Visualizing Carrier
Aggregation Combinations
Fredrik Helders LiTH-ISY-EX--19/5231--SE
Supervisor: Ema Becirovic
ISY, Linköpings universitet
Linnea Faxén
Ericsson
Examiner: Mikael Olofsson
ISY, Linköpings universitet
Division of Communication Systems Department of Electrical Engineering
Linköping University SE-581 83 Linköping, Sweden Copyright © 2019 Fredrik Helders
I samband med att trådlösa kommunikationssystem blir en allt större del av våra liv och mängden data som skickas fortsätter att stiga, skapas en efterfrågan för ökade datatakter. En av teknologierna som används för att skapa högre
datatak-ter ärbäraraggregering (carrier aggregation), som möjliggör för trådlösa enheter
att kombinera flertalet uppkopplingar mot det mobila nätverket. Det finns dock bara ett begränsat antal kombinationer definierade, vilket skapar ett behov av att söka upp den bästa kombinationen i varje givet tillfälle. Detta arbete introducerar mjukvara som organiserar dessa kombinationer i trädstrukturer, vilket förenklar sökning efter optimala kombinationer tillsammans med möjligheten att visuali-sera de potentiella uppkopplingarna. I arbetet presenteras en föreslagen metod för att skapa dessa träd, tillsammans med uppslag på hur viktiga egenskaper hos kombinationerna kan visualiseras. Olika trädsökningsalgoritmer har också undersökts, och det visas att det inte är nödvändigt att söka igenom hela träd. Istället visar sig giriga algoritmer ha hög prestanda, samtidigt som sökstorleken kan hållas kraftigt begränsad.
As wireless communications is becoming an increasingly important part of our every day lives, the amount of transmitted data is constantly growing, creating a demand for ever-increasing data rates. One of the technologies used for boosting
data rates iscarrier aggregation, which allows for wireless units to combine
mul-tiple connections to the cellular network. However, there is a limited number of possible combinations defined, meaning that there is a need to search for the best combination in any given setup. This thesis introduces software capable of orga-nizing the defined combinations into tree structures, simplifying the search for optimal combinations as well as allowing for visualizations of the connections possible. In the thesis, a proposed method of creating these trees is presented, together with suggestions on how to visualize important combination character-istics. Studies has also been made on different tree traversal algorithms, showing that there is little need for searching through all possible combinations, but that a greedy approach has a high performance while substantially limiting the search complexity.
First of all, I would like to thank Ericsson for giving me the opportunity to write this thesis. A special thanks to my Ericsson supervisor Linnea Faxén, for always knowing the answers to my questions and for our many discussions on how to solve the problems I have faced. I would also like to thank my office mate Niklas Blomqvist for sharing interesting results from his thesis whenever I grew tired of writing my own report. At the university, I would like to thank my examiner Mikael Olofsson for his swift responses to my various questions and for providing valuable input on the report. Lastly, my deepest thanks to my supervisor Ema Becirovic for tirelessly scrutinizing my report during these past months, allowing me to improve its quality immensely. Writing my thesis with such an amazing team by my side has truly been a great privilege!
Linköping, June 2019 Fredrik Helders
List of Figures xiv
List of Tables xviii
Notation xix 1 Introduction 1 1.1 Purpose . . . 3 1.2 Problem Statements . . . 3 1.3 Limitations . . . 3 2 Theoretical Background 5 2.1 LTE . . . 5
2.1.1 Frequency Bands and Cells . . . 7
2.1.2 Multiple Frequency Band Indicator . . . 9
2.1.3 OFDM and Resource Blocks . . . 9
2.1.4 MIMO . . . 11 2.1.5 Link Adaptation . . . 13 2.1.6 Throughput . . . 15 2.1.7 Load . . . 15 2.2 Carrier Aggregation . . . 16 2.2.1 History . . . 18 2.2.2 UE Capabilities . . . 19 2.2.3 Power Consumption . . . 20
2.3 Basic Graph Theory . . . 22
2.3.1 Layouts . . . 23
2.4 Graph Traversal Algorithms . . . 23
2.4.1 Depth-First Search . . . 25 2.4.2 Beam Search . . . 26 3 Method 29 3.1 Assumptions . . . 29 3.1.1 Load Model . . . 30 xi
3.1.2 Unknown Signal Quality . . . 30
3.1.3 TDD and FDD are Considered Equal . . . 30
3.1.4 Base Stations Support Eight MIMO layers . . . 30
3.1.5 No Multi-Band Support . . . 30 3.2 Input . . . 31 3.2.1 3GPP Combinations . . . 31 3.2.2 Network Configurations . . . 32 3.2.3 UE Capabilities . . . 32 3.3 Graph Building . . . 35 3.3.1 Contiguous Cells . . . 37
3.3.2 Different Uplink Cases . . . 38
3.3.3 Bandwidth Combination Sets . . . 39
3.3.4 Compression . . . 40
3.4 Graph Traversal . . . 40
3.5 Load Balancing . . . 41
3.6 Visualization . . . 42
3.6.1 The Graph Modeling Language . . . 43
3.6.2 Tree Design . . . 44
4 Results 47 4.1 Graph Traversal Algorithms . . . 47
4.2 Graph Traversal Algorithms in Load . . . 56
4.2.1 Load Balancing Performance . . . 58
4.3 Carrier Aggregation Combination Trees . . . 60
4.4 Case Studies . . . 64
4.4.1 Influence of MIMO layers . . . 64
4.4.2 Investigation of a Combination Tree . . . 65
4.4.3 Chosen Cells in Different Load Conditions . . . 68
5 Discussion 69 5.1 Results . . . 69
5.1.1 Graph Traversal Algorithms . . . 69
5.1.2 Load Balancing . . . 70
5.1.3 Usefulness of Carrier Aggregation in Load . . . 71
5.1.4 Accidental Performance of Hill-Climbing . . . 71
5.2 Method . . . 72
5.2.1 Graph Building Approach . . . 72
5.2.2 Input Data . . . 73
5.2.3 Chosen Graph Traversal Algorithms . . . 73
5.2.4 Load Balancing Algorithm . . . 73
5.2.5 Source Criticism . . . 74
5.3 The Thesis from a Wider Perspective . . . 75
6 Conclusions 77 6.1 Answers to the Problem Statements . . . 77
6.1.2 Statement 2 . . . 78
6.1.3 Statement 3 . . . 78
6.2 Future work . . . 79
6.2.1 More Input Data . . . 79
6.2.2 Generating Network Input Data . . . 79
6.2.3 Multi-Band Support . . . 79
6.2.4 Compatibility with NR . . . 79
6.2.5 Making the Software Pure Python . . . 80
6.2.6 Throughput Estimations . . . 80
6.2.7 MIMO Capabilities and Throughput . . . 80
6.2.8 Improved Load Balancing . . . 80
A Additional Graph Search Results 83
B Additional Ghost Trees 89
2.1 Schematic overview of an LTE cellular network. . . 6
2.2 Illustration of how downlink and uplink are separated in TDD and FDD. . . 6
2.3 The possible cell BWs in LTE. . . 7
2.4 Length of the LTE radio frame, subframe and slot. . . 10
2.5 The time-frequency resource allocation of an RB with 12 subcarri-ers and 7 consecutive OFDM symbols. . . 11
2.6 Example of space diversity. The same information is sent over both transmitter antennas, protecting it from bit errors. . . 12
2.7 Example of spatial multiplexing. The information is split up and each half is sent through one of the two transmitter antennas, pos-sibly increasing the throughput with a factor two. . . 12
2.8 Example of both space diversity and spatial multiplexing. The in-formation is split into two parallel streams, which are sent by two transmitter antennas each. . . 13
2.9 Example of the maximum possible BW usage of LTE band 40 for a single UE with and without CA. . . 16
2.10 The three categories of CA combinations. . . 17
2.11 Cell distribution of the combination CA_1C-5A. . . 18
2.12 Power consumption as a function of transmitted file size. . . 20
2.13 Power consumption when using different number of CCs with the same total BW. . . 21
2.14 Power consumption when comparing intra-band to inter-band CA. 21 2.15 Example of a directed tree. All blue nodes belong to the same layer. The dashed edges mark a branch from the root node to a leaf node. 22 2.16 Axis-parallel tree layout. The name refers to that each layer is placed parallel to a horizontal axis. . . 24
2.17 Radial tree layout. The name refers to that each layer is placed on the same radius from the root node. . . 24
2.18 Search order of DFS in a tree. When choosing between several children, they can be picked in any order. In this example, the left child is always visited first. . . 25
2.19 Example of a beam search with β = 2. The investigated nodes are marked as blue. For this β, the algorithm misses optimal branch to the left. . . 27
3.1 Illustration of the ghost node used to bind PCells together. In the final graphs, the ghost is completely invisible, as are all the edges
connected to it. . . 35
3.2 The layer-by-layer build order of the nodes in a combination tree,
displayed by the node labels. . . 36
3.3 Flowchart over the tree building process. . . 37
3.4 A network and the corresponding CA combination tree. Cell 1 is chosen as PCell. In the tree, solid edges mark contiguous cells and dashed edges mark non-contiguous cells. All green nodes can be added according to the rules described. However, the black node is not added as cell 2 is contiguous with both cell 1 and cell 3, but
it is not adjacent to cell 1 in the tree. . . 38
3.5 An example of the handling of different UL configurations. Cell 1 is chosen as PCell, and therefore must have UL activated. Cell 2 can then be added with its UL either activated or deactivated,
which results in two separate branches. . . 39
3.6 An example of the handling of BCSs. Combining cell 1 and 2 re-sults in the same combination as combining cell 1 and 3. The BW of cell 2 corresponds to BCS 0, while the BW of cell 3 corresponds
to both BCS 1 and 2. . . 39
3.7 Example of a exponential search with β = 2. The investigated nodes are marked as blue. For this β, the algorithm misses
opti-mal branch to the left. . . 40
3.8 Coloring of the different cell BWs. The colors are chosen as shades of blue, where a lighter blue corresponds to a higher BW. Moreover, the label text color is also affected by the BW in order to ensure a
high contrast between text and background. . . 44
3.9 The CA combination tree of the Swedish UE in the Swedish net-work as visualized in the thesis. The PCell is chosen to be a 5 MHz
cell in band 3, which has been assigned the cell id number 2. . . . 45
3.10 The ghost mode CA combination tree of the Swedish UE in the Swedish network as visualized in the thesis. The tree from
Fig-ure 3.9 is seen in the lower right part of the ghost tree. . . 46
4.1 Found effective BW for six different graph search methods when
investigating the Swedish network. . . 48
4.2 Number of searched nodes for six different graph search methods
when investigating the Swedish network. . . 49
4.3 Found effective BW for six different graph search methods when
investigating the American network. . . 50
4.4 Number of searched nodes for six different graph search methods
when investigating the American network. . . 51
4.5 Found effective BW for six different graph search methods when
investigating the Swedish UE in the Swedish network. . . 52
4.6 Number of searched nodes for six different graph search methods
4.7 The found effective BW in the Swedish network for the search al-gorithms under different load. In each simulation, 50% of the
con-nected UEs were Swedish, and 50% were International. . . 56
4.8 The found effective BW in the American network for the search algorithms under different load. In each simulation, 50% of the
connected UEs were American, and 50% were International. . . . 57
4.9 The relative standard deviation of the assigned effective BW for the connected UEs in the two test networks under different load, when
using DFS for searching the graphs. . . 59
4.10 The ghost tree of the Swedish UE in the Swedish network. It is notable that the maximum number of CCs is three, compared to the network maximum of five which is seen in Figure 4.11. It is also shown that the best combination, marked by square nodes, in
this case is CA_3C, with one 10 MHz cell and one 20 MHz cell. . . 61
4.11 The ghost tree of the Swedish network. It is notable that the maxi-mum number of CCs is five and that there are very few green edges
marking contiguous cells present. . . 62
4.12 The ghost tree of the American network. It is notable that the max-imum number of CCs is five and that there is a significant number of green edges marking contiguous cells present, as opposed to the
Swedish network displayed in Figure 4.11. . . 63
4.13 The combination tree for the Swedish UE in the Swedish network with cell number 7 as PCell. Note that due to the increase in effec-tive BW from MIMO layers, it is better to stop at 2 CCs than to use
the full 3 CC branch. . . 64
4.14 The CA combination tree for the American network using cell
num-ber 2 as PCell. . . 67
A.1 Found effective BW for six different graph search methods when
investigating the International UE in the Swedish network. . . 84
A.2 Found number of searched nodes for six different graph search methods when investigating the International UE in the Swedish
network. . . 84
A.3 Found effective BW for six different graph search methods when
investigating the American UE in the American network. . . 85
A.4 Found number of searched nodes for six different graph search methods when investigating the American UE in the American
net-work. . . 86
A.5 Found effective BW for six different graph search methods when
investigating the International UE in the American network. . . . 87
A.6 Found number of searched nodes for six different graph search methods when investigating the International UE in the American
B.1 The ghost tree of the International UE in the Swedish network. No-table is that the maximum number of CCs is two. It is also shown that the best combination, marked by square nodes, in this case is
CA_3A-7A, with one 20 MHz cell and one 15 MHz cell. . . 90
B.2 The ghost tree of the American UE in the American network. No-table is that the maximum number of CCs is five. It is also shown, if zoomed in, that the best combination, marked by square nodes,
in this case is CA_2A-66C, with three 20 MHz cells. . . 91
B.3 The ghost tree of the International UE in the American network. Notable is that the maximum number of CCs is three. It is also shown that the best combination, marked by square nodes, in this
2.1 Properties of LTE band 1 and 4. . . 7
2.2 EARFCN settings for LTE band 1-5. . . 8
2.3 Frequency range of LTE band 3 and 9. . . 9
2.4 The possible RB configurations in LTE. . . 10
2.5 Number of RBs in the different LTE cell BWs. . . 10
2.6 LTE modulation schemes and channel code rates based on CQI. This was the first set of settings to be defined in LTE. . . 14
2.7 Throughput of three example UEs. . . 15
2.8 Characteristics of the LTE CA BW classes. . . 17
2.9 Possible BWs for each cell for the combination CA_1C-5A. . . 18
2.10 Possible BWs for each CC for the combination CA_3A-8A. . . 19
3.1 Assumptions made in the thesis. The section column tells where each assumption is described. . . 29
3.2 The estimated use of LTE bands by Telia. . . 32
3.3 The cell configuration in the estimated Swedish network. . . 33
3.4 The cell configuration in the estimated American network. . . 33
3.5 Some properties of the UEs used in the thesis. . . 34
3.6 The use of tree attributes to visualize CA combination characteris-tics. . . 44
4.1 The average found effective BW and number of searched nodes for all the tested search algorithms, given as percentages of the the-oretical maximums. The numbers are divided into network tree averages and UE tree averages. . . 54
4.2 Resulting effective BW and number of searched nodes when using the six different search algorithms on the ghost trees. . . 55
4.3 Number of PCells with optimal combinations of different number of CCs for the Swedish and American UEs, both with and without the usage of MIMO layers. . . 65
4.4 Number of UEs connected to each cell in the Swedish network un-der different load conditions. In each simulation, 50% of the con-nected UEs were Swedish, and 50% were International. None of these UEs can connect to cell 9 and 10, and these cells are thus marked as unavailable. . . 68
Abbreviations
Abbreviation Description
3GPP 3rd Generation Partnership Project
BCS Bandwidth Combination Set
BFS Breadth-First Search
BW Bandwidth
CA Carrier Aggregation
CC Component Carrier
CQI Channel Quality Indicator
CSV Comma-Separated Value
DFS Depth-First Search
DL Downlink
EARFCN E-UTRA Absolute Radio Frequency Channel Number
E-UTRA Evolved Universal Terrestrial Radio Access
FDD Frequency-Division Duplex
GML Graph Modeling Language
ITU International Telecommunication Union
LTE Long-Term Evolution
MFBI Multiple Frequency Band Indicator
MIMO Multiple-Input Multiple-Output
NR New Radio
OFDM Orthogonal Frequency-Division Multiplexing
PCell Primary Serving Cell
QAM Quadrature Amplitude Modulation
QPSK Quadrature Phase-Shift Keying
RB Resource Block
RSD Relative Standard Deviation
SCell Secondary Serving Cell
TDD Time-Division Duplex
UE User Equipment
UL Uplink
Defined Parameters
Parameter Description
α Number of active UEs
β Beam width
BWeff Effective BW
fc Center frequency
flow Lower frequency of an LTE band
e Number of edges in a graph
G Graph
L Number of MIMO layers
µ Mean value
N EARFCN
NOffs EARFCN offset
σ Standard deviation
T Throughput
Tmax Maximum throughput of a UE
Tavg Average throughput of a UE
1
Introduction
The usage of mobile data is currently exploding. The global data traffic today is ten times higher than five years ago, and has almost doubled during 2018 alone. Looking forward, this trend will continue. Ericsson estimates that the data traffic will be five times higher in 2024, than in 2018. If this prediction comes true, the
amount of data traffic globally will be at 130 Exabytes (1018bytes) per month in
2024 [1]. Looking at individual users, the amount of data traffic per smartphone is also estimated to increase with about a factor five from 2016 to 2022, to 11 Gigabytes per month [2]. Similar predictions made by the International Telecom-munication Union (ITU) go even further. They expect the global data traffic to reach 353 Exabytes per month in 2024, excluding machine-to-machine commu-nication, and that the traffic per subscription will increase to 12.1 Gigabytes per month in 2022 [3]. Furthermore, the portion of traffic consisting of video is be-lieved by Ericsson to increase from 60% in 2018 to 74% in 2024 [1], and by ITU to increase to 80% in 2025 [3], leading to an increasing demand on high data rates for the users. Thus, one of the most fundamental challenges in the evolution of mobile communications today is to find ways for increasing the data rates in order to meet the rising demands from the users.
In order to do increase the user data rates, there are two fundamental ap-proaches. The first is to improve the spectral efficiency, i.e. increase the data rates possible for a given bandwidth (BW) [4, Ch. 1]. One way of doing this is by increasing the number of used antennas, known as MIMO (multiple-input multiple-output) [4, Ch. 11], [5, Ch. 8]. MIMO has been an important part of Long-Term Evolution (LTE), and enhancements to multi-antenna transmission
has been added in several of the LTE Releases1 [7, Ch. 4]. The other solution to
boosting data rates is to increase the BW available to each user [4, Ch. 1], and the
1The termRelease is used for the different versions of mobile standards by 3GPP [6]. LTE was
introduced in Release 8.
main technology for doing this in LTE iscarrier aggregation (CA), which will be the focus for this thesis [4, Ch. 28], [7, Ch. 4].
CA increases the total BW for units of user equipment (UEs) connected to the mobile network by connecting each UE to multiple cells. When CA is not used, a device using LTE will be assigned to a single cell. These cells can have a BW of either 1.4, 3, 5, 10, 15, or 20 MHz [8, Ch. 5]. In Release 8, before CA was introduced, the theoretical peak downlink (DL) data rate was 150 Mbit/s, which was achieved when using 20 MHz of BW [7, Ch. 4]. When CA was introduced in Release 10, it supported up to five different component carriers (CCs), resulting in a maximal BW of 100 MHz for a UE [4, Ch. 28]. Later on, in Release 13, the num-ber of possible CCs was increased from five to 32, thus giving a new maximal BW of 640 MHz. In total, utilizing both improved spectral efficiency and increased BW, the theoretical peak DL data rates in Release 13 was 25 Gbit/s [7, Ch. 4]. Note however, that the theoretical limit is not the same as actually achievable data rates, as optimal conditions can never be met in reality.
The problem with CA is that there is a limited number of ways to combine the different LTE cells. These combinations are today listed in tables in a techni-cal specification document from the 3rd Generation Partnership Project (3GPP), the standardization organization for LTE, see [8, Ch. 5]. These tables are by their nature not easily handled by neither human nor computer, making the subject difficult to work with. However, far from all combinations are possible in reality. Operators own different parts of the spectrum, and not all defined LTE frequency bands are present everywhere in the world [9]. Moreover, every UE can not han-dle all combinations [10], [11], further reducing the number of possible ways to aggregate the carriers. Thus, the maximum BW of 640 MHz is never used, which is one of the reasons to why the theoretical peak DL data rates are never reached in reality.
Given the possible CA combinations, the task when using CA is to decide which cells that a given UE should be assigned to, with the goal of finding the combination that maximizes the achievable data rate. However, the specification [8] has several thousand defined combinations, making it unfeasible to consider them all when deciding on what combination to use. Furthermore, there are several parameters that affects the actual data rates. The fundamental parame-ter is BW, but factors such as channel quality or current load in different cells also influence the final data rate. As a result, it is tractable to limit the searches through possible combinations in an efficient way, so that the search complexity is reduced while maintaining a result not too far from the optimum.
This thesis will investigate the possibilities of structuring the CA combina-tions into graphs for analysis and visualization. The main advantage of using graphs is the existence of a large number of graph traversal algorithms, enabling calculations of feasible combinations for a given setup. Utilizing the structure of a graph for visualization is also an intuitive way of describing the problem for a human observer. Moreover, the graph traversal algorithms will also be studied in different load conditions. This investigation will consider the possibilities of assigning multiple UEs in a network, such that their resulting data rates are fairly distributed, while maintaining a high throughput in the network as a whole.
1.1
Purpose
The purpose of this master thesis is to create software capable of finding good choices of CA combinations in order to get high data rates, while retaining a low time complexity. The software is also to produce visualizations of the possible combinations to give a user-friendly representation of the problem, simplifying human analysis of the combination characteristics.
1.2
Problem Statements
The thesis aspires to answer the following questions:
1. When visualizing CA combinations, which characteristics are most impor-tant to display and how should each of them be presented?
2. When searching for CA combinations, what is the most efficient way to per-form graph traversals when considering the resulting effective bandwidth and the number of investigated nodes?
3. How are the graph searches affected by the load of the network?
1.3
Limitations
This thesis is limited to CA combinations in LTE, and does not study the New Radio (NR) case. The main reason for this is that there are only a few dozen combinations defined for NR, as of early 2019, as opposed to the thousands of combinations defined for LTE [8, Ch. 5], [12, Ch. 5].
In the typical use case, most data is sent through the DL. Thus, the primary goal of CA is to increase the DL data rates [7, Ch. 4], [13]. Hence, this thesis will focus solely on the DL case, and no calculations will be done on uplink (UL) data rates. Further assumptions made in the thesis can be found in Section 3.1.
2
Theoretical Background
This chapter presents the theoretical background related to the thesis. In Sec-tion 2.1, relevant parts of the LTE standard are described. The main themes in this description are LTE band and cell characteristics, and throughput factors. CA itself is then covered in Section 2.2, with a focus on the possibilities and lim-itations in the combining of carriers. Section 2.3 describes some basic graph the-ory, including definitions of relevant graph characteristics and different methods of positioning the nodes in a graph when performing visualizations. Section 2.4
describes thedepth-first search and beam search algorithms, which will be used in
order to analyze the CA combinations.
2.1
LTE
LTE is a cellular communications technology developed by 3GPP. It was intro-duced in 3GPP Release 8, launched commercially in 2009 in northern Europe [4, Ch. 1] and is now used globally [9]. The purpose of LTE was to fulfill the re-quirements set for the fourth generation of mobile communications systems, a
goal that was achieved in Release 10LTE-Advanced. Compared to the third
gen-eration technologies, some of the main areas of development for LTE included reduced delays, increased data rates and a greater flexibility of spectrum usage [4, Ch. 1].
As in any cellular communications system [14, Ch. 9], LTE has a network
architecture consisting of base stations, known aseNodeBs [4, Ch. 1]. When
con-necting a UE to an LTE network, it will connect to the eNodeB with the strongest signal, which depends on the UE’s geographical location, as seen in Figure 2.1.
eNodeB UE
Figure 2.1:Schematic overview of an LTE cellular network.
In order to separate DL transmissions from UL, LTE uses eithertime-division
duplex (TDD) or frequency-division duplex (FDD). In TDD, DL and UL transmis-sions are separated in the time domain, meaning that the UE and the eNodeB do not both transmit at the same time. For FDD, the DL and UL transmissions are instead located on separate frequencies [14, Ch. 7]. Both duplex modes are illustrated in Figure 2.2.
time
frequency
time
frequency
Uplink
Downlink
TDD
FDD
Figure 2.2: Illustration of how downlink and uplink are separated in TDD
2.1.1
Frequency Bands and Cells
3GPP has divided the assigned spectrum for LTE into 66 different frequency bands, with some important properties defined for each band. Firstly, a fre-quency range for both UL and DL transmission is specified, including upper and lower bounds for the frequencies. Secondly, the available duplex mode is chosen to be either TDD or FDD. Lastly, the possible cell BWs are defined. To illustrate, the properties for band 1 and 4 are listed in Table 2.1. Note that bands might overlap in frequency, such as band 1 and 4 do in the DL [8, Ch. 5].
Table 2.1:Properties of LTE band 1 and 4 [8, Ch. 5].
Band UL frequencies [MHz] DL frequencies [MHz] Duplex Possible cell BWs [MHz] 1 1920 - 1980 2110 - 2170 FDD 5, 10, 15, 20 4 1710 - 1755 2110 - 2155 FDD 1.4, 3, 5, 10, 15, 20
In this thesis, the termcell will be used for a part of a frequency band that a
UE can connect to with a CC. With this definition, there can be several cells in a
single eNodeB. Within CA, this is referred to asserving cells, which is discussed
in Section 2.2 [4, Ch. 28]. The creation of cells in a network is done by the mobile network operators, and the main CA related limitation inferred by 3GPP is that all cells must have a BW of either 1.4, 3, 5, 10, 15, or 20 MHz [8, Ch. 5], as illustrated in Figure 2.3. There are several other limitations on cell creation in LTE, but these are not directly related to CA and thus omitted in this thesis.
15 MHz f 10 MHz f 5 MHz f 3 MHz f 1.4 MHz f 20 MHz f
Something that is worth noting is that the maximum BW of a cell differs be-tween FDD and TDD bands. In a TDD band, a 20 MHz cell transmits both UL and DL data within these 20 MHz. A FDD cell on the other hand will instead have a 20 MHz channel for UL transmissions, and another 20 MHz channel for DL transmissions. However, considering that the focus in this thesis is DL data rates, these two cases will be treated as equal. The motivation for this is that a TDD cell that only transmits DL data could have the same amount of resources available for DL data as a FDD cell of the same BW. This is not entirely true in LTE, where a TDD cell can not use more than 80% of its resources for DL [4, Ch. 6], but it is an assumptions used for simplifying the implementation process.
To specify the band and center frequency, fc, of a cell, LTE uses a system
of E-UTRA Absolute Radio Frequency Channel Numbers1 (EARFCNs). Using a
EARFCN, the fcis calculated as
fc= flow+ 0.1(N − NOffs) [MHz] (2.1)
where flow is the lowest frequency in the current band, N is the given EARFCN
and NOffsis a band-specific offset. The same formula is used for both DL and UL,
but with other values of flow, N and NOffs[15, Ch. 5]. Examples of the variable
values for band 1-5 can be found in Table 2.2. One advantage of the EARFCN system is that it can be used to tell overlapping LTE bands apart, see Example 2.1.
Table 2.2:EARFCN settings for LTE band 1-5 [15, Ch. 5].
Band Downlink Uplink
flow NOffs Range ofN flow NOffs Range ofN
1 2110 0 0 - 599 1920 18000 18000 - 18599
2 1930 600 600 - 1199 1850 18600 18600 - 19199
3 1805 1200 1200 - 1949 1710 19200 19200 - 19949
4 2110 1950 1950 - 2399 1710 19950 19950 - 20399
5 869 2400 2400 - 2649 824 20400 20400 - 20649
Example 2.1: EARFCN to tell overlapping bands apart
As seen in Table 2.1, band 1 and 4 are overlapping in the DL. Thus, a DL center
frequency fc = 2115 MHz could possibly belong to either band 1 or 4. However,
by using the EARFCN, it is possible to calculate both the fc and what band is
used. So, using (2.1) and Table 2.2, both the following EARFCNs would result in
a fc= 2115 MHz:
• EARFCN = 50 → fc= 2115 MHz in band 1.
• EARFCN = 2000 → fc= 2115 MHz in band 4.
2.1.2
Multiple Frequency Band Indicator
As mentioned in Section 2.1.1, some of the defined frequency bands are over-lapping [8, Ch. 5], which has the consequence that some cells could belong to more than one band. LTE has support for assigning several bands to a cell, which
is done with the help ofmultiple frequency band indicators (MFBIs). The MFBI is
used in both eNodeBs and UE, but with different approaches. In an eNodeB, each
cell is assigned amain band. If a cell is to be present in multiple bands, this is
indicated by the MFBI and it is assigned analternative band. The UE on the other
hand simply indicates whether it can connect to alternative bands or not, only using one single bit MFBI. An example is found in Example 2.2.
Example 2.2: UE and eNodeB use of MFBI
The operating frequencies for LTE band 3 and 9 are shown in Table 2.3, where it is clear that all cells placed within band 9 are also placed within band 3.
Table 2.3:Frequency range of LTE band 3 and 9 [8, Ch. 5].
Band UL frequencies [MHz] DL frequencies [MHz]
3 1710 - 1785 1805 - 1880
9 1749.5 - 1784.9 1844.5 - 1879.5
Say that an eNodeB has one single cell at fc, UL = 1760 MHz and fc, DL =
1860 MHz. This cell could then possibly belong to both band 3 and 9. We choose to set the cell’s main band to be band 9 and, as we want to specify an alternative band as well, set the cell’s MFBI to true and specifies its alternative band to be band 3.
If a UE that is trying to connect to this eNodeB only supports band 3 it might not be able to connect to the network, as band 3 is the alternative band of the cell. The two possibilities are:
• If the UE’s MFBI is true, meaning that it can connect to alternative bands, it will be able to connect to the network.
• If the UE’s MFBI is false, it will not be able to connect to the alternative band, and therefore can not connect to the network at all.
2.1.3
OFDM and Resource Blocks
LTE uses the multicarrier technology calledorthogonal frequency-division
multi-plexing (OFDM) when modulating downlink signals. The idea behind OFDM is to separate a channel into several streams that are overlapping in frequency, but that are spaced such that they remain orthogonal to each other. Thus, OFDM achieves an efficient use of the frequency spectra by avoiding the guard bands between subcarriers needed in other modulation schemes [4, Ch. 5], [14, Ch. 4].
In LTE, the time resources are divided into 10 ms radio frames. Every radio frame is then divided into 10 subframes of 1 ms each. The subframes are then further split into two 0.5 ms slots, see Figure 2.4 [4, Ch. 5].
t t t 1 ms subframe 0.5 ms slot 10 ms radio frame
Figure 2.4:Length of the LTE radio frame, subframe and slot.
For every time slot, the frequency resources are divided intoresource blocks
(RBs) of 180 kHz each. These RBs then contain OFDM symbols. The number of OFDM symbols in an RB depends on the number of consecutive OFDM symbols in the time domain and the amount of subcarriers in the RB. The amount of sub-carriers is in turn dependent on the subcarrier spacing, i.e the distance between the subcarrier center frequencies [16, Ch. 6]. The possible RB configurations are listed in Table 2.4 and a graphical representation of the topmost configuration in Table 2.4 is found in Figure 2.5. The number of RBs per time slot in a cell is dependent on the cell BW [8, Ch. 5] and the conversion between cell BW and RBs is found in Table 2.5.
Table 2.4:The possible RB configurations in LTE [16, Ch. 6].
Subcarrier spacing Subcarriers Consecutive symbols OFDM symbols 15 kHz 12 7 84 15 kHz 12 6 72 7.5 kHz 24 3 72 1.25 kHz 144 1 144
Table 2.5:Number of RBs in the different LTE cell BWs [8, Ch. 5].
BW [MHz] 1.4 3 5 10 15 20
12 11 10 9 8 7 6 5 4 3 2 1 2 3 4 5 6 7 0.5 ms 180 kHz
Resource block
OFDM symbolFigure 2.5:The time-frequency resource allocation of an RB with 12
subcar-riers and 7 consecutive OFDM symbols.
2.1.4
MIMO
As mentioned in Chapter 1, MIMO (multiple-input multiple-output) increases the spectral efficiency with the help of multiple antennas at the transmitter and receiver. Usually, the MIMO concept is divided into three categories:
• Single-user MIMO (also called point-to-point MIMO), • Multi-user MIMO, and
• Massive MIMO.
In single-user MIMO, a base station uses multiple antennas to communicate with a UE with multiple antennas. Different users are multiplexed orthogonally, for example by using FDD or TDD. Multi-user MIMO is based on the idea to serve several UEs within the same time-frequency resources, and multiple antennas are used in the base station to allow separation of the different data streams. Lastly, there is massive MIMO. Just as in multi-user MIMO, several UEs are served within the same time-frequency resources in massive MIMO. However, massive MIMO is a much more scalable technique are therefore can be used to boost the network performance considerably, essentially by simply adding more base station antennas [17, Ch. 1]. Both single-user MIMO and multi-user MIMO are used in LTE [4, Ch. 11], but the focus for this section will be the single-user case.
The benefits of single-user MIMO can be divided intodiversity gain and
mul-tiplexing gain, which will both be briefly described here. Diversity techniques are used to lower the bit error rate of a transmission. The idea of diversity is to send several instances of the same information. There are a number of
example. In a time diversity system, all information is sent more than once at different times, giving the receiver more information to use when decoding the
data. The same principle can be used with multiple antennas, calledspace
diver-sity. By transmitting the same information over several antennas, and likewise receiving the information on several antennas, the different data streams give the same types of benefits for decoding data as time diversity does [14, Ch. 5]. An example of space diversity is illustrated in Figure 2.6.
...01011100... ...01011100...
Figure 2.6: Example of space diversity. The same information is sent over
both transmitter antennas, protecting it from bit errors.
Diversity is only used to decrease bit error rates, which indirectly can improve the data rates by allowing for higher order modulation schemes. Multiplexing on the other hand, is directly used to improve data rates. When using multiple
an-tennas, it is possible to employspatial multiplexing to increase the amount of data
sent over the channel. Instead of transmitting the same information over sev-eral antennas, the antennas are used to transmit parallel data streams. This has the potential of increasing the data rate proportionally to the number of anten-nas, so that doubling the number of antennas doubles the achievable data rate. Note however that both the transmitter and receiver must be able to handle all the individual data streams. Thus, if there is a different number of antennas on the transmitting and the receiving side, it is only possible to use as many data streams as the lower number of antennas [4, Ch. 11], [14, Ch. 5]. An example of spatial multiplexing is illustrated in Figure 2.7.
...01011100... ...01011100...
...0101...
...1100...
...0101...
...1100...
Figure 2.7: Example of spatial multiplexing. The information is split up
and each half is sent through one of the two transmitter antennas, possibly increasing the throughput with a factor two.
In LTE, the termMIMO layer is used for a data stream generated by the help of spatial multiplexing [4, Ch. 11]. LTE supports a maximum of eight MIMO layers for the DL, and four layers for the UL [4, Ch. 29], [7, Ch. 4]. It is also possible to combine spatial multiplexing and space diversity [4, Ch. 29]. As an example, consider DL transmissions from an eNodeB with four antennas to a UE with two antennas. It would then be possible to use two MIMO layers, where each layer is transmitted through two transmit antennas. By increasing the number of UE antennas to four, it would be possible to use four MIMO layers, but at the cost of removed diversity. Theoretically, the throughput could increase a factor two by using the higher number of UE antennas, and thus twice as many layers. However, the bit error rate of each layer will increase, which could limit the data rate improvements. An example of combined space diversity and spatial multiplexing is illustrated in Figure 2.8.
...01011100... ...01011100...
...1100...
...0101... ...0101...
...1100...
Figure 2.8: Example of both space diversity and spatial multiplexing. The
information is split into two parallel streams, which are sent by two trans-mitter antennas each.
2.1.5
Link Adaptation
The purpose of link adaptation is to maximize the throughput at a given signal-to-noise ratio, i.e. to maximize the rate of successfully transmitted information bits. When performing the link adaptation in a system, the two main design variables are the modulation scheme and the channel coding. Higher order modulation techniques give a higher potential data rate, but also an increased probability
of bit errors. As for the channel coding, a code with a low probability of error will consequently have a lower information data rate. This results in a trade-off situation where, depending on the channel, different setups of modulation schemes and channel codes give the best throughput [18, Ch. 9].
In LTE, achannel quality indicator (CQI) is used to determine the used
modu-lation scheme and channel code. Once every few milliseconds, a UE performs an estimation of the channel and then reports the corresponding CQI value to the eNodeB. The CQI is a four bit value, creating 16 possible options for the modula-tion scheme and channel code to choose from [4, Ch. 10]. However, depending on the UE, there is a total of six different sets of options available in Release 15. One of the main differences between these sets is that some only supports quadrature phase-shift keying (QPSK) and quadrature amplitude modulation (QAM) of order 16 (16QAM) and 64 (64QAM) respectively, while other sets also support 256QAM and 1024QAM [19, Ch. 7]. The set that was first defined for LTE [4, Ch. 10] is shown in Table 2.6.
Table 2.6: LTE modulation schemes and channel code rates based on CQI.
This was the first set of settings to be defined in LTE [4, Ch. 10], [19, Ch. 7].
CQI Modulation Channel code rate
[info bits/transmitted bit]
Efficiency
[info bits/OFDM symbol]
0 Channel too weak to use
1 QPSK 0.076 0.1523 2 QPSK 0.117 0.2344 3 QPSK 0.188 0.3770 4 QPSK 0.301 0.6016 5 QPSK 0.438 0.8770 6 QPSK 0.588 1.1758 7 16QAM 0.369 1.4766 8 16QAM 0.479 1.9141 9 16QAM 0.602 2.4063 10 64QAM 0.455 2.7305 11 64QAM 0.554 3.3223 12 64QAM 0.650 3.9023 13 64QAM 0.754 4.5234 14 64QAM 0.853 5.1152 15 64QAM 0.926 5.5547
It is important to note that the CQI value is calculated based on channel mea-surements and is therefore unknown before connecting to a cell, meaning that it cannot be used for cell selection. Instead, LTE uses other measurements of the
signal strength, known as Reference Signal Received Power and Reference Signal
2.1.6
Throughput
To summarize, the throughput of an LTE channel is directly dependent on several factors:
• The number of OFDM symbols per RB, given by Table 2.4.
• The number of RBs per slot, depending on the cell BW as seen in Table 2.5. • The number of information bits per OFDM symbol, given by Table 2.6. • The number of MIMO layers, denoted as L, as described in Section 2.1.4. Consequently, the resulting throughput can be calculated as:
T = 2000 slots s · RBs slot· OFDM symbols RB · info bits
OFDM symbol· L [bit/s] (2.2)
Note that this equation does not consider space diversity, as the effect on through-put from the lowered bit error rate depends on the CQI, making the calculations quite complex. An example comparing the effect of BW and CQI on the resulting throughput is found in Example 2.3.
Example 2.3: The effect on throughput from BW and CQI
By comparing three UEs with different BWs and reported CQI values, it is possi-ble to see the effect of these parameters on the throughput. In Tapossi-ble 2.7, UE 1 has the smallest cell BW possible, but the best channel strength. UE 2 is the opposite of UE 1, having maximum BW and low channel strength. UE 3 is a compromise with a medium BW and channel strength.
The throughput is then calculated by using (2.2). The RB configuration is chosen to be 84 OFDM symbols/RB, and L is assumed to be 1. Moreover Ta-ble 2.5 is used to find the number of RBs, and TaTa-ble 2.6 to find the number of info bits/OFDM symbol. The results are presented in Table 2.7, where it can be seen that having average values for both BW and signal quality result in signifi-cantly higher data rates.
Table 2.7:Throughput of three example UEs.
UE BW [MHz] CQI Throughput [Mbit/s]
1 1.4 15 5.60
2 20 1 2.56
3 10 8 16.08
2.1.7
Load
As discussed in Section 2.1.6, many factors such as the cell BW and channel qual-ity affect the resulting data rates. Another factor to consider is the current load
of the cell, i.e how many UEs a cell is handling at a given moment. When several UEs are connected to the same cell, they must share the RBs of that cell, resulting in fewer resources available for each user per time slot. The average throughput can be described as Tavg= Tmax· E 1 α , α ≥ 1 (2.3)
where Tmax is the maximum achievable user throughput in bits/s, calculated
us-ing (2.2), α is the number of active UEs, and E { · } is the expected value [20].
However, the term Enα1ois not always possible to compute and [20] therefore
pro-poses several approximations for Tavg. In this thesis, the number of active users
is instead assumed to be known and constant. This assumption simplifies (2.3) into the easily calculated
Tavg=
Tmax
α , α ≥ 1 (2.4)
2.2
Carrier Aggregation
The fundamental idea of CA is to aggregate several carriers by letting a UE con-nect to multiple cells, by using multiple CCs. This way, a UE can utilize a higher BW than the 20 MHz limit for a cell in LTE, which results in higher data rates [4, Ch. 28]. An illustration of the difference in possible BW usage for a UE is found in Figure 2.9. 100 MHz 100 MHz 20 MHz
Without CA
With CA
20 MHz 20 MHz 20 MHz 20 MHz 20 MHzFigure 2.9:Example of the maximum possible BW usage of LTE band 40 for
a single UE, with and without CA [8, Ch. 5].
As a UE connects to a network, it will be assigned a Primary Serving Cell
(PCell), regardless of whether CA is used or not. However, by using CA, the UE
is also assigned to one or severalSecondary Serving Cells (SCells), with the main
purpose of increasing the user BW [4, Ch. 28]. One difference between the PCell and SCells is that while the PCell always handles UL data, the UL for the SCells is optional. However, both the PCell and SCells will always handle DL data. As
a consequence, the number of DL carriers is always larger than or equal to the number of UL carriers for all UEs [21, Ch. 7].
When aggregating carriers, there are three categories of combinations: intra-band contiguous, intra-intra-band non-contiguous and inter-intra-band. Intra-intra-band indi-cates that all CCs are within the same LTE band, while inter-band on the other hand implies that several LTE bands are present in the combination. For contigu-ous aggregation, the CCs are adjacent in frequency, while there are frequency-gaps in the non-contiguous case. As a consequence, inter-band aggregation is al-ways non-contiguous. The main advantage of non-contiguous CA is that it allows for higher user BWs for mobile network operators with a fragmented spectrum [13]. The three cases are illustrated in Figure 2.10.
LTE band X
LTE band Y
Intra-band contiguous
Intra-band non-contiguous
Inter-band
Figure 2.10:The three categories of CA combinations.
For CA, there are seven definedbandwidth classes to specify contiguous blocks
of cells. These are denoted with a letter and indicate the number of CCs as well as a possible range for the resulting BW [8, Ch. 5]. The LTE CA BW classes are listed in Table 2.8.
Table 2.8:Characteristics of the LTE CA BW classes [8, Ch. 5].
BW class Aggregated BW [MHz] Number of CCs
A BW ≤ 20 1 B 5 < BW ≤ 20 2 C 20 < BW ≤ 40 2 D 40 < BW ≤ 60 3 E 60 < BW ≤ 80 4 F 80 < BW ≤ 100 5 I 140 < BW ≤ 160 8
Note: BW class I is currently not in use.
be found in [8]. For each combination, 3GPP specifies the combined CCs together with their available BWs. Furthermore, each combination has a maximum
aggre-gated BW and a bandwidth combination set (BCS) value. The BCS is further
ex-plained in Section 2.2.2. When denoting the different combinations, contiguous blocks of CCs are listed with their LTE band and BW class while non-contiguous CCs are separated using a hyphen. Potential BWs for contiguous CCs are listed in the order of rising center frequency [8, Ch. 5]. An example of a combination defined by 3GPP is found in Example 2.4.
Example 2.4: CA combination definition
The combination CA_1C-5A consists of two contiguous CCs in band 1 and a single CC in band 5, as seen in Figure 2.11. The possible BWs for each CC are listed in Table 2.9, based on Table 5.6A.1-1 and Table 5.6A.1-2 in [8]. Note that there are two disjoint alternatives, depending on the chosen BW for the band 1
CC with the lower fc[8, Ch. 5].
1C
5A
20 – 40 MHz
≤20 MHz
Figure 2.11:Cell distribution of the combination CA_1C-5A.
Table 2.9:Possible BWs for each cell for the combination CA_1C-5A.
Cell BW [MHz] Alternative Band 1 Lowerfc Band 1 Higherfc Band 5 1 5, 10, 15 20 5, 10 2 20 5, 10, 15, 20 5, 10
2.2.1
History
The first LTE specification was 3GPP Release 8, commercially launched in late 2009. CA was however not introduced until Release 10 in 2010 [7, Ch. 4]. The first version of CA supported up to five CCs, and thus a maximum aggregated BW of 100 MHz [4, Ch. 28], [7, Ch. 4]. Despite the theoretical limit of five CCs, 3GPP only specified three possible CA band combinations of two CCs each:
• CA_1C, • CA_40C, and
• CA_1A-5A [22, Ch. 5].
In Release 10, all CCs needed to use the same duplex scheme. However, this demand was relaxed in Release 12, where aggregation between FDD and TDD car-riers was defined. With Release 13, the maximum number of CCs was increased to 32, enabling a total BW of 640 MHz [7, Ch. 4]. However, just as in Release 10, there are no combinations with the maximum number of CCs. As of Release 15, the largest number of CCs in a combination was seven [8, Ch. 5].
Since CA has been developed under the lifetime of LTE, there have always been UEs which do not support the latest Release, and thus not the latest specifi-cation of CA. For example, when CA was introduced in Release 10, the UEs on the market were not capable of using CA at all. For this reason, CA has always been backwards compatible, and each CC still use the structure as it did in Release 8 [7, Ch. 4].
2.2.2
UE Capabilities
The possible CA combinations in a mobile network are determined by 3GPP and the network configuration. However, each UE can only handle a limited part
of all combinations. This is referred to as UE capabilities. As opposed to the
combination limitations inferred by 3GPP and the network configuration, the UE capabilities do not directly specify cell BWs. Instead, the UE defines available band combinations and BCSs for each such combination. Moreover, the UE also reports how many MIMO layers it can support for each cell in a combination [11].
The BCSs are groups of potential cell BWs for a given band combination. Thus, a UE can indicate what group of BW configurations that it supports, rather than listing every possible combination [8, Ch. 5]. An example of UE capabilities and BCS is given in Example 2.5.
Example 2.5: UE capabilities and BCS
Table 2.10 displays the band combination CA_3A-8A, as defined by [8]. A UE can then, through UE capability messages, report that it supports the Combina-tion CA_3A-8A with BCS 1 and 3. The possible BW combinaCombina-tions for CA_3A-8A would in this case be given by alternative two and four in Table 2.10.
Table 2.10:Possible BWs for each CC for the combination CA_3A-8A.
Alternative Band 3 BWs [MHz] Band 8 BWs [MHz] BCS
1 10, 15, 20 5, 10 0
2 10 5, 10 1
3 5, 10, 15, 20 3, 5, 10 2
2.2.3
Power Consumption
Power consumption in mobile communications is most often an issue of battery life for UEs. Therefore, it is relevant to examine the effects on power consumption caused by CA.
In [23], several scenarios have been investigated in order to measure the ef-fects on power consumption. Some of their results are presented in this section. When performing the tests, they used two different UEs:
• An LG G5 (called DUT-A) and
• A Samsung Galaxy S5 Neo (called DUT-B).
When simulating the power consumption depending on the size of a received (DL) file, they found that for small file sizes, the number of carriers did not matter all that much. The reason for this is that only a small fraction of the power is used to actually receive the file. However, for larger file sizes, there is a significant decrease in power consumption when using two CCs instead of just one. For a file size of 1 Gigabit, the savings were 20-30%, depending on the carrier frequency. This reduction in power consumption is mainly due to the reduced time to receive the files, meaning that a UE using CA can enter idle mode earlier than a UE that does not use CA. The resulting graph is found in Figure 2.12.
Figure 2.12: Power consumption as a function of transmitted file size. The
blue lines represent transmission using 2600 MHz carriers, and the black lines represent transmission using 800 MHz carriers. From [23] ©2017 IEEE.
The use of CA does not always reduce the power consumption, since the use of several CCs is cause for an increase in consumption by itself. When examining the effect of using two CCs with the same aggregated BW as a single CC for DUT-A, there is a significant increase in power usage, as seen in Figure 2.13. As a result, it is highly beneficial to use one CC with 20 MHz instead of two CCs with 10 MHz each [23].
Figure 2.13:Power consumption when using different number of CCs with
the same total BW. From [23] ©2017 IEEE.
A third experiment deducted in [23] compares the power consumption be-tween intra-band and inter-band CA. The results show that intra-band CA has the overall lowest power consumption, but that the results vary quite heavily be-tween the tested UEs, see Figure 2.14. Unfortunately, it is not stated whether the intra-band CA is contiguous or not, which somewhat lowers the value of these results.
Figure 2.14:Power consumption when comparing intra-band to inter-band
2.3
Basic Graph Theory
Agraph G is a set of data points, called nodes or vertices, and their relationships,
marked byedges. In a graph, the edges can be either directed or undirected. For
a directed graph, each edge has an origin and a destination, describing a
hierar-chical relation between the nodes. The origin node is then called theparent and
the destination node achild. Nodes with the same parent are called siblings. For
undirected edges there is no hierarchical relation between the connected nodes [24, Ch. 1].
A special type of graph is thetree. Trees are graphs without any cycles and
where all nodes are connected. Cycles are routes in a graph, where it is possible to travel away from a node and then return to the same node, without traversing the same edge twice. For all nodes to be connected, there must be a route from any given node to all other nodes in the graph. Both these definitions do not regard directed edges, and thus all edges are treated as undirected in these cases [24, Ch. 1].
There are several other special characteristics of trees, one being that the num-ber of nodes v are always one more than the numnum-ber of edges e, i.e. v = e+1. More-over, there is one unique path between all nodes of an undirected tree, while a directed tree has at most one unique path between all the nodes. Also, in a di-rected tree, all nodes can have an arbitrary number of children, but only one
parent. The sole exception to this is the root node, which does not have a
par-ent at all. Another special case of nodes are those without any children, which
are calledleaves [24, Ch. 1]. Furthermore, all nodes placed on the same distance
from the root node are said to belong to the samelayer, not to be confused with
the MIMO layers. We also define abranch in a tree as the path from the root node
to a given node. In this thesis, all graphs will be directed trees. An example tree which illustrates the defined notation can be found in Figure 2.15.
Parent Child/Leaf Current Sibling/Leaf Root Leaf Leaf Leaf
Figure 2.15: Example of a directed tree. All blue nodes belong to the same
For any graph, it is possible to createspanning trees. A spanning tree is a set of edges that connects all nodes of a graph, without creating any cycles. Thus, the spanning tree is indeed a tree, as all nodes are connected and there are no cycles [24, Ch. 1]. Consequently, the spanning tree of a tree, is the tree itself.
2.3.1
Layouts
When visualizing a graph, there are numerous methods of positioning the nodes,
so calledlayouts. Only considering trees, the different methods can be categorized
using three parameters: • Dimension,
• Edge representation, and • Node alignment.
In this thesis, the focus is on two-dimensional trees with an explicit edge repre-sentation. A graph with explicit edges have the node relations explicitly drawn as lines between the nodes. In implicit edge representations, the relations be-tween nodes are instead directly shown by the node positioning, e.g. by placing children inside parent nodes [25]. The most common node alignments are the axis-parallel and radial layouts [25], [26]. Figure 2.16 and Figure 2.17 show exam-ples of these node alignments for the same tree, consisting of 169 nodes divided into five layers. When comparing Figure 2.16 and Figure 2.17, it can be seen that the axis-parallel layout does not work very well for trees with many nodes but few layers. For these types of trees, the radial layout give a much clearer view of the nodes than the axis-parallel layout.
2.4
Graph Traversal Algorithms
Most methods of analyzing a graph is based on iterating over all nodes while calculating some measure of quantity, e.g. data rate. This require some way to
choose the order in which the nodes shall be visited, so called graph traversal
algorithms. One of the most common graph traversal algorithms is the depth-first search (DFS), which is described in Section 2.4.1.
When analyzing large graphs, it is sometimes of interest to limit the number of investigated nodes, in order to shorten the time needed for the analysis. For these limited algorithms, one must decide how to choose which nodes to
investi-gate. There are several ways of doing this, and the method calledbeam search is
Figure 2.16: Axis-parallel tree layout. The name refers to that each layer is placed parallel to a horizontal axis.
Figure 2.17:Radial tree layout. The name refers to that each layer is placed
2.4.1
Depth-First Search
In its normal implementation, DFS is a method for full graph searches. This means that all nodes are visited by the algorithm, resulting in a spanning tree that represents the order in which the nodes are explored. The order of exploration is determined by the algorithm, and the idea behind DFS is to examine children before siblings when traversing the graph [27, Ch. 3]. In the case of searching a tree, the DFS algorithm will therefore explore the nodes one branch at a time, as seen in Figure 2.18.
1
4
3
2
6
5
7
Figure 2.18:Search order of DFS in a tree. When choosing between several
children, they can be picked in any order. In this example, the left child is always visited first.
Algorithm 1 shows pseudocode for the DFS algorithm, with a recursive imple-mentation. The Algorithm uses the DFS approach of exploring children before
siblings, while calculating abranch value for each visited node by adding a node
value to the previous value calculated for the branch. Lastly, the Algorithm re-turns the maximum branch value, i.e. the maximum sum of values of all nodes in a branch, found in the graph.
Algorithm 1Depth first search of finding the maximum branch value
Define: DFS(Graph, current_node, branch_value)
branch_value ← branch_value + Graph.nodes(current_node).value max_value ← branch_value
children ← Graph.nodes(current_node).children
forchild ← children.first to children.last do
child_branch_value ← DFS(Graph, child, branch_value)
ifchild_branch_value > max_value then
max_value ← child_branch_value end if
end for
return max_value
As an example of how to use Algorithm 1, consider evaluating the tree in Figure 2.18 and let the node labels be interpreted as node values instead of search order. The algorithm would then be initiated by calling
DFS(Graph from Figure 2.18, root, 0) and it would return the value 14, found in the rightmost branch.
A graph traversal algorithm that is closely related to the DFS, is the
breadth-first search (BFS). As indicated by its name, BFS examines siblings before children, as opposed to the DFS that instead prioritizes the children [27, Ch. 3]. For this thesis however, DFS is a better choice to use. This is because branches of the created trees represent the CA combinations. Thus, the implementation is sim-plified by using an algorithm that explores the tree one branch at a time, just as DFS does.
2.4.2
Beam Search
Unlike DFS, beam search does not perform full searches. Therefore, the beam search algorithm must both decide on which nodes to investigate, and in which order. The idea of beam search is to keep a constant number of nodes that are about to be investigated. This number is called the beam width, β, and can range all the way from one to infinity. For each step in the algorithm, it will evaluate the children of β nodes, and then keep the β best children to be investigated in the following step [28, Ch. 6]. Pseudocode for the beam search is found in Algorithm 2.
Algorithm 2Beam search of finding the maximum branch value
Define: Beam_search(Graph, current_nodes, branch_values, β)
fornode ← 1 to β do
local_value ← Graph.nodes(current_nodes[node]).value branch_values[node] ← branch_values[node] + local_value end for
children ← Graph.nodes(current_nodes).children
forchild ← children.first to children.last do
child_branch_value ← branch_value + Graph.nodes(child).value end for
Keep best β: children current_nodes ← children
branch_values ← Beam_search(Graph, children, branch_values, β)
return max(branch_values)
An example of a beam search using Algorithm 2 can be seen in Figure 2.19, where the node labels represent node values. If β = 2, the algorithm is used by calling
Beam_search(Graph from Figure 2.19, root, 0, 2)
which would return the value 23 after visiting all the nodes marked as blue. As can be seen by this example, the choice of β can highly affect the search result. With a β value of two, the optimal branch to the left of the tree is missed. By instead using β = 3, the left branch would be investigated and the optimum would be found. Low values of β has the advantage of decreasing the number of investigated nodes, thus lowering the time required for the search, but it also increases the risk of missing the optimum. Setting β to infinity results in all nodes being investigated, and the algorithm transfers into another method known as best-first search. At the other end, setting β to one results in a DFS where only the
currently strongest branch is investigated, also known ashill-climbing [28, Ch. 6].
11 9
25 13 11 8 10 6 13
5
1 7 5
Figure 2.19:Example of a beam search with β = 2. The investigated nodes
are marked as blue. For this β, the algorithm misses optimal branch to the left.
3
Method
This chapter describes the work conducted in the thesis. Section 3.1 discusses some of the assumptions that has been made and that are valid for all thesis results. In Section 3.2, the used input data is presented, along with descriptions of how this data was created as well as how it is formatted. The main part of the chapter is Section 3.3, which describes the graph building process. Section 3.4 and Section 3.5 describe the analysis parts of the thesis, divided into one section on the implementations of graph traversal algorithms, and one section about load balancing. Lastly, Section 3.6 presents the tools used for visualizing the graphs, as well as how they are used to illustrate different combination characteristics.
3.1
Assumptions
In the thesis, some assumptions have been made. These are presented in this sec-tion, as a clarification of what the thesis does not cover. The assumptions are also summarized in Table 3.1, with references to the section where each assumption is described.
Table 3.1:Assumptions made in the thesis. The section column tells where
each assumption is described.
Assumption Section
Load model 3.1.1
Unknown signal quality 3.1.2
TDD and FDD are considered equal 3.1.3
Base stations support full spatial multiplexing 3.1.4
No multi-band support 3.1.5
3.1.1
Load Model
The model used when analyzing load is that a given number of UEs, with varying capabilities, are simultaneously connecting to a network, and need to be assigned to serving cells. It is assumed that all UEs will actively transmit data for the same amount of time, meaning that the number of active UEs will be constant. Under this assumption, the simplified equation (2.4) can be used, which is repeated here:
Tavg=
Tmax
α , α ≥ 1.
3.1.2
Unknown Signal Quality
As mentioned in Section 2.1.5, the CQI is unknown when connecting to a cell, meaning that it cannot be used for selecting cells, and that other types of signal strength measurements are used for cell selection. Performing such a measure-ment does however, as all measuremeasure-ments do, take some time. It is therefore as-sumed that it is not an option to perform such measurements on all available cells, and that assumption is extended so that no measurements are made at all. Thus, the signal quality of all cells is completely unknown when choosing the CA combinations.
3.1.3
TDD and FDD are Considered Equal
As was discussed in Section 2.1.1, the resources available for DL transmission vary between TDD and FDD cells. However, in order to simplify the implementa-tion process in the thesis, this difference is ignored and the two duplex schemes are considered equal in this regard.
3.1.4
Base Stations Support Eight MIMO layers
As mentioned in Section 2.1.4, the maximum number of MIMO layers supported in LTE is eight. For simplicity, it is assumed that every eNodeB can handle all eight layers. Thus, the number of MIMO layers possible is always limited by the UE capabilities. The consequence of this assumption is that only the UE’s MIMO capabilities need to be considered when examining the possible number of MIMO layers in a network.
3.1.5
No Multi-Band Support
The implemented program does not support the use of MFBI. Hence, it is as-sumed that each cell only belongs to one frequency band. Multi-band support is instead left as future work.
3.2
Input
This section describes the input used for creating the trees, with focus on how the data has been retrieved and how it is structured. The section is divided into the 3GPP combinations, network configurations and UE capabilities.
3.2.1
3GPP Combinations
The combinations defined by 3GPP in [8] are written and published in Word
ta-bles. However, a script has been developed to convert these tables into a
comma-separated values file (CSV file). There are two advantages in doing this conversion. First, it is easier to read data from a CSV file than from a Word table. Second, when defining a new combination, 3GPP does not directly provide all BW infor-mation. Instead, cross-references to other combinations are used, resulting in the data being fragmented. These cross-references have been removed in the CSV file, so that all information regarding a combination is present on the same line in the file, which results in a much simpler data extraction process. The information included in the CSV file is:
• Combination name,
• Included bands and BW classes in the DL, • Included bands and BW classes in the UL, • BCS,
• Possible cell BWs, and
• What 3GPP Release the combination was introduced in. As an example, the information for the combination CA_2A-12B is:
• Name: CA_2A-12B. • DL information: 2A, 12B. • UL information: 2A, 12B. • BCS: 0. • Band 2 BWs: 5, 10, 15, or 20 MHz. • Band 12 (lower fc) BWs: 5 MHz. • Band 12 (higher fc) BWs: 5 or 10 MHz. • Release: 14.0.0.
