Interference Analysis in a LTE-A HetNet Scenario ... · PDF fileInterference Analysis in a LTE-A HetNet Scenario: Coordination vs. Uncoordination Nuno Emanuel Cabral Monteiro No 63158

Interference Analysis in a LTE-A HetNet Scenario:

Coordination vs. Uncoordination

Nuno Emanuel Cabral Monteiro

No 63158

Dissertation submitted for obtaining the degree of

Master in Electrical and Computer Engineering

Jury Members

President: Prof. Fernando Duarte Nunes (IST)

Supervisor: Prof. Antonio Jose Castelo Branco Rodrigues (IST)

Co-Supervisor: Prof. Neeli Rashmi Prasad (AAU)

Member: Prof. Pedro Manuel de Almeida Carvalho Vieira (ISEL)

November 2012

ii

Acknowledgements

First I would like to thank to my supervisor at AAU, Associate Professor Neeli Prasad, for

letting me take part of her work team and for helping me during my thesis. I would also like

to thank to my co-supervisor, Associate Professor Albena Mihovska, for giving me guidance

and valuable counsels whenever I needed. Thanks also to my supervisor at IST, Professor

Antonio Rodrigues, for all the support given.

To all my lab partners: Alexandros Fragkopoulos, Bayu Anggorojati, Francisco Paisana, Re-

naud Garigues, Simao Eduardo, Stefano Giuliana and Yasamin Mustamandi, thank you for

the great work environment and stimulating discussions.

To all my friends that from Portugal were always there for me. Namely, Francisco Pereira,

Andre Vieira e Castro, Miguel Ferraz, Andre Bernardino, Joao Pedro Costa, Duarte Leitao,

Armando Rosa, Diogo Matias, Jose Miguel Oliveira, Claudia Martins and Pedro Amaro -

Obrigado!

I would also like to thank you to my father, my mother and to the rest of my family that,

from the first moment I decided to do my thesis in Denmark, always supported my decisions.

- Muito Obrigado!

Last but for sure not least, I would like to give a special thanks to my sister for all the help

and support. - Obrigado!

To everyone who was always there for me,

Tak, Thank You, Merci, ευχαριστω, Grazie, Terima Kasih, Obrigado!

iii

iv

Abstract

The electromagnetic spectrum is a scarce resource that needs to be efficiently and effectively

reused to allow the provider the necessary conditions to satisfy its costumers.

The use of Heterogeneous Networks (HetNets), as proposed in the Long Term Evolution

(LTE) project, where there is an introduction of more cells in the network, with lower cover-

age than the ones that already exist, allows a better spatial reuse of the spectrum. However,

the introduction of more cells also leads to high-interference scenarios (low values of Signal

to Interference and Noise Ratios (SINRs)). Thus, it is necessary to create tools that help to

mitigate the interference, increasing the effectiveness of spectrum reuse.

The study here presented focus on the use of Game Theory in the mitigation of the interfer-

ence. The results are given in terms of the network user throughputs.

They show that although the use of closed access policies can benefit from the use of cell-

driven algorithms, open access policy is preferential to use with user-driven algorithms, in

particular for the increase of the service capacity.

It is also shown that although more complex, a coordinated architecture does not necessarily

lead to a better solution, when using schedulers that try to treat fairly all the users.

Keywords: LTE, Interference, SINR, Game Theory, Mitigation

v

vi

Resumo

O espectro electromagnetico e um recursos escasso que precisa de ser eficientemente re-

utilizado, de forma a permitir aos operadores da rede as condicoes necessarias para satisfazer

os seus clientes.

A introducao de mais celulas na rede, tal como proposto no projecto Long Term Evolution

(LTE), com menor cobertura do que as ja existentes, as redes heterogeneas (HetNets) per-

mitem uma mais eficiente reutilizacao do espectro. No entanto, essa reutilizacao pode nao

ser eficaz se conduzir a criacao de zonas de muita interferencia (valores baixos da relacao

sinal-(ruıdo e interferencia) (SINR)). E preciso, por isso, criar ferramentas capazes de ajudar

na mitigacao da interferencia, aumentando a eficacia da re-utilizacao espectral.

O estudo aqui apresentado debruca-se sobre a utilizacao de Teoria de Jogos na mitigacao da

interferencia. O desempenho dos algoritmos propostos foi avaliada atrves da medicao dos

debitos oferecidos aos utilizador da rede.

Mostra-se que um algoritmo mais dirigido a celula pode ser benefico a quando da utilizacao

de uma polıtica de acesso fechada, enquanto que um algoritmo dirigido ao utilizador pode ser

mais benefico no caso de uma polıtica de acesso aberta.

Mostra-se tambem que embora mais complexo, um sistema coordenado nao representa obriga-

toriamente uma melhor solucao para a rede quando se tenta escalonar os utilizadores atraves

de um escalonador proporcionalmente justo (PF).

Keywords: LTE, Interferencia, SINR, Teoria dos Jogos, Mitigacao

vii

viii

Contents

Abstract v

Resumo vii

List of Figures xi

List of Tables xiv

List of Abbreviations xvi

1 Introduction 1

1.1 Motivation & Goals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.2 Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.3 Publications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2 Background 5

2.1 Long Term Evolution - Advanced . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2.2 Pico/Femto Cells . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2.2.1 Access Policy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2.3 Interference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2.3.1 Spectrum Sharing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2.3.2 Interference Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2.4 Mitigation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2.4.1 Coordination . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

2.4.2 Game Theory and Coordination . . . . . . . . . . . . . . . . . . . . . . 12

2.5 Scheduling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

ix

x CONTENTS

3 Technical Approach 15

3.1 Introduction to the Simulator . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

3.1.1 Scenarios and Simulator Specifications . . . . . . . . . . . . . . . . . . . 15

3.1.2 Main Parameters of the Simulations . . . . . . . . . . . . . . . . . . . . 18

3.1.3 Interference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

3.1.4 Traffic Model and other details . . . . . . . . . . . . . . . . . . . . . . . 20

3.1.5 Attachment of the UEs to the Cells . . . . . . . . . . . . . . . . . . . . 22

3.2 Scheduling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

3.2.1 Potentially achievable data rate estimation . . . . . . . . . . . . . . . . 22

3.2.2 Details of the Scheduling Algorithm . . . . . . . . . . . . . . . . . . . . 23

3.3 Game Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

3.4 Cell-Driven Algorithms: Coordinated vs. Uncoordinated . . . . . . . . . . . . . 25

3.4.1 Uncoordinated . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

3.4.2 Coordinated . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

3.4.3 Overview of the Approach . . . . . . . . . . . . . . . . . . . . . . . . . . 28

3.5 User-Driven Algorithms: Coordinated vs. Uncoordinated . . . . . . . . . . . . 28

3.5.1 Uncoordinated & Coordinated . . . . . . . . . . . . . . . . . . . . . . . 29

3.6 Conclusion of the Technical Approach . . . . . . . . . . . . . . . . . . . . . . . 30

4 Results and Discussion 31

4.1 Pcell Density Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

4.2 Influence of the distance between PBSs and MBSs . . . . . . . . . . . . . . . . 37

4.3 Throughput variation with the number of users per PBSs . . . . . . . . . . . . 43

4.4 Impact of different Attachment Functions . . . . . . . . . . . . . . . . . . . . . 46

5 Conclusions and Future Work 51

A UE Attachment Algorithm 55

B Convexity of the Utility Functions 57

C Number of Scenarios per Sample 59

D Open Access Policy Criteria: Statistical Analysis 61

References 64

List of Figures

1.1 Schematic outline of the thesis. . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2.1 Scenario where Co-Channel Interference(CCI) can occur . . . . . . . . . . . . . 8

2.2 No shared-band between Pcells and Mcells. . . . . . . . . . . . . . . . . . . . . 9

2.3 Frequency Reuse 1 between Pcells and Mcells. . . . . . . . . . . . . . . . . . . . 9

2.4 Fractional Frequency Reuses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

2.5 Soft Frequency Reuse . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

3.1 Overview of the scenarios that were studied in this project . . . . . . . . . . . . 16

3.2 Vertical and Horizontal Antenna Patterns of the MBSs . . . . . . . . . . . . . . 17

3.3 Graphical representation of θ and ϕ . . . . . . . . . . . . . . . . . . . . . . . . 18

3.4 PBSs Antenna Pattern . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

3.5 Representation of one site with three Mcells. . . . . . . . . . . . . . . . . . . . 21

3.6 Schematic representation of Uncoordinated and Coordinated Algorithms . . . . 24

3.7 Cell-Driven Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

3.8 User-Driven Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

4.1 Dependence of the average throughput offered to the UEs of the MBS with the

number of PBS: PF scheduler. . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

4.2 Dependence of the average throughput offered to the UEs of the PBSs with the

number of PBS: PF scheduler. . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

4.3 Dependence of the average throughput offered to the UEs of the MBS with the

number of PBS: RR scheduler. . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

4.4 Dependence of the average throughput offered to the UEs of the PBSs with the

number of PBS: RR scheduler. . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

xi

xii LIST OF FIGURES

4.5 Dependence of the throughput offered to the worst served MUE with the num-

ber of PBS: PF scheduler. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

4.6 Dependence of the throughput offered to the worst served PUE with the number

of PBS: PF scheduler. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

4.7 Dependence of the throughput offered to the worst served MUE with the num-

ber of PBS: RR scheduler. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

4.8 Dependence of the throughput offered to the worst served PUE with the number

of PBS: RR scheduler. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

4.9 Graphical representation of the tested scenarios. . . . . . . . . . . . . . . . . . 37

4.10 Effect of the distance between pico and macro BSs on the average throughput

offered to the MUEs: PF scheduler. . . . . . . . . . . . . . . . . . . . . . . . . . 38


offered to the PUEs: PF scheduler. . . . . . . . . . . . . . . . . . . . . . . . . . 38


offered to the MUEs: RR scheduler. . . . . . . . . . . . . . . . . . . . . . . . . 39


offered to the PUEs: RR scheduler. . . . . . . . . . . . . . . . . . . . . . . . . . 39


of the worst served MUEs: PF scheduler. . . . . . . . . . . . . . . . . . . . . . 40


of the worst served PUEs: PF scheduler. . . . . . . . . . . . . . . . . . . . . . . 40


of the worst served MUEs: RR scheduler. . . . . . . . . . . . . . . . . . . . . . 41


of the worst served PUEs: RR scheduler. . . . . . . . . . . . . . . . . . . . . . . 41

4.18 Effect of the number of UEs attached to the PBS on the average throughput

offered to the UEs connected to the MBS . . . . . . . . . . . . . . . . . . . . . 43


offered to the UEs connected to the PBS . . . . . . . . . . . . . . . . . . . . . . 44


of the worst served MUEs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

LIST OF FIGURES xiii


of the worst served PUEs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

4.22 Average throughput offered to the worst served network UE for the uncoordi-

nated user-driven algorithm. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

4.23 Average throughput offered to the worst served network UE for the uncoordi-

nated cell-driven algorithm. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

4.24 Average throughput offered by the network to its UEs for the uncoordinated

user-driven algorithm. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

4.25 Average throughput offered by the network to its UEs for the uncoordinated

cell-driven algorithm. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

C.1 Obtained value of the average throughput offered to the UEs of the MBS, with

different number of scenarios per sample. . . . . . . . . . . . . . . . . . . . . . 60

C.2 Obtained value of the average throughput offered to the UEs of the PBS, with

different number of scenarios per sample. . . . . . . . . . . . . . . . . . . . . . 60

D.1 Statistical Analysis of the Open Access Policy Criterion (Distance: 30 m) . . . 61

D.2 Statistical Analysis of the Open Access Policy Criterion (Distance: 40 m) . . . 62

D.3 Statistical Analysis of the Open Access Policy Criterion (Power Ratio: 10 dB) 62

D.4 Statistical Analysis of the Open Access Policy Criterion (Power Ratio: 15 dB) 62

xiv LIST OF FIGURES

List of Tables

2.1 Major Parameters in LTE Release 8. Adapted from [1]. . . . . . . . . . . . . . . 5

2.2 Rate-based priority policies. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

2.3 Utility-based policies. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

3.1 UEs and PBSs deployment restrictions: minimal distance [2] . . . . . . . . . . . 21

xv

xvi LIST OF TABLES

List of Abbreviations

3G 3rd-Generation Wireless

3GPP 3rd Generation Partnership Project

4G 4th-Generation Wireless

ACI Adjacent-Channel Interference

AWGN Additive White Gaussian Noise

BS Base Station

CCI Co-Channel Interference

CQI Channel Quality Indicator

DLink Downlink

FDD Frequency Division Duplexing

FR-1 Frequency Reuse 1

HetNet Heterogeneous Network

HII High Interference Indicator

ICIC Inter-cell interference coordination

IMT International Mobile Telecommunications

ISI Inter-Symbol Interference

ITU-R International Telecommunications Union Radiocommunication Sector

LOS Line of Sight

xvii

xviii LIST OF ABBREVIATIONS

LTE Long Term Evolution

MBS Macro Base Station

Mcell Macro Cell

MIMO Multiple-Input Multiple-Output

MUE Macro User Equipment

OFDMA Orthogonal Frequency Division Multiple Access

PBS Pico/Femto Base Station

Pcell Pico/Femto Cell

PF Proportionally Fair Scheduling Policy

PL PathLoss

PRB Physical Resource Block

PUE Pico User Equipment

QAM Quadrature Amplitude Modulation

QoS Quality of Service

QPSK Quadrature Phase Shift Keying

RNTP Relative Narrowband Transmitted Power

RR Round-Robin Scheduling Policy

SC-FDMA Single Carrier – Frequency Division Multiple Access

SFR Soft Frequency Reuse

SINR Signal to Interference and Noise Ratio

TTI Transmission Time Interval

UE User Equipment

ULink Uplink

Chapter 1

Introduction

The increasing demand of mobile broadband services has lead researchers to focus all their

attention on the 4th-Generation Wireless (4G) of wireless cellular systems. This followed the

formal definition of the 3rd-Generation Wireless (3G) by ITU-R in 1997, with the launch of

the IMT-2000 specifications [3]. 4G systems are expected to have peak rates of 100 Mbit/s for

high mobility and 1 Gbit/s for low mobility, with a good Quality of Service (QoS) [4].

The macro cells (Mcells), already deployed by the operator in the network, do not allow

the achievement of such high data rates. Making it necessary the deployment of pico cells

(Pcells). The uncoordinated nature of the deployment of these smaller cells and the limited

amount of electromagnetic spectrum bands, identified as suitable for International Mobile

Telecommunications [5], leads to high interference among cells.

Pcells offer small area coverage and low-power consumption. Furthermore, these cells can

offer better coverage and better data rate services in the zones in which they are deployed,

which makes them an interesting technology for the improvement of service in HotSpot zones.

Nevertheless, this technology presents some drawbacks. The spectrum is a natural scarce

resource that needs to be shared and reused among cells. The reuse of the spectrum leads to

high interference scenarios that need to be taken into account. These scenarios need to be

dynamically treated, in order to offer a better service to all network users.

1.1 Motivation & Goals

Studies based on wireless technology usage indicate that more than 50% of voice calls, and

70% of data traffic are originated indoors [6]. This also suggests that a big percentage of data

1

2 CHAPTER 1. INTRODUCTION

traffic and voice calls are made in HotSpot zones that in fact are business buildings during

the day and inhabited buildings during the night time. These studies motivated the research

community to try to find a good way of improving the network coverage in these type of

zones. PBSs were chosen as the technology to provide this type of improvement, due to their

low-power consumption, low-cost and user-deployment.

However, the need to share spectrum between MBSs and PBSs creates big problems of co-

existence between the two technologies, as the signal of one is the noise of the other. Thus,

the aim of this work is to study the risks associated with the deployment of PBSs and how

to mitigate them, and thus prevent the malfunction of the network. This study will also

focus on how the network can profit from allowing coordination between BSs, as the use of a

coordinated architecture implies that more complexity is added to the network (new physical

channel and more data to process). Finally, the use of different access policies to the BSs will

also be tested, with the aim of understanding how the network behaves with private (closed

access policy) and public (open access policy) PBSs.

1.2 Structure

A schematic overview of the thesis can be seen in Figure 1.1 In the current chapter the goal of

the work developed as well as a contextualization are given. Chapter 2 presents an overall

view of the state of the art in interference analysis and interference mitigation. This chapter

also focuses on information about LTE/LTE-Advanced. Chapter 3 presents the algorithms

proposed for the mitigation of the interference. Four algorithms are presented in this chapter.

In addition, the results obtained are also discussed in this chapter. Finally, in Chapter 5 the

conclusions withdrawn from this work and future perspectives are presented.

1.3. PUBLICATIONS 3

Figure 1.1: Schematic outline of the thesis.

1.3 Publications

Two papers have originated from the work done by the author of this thesis:

• N.Monteiro, A. Mihovska, A. Rodrigues, N. Prasad, and R. Prasad, ”Interference Analy-

sis in a LTE-A HetNet Scenario: Coordination vs. Uncoordination”, 2013 IEEE Wireless

Communications and Networking Conference, Shangai, China 7-10 April 2013 (submit-

ted for publication). [7]

• N.Monteiro, A. Rodrigues, A. Mihovska, N. Prasad, and R. Prasad, ”Interferencia em

Redes Heterogeneas LTE-Advanced Coordenadas e Nao Coordenadas”, 6.o Congresso

do Comite Portugues da URSI, Lisboa, Portugal, 16 November 2012. [8]

4 CHAPTER 1. INTRODUCTION

Chapter 2

Background

2.1 Long Term Evolution - Advanced

In order to achieve higher data rates and better QoS the 3rd Generation Partnership Project

(3GPP) started to work on the Long Term Evolution (LTE) project, which is part of the 3GPP

Release 8, that was frozen in December 2008 [1]. The key features presented in this release were

the use of Orthogonal Frequency Division Multiple Access (OFDMA) in Downlink (DLink)

in order to avoid inter-symbol interference (ISI) provoked by multipath; Single Carrier –

Frequency Division Multiple Access (SC-FDMA) in Uplink (ULink) connections, which offers

Low Peak-to-Average Power Ratio, and uses orthogonality in frequency domain, and Multiple-

Input Multiple-Output (MIMO) techniques which are used to increase the spectral efficiency.

The major parameters of this release are presented in table 2.1.

Table 2.1: Major Parameters in LTE Release 8. Adapted from [1].

Supported Bandwidths [MHz] 1.4; 3; 5; 10; 15; 20

Minimum TTI [ms] 1

Sub-carrier spacing [kHz] 15

Modulation QPSK; 16-QAM; 64-QAM

In December 2009, the first publicly implemented LTE service was tested by TeliaSonera in

Stockholm and Oslo [6]. This LTE service presented great improvements, especially when com-

pared with the previous data rates and QoS achieved. However, the measurements showed that

the system did not fully comply the ITU-R requirements for 4G systems. These requirements

had been published through a circular letter in July 2008 and are known as IMT-Advanced.

5

6 CHAPTER 2. BACKGROUND

Due to these problems, LTE started to be widely referred in the scientific community as 3.9G

and in the commercial world as 4G-LTE. December 2009 was also the time when 3GPP frozen

the Release 9 of the LTE project, which included minor changes to the previous release and

thus it was not seen as the real 4G wireless technology project. In these minor changes it is

important to emphasize the introduction of picocells (section 2.2) and dual-layer beamform-

ing. And, from this point onwards Pcells started to gain more popularity in the research

world.

The real attempt by 3GPP to achieve the IMT-Advanced demands started with the Release

10 of the LTE project, also known as LTE-Advanced. One of the key features taken into

account was that this new Release needed to be backward-compatible, which means that the

deployment of LTE-Advanced technology in a spectrum already occupied by LTE should suf-

fer no impact. Another key point was that LTE already achieved data rates very close to

Shannon limit. Thus, the main focus should be to increase the Signal to Interference and

Noise Ratio (SINR) experienced by the UEs and hence provide higher data rates over a larger

portion of the cell [6]. With that purpose the maximum bandwidth was increased to 100 MHz.

In order to allow bandwidths of 100 MHz without breaking the backward-compatibility with

LTE requirements, a carrier aggregation scheme was proposed, which consisted of grouping

several LTE Component Carriers (e.g. up to 20 MHz) in order to obtain greater amounts

of bandwidth. This aggregation can be even developed in non-contiguous bandwidth and

multiple bands [6].

Other important upgrades, demanded by this new release, were the evolution to MIMO with

up to 8 × 8 antennas in DLink and 4 × 4 in ULink connections, as well as the use of relay

nodes as a simple transmission solution.

For the purpose of this thesis, the most important upgrade was the introduction of heteroge-

neous networks and the necessity to optimize the interworking between cell layers, Mcell vs

Pcell [9].

2.2 Pico/Femto Cells

As stated in 2.1, the surest step to improve the capacity of the system is to increase the

SINR and the bandwidth (amount of Physical Resource Blocks (PRBs)) offered to each User

Equipment (UE). One way to guarantee this is to get transmitters and receivers closer to each

2.3. INTERFERENCE 7

other, which guarantees a higher quality link (lower values of path loss) and bigger spatial

reuse of the frequency bands. This step is achievable with the introduction of Pico and Femto

Base Stations (PBSs).

The path losses cause the signal to decay with C ·d–α, where C is a fixed loss, d is the distance

between the transmitter and receiver and α is the path loss exponent, which depends on the

radio-environment. Therefore the maximization of the Signal to Interference and Noise Ratio

(SINR) depends on the minimization of d and/or −α [6].

PBSs have short transmit-receive distance when compared with a MBS, which helps to greatly

lower the transmission power and prolonging handset battery life. This ensures better coverage

and capacity, with the drawback of provoking higher problems of interference in the cells, if

both MBS and PBS are using the same frequency bands.PBSs are normally deployed in

HotSpot zones (indoor or outdoor), in indoor offices, or dense blocks, being located on walls,

ceilings or masts. [10]

Femto BSs are also known as Home NodeB, containing smaller coverage regions than Pico

BSs. This happens because their aim is only to cover the area of a house or even just some

compartments of a house.

Another point that needs to be taken into consideration when talking about Pcells is access

policy.

2.2.1 Access Policy

PBSs access policy highly depends on ”who the owner of the cell is”. If the cell belongs to a

private/home user it is expected that he wants to have all the capacity of the cell to himself

and his gadgets. Normally, in these cases we are talking about a Femto BS and the access

policy used is known as ”closed access”, since it offers a private access to its user.

On the other hand, Pico BSs are normally deployed with the intention to serve the users in

HotSpot area, thus demanding an ”open access” policy. However, they can also have a ”closed

access” policy if they belong to a company and thus the cell will only serve its employees.

2.3 Interference

The principal types of interference in a mobile communication are Inter-Symbol Interference

(ISI), Adjacent-Channel Interference (ACI) and Co-Channel Interference (CCI).


As stated in section 2.1, in LTE/LTE-Advanced the main radio access modes in DLink and

ULink, OFDMA and SC-FDMA respectively, where chosen with the intent to avoid ISI.

The ACI is provoked by extraneous power from a signal in an adjacent channel. The OFDMA

case (DLink) is quite robust to ACI. SC-FDMA is not so robust as data symbols are spread

across the allocated transmission band and thus interference on a few edge subcarriers will

affect all the data symbols. However, as stated by Sesia et. al. [11], this can be neglected when

compared with the interference-limiting effect of the CCI.

CCI occurs when two transmitting equipments electromagnetically close to each other are

working with overlapping frequency bands. Hence, to avoid interference problems, it is im-

portant that Macro User Equipments (MUEs) and Pico User Equipments (PUEs), positioned

next to each other, do not use the same Physical Resource Blocks (PRBs). To do so, MBSs

and PBSs must be able to know which resources their neighbouring stations are using in each

region of the cell, so that the Signal-to-Interference and Noise Ratio (SINR) does not decrease

to forbidden levels that prevent good QoS. Figure 2.1 shows an example of a scenario where

CCI can occur.

Figure 2.1: Scenario where Co-Channel Interference(CCI) can occur: The MUEs suffer CCI from the PBS when it is

emitting in the same frequency channels. The same happens between the PUE and the MBS.

2.3.1 Spectrum Sharing

There are several possible ways to spread/share the spectrum between Pcells and Mcells. In

terms of interference analysis, two extreme approaches exist. In one, only CCI among cells

from the same type is observed (Figure 2.2), whereas in the other all the cells are deployed on

the same band (Figure 2.3) [12]. The first case (Figure 2.2) suffers from inefficient spectrum

reuse, while the second one (Figure 2.3) presents the worst-case interference scenario, also

known as Frequency Reuse-1 (FR-1). There are also hybrid scenarios, where cells have a

2.3. INTERFERENCE 9

shared band and a private band at the same time.

Figure 2.2: Best Interference-case Scenario: No shared-band between Pcells and Mcells.

Figure 2.3: Worst Interference-case Scenario: Frequency Reuse 1 between Pcells and Mcells.

Previous works have presented alternative ways of Frequency Reuse [13,14]. Al-Shalash et.

al. have presented the Fractional Frequency Reuses (FFR) and the Soft Frequency Reuse

(SFR) [13]. In the former, the UEs in the center of each Mcell use the same band, where the

UEs near the edge of each cell receive a band with Frequency Reuse 1/3 (Figure 2.4). In the

latter, each cell has a preferred sub-band that is used by the cell edge UEs, where higher power

is permitted, and users placed closer to the center of the cell reuse the preferred sub-bands of

adjacent cells at a lower power (Figure 2.5).

Figure 2.4: Frequency Allocation: Fractional Frequency Reuses


Figure 2.5: Frequency Allocation: Soft Frequency Reuse

2.3.2 Interference Analysis

Another relevant step is to understand how the interference can be detected. To do so, the

UE must be able to sense the environment and calculate the SINR it is receiving. Afterwards,

this value must be used by the Base Stations as a decision factor to determine which are the

Physical Resource Blocks (PRBs) that better serve each UE. This information is exchanged

through the Channel Quality Indicator (CQI) to the cell the UE is connected to, [4].

2.4 Mitigation

Mitigation of the interference in Heterogeneous Network (HetNets) Scenarios has been a sub-

ject of huge interest in the last years. Different approaches to this topic were chosen and

analysed in Chapters 3 and 4. The most used approaches in the mitigation of interference

are: Reinforcement-Learning and Game Theory.

The use of Reinforcement-Learning, as in a Q-Learning strategy, is based on a trial-and-error

approach, where an agent (transmitting equipment) learns from its previous adaptations [15,16].

The agent is challenged to discover which actions yield the biggest reward by trying them.

However, it is not told what action to take, it has to discover by itself. The core feature of a

Reinforcement-Learning algorithm is the duality/dilemma between exploring and exploiting.

A reinforcement-learning agent must seek the actions that gave it a higher reward in the

past. However, to discover such actions, it has to undertake actions that it has not performed

before [17].

In the Game Theory approach the agents are understood as players/decision takers in a

2.4. MITIGATION 11

board-game, trying to create strategies, based on previous strategies of their opponents and

thus maximizing their objective function [18–20]. Here, a player needs to look at all possible

courses of action available and choose the one which gives the preferred outcome. In equation

2.1, a∗ is the action that maximizes the utility function u(a). [21]

a∗ ∈ argmaxa∈A

u(a) (2.1)

2.4.1 Coordination

There are two different network architectures that must be analysed when trying to mitigate

the interference and to increase the performance of the network: coordinated and uncoordi-

nated architectures. The former is expected to offer a more accurate mitigation since it allows

the exchange of control information among different cells through the X2 interface (a wired

channel like a digital subscriber line (DSL)). The latter does not allow information exchange

between cells, leading to a more simple and fast approach where the PBSs are responsible

for sensing the spectrum, with the help of the UEs, and thus understand which frequency

channels are being used by the neighbouring BSs.

The coordinated architecture uses the Inter-cell interference coordination (ICIC) that is sent

to the neighbouring MBSs and to the PBSs through the X2 interface. ICIC is filled with

information measured by the UEs, as the High Interference Indicator (HII), for the ULink,

and the Relative Narrowband Transmitted Power (RNTP), for the DLink, that informs about

the Physical Resource Blocks where a UE is sensing a bigger load of interference [22,23]. This

exchange of information has its drawbacks as it increases the overheads and the delays pro-

voked by the signalling.

On the other side, in the uncoordinated architecture there is no physical interface between

base stations, which does not allow any type of complex signalling. In this way they have to

fully rely on their sensing capacity, as well as on their UEs sensing capacity, to understand

which frequencies are being used by the neighbouring MBSs and thus avoid Macro-Pico in-

terference. Furthermore, PBSs also need to be able to broadcast beacons that are further

processed by PUEs and sent back to the PBSs they are connected to, thus avoiding interfer-

ence from nearby PBSs [22].


2.4.2 Game Theory and Coordination

The decision of allowing or interdicting coordination along the network can lead to different

Game Theory algorithms. If cells are not allowed to communicate with each other the Game

Theory chosen has to be a selfish one, once the player does not know how the others will act,

and so it has to look for its welfare. A selfish-type algorithm was presented by Bennis et. al.

in [18].

When coordination is allowed, players can communicate with each other, exchanging informa-

tion about what actions they are going to take. In this case there are two different options.

One is a centralized optimization, where a prime-player, e.g. a MBS, receives the information

from all the PBSs and UEs in its cell area and chooses the play that most benefits everyone [24].

The other option is a hierarchical game, where cells are hierarchically treated. Thus, a cell

with a lower rank must choose its action and pass the information to the higher rank cells so

they can play their own game with the information of how the lower ranked ones are going

to act. A two-ranked hierarchy where PBSs find their Best Response using the information

sensed by them in the previous time-slot, and then, report their future actions to the MBSs

so that they can better serve their UEs has also been described by Bennis et. al. [18].

The centralized alternative is quite heavy to the system since it expects that a BS optimizes

all the system behaviour very fast and independently of the amount of UEs on it. It is im-

portant to note that the time spent sending the information through the X2 interface in both

directions plus the duration of the optimization must be quite small when compared with

a Transmission Time Interval (TTI). This implies the use of more powerful and expensive

processors or the increase of the TTI, which would deteriorate the system performance.

2.5 Scheduling

Another important step when trying to mitigate the interference in a network is to try to fairly

schedule all the different UEs along the time, so that all of them can achieve a good QoS.

If this is not taken into account a network optimization algorithm can end up not feeding

some UEs with worst SINR, to the benefit of the ”greater good”. Lassila and Aalto presented

some schedulers using priority policies [25,26], (as the one in the 1st row of Table 2.2), that

2.5. SCHEDULING 13

prioritizes the currently highest rate. Some index policies, that look for the trade-off between

instantaneous rate and expected rate (based on the past experience), are also presented (2nd

and 3rd row of Table 2.2 and Table 2.3). More complex schedulers than the ones presented

in Table 2.2 and 2.3 can be found in [25,26].

Table 2.2: Rate-based priority policies: use information related to the channel state to define the priority of any

flow. [25,26]

Maximum Rate Greedy policy that serves the UEs with

higher instantaneous transmission rate.

Relatively Best Serves the UEs that have the better channel

quality when compared with its channel

expected quality.

Proportionally Best Serves the UEs whose channel quality is

the best when compared with the best channel

quality each of them has experienced in the past.

If a tie is verified between actors fighting for the same resource, the choice must be made

randomly between the tied UEs.

The scheduling can also be made with a Round Robin Policy (RR), where the UEs are served

sequentially without any concern for current or past channel conditions or even the experienced

throughput.

Table 2.3: Utility-based policies: gives an abstraction of the instantaneous states of the channel taking into account

the real throughput experienced by the flows. [25,26]

Proportionally Fair Allocates the time slot to the UE that

has the highest instantaneous rate relative to its

throughput (estimated as explained in [27]).

Potential Delay Similar to the Proportionally Fair Policy,

minimization gives quadratic weight to the experienced

throughput.


Chapter 3

Technical Approach

3.1 Introduction to the Simulator

3.1.1 Scenarios and Simulator Specifications

The network scenarios that will be analysed in this thesis were chosen regarding what was

presented by 3GPP as carrier aggregation scenarios (for a better description see [28]). A

scenario where Macro Sites have three MBS beams, forming three Mcells, will be taken into

account.

Since the goal of this work is to study the behaviour of the cells when interference, more

precisely Co-Channel Interference (CCI), occurs, the worst interference-case scenario will be

considered. This was already shown in Figure 2.3, subsection 2.3.1, where there is FR-1

between Pcells and Mcells. Following, this study will evolve among several scenarios with

different complexities.

Firstly, a scenario with one site with only one active MBS and one PBS will be taken into

consideration (Figure 2.1). Following, the number of PBSs will be increased and the behaviour

of the network will be analysed, hence giving an interpretation of how different PBSs densities

can influence the network.

The number of UEs distributed in the Mcell- and Pcell-areas will also be increased in order

to try to understand how the network would react to different densities of UEs.

Two identical scenarios will always be analysed - one with a physical interface between the

cells (X2 interface), and another without any physical interface.

The specifications of the network architecture will be chosen taking into account the 3GPP

Technical Specifications presented in [29] and [10].

15

16 CHAPTER 3. TECHNICAL APPROACH

The MBSs have a height of 30 meters and an electrical down-tilt of 15◦ as proposed by 3GPP

in [2].

Figure 3.1 shows an aerial representation of the network architecture:

Figure 3.1: Overview of the scenarios that were studied in this project

The PathLoss Model used in this project is Model 2 proposed by 3GPP in [2], which consid-

ers different PL for Line of Sight (LOS) and Non-LOS (NLOS) conditions, where transmitter

and receiver do not have a direct channel between them. Equations (3.1) and (3.2) express

the PLLOS and the PLNLOS from the MBSs to the UEs, whereas equations (3.3) and (3.4)

express the PLs from the PBSs to the UEs. The existence of LOS was estimated through

the Probability of LOS (ProbLOS) also proposed in [2] by 3GPP for case 1 - Urban scenario

- represented in equations (3.5) and (3.6) for the MBSs to UEs and PBSs to UEs, respectively.

PLmacroLOS = 103.4 + 24.2 log10(R[km]) (3.1)

PLmacroNLOS = 131.1 + 42.8 log10(R[km]) (3.2)

PLpicoLOS = 103.8 + 20.9 log10(R[km]) (3.3)

PLpicoNLOS = 145.4 + 37.5 log10(R[km]) (3.4)

ProbmacroLOS = min

{0.018

R[km], 1

}∗(

1− e−R[km]0.063

)+ e−

R[km]0.063 (3.5)

ProbpicoLOS = 0.5−min{

0.5, 5e− 0.156

R[km]

}+ min

{0.5, 5e−

R[km]0.3

}(3.6)

Where R is the direct distance between the BS and the UE.

3.1. INTRODUCTION TO THE SIMULATOR 17

The MBSs Antennas Patterns follow equations (3.7) and (3.8) [2]. This results in the vertical

and horizontal footprints presented in Figure 3.2-A and Figure 3.2-B, respectively. The overall

gain is calculated through equation (3.9).

GainV = −min

{12 ∗

(θ − εdtiltθ3dB

)2

, Gainθmin

}(3.7)

Where θ is the vertical angle (Figure 3.3), εdtilt = 10◦ is the electrical down-tilt of the antenna,

θ3dB the value of θ at −3dB and Gainθmin = 20 dB the minimum vertical gain. All angles are

in degrees [◦].

GainH = −min

{12 ∗

(ϕ

ϕ3dB

)2

, Gainϕmin

}(3.8)

Where ϕ is the horizontal angle (Figure 3.3), ϕ3dB = 70◦ the value of ϕ at −3dB and

Gainϕmin = 25 dB the minimum horizontal gain of the antenna. All angles are in degrees [◦].

GainMacro = −min {− (GainV +GainH) , Gainϕmin} (3.9)

Figure 3.2: (A): Vertical Antenna Pattern with the representation of the antenna mast; (B): Horizontal Antenna

Pattern of 7 sites, each with 3 MBSs


Figure 3.3: Graphical representation of θ and ϕ

For its turn, PBSs have omnidirectional antenna patterns, with Gainpico = 5 dB, resulting

on the footprint shown in Figure 3.4.

Figure 3.4: PBSs Antenna Pattern

3.1.2 Main Parameters of the Simulations

For the simulations, the following main parameters will be taken into account:

1. Number of users per Picocell: 10

2. Number of users per Macrocell: 20

3. System Bandwidth: 40 MHz


4. Carrier Frequency: 2 GHz

5. Number of PRBs per TTI: 200

6. PBSs Transmission Power: 30 dBm

7. MBSs Transmission Power: 49 dBm

8. Cells Operating Mode: FDD

9. Transmission Time Interval (TTI): 1 ms (≥ 1 ms)

These parameters were chosen taking into account 3GPP recommendations on [1,10,29].

3.1.3 Interference

Firstly, it is necessary to understand what are harmful scenarios in an heterogeneous network.

It is important to take a look at the key factor for this analysis, the SINR, equation 3.10

SINRnc,u =PnTX,c,u · |hnc,u|2

σ2 + Pnpicos,u + PnMacros,u

(3.10)

Where u is the index of the UE, c the index of the Cell and n the index of the PRB, PTX the

transmission power of the BS, |h|2 the channel gain between the user and the cell and σ2 is

the variance of the AWGN. Ppicos and PMacros are the sum of the powers received by the UE,

coming from the neighbour Pcells and Mcells, respectively, except to the one it is connected

to (equation 3.11).

Pnpicos,u + PnMacros,u =C∑j 6=c

Pnj · |hnj,u|2 (3.11)

Where c is the cell the user u is attached to and C is the set of all the cells in the network.

With this information the maximum achievable rate can be calculated, as expressed in equa-

tion 3.12 :

Ru =∑n

log2

(1 +At

nc,u · SINRnc,u

)(3.12)


Where At depicts the influence of a Rayleigh Fading Channel, which is used in the simulation

to give a more realistic approach. The Rayleigh fading channel, as proposed in [30], will be

simulated as a random variable that follows an exponential distribution with mean value 1.

In the following sections of this chapter the At variable will be omitted in all the equations.

This will be done to help simplify the reading of the equations. Since it represents a channel

power gain it can be seen as making part of the channel gain between the BS and the user in

the following equations.

Following, it is important to understand how different deployments of the PBSs inside a Mcell-

area affect the SINR. If a PBS is next to a MBS it can not use the same PRBs the MBS is

using. This is due to the fact that the signal of one of the BS would provoke high interference

in the signal being emitted by the other, leading to a small SINR and thus preventing the

achievement of good data rates, given by equation 3.12. If a PBS is far enough from the MBS

it can use the same channels the MBS is using. However, it will need to take into account

that high signaling power can provoke interference to MUEs using those same channels, even

when they are far away. Thus, it is important that the chosen algorithm can act efficiently in

both of these harmful scenarios.

The information previously stated only refers to the case of Macro-Pico interference, but the

ideas behind the Pico-Pico interference or even the Macro-Macro interference, are the same.

If two cells are close enough and both need to use the same PRB, they have to use a lower

power in order not to kill the communications of the other cell.

In the present work, a FR-1 approach in Pcells and Mcells, where both are working in a FDD

scheme, will be used. These features were chosen because they provide the worst-case scenario

of interference, thus offering a better view over the benefits and constraints of using a physical

interface to help in the interference mitigation.

3.1.4 Traffic Model and other details

The traffic model used in the simulation is the Full-Buffer [4]. It is not as realistic as the Burst

Traffic model, but it offers a worst interference scenario as it considers that the UEs and the


Base Stations always have the buffer full of information that needs to be sent.

The simulation will be focused in the DLink connection since it is the one that demands larger

data rates, thus making it more sensitive to lower SINRs.

The UEs will be deployed uniformly along the cell areas. The PBSs will also be deployed

uniformly along the corresponding Mcell-area. To avoid zones of huge interference or UEs

in nearly perfect SINR conditions, some restrictions were taken into account (Table 3.1), as

proposed by 3GPP in [2].

Table 3.1: UEs and PBSs deployment restrictions: minimal distance [2]

PBS MBS 75 m

PBS PBS 40 m

UE MBS 35 m

UE PBS 10 m

Mcells are represented as hexagons with inter-site distance of 500 [m] as referred in [2], case 1

(urban scenario), which corresponds to a hexagon inscribed in a circle with a radius of 500/1.5

[m] (Figure 3.5). On the other side, Pcells have a circular shape with a radius of 40 [m].

Figure 3.5: Representation of one site with three Mcells: Inter-site distance (thick black line); Mcell inscribed in circle

(thick and dashed blue line) with radius (thick purple line).


3.1.5 Attachment of the UEs to the Cells

After the random deployment of the users in their cell areas, it is necessary to attach the users

to each cell. The choice of which cell a user should be attached to must be made taking into

consideration the cell that can serve better each user. One simple strategy could be choosing

the cell that offers the higher nominal power at the UE position. However, due to the big

difference of Total Available Transmission Power between MBSs and PBSs, the choice would

almost always lie in the Mcell since the PL difference would not cover the PTX difference.

Some algorithms will be tested, simpler ones that only consider the deployment or the distance

from the UEs to the BSs, and some more complex based on the work developed by Pantisano

et. al. [19] and thoroughly explained in Appendix A.

3.2 Scheduling

The scheduling policy used in the simulations will be the Index and Utility-Based Policy: Pro-

portionally Fair (PF), previously presented in Chapter 2, section 2.5. This choice was made

taking into consideration the performance of this policy when compared with others [25,26].

This policy tries to maximize the following priority function:

P =TαPF

RβPF(3.13)

Where T represents the potentially achievable data rate, R the historical average data rate,

calculated as in equation 3.14 [27]. αPF and βPF will be used with unitary value.

Ru,t = (γ) ·Ru,t−1 + (1− γ) · Tu,t−1 (3.14)

Where γ = 0.95, Rt−1 represents the value of the historical average data rate in the previous

TTI and Tt−1 the total throughput achieved by the user u in the previous TTI.

3.2.1 Potentially achievable data rate estimation

When a PF scheduler is used, it is necessary to estimate the potentially achievable data rate

that a user would experience when using each PRB. To do so it is necessary to estimate the

3.3. GAME THEORY 23

amount of power the BS would have assigned to a PRB n if it was attached to a UE u even

when that is not observed. For that, the following method is proposed (equation 3.15):

AvgPowernu,t = (1− γpwr)[(1− αpwr) · pwrnu,t + αpwr ·AvgPowernu,t−1

]+γpwr [(1− βpwr) · apwru,t + βpwr · aAvgPoweru,t−1]

(3.15)

Where γpwr, αpwr and βpwr ∈ [0; 1]. pwrnu,t is the power attributed to the nth PRB if it was

attributed to user u in the current TTI t. Otherwise, it will have the value of AvgPowernu,t−1.

apwru,t is the average power attributed to each PRB, attached to the user u, in the current

TTI t. If none was attributed in the current TTI it will have the value of aAvgPoweru,t−1,

that is the average of AvgPowernu,t−1 per PRB.

The estimation of the potentially achievable data rate for the next TTI, is done through the

SINR calculated with the real Noise and Interference and with the estimated power.

The simulations were done making γpwr, αpwr and βpwr equal to 0.3. This values were chosen

with the purpose of giving more importance to the recent power attributions and to the duo

PRB-UE, rather than the average throughput offered to the UE per PRB.

3.2.2 Details of the Scheduling Algorithm

When the algorithm starts there is no previous information about the states of each user or

cell. This then prevents the use of the PF scheduler. Thus, in the first run, the algorithm will

run the round-robin scheduling algorithm, previously explained in chapter 2 section 2.5. All

the following runs will be done using the PF scheduling algorithm.

The scheduler assigns a UE to each of the PRBs. It is necessary to note that a UE can have

more that one PRB in each TTI or even no PRB in a specific TTI.

3.3 Game Theory

The interference mitigation among cells and the increase of the throughput experienced by

the network users are only one problem, as the throughput deeply depends on the interference


felt by the receivers.

It is easily understood that a centralized approach does not reflect a realistic way of treat-

ing the interference problem of a network as previously explained in 2.4.2. Thus, it was

considered that both uncoordinated and coordinated cell architectures would have small op-

timization problems to be solved in each cell.

The big difference between the uncoordinated and the coordinated cell architecture is that, in

the second case, MBSs will act after receiving, from PBSs in their cell region, the data that

indicates its new strategies (Figure 3.6).

Figure 3.6: Schematic representation of Uncoordinated (A) and Coordinated (B) Algorithms

To the Coordinated case the best choice seems to be the Stackelberg game approach, as pro-

posed by Bennis et.al. in [18]. This approach presents a rigid hierarchy, where the MBS is seen

as the leader, since it is the first one to be deployed and also the strong one, like a market

leader, and PBSs are seen as the followers, due to their random and uncoordinated nature.

To the Uncoordinated case the best choice seems to be the Nash Equilibrium, as proposed

in the same study [18]. This happens because, without any physical interface to communicate

3.4. CELL-DRIVEN ALGORITHMS: COORDINATED VS. UNCOORDINATED 25

strategies among cells, the best approach is to let each player find the best strategy to take

advantage of the last strategies of their opponents.

A more detailed analysis of the algorithms can be seen in the next sections of this Chapter

(section 3.4 and 3.5).

The Utility Function that will be used to help mitigate the interference is presented in ap-

pendix B equation B.1.

3.4 Cell-Driven Algorithms: Coordinated vs. Uncoordinated

The Cell-Driven Algorithms will be focused in the overall optimization of the cell.

The scheduler assigns a UE to each PRB. Therefore, in the following sections of this chapter,

it is considered that when omitted, the index of the user u in a variable is inherent to the duo

{c, n}.

3.4.1 Uncoordinated

After the schedule is done, each BS will try to arrange its total transmission power (Pc) among

all the N frequency channels in a way that maximizes the global throughput offered by the

cell (equation 3.16). For that, it will consider the SINRs that the UE would be sensing at

that moment, if it was already using that same PRB.

The utility function in equation 3.16 was derived from equations 3.10, 3.11 and 3.12, presented

in section 3.1 of this chapter.

maxpc

N∑n=1

log2

(1 +

pnc · |hnc |2

σ2 +∑C

j 6=c pnu,j · |hnu,j |2

)

s.t.

N∑n=1

pnc ≤ Pc (3.16)

pnc ≥ 0

The demonstration of the convexity of the optimization problem in equation 3.16 can be seen


in Appendix B.

As presented in [18] the optimization problem can be simplified with the Water-Filling tech-

nique [31], obtaining the following solution for each BS (equation 3.17):

pnc = (K − λnc )+ (3.17)

with,

λnc =σ2 +

∑Cj 6=c p

nj · |hnj |2

|hnc |2(3.18)

Where (x)+ = max {x, o}, K > 0 is a constant chosen so that∑N

n=1 pnc ≤ Pc, which means

that all the power of the cell is being used where it is most useful.

The Water-Filling [31] technique can be coded as follows:

Algorithm 3.4.1: Water-Filling(MatLabcode)

[λc idx] = sort(λc, ’ascend’);

comment: orders the frequency channels from the one with less

interference and noise to the one with more

pc = −1 ∗ ones(1, N);

while (min(pc) < 0)

do

Kc = (Pc + sum(1. ∗ λc)) /length(λc);

pc = Kc − 1. ∗ λc;

λc = λc(1 : end− 1);

pc = [pc zeros {1, length(idx)− length(pc)}];

comment: assigning zero power for weak eigenmodes, frequency

channel with too much interference and noise.

pc = pc(idx);

comment: rearranging the power levels

3.4. CELL-DRIVEN ALGORITHMS: COORDINATED VS. UNCOORDINATED 27

Finally, the throughput of each cell can be calculated as follows:

Rc =

N∑n=1

log2 (1 + pnc /λnc ) (3.19)

3.4.2 Coordinated

In the Coordinated Algorithm it is expected that a better service is offered to the MUEs -

the users linked to the network of the provider.

In this algorithm, the strategies of the PBSs continue to be calculated as in the Uncoordi-

nated algorithm (subsection 3.4.1). However, the MBSs power distribution must suffer some

changes, and so it will be calculated as indicated in [18] through the optimization of the fol-

lowing problem:

maxp1

N∑n=1

log2

(1 +

pn1 · |hn1 |2

σ2 +∑C

j 6=1 pn,SEj · |hnj |2

)

s.t.N∑n=1

pn1 ≤ P1 (3.20)

pn1 ≥ 0

In this case it is assumed that the MBSs receive the information of the power distribution that

each PBS is going to use in the next TTI (pn,SEj ) through the X2 interface, where SE stands

for Stackelberg Equilibrium. Hence, pSE is the Best Response of the PBSs to the environment

characteristics felt by its UEs in the previous TTI.

It is also assumed that MBSs have access to the value of the fading channel (hj,n) on the nth

carrier from the transmitter j to the MUE that was previously scheduled to use that carrier.

Contrary to what was expressed in [18], this problem is convex, and so it can be solved with

the help of the Water-Filling algorithm [31] (code 3.4.1). The complete demonstration of the

convexity of the problem is presented in Appendix B.


3.4.3 Overview of the Approach

In Figure 3.7 an overview of this approach is presented:

Figure 3.7: Cell-Driven Algorithm: chooses the new state of each PRB while focusing the overall offered throughput

of the cell

3.5 User-Driven Algorithms: Coordinated vs. Uncoordinated

The User-Driven Algorithms will be focused in each user overall optimization. The algorithms

are quite similar to the previous ones (section 3.4), but instead of trying to maximize the over-

all throughput of the cell (equation 3.16) they will focus on maximizing the throughput of

each user of the cell.

With this new approach a drop in the overall performance of the cell is expected. Moreover,

it is also expected that the users exposed to bigger interference get a better service from the

cell. In the Cell-Driven approach (section 3.4), a user with a small SINR would be allocated,

by the PF Scheduler, to one or more PRBs, but could end up not being served, since the focus

of the problem was the best overall offer and not to better serve each UE.

In the next subsection (3.5.1) only the changes to the previous algorithms will be reported. If

a step in the algorithm is not reported it means it stays equal to the same step in subsections

3.4.1 or 3.4.2.

3.5. USER-DRIVEN ALGORITHMS: COORDINATED VS. UNCOORDINATED 29

3.5.1 Uncoordinated & Coordinated

This new approach (equation 3.21 and Figure 3.8) will divide the PRBs by its UEs before

running the optimization. It will treat PRBs from different users within a cell separately,

with a similar optimization algorithm to the one shown in equation 3.21.

The optimization problem is now:

maxpc,u

Nu,t∑n=1

log2

(1 +

pnc · |hnc |2

σ2 +∑C

j 6=c pnj · |hnj |2

)

s.t.

N∑n=1

pnc ≤ Pc,u,t (3.21)

pnc ≥ 0

Where Nu,t is the number of PRBs allocated to user u in TTI t and where Pc,u,t = Nu,t ∗

PwrPerPRB, with PwrPerPRB = Pc/N .

The inclusion of the t dependence on P and N when compared to the Cell-Driven Ap-

proach(section 3.4) is made with the intent of better reflecting the variance of these values

over time.

Figure 3.8: User-Driven Algorithm: chooses the new state of each PRB while focusing in optimizing the offered

throughput to each user who was scheduled to be served in the current TTI.


Due to similarities with the Cell-Driven Approach (section 3.4), it is easy to see that the new

optimization problem is also convex. Therefore, the same optimization technique (Water-

Filling [31]), with the pseudo-code scratched in 3.4.1, will be used.

3.6 Conclusion of the Technical Approach

With the increase in the number of Pcells in the same Mcell area it will be possible to un-

derstand how the algorithms behave when facing different PBSs densities. It is important to

notice that due to the design of the cells, a Mcell has an area of around 72× 103[m2] whereas

a Pcell has around 5× 103[m2] which corresponds to around 7% of the area of a Mcell.

The number of UEs per Mcell and Pcell can be increased to understand how the cells would

behave with higher user densities.

At the end a good analysis of the trade-off achieved with the introduction of the coordinated

complexity is expected.

Chapter 4

Results and Discussion

In this chapter the four algorithms presented in chapter 3 will be tested and compared when

facing different scenarios. The use of only one Mcell-region in the simulations will be con-

sidered. Moreover, unless referred, the specifications presented in the previous Chapter are

taken into account. The analysis were done by averaging the behaviour of 100 scenarios with

the same base characteristics. The number of scenarios with the same base characteristics

was limited by the computational weight of the simulator, see Appendix C.

In the first three sections of this chapter (sections 4.1,4.2 and 4.3) the use of a closed access

policy (section 2.2.1) was considered. The use of an open access policy would make it impos-

sible to control the number of users connected to each BS. In section 4.4 the benefits of using

an open access policy will be tested.

31

32 CHAPTER 4. RESULTS AND DISCUSSION

4.1 Pcell Density Analysis

Firstly, the way the amount of interference in the network can affect the UEs performance will

be analysed. As this work is focused in DLink connections, the interferers (transmitters) are

the BSs and not the UEs. Therefore, the amount of interference in a cell-region is controlled

by the number of neighbouring BSs in that region.

In every Pcell-region 10 UEs were placed, whereas 20 UEs were placed all over the Mcell-

region. To guarantee that this number was fixed, the attachment of the users to the cell was

done automatically (closed access policy).

Concerning the scheduling of the users, the use of a PF scheduler that tries to fairly schedule

the UEs and the use of a RR scheduler was analysed and compared. The tests using RR were

made to compare how the algorithms would behave when facing the exact same schedules, for

the same scenarios.

Figures 4.1 and 4.2 show the evolution of the average throughput offered to the MUEs and

PUEs when the number of PBSs varies in the system, while using the PF scheduler. On the

other hand, figures 4.3 and 4.4 show the dependence of the average throughput offered to the

UEs while using the RR scheduler.

Figure 4.1: Dependence of the average throughput offered to the UEs of the MBS with the number of PBS: PF

scheduler.

4.1. PCELL DENSITY ANALYSIS 33

Figure 4.2: Dependence of the average throughput offered to the UEs of the PBSs with the number of PBS: PF

scheduler.

Figure 4.3: Dependence of the average throughput offered to the UEs of the MBS with the number of PBS: RR

scheduler.


Figure 4.4: Dependence of the average throughput offered to the UEs of the PBSs with the number of PBS: RR

scheduler.

In the simulation with a RR scheduler, the average throughput observed in the coordinated

algorithms (black and blue triangles, Figures 4.3 and 4.4) is always slightly higher or equal

to the average throughput achieved by the correspondent uncoordinated algorithm, as was

expected. On the other side, the simulations with a PF scheduler show better results when

using the uncoordinated algorithms, and never better results than the ones observed in the

previous case. This can be explained by the different nature of the algorithms and the PF

scheduler. While the former tries to maximize the offered throughput, the latter tries to fairly

homogenize it among all users, through time.

The simulations show that the user-driven algorithms (black triangle and red cross, Figures

4.1, 4.2, 4.3, 4.4) present a worse average offered service to the MUEs. In fact, the MUEs

are more affected by the introduction of more PBSs in the system. On the other hand, they

present a better average offered service to the PUEs, nearly equal to the one offered to the

MUEs by the MBS.

While the cell-driven algorithms benefit the Mcell users to the detriment of the Pcell users,

the user-driven algorithm offers a similar service to all the network users.

It is now important to analyse the way the worst served user gets affected by the number of

PBSs in the Mcell region. In the cases where there is more than one PBS in the Mcell region,

the average throughput of the worst served user in every Pcell will be taken into consideration:

4.1. PCELL DENSITY ANALYSIS 35

Figure 4.5: Dependence of the throughput offered to the worst served MUE with the number of PBS: PF scheduler.

Figure 4.6: Dependence of the throughput offered to the worst served PUE with the number of PBS: PF scheduler.


Figure 4.7: Dependence of the throughput offered to the worst served MUE with the number of PBS: RR scheduler.

Figure 4.8: Dependence of the throughput offered to the worst served PUE with the number of PBS: RR scheduler.

The evolution of the throughput offered to the worst served user (Figures 4.5 to 4.8) presents

characteristics quite similar to the ones of the average throughput offered to all users. Com-

paring the results obtained with the two schedulers (PF and RR) it is possible to state that

the worst served MUE and PUE are better served while using a PF scheduler.

4.2. INFLUENCE OF THE DISTANCE BETWEEN PBSs AND MBSs 37

4.2 Influence of the distance between PBSs and MBSs

In this section the way the distance between a PBS and a MBS can affect their performance

will be studied. To help making a fairer comparison between the different distance points, a

closed access policy was used. Thus, the number of UEs connected to each BS is fixed.

This study was made considering that the PBS was placed over the line of highest horizontal

gain of the antenna of the MBS, with an horizontal angle: ϕ = 0 (Figure 3.3). Eleven

equidistant points over that line were considered, where the first step (step 0 ) corresponds to

the point of minimal distance between a PBS and a MBS (see subsection 3.1.4). Figure 4.9

shows a graphical representation of the scenarios tested.

Figure 4.9: Graphical representation of the tested scenarios.


Firstly the average throughput offered to the MBS and PBS users will be analysed:

Figure 4.10: Effect of the distance between pico and macro BSs on the average throughput offered to the MUEs: PF

scheduler.

Figure 4.11: Effect of the distance between pico and macro BSs on the average throughput offered to the PUEs: PF

scheduler.


Figure 4.12: Effect of the distance between pico and macro BSs on the average throughput offered to the MUEs: RR

scheduler.

Figure 4.13: Effect of the distance between pico and macro BSs on the average throughput offered to the PUEs: RR

scheduler.

In Figures 4.11 and 4.13 it is possible to see that the throughput offered to the pico users

increases with the distance between BSs. This is caused by the increase of the PL between

PUEs and MBS, contributing to the decrease of interference power received by the PUEs. The

PUEs attached to cells using the cell-driven algorithms tend to stabilise and then start to lose

some performance with distance. This happens because the absence of high interference from


the MBS makes the cell-driven algorithms to serve with higher transmission power the PUEs

with lower PL, while the user-driven algorithm will equitably serve all the UEs of each PBS,

regardless of its PLs.

Finally, the effect of the distance in the average throughput offered to the worst served user

will be analysed.

Figure 4.14: Effect of the distance between pico and macro BSs on the average throughput of the worst served MUEs:

PF scheduler.

Figure 4.15: Effect of the distance between pico and macro BSs on the average throughput of the worst served PUEs:

PF scheduler.


Figure 4.16: Effect of the distance between pico and macro BSs on the average throughput of the worst served MUEs:

RR scheduler.

Figure 4.17: Effect of the distance between pico and macro BSs on the average throughput of the worst served PUEs:

RR scheduler.

The curves obtained for the worst served user have the same characteristics than the ones

obtained for the users average throughput. However, a big decrease in the mid-distance for

the user-driven algorithms is observed. This is provoked by the natural behaviour of this

algorithm that tries to serve well even the UEs in bad conditions, which ends up feeding

more interference to the other cells. Since this is the point where the PBS is more central


to the Mcell-area, thus allowing higher interference in certain channels, this will lead to the

deterioration of the performance of the MUEs.

4.3. THROUGHPUT VARIATION WITH THE NUMBER OF USERS PER PBSs 43

4.3 Throughput variation with the number of users per PBSs

In this section the way the throughput is affected by the variation of the number of users

attached to a PBS, while the number of users attached to the MBS is maintained constant,

(number of MUEs=20) will be analysed.

Only one PBS was placed in the network while the number of PUEs was altered between

4 and 16. To obtain the average values, 100 simulations with the same characteristics were

considered. To fix the number of UEs in each cell a closed access policy was used, as in the

previous sections of this chapter.

As previously, the analysis of the variation provoked by changing the number of UEs connected

to a PBS will be made through the evaluation of the average throughput offered to the users

of each cell (Figures 4.18 and 4.19) and the average throughput that was offered to the worst

served user (Figure 4.20 and 4.21).

Figure 4.18: Effect of the number of UEs attached to the PBS on the average throughput offered to the UEs connected

to the MBS


Figure 4.19: Effect of the number of UEs attached to the PBS on the average throughput offered to the UEs connected

to the PBS

Figure 4.20: Effect of the number of UEs attached to the PBS on the average throughput of the worst served MUEs

4.3. THROUGHPUT VARIATION WITH THE NUMBER OF USERS PER PBSs 45

Figure 4.21: Effect of the number of UEs attached to the PBS on the average throughput of the worst served PUEs

Through the analysis of the graphics it is possible to see that the throughput of the MUEs

(Figures 4.18 and 4.20) seems to oscillate over the same values with the variance of the number

of PUEs. This behaviour was expected, since the interference focus is the PBS and not the

PUEs. The oscillations show the same behaviour regardless of what the used algorithm is,

which indicates that it is provoked by the scenarios and not by the algorithms. With a higher

number of simulations the average throughput of the MUEs would probably tend to a fixed

value.

It can also be seen that the average throughput of the PUEs tends to follow the curve that

reflects the inverse proportionality (ie. when the number of PUEs doubles the throughput

offered to each of them drops to half.).

It is also important to note that, to have equal values of average throughput offered to its users

and worst served user throughput for both Macro and Pico cells, the ratio of PUEs/MUEs

should be around 5/20 = 0.25 for the cell-driven algorithms and around 10/20 = 0.5 for the

cell-driven algorithms.


4.4 Impact of different Attachment Functions

In the present section the average throughput offered to each user through 100 TTIs was

analysed when testing different attachment techniques.

In the previous analysis the users were distributed over the cells and automatically attached

to the BS of that cell, creating scenarios where a MUE would be in a PBS cell area suffering

high interference from that BS. To avoid scenarios were that would be possible, two different

attachment functions were tested.

In the first algorithm, PBSs ”absorb” all the MUEs that are at a close range from them.

In the forward graphics this algorithm is represented by purple and green colours (Figures

4.22, 4.23, 4.24, 4.25). The former to a distance of absorption of 30 meters and the latter

corresponds to a distance of absorption of 40 meters. The second algorithm is presented in

Appendix A and will be used with a SINR threshold (step 4) of 10 dB (dark yellow) and 15

dB (light blue). This algorithm will be hereinafter referred to as the power ratio criterion

algorithm.

In the next plots the dark blue line corresponds to the result obtained through the use of a

closed access policy, as in the previous sections of this chapter. Since the analysis is focused in

an open access policy the users were considered as network users and not cell users. Therefore,

the analysis are made considering all UEs as equals.

Figure 4.22: Average throughput offered to the worst served network UE for the uncoordinated user-driven algorithm.

4.4. IMPACT OF DIFFERENT ATTACHMENT FUNCTIONS 47

Figure 4.23: Average throughput offered to the worst served network UE for the uncoordinated cell-driven algorithm.

The results obtained, for the average throughput offered to the worst served UE in the network

for the uncoordinated cell-driven algorithm (Figures 4.23), show that both power ratio crite-

rion algorithms (dark yellow and light blue marks) present better results than the obtained

with a closed access policy. The distance criterion present similar (purple mark, cell-driven

algorithm) or worst results to the ones obtained with the previously used attachment tech-

nique (dark blue line). On the other hand, the uncoordinated user-driven algorithm (Figures

4.22) only presents better results for the open access policies when there are more than one

PBS in the cell area.

The use of the cell-driven algorithm with a power ratio criterion, with a threshold of 10 dB

(dark-yellow mark), seems to be the best choice concerning the average service offered to the

worst served UE.

It is important to note that, although here the results for the uncoordinated algorithms are

the only one presented, the coordinated ones showed the same behaviour.


Figure 4.24: Average throughput offered by the network to its UEs for the uncoordinated user-driven algorithm.

Figure 4.25: Average throughput offered by the network to its UEs for the uncoordinated cell-driven algorithm.

Figures 4.24 and 4.25 show that the network can benefit with the use of an open access policy

(subsection 2.2.1), where the BS the UE is connected to is determined according to the con-

dition of the channel between them. It is possible to see that the results obtained with the

use of a power ration criterion with a threshold of 10 dB (dark yellow marks) increases the

average service offered to the network UEs. It is notorious that while considering the aver-

age throughput offered to the network UEs the user-driven algorithm presents the best results.

4.4. IMPACT OF DIFFERENT ATTACHMENT FUNCTIONS 49

The access policies using a distance criterion (purple and green marks) showed better results

for the average offered throughput while using the user-driven algorithm. However, even for

that algorithm, they presented worst results while considering the average throughput offered

to the worst served user. Thus, using a fixed distance as threshold does not present a good

choice for an open access policy criterion.

In Appendix D it is possible to see how the different criteria tend to distribute the users

through the PBSs. For statistical analysis purpose, 5000 simulations were made for each case

scenario.


Chapter 5

Conclusions and Future Work

In this chapter, the results analysed previously (chapter 4) as well as the conclusion drawn

throughout the work will be summarized. All the results obtained in Chapter 4 were taken

by averaging the results of 100 scenarios with the same characteristics. More precise results

could be found with a higher number of scenarios, but the computational power and time

needed would be too big due to cache problems (Appendix C).

Coordinated architectures offer a more precise optimization of the system, at each iteration,

at the cost of more hardware complexity and delays provoked by the exchange of information

between BSs. The Stackelberg game [18,20] used had the purpose of benefiting the UEs of the

MBS in detriment of the UEs of the PBSs, as proven with the results obtained with the RR

scheduling (sections 4.1 and 4.2). However, when trying to introduce fairness into the system

through the use of a PF scheduler, the coordinated architecture presents worse results than

the uncoordinated one. This is caused by the opposed natures of both strategies (scheduler

and algorithm).

Both the presented algorithms (cell-driven and user-driven) work in completely different ways.

The former can be used to benefit the MUEs over the PUEs, for high density Pcells. In fact,

this can be an interesting feature, considering a closed access policy, where the network

provider prefers to better serve its users over the private UEs of a Pcells. The latter offers a

similar throughput to all the network, for high density Pcells. These opposite behaviours can

have different implementations, both interesting to the system.

Taking into consideration a closed access policy, the network provider does not have any

interest in harming its UEs while protecting the private UEs of the PBSs. Therefore, the

cell-driven algorithm seems to be the better choice. It offers a better service to the MUEs

51

52 CHAPTER 5. CONCLUSIONS AND FUTURE WORK

(section 4.1), presents high robustness against the distance between PBS and MBS (section

4.2) and also presents better results for the worst served MUE. Hence, this makes it the most

effective approach from the point of view of the network provider.

The use of an open access policy happens when the network provider wants to increase the

service capacity in a small zone of the network (HotSpot). When that happens, the interest

of the provider is to equally serve the PUEs and MUEs, since all of them are network UEs.

The user-driven algorithm showed that same characteristic when tested with a closed access

policy with high density Pcells. The cell-driven algorithm would need that the ratio between

the number of PUEs and MUEs was equal or lower than 1/4 to present similar average results

to both PUEs and MUEs (section 4.3).

The results obtained show that the network can benefit with the use of an open access policy,

where the attachment criterion is based on a power ratio. The cell-driven algorithm continues

to present the best response when trying to increase the average throughput offered to the

network users. However, when taking into consideration the protection of the worst served UE

of the network, the use of the user-driven algorithm seems to be the best approach possible.

Although interesting, the values of throughput achieved in this work are quite low when

compared with the expected values for a LTE/LTE-Advanced system [6]. Nevertheless, it is

important to notice that some network characteristics were chosen to provoke the worst-case

scenario. Changing the data traffic model from Full-Buffer to a Burst Traffic model would

create a more realistic network with higher throughputs, since the UEs would not always

have outstanding data to receive, thus leading to less congestion in the BSs, which would

then liberate more PRBs to each UE when needed.

As, a future work, it would be interesting to try to find a net attachment criterion capable

of combining both the power ratio and the ratio between the number of PUEs and MUEs.

Then, the algorithm used to the optimization of the system would also depend on the results

of the attachment criterion.

The use of different frequency reuse schemes would also be interesting to test. Motivated by

the frequency liberation, promoted by the substitution of the analog television for the Digital

Terrestrial Television, the use of completely orthogonal frequency bands in both MBSs and

PBSs can lead to great improvements in the reachable throughput. Improvements can also be

achieved with the use of more complex frequency reuse schemes, as the Soft Frequency Reuse

(SFR) scheme, which divides them into two layers: 1. The UEs, placed close to the MBS, use

53

all the spectrum range, with low transmission power; 2. The UEs, placed in the border of the

Mcell, use a specific spectrum range, orthogonal to the ones used by the nearby cells in their

border zones, with high transmission power.

The introduction of mobility in the scenarios would also be interesting to test. In this case a

new tier could be introduced in the algorithm, as the one presented in [18]. The tier presented

in that work used a Reinforcement-Learning mechanism to help the MBSs achieve better bit

rates, through the learning caught from the previous behaviours of the other network agents.

54 CHAPTER 5. CONCLUSIONS AND FUTURE WORK

Appendix A

UE Attachment Algorithm

STEP 1:

• calculates which is the cell that offers a higher receiving power to the UE.→ C1

• calculates which is the cell that offers the second higher receiving power to the UE.→ C2

STEP 2:

if C1 is a Pico do

UE⇐⇒ C1.

EXITS

else do{

CONTINUES to STEP 3

STEP 3:

if C2 is a Macro do

UE⇐⇒ C1.

EXITS

else do{

CONTINUES to STEP 4

STEP 4:

calculates what the SINR would be if only C1 and C2 existed on the network and if the

UE was connected to C1 (the Macro).

55

56 CHAPTER A. UE ATTACHMENT ALGORITHM

if SINR > 10dB do

UE⇐⇒ C1.

EXITS

else do{

CONTINUES to STEP 5

STEP 5:

estimates the distance between C2 and the UE, considering that it is in LOS → r.

if r > 40m do

UE⇐⇒ C1.

EXITS

else do

UE⇐⇒ C2.

EXITS

Where, ⇐⇒ means: ”is ATTACHED to”.

Appendix B

Convexity of the Utility Functions

The convexity of the utility functions, including the utility function of the MBS 1 on the

Coordinated Cells Architecture is proven in this appendix. From the optimization problem

in chapter 3 the utility function B.1 is obtained:

− u(p11, . . . , p

N1 ) = −

N∑n=1

log2

(1 +

pn1 · |hn1 |2

σ2 +∑C

j 6=1 pn,SEj · |hnj |2

)(B.1)

Where each |hnj |2 depends only on the user that the PF scheduler attached to the PRB n in

the TTI that is being evaluated. Consequently, C1 = |hn1 |2 ≡ const. pn,SEj = BRj(pn−j) is

the Best Response function of the player j according to the previous state of its opponents

(equations 3.17 and 3.18) and where SE stands for Stackelberg Equilibrium. In this way,

pn,SEj are constants of the problem, since they do not change during the optimization of the

MBS 1 service. Consequently C2 = σ2 +∑C

j 6=1 pn,SEj · |hnj |2 ≡ const.

By re-writing equation B.1, equation B.2 is obtained:

− u(p11, . . . , p

N1 ) = −

N∑n=1

log2 fn (B.2)

Where fn is an affine function (equation B.3):

fn(x) = b+ x · a

a =C1

C2, b = 1, x = pn1

(B.3)

57

58 CHAPTER B. CONVEXITY OF THE UTILITY FUNCTIONS

The g(x) = − log2(x) function is a convex function, since it is C2 and

∇2g(x) = − d2

dx(log2(x)) = − d

2

dx

(1

x · ln(2)

)=

1

x2 · ln(2)> 0∀x (B.4)

Where h(x) = g ◦ f(x) = − log2(fn) also convex, due to the convexity-preservation of a com-

position function (g ◦ f) when g is a convex function and f an affine function, as presented

by Boyd and Vandenberghe in [32].

Finally, u(p11, . . . , p

N1 ) =

∑Nn=1 h(pn1 ). Moreover, since the sum of convex functions preserves

the convexity of the function [32], it is proved that u(p11, . . . , p

N1 ) is a convex function, contrary

to what was presented in [18].

Appendix C

Number of Scenarios per Sample

Throughout the work, samples of 100 scenarios were averaged to obtain the characteristic

behaviour of a certain group of scenarios. As stated previously, this number was limited by

time and computational power. In the present Appendix the scenario with one PBS in the

Mcell-area using the uncoordinated cell-driven algorithm was tested with different number

of scenarios in the samples. In order to do that, 6640 independent scenarios were simulated.

Following, 20 sets of scenarios were created, 4 with 1000 scenarios, 4 with 500 scenarios, 4

with 100 scenarios, 4 with 50 scenarios and 4 with 10 scenarios. The average throughput

offered to the MUEs and PUEs of each set was then calculated and is presented in Figure C.1

and C.2. It is important to note that the x axis scale is logarithmic.

59

60 CHAPTER C. NUMBER OF SCENARIOS PER SAMPLE

Figure C.1: Obtained value of the average throughput offered to the UEs of the MBS, with different number of scenarios

per sample.

Figure C.2: Obtained value of the average throughput offered to the UEs of the PBS, with different number of scenarios

per sample.

The red marks represent samples with 100 scenarios as the ones used through the presented

work. The results show that a bigger number of scenarios should be assembled to each set

in order to obtain better average values. This variance is caused by the infinite number of

positions PBSs and UEs can have in the Mcell-area.

Appendix D

Open Access Policy Criteria:

Statistical Analysis

Here, the Statistical Analysis of the Number of PUEs taking in consideration the Open Access

Policy Criterion used, is shown

The criteria based on the distance from the PBS, drawn to give PBSs the ability to ”absorb”

the MUEs that are at a close (predetermined) distance from them, are analysed in Figures

D.1 and D.2.

Figure D.1: Statistical Analysis of the Open Access Policy Criterion (Distance: 30 m). (A) 1 Pcell in the Mcell-area.

(B) 2 Pcells in the Mcell-area. (C) 3 Pcells in the Mcell-area.

61

62 CHAPTER D. OPEN ACCESS POLICY CRITERIA: STATISTICAL ANALYSIS

Figure D.2: Statistical Analysis of the Open Access Policy Criterion (Distance: 40 m). (A) 1 Pcell in the Mcell-area.

(B) 2 Pcells in the Mcell-area. (C) 3 Pcells in the Mcell-area.

The plots show that, when using a 30 m distance criterion (smaller than the Pcell radius, see

3.1.4), more than 50% of the time, no MUE is ”absorbed” by the PBSs. On the other hand,

for the 40 m distance criterion (equal to the Pcell radius, see 3.1.4), the most common event is

the ”absorption” of 1 MUE (35% probability). In both cases there is less than 5% probability

of more than 3 MUEs being ”absorbed” by a PBS. The statistical results also show that the

probability of ”absorption” is quite independent from the number of PBSs in the Mcell-area.

The criteria based on the power ratio (Appendix A) are analysed in Figures D.3 and D.4.

Figure D.3: Statistical Analysis of the Open Access Policy Criterion (Power Ratio: 10 dB). (A) 1 Pcell in the

Mcell-area. (B) 2 Pcells in the Mcell-area. (C) 3 Pcells in the Mcell-area.

Figure D.4: Statistical Analysis of the Open Access Policy Criterion (Power Ratio: 15 dB). (A) 1 Pcell in the

Mcell-area. (B) 2 Pcells in the Mcell-area. (C) 3 Pcells in the Mcell-area.

63

The power ratio criteria show a more spread statistic, this happens because it will tend to

give few UEs to the PBSs if they are near the MBS and to give more UEs to the PBSs in the

cases where they are too far from it. For a threshold value of 10 dB (Figure D.3) the event

with more probability (±11% probability) is when there are 11 UEs connected to each PBS.

However, the tendency is to have less than 11 UEs connected to each PBS. The probability

of no UE being connected to the PBSs is quite high (±7%). Moreover, the results show that

less than 5% of the times the PBS receive more than 15 UEs, which is the case where PBSs

are (electromagnetically) too far away from the MBS. The results obtained for the threshold

value of 15 dB (Figure D.4) are different from the results obtained for the 10 dB power ratio

criterion by giving the PBSs a higher probability of accepting more UEs.

64 CHAPTER D. OPEN ACCESS POLICY CRITERIA: STATISTICAL ANALYSIS

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