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Resource Allocation and Interference Management for

LTE-Advanced Systems with Carrier Aggregation

By

Mohammed Saad Hassan ElBamby

A Thesis Submitted to the

Faculty of Engineering at Cairo University

in Partial Fulfillment of the

Requirements for the Degree of

Master of Science

in

Electronics and Electrical Communications Engineering

Faculty of Engineering, Cairo University

Giza, Egypt

2013



By


A Thesis Submitted to the Faculty of Engineering at Cairo University

in Partial Fulfillment of the Requirements for the Degree of

Master of Science in


Thesis Main Advisor: Prof. Dr. Khaled M.F. Elsayed Thesis Advisor: Dr. Ahmed Salah Ibrahim


Giza, Egypt

2013

iii



By


A Thesis Submitted to the Faculty of Engineering at Cairo University

in Partial Fulfillment of the

Requirements for the Degree of

Master of Science in


Approved by the Examining Committee

______________________________________________________

Prof. Dr. Masoud B. Alghoniemy Member

______________________________________________________

Prof. Dr. Hebat-Allah M. Mourad Member

______________________________________________________

Prof. Dr. Khaled M.F. Elsayed Thesis Main Advisor

______________________________________________________


Giza, Egypt

2013

iv

Acknowledgements

First of all, I must thank my God for his great mercy supporting me all the

way till the end. If it weren’t for his help, I wouldn’t have reached this point.

I wish to express my utmost gratitude to my supervisors, Prof. Dr. Khaled

Mohamed Fouad Elsayed and Dr. Ahmed Salah Ibrahim, the 4G++ project

team and other researchers, who all contributed to this work and were always

ready to provide help.

I would like also to thank my parents who have been a backbone during my

whole life, in good and bad times, and were ready to support me whenever

needed, my sisters and brothers for their continuous support and

encouragement during all working days and nights.

Lastly, I offer my regards and blessings to all of those who supported me in

any respect during the completion of the project.

v

Abstract

Carrier aggregation is one of the promising features that enables expanding

the bandwidth of the Long Term Evolution-Advanced (LTE-A) system through

aggregating multiple LTE component carriers (CCs) to support high data rate

up to 1 Gbit/s. In this thesis, we formulate the downlink multi-CC resource

allocation problem in LTE-A (CA) systems as a transportation problem (TP).

The sub-bands on each CC represent the supply points whereas the users

requesting traffic represent the demand points. The cost of shipping from a

supply point to a demand point is set as a function of the proportional fairness

(PF) metric. Backward compatibility with the legacy LTE Release 8 (Rel-8) is

maintained by adjusting the cost of shipping to Rel-8 users to restrict them to

operate on a single CC. The results show that using Vogel approximation

method (VAM), which is a sub-optimal efficient method, provides near-

optimum results in terms of throughput and fairness and is shown to achieve

performance gains over a PF scheduler that handles multiple CCs in the

presence of both Rel-8 and LTE-A users.

Furthermore, when considering a multi-cell scenario, an appropriate resource

allocation method that aims at minimizing the inter-cell interference should be

used. We investigate different soft frequency reuse (SFR) schemes and discuss

how they should be applied in the presence of multiple carriers. In particular,

we propose two configurations for performing the frequency partitioning

process on the component-carrier level: local partitioning (LP) that individually

partitions each carrier between cell-center and cell-edge users, and global

partitioning (GP) that partitions at the level of the aggregate bandwidth. We

demonstrate that the LP method performs better when most of users are LTE-A

capable terminals, whereas if the majority is for the Rel-8 terminals, the GP

method is advantageous.

Finally we propose a novel distributed resource allocation scheme in an LTE

multi-cell system using an auction algorithm. In this scheme, the users at each

vi

cell bid for their demand of resources in a distributed manner by raising the

prices of favorable resources whereas the cell exchanges infrequent information

with the neighboring cells about the prices of the resources allocated to its cell-

edge users showing the importance of each resource to its cell-edge users. Each

cell uses this information to modify the bidding of its cell-edge users to the

corresponding resources in order to avoid inter-cell interference (ICI) by

prioritizing the users’ opportunity to be allocated to the necessary resources.

The scheme is shown to achieve significant gains in terms of cell-edge

throughput as compared to the case without pricing exchange. It is shown that

increasing the frequency of exchanging the prices improve the system

performance but at the expense of higher overhead.

vii

Contents

Resource Allocation and Interference Management for LTE-Advanced

Systems with Carrier Aggregation ................................................................... i

Acknowledgements ....................................................................................... iv

Abstract .......................................................................................................... v

List of Figures ................................................................................................ x

List of Tables ................................................................................................ xii

List of Abbreviations .................................................................................. xiv

List of Symbols ........................................................................................... xvi

Chapter 1. Introduction ................................................................................. 18

1.1 Contributions ....................................................................................... 20

1.2 Related Work ....................................................................................... 21

1.3 Thesis Outline ..................................................................................... 22

Chapter 2. Preliminaries ................................................................................ 23

2.1 LTE-Advanced Overview ................................................................... 23

2.2 LTE-A Radio Resource Management ................................................. 23

2.2.1 FDD and TDD Modes .................................................................. 24

2.3 Overview of Carrier Aggregation ....................................................... 25

2.3.1 Deployment Scenarios ................................................................. 26

2.3.1 Spectrum Scenarios ...................................................................... 27

2.4 System Model ...................................................................................... 28

2.4.1 CQI Reporting Method ................................................................ 29

2.4.2 Channel Model ............................................................................. 30

2.4.3 Modulation and Coding Schemes ................................................ 33

viii

Chapter 3. The Single Cell Resource Allocation as a Transportation Problem

........................................................................................................................... 35

3.1 Transportation Problem Basics ........................................................... 35

3.2 Mapping of the Resource Allocation Problem to a Transportation

Problem ......................................................................................................... 37

3.3 Solution Methods ................................................................................ 41

3.3.1 VAM Method Procedures ............................................................ 41

3.3.2 Integer Solutions Property ............................................................ 42

Chapter 4. CA-based ICIC Scheme in a Multi-Cell Resource Allocation

Problem ............................................................................................................. 44

4.1 Soft Frequency Reuse Schemes .......................................................... 44

4.1.1 Inter-Cell Interference Coordination ............................................ 44

4.1.1.1 Conventional Frequency Reuse ....................................................................45

4.1.1.2 Fractional Frequency Reuse .........................................................................45

4.1.2 Proposed Configurations .............................................................. 49

4.1.3 Power Ratio .................................................................................. 50

4.2 Masking Concept ................................................................................ 50

4.2.1 Effect of Masking on the Transportation Problem Cost .............. 51

Chapter 5. An Auction Approach to Resource Allocation with Interference

Coordination ...................................................................................................... 53

5.1 System Model ...................................................................................... 54

5.2 The Assignment Problem .................................................................... 55

5.3 Problem Mapping ................................................................................ 56

5.4 The Auction Algorithm ....................................................................... 57

5.5 Price Exchange Mechanism ................................................................ 59

Chapter 6. Performance Evaluation .............................................................. 63

ix

6.1 The TP-Based Scheme ........................................................................ 63

6.1.1 Simulation Assumptions .............................................................. 63

6.1.2 Single Cell Scenario ..................................................................... 64

6.1.3 Multi-Cell Scenario ...................................................................... 69

6.2 The Auction-Based Scheme ................................................................ 74

6.2.1 Simulation Assumptions .............................................................. 74

6.2.2 Simulation Results ....................................................................... 75

Chapter 7. Conclusions ................................................................................. 79

References ..................................................................................................... 81

x

List of Figures

Figure 2.1. LTE-A physical resource block structure ................................... 25

Figure 2.2. CA deployment scenarios: a) scenario 1; b) scenario 2; c)

scenario 3; d) scenario 4 (excerpted from [7]). ................................................. 27

Figure 2.3. Carrier aggregation spectrum configurations: a) intra-band

contiguous; b) intra-band non-contiguous; c) inter-band non-contiguous. ....... 28

Figure 3.1. Mapping of CA problem to a transportation problem ................ 38

Figure 3.2. Scheme flowchart ....................................................................... 40

Figure 4.1. Frequency reuse based ICIC schemes (excerpted from [3])....... 46

Figure 4.2. Three-cell layout ......................................................................... 47

Figure 4.3. Two SFR schemes (a) SFR-1 (b) SFR-2 .................................... 47

Figure 4.4. SFR-1 partitioning and the corresponding power levels (a) Local

partitioning (b) Global partitioning ................................................................... 48


partitioning (b) Global partitioning ................................................................... 49

Figure 4.6. Example for the masking concept ............................................... 52

Figure 5.1. An example for the Price Exchange Matrix (PEM) ................... 61

Figure 6.1. Average UE throughput and Fairness (100% of users are LTE-A)

........................................................................................................................... 66

Figure 6.2. Average UE throughput and Fairness (50% of users are LTE-A,

rest are Rel-8) .................................................................................................... 66

Figure 6.3. Average Rel-8 UE throughput and average LTE-A UE

throughput (50% of users are LTE-A, rest are Rel-8) ...................................... 67

Figure 6.4. VAM versus simplex method in obtaining average UE

throughput ......................................................................................................... 68

Figure 6.5. Average UE throughput versus percentage of LTE-A users for

different schedulers ........................................................................................... 68

Figure 6.6. Cells layout ................................................................................. 69

xi

Figure 6.7. Average geometric throughput versus cell-edge throughput for

different SFR schemes against reuse-1 scheme ................................................ 71

Figure 6.8. Performance under different load conditions of 20, 30 and 100

Mbps per cell for the different SFR schemes with a constant power ratio of 10.

........................................................................................................................... 72

Figure 6.9. Average cell-edge UE throughput for different schemes against

the percentage of LTE-A users ......................................................................... 73

Figure 6.10. Average cell-center UE throughput for different schemes against

the percentage of LTE-A users ......................................................................... 73

Figure 6.11. Cells layout ............................................................................... 75

Figure 6.12. Performance of the proposed scheme compared with the scheme

without exchange for different power ratios (price exchange each 10 sub-

frames) .............................................................................................................. 76

Figure 6.13. Geometric average throughput against cell-edge throughput for

the proposed scheme with for different exchange periods compared to the case

without price exchange ..................................................................................... 77

Figure 6.14. Performance of the proposed scheme compared with the scheme

without exchange and the scheme with full price exchange for different

exchange periods ............................................................................................... 78

xii

List of Tables

Table I. System Performance Requirements for LTE-A ............................... 23

Table II. Sub-band size in terms of carrier bandwidth .................................. 30

Table III. Path loss Model for C2 WINNER II Scenario .............................. 31

Table IV. Shadow fading parameters for C2 WINNER II Scenario ............. 32

Table V. Modulation and Coding Schemes [21] ........................................... 33

Table VI. Transportation problem parameters .............................................. 36

Table VII. Simulation parameters ................................................................. 63

Table VIII. Simulation parameters ................................................................ 74

xiii

List of Publications [1] M. Saad Elbamby and Khaled Elsayed, "A Transportation Problem based Resource Allocation Scheme for an LTE-Advanced System with Carrier Aggregation," in IEEE/IFIP Wireless Days 2012, Dublin, Ireland. [2] M. Saad Elbamby and Khaled Elsayed, "Performance Analysis of Fractional Frequency Reuse Schemes for a Multi-Cell LTE-Advanced System with Carrier Aggregation," -Submitted.

xiv

List of Abbreviations

AMC Adaptive Modulation and Coding CA Carrier Aggregation CBR Constant Bit Rate CC Component Carrier CQI Channel Quality Indicator CSI Channel State Information DL Downlink EESM Exponential Effective SINR Mapping eICIC Enhanced Inter-Cell Interference Coordination eNB enhanced NodeB FDD Frequency-Division Duplex FFR Fractional Frequency Reuse FFT Fast Fourier Transform FI Fairness Index GJ Gauss-Jordan GP Global Partitioning HARQ Hybrid automatic repeat request HetNets heterogeneous networks ICI Inter-Cell Interference ICIC Inter-Cell Interference Coordination ITU International Telecommunication Union LOS Line-of-Sight LP Local Partitioning LTE Long Term Evolution LTE-A Long Term Evolution-Advanced MCS Modulation and Coding Scheme MH Mobile Hashing MIMO Multi-Input-Multi-Output NLOS Non Line-of-Sight OFDMA Orthogonal Frequency Division Multiple Access PEM Price Exchange Matrix PF Proportional Fairness PFR Partial Frequency Reuse PRB Physical Resource Block PS Packet Scheduling QoS Quality of Service RF Radio Frequency

xv

RNTP Relative Narrowband Transmit Power RR Round Robin RRH Remote Radio Head RRM Radio Resource Management RSRP Reference Signal Received Power SB Sub-Band SFR Soft Frequency Reuse SINR Signal-to-Interference-plus-Noise Ratio TBS Transport Block Size TP Transportation Problem TTI Transmission Time Interval UE User Equipment UL Uplink VAM Vogel Approximation Method

xvi

List of Symbols

α Masking value β Masking scale factor 𝜂𝑗,𝑖 A 0-1 combinatorial factor equals 1 if the object i is assigned to

the person j in auction ϵ Auction bidding increment

𝑐𝑖.𝑗 Cost of transferring one unit from supply point i to demand point j in the transportation problem

𝐷 Number of demand points in the transportation problem

𝑑𝑗 Number of needed units at demand point j in the transportation problem

𝑑𝐵𝑃 The breakpoint distance

d Distance between the transmitter and receiver

ℰ𝑖 Set of eligible users to be assigned to a source point 𝑠𝑖 e Number of eligible users to be assigned to a source point ℱ𝑗 Set of component carriers for user j 𝑓𝑐 Center frequency

𝑓𝑗.𝑖 The benefit from assigning the object i to the person j in auction

ℎ𝑈𝐸 UE antenna height

ℎ𝑒𝑁𝐵 eNB antenna height L Number of component carriers N Number of cells in the system 𝑁𝑆𝐶 Number of subcarriers per physical resource block

n Auction problem size 𝑃𝑇 Total transmitting power per component carrier 𝑃𝐿𝑂𝑆 Probability of line-of-sight

𝑝𝑐 the total power of the cell-center portion

𝑝𝑒 the total power of the cell-edge portion

𝑅𝑖.𝑗 The instantaneous rate of user 𝑢𝑗 in the source point 𝑠𝑖

𝑅�𝑖.𝑗 The average rate of user 𝑢𝑗 over source point 𝑠𝑖

𝑅�𝑗 The historical total average rate for user 𝑢𝑗 over all component carriers

𝑅� geometric average rate

xvii

𝑟𝑗 Price of object j in auction

𝑆 Number of supply points in the transportation problem

𝑠𝑖 Number of available units at supply point i in the transportation problem

𝑠ℎ Higher values scaling factor in auction

𝑠𝑙 Lower values scaling factor in auction U Total number of users in the system 𝒰 Set of users in the system V Number of physical resource blocks per component carrier

𝑤𝑐 Cell-center power share factor 𝑤𝑒 Cell-edge power share factor 𝑥𝑖.𝑗 Number of assigned units from supply point i to demand point j in

the transportation problem

18

Chapter 1. Introduction

In order to cope with the increasing demand for high data rate requirements of IMT-

Advanced, as defined by the International Telecommunication Union (ITU), the Third

Generation Partnership Project (3GPP) has introduced carrier aggregation (CA) as one

of the Long Term Evolution-Advanced (LTE-A) key features that could achieve this

aim [1]. With CA, multiple carrier chunks, namely component carriers (CCs), are

aggregated to form a larger bandwidth in which a user can be scheduled

simultaneously on multiple CCs, thus higher data rates can be achieved.

An important problem that arises in resource scheduling in CA is the backward

compatibility. Backward compatibility should be guaranteed such that a legacy LTE

Release 8 (Rel-8) user equipment (UE), which naturally only supports a single CC,

should still be able to coexist with Rel-10 UE (LTE-A UE), which can be scheduled

on the entire aggregated CCs. This requires each of these CCs to have the physical

characteristics and bandwidth configurations of a regular LTE carrier.

Furthermore, the downlink radio resource management (RRM) of LTE-A should

have some new functionalities and improvements to support carrier aggregation. For

example, load balancing between Rel-8 users and LTE-A users should be considered

in a way to enhance both throughput and fairness under different load conditions

among the existing CCs. In addition channel-aware packet scheduling (PS) is required

to exploit the channel diversity not only between the users across a given CC but also

for a given user across multiple CCs to provide frequency domain scheduling gain.

This adds a new dimension to inspect in the scheduling and resource allocation which

is the CC dimension in addition to the time and frequency dimension typically

associated with orthogonal frequency division multiple access (OFDMA)-based

wireless access systems.

The most limiting factor that affects the cell-edge performance of the cellular LTE

system is the inter-cell interference (ICI) [2] between users in different cells being

served in the same physical resource block (PRB). Although the aggressive spectrum

reuse (reuse-1) achieves the highest system capacity by allocating the whole available

19

resources to the users in each cell, it causes the largest degradation in signal-to-

interference-plus-noise ratio (SINR) due to the ICI, especially at the cell edge where

users of two neighboring cells may share the same resource, which results in high ICI

levels and severe decrease in the cell-edge throughput. Several interference

management solutions are made [3] [4] to improve the cell edge throughput including

the frequency reuse concept which divides the system into “patterns” in which each

pattern contains more than one cell. The total frequency resources are then divided

between the cells of a certain pattern and re-used in the other patterns. This reduces

the interference levels significantly at the expense of the reduction in the available

bandwidth, since each of the cells uses only a subset of the resources. To strike a

balance between the need of a high system throughput and sufficient cell-edge spectral

efficiency, the concept of fractional frequency reuse (FFR) is presented. Using this

concept, some of the available PRBs are assigned to the cell-center users, typically in

a reuse-1 manner, whereas the rest are divided between the edge users of the adjacent

cells. Since the whole resources can be used in the cell-center, they should be of a

lower power level than those allocated in the cell-edge to avoid interference on the

neighboring cells. By the use of this scheme, the cell-center users can benefit from

being able to use all of the available resources whereas only cell-edge users use subset

of the resources, but this subset is used only once per one pattern, thus the ICI is

minimized.

In the presence of multiple carriers and users with different capabilities, carrier

aggregation is not only deployed as a capacity-boosting technique, but it can also be

used as an interference coordination scheme to alleviate the interference from

neighboring cells and hence improve the cell-edge efficiency. Herein, we consider the

deployment of the soft-frequency-reuse (SFR) scheme, which is an FFR method

commonly used in LTE systems, in the existence of multiple carriers with the aim of

minimizing ICI without much affecting the cell-center throughput.

20

1.1 Contributions

First, this work proposes a novel resource allocation scheme for a multi-carrier

LTE-A system based on the transportation problem. The cost of shipment in the

transportation problem is used to model an allocation that considers the proportional

fairness metric of the users in a global way. The formulated transportation problem is

converted to a linear programming problem and solved using both the exact simplex

solution and the Vogel Approximation Method (VAM). The VAM solves the problem

efficiently and gives near-optimum results as compared with the simplex method but

in a much shorter time [5]. We show that the scheme is an efficient solution to obtain

the resource block allocations for both LTE-A users and Rel-8 users coexisting in a

single-cell scenario. The proposed scheme is shown to achieve performance gains

compared with a proportional fairness (PF) scheduler that is adapted to allocate

through multiple CCs. Then, we extend the solution to a multi-cell scenario to

investigate the appropriate SFR coordination scheme in the LTE-A system operating

with CA for different users’ type conditions and partitioning methods. In particular,

we propose and compare two methods of partitioning the available resources. One

method performs the partitioning on each CC separately (local partitioning (LP))

whereas the other considers the whole aggregated bandwidth as one segment and

perform the partitioning over it (Global Partitioning (GP)). To our knowledge, the

performance of SFR schemes with carrier aggregation is not investigated in the

literature.

Second, we introduce a novel inter-cell interference coordination (ICIC) scheme

based on the auction algorithm [6]. We propose a pricing exchange mechanism that

allows cells to exchange infrequent data about the resources allocated to their cell-

edge users. Each cell measures the interference on the resources used on its edge and

report to other cells how important are the highly interfered resources to it. Each cell

then modifies the bidding of its cell-edge users to these resources so that it increases

their chance to win important resources and reduce chances of winning resources that

are important to other neighbors.

21

1.2 Related Work

The performance gain of CA over independent carriers is evaluated in [8].

Simulation results for different traffic models show that CA can enhance the

throughput, fairness and latency comparing with independent carrier scenario. In [9],

different load balancing methods across CCs are investigated, it shows that using

Round Robin (RR) load balancing is better than mobile hashing (MH) to balance Rel-

8 users over CCs whereas LTE-A users are scheduled across the entire CCs. It also

shows that the proposed cross CC packet scheduling (PS) algorithm provides better

performance than independent scheduling per CC. An uplink (UL) resource allocation

framework for CA-based LTE-A systems is presented in [10]. Performance

evaluations results show that CA with specific CC selection algorithm improves

performance of the average and cell center users’ throughput, particularly in low load

traffic conditions. On the other hand, the cell edge user throughput of LTE-A UEs

maintains the same level of performance as Rel-8 UEs. In [11], the problem of

resource allocation in the IEEE 802.16 band-AMC Mode is modeled as an unbalanced

transportation problem and solved so that the total power is minimized with

proportional rate constraints between the users.

The FFR schemes are extensively discussed in the literature, we provide herein a

sample of some the most relevant works. In [12], the authors compare different FFR

schemes in OFDMA-based networks and show that the soft-frequency-reuse (SFR)

achieves higher spectrum efficiency than the partial-frequency-reuse (PFR). An FFR

scheme is introduced in [13] that divides the resources allocated to the cell-center

region and the cell-edge region not only by frequency sub-bands but also by time

slots. The performance of SFR in LTE networks under different load and power setups

is discussed in [15].

The auction algorithm is previously proposed in [6] as an efficient solution to the

symmetric assignment problem, and is shown in [16] to be a suitable solution for

parallel synchronous and asynchronous implementations. A resource allocation

algorithm based on the auction method for uplink OFDMA cellular networks is

22

proposed in [17] and is shown to offer near-optimal performance. It is also shown that

the scheme is well-suited to parallel and distributed implementations. In [18], the

authors consider the uplink interference problem in OFDMA-based femtocell

networks with partial co-channel deployment. The auction algorithm for macrocell

users and femtocell users is shown to independently reduce the inter- and intra-tier

inferences in the system better than the existing methods.

1.3 Thesis Outline

This thesis is organized as follows. In chapter 2 we give an overview of the carrier

aggregation spectrum scenarios and network deployment scenarios, and then we

describe the system model, channel model, and modulation and coding schemes used

in this thesis. In chapter 3 we briefly discuss the transportation problem, introduce the

resource allocation problem formulation as a transportation problem in a single-cell

scenario and then we present the solution methods to the transportation problem.

Chapter 4 discusses the multi-cell resource allocation scheme and explains the applied

SFR schemes. In particular, we illustrate the two proposed configurations to partition

the resources in the two SFR schemes adopted, and then we introduce the concept of

masking that is applied to the transportation problem to adjust it to different schemes

and configurations. In Chapter 5, we discuss the auction algorithm and discuss the

proposed auction based resource and interference management scheme and then we

introduce the proposed pricing exchange mechanism. Simulation parameters, results

and performance evaluation for the proposed schemes are presented in chapter 6.

Finally, chapter 7 concludes the thesis and discusses the possible future work to

extend this work.

23

Chapter 2. Preliminaries

2.1 LTE-Advanced Overview

The International Telecommunication Union (ITU) defined the IMT-Advanced

requirements which included further significant enhancements in terms of

performance and capability compared to legacy cellular systems, including the first

release of LTE. With the aim of reaching and even surpassing these requirements, the

3GPP worked on further evolution of their first release of the LTE standard. The key

goals for this evolution [14] are increased data rate, improved coverage, reduced

latency and spectrum flexibility. The key performance targets of LTE-A as compared

to LTE are illustrated in Table I.

Table I. System Performance Requirements for LTE-A

Target LTE LTE-A DL peak data rate 300 Mb/s 1 Gb/s UL peak data rate 75 Mb/s 500 Mb/s

DL Peak spectrum efficiency 16 (b/s/Hz) 30 (b/s/Hz) UL Peak spectrum efficiency 3.75 (b/s/Hz) 15 (b/s/Hz)

This evolution makes it possible to meet these requirements by the introduction of

new features such as carrier aggregation, enhanced inter-cell interference coordination

(eICIC) for heterogeneous networks (HetNets), and enhanced multiple antenna

transmission supporting up to eight downlink layers. These new features require

significant improvement of the UE, and pose various design challenges.

2.2 LTE-A Radio Resource Management

Radio Resource Management is used in LTE-A to ensure that the available

resources are allocated to users efficiently. It consists of the following levels:

1- Admission Control: in which the admission decision of a user is made according

to the user’s channel state, Quality of Service (QoS) requirements, and the

current cell load conditions.

24

2- CC Assignment: in this level, the admitted user is assigned one or more of the

available CCs according to the user’s terminal type and traffic requirement.

3- Packet Scheduling: after each user is assigned to its CCs, a packet scheduling

process starts that allocates the available PRBs to users. The PRB is the

minimum unit that can be allocated to a user at once in LTE and LTE-A

systems. The PRB structure is depicted in Figure 2.1. In the frequency domain,

it is equivalent to 12 subcarriers that span 180 KHz, 15 KHz each. In the time

domain, it consists of 7 OFDM symbols for the short Cyclic Prefix (CP) case

and 6 symbols for the long CP case. The length of a PRB in the time domain

equals 0.5 ms. It is worth mentioning that two consecutive PRBs in the time

domain, that is 1 ms, form one subframe. This subframe is defined as the

Transmission Time Interval (TTI) in LTE. An LTE frame has a total duration of

10 ms and consists of 10 TTIs.

4- Link Adaptation: in the link adaptation stage, a suitable Modulation and Coding

Scheme (MCS) is selected for the user to satisfy certain spectral efficiency

requirements and constrained by a certain Block Error Rate (BLER).

After selecting the proper MCS and the Multi-Input-Multi-Output (MIMO) mode (if

exists), layer 1 transmission is carried out on each CC separately.

2.2.1 FDD and TDD Modes

The uplink (UL) and downlink (DL) transmissions are normally duplexed in

frequency domain, Frequency Division Duplexing (FDD), or in time domain, Time

Division Duplexing (TDD). FDD systems typically use paired resources for the DL

and UL. That is why it is more suitable to voice applications in which DL and UL

traffic is nearly symmetric. TTD-based systems allow users of DL and UL to share the

same resource but at different times. It is typically used in data communications since

in this case, the UL and DL traffic are no longer symmetric.

25

Figure 2.1. LTE-A physical resource block structure

2.3 Overview of Carrier Aggregation

Carrier aggregation (CA) is one of the LTE-A Release 10 (Rel-10) main features.

LTE-A is designed to meet the peak data rates required by IMT-Advanced: 1 Gb/s for

the downlink and 500 Mb/s for the uplink [19]. This requires users’ access to a total

bandwidth up to 100 MHz. Since the maximum supported bandwidth in LTE is 20

MHz, bandwidth is expanded through aggregating up to five CCs. Moreover, CA is

26

designed to be backward compatible, meaning that both LTE Rel-8 and LTE-A user

equipment (UE) can be supported in the same CC deployed by the Rel-10 eNodeB

(eNB). Each CC should inherit the bandwidth configurations of the Rel-8 carriers, for

example, it should be in the size of 1.4, 3, 5, 10, 15, or 20 MHz which are the typical

LTE carrier sizes. Moreover, different carriers may be in different sizes, giving

operators flexibility in forming the required bandwidth subject to the available

spectrum constraints. Such spectrum compatibility is of critical importance for a

smooth, low-cost transition to LTE-Advanced capabilities within the network.

2.3.1 Deployment Scenarios

CA can be implemented using different network deployments, as shown in

Figure 2.2, assuming only two CCs [7]. These cases can then be extended to a larger

number of CCs for practical implementations as well as deployments with mixed

scenarios. The first scenario, depicted in Figure 2.2-a, is when eNBs use the same

beam patterns; CC1 and CC2 cells are co-located and overlaid, providing nearly the

same coverage. This is a likely scenario when the two CCs are of the same band and

hence span the same coverage area. Figure 2.2-b shows the second deployment

scenario when the coverage of a CC is larger in area than another CC. This often

occurs when one of the CCs is of a smaller frequency than the other one, or when the

power levels of the carriers are not the same (e.g. for interference management

purposes). In this case, the CC with lower frequency (or higher power) will have a

larger coverage area. Note that higher throughput is expected at areas where both CCs

exist as users can benefit from being allocated resources from multiple CCs. The third

scenario, in Figure 2.2-c is when CCs are different in directions (patterns). This may

be because CCs are used in cell with different number of sectors (e.g., CC in three-

sectored or six-sectored cell), or in deployments with shifted antenna beams direction

to improve throughput at cell boundaries. CA gives higher throughput with areas

where CCs overlap. The last case takes the advantage of CA in the sense that not each

spot should be covered with all CCs. So a CC is providing a macrocell coverage to the

whole cell whereas remote radio head (RRH) cells (connected to the eNB through

27

optical fiber cables) are placed inside this macrocell to enhance throughput at areas

with high traffic using different set of CCs, as depicted in Figure 2.2-d. Choosing an

appropriate scenario depends on the nature of the area to be covered; covering of an

urban area is different than that of a suburban or rural area. The existence of hot spots

may also affect the deployment.

Figure 2.2. CA deployment scenarios: a) scenario 1; b) scenario 2; c) scenario 3; d)

scenario 4 (excerpted from [7]).

2.3.1 Spectrum Scenarios

Due to the scarcity of radio spectrum, there are different spectrum scenarios where

CA can be used. The CA may be intra-band (CCs are located at the same band) or

inter-band (CCs are located at different bands). CCs in the intra-band CA may be

contiguous, as in Figure 2.3-a or non-contiguous as in Figure 2.3-b, depending on the

spectrum availability. Figure 2.3-c depicts the inter-band CA (sometimes denoted as

spectrum aggregation) wherein CCs are in different bands and hence have different

radio propagation characteristics. This may require additional radio frequency (RF)

front-end complexity in the LTE-A user terminal. That’s why it is only adopted in the

Rel-10 for the downlink whereas the uplink uses only intra-band carrier aggregation.

Moreover, different CCs may in principle be of different bandwidths according to

spectrum availability and traffic needs. An example of this may be in the case of

28

macro-femto deployments where larger CCs typically used in macrocells than the CCs

used in the femtocells.

Figure 2.3. Carrier aggregation spectrum configurations: a) intra-band contiguous;

b) intra-band non-contiguous; c) inter-band non-contiguous.

2.4 System Model

We consider an LTE-A system consisting of N cells with a reuse factor of one under

SFR-based inter-cell interference coordination (ICIC). We focus on the resource

allocation for the downlink direction. The number of CCs in the system is equal to L.

Each CC has V physical resource blocks (PRB), where the PRB is the smallest

allocation unit for the scheduler. We assume a uniform transmitted power of 𝑃𝑇/𝑉 on

each PRB, where PT is the transmitting power of each CC. CCs operate in Frequency-

Division Duplex (FDD) mode, meaning that downlink and uplink transmission take

place in different CCs. Each cell in the system is comprised of an enhanced NodeB

(eNB) that serves a number of UEs, labeled as 𝒰 = {𝑢1,𝑢2, … ,𝑢𝑈} randomly dropped

in the layout. Assume that each UE 𝑢𝑗 for 𝑗 ∈ {1,2, … ,𝑈} is able to connect to a set of

CCs ℱ𝑗:

ℱ𝑗 = {𝑓1, 𝑓2, … , 𝑓𝑙} (1)

29

where

𝑙 = �1, for Rel‐8 UE,𝐿, for LTE‐A UE.

As Rel-8 UEs are capable of connecting to a single CC only, a load balancing

scheme is needed to distribute their load across CCs. Round Robin (RR) is used herein

to balance loads among CCs. It is shown in [9] that RR load balancing provides better

performance than the mobile hashing (MH) balancing scheme.

The Exponential Effective SINR Mapping (EESM) model [20] is used to combine

the SINR on each subcarrier to obtain the PRBs’ effective SINR, which is:

SINReff = − ln�1𝑁𝑆𝐶

�𝑒−SINR𝑖

𝑁𝑆𝐶

𝑖=1

� (2)

where SINRi is the SINR of subcarrier i and 𝑁𝑆𝐶 is the number of subcarriers on each

resource block.

Each user requests a specified number of bytes (generated in accordance with an

arbitrary traffic model) each subframe of 1 millisecond. The resource allocation is

dynamically performed on a subframe basis. Unsatisfied demand in a certain subframe

is accumulated to the added demand of the next subframe.

2.4.1 CQI Reporting Method

In the LTE downlink (DL) systems, UEs shall report the channel state information

(CSI) of their available resources to their serving eNB in terms of an index called the

Channel Quality Indicator (CQI) index [27]. This index has an integer value ranging

from 1 to 15, each corresponding to a certain SINR range. The higher the SINR value,

the higher the CQI index. The CQI reporting may be periodic or aperiodic. The eNB

choose if the CQI feedback from the UEs is periodic or not and also choose how

frequent this reporting should be. This is to balance between having an updated CSI

that can be used in a channel-aware scheduling while trying to keep the uplink

overhead minimized.

30

In a CA-enabled system, the user may be allocated resource blocks across different

CCs. Since reporting the CQI per-PRB over all CCs would place a large signaling

overhead for the UE uplink channel, 3GPP has defined a sub-band which is a number

of PRBs grouped together. In order to reduce signaling overhead, the CQI index will

be reported in terms of sub-bands (SBs) and one CQI value is reported representing

their average channel state. In addition to reporting the CQI for each SB, each UE also

reports one CQI value representing the average wide-band channel state of the whole

bandwidth. The size of each SB depends on the carrier bandwidth, i.e. the total

number of PRBs per single CC, and is shown in Table II.

Table II. Sub-band size in terms of carrier bandwidth

Carrier Bandwidth V (PRBs)

Sub-band Size k (PRBs)

6 – 7 NA

8 – 10 2

11 – 26 2

27 – 63 3

64 – 110 4

The CQI mapping and reporting method is explained in more detail in [27].

2.4.2 Channel Model

The WINNER II channel model for system level simulations is used in this thesis. It

generates a multidimensional channel matrix according to a certain propagation

scnario. The WINNER propagation scenarios are indoor office, large indoor hall,

indoor-to-outdoor, urban micro-cell, bad urban micro-cell, outdoor-to-indoor,

stationary feeder, suburban macro-cell, urban macro-cell, bad urban macro-cell, rural

macro-cell, and rural moving networks. In our channel model, we used the typical

urban macro-cell model, denoted as C2.

31

In typical urban macro-cell mobile station is located outdoors at street level and

fixed base station clearly above surrounding building heights. As for propagation

conditions, non- or obstructed line-of-sight is a common case, since street level is

often reached by a single diffraction over the rooftop. The building blocks can form

either a regular Manhattan type of grid, or have more irregular locations. Typical

building heights in urban environments are over four floors. Buildings height and

density in typical urban macro-cell are mostly homogenous.

The path loss model [33] used in the WINNER II for the typical urban scenario is

provided in Table III for the LOS and NLOS cases.

Table III. Path loss Model for C2 WINNER II Scenario

Scenario Pathloss

LOS 𝑃𝐿 = 40 log10(𝑑[M]) + 13.47 − 14 log10(ℎ𝑒𝑁𝐵)

−14 log10(ℎ𝑈𝐸) + 6 log10 �𝑓𝑐

5.0�

NLOS 𝑃𝐿 = (44.9−6.55 log10(ℎ𝑒𝑁𝐵))log10(𝑑[M]) + 31.46

+5.83 log10(ℎ𝑒𝑁𝐵) + 23 log10 �𝑓𝑐

5.0�

where 𝑑 is the distance between the transmitter and receiver in [m], 𝑓𝑐 is the center

frequency in [GHz], ℎ𝑒𝑁𝐵 is the eNB antenna height and ℎ𝑈𝐸 is the UE antenna

height.

The system level simulations require estimates of the probability of line-of-sight. For

the C2 scenario, the probability of being LOS is estimated based on assumptions and

approximations regarding the location of obstacles in the direct path, and it is

expressed as:

𝑃𝐿𝑂𝑆 = min �18𝑑

, 1� .�1 − exp �−𝑑

63�� + exp �−

𝑑63� (3)

The distribution of the shadow fading is log-normal, and the standard deviation for

the typical urban scenario is given in

32

Table IV.

Table IV. Shadow fading parameters for C2 WINNER II Scenario

Scenario Shadow fading std [dB] Applicability range

LOS σ = 4 σ = 6

10m < d < 𝑑𝐵𝑃 𝑑𝐵𝑃< d < 5km

NLOS σ = 8 50m < d < 5km,

where 𝑑𝐵𝑃 is the breakpoint distance and is defined as:

𝑑𝐵𝑃 = 4 ℎ𝑒𝑁𝐵 ℎ𝑈𝐸 𝑓𝑐𝑐

(4)

The eNB antenna height and UE antenna height ℎ𝑒𝑁𝐵 and ℎ𝑈𝐸 in the typical urban

model equal 25 m and 1.5 m, respectively, and 𝑐 = 3 x 108𝑚/s is the propagation

velocity in free space.

The WINNER channel model is generated in the time domain, it is then converted

into the frequency domain by the use of the Fast Fourier Transform (FFT) with a

sampling rate calculated as explained in the following steps.

Considering 𝑁𝐹𝐹𝑇 as the FFT size and 𝑁𝑆𝐶 as the number of subcarriers (equals 12 *

number of PRBs per CC) and ∆𝑓 as the subcarrier width (15 KHz), then:

𝑁𝐹𝐹𝑇 = 2⌈log2 𝑁𝑆𝐶⌉ (5)

where ⌈𝑥⌉ is the smallest integer not less than x. Then the FFT size 𝑁𝐹𝐹𝑇 obtained

from (5) is used to calculate the sampling rate 𝑓𝑠 as follows:

𝑓𝑠 = 𝑁𝐹𝐹𝑇 .∆𝑓 (6)

33

2.4.3 Modulation and Coding Schemes

The scheme changes the transmission parameters to match the time-varying channel

conditions aiming at achieving an efficient use of the available resources. This is done

by using Adaptive Modulation and Coding (AMC).

The supported modulation schemes are QPSK, 16QAM and 64 QAM. Higher

modulation schemes achieve higher data rates at the expense of increasing the

probability of error due to variations encountered by noise and interference. Thus,

each CQI reported by the UE mapped to a modulation scheme in which higher CQI

values (that is corresponding to higher SINR values) mapped to higher modulation

orders and also to higher coding rates thus certain effective code rate (ECR) is

maintained.

Table V [29] shows the modulation and coding scheme (MCS) corresponding to

each CQI value.

Table V. Modulation and Coding Schemes [21]

CQI Modulation ECR Coding Rate(x1024)

1 QPSK 0.0762 78

2 QPSK 0.1172 120

3 QPSK 0.1885 193

4 QPSK 0.3008 308

5 QPSK 0.4385 449

6 QPSK 0.5879 602

7 16QAM 0.3691 378

8 16QAM 0.4785 490

9 16QAM 0.6016 616

34

10 64QAM 0.4551 466

11 64QAM 0.5537 567

12 64QAM 0.6504 666

13 64QAM 0.7539 772

14 64QAM 0.8525 873

15 64QAM 0.9258 948

35

Chapter 3. The Single Cell Resource Allocation as a

Transportation Problem

In this chapter, we formulate the single-cell multi-CC resource allocation problem

as an unbalanced transportation problem where the users’ demand may exceed the

capacity of the sources. This essentially models a highly loaded system. The goal of

the optimization problem is to efficiently allocate the resources to the users in order to

maximize the overall system throughput and maintain fairness between users with

different conditions/capabilities. The aim of this study is to show the effectiveness of

the proposed scheme that is based on the transportation problem, and compare it

against a traditional PF scheduler that is tailored to cope with multiple carriers. Then,

in the next chapter, we apply this resource allocation scheme to a realistic multi-cell

LTE-A system and show how this scheme can be used as an interference-coordination

scheme.

This chapter is organized as follows; the first section briefly describes the

transportation problem basics and explains its parameters. In the second section, we

introduce our mapping of the resource allocation problem to a transportation problem.

The third section describes the different methods to solve the transportation problem.

3.1 Transportation Problem Basics

Transportation problem is one of the classical problems in the operations

research [30]. A transportation problem minimizes the cost of shipping of units from

supply points to demand points so that the needs of each demand point is satisfied and

each supply point serves within its capacity. It consists of number of source points and

demand points, and each of them contains possibly different number of units. It is

similar to the assignment problem but the supply and demand units need not be one.

The main parameters of the transportation problem are listed in Table VI. A balanced

transportation problem can be efficiently solved as linear programming optimization

problem. The problem may be unbalanced for one of the following two reasons. The

first is when the total number of units contained in the supply points is higher than the

36

total number of required units at the demand points. In this case, the problem is

balanced by adding an artificial dummy demand point with its demand value as the

excess available units in the supply. Shipping to the dummy demand point from any

supply will be of zero cost as actually this shipping will not occur.

Table VI. Transportation problem parameters

Parameter Description

𝑆 Number of supply points.

𝐷 Number of demand points.

𝑠𝑖 Number of available units at supply point i, i ∈ {1, 2, …, S}.

𝑑𝑗 Number of needed units at demand point j, j ∈ {1, 2, …, D}.

𝑐𝑖.𝑗 Cost of transferring one unit from supply point i to demand point j.

𝑥𝑖.𝑗 Number of assigned units from supply point i to demand point j.

The second reason that makes the transportation problem unbalanced is when the

total number of units in the supply points is less than those needed at the demand

points. The problem is balanced herein by adding an artificial dummy supply point

with its supply value as the shortage of the required units. The cost of shipping from

the dummy supply point to each demand point should reflect the waste in profits that

occurs when this demand point gets one unit less than the needed number of units.

After solving the problem, units that are shipped from this supply point will represent

the deficit in satisfying the demand. In both cases, this addition converts the problem

to a balanced transportation problem which is formulated as follows:

min𝑋��𝑥𝑖,𝑗𝑐𝑖,𝑗

𝐷

𝑗=1

𝑆

𝑖=1

subject to

(7)

37

�𝑠𝑖 = �𝑑𝑗

𝐷

𝑗=1

𝑆

𝑖=1

�𝑥𝑖,𝑗 = 𝑑𝑗 , ∀𝑗𝑆

𝑖=1

�𝑥𝑖,𝑗 = 𝑠𝑖 , ∀𝑖𝐷

𝑗=1

𝑥𝑖,𝑗 ≥ 0 , ∀𝑖,∀𝑗

where the above parameters are defined in Table VI.

3.2 Mapping of the Resource Allocation Problem to a

Transportation Problem

The mapping of supply points herein is related to the CQI reporting frequency

resolution. As the CQI feedback is reported on a UE-selected SB basis (described in

the previous chapter), the whole SB will have one CQI value and hence we choose

each SB inside a CC to represent a separate supply point containing a number of

PRBs. This is because the cost of shipping a unit from a supply point to a demand

point depends on the achieved rate (as will be discussed later), so it is a function of the

user’s CQI.

The downlink users’ queues at the eNB with pending traffic demand at a certain

subframe will represent the demand points. The demand at each point is represented

by the number of PRBs required to satisfy the user’s pending traffic. The user’s

pending traffic demand is expressed in terms of bytes, and therefore needs to be

mapped to a number of PRBs using the user’s average wide-band channel state. This

is done by calculating the average CQI of the user over all carriers. Then, the demand

bits are divided by the corresponding transport block size (TBS) of one PRB at this

value of the CQI. This gives the demand in terms of PRBs. The TBS can be obtained

by mapping the CQI index to the corresponding Modulation and Coding Scheme

(MCS) level and then, the TBS tables of [27] are used to determine the block size in

38

bits. The mapping of CA problem to a transportation problem is conceptually

explained in Figure 3.1 which illustrates the demand points being the user queues at

the eNBs requesting a number of PRBs and the supply points being the CCs each

comprised of a numbers of SBs each supplying a number of PRBs to satisfy the

demand.

The cost of assigning a resource to a UE should be defined as to minimize the total

cost. We define it as the negative of the proportional fairness (PF) metric, so that a

higher PF metric lead to a lower assignment cost, as follows:

𝐶𝑖.𝑗 = −𝑅𝑖.𝑗𝑅�𝑗

(8)

where 𝐶𝑖.𝑗 is the cost of assigning one unit from SB 𝑠𝑖 to user 𝑢𝑗, 𝑅𝑖.𝑗 is the

instantaneous rate of user 𝑢𝑗 in the SB 𝑠𝑖 and 𝑅�𝑗 = ∑ 𝑅�𝑖.𝑗 𝑖 is the historical total

average rate for user 𝑢𝑗 in the previous allocations over all CCs, 𝑅�𝑖.𝑗 is the average

rate of user 𝑢𝑗 over CC/SB 𝑠𝑖.

Figure 3.1. Mapping of CA problem to a transportation problem

39

A dummy supply will be added to represent the shortage in satisfying the demand if

it is greater than the available resources. The cost of assignment from this supply is

selected higher than the range of the available costs 𝐶𝑖.𝑗 to increase the opportunity for

users to be allocated to a real supply point.

As some users in the system are Rel-8 users, capable of connecting to only one CC

at a time, the cost of shipping from other CCs to these users is set to a high value α.

This ensures that these users will be allocated resources only from the selected CC.

This introduces a great advantage of the scheduling using the transportation problem,

which is the masking concept. This concept and its effect on the cost of the

transportation problem are explained in section 4.2. A flowchart of the proposed

scheme is shown in Figure 3.2.

40

Figure 3.2. Scheme flowchart

41

3.3 Solution Methods

To solve the transportation problem, it is transformed into a linear programming

problem and then can be solved using the simplex method for optimal solution. The

simplex method can be considered a substantial generalization of standard Gauss-

Jordan (GJ) elimination in linear algebra. It starts by the pivot operation which is

similar to the pivot used in solving systems of linear equations, but restricts the choice

of pivot by the use of a pair of simple rules; the entrance rule that determines the pivot

column and the exit rule that determines the pivot row. These rules are explained

in [31]. By following these two rules starting from the initial data, the optimal solution

of the transportation problem is obtained after a finite number of pivots. Other

methods that can be used to get the optimal solution include the stepping stone

method, the modified distribution method, the modified stepping stone method and the

dual-matrix approach.

However, there are some other methods which can efficiently solve the problem if it

is balanced, i.e., total number of available supply units equals the total demand. We

use the Vogel’s Approximation Method (VAM) since it can be used to obtain a

feasible solution that is close to the optimal one and in a much shorter time. In such

real-time applications, getting a reasonable solution before the deadline may be more

important than getting the optimal solution. Some experimental research showed that

on the average, VAM yielded the optimal solution about 20% of the time and it

yielded very efficient solutions with around 0.5-1% loss of optimality about 80% of

the time. The performance measure that was used to evaluate this experiment is the

number of best solutions (NBS) observed over a set of problem instances [5].

3.3.1 VAM Method Procedures

The transportation problem is solved using the VAM method by applying the

following steps:

0. Construct an assignment matrix whose dimension is S by D, begin with all cells

unallocated.

42

1. Compute for each row and each column the difference between the lowest and

next lowest cost cell in the row or column, in case two cells contain the same least

cost, and then take the difference as zero.

2. From amongst those rows and columns differences, select the one with maximum

difference.

3. Allocate as much as possible to the 𝑥𝑖,𝑗 with the lowest cost cell in the selected

row or column. If there occurs a tie between the largest differences, the choice may be

the row or column that has least cost. In case there is a tie in cost cell also, choice may

be made for a row or column by which maximum requirement is exhausted. Match

that column or row containing this cell whose totals have been exhausted so that this

column or row is ignored in further consideration.

4. Decrease the corresponding supply and demand. Drop the row and/or column

whose supply or demand is zero.

5. Make any allocations where only one unallocated cell remains in a row or

column. After reducing the corresponding supply and demands and dropping the row

and/or column, repeat Step 5 as necessary.

6. Stop if no rows and columns remain. Otherwise return to Step 1 with the reduced

problem.

3.3.2 Integer Solutions Property

An important property of the TP is the integer solutions property. Unlike other LP

problems that could end up with solutions that make fractions of units that do not

make sense as fractions (e.g. trucks or persons), when solving a transportation

problem, if all units in the source points and demand points have an integer value, all

basic feasible solutions for 𝑥𝑖,𝑗, including the optimal solution also have integer

values. That is why some problems that may have no relation to transporting goods

are mapped to a transportation problem to ensure integer solutions as long as the

problem can be set up in a transportation problem form with integer supply and

43

demand points. For example, it may be used to efficiently place employees at certain

jobs within an organization.

44

Chapter 4. CA-based ICIC Scheme in a Multi-Cell Resource

Allocation Problem

In this study, we consider a multi-cell scenario where we perform the dynamic

resource allocation process on the scheduled cells concurrently on each subframe. The

transportation problem is solved on each cell in a distributed manner. Each cell solves

the problem using the CQI feedback that is reported by its users corresponding to their

current SINR levels [27]. The interference is calculated from the allocation of the

previous subframe assuming the difference in the allocation is not significant, which is

reasonable if all PRBs are used and no power control is implemented. Hence, there is

no need of information exchange between cells in this scheme and the scheduling can

be performed in a totally autonomous manner. To alleviate the ICIC between the

neighboring cells and hence improve the throughput in the cell-edge, an SFR based

resource allocation scheme is deployed, as explained in the following section.

4.1 Soft Frequency Reuse Schemes

4.1.1 Inter-Cell Interference Coordination

Next generation wireless networks are expected to provide high data rates and

spectral efficiency as compared to the previously existed systems. Accordingly, every

single frequency resource is needed to satisfy these requirements. Efficient use of the

scarce spectrum makes it important to use it in a dense reuse manner in order to fully

utilize the use of resources on each cell. Since the next generation systems are mainly

based on OFDMA in which the inter-cell interference is a limiting factor that should

be considered seriously, greater-than-one reuse factor schemes, commonly known as

conventional frequency reuse schemes, are then not favorable due to the under-

utilization of resources caused by using only a subset of the resources in each cell.

Instead of this, another approach is to avoid interference by going towards fractional

frequency reuse (FFR) schemes. In the rest of this subsection, we give a brief

overview and comparison of the common types of these schemes. In general, the aim

45

of each of these schemes is to control the use of frequency resources over the various

channels in the network.

4.1.1.1 Conventional Frequency Reuse

The easiest way frequency planning is to use the frequencies in a reuse one manner,

i.e., all resources are used in all cells without any type of coordination or power

control. This scheme achieves the highest peak data rate. However, this is always

associated with very high values of ICI, especially in the case of overloaded systems

where resources are more likely to be used be adjacent edge users in neighboring

cells.

To overcome the issue resulting from the reuse-1 scheme, the spectrum can be

divided among a pattern of cells and then repeated in another patterns. This reduces

the ICI significantly. Nonetheless, this comes at the expense of under-utilization of the

spectrum by imposing restrictions on the reuse of each channel on each cell, i.e., a

reuse pattern of 3, sometimes referred to as hard frequency reuse, leads to only one

third of resources to be used on each cell, which is not favorable with the scarce

frequency resources.

The above discussion shows that conventional frequency reuse schemes can be

considered the upper and lower bounds on the interference as well as spectrum

utilization in the network. While reuse 1 does not employ any interference

coordination, reuse 3 can be regarded as an extreme case of partition based

interference coordination.

4.1.1.2 Fractional Frequency Reuse

FFR is a frequency planning technique in which the available spectrum is

partitioned into multiple portions; each portion is reserved for the use of a specific part

of the cell in a coordinated way such that the inter-cell interference is reduced. The

FFR schemes strike a balance between the reuse-1 scheme and higher than one

schemes by allowing center users who typically do not suffer from ICI to be allocated

46

from the whole or most of the resources whereas the cell-edge users of a pattern of

cells share the resources that they do not interfere with each other.

Figure 4.1. Frequency reuse based ICIC schemes (excerpted from [3])

Figure 4.1 depicts the various categories of frequency reuse-based ICIC scheme. As

shown, the FFR schemes in general can be divided into three main categories:

1) Partial Frequency Reuse (PFR) Schemes: in these schemes a common portion of

the frequency band is used in all pattern cells (i.e., a frequency reuse of 1) with equal

power, while the power allocation of the remaining portion is coordinated among the

neighboring cells in order to create one portion with a low ICI level in each cell.

2) Soft Frequency Reuse (SFR) Schemes: in these schemes, each cell transmits in

the whole frequency band. However, the sector uses higher power level in some

frequency resources while reduced power is used in the rest of the frequency band.

3) Intelligent Reuse Schemes: in these schemes, band allocated to different cells

expands and dilates based on the existing workloads. They typically start with a reuse-

3 like configuration at low workloads and then it can be changed with the increase of

workloads to become PFR, SFR or even reuse-1.

47

Figure 4.2. Three-cell layout

(a)

(b)

Figure 4.3. Two SFR schemes (a) SFR-1 (b) SFR-2

48

(a)

(b)


partitioning (b) Global partitioning

In this study, we consider two FFR schemes, although both of them are commonly

defined as soft frequency reuse (SFR) [3], their realizations are different. The first

definition of SFR [21], denoted herein as SFR-1, divides the spectrum into N parts (for

a reuse pattern of N cells). Each cell in the pattern uses one of these parts with high

power in the cell-edge and uses the remaining parts in the cell-center with reduced

power. This scheme is depicted in Figure 4.3-a for an example of three-cell layout as

in Figure 4.2. As shown, SFR-1 scheme gives cell-center UEs access to all resources

with reduced power, so it is equivalent to a reuse factor of 1 in the cell-center.

However, cell-edge UEs are scheduled in one third of the bandwidth only, therefore

resulting in a reuse-3 in the cell-edge.

49

The second definition of the SFR [22], denoted herein as SFR-2, is different from

SFR-1 in that the portion allocated to the cell edge users is not used in the cell-center.

Thus, there is orthogonality between the resources used by cell-center and cell-edge

users within a certain cell, which guarantees improving the cell-edge spectral

efficiency as a given portion of the band is fully dedicated to their usage. This scheme

is depicted in Figure 4.3-b.

(a)

(b)


partitioning (b) Global partitioning

4.1.2 Proposed Configurations

Since our model inherently has multiple CCs, we propose two configurations to

partition the resources between cell center and cell edge users. We define the first

50

configuration as local partitioning (LP) in which we consider each CC individually as

if there are no other CCs in the system. In this configuration, each CC will be

partitioned into multiple parts according to the reuse pattern. This is depicted in

Figure 4.4-a for the cells layout of Figure 4.2 in case of SFR-1. We define the second

configuration as the global partitioning (GP) in which the spectrum formed by the

whole CCs is considered as one portion while partitioned. Figure 4.4-b depicts this

configuration for the previous example. Also, the configuration of the SFR-2 scheme

is depicted in Figure 4.5-a and Figure 4.5-b for the LP and GP cases, respectively.

4.1.3 Power Ratio

We define a parameter called the power ratio = 𝑝𝑒/𝑝𝑐 where 𝑝𝑒 is the total power

of the cell-edge portion and 𝑝𝑐 is total power of the cell-center portion. Note that the

higher the power ratio, the more we expect the cell-edge throughput to improve. This

parameter has no specific value in the standards; instead, a reasonable value should be

set to satisfy the network requirements. A study in [23] optimizes the allocation

process by varying the power ratio jointly with varying the number of resources

dedicated for the cell-edge on each cell according to traffic loads.

4.2 Masking Concept

We formulate the multi-cell resource allocation problem as a transportation

problem. The goal of the optimization problem is to efficiently allocate the resources

to the users in order to minimize the inter-cell interference. This is done by tailoring

the transportation problem cost values to fit the required SFR scheme and

configuration through masking.

By the use of the transportation problem, masking of a number of source points for

a certain user is done by simply setting costs from these source points to a high value,

denoted here as α, much higher than the typical cost values in the transportation

problem. This makes it easy to manage who to serve and from which source, for

example, if a UE is in the cell-edge then it is allowed to be served only from the

portion reserved for cell-edge, so we simply set high cost values between this UE and

51

all sources (SBs) except in that portion. Figure 4.6 illustrates an example of the

masking concept, assuming the system has two CCs and each CC is divided into two

portions, one for the center and the other for the edge. In the first case, since the user

is an LTE-A user, he is capable of connecting to both CCs but being a cell-center UE

allows him to be allocated only from the first portion of each CC so the sources from

the other portion is masked. The second case is the same but for a cell-edge user. In

the third case, the user is a Rel-8 UE who is connected to the first CC only so the

whole sources in the second CC is masked whereas only the first portion of the first

CC is available as the user is in the cell-center. The fourth case is similar but for a

cell-edge Rel-8 user.

This concept results in an adaptive transportation problem-based scheduler that can

be easily adjusted to cope with different setups/schemes by simple setting of cost

values and then it arrives at an efficient solution that does not deviate from the

constraints.

4.2.1 Effect of Masking on the Transportation Problem Cost

It is important to note that the high value of α will cause some cost values to be

positive whereas the typical values in the problem are negative. To avoid this, we

initially scale the whole costs to higher values by multiplying them by a large value β,

where β > α, so that the addition of α will keep all of them negative. The suitable

absolute value of α should be approximately 100 times the average of the available

costs 𝐶𝑖.𝑗, increasing it above this value has no effect on the solution. To perform the

masking, we define for each source point 𝑠𝑖 a set of users that are eligible to be

assigned its PRBs, labeled as ℰ𝑖 = {𝑢1,𝑢2, … ,𝑢𝑒} where 𝑖 ∈ {1,2, … , 𝑆} and 𝑒 ≤ 𝑈.

Hence, we can modify the cost of shipping one unit from SB 𝑠𝑖 to user 𝑢𝑗 defined in

(8) to be expressed as:

𝐶𝑖.𝑗 = −β 𝑅𝑖.𝑗𝑅�𝑗

+ 𝛼. 1𝑢𝑗∉ℰ𝑖 (9)

where

52

1𝑢𝑗∉ℰ𝑖 = �1, 𝑢𝑗 ∉ ℰ𝑖0, otherwise

It is noting that we are interested in obtaining the solution with minimum total cost

rather than the value of the total cost itself. The exact values of α as well as the scaling

factor β are not of a particular importance in the problem as long as they prevent

assignment from the masked resources.

Figure 4.6. Example for the masking concept

53

Chapter 5. An Auction Approach to Resource Allocation

with Interference Coordination

In OFDMA systems, interference between the neighboring cells significantly affects

the system performance, especially at the cell edge. Due to the scarcity of the

frequency resources, it is not favorable to deploy greater than one frequency reuse

systems. Instead, a reuse-1 frequency management scheme where the whole resources

are used in each cell should be deployed. Although it achieves the highest peak data

rate, reuse-1 frequency planning technique suffers high ICI which results in

unfavorable conditions for the users at the cell edge. Several solutions are proposed to

mitigate the effect of ICI in OFDMA based wireless networks, inter-cell interference

coordination (ICIC) is one of these solutions that aims at avoiding possible ICI

occurring due to sharing of the same resource block by two users in two neighboring

cells.

Most of the existing work in this field focuses on minimizing the ICI without

paying attention to the needs of cell-edge users in different cells. If there is a resource

that should not be used in two adjacent cells, existing schemes may only prevent one

of them from being assigned to this resource without considering who needs it the

most. In this work, we propose an auction based ICIC scheme that aims at minimizing

ICI while taking priorities of users in the cells’ edge into account. The contribution of

this study is three-fold: (1) a distributed resource allocation scheme based on auction

algorithm is proposed where each UE on each cell bids for its demand of resources

each sub-frame in a dynamic manner; (2) an infrequent price exchange method is

proposed to minimize ICI in which each cell in the network exchange the prices of

resources with its neighbors where these prices reflect how crucial these resources are

for the cell users; (3) Explicit exploitation of the Relative Narrowband Transmit

Power (RNTP) indicator that is standardized in the LTE systems [24] to be exchanged

between neighboring cells for the resources that suffer from high interference levels.

The proposed methodology leads to two positive effects on the performance. First, it

minimizes the amount of information exchange, particularly in LTE-A systems

54

operating on large spectrum bandwidths in which exchanging information regarding

all resources causes high overhead. Second, the use of RNTP prevents releasing some

allocations from neighboring cells that actually do not cause much interference, so it

restricts the coordination on the resources that suffer from high ICI. It is shown that

the proposed scheme produces significant gains in the cell-edge throughput as

compared with systems without pricing exchange.

This chapter is organized as follows. In the first section we describe the system

model. The assignment problem is described in the second section. The problem

mapping is provided in the third section. The fourth section discusses the auction

algorithm. Finally, we introduce the price exchange mechanism in the fifth section.

5.1 System Model

We consider a downlink LTE system with N cells operating in FDD mode, namely,

the resources used in the downlink are orthogonal to those used in the uplink. Each

cell in the system is comprised of an eNB, and a number of UEs, labeled as 𝒰 =

{𝑢1,𝑢2, … ,𝑢𝑈} uniformly distributed in the cell area. The terms user and UE are used

interchangeably throughout this chapter. UEs request a constant amount of data,

expressed in bytes each sub-frame of 1 millisecond. A dynamic resource allocation is

performed each sub-frame in which unsatisfied demand is added to the demand of the

next sub-frame.

We consider a two-level power allocation scheme in which the power of a resource

allocated to the edge-user, denoted as 𝑝𝑒, is greater than the cell-center resource

power, denoted 𝑝𝑐. The ratio between them is called the power ratio (PR) and is

defined as

𝑃𝑅 = 𝑝𝑒/𝑝𝑐 (10)

and obviously it is greater than one. To calculate 𝑝𝑒 and 𝑝𝑐 we assume that both cell-

edge users and cell-center users have a share factor of the total power 𝑃𝑇 denoted as

𝑤𝑒 and 𝑤𝑐, respectively, where 0 < 𝑤𝑒 , 𝑤𝑐 < 1 and 𝑤𝑒 + 𝑤𝑐 ≤ 1. The share factors

55

of cell-center and cell-edge users are determined according to the ratio of each of them

in the system with respect to the total number of users. Then we can state that:

𝑃𝑇 = 𝑤𝑒 . 𝑝𝑒 + 𝑤𝑐 . 𝑝𝑐 (11)

and therefore for a given 𝑃𝑇 and PR, we can get 𝑝𝑐 by substituting 𝑝𝑒from (10) in (11)

and vice versa.

5.2 The Assignment Problem

We formulate the problem as a symmetric assignment problem and solve it using

the auction algorithm [6]. The assignment (weighted matching) problem is a 0-1

combinatorial optimization problem that can solved easier than other combinatorial

optimization problems since its linear programing polytope is the convex hull of its

integer solutions [25]. It is usually solved by either the simplex method or the

Hungarian method [26].

It is similar to transportation problem in that both problems aim at minimizing the

cost (or maximizing the benefit) of shipping of units from supply points (objects) to

demand points (persons), but the difference is that in the assignment problem, the

number of units on each supply point and demand point equals one. That is why it is

considered a one-to-one matching problem. The objective of solving the assignment

problem is to find a solution with maximum total benefit. The formulation of the

assignment problem is as follows:

56

maxΗ�

��𝑓𝑗.𝑖 𝜂𝑗.𝑖𝑗𝑖

subject to

�𝜂𝑗,𝑖 = 1 , ∀𝑗𝑖

�𝜂𝑗,𝑖 = 1 , ∀𝑖𝑗

𝜂𝑗,𝑖 ∈ {0,1} , ∀𝑖,∀𝑗

(12)

where 𝜂𝑗,𝑖 is a 0-1 combinatorial factor that determines if the object i is assigned to the

person j or not and 𝑓𝑗.𝑖 is the benefit from assigning the object i to the person j.

5.3 Problem Mapping

The problem of LTE resource assignment is formulated as an assignment problem

as explained in the following steps:

1- The physical resource blocks (PRBs) being assigned to users represent the

problem objects. Each resource block represents a separate unit in the problem.

2- Each user in the system is divided into a number of sub-users equals to the

number of PRBs needed to satisfy its traffic demand. This number of PRBs is

calculated by converting their demand originally in bytes using their wideband

CQI values. Thus, the assignment problem objects will be the sub-users, in

which each of them requesting only one PRB, as to maintain the one-to-one

matching of the formulation.

3- The benefit of assigning an object to a person in the problem should be chosen

to reflect the main objective of the optimization problem. Since the proportional

fairness (PF) metric is known to be one of the most efficient and fair scheduling

metrics, we choose the benefit to be the PF metric such that higher PF values

increase the opportunity of assigning the corresponding resources. Therefore,

the benefit can be expressed as:

57

𝑓𝑗.𝑖 =𝑅𝑖.𝑗𝑅�𝑗

(13)

where 𝑓𝑗.𝑖 is the benefit of assigning PRB i to user j, 𝑅𝑖.𝑗 is the instantaneous rate of

user j when assigned the PRB i and 𝑅�𝑗 = ∑ 𝑅�𝑖.𝑗 𝑖 is the historical total average rate for

user j in the previous allocations over the entire bandwidth, and 𝑅�𝑖.𝑗 is the average

rate of user j over PRB i.

The instantaneous rate is calculated by the use of the transport block size (TBS)

tables standardized in [27]. This done by mapping the reported CQI index to its

corresponding MCS level and then, the TBS tables are used to determine the block

size of one PRB in terms of bits.

The proposed solution is inspired from the auction algorithm [6] which is an

intuitive method operated like real auctions where persons compete for their favorable

objects by raising their prices through competitive bidding. We apply the auction

algorithm in a distributed fashion in each cell in the system to allocate the PRBs to

users. However, cells apply infrequent prices exchange that represents how important

the resources allocated to its cell-edge users are. This exchange is not for all resources

allocated to cell-edge users but for resources that is highly interfered by the neighbors

and hence a cell try to coordinate with other cells in order to choose which cell needs

this resource the most. The auction algorithm and pricing exchange mechanism is

explained in the following sections.

5.4 The Auction Algorithm

In the symmetric assignment problem, the objective is to match in a one-to-one

basis n persons and n objects in such a way that the total benefit is maximized given a

benefit 𝑓𝑗.𝑖 for matching person i to object j. If the problem is an asymmetric version

of the assignment problems, namely the number of persons is greater or lower than the

number of objects then the problem is converted to a symmetric one by adding

dummy persons or objects in order to be able to solve it. Any matching of a dummy

person to an object will not be considered after solving the problem. The auction

58

algorithm is one of the efficient solutions to the assignment problems. It emulates the

bidding process in real auctions by performing a competitive bidding process in which

persons simultaneously bid for the objects and raise their prices to win their favorable

ones. It mainly consists of two phases: the bidding phase, in which persons bid for

objects and the assignment phase in which objects are assigned to the highest bidder.

It terminates when all persons become happy with their assignment. The person is

considered happy for being within a positive scalar ϵ from the optimal. The optimal

assignment is when the person profit (profit is benefit minus price) from the

assignment is maximum, i.e. 𝑓𝑗.𝑖 − 𝑟𝑗 is maximum for all j, where 𝑟𝑗 is the current price

of object j which is initialized to zero and updated as described in algorithm 1. The

update of 𝑟𝑗 attempts to make the difference between the best and the second best

object to the bidder as the price that can be afforded by this user to win the best object.

Hence the person i is defined as happy with object j if:

𝑓𝑗.𝑖𝑗 − 𝑟𝑖𝑗 ≥ max𝑖

�𝑓𝑗.𝑖 − 𝑟𝑖� − ϵ (14)

Algorithm 1: Basic Auction Algorithm

1. Initialization: Set 0<ϵ< 1/n; start with all prices equal zero (i.e., 𝑟𝑖 = 0, 𝑖 =1, … ,𝑛); start with all persons unhappy.

2. Repeat a) Choose an unhappy person and calculate its maximum profit

𝛾𝑗.𝑖𝑗 = max𝑖 �𝑓𝑗.𝑖 − 𝑟𝑖� and its second maximum profit 𝜙𝑗.𝚤𝚥� = max𝑖,𝑖≠𝑖𝑗 �𝑓𝑗.𝑖 − 𝑟𝑖�.

b) Allocate the object 𝑖𝑗 to person 𝑗. If the object was pre-assigned to another person 𝑗′, release the object from this person and set it as unhappy.

c) Update the price of object 𝑖𝑗 to be 𝑟𝑖𝑗 = 𝑟𝑖𝑗 + �𝛾𝑗.𝑖𝑗 − 𝜙𝑗.𝚤𝚥�� + ϵ.

d) Set person 𝑗 as happy. 3. Until all persons are happy.

It was shown in [28] that the auction algorithm terminates in a finite number of

iterations with an optimal assignment when ϵ < 1/n. Practically speaking, lower

values of ϵ leads to higher solution times so it is chosen to be 1/(n + 1).

59

5.5 Price Exchange Mechanism

In the proposed solution, the auction algorithm is applied separately on each cell to

allocate PRBs to users. By using the two level power allocation scheme described

above, and without coordination between neighboring cells, the same allocation may

be given to two edge users in two adjacent cells, and hence high ICI values is

expected on both of them. Although the resource allocation already considers the PF

metric that is function of the reported CQI index (and hence the SINR level) this CQI

value cannot be a direct indication to the source of this interference, so it does not

guarantee minimizing ICI by preventing allocations to adjacent cell-edge users.

To solve this issue, we propose a price exchange mechanism that helps adjacent

cells to determine which resource to use to serve edge-users and which to leave for

other cells that need it. The proposed scheme exploits the auction algorithm

mechanism in which the price paid by a user represents the difference between the

maximum and the second maximum profit and hence it can be used as an indication of

how important that resource is for this user. Since users compete for a resource by

raising its price until one of them get it, the latest price indicates how important this

resource is for the winning user. The idea is to exploit this to determine the most

eligible cell-edge user for a resource. This is done by allowing cells to exchange the

latest prices of the cell-edge resources after an allocation and then, in the next sub-

frames, they will modify their edge-users’ bids to these resources by scaling them to

higher or lower values, and therefore increase or decrease their opportunity to win

certain resources. Subsequently, when a cell-edge user submits a regular bid then the

cell will scale this bid to increase/decrease its possibility of winning this resource. We

further define the factors of scaling the bid to higher and lower values to be 𝑠ℎand𝑠𝑙,

respectively. The proposed scheme is performed according to the following steps:

1- Each cell reports to its neighbors the prices paid by its cell-edge users for their

associated resources in an infrequent manner (e.g. each 10 sub-frames), so that,

if another cell finds that the price of a resource in the first cell is higher, then it

should try to minimize the probability of assigning this resource to its edge-users

60

by scaling their bids in the next sub-frames to lower values by a factor 𝑠𝑙. To

guarantee that the first cell will benefit from this resource that is released for it,

when it finds that its price is greater than that of the second cell, it will scale the

bids of its edge-users on this resource to higher values by a factor 𝑠ℎ to benefit

from this released resource in the following sub-frames.

2- Since the interference seen by a certain cell on different PRBs varies due to the

different propagation conditions on different frequencies, not each resource

allocated to its cell-edge users suffers from high ICI values, and hence asking

the other cells to release it will cause degradation in the those cells without

benefiting the first cell. For this reason, the scheme exploits the Relative

Narrowband Transmit Power (RNTP) indicator that is exchanged by the

neighboring cells in LTE systems. The RNTP is reported once per PRB in the

downlink [24], indicating if the received interference power on that PRB with

respect to the intended received signal power will be greater than a given

threshold. Thus, neighboring cells can anticipate which resources would suffer

more severe interference and take the right scheduling decisions rather than

relying on the UEs’ CQI reports only. In our scheme, each cell report only the

prices of the PRBs allocated to its edge-users if these PRBs suffer from high

interference, i.e. their RNTP indicator equals one. These PRBs are defined as the

interfering PRBs, other PRBs are defined as the non-interfering PRBs. In this

case, the cell report the RNTP value as standardized in LTE and report the price

of this resource on the last allocation.

3- After the cell receives prices from the neighboring cells, it forms a matrix called

the Price Exchange Matrix (PEM). It uses it to modify the bids of cell-edge

users before each allocation as described in step 1. It keeps the PEM to use in

the subsequent sub-frames until cells prices are updated again. Figure 5.1 shows

an illustrative example of the PEM in a three-cell pricing exchange example

with an arbitrary price values. The example shows only the first three PRBs and

is observed from the first cell’s point of view. This table is assumed to be

61

formed using the latest prices of the PRBs at the last sub-frame before the

exchange. As shown, the first cell has the highest price for the first PRB so it

should scale cell-edge users’ bids to this resource to higher values (it is expected

that cell 2 and 3 will scale the resource to lower values to decrease the

probability of assigning it to their cell-edge users). For the second PRB, the

second cell has the highest price for it, so the first cell should scale cell-edge

users’ bids to lower values to release it to the second cell. For the third PRB, no

other cell is interested in the resource while suffering high ICI from it, so no

scaling will occur and we call this PRB a non-interfering PRB, others are called

interfering PRBs.

Figure 5.1. An example for the Price Exchange Matrix (PEM)

The auction algorithm for the resource allocation problem after the applying the

price exchange mechanism is explained in the following Algorithm.

Algorithm 2: Auction Algorithm for resource allocation with prices exchange

1. Initialization: Set ϵ > 0, 𝑠𝑙 < 1, 𝑠ℎ > 1; start with all prices equal zero (i.e., 𝑟𝑖 = 0, 𝑖 = 1, … ,𝑛. ); start with all sub-users unhappy; start with the latest PEM version.

2. Repeat a) Choose an unhappy sub-user, if it is located in the cell edge, scale its bids to the

interfering PRBs by the scaling factors 𝑠𝑙 or 𝑠ℎ according to the price values in

62

the PEM. b) Calculate its maximum profit 𝛾𝑗.𝑖𝑗 = max𝑖 �𝑓𝑗.𝑖 − 𝑟𝑖� and its second maximum

profit 𝜙𝑗.𝚤𝚥� = max𝑖,𝑖≠𝑖𝑗 �𝑓𝑗.𝑖 − 𝑟𝑖�. c) Allocate the PRB 𝑖𝑗 to sub-user 𝑗. If the PRB was pre-assigned to another

sub-user 𝑗′, release the PRB from this sub-user and set it as unhappy.

d) Update the price of PRB 𝑖𝑗 to be 𝑟𝑖𝑗 = 𝑟𝑖𝑗 + �𝛾𝑗.𝑖𝑗 − 𝜙𝑗.𝚤𝚥�� + ϵ.

e) Set sub-user 𝑗 as happy. 3. Until all sub-users are happy.

63

Chapter 6. Performance Evaluation In this chapter, we evaluate the performance of the proposed schemes based on

simulations and discuss the results obtained. In the first section, we provide the

simulation assumptions and results of the TP-based scheme for the single-cell and the

multi-cell scenarios, respectively. The second section discusses the simulation

assumptions and results of the auction based scheme.

6.1 The TP-Based Scheme

6.1.1 Simulation Assumptions

The proposed scheme is evaluated using system level simulations. The channel

model on the links is the WINNER II C2 model as specified in [32]. The main

parameters used in the simulation are summarized in Table VII. The traffic demand

for the users is generated for each experiment in terms of a constant bit rate (CBR)

application. The rate is changed in order to change the system offered load. We

assume there are no packet transmission errors; hence no hybrid automatic repeat

request (HARQ) operation is applied. We perform two studies to investigate the

performance of the proposed TP-based scheme. In the first study, we evaluate the

performance against a multi-CC PF scheduler in a single-cell scenario. In the second

study, we extend the problem to a multi-cell scenario and investigate the performance

of the SFR schemes with different configurations as introduced in section 4.1.

Table VII. Simulation parameters

Parameter Value/description Layout scenario Typical urban macro-cell [32]

Carrier aggregation pattern Single cell Scenario: 4 × 10 MHz non-contiguous CCs Multi-cell Scenario: 3 × 10 MHz non-contiguous CCs

Shadowing Log-normal shadow fading

Site-to-site distance 500 m

Number of PRBs per CC 50 PRB, each contains 12 subcarriers

64

Subcarrier spacing 15 KHz

Max. eNB Tx power/CC 46 dBm

Duplex mode FDD

Sub-frame duration 1 ms

FFT size 1024

Sampling frequency 15.36 MHz

Antenna configuration 1*1

Modulation schemes QPSK, 16-QAM, 64-QAM

Traffic model CBR

Power ratio (Pe/Pc) 5-15

CQI reporting resolution 3 PRBs/sub-band

Thermal noise spectral density -174 dBm/Hz

6.1.2 Single Cell Scenario

In this study, the performance of the proposed scheme is compared against an

adapted version of Proportional Fair (PF) scheduler to cope with multiple CCs in a CA

setup. This scheduler allocates a resource in a certain CC to the user with the highest

PF metric only if the user is connected to this CC. The main metrics are the average

user throughput and fairness index expressed by the Jain’s Fairness Index (FI) [34],

which is formulated as follows:

FI =(∑𝑅�𝑗)2

𝑈∑𝑅�𝑗2 (15)

where U is the number of UEs in the system. This index measures the degree of

fairness in the allocated rates between users and it has value that falls between zero

and one with more fairness achieved as we are close to one.

For each experiment, we generate 50 different channel and user distributions and

simulate each one independently then we take the average of the 50 simulations as the

reported value. Each simulation is a 10000 subframe-long dynamic resource allocation

process and it contains a number of 20 users uniformly distributed in the cell.

65

In the first experiment, we increase the offered load and measure the average UE

throughput and fairness comparing the performance of the proposed scheme with the

adapted PF scheduler. The results show that the average UE throughput increases with

increasing the offered loads until certain value then it tends to saturate as the cell

capacity is therefore limited by the number of available PRBs, as shown in Figure 6.1

and Figure 6.2 for a percentage of LTE-A users of 100% and 50%, respectively. As

compared to the PF scheduler, the proposed scheme can achieve about 4% throughput

gain at moderate loads if all users are LTE-A and 3% if half of them are LTE-A. At

low loads, the users demand is lower than the available resources so they get their

entire traffic, and hence no difference between the two schemes is expected. Also

there is no noticeable difference in their performance at high loads, as the system

capacity is approached. Thus a certain bound cannot be exceeded and the two schemes

typically achieve the same throughput.

Figure 6.3 depicts the average Rel-8 UE throughput and average LTE-A UE

throughput versus the offered load for the two schemes. The throughput of LTE-A

users is greater as they are scheduled on the entire bandwidth. It is shown that our

scheduler achieves better throughput than the PF scheduler in moderate load

conditions, especially for Rel-8 users who achieves up to 5% throughput gain. Being

served well in the presence of LTE-A users, Rel-8 coexistence in the system does not

degrade the overall performance and hence the fairness of the system remains high.

The proposed scheme also achieves better fairness at all load conditions; this is

because in the PF scheduler case, the best user (i.e., the user with the highest metric) is

scheduled each time in a greedy approach whereas the TP-based scheduler applies the

proportional fairness metric in a more global way in which the metrics of all users

play a role in obtaining the solution. Therefore, the TP-based scheduler achieves better

fairness in the long-term. In both cases, the fairness decreases with increasing load but

remains in a favorable range (above 0.9).

In the second experiment, we assess the results of the VAM method as compared

with the optimal simplex method. The difference between the two methods in the

66

realizable average UE throughput is shown in Figure 6.4. The figure depicts the

performance in three different scenarios: when all users are LTE-A, half of the users

are LTE-A and the rest being Rel-8 users, and all users are Rel-8. VAM performance

is slightly degraded with around 0.5% loss due to the sub-optimality of the scheme.

However, the time consumed in the simplex method is nearly 30 times larger than that

of the VAM method.

2.5

3

3.5

4

4.5

5

50 100 150 200 250 300

PF TP

UE Thr

oughpu

t (M

bps)

Offered Load (Mbps)

0.9

0.92

0.94

0.96

0.98

1

50 100 150 200 250 300

PF TP

Fair

ness

Offered Load (Mbps) Figure 6.1. Average UE throughput and Fairness (100% of users are LTE-A)

2.5

3

3.5

4

4.5

5

50 100 150 200 250 300

PF TP

UE Thr

oughpu

t (M

bps)

Offered Load (Mbps)

0.9

0.92

0.94

0.96

0.98

1

50 100 150 200 250 300

PF TP

Fair

ness

Offered Load (Mbps)

Figure 6.2. Average UE throughput and Fairness (50% of users are LTE-A, rest are

Rel-8)

67

2.5

3

3.5

4

4.5

50 100 150 200 250 300

Rel-8, TPLTE-A, TPRel-8, PFLTE-A, PF

Offered Load (Mbps)

UE

Th

rou

gh

pu

t (M

bps)

Figure 6.3. Average Rel-8 UE throughput and average LTE-A UE throughput (50% of

users are LTE-A, rest are Rel-8)

In the third experiment, we assess the advantage of increasing the percentage of

LTE-A capable user. Figure 6.5 illustrates the throughput performance versus the

percentage of LTE-A users at moderate load condition (100 Mbps). It is shown that

the system performs better as the percentage of LTE-A users increases; the more the

number of LTE-A users the better performance is achieved as more users become able

to access more than one CC and this can take advantage of the best channel states for

the PRBs available in the different CCs, hence, the advantage of CA can be exploited.

The gain of the proposed method compared with the PF scheduler varies from 3-4%

when VAM is used, VAM loss due to sub-optimality is always less than 1%.

In brief, our proposed scheme obtains considerable performance gain than the

traditional PF scheduler in terms of throughput and fairness, either by using the VAM

method or the simplex method.

68

2.5

3

3.5

4

4.5

5

50 100 150 200 250 300

All LTE-A, VAM50% LTE-A, VAMAll Rel-8, VAMAll LTE-A, simplex50% LTE-A, simplexAll Rel-8, simplex

UE

Th

rou

gh

pu

t (M

bp

s)

Offered Load (Mbps)

Figure 6.4. VAM versus simplex method in obtaining average UE throughput

3.8

3.9

4

4.1

4.2

4.3

4.4

0 20 40 60 80 100

TP-VAMPF

TP-simplex

UE

Th

rou

gh

pu

t (M

bp

s)

LTE-A Users (%)

Figure 6.5. Average UE throughput versus percentage of LTE-A users for different

schedulers

69

6.1.3 Multi-Cell Scenario

In the second study, we investigate the performance of different SFR schemes using

system level simulations. The cells layout is depicted in Figure 6.6, all cells in the

layout are scheduled, however, only the three interior cells are used to calculate the

throughput whereas the cells in the outer tier are used only to generate inter-cell

interference on the interior cells. On each subframe, the simulation is performed in the

whole cells, one after another. Each cell contains 10 UEs uniformly distributed in the

cell area. For the ease of simulation, a UE is defined as a cell-edge one if its distance

from the center is more than 70% of the cell radius. A constant rate of 100 Mbps is

offered in each cell, thus each user requires 10 Mbps, unless we vary the load on a

certain experiment.

Figure 6.6. Cells layout

We investigate the performance of the SFR-1 and SFR-2 schemes, each with the

local and global partitioning configurations. Hence, we denote them as LP-SFR-1, LP-

70

SFR-2, GP-SFR-1 and GP-SFR-2. We use the geometric average as in [35], expressed

as:

𝑅� = ��𝑅�𝑗

𝑈

𝑗=1

�

1𝑈

= exp�1𝑈� ln (𝑅�𝑗)𝑈

𝑗=1

� (16)

since it is a good measure of system rate utility as it can be defined as sum of the log

the users rate (the geometric average is then be the exponent of the utility).

In Figure 6.7, the geometric average UE throughput versus the cell-edge UE

throughput is compared for the four schemes against the reuse-1 scheme. The power

ratio is varied from 5 to 15 with a step of 3. The experiment is repeated three times

under different percentage of LTE-A UEs and Rel-8 UEs (0%, 50%, and 100% LTE-

A users). It is shown that, in all cases, the different SFR schemes perform better in

terms of cell-edge throughput at the expense of the geometric average throughput

which is decreased due to the lower utilization of resources caused by using fractional

reuse planning, these two effects increase as the power ratio increases, since

increasing the cell-edge power decreases the power dedicated to the cell-center to

keep the total power constant within a CC. The SFR-2 always achieves better cell-

edge throughput than the SFR-1 scheme but with higher degradation in the geometric

average throughput. This difference is due to the orthogonality in dividing the cell-

center and cell-edge resources in the SFR-2 scheme which restrict the high power

spectrum portion to cell-edge users only, thus increasing their throughput to the

detriment of decreasing the cell-center and average throughput.

When all users are LTE-A users, the LP schemes perform better than the GP

schemes. Nevertheless, this preference vanishes as the percentage of LTE-A users

decreases. On the contrary, when all users are Rel-8 users, the GP schemes perform

better. The explanation of this behavior is as follows, when all users are LTE-A, all of

them are able to connect to the whole CCs. Therefore, using the LP schemes will

enable both cell-edge and cell-center users to be scheduled on the whole bandwidth

and take advantage of the frequency diversity, in particular, all of them will be able to

71

access one third or two thirds of the available bandwidth as they are supposed to. But

if the GP schemes are used in this case, they will limit some users from using some of

the CCs in which they are technically able to connect to them. Conversely, if all users

are Rel-8 users, they are able to connect to a single CC only regardless of being in the

cell-center or cell-edge, therefore, a GP scheme will be better for them, as it will allow

any user to benefit from the entire of his CC whereas an LP scheme will allow him to

be scheduled only on a portion of his single CC. It is worth mentioning that there will

be no difference between GP-SFR-1 and GP-SFR-2 in the case of 0% LTE-A users, as

all users are connected to a single CC so cell-center users are restricted to their CC

and cannot be scheduled on cell-edge resources.

Figure 6.7. Average geometric throughput versus cell-edge throughput for different

SFR schemes against reuse-1 scheme

Figure 6.8 illustrates the system behavior under different offered load conditions of

20, 30 and 100 Mbps per cell, respectively. It is shown that the edge UE throughput

decreases with increasing the offered load in SFR-1 schemes in which the center users

have access to the edge resources along with their dedicated resources. In this case,

72

increasing the load makes the edge resources more vulnerable to be assigned to cell-

center users, and hence the edge throughput decreases. On the contrary, as portion of

the bandwidth is dedicated to cell-edge UEs in the SFR-2 schemes, the edge

performance is guaranteed and thus throughput increases with increasing the offered

load. It is shown also that in the case of reuse-1 scheme, the cell-edge throughput

decreases with increasing load as high traffic leads to high inter-cell interference,

which affects the cell-edge performance considerably.

Figure 6.8. Performance under different load conditions of 20, 30 and 100 Mbps per

cell for the different SFR schemes with a constant power ratio of 10.

The performance is then investigated while varying the percentage of LTE-A users

in the system at a constant power ratio of ten. Figure 6.9 and Figure 6.10 show the

average cell-edge UE throughput and the average cell-center UE throughput,

respectively, for the different schemes. It is shown that at lower percentage of LTE-A

users, GP schemes give better edge throughput. But when the LTE-A percentage

increases, LP schemes achieve almost the same edge throughput and with higher

center throughput.

73

Figure 6.9. Average cell-edge UE throughput for different schemes against the

percentage of LTE-A users

Figure 6.10. Average cell-center UE throughput for different schemes against the

percentage of LTE-A users

In brief, the GP schemes perform better if most of UEs are Rel-8. As the percentage

of LTE-A UEs increase, the performance of the LP schemes turn out to be better. In

both cases, SFR-2 gives better cell-edge throughput and less center and average

throughput, especially at high system loads. This gives the networks flexibility in

choosing the appropriate scheme according to the density of each type of UEs in the

system and also according to the UEs distribution and demand in the system.

74

6.2 The Auction-Based Scheme

6.2.1 Simulation Assumptions

In this section, we evaluate the performance of the proposed scheme. We use the

WINNER II C2 channel model as specified in [32]. We consider a multi-cell scenario,

in which we perform the dynamic resource allocation process on the scheduled cells

concurrently on each sub-frame. The main parameters used in the simulations are

summarized in Table VIII. The cells layout is depicted in Figure 6.11 where all cells

in the layout are scheduled, however, only the three interior cells are used to calculate

the throughput whereas the cells in the outer tier are used only to generate inter-cell

interference on the interior cells.

Table VIII. Simulation parameters

Parameter Value/description

Layout scenario Hexagonal grid with 3 interior cells, and 9 outer cells. Typical urban scenario [32]

Shadowing Log-normal [32]

Carrier Bandwidth 20 MHz

Site-to-site distance 500 m

Max. BS Tx power/CC 49 dBm

Number of PRBs per CC

100 PRB, each containing 12 subcarriers

Sub-frame duration 1 ms

Simulation time 1000 sub-frames

FFT size 2048

Antenna configuration 1*1

Traffic model CBR (40 Mbps/cell)

Number of users 10 users per cell

Thermal noise spectral density -174 dBm/Hz

CQI reporting resolution 4 PRBs/sub-band

75

Figure 6.11. Cells layout

Each cell contains 10 UEs distributed randomly in the cell area. Without loss of

generality, we assume that 20-30% of UEs are located in the cell-edge whereas the

rest are in the cell-center. A UE is considered as a cell-edge one if its distance from

the center is more than 80% of the cell radius. The traffic demand for the users is

generated in terms of a constant bit rate (CBR) application. A constant rate of 40

Mbps is offered in each cell.

6.2.2 Simulation Results

To evaluate the performance of the proposed scheme, we first compare it against a

regular auction based scheme without any exchange between cells. In this experiment,

we set the exchange rate to be once each 10 sub-frames. We choose the scaling factors

𝑠𝑙 and 𝑠ℎ to be 0.1 and 5, respectively. Further, we choose the RNTP threshold to be 1

so that the PRB is considered interfered when the Reference Signal Received Power

(RSRP) of the interfering cells RSRPi is approximately 25% higher than the RSRP

from the serving cell RSRPs (i.e RSRPi / RSRPs=1 dB ≈ 1.25). We also assume that

the cell calculate the RSRP as expressed by its worst cell-edge user.

76

In Figure 6.12, the performance of the proposed scheme is compared against the

scheme without price exchange. The performance is measured in terms of average UE

throughput, average center-UE throughput and average edge-UE throughput. It is

shown that the proposed scheme achieves significant gains in terms of cell-edge

throughput at the expense of a decrease in the cell-center throughput. The cell-edge

throughput increases, as well as the gain due to price exchange when the power ratio

increases. These results are obtained for an exchange rate of once each 10 sub-frames.

The exchanged prices are used to form the PEM and this matrix is kept for use during

the 10 sub-frame period. In Figure 6.13, the same comparison is made with the

performance measure as to be the geometric average UE throughput against the

average cell-edge UE throughput. The experiment is conducted while varying the

power ratio from 4 to 10 with a step of two. It is shown that the proposed scheme

achieves considerable gains in terms of cell-edge throughput for the same geometric

average throughput. Increasing the rate of exchanging prices increases the gains

achieved by using the proposed scheme.

Figure 6.12. Performance of the proposed scheme compared with the scheme without

exchange for different power ratios (price exchange each 10 sub-frames)

77

Figure 6.13. Geometric average throughput against cell-edge throughput for the

proposed scheme with for different exchange periods compared to the case without

price exchange

In the second experiment, we compare the proposed scheme against two schemes,

the scheme without price exchange, and a scheme with full price exchange that

exchanges all prices of cell-edge resources without considering the RNTP

measurements. We conduct the experiment for different exchange rates of once each

5, 10, 20 and 30 sub-frames. As expected, it is shown in Figure 6.14 that lower

exchange times (i.e., with higher frequency) lead to higher performance in terms of

cell-edge UE throughput. Nevertheless, the proposed scheme always improves the

cell-edge throughput even with infrequent exchange rates. It is also noted that the

scheme with full price exchange does not improve throughput unless at high exchange

rates, and it is performance is lower than the proposed scheme that uses the RNTP.

Although it may be thought that the exchange with higher frequency will always lead

to better performance, the results show the opposite. That is because exchanging

prices of resources that are in fact not suffering from high interference values make

the whole set of neighboring cells try not to allocate these resources to their edge users

in which their allocation is not harmful to the cell that reported the prices. Moreover, a

78

great advantage of the RNTP is that it significantly reduces the amount of data

exchange needed since only a subset of the cell-edge resources will be considered in

the coordination process. Hence, we can conclude that RNTP is a good measure of the

need to coordinate the allocation on a resource with neighbors or not.

Figure 6.14. Performance of the proposed scheme compared with the scheme without

exchange and the scheme with full price exchange for different exchange periods

79

Chapter 7. Conclusions We proposed and evaluated the performance of a transportation problem based

resource allocation in an LTE-A setup operating with carrier aggregation. First, the

downlink multi-carrier resource allocation is formulated as a transportation problem

(TP). It is shown that the proposed TP scheme with cost metric that is the negative of

the PF metric achieves better performance than the Proportional Fair (PF) scheduler.

Both the simplex (optimum) method and Vogel Approximation Method (VAM) solve

the TP efficiently. VAM is a sub-optimal but efficient solution that solves TP in much

smaller time than the simplex method. Then, the performance of different soft-

frequency-reuse (SFR) based inter-cell interference coordination schemes are studied

for a multi-cell multi-carrier LTE-A system using the proposed scheduler. Two

schemes are proposed and investigated with two different partitioning configurations,

local partitioning (LP) and global partitioning (GP). Simulation results show that the

second SFR method performs better in terms of the cell-edge throughput at the

expense of higher geometric average throughput degradation. The LP method applies

the partitioning on each CC individually and it performs better when most of the users

are LTE-A. If most of the users are Rel-8, the GP method, which performs the

partitioning globally on the entire bandwidth, performs better. Furthermore, the

proposed scheduling scheme can be easily adjusted by simply changing the

transportation problem cost values to adapt the network to any of the SFR schemes

whenever the users’ conditions change.

Then we proposed a novel resource allocation scheme in LTE downlink system

based on auction algorithm is proposed. The problem is formulated as an assignment

problem and a pricing exchange mechanism is proposed that is shown to reduce the

inter-cell interference (ICI) significantly. Furthermore, the Relative Narrowband

Transmit Power (RNTP) indicator is exploited to exchange only the prices of the

resources that suffer high levels of interference to consider them only in the

coordination process. It is shown that the proposed scheme significantly improve the

cell-edge throughput at different exchange frequencies. Frequent exchange rates are

80

shown to provide better performance, however, infrequent exchange rates also

improve the cell-edge performance.

Future work suggested for the TP-based scheme includes the deployment of the

proposed scheme in a heterogeneous network (HetNet) in which macrocells and

femtocells co-exist in the same deployment. The masking concept introduced in the

scheme can then be used as an inter-cell interference coordination scheme to mitigate

the intra-tier interference (femto-to-femto interference) and the inter-tier interference

(macro-to-femto interference).

As for the auction-based scheme, the effect of multi-carrier presence can be studied

for the proposed scheme. Moreover, the exploitation of the Relative Narrowband

Transmit Power (RNTP) can be extended to decide which component carrier (CC) is

assigned to the LTE Release-8 users on each cell according to the interference on each

carrier.

81

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