placed on or in every

circle for respectively a fixed or a bounded D2D link length. Note that all nodes must

always be located within both their cluster and the cell.

6.2 Scenarios

In this paragraph we introduce the scenarios we will simulate. Note that because we are

only interested in the nodes active in a D2D session, these are the only nodes that are

plotted in the cell. Considering we have chosen for the allocation of dedicated timeslots

for D2D communication (as explained in paragraph (4.2)), we assume that the cellular-

and D2D communication do not interact directly on each other. Therefore idle nodes

and nodes communicating with the BS are not shown. In figures (6.1)-(6.5) we show

examples of how the cell is populated in every scenario.

All scenarios are evaluated with three different SINR requirements, being 6, 9 and 12

decibels, for both the greedy and the fair algorithm. Throughout all simulations the

parameters shown in table (3.2) have been used with a path loss exponent of n � 4 and


frequency of f � 2 GHz. The radius R of the cell is always taken to be equal to 1000

meters. To be able to comment on the average behavior of a certain scenario, we run

100 simulations of every scenario.

In the first scenario (example cells shown in figure (6.1)), the cell is populated with 250

randomly placed links (500 nodes) of equal length. We can consider the cell to contain

one large cluster with a radius equal to the radius of the cell. We start with a fixed link

length for all links of 1000 meters and decrease the link length to 500, 250, 100, 50 and

finally 10 meters. We do the same in the second scenarios (example cells shown in figure

(6.2)), but now with 50 randomly placed links (100 nodes) of equal length. We have

chosen to evaluate this scenario to see the influence of the link length on the grouping

of links; when links are very long, it will be hard to form groups of links which can

operate simultaneously. As we reduce the link lengths gradually, we expect to be able

to fit more links in the same group. We compare the results of cells with 500 nodes and

cells with 100 nodes with each other. The chosen parameters of 500 and 100 nodes are

not completely arbitrary; 100 nodes form 50 links, which is enough to populate a cell

substantially to analyse their influence on each other. If we do not place enough links,

the results will not be representative and reproducible, because of the random placement

of the links. To research the influence of the node density in the cell, we have chosen to

multiply the number of nodes with a factor 5.

In the third scenario (example cells shown in figure (6.3)), we take variable link lengths;

in the figures (6.3(a)), (6.3(b)) and (6.3(c)), 250 links (500 nodes) are randomly placed

in the cell. A link can have a length varying from 10 meters to 1000, 500 or 100 meters

respectively. All lengths have equal probability. In the figures (6.3(d)-(f)) we do the

same, but now with 50 randomly placed links (100 nodes) of variable length. This

scenario will tell us whether it matters if the lengths of the links differ from each other.

We randomly distribute large clusters (cluster radius of 100 meters) over the cells in the

fourth scenario (example cells shown in figure (6.4)). In the figures (6.4(a)), (6.4(b))

and (6.4(c)), 50 links (100 nodes) are active in every cluster and 50, 25 and 10 clusters

respectively are present in the cell. In the figures (6.4(d)-(f)) the same is done, but now

with 5 active links (10 nodes) per cluster. This scenario will give us some insight about

the influence of clustering on the performance of our models and the dependency on the

cluster density (amount of clusters in a cell) and denseness of a large cluster.

Finally, in the fifth scenario (example cells shown in figure (6.5)) 100 small clusters

(cluster radius of 10 meters) are randomly distributed over the cells. Every cluster

contains 10, 5 and 2 active links respectively. This scenario tells us something about the

influence of the link density in a cluster.


Table (6.1) gives an overview of all relevant parameters of the scenarios introduced

above. In this table we also show the theoretical average link length in every scenario.

For the first two scenarios the link lengths are fixed, so the average link length is equal

to the actual link lengths. For the third scenario, the link length is distributed uniformly

between two given values, so the average link length is the mean of those two values.

Finally, for the fourth and fifth scenario, the average link length is calculated with

equation (3.4).

A real cell can be approximated by making a mix of the scenarios described above; it

can contain some large (sparse and/or dense) clusters, some small (again, sparse and/or

dense) clusters and some randomly sized and placed links, not belonging to a cluster.

In paragraph 6.3.3 we construct such a realistic cell for our simulations with power

optimization.


Sce

nar

io

Sce

nar

ioE

xam

ple

Cel

lF

igu

re

Cel

lR

adiu

s(m

eter

s)

Tot

al

Nu

mb

erof

Lin

ks

Nu

mb

erof

Clu

ster

s

Clu

ster

Rad

ius

(met

ers)

Nu

mb

erof

D2D

Lin

ks

per

Clu

ster

Lin

kL

engt

h(m

eter

s)

(Ave

rage

Lin

kL

ength

)

R Ltotal K RC LC dD2D

1 6.1 1000 250 1 1000 250

1000 (1000)500 (500)250 (250)100 (100)50 (50)10 (10)

2 6.2 1000 50 1 1000 50

1000 (1000)500 (500)250 (250)100 (100)50 (50)10 (10)

3 6.3 1000

250

1 1000

25010-1000 (505)

10-500 (255)

50 5010-100 (55)

4 6.4 1000

250050

100

50

0-200 (90.54)

1250500

25250

512510

50

5 6.5 10001000

100 1010

0-20 (9.05)500 5200 2

Table 6.1: All Scenarios


(a) 500 nodes, 1000 meter links

(b) 500 nodes, 500 meter links

(c) 500 nodes, 250 meter links

(d) 500 nodes, 100 meter links

(e) 500 nodes, 50 meter links

(f) 500 nodes, 10 meter links

Figure 6.1: Examples of cell scenarios with fixed D2D link lengths (500 nodes)


(a) 100 nodes, 1000 meter links

(b) 100 nodes, 500 meter links

(c) 100 nodes, 250 meter links

(d) 100 nodes, 100 meter links

(e) 100 nodes, 50 meter links

(f) 100 nodes, 10 meter links

Figure 6.2: Examples of cell scenarios with fixed D2D link lengths (100 nodes)


(a) 500 nodes, 10 to 1000 meter links

(b) 500 nodes, 10 to 500 meter links

(c) 500 nodes, 10 to 100 meter links

(d) 100 nodes, 10 to 1000 meter links

(e) 100 nodes, 10 to 500 meter links

(f) 100 nodes, 10 to 100 meter links

Figure 6.3: Examples of cell scenarios with variable D2D link lengths


(a) 50 clusters, 50 links per cluster

(b) 25 clusters, 50 links per cluster

(c) 10 clusters, 50 links per cluster

(d) 50 clusters, 5 links per cluster

(e) 25 clusters, 5 links per cluster

(f) 10 clusters, 5 links per cluster

Figure 6.4: Examples of cell scenarios with clusters (cluster radii: 100 meters)


(a) 100 clusters, 10 links per cluster

(b) 100 clusters, 5 links per cluster

(c) 100 clusters, 2 links per cluster

Figure 6.5: Examples of cell scenarios with clusters (cluster radii: 10 meters)


6.3 Simulation Results

To learn more about the performance of our grouping algorithms combined with the

distance criterium models, we have performed simulations for all the scenarios discussed

in the previous paragraph. The results can be found in appendix A on page 94. We

are particularly interested in the number of groups that are formed given that a certain

SINR requirement has to be guaranteed. We also calculate the actual smallest SINR

that is achieved when the grouping of the D2D links is adopted, to verify to what extent

the SINR requirement is fulfilled.

In our first scenario, we take fixed D2D link lengths. In this case, the scenario dictates

the total number of D2D links and the size of every D2D link. Multiple simulations

of the same scenario can yield different outcomes, because every time a simulation is

performed, the D2D links are randomly distributed over the cell. In every simulation

M groups are created. Over all performed simulations we observe the smallest M , the

average of M and the largest M that is obtained, anotated as min�M�, M and max�M�respectively.

Besides the smallest, average and largest number groups that are formed, we also cal-

culate the worst SINR that is achieved in every scenario. From this we can see that the

minimum SINR requirement is always fulfilled, in all simulated scenarios.

6.3.1 First Distance Model with Greedy Grouping Algorithm

In figures (6.6)-(6.10) bar plots are shown, plotting the number of necessary groups

(min�M�, M and max�M�) relative to the total number of links for all simulated

scenarios and SINR requirements. In other words: the height of a bar, corresponds with

the fraction of groups that are needed relative to the total number of links. Hence the

lower a bar, the higher the efficiency in terms of the number of groups that are utilised

relative to the number of groups that would be needed if every individual link would be

assigned its own group. These bar plots gives us a better view of what happens when

certain parameters are changed and allow us to compare scenarios with each other in an

easier way, because the number of groups are normalized with the total number of links.

In table (A.1) on page 95 the numerical results are shown of the simulations of the first

scenario, in which 250 links with fixed link length are distributed over the cell. For

very long links with a length of 1000 meters (figure 6.1(a)), no links can be combined in

groups. We can see that for every link, a single group is created. The reason for this is

that for a maximum D2D link length of 1000 meters, the minimum distance requirement

dmin is equal to 2.210,7, 2.627,5 and 3.122,8 meters for respectively 6, 9 and 12 dB as


the minimum SINR. Because the diameter of the cell is 2000 meters, no links can be

combined in the same group. In this case the achieved minimum SINR in our simulation

is infinite, because we assume that no noise is present. In reality there is always some

noise, but if we assume that the noise levels are low, the achieved SINR will still be

much higher than the required SINR. This is a disadvantage of the first distance model:

to derive dmin, we have taken the interference contribution of six interferers placed in a

hexagon around the receiving device. However, when there are less than six interferers,

the dmin is unnecessarily large.

As the link lengths decrease, more links can be placed in the same group, so less groups

are necessary to acommodate all links. In figure (6.6) it can be seen that as the link

lengths decrease, a higher SINR can be guaranteed at a lower ‘cost’, where in this case the

‘cost’ is the number of necessary groups. The reason for this is that the dmin increase to

guarantee a higher minimum SINR is smaller when the maximum link length is shorter,

hence more D2D links fit in the same group. It can be seen that the smaller the D2D

links are, the smaller the number of groups; to acommodate 250 randomly distributed

D2D links with a length of 10 meters, on average approximately only two timeslots are

nescessary (on average approximately two groups are formed).

The second scenario is almost the same as the first one; instead of distributing 250 D2D

links, we distribute 50 D2D links randomly over the cell. The numerical results are

shown in table (A.2) on page 96. The number of groups relative to the total number of

links is plotted in figure (6.7). Overall, comparable results with the first scenario, which

has a higher link density, can be observed. There are a few differences though. The

efficiency varies more per simulation. We can explain this difference as follows: when

the link density is high, the different simulations are more similar to each other than

when the link density is low. We also observe that for a high link density, the relative

efficiency (i.e. the number of needed groups relative to the number of links) is slightly

better compared to the low density simulations. The reason for this is that it becomes

more probable to fill groups more densely when there are more links distributed over

the cell, because there are more links to choose from.

In our third scenario, the D2D link lengths vary uniformly between the stated values,

as shown in figure (6.3). The simulations are performed with both a high link density

(250 links) as for a low link density (50 links). The numerical results are shown in table

(A.3) on page 97. It can be seen that when the D2D link lengths vary from 10 to 1000

meters, every link is assigned its own timeslot. So despite of the fact that the average

link length is 505 meters, we see no improvement at all in the number of groups. The

bad performance is due to the same reason as with the fixed link length, viz. the large

dmin. When the link lengths vary from 10 to 500 meters, the average link length is 255


meters. Hence we can make a comparison with the scenarios with fixed link lengths

of 250 meters. For both the link densities of 250 and 50 links, it can be seen that the

efficiency is much worse when the links vary in length; more than two times more groups

are formed as compared to the fixed link length scenarios. When the link lengths vary

from 10 to 100 meters, the average link length is 55 meters. When we compare the

results with the scenarios with fixed link lengths of 50 meters, the differences in the

number of groups are less apparent but still present. From these results we can already

conclude that the greedy grouping method with the first distance model is very sensitive

to changes in the length of the links. We can hardly take advantage of the fact that

smaller links are present, because of the presence of the large links; for the link lengths

of 10 to 500 meters and 10 to 100 meters we observe only a slightly better efficiency

compared to the scenarios with a fixed link lengths of 500 and 100 meters respectively.

The numerical results of the simulations with the fourth scenario are shown in table

(A.4) on page 98. The bar plot is shown in figure (6.9). When links are clustered in

large clusters (with a radius of 100 meters), as shown in figure (6.4), we can see the

same effects as for the previous scenarios (with no clustering) when the link density is

increased; the efficiency between the scenarios with 50 and 5 links per cluster is almost

equal, with a slight advantage for the dense cluster scenario. The average link length

is 90.54 meters, so we can make a comparison with the scenario with fixed link lengths

of 100 meters and no clustering. We only compare the scenarios which have an equal

amount of links in total and approximately the same average link length. In this case the

scenarios that can be compared to each other are like the ones shown in figure (6.4(d))

and figure (6.1(d)) (both having 250 links) and the scenarios like the ones shown in figure

(6.4(f)) and figure (6.2(d)) (both having 50 links). From this comparison we can see

that in the clustered scenario we need almost three times more groups as the scenario

with fixed link lengths and no clustering. This is due to two reasons: the first reason is

the variable link length, which we have shown earlier to account for roughly two times

more groups. The second reason is the clustering. As links are clustered it is harder to

combine links in clusters close to each other into the same group and even impossible to

combine links in the same cluster into the same group.

In table (A.5) on page 99 the numerical results are shown for the fifth scenario, where

100 small clusters (with a radius of 10 meters) are distributed randomly over the cell.

Three cases are simulated, with 10, 5 and 2 links per cluster respectively. From the bar

plot shown in figure (6.10) it can be seen that the efficiency does not depend on the

number of links per cluster. An increase in the number of links per cluster by a factor F

will approximately result in an increase of the number of groups by a factor F as well.

This is because links in the same small cluster cannot be combined into the same group.


Because the clusters and their links are small, an increase in the number of links per

cluster barely results in more interference between the clusters.

For all simulations with the greedy grouping algorithm combined with the first distance

model, it can be seen that the minimum SINR requirement is satisfied with a very large

margin. In the scenarios with a higher link density, the achieved worst SINRs are more

close to the required SINRs, when compared to the same scenario with a lower link

density. As mentioned before, the reason for this is that when there are more links,

it becomes more probable to fit more links in the same group. But even in the dense

link scenarios it can be seen that it would be possible to use the resources even more

efficiently, because there is quite some margin left in the SINR levels.

To make a comparison between a D2D scenario and a cellular scenario, the total aggre-

gate throughput of the cell in both cases would be a parameter of interest. However, it

would not be fair to compare only the number of groups, because the achieved SINRs

are not equal in both cases. In cellular communication every link has its own timeslot,

and thus a much better SINR. A higher SINR usually corresponds with a higher bitrate,

but this is not a linear relation and depends on many factors such as modulation and

error correcting mechanisms.

We can get an indication with a rough calculation. Suppose the throughput of a single

cellular link is 100%, the highest achievable throughput. The throughput of a D2D link

with a certain SINR can be expressed as a fraction of the highest achievable throughput.

Suppose that SINRs of 6, 9 and 12 dB correspond with a throughput of 5%, 10% and

15% of the cell scenario respectively. These throughput values are deliberately chosen

to be so low, to make a conservative approach.

Under this assumption we can now calculate the total aggregate throughput relative to

the cellular scenario by multiplying the average number of links per timeslot (group)

with the relative throughput per link and normalizing with a factor. This factor is to

make it a fair comparison, where the required number of groups should be acommodated

in the same amount of time. Therefore we should normalize by multiplying with LtM .

For example: when 250 groups are acommodated in 50 ms, every group will have 50250 �

0.2 ms, whereas with 50 groups, every group would have 5050 � 1 ms. Hence latter

configuration achieves a throughput that is 25050 � 5 times as high.

Aggregate Throughput � �Lt

M�2

Λ�SINR�, (6.1)

where Lt is the total number of links, M is the average number of groups as defined

by the grouping algorithm and Λ�SINR� is the relative throughput as a function of the

SINR. We perform these calculations with the results of the first scenario and assume all


receivers to have the guaranteed minimum SINR (worst case). The aggregate throughput

relative to the cellular scenario is shown in table (6.2).

HHHH

HHHHφ

dD2D1000 500 250 100 50 10

6 5%� 12% 111% 1.389% 6.028% 46.228%

9 10%� 16% 146% 2.018% 9.295% 79.719%

12 15%� 18% 136% 2.009% 10.388% 104.167%

Table 6.2: Total aggregate cell throughput for scenario 1.

The values in table (6.2) are calculated under the assumption that all links have the

worst SINR of 6, 9 or 12 dB. As we have seen and explained before, for link lengths

equal to 1000 meters, every link is assigned its own group. Hence the experienced SINR

will not be anywhere near the worst SINR, but will rather be similar to that of a cellular

link, where every link has its own timeslot as well. The advantage of D2D is that the data

does not have to be routed via the BS. However, the overhead involved in setting up and

managing the D2D links will make it less likely that large D2D links are advantageous.

For link lengths equal to 500 meters, the total throughput is much lower than the

aggregate throughput we would achieve with cellular links. For link lengths of 250

meters, grouping with φ � 9 dB yield the highest aggregate throughput, which is only

marginally better than it would be with cellular communications. Again, considering the

signalling overhead the advantage of by D2D communication over cellular communication

is questionable.

It is interesting to see that for link lengths of 100 meters, grouping with φ � 9 dB yield

an aggregate throughput that is almost equal to when φ � 12 and for link lengths smaller

than 50 meters, grouping with φ � 12 dB seems to be the best option to achieve the

highest aggregate throughput. Of course, by changing the throughput values coupled

to the SINRs, these relations will change as well, but this example does illustrate that

a lower number of groups does not automatically correspond with a higher aggregate

throughput. In reality the potential aggregate throughput gains will be higher than

listed in table (6.2), because the achieved SINRs are often much higher then the guar-

anteed minimum SINR and the values we have coupled to the minimum SINRs are very

conservative.

As expected, the greedy grouping strategy is the most efficient in terms of the number

of groups when the links are short, of equal size and not clustered. But what is short,

when the choice has to be made between cellular and D2D communications and the

goal is to maximize the cell throughput? Table (6.2) show us that there is a point at


which D2D communication could potentially provide a major performance increase. For

scenario 1, this value would be somewhere between 250 and 100 meters, depending on

the signalling overhead.


0

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0.5

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0.8

0.9

1

6dB 9dB1000

12dB 6dB 9dB500

12dB 6dB 9dB250

12dB 6dB 9dB100

12dB 6dB 9dB50

12dB 6dB 9dB10

12dB

M Lt

Link Length (meters)

min(M)

Lt

M

Lt

max(M)

Lt

Figure 6.6: Plot of the number of groups formed with scenario 1, with 250 links andfixed link lengths, using the first distance model with the greedy grouping algorithm.

0

0.1

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0.4

0.5

0.6

0.7

0.8

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1

6dB 9dB1000

12dB 6dB 9dB500

12dB 6dB 9dB250

12dB 6dB 9dB100

12dB 6dB 9dB50

12dB 6dB 9dB10

12dB

M Lt


min(M)

Lt

M

Lt

max(M)

Lt

Figure 6.7: Plot of the number of groups formed with scenario 2, with 50 links andfixed link lengths, using the first distance model with the greedy grouping algorithm.


0

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0.4

0.5

0.6

0.7

0.8

0.9

1

6dB 9dB10−1000

12dB 6dB 9dB10−500

12dB 6dB 9dB10−100

12dB

M Lt


min(M)

Lt

M

Lt

max(M)

Lt

(a)

0

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0.9

1

6dB 9dB10−1000

12dB 6dB 9dB10−500

12dB 6dB 9dB10−100

12dB

M Lt


min(M)

Lt

M

Lt

max(M)

Lt

(b)

Figure 6.8: Plot of the number of groups formed with scenario 3, with 250 links (a)and 50 links (b) and varying link lengths, using the first distance model with the greedy

grouping algorithm.


0

0.1

0.2

0.3

0.4

0.5

0.6

6dB 9dB50

12dB 6dB 9dB25

12dB 6dB 9dB10

12dB

Number of Clusters

M Lt

min(M)

Lt

M

Lt

max(M)

Lt

(a)

0

0.1

0.2

0.3

0.4

0.5

0.6

6dB 9dB50

12dB 6dB 9dB25

12dB 6dB 9dB10

12dB

Number of Clusters

M Lt

min(M)

Lt

M

Lt

max(M)

Lt

(b)

Figure 6.9: Plot of the number of groups formed with scenario 4, with 50 links percluster (a) and 5 links per cluster (b) and varying number of clusters (RC � 100 meters),

using the first distance model with the greedy grouping algorithm.


0

0.01

0.02

0.03

0.04

6dB 9dB10

12dB 6dB 9dB5

12dB 6dB 9dB2

12dB

Number of Links per Clusters

M Lt

min(M)

Lt

M

Lt

max(M)

Lt

Figure 6.10: Plot of the number of groups formed with scenario 5, with 100 clusters(RC � 10 meters) and varying number of links per cluster, using the first distance model

with the greedy grouping algorithm.

6.3.2 Second Distance Model with Fair Grouping Algorithm

Simulations with the same five scenarios as in paragraph 6.3.1 have been performed

with our fair grouping algorithm combined with our second distance model, in order

to be able to examine the performance of the fair grouping method and compare the

performances with the greedy grouping method.

The numerical results of the first scenario, with 250 links and fixed link lengths, can be

found in table (A.6) on page 100. For the large 1000 meter links, it can be seen that

when the SINR requirement is 6 dB, some groups are able to acommodate two of these

large links, whereas with the greedy method this was not possible. This is because of

the second distance model, which relaxes the distance requirement strongly in this case.

For link lengths of 500 meters, the fair method performs much better than the greedy

method; on average 30% less groups are formed. Overall, the fair grouping algorithm

with the second distance model is more economic with groups compared to the greedy

grouping algorithm, but as the link lengths decrease, the advantage approaches zero.

This can also be seen by comparing the bar plots of figures (6.6) and (6.11) to each

other. The reason for this is that when the links are large, the worst case scenario used


for the first distance model to find dmin is not a good approximation of the reality. As

the link lengths decrease, the worst case model becomes a better approximation of the

actual scenario.

The same behaviour as was seen for the greedy grouping can be observed when we

compare the first scenario with the second scenario using fair grouping; the denser the

scenario, the higher the efficiency. The explanation is also the same; in a dense scenario

there are more links to choose from and hence more links can be placed per group.

The numerical results are shown in table (A.7) on page 101. The achieved minimum

SINR levels show that the fair grouping algorithm performes closer to the target SINR

than the greedy grouping algorithm, achieving better results in terms of the number of

created groups.

In our third scenario, the D2D link lengths vary uniformly between the values stated in

table (6.1). The numerical results are shown in table (A.8) on page 102. For both the

high- and the low link density scenarios, the fair grouping algorithm shows significant

improvement over the greedy grouping algorithm. When the D2D link lengths vary

between 10 and 500 meters, we see that the efficiency (number of links per group) is on

average around 40% better than the greedy grouping algorithm simulation results. For

the link lengths between 10 and 100 meters, the number of groups is on average around

25% less. This can also be seen by comparing the bar plots in figures (6.8) and (6.13)

to each other.

When the link lengths vary from 10 to 1000 meters, from 10 to 500 meters and from

10 to 100 meters, the average link length is 505, 255 and 55 meters respectively. When

we compare the results of the variable link length scenarios with the results of the fixed

link length scenarios with link lengths of 500, 250 and 50 meters respectively, we see

that around 50% more groups are needed for the scenario with varying link lengths.

Recall that for the same comparison with the greedy grouping algorithm, the number

of groups more than doubled. This performance difference between the greedy and the

fair grouping methods was expected, because the second distance model is designed

specifically to perform better in situations where the transmit powers vary widely. The

achieved minimum SINR levels with the fair grouping algorithm are much closer to the

minimum SINR requirement, indicating that the number of links located in the same

group is closer to the achievable maximum.

When links are clustered in large clusters (with a radius of 100 meters), as in the

fourth scenario, the fair grouping algorithm also shows a major improvement over the

greedy grouping algorithm. The bar plot is shown in figure (6.14) and the numerical

results in table (A.9) on page 103. On average, the fair method forms roughly 40%

less groups than the greedy variant. If we compare the clustered scenario (scenario 4)


with the scenario without clusters and with fixed link lengths (scenario 1), we see that

the number of groups is roughly twice as large for the scenario with clusters. With

the greedy simulations we have seen that in the clustered scenario three times as many

groups where needed, when compared to the scenario with no clusters and with fixed

link lengths. The superior performance of the fair grouping algorithm is because of its

ability to handle different link lengths. For the cluster scenario with a high link density,

it can be seen that the achieved SINR levels approach the imposed minimum SINR much

more compared to the greedy grouping algorithm.

For our fifth scenario the numerical results are shown in table (A.5) on page 99. The

bar plot is shown in figure (6.15). The efficiency is slightly better than the greedy

grouping algorithm, but no spectacular improvements are observed. This is because the

fair grouping algorithm outperforms the greedy grouping algorithm especially when link

lenghts vary widely. This is not the case in this scenario. We see the same effect as with

the greedy algorithm, that the efficiency (number of links per group) hardly depends on

the number of links per cluster. This is because we are close to the minimum number

of groups possible, as it is unlikely that two links in the same cluster can communicate

simultaneously (i.e. can be placed in the same group). It can be seen that the achieved

minimum SINR levels still remain higher than the required minimum SINR.


0

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0.7

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0.9

1

6dB 9dB1000

12dB 6dB 9dB500

12dB 6dB 9dB250

12dB 6dB 9dB100

12dB 6dB 9dB50

12dB 6dB 9dB10

12dB

M Lt


min(M)

Lt

M

Lt

max(M)

Lt

Figure 6.11: Plot of the number of groups formed with scenario 1, with 250 links andfixed link lengths, using the second distance model with the fair grouping algorithm.

0

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12dB 6dB 9dB500

12dB 6dB 9dB250

12dB 6dB 9dB100

12dB 6dB 9dB50

12dB 6dB 9dB10

12dB

M Lt


min(M)

Lt

M

Lt

max(M)

Lt

Figure 6.12: Plot of the number of groups formed with scenario 2, with 50 links andfixed link lengths, using the second distance model with the fair grouping algorithm.


0

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12dB 6dB 9dB10−500

12dB 6dB 9dB10−100

12dB

M Lt


min(M)

Lt

M

Lt

max(M)

Lt

(a)

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12dB 6dB 9dB10−500

12dB 6dB 9dB10−100

12dB

M Lt


min(M)

Lt

M

Lt

max(M)

Lt

(b)

Figure 6.13: Plot of the number of groups formed with scenario 3, with 250 links (a)and 50 links (b) and varying link lengths, using the second distance model with the fair

grouping algorithm.


0

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0.4

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12dB 6dB 9dB25

12dB 6dB 9dB10

12dB

Number of Clusters

M Lt

min(M)

Lt

M

Lt

max(M)

Lt

(a)

0

0.1

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0.4

6dB 9dB50

12dB 6dB 9dB25

12dB 6dB 9dB10

12dB

Number of Clusters

M Lt

min(M)

Lt

M

Lt

max(M)

Lt

(b)

Figure 6.14: Plot of the number of groups formed with scenario 4, with 50 links percluster (a) and 5 links per cluster (b) and varying number of clusters (RC � 100 meters),

using the second distance model with the fair grouping algorithm.


0

0.01

0.02

0.03

6dB 9dB10

12dB 6dB 9dB5

12dB 6dB 9dB2

12dB

Number of Links per Clusters

M Lt

min(M)

Lt

M

Lt

max(M)

Lt

Figure 6.15: Plot of the number of groups formed with scenario 5, with 100 clusters(RC � 10 meters) and varying number of links per cluster, using the second distance

model with the fair grouping algorithm.

6.3.3 Optimization with Power Control

To demonstrate the functioning of our power optimization solution given in chapter 5,

we construct a more realistic urban scenario, by populating a cell with a mix of link

types which we introduced in the previous paragraph. Our urban scenario, an example

of which is shown in figure (6.18), consists of 5 large and 100 small clusters and 50

randomly placed links of random length. A large cluster has a radius of 100 meters

and 50 active D2D links. A small cluster has a radius of 10 meters and 1 to 10 active

D2D links. Finally, 50 random D2D links are distributed with a link length of 10 to 300

meters. Hence in total we have 850 active D2D links in our cell.

The simulations are again performed for three minimum SINR requirements of 6, 9 and

12 dB. For both grouping models individually we gradually decrease the initial distance

requirement dmin respectively dmargin with steps of 10 meters. We observe if a solution

can be found for a random assignment of the transmitter and receiver roles in every

D2D link. If this is the case, we continue to decrease dmin respectively dmargin until no

solution is possible. 100 simulations are performed for each SINR requirement.

The results are shown in figures (6.16) and (6.17) for the greedy and fair grouping

algorithms respectively. From these figures it can be seen that the distance requirement


φ (dB) dmin,initial (meters) M initial dmin,reduced (meters) M reduced

6 664 227 384 (-42,17%) 129 (-43,17%)9 789 284 449 (-43,09%) 152 (-46,48%)12 937 344 527 (-43,76%) 175 (-49,13%)

Table 6.3: Average number of groups formed with the initial minimum distancerequirement dmin,initial and the average number of groups formed with the reduced

minimum distance dmin,reduced, with our greedy grouping algorithm.

φ (dB) dmargin,initial (meters) M initial dmargin,reduced (meters) M reduced

6 258 110 68 (-76,36%) 61 (-44,55%)9 363 143 133 (-63,36%) 76 (-46,85%)12 488 188 228 (-53,28%) 104 (-44,68%)

Table 6.4: Average number of groups formed with the initial minimum distancerequirement dmargin,initial and the average number of groups formed with the reduced

minimum distance dmargin,reduced, with our fair grouping algorithm.

can be decreased significantly, while still being able to find a solution for all receivers to

achieve the minimum SINR. In the vertical axis the probability P is denoted of finding

a solution with the given distance requirement. This probability is derived empirically

from the 100 simulation cycles performed on the realistic urban cell scenario. We are

specifically interested in the minimum distance requirement for which all simulations

could be solved, i.e. the smallest dmin and dmargin for which P � 1. We denote this

‘reduced’ minimum distance requirements with dmin,reduced and dmargin,reduced for the

greedy and the fair grouping algorithms respectively. In tables (6.3) and (6.4) the average

number of groups M are shown for the initial minimum distance requirement and for

the reduced minimum distance requirement. The percentual decrease of the distance

requirements and the number of groups relative to the initial values are shown between

parents behind the reduced values. The initial minimum distance is determined with

our equations derived in chapter 3, while the reduced minimum distance is determined

empirically from our simulations.

From tables (6.3) and (6.4) it can be seen that it is possible to decrease the number of

necessary groups significantly by decreasing the minimum distance requirement. For the

greedy grouping algorithm, when φ = 6 dB, 227 groups are necessary to accommodate

all 850 D2D links when the initial dmin is used. With power optimization it is possible

to decrease the number of groups with 43% to 129. Please note that for the latter

configuration, the hard guarantee of achieving the minimum SINR is not valid any

more; in our simulation we randomly assigned transmitter-receiver duties to every node

in a link and observed whether a solution existed to achieve the minimum SINR. There

may be configurations of transmitter-receiver roles for which no solution can be found.

However, the probability that this occurs is very low, as has been shown from our

simulation.


0 100 200 300 400 500 600 700 800 900 10000

0.1

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0.5

0.6

0.7

0.8

0.9

1

dmargin (meters)

P

φ = 6dBφ = 9dBφ = 12dB

Figure 6.16: Decrease of the minimum distance requirement dmin versusthe empirical probability P of being able to find a solution.

0 50 100 150 200 250 300 350 400 450 5000

0.1

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0.6

0.7

0.8

0.9

1

dmargin (meters)

P

φ = 6dBφ = 9dBφ = 12dB

Figure 6.17: Decrease of the minimum distance requirement dmargin versusthe empirical probability P of being able to find a solution.


Figure 6.18: Example of our realistic cell scenario. The cell is populated by five largeclusters (with a radius of 100 meters), 100 small clusters (with a radius of 10 meters)and 50 links with a link length between 10 and 300 meters. A large clusters contain 50

D2D links while in a small cluster 1 to 10 D2D links are present.

6.4 Conclusions

In this chapter we introduced our Matlab model with its building blocks which enables

us to populate cells with D2D links varying in size and position. With this model we

constructed different scenarios, to learn more about the grouping performance in cells

with varying node densities, D2D link lengths and clustering parameters.

We proved that our two grouping methods function correctly in all scenarios (i.e. achieve

the set minimum SINR requirement), under different SINR requirements. We discussed

the shortcomings of the greedy grouping method and have shown that this method is

always outperformed by the fair grouping method. Especially when the lengths of the

D2D links vary strongly, we have seen that the fair grouping algorithm performs much

better.

Finally we implemented an optimization with power control as described in chapter 5

and used it to run simulations with a realistic urban cell scenario. We discovered that by

relaxing the minimum distance requirements significant additional gain can be achieved

in terms of the number of groups. In this section our findings are summarized briefly.

First distance model with the greedy grouping algorithm

In our first and second scenario with fixed link lengths, we have shown that as the

link lengths decrease, more links can be placed in the same group, so less groups are

necessary to acommodate all links. We also observed that as the link lengths decrease, a

higher SINR can be guaranteed at a lower cost, i.e. the (relative) increase in the number


of groups becomes smaller. We showed that for a higher link density, relatively fewer

groups are necessary, given that the links are distributed uniformly.

We have seen that when the link lengths vary, the performance of the greedy grouping

strategy deteriorates strongly. In a scenario with varying link lengths, more than two

times more groups are needed as compared to a fixed link length scenario with compa-

rable average link length. This is due to the distance model, that is a function of the

maximum link length, to guarantee a certain minimum SINR.

When links are clustered in large clusters, the grouping of links becomes even harder.

We learned this by comparing the results from the fourth scenario with results from

the first and second scenario; in a clustered scenario, we need almost three times more

groups as a scenario with fixed link lengths and no clustering. This is because clustering

reduces the average distance between links.

When links are clustered in small clusters randomly distributed, we showed that an

increase in the number of links per cluster by a factor F will approximately result in

an increase of the number of groups by a factor F as well. This is because links in the

same small cluster cannot be combined into the same group and the interference between

clusters remains approximately the same when the link density per cluster increases.

We explained the relation between the number of groups and the aggregate cell through-

put. With a rough calculation, we showed that the aggregate throughput of the cellular

system could potentially be improved by orders of magnitude, by employing D2D com-

munications, depending on the scenario.

Second distance model with the fair grouping algorithm

In the first and second scenario we have seen that for larger links, the fair grouping strat-

egy performs much better than its greedy variant. Overall, the fair grouping algorithm

with the second distance model is more economic with groups when compared to the

greedy grouping algorithm, but as the link lengths decrease, the advantage approaches

zero. The same behaviour as was seen for the greedy grouping has been observed: the

higher the link density, the higher the efficiency, provided that the links are distributed

uniformly.

For both the high- and the low link density scenarios, the fair grouping algorithm showed

significant improvement over the greedy grouping algorithm when the link lengths vary.

This performance difference between the greedy and the fair grouping methods was

expected, because the second distance model is designed specifically to perform better

in situations where the transmit powers vary widely.


We have also seen major improvement over the greedy grouping algorithm when links

are clustered in large clusters. On average, the fair method forms roughly 40% less

groups than the greedy variant.

For small clusters, the efficiency was slightly better than the greedy grouping algorithm,

but no spectacular improvements have been observed. This is because the link lengths

varies less when clusters are small, and N links in a small clusters typically requires at

least N groups.

The achieved minimum SINR levels showed that in all scenarios the fair grouping algo-

rithm performes closer to the target minimum SINR than the greedy grouping algorithm,

i.e. it offers a worse average SINR (but equal minimum SINR, within the requirements),

while offering a better performance as measured by the number of groups.

Optimization with Power Control

We constructed a realistic urban cell scenario by populating a cell with a mix of link

types and we proved that the optimization solution provided in chapter 5 functions

correctly. Because this optimmization solution cannot guarantee absolutely (i.e. with

probability 1) that the set minimum SINR is met, we empirically derived the probabilities

of finding a power control solution for the given scenario, provided that a minimum SINR

requirement of 6, 9 or 12 dB has to be fulfilled at every receiving node. We showed that

the distance requirements can be decreased significantly, while still being able to find

a solution for all receivers to achieve the minimum SINR with a high probability. The

number of necessary groups can be decreased by up to 40% to 50%, for both grouping

methods.

Chapter 7

Business Opportunities Enabled

by D2D Communications

D2D communications could be especially beneficial for some uniquely mobile applications

which are already emerging. In this chapter a few examples of applications are given in

which D2D capabilities can be beneficial in particular. We will consider the following

applications:

� Augmented Reality

� Social Networking

� Mobile Commerce and Advertising

This is not an exhaustive list of examples. Other application areas may include mobile

entertainment, health care applications, machine-to-machine communications, services

on location, etc.

7.1 Augmented Reality

A lot of excitement has been building around a new category of mobile technology called

“augmented reality” applications or “social augmented reality” mobile location-based

services. Augmented Reality (AR) is a relatively new technology that blends real-world

footage and computer-generated graphics in real time, blurring the line between the real

world and a virtual world by enhancing what we perceive. It superimposes graphics,

audio and other sense enhancements from computer screens onto real time environments,

opening a whole lot of possibilities in many fields, from medical to engineering, including

85

Chapter 7. Business Opportunities Enabled by D2D Communications 86

entertainment. Early forms of AR have already arrived. After downloading software,

smartphones owners can use built-in GPS, compass, and camera to find information

about for example nearby ATMs and restaurants, the closest subway station, and other

points of interest.

With AR you can aim the camera of your mobile phone at an object, and on the screen

you will be able to see information about that object. An example is illustrated in

figure (7.1), where the camera of a mobile phone is aimed towards the most-visited paid

monument in the world, the Eiffel Tower. A dedicated antenna could be placed at the

sight, with a wired broadband link to a datacenter where multimedia content is stored.

Visitors are then able to stream content directly to their mobile devices upon request.

This way of offering data to users is crucially different from the way data is offered

by providers at present. The operator has exact knowledge of the source of the traffic

and is able to allocate resources according to the demand and the availability. More

importantly, the operator is able to charge directly to the parties that are responsible

for the occupation of the resources. This could be an answer to the ongoing debate

questioning whether Google Inc. and other providers of Web content are contributing

enough to the costs of telecommunications networks.

D2D communications as proposed puts the operator in total control of the communica-

tion sessions. For the providers of content it is appealing to be able to deliver content

quickly to interested users, containing for example personalized advertising, especially

when potential customers are on the site.

A cell phone will change the way we look and interact with the world around us. Aug-

mented reality will give us more information about the places we go and things we see,

opening doors for new ways to generate business. Mobile operators play an important

role in transporting the information and should seek for new business models to benefit

more from the vastly expanding mobile market, other than just transport the bits.

In our research we have constructed cell scenarios by distributing various types of links,

one of which are links clustered together over a certain geographic area. A site like

the Eiffel Tower may represent such a large cluster with increased mobile traffic over a

known area.

7.2 Social Networking

As the popularity of social networking is constantly rising, new uses for the technol-

ogy are constantly being developed. D2D communications are able to provide a high


Figure 7.1: Augmented Reality.

speed direct link between users in each others proximity, over which they may exchange

multimedia content.

A good example of how D2D communication can assist in the local exchange of infor-

mation between mobile personal devices is given by Bump, a very popular application

for the Apple iOS and Google Android operating systems. Bump has millions of users

worldwide, allowing them to send contact information, photos, and other objects be-

tween phones. To use the application, two people bump their phones together, and

within about five to ten seconds, a screen appears on both users’ screens allowing them

to confirm what they want to send to each other. When two users bump their phones, the

data is automatically sent through a separate internet server to the other user, which is

able to detect when any two phones using the application bump each other. Screenshots

of the application are shown in figure (7.2).

The developers of Bump claim to use a matching algorithm that listens to the bumps

from phones around the world and pairs up phones that felt the same bump. Various

techniques are used to limit the pool of potential matches, including location information

and characteristics of the bump event.

It is evident that when large files are exchanged through applications like Bump, this

generates a very large load on the operators network. This scenario is perfect for D2D

communication as described in this document: in chapter 6 we have shown that D2D

communications is very profitable for short, randomly distributed links. Another advan-

tage brough by communicating with D2D links, is that the security is increased, because


Figure 7.2: Bump screenshots. The slogan of Bump sounds: “makes connecting assimple as bumping two phones together.” (source: Apple iTunes App Store)

data is not routed via internet clouds and thus not stored anywhere but on the intended

devices. A security issue of D2D communication is the eavesdropping thread. Special

care must be taken in order to constrain this thread.

Social networks are also used by teachers and students as a communication tool. In a

lecture hall the teacher could exchange information with the students on-the-spot. This

sort of scenarios is represented by the small clusters in our simulations.

Direct communication would also be possible with technologies like Bluetooth. However,

as mentioned in chapter 2, no QoS can be guaranteed because communication over

Bluetooth takes place in the unlicensed ISM frequency band.

7.3 Mobile Commerce and Advertising

Many applications can be thought of to stimulate business by using wireless commu-

nication technologies. Earlier this chapter, we mentioned advertising with the use of

augmented reality, but more is possible, not necessarily utilising augmented reality fea-

tures.

An example is to use D2D links to update and interact with digital billboards. This

allows advertisers to display different messages based on the profile of the person(s),

standing next to the bill board. This can be adapted based on their own personal

privacy settings. Another example is the ability to offer complete up-to-date overviews

of available products being sold in particular stores, emphasizing special discounts or to

provide a real-time stream of the kitchen for restaurant visitors.

Chapter 8

Conclusions and Final Remarks

8.1 Conclusions

The popularity of mobile communications has increased immensely the past decade. In

chapter 1 we performed a survey illustrating the growth of mobile data traffic. We

argued that mobile operators need innovative solutions to cope with the rising demand

of mobile traffic while minimizing operating costs. A recent research topic is D2D

communications as an underlay to cellular networks. A D2D link is a direct connection

between two communicating devices. The goal of using D2D links as such is to: (a)

increase the spectral efficiency, (b) reduce the load on the network and (c) introduce

and facilitate new services. In this thesis we have presented a strategy for the application

of device-to-device (D2D) communication in a cellular network.

The concept of D2D communication is as follows: the base station (BS) detects when

two devices requesting a communication session are in each other’s proximity. Then

the BS can choose between a cellular- or a D2D link. Multiple D2D links may operate

simultaneously, increasing the spectral efficiency. More advantages of D2D- over cellular

links are listed in section 1.3.

The D2D sessions take place in the same (licensed) frequency band as the cellular com-

munication. This implies that the BS covering the area in which the devices are present

is in control, provisioning and managing the communication links. This control func-

tionality is indispensable, because at no time D2D communication may interrupt the

cellular communication. D2D links also interfere with each other. This interference

problem is the main challenge when facilitating D2D communication as proposed.

In chapter 2 we explained the concept and evolution of cellular networks briefly and

positioned D2D communication as proposed in this research in the contemporary wireless

89

Chapter 8. Conclusions and Final Remarks 90

networking landscape. We argued that D2D communication is a valuable addition to

4G� cellular networks and a reliable alternative to communications suffering from the

growing interference in the unlicensed frequency band.

We formulated a novel strategy with which D2D links can be set-up with a guaranteed

minimum signal-to-noise plus interference ratio at every receiver. Multiple D2D links

may operate simultaneously using the same resources, as long as the spatial distance

separating these links is large enough. In chapter 3 we derived two equations, specifying

the minimum distance requirement between simultaneously operating links, given that a

minimum SINR that has to be achieved. To find the first equation, we derived an upper

bound on the interference in a worst case scenario. We recognized that when links vary

in length, our first minimum distance model is not optimal. Hence we also devised a

second minimum distance model, which assumes that there is power control in place,

and thus take varying link lengths into account.

In chapter 4 we applied graph link theory to form groups of links in a way that all links

belonging to the same group fulfill a given minimum distance requirement with respect

to each other. We applied the well known Welsh-Powell algorithm for the grouping

of links in combination with our first distance model and explained how we adapted

this algorithm so it could be used with our second distance model. Throughout this

thesis the grouping algorithms used with the first and the second distance models are

commonly refered to as the greedy and the fair grouping algorithm respectively. We

stated all possible spectrum sharing strategies and argued that the best strategy is to

allocate dedicated resources for the D2D sessions in both the cellular up- and downlink

frequency bands.

The minimum distance requirements are derived based on worst case scenarios. We

may try to reduce the distance criterium in order to be able to form less groups. In

chapter 5 we stated the consequences of doing so, viz. that the SINR at one or more

receivers might fall below the minimum SINR requirement. We also explained that if

this is the case, it might still be possible to achieve the required minimum SINR at

all the receivers, by adjusting the transmit powers of the transmitters with coordinated

power control. We proved that this problem is of a linear program type and derived the

system equations. With these equations it is possible to find out if a solution exists for

which the SINR requirement is fulfilled at all the receivers, while the sum of transmit

powers is minimized.

In chapter 6 simulations were performed in five different scenarios to learn more about

the grouping performance in cells with varying node densities, D2D link lengths and

clustering parameters. We proved that our two grouping methods function correctly in

all scenarios, under different minimum SINR requirements.


For the first distance model with the greedy grouping algorithm the following conclusions

have been drawn:

� As the link density increases, the grouping becomes more efficient, i.e. relatively

less groups can be formed.

� Large links (around the size of the cell radius) can not be combined into groups

together; every D2D link is allocated its own group (and thus its own timeslot).

� The greedy grouping method is very sensitive to variations in the link lengths.

When link lengths vary, the grouping performance decreases quickly: more than

two times more groups are needed when compared to scenarios with fixed link

lengths, equal link densities and comparable average link lengths.

� Clustering of links has a negative impact on the grouping performance: up to

almost three times more groups are needed as compared to scenarios with no

clustering, fixed link lengths, equal link densities and comparable average link

lengths.

� An increase in the number of links per cluster by a factor F will approximately

result in an increase of the number of groups by a factor F .

For the second distance model with the fair grouping algorithm we have seen the same

behaviour as with the greedy grouping method with regard to the influence of the link

density. Overall, the fair grouping algorithm with the second distance model is more

economic with groups when compared to the greedy grouping algorithm, but as the link

lengths decrease, the advantage approaches zero. Furthermore, the following conclusions

have been drawn:

� Large links (around the size of the cell radius) can occasionally be combined into

groups together. For links with a length of around half the cell radius, the fair

grouping method performs much better when compared to the greedy grouping

method.

� The fair grouping method is less sensitive to variations in the link lengths than

the greedy grouping method. Significantly higher performance is achieved com-

pared with the greedy grouping method: from 25% to 40% less groups are formed

depending on the scenario. However, there is still a drop in performance when

compared to scenarios with fixed link lengths, equal link densities and comparable

average link lengths: around 50% more groups are formed.


� Clustering of links has a negative impact on the grouping performance, but less

so than with the greedy grouping method. The number of groups is roughly twice

as large as compared to scenarios with no clustering, fixed link lengths, equal link

densities and comparable average link lengths.

� As with the greedy grouping, an increase in the number of links per cluster by

a factor F will approximately result in an increase of the number of groups by

a factor F as well. The performance is slightly better than the greedy grouping

algorithm, but no spectacular improvements are observed.

We explained the relation between the number of groups and the aggregate cell through-

put. With a rough calculation, we showed that the aggregate throughput of the cellular

system could potentially be improved by orders of magnitude, by employing D2D com-

munications, depending on the scenario.

Finally, we constructed a realistic urban cell scenario by populating a cell with a mix of

link types and we proved that the optimization solution provided in chapter 5 functions

correctly. We empirically derived the probabilities of finding a power control solution

for the given scenario, provided that a minimum SINR requirement of 6, 9 or 12 dB

has to be fulfilled at every receiving node. We showed that the distance requirements

can be decreased significantly, while still being able to find a solution for all receivers to

achieve the minimum SINR with a high probability. The number of necessary groups

can be decreased by up to 40% to 50%, for both grouping methods.

8.2 Future Studies

Research on D2D communication underlaying cellular communication systems has been

under the attention of scientific researchers for a short time and therefore is in its initial

stages. We introduced a novel methodology of allocating D2D links in the same spectrum

as cellular links. We believe this work provides an appropiate framework for realizing

D2D communication underlaying a cellular network. However, future study is required

to learn more on the interactions between the performance of our system and:

� User mobility. Our simulated scenarios in chapter 6 assume static nodes, whereas

in reality nodes might be moving. The dynamics as consequence of moving nodes

is a topic for further study.

� Signalling protocols and overhead. In section 4.2.3 we discussed briefly the essential

signalling that is needed. A more detailed research on the necessary protocols and

the overhead caused by the signalling is required.


� Signal model and system parameters. All our simulations have been performed

with the parameters stated in table (3.2). By altering these parameters different

results are obtained. A research on the relation between the system parameters

and the performance can be performed.

� A multicell environment. We assumed perfect separation of neighbouring cells,

whereas this might not always be the case. Also, by letting base stations work

together, D2D links can be set-up between nodes under different base stations.

Also, a detailed survey is necessary for the standardisation of specificated communicating

protocols and the possibilities of fitting a D2D communication system into a developed

4G networks.

Figure 8.1: A metaphor for the device-to-device linking concept: the ancient tin cantelephone.

Appendix A

Simulation Results

94

Appendix A. Simulation Results 95

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min�SIN

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1~2�SIN

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62.

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750

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50,0

ÐÐÐÐ�

500,

00ª

ª

92.

627,

550

�ÐÐÐÐ

50,0

ÐÐÐÐ�

500,

00ª

ª

123.

122,

850

�ÐÐÐÐ

50,0

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500,

00ª

ª

10-

1000

61.

105,

424

�ÐÐÐÐ

29,1

ÐÐÐÐ�

352,

4113

,88

32,4

89

1.31

3,7

31�ÐÐÐÐ

34,7

ÐÐÐÐ�

422,

2116

,83

48,6

312

1.56

1,4

38�ÐÐÐÐ

42,6

ÐÐÐÐ�

472,

0019

,86

ª

10-5

00

622

1,1

4�ÐÐÐÐ

4,9

ÐÐÐÐ�

70,

7512

,44

26,5

89

262,

74

�ÐÐÐÐ

5,5

ÐÐÐÐ�

80,

7815

,31

27,0

612

312,

35

�ÐÐÐÐ

6,4

ÐÐÐÐ�

101,

1216

,84

28,4

210

-100

TableA.3:

Sim

ula

tion

resu

lts

ofsc

enar

io3,

wit

h250/50

lin

ks

an

dva

ryin

gli

nk

len

gth

s,u

sin

gth

efi

rst

dis

tan

cem

od

elw

ith

the

gre

edy

gro

up

ing

alg

ori

thm

.


50L

inks/

Clu

ster

MG

rou

ps

per

Sim

ula

tion

,10

0S

imu

lati

ons

Ach

ieve

dS

INR

dB

Am

ou

nt

ofC

lust

ers

SIN

Rmin

(dB

)dmin

(m)

min�M�

�ÐÐÐÐ

MÐÐÐÐ�

max�M�

σ�M�

min�SIN

RdB�µ

1~2�SIN

RdB�

644

2,1

254

�ÐÐÐÐ

279,

5ÐÐÐÐ�

301

9,56

10,2

422

,95

952

5,5

331

�ÐÐÐÐ

356,

8ÐÐÐÐ�

390

12,5

113

,73

26,3

212

624,

643

3�ÐÐÐÐ

461,

8ÐÐÐÐ�

489

12,8

116

,56

29,1

550

644

2,1

167

�ÐÐÐÐ

194,

9ÐÐÐÐ�

235

14,9

511

,57

24,8

59

525,

520

1�ÐÐÐÐ

239,

7ÐÐÐÐ�

282

17,6

714

,26

26,9

812

624,

625

8�ÐÐÐÐ

303,

6ÐÐÐÐ�

380

24,0

817

,27

30,9

425

644

2,1

99�ÐÐÐÐ

130,

3ÐÐÐÐ�

179

19,5

112

,82

30,1

49

525,

510

0�ÐÐÐÐ

151,

5ÐÐÐÐ�

214

20,8

915

,73

31,9

312

624,

613

1�ÐÐÐÐ

172,

8ÐÐÐÐ�

244

22,7

617

,69

33,1

110

5L

inks/

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ster

MG

rou

ps

per

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ula

tion

,10

0S

imu

lati

ons

Ach

ieve

dS

INR

dB

Am

ou

nt

ofC

lust

ers

SIN

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(dB

)dmin

(m)

min�M�

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MÐÐÐÐ�

max�M�

σ�M�

min�SIN

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1~2�SIN

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644

2,1

30�ÐÐÐÐ

31,6

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351,

0611

,87

24,0

39

525,

536

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39,5

ÐÐÐÐ�

451,

6415

,18

26,1

912

624,

646

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50,4

ÐÐÐÐ�

551,

9517

,74

30,8

150

644

2,1

18�ÐÐÐÐ

21,0

ÐÐÐÐ�

271,

6413

,13

25,0

89

525,

523

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26,2

ÐÐÐÐ�

332,

2815

,20

28,8

812

624,

628

�ÐÐÐÐ

32,0

ÐÐÐÐ�

382,

0718

,61

31,2

225

644

2,1

10�ÐÐÐÐ

13,8

ÐÐÐÐ�

202,

2314

,01

28,5

59

525,

510

�ÐÐÐÐ

16,1

ÐÐÐÐ�

242,

4217

,48

32,1

712

624,

615

�ÐÐÐÐ

19,2

ÐÐÐÐ�

282,

9619

,67

34,9

710

TableA.4:

Sim

ula

tion

resu

lts

ofsc

enar

io4,

wit

h50

/5

lin

ks

per

clu

ster

an

dva

ryin

gnu

mb

erof

clu

ster

s(R

C�

100

met

ers)

,u

sin

gth

efi

rst

dis

tance

mod

elw

ith

the

gre

edy

gro

up

ing

alg

ori

thm

.


100

Clu

ster

sM

Gro

up

sp

erS

imula

tion

,10

0S

imu

lati

ons

Ach

ieve

dS

INR

dB

Lin

ks/

Clu

ster

SIN

Rmin

(dB

)dmin

(m)

min�M�

�ÐÐÐÐ

MÐÐÐÐ�

max�M�

σ�M�

min�SIN

RdB�µ

1~2�SIN

RdB�

644

,219

�ÐÐÐÐ

21,4

ÐÐÐÐ�

303,

0314

,21

37,6

59

52,6

20�ÐÐÐÐ

22,9

ÐÐÐÐ�

303,

7416

,30

38,6

512

62,5

20�ÐÐÐÐ

26,4

ÐÐÐÐ�

404,

6220

,00

40,4

410

644

,210

�ÐÐÐÐ

10,7

ÐÐÐÐ�

151,

5014

,49

38,7

39

52,6

10�ÐÐÐÐ

11,6

ÐÐÐÐ�

151,

9717

,25

39,3

112

62,5

10�ÐÐÐÐ

12,9

ÐÐÐÐ�

202,

3919

,29

40,4

95

644

,24

�ÐÐÐÐ

4,2

ÐÐÐÐ�

60,

5914

,55

38,1

99

52,6

4�ÐÐÐÐ

4,7

ÐÐÐÐ�

60,

8717

,43

37,8

912

62,5

4�ÐÐÐÐ

5,2

ÐÐÐÐ�

70,

9119

,82

38,5

72

TableA.5:

Sim

ula

tion

resu

lts

ofsc

enar

io5,

wit

h10

0cl

ust

ers

(RC�

10

met

ers)

an

dva

ryin

gnu

mb

erof

lin

ks

per

clu

ster

,u

sin

gth

efi

rst

dis

tan

cem

od

elw

ith

the

gre

edy

gro

up

ing

alg

ori

thm

.


250

Lin

ks

MG

rou

ps

per

Sim

ula

tion

,10

0S

imu

lati

ons

Ach

ieve

dS

INR

dB

Lin

kL

engt

h(m

)S

INR

min

(dB

)min�M�

�ÐÐÐÐ

MÐÐÐÐ�

max�M�

σ�M�

min�SIN

RdB�µ

1~2�SIN

RdB�

623

8�ÐÐÐÐ

243,

4ÐÐÐÐ�

249

2,28

6,00

ª

925

0�ÐÐÐÐ

250,

0ÐÐÐÐ�

250

0,00

ªª

1225

0�ÐÐÐÐ

250,

0ÐÐÐÐ�

250

0,00

ªª

100

0

610

8�ÐÐÐÐ

116,

0ÐÐÐÐ�

127

3,86

6,01

12,9

79

131

�ÐÐÐÐ

140,

7ÐÐÐÐ�

156

5,45

9,11

15,8

312

130

�ÐÐÐÐ

147,

0ÐÐÐÐ�

186

12,0

412

,00

15,9

6500

644

�ÐÐÐÐ

48,4

ÐÐÐÐ�

562,

476,

8414

,71

951

�ÐÐÐÐ

58,6

ÐÐÐÐ�

662,

779,

7216

,53

1263

�ÐÐÐÐ

69,0

ÐÐÐÐ�

772,

7912

,06

18,4

7250

611

�ÐÐÐÐ

13,1

ÐÐÐÐ�

160,

906,

4517

,27

913

�ÐÐÐÐ

15,7

ÐÐÐÐ�

211,

259,

1319

,51

1216

�ÐÐÐÐ

18,6

ÐÐÐÐ�

211,

0512

,15

21,6

5100

65

�ÐÐÐÐ

6,4

ÐÐÐÐ�

80,

707,

4420

,95

96

�ÐÐÐÐ

7,2

ÐÐÐÐ�

90,

8110

,16

22,2

012

7�ÐÐÐÐ

8,3

ÐÐÐÐ�

120,

8212

,56

23,6

150

62

�ÐÐÐÐ

2,4

ÐÐÐÐ�

40,

519,

3935

,30

92

�ÐÐÐÐ

2,6

ÐÐÐÐ�

40,

5111

,89

36,9

912

2�ÐÐÐÐ

2,8

ÐÐÐÐ�

40,

5414

,18

38,3

510

TableA.6:

Sim

ula

tion

resu

lts

ofsc

enar

io1,

wit

h25

0li

nks

an

dfi

xed

lin

kle

ngth

s,u

sin

gth

ese

con

dd

ista

nce

mod

elw

ith

the

fair

gro

up

ing

alg

ori

thm

.


50L

inks

MG

rou

ps

per

Sim

ula

tion

,10

0S

imu

lati

ons

Ach

ieve

dS

INR

dB

Lin

kL

engt

h(m

)S

INR

min

(dB

)min�M�

�ÐÐÐÐ

MÐÐÐÐ�

max�M�

σ�M�

min�SIN

RdB�µ

1~2�SIN

RdB�

648

�ÐÐÐÐ

49,5

ÐÐÐÐ�

500,

666,

05ª

950

�ÐÐÐÐ

50,0

ÐÐÐÐ�

500,

00ª

ª

12

50�ÐÐÐÐ

50,0

ÐÐÐÐ�

500,

00ª

ª

100

0

623

�ÐÐÐÐ

26,2

ÐÐÐÐ�

301,

606,

0013

,87

925

�ÐÐÐÐ

28,9

ÐÐÐÐ�

352,

299,

0017

,07

12

27�ÐÐÐÐ

31,6

ÐÐÐÐ�

382,

5412

,00

18,1

850

0

69

�ÐÐÐÐ

12,1

ÐÐÐÐ�

181,

366,

2816

,44

912

�ÐÐÐÐ

14,0

ÐÐÐÐ�

181,

369,

8018

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12

14�ÐÐÐÐ

16,5

ÐÐÐÐ�

201,

2812

,03

20,5

125

0

64

�ÐÐÐÐ

4,8

ÐÐÐÐ�

70,

757,

8121

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94

�ÐÐÐÐ

5,4

ÐÐÐÐ�

70,

8310

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23,8

012

5�ÐÐÐÐ

6,2

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90,

8312

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24,7

510

0

62

�ÐÐÐÐ

2,9

ÐÐÐÐ�

50,

558,

1025

,86

92

�ÐÐÐÐ

3,3

ÐÐÐÐ�

50,

6111

,37

27,1

112

3�ÐÐÐÐ

3,5

ÐÐÐÐ�

50,

5814

,31

29,5

050

61

�ÐÐÐÐ

1,5

ÐÐÐÐ�

20,

509,

9844

,90

91

�ÐÐÐÐ

1,6

ÐÐÐÐ�

20,

4913

,83

42,7

412

1�ÐÐÐÐ

1,8

ÐÐÐÐ�

30,

4614

,71

46,9

610

TableA.7:

Sim

ula

tion

resu

lts

ofsc

enar

io2,

wit

h50

lin

ks

an

dfi

xed

lin

kle

ngth

s,u

sin

gth

ese

con

dd

ista

nce

mod

elw

ith

the

fair

gro

up

ing

alg

ori

thm

.


250

Lin

ks

MG

rou

ps

per

Sim

ula

tion

,10

0S

imu

lati

ons

Ach

ieve

dS

INR

dB

Lin

kL

engt

h(m

)S

INR

min

(dB

)min�M�

�ÐÐÐÐ

MÐÐÐÐ�

max�M�

σ�M�

min�SIN

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1~2�SIN

RdB�

613

9�ÐÐÐÐ

156,

0ÐÐÐÐ�

181

7,85

6,08

36,5

19

156

�ÐÐÐÐ

189,

4ÐÐÐÐ�

212

7,42

9,65

ª

12

176

�ÐÐÐÐ

199,

5ÐÐÐÐ�

233

14,8

614

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ª

10-

1000

665

�ÐÐÐÐ

75,1

ÐÐÐÐ�

904,

056,

0519

,70

986

�ÐÐÐÐ

97,1

ÐÐÐÐ�

107

4,15

9,52

23,9

412

101

�ÐÐÐÐ

113,

5ÐÐÐÐ�

130

6,88

12,7

228

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10-

500

68

�ÐÐÐÐ

9,9

ÐÐÐÐ�

130,

857,

7222

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910

�ÐÐÐÐ

11,9

ÐÐÐÐ�

140,

8911

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25,3

512

13�ÐÐÐÐ

14,7

ÐÐÐÐ�

181,

2214

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27,6

010-

100

50L

inks

MG

rou

ps

per

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ula

tion

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0S

imu

lati

ons

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ieve

dS

INR

dB

Lin

kL

engt

h(m

)S

INR

min

(dB

)dmin

(m)�ÐÐÐÐ

MÐÐÐÐ�

max�M�

σ�M�

min�SIN

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1~2�SIN

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626

�ÐÐÐÐ

33,1

ÐÐÐÐ�

382,

486,

3934

,84

930

�ÐÐÐÐ

36,5

ÐÐÐÐ�

433,

499,

27ª

12

37�ÐÐÐÐ

41,3

ÐÐÐÐ�

472,

2415

,36

ª

10-

1000

614

�ÐÐÐÐ

18,2

ÐÐÐÐ�

241,

456,

8820

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918

�ÐÐÐÐ

21,0

ÐÐÐÐ�

251,

6810

,90

25,1

012

19�ÐÐÐÐ

25,2

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302,

1812

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31,4

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63

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4,2

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60,

6311

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27,5

19

4�ÐÐÐÐ

5,1

ÐÐÐÐ�

70,

8113

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30,5

512

4�ÐÐÐÐ

5,8

ÐÐÐÐ�

90,

9417

,67

31,2

610-

100

TableA.8:

Sim

ula

tion

resu

lts

ofsc

enar

io3,

wit

h250/50

lin

ks

an

dva

ryin

gli

nk

len

gth

s,usi

ng

the

seco

nd

dis

tan

cem

od

elw

ith

the

fair

gro

up

ing

alg

ori

thm

.


50L

inks/

Clu

ster

MG

rou

ps

per

Sim

ula

tion

,10

0S

imu

lati

ons

Ach

ieve

dS

INR

dB

Am

ount

of

Clu

ster

sS

INR

min

(dB

)min�M�

�ÐÐÐÐ

MÐÐÐÐ�

max�M�

σ�M�

min�SIN

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1~2�SIN

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614

7�ÐÐÐÐ

158,

6ÐÐÐÐ�

169

4,90

6,78

21,4

49

200

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213,

3ÐÐÐÐ�

224

5,39

10,2

824

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1226

3�ÐÐÐÐ

279,

1ÐÐÐÐ�

294

7,80

13,0

827

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50

610

1�ÐÐÐÐ

116,

0ÐÐÐÐ�

131

7,12

7,73

23,0

49

126

�ÐÐÐÐ

148,

0ÐÐÐÐ�

168

9,40

11,2

526

,34

1216

6�ÐÐÐÐ

188,

1ÐÐÐÐ�

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11,9

614

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28,8

725

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84,7

ÐÐÐÐ�

120

11,0

48,

7626

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962

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155

14,2

311

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28,7

912

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4ÐÐÐÐ�

149

18,1

914

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31,0

110

5L

inks/

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ster

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per

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ula

tion

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imu

lati

ons

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ieve

dS

INR

dB

Am

ount

of

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ster

sS

INR

min

(dB

)min�M�

�ÐÐÐÐ

MÐÐÐÐ�

max�M�

σ�M�

min�SIN

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1~2�SIN

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617

�ÐÐÐÐ

19,6

ÐÐÐÐ�

220,

988,

2422

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923

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ÐÐÐÐ�

291,

2111

,01

25,7

312

29�ÐÐÐÐ

32,6

ÐÐÐÐ�

351,

2314

,35

28,5

950

611

�ÐÐÐÐ

13,6

ÐÐÐÐ�

171,

029,

1824

,18

915

�ÐÐÐÐ

17,2

ÐÐÐÐ�

211,

2111

,32

27,2

912

18�ÐÐÐÐ

21,0

ÐÐÐÐ�

241,

4215

,05

29,4

125

66

�ÐÐÐÐ

10,0

ÐÐÐÐ�

151,

5110

,33

27,1

59

8�ÐÐÐÐ

11,3

ÐÐÐÐ�

151,

6713

,74

29,8

312

10�ÐÐÐÐ

13,6

ÐÐÐÐ�

181,

8615

,37

31,8

410

TableA.9:

Sim

ula

tion

resu

lts

ofsc

enar

io4,

wit

h50

/5

lin

ks

per

clu

ster

an

dva

ryin

gnu

mb

erof

clu

ster

s(R

C�

100

met

ers)

,u

sin

gth

ese

con

dd

ista

nce

mod

elw

ith

the

fair

gro

up

ing

alg

ori

thm

.


100

Clu

ster

sM

Gro

up

sp

erS

imu

lati

on,

100

Sim

ula

tion

sA

chie

ved

SIN

RdB

Lin

ks/

Clu

ster

SIN

Rmin

(dB

)min�M�

�ÐÐÐÐ

MÐÐÐÐ�

max�M�

σ�M�

min�SIN

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1~2�SIN

RdB�

612

�ÐÐÐÐ

17,3

ÐÐÐÐ�

211,

9211

,04

41,9

89

11�ÐÐÐÐ

19,3

ÐÐÐÐ�

261,

7012

,83

43,4

112

18�ÐÐÐÐ

21,0

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302,

3316

,01

43,2

810

66

�ÐÐÐÐ

9,2

ÐÐÐÐ�

121,

0211

,28

41,9

49

7�ÐÐÐÐ

10,0

ÐÐÐÐ�

130,

6914

,13

42,8

712

10�ÐÐÐÐ

10,7

ÐÐÐÐ�

151,

3316

,93

43,5

95

63

�ÐÐÐÐ

3,9

ÐÐÐÐ�

50,

3811

,25

42,0

99

3�ÐÐÐÐ

4,2

ÐÐÐÐ�

60,

5314

,22

42,5

912

4�ÐÐÐÐ

4,3

ÐÐÐÐ�

60,

6217

,22

44,1

42

TableA.10:

Sim

ula

tion

resu

lts

ofsc

enar

io5,

wit

h10

0cl

ust

ers

(RC�

10

met

ers)

an

dva

ryin

gnu

mb

erof

lin

ks

per

clu

ster

,u

sin

gth

ese

con

dd

ista

nce

mod

elw

ith

the

fair

gro

up

ing

alg

ori

thm

.

Appendix B

KPN Company Profile

KPN is the leading telecommunications and ICT service provider in The Netherlands,

offering wireline and wireless telephony, internet and TV to consumers, end-to-end

telecommunications and ICT services to business customers. KPNs subsidiary Getronics

operates a global ICT services company with a market-leading position in the Benelux,

offering end-to-end solutions in infrastructure and network-related IT. In Germany and

Belgium, KPN pursues a multi-brand strategy in its mobile operations and holds num-

ber three market positions through E-Plus and BASE. KPN provides wholesale network

services to third parties and operates an efficient IP-based infrastructure with global

scale in international wholesale through iBasis.

KPN markets a big portfolio of quality products. Separate brands serve different target

groups. Consumers in the Netherlands can choose from KPN (fixed and mobile tele-

phony for families), Hi (mobile telephony for young people), Telfort (no-frills mobile

telephony and Internet) and XS4ALL (the innovating Internet provider). The Nether-

lands, Germany and Belgium have the mobile telephone services of Simyo (competitively

priced SIM card) and Ay Yildiz (focused on the Turkish community). BASE and E-Plus

are the third mobile telephony brands in Belgium and Germany, respectively. For all

their service requirements, the Dutch and international business community can rely on

the KPN, Getronics, XS4ALL, Gemnet, Newtel and CSS brands. I-Basis is one of the

world’s largest carriers of international voice traffic.

Source: http://www.kpn.com/corporate/en/Company-profile-1/company-1/this-is-KPN.htm

105

http://www.kpn.com/corporate/en/Company-profile-1/company-1/this-is-KPN.htm

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