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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
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
Thesis Main Advisor: Prof. Dr. Khaled M.F. Elsayed Thesis Advisor: Dr. Ahmed Salah Ibrahim
Faculty of Engineering, Cairo University
Giza, Egypt
2013
iii
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
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
______________________________________________________
Faculty of Engineering, Cairo University
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
Figure 4.5. SFR-2 partitioning and the corresponding power levels (a) Local
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)
Figure 4.4. SFR-1 partitioning and the corresponding power levels (a) Local
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)
Figure 4.5. SFR-2 partitioning and the corresponding power levels (a) Local
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
max�
��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
References
[1] 3GPP, “Feasibility study for Further Advancements for E-UTRA (LTE-
Advanced),” Tech. Spec. 36.912 V.9.2.1, Mar. 2010.
[2] R1-050764, “Inter-cell interference handling for E-UTRA,” in 3GPP TSG-RAN
WG1 Meeting #42, Aug. 2005.
[3] A. Hamza, S. Khalifa, H.S. Hamza and K.M.F. Elsayed, "A survey on inter-cell
interference coordination techniques in OFDMA-based cellular networks,"
Accepted for publication in IEEE Communication Surveys.
[4] G. Boudreau, J. Panicker, N. Guo, R. Chang, N. Wang, and S. Vrzic,
“Interference coordination and cancellation for 4G networks,” IEEE
Communications Magazine, vol. 47, pp. 74-81, 2009.
[5] M. Mathirajan, and B. Meenakshi, “Experimental Analysis of Some Variants of
Vogel’s Approximation Method,” Asia-Pacific Journal of Operational
Research, vol. 21, no. 4, pp. 447-462, 2004.
[6] D. P. Bertsekas, “Auction algorithms,” Encycl. Optimiz., 2001.
[7] M. Iwamura et al., "Carrier Aggregation Framework in 3GPP LTE-Advanced,"
IEEE Commun. Mag., Aug. 2010, pp. 60-67.
[8] L. Chen, W.W. Chen, X. Zhang, and D.C. Yang: “Analysis and Simulation for
Spectrum Aggregation in LTE-Advanced System,” in Proc. IEEE Vehicular
Technology Conference Fall, Sep. 2009.
82
[9] Y. Wang, K. Pedersen, T. Sørensen, and P. Mogensen, “Carrier load balancing
and packet scheduling for multi-carrier systems,” IEEE Trans. Wireless
Commun., vol. 9, pp. 1780–1789, May 2010.
[10] H. Wang, C. Rosa, and K.I. Pedersen: “Uplink Component Carrier Selection
for LTE-Advanced Systems with Carrier Aggregation,” in Proc. IEEE
International Conference on Communications, June 2011.
[11] Mina A.A. Sokar, and Khaled M.F. Elsayed, “A dynamic radio resource
management scheme for the IEEE 802.16 band-adaptive modulation and coding
mode with proportional rate constraints,” Wiley's European Transactions on
Telecommunications, Article first published online: 9 Dec. 2011, DOI:
10.1002/ett.1529.
[12] S. E. Elayoubi, O. Ben Haddada, and B. Fourestie, "Performance evaluation of
frequency planning schemes in OFDMA-based networks," IEEE Trans. on
Wireless Commun., vol. 7, pp. 1623-1633, 2008.
[13] R. Giuliano, C. Monti, and P. Loreti, WiMAX fractional frequency reuse for
rural environments. IEEE Wireless Communications, 15(3), 60-65.
[14] D. Bai, H. Nguyen, T. Kim, and I. Kang, "LTE-Advanced modem design:
challenges and perspectives," IEEE Communications Magazine, vol. 50, no. 2,
pp. 178-186, February 2012.
[15] Y. Yu, E. Dutkiewicz, X. Huang, M. Mueck, and G. Fang, “Performance
analysis of soft frequency reuse for inter-cell interference coordination in LTE
networks,” in Proc. International Symposium on Communications and
Information Technologies (ISCIT), October 2010.
83
[16] Bertsekas, D. P., & Castañon, D. A. (1991). Parallel synchronous and
asynchronous implementations of the auction algorithm. Parallel Computing,
17(6), 707-732.
[17] Yang, K., Prasad, N., & Wang, X., “An auction approach to resource allocation
in uplink OFDMA systems,” IEEE Transactions on Signal Processing, 57(11),
4482-4496, 2009.
[18] Sun, Y., Jover, R. P., & Wang, X., “Uplink interference mitigation for OFDMA
femtocell networks,” IEEE Transactions on Wireless Communications, 11(2),
614-625, 2012.
[19] G.X. Yuan, X. Zhang, W.B. Wang, and Y. Yang, “Carrier Aggregation for
LTE-Advanced Mobile Communication Systems,” IEEE Commun. Mag., Feb.
2010, pp. 88–93.
[20] K. Brueninghaus, D. Astely, T. Salzer et al., “Link performance models for
system level simulations of broadband radio access systems,” in Proc. IEEE
PIMRC, vol. 4, Sep. 2005, pp. 2306–2311.
[21] 3GPP, R1-050507, Huawei, “Soft frequency reuse scheme for UTRAN LTE,”
2005.
[22] F. Khan, LTE for 4G Mobile Broadband: Air Interface Technologies and
Performance, Cambridge University Press, 2009.
[23] M. Qian, et al. "Inter-cell interference coordination through adaptive soft
frequency reuse in LTE networks." In Proc. IEEE Wireless Communications and
Networking Conference (WCNC), Apr. 2012.
84
[24] S. Sesia, I. Toufik, and M. Baker, “LTE — The UMTS Long Term Evolution:
from theory to practice,” Wiley publishing, 2009.
[25] R.E. Burkard, and E. Cela, Linear assignment problems and extensions,
Springer US, 1999.
[26] H. W. Kuhn, The Hungarian method for the assignment problem, Naval
research logistics quarterly, 2(1‐2), pp. 83-97, 1995.
[27] 3GPP, “Evolved universal terrestrial radio access (E-UTRA); physical layer
procedures,” Tech. Spec. 36.213 V10.4.0, Dec. 2011.
[28] D. P. Bertsekas, “Auction algorithms for network flow problems: A tutorial
introduction,” Computational Optimization and Applications, 1(1), 7-66, 1992.
[29] 3GPP Tech. Specif. Group Radio Access Network; Conveying MCS and TB
size via PDCCH, 3GPP TSG-RAN WG1 R1-081483.
[30] W. L. Winston, “Operations Research: Applications & Algorithms,” Duxbury
Press, 4th edition, Jul. 2003.
[31] D. Gale, "Linear Programming and the simplex method," Notices of the
American Mathematical Society, vol. 54, pp. 364–369, Mar. 2007.
[32] IST-2003-507581 WINNER, “D5.4: Final Report on Link Level and System
Level Channel Models,” Nov. 2005.
[33] Kyösti, P., et al. "IST-4-027756 WINNER II D1. 1.2 V1. 1 WINNER II
Channel Models." Information Society Technologies.–Forschungsbericht.
[34] R. Jain, W. Hawe, and D. Chiu, “A Quantitative Measure of Fairness and
Discrimination for Resource Allocation in Shared Computer Systems,” DEC-
TR-301, Sep. 1984.
85
[35] B. Rengarajan, A. L. Stolyar, and H. Viswanathan, "Self-organizing dynamic
fractional frequency reuse on the uplink of OFDMA systems," in Proc. CISS,
2010, pp.1-22.