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- Herausgeber: John Wiley & Sons
- Kategorie: Wissenschaft und neue Technologien
- Sprache: Englisch
An introduction to technical details related to the Physical Layer of the LTE standard with MATLAB®
The LTE (Long Term Evolution) and LTE-Advanced are among the latest mobile communications standards, designed to realize the dream of a truly global, fast, all-IP-based, secure broadband mobile access technology.
This book examines the Physical Layer (PHY) of the LTE standards by incorporating three conceptual elements: an overview of the theory behind key enabling technologies; a concise discussion regarding standard specifications; and the MATLAB® algorithms needed to simulate the standard.
The use of MATLAB®, a widely used technical computing language, is one of the distinguishing features of this book. Through a series of MATLAB® programs, the author explores each of the enabling technologies, pedagogically synthesizes an LTE PHY system model, and evaluates system performance at each stage. Following this step-by-step process, readers will achieve deeper understanding of LTE concepts and specifications through simulations.
Key Features:
• Accessible, intuitive, and progressive; one of the few books to focus primarily on the modeling, simulation, and implementation of the LTE PHY standard
• Includes case studies and testbenches in MATLAB®, which build knowledge gradually and incrementally until a functional specification for the LTE PHY is attained
• Accompanying Web site includes all MATLAB® programs, together with PowerPoint slides and other illustrative examples
Dr Houman Zarrinkoub has served as a development manager and now as a senior product manager with MathWorks, based in Massachusetts, USA. Within his 12 years at MathWorks, he has been responsible for multiple signal processing and communications software tools. Prior to MathWorks, he was a research scientist in the Wireless Group at Nortel Networks, where he contributed to multiple standardization projects for 3G mobile technologies. He has been awarded multiple patents on topics related to computer simulations. He holds a BSc degree in Electrical Engineering from McGill University and MSc and PhD degrees in Telecommunications from the Institut Nationale de la Recherche Scientifique, in Canada.
http://www.wiley.com/go/zarrinkoub
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Table of Contents
Title Page
Copyright
Preface
List of Abbreviations
Chapter 1: Introduction
1.1 Quick Overview of Wireless Standards
1.2 Historical Profile of Data Rates
1.3 IMT-Advanced Requirements
1.4 3GPP and LTE Standardization
1.5 LTE Requirements
1.6 Theoretical Strategies
1.7 LTE-Enabling Technologies
1.8 LTE Physical Layer (PHY) Modeling
1.9 LTE (Releases 8 and 9)
1.10 LTE-Advanced (Release 10)
1.11 MATLAB® and Wireless System Design
1.12 Organization of This Book
References
Chapter 2: Overview of the LTE Physical Layer
2.1 Air Interface
2.2 Frequency Bands
2.3 Unicast and Multicast Services
2.4 Allocation of Bandwidth
2.5 Time Framing
2.6 Time–Frequency Representation
2.7 OFDM Multicarrier Transmission
2.8 Single-Carrier Frequency Division Multiplexing
2.9 Resource Grid Content
2.10 Physical Channels
2.11 Physical Signals
2.12 Downlink Frame Structures
2.13 Uplink Frame Structures
2.14 MIMO
2.15 MIMO Modes
2.16 PHY Processing
2.17 Downlink Processing
2.18 Uplink Processing
2.19 Chapter Summary
References
Chapter 3: MATLAB® for Communications System Design
3.1 System Development Workflow
3.2 Challenges and Capabilities
3.3 Focus
3.4 Approach
3.5 PHY Models in MATLAB
3.6 MATLAB
3.7 MATLAB Toolboxes
3.8 Simulink
3.9 Modeling and Simulation
3.10 Prototyping and Implementation
3.11 Introduction to System Objects
3.12 MATLAB Channel Coding Examples
3.13 Chapter Summary
References
Chapter 4: Modulation and Coding
4.1 Modulation Schemes of LTE
4.2 Bit-Level Scrambling
4.3 Channel Coding
4.4 Turbo Coding
4.5 Early-Termination Mechanism
4.6 Rate Matching
4.7 Codeblock Segmentation
4.8 LTE Transport-Channel Processing
4.9 Chapter Summary
References
Chapter 5: OFDM
5.1 Channel Modeling
5.2 Scope
5.3 Workflow
5.4 OFDM and Multipath Fading
5.5 OFDM and Channel-Response Estimation
5.6 Frequency-Domain Equalization
5.7 LTE Resource Grid
5.8 Configuring the Resource Grid
5.9 Generating Reference Signals
5.10 Resource Element Mapping
5.11 OFDM Signal Generation
5.12 Channel Modeling
5.13 OFDM Receiver
5.14 Resource Element Demapping
5.15 Channel Estimation
5.16 Equalizer Gain Computation
5.17 Visualizing the Channel
5.18 Downlink Transmission Mode 1
5.19 Chapter Summary
References
Chapter 6: MIMO
6.1 Definition of MIMO
6.2 Motivation for MIMO
6.3 Types of MIMO
6.4 Scope of MIMO Coverage
6.5 MIMO Channels
6.6 Common MIMO Features
6.7 Specific MIMO Features
6.8 Chapter Summary
References
Chapter 7: Link Adaptation
7.1 System Model
7.2 Link Adaptation in LTE
7.3 MATLAB® Examples
7.4 Link Adaptations between Subframes
7.5 Adaptive Modulation
7.6 Adaptive Modulation and Coding Rate
7.7 Adaptive Precoding
7.8 Adaptive MIMO
7.9 Downlink Control Information
7.10 Chapter Summary
References
Chapter 8: System-Level Specification
8.1 System Model
8.2 System Model in MATLAB
8.3 Quantitative Assessments
8.4 Throughput Analysis
8.5 System Model in Simulink
8.6 Qualitative Assessment
8.7 Chapter Summary
References
Chapter 9: Simulation
9.1 Speeding Up Simulations in MATLAB
9.2 Workflow
9.3 Case Study: LTE PDCCH Processing
9.4 Baseline Algorithm
9.5 MATLAB Code Profiling
9.6 MATLAB Code Optimizations
9.7 Using Acceleration Features
9.8 Using a Simulink Model
9.9 GPU Processing
9.10 Case Study: Turbo Coders on GPU
9.11 Chapter Summary
Chapter 10: Prototyping as C/C++ Code
10.1 Use Cases
10.2 Motivations
10.3 Requirements
10.4 MATLAB Code Considerations
10.5 How to Generate Code
10.6 Structure of the Generated C Code
10.7 Supported MATLAB Subset
10.8 Complex Numbers and Native C Types
10.9 Support for System Toolboxes
10.10 Support for Fixed-Point Data
10.11 Support for Variable-Sized Data
10.12 Integration with Existing C/C++ Code
10.13 Chapter Summary
References
Chapter 11: Summary
11.1 Modeling
11.2 Simulation
11.3 Directions for Future Work
11.4 Concluding Remarks
Index
© 2014, John Wiley & Sons, Ltd
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Library of Congress Cataloging-in-Publication Data
Zarrinkoub, Houman.
Understanding LTE with MATLAB : from mathematical foundation to simulation, performance evaluation and implementation / Houman Zarrinkoub.
pages cm
Includes bibliographical references and index.
ISBN 978-1-118-44341-5 (hardback)
1. Long-Term Evolution (Telecommunications)--Computer simulation. 2. MATLAB. I. Title.
TK5103.48325.Z37 2014
621.3845′6–dc23
2013034138
A catalogue record for this book is available from the British Library.
ISBN: 9781118443415
Preface
The LTE (Long Term Evolution) and LTE-Advanced are the latest mobile communications standards developed by the Third Generation Partnership Project (3GPP). These standards represent a transformative change in the evolution of mobile technology. Within the present decade, the network infrastructures and mobile terminals have been designed and upgraded to support the LTE standards. As these systems are deployed in every corner of the globe, the LTE standards have finally realized the dream of providing a truly global broadband mobile access technology.
In this book we will examine the LTE mobile communications standard, and specifically its PHY (Physical Layer), in order to understand how and why it can achieve such a remarkable feat. We will look at it simultaneously from an academic and a pragmatic point of view. We will relate the mathematical foundation of its enabling technologies, such as Orthogonal Frequency Division Multiplexing (OFDM) and Multiple Input Multiple Output (MIMO), to its ability to achieve such a superb performance. We will also show how pragmatic engineering considerations have shaped the formulation of many of its components. As an integral part of this book, we will use MATLAB®, a technical computing language and simulation environment widely used by the scientific and engineering community, to clarify the mathematical concepts and constructs, provide algorithms, testbenches, and illustrations, and give the reader a deep understanding of the specifications through the use of simulations.
This book is written for both the academic community and the practicing professional. It focuses specifically on the LTE standard and its evolution. Unlike many titles that treat only the mathematical foundation of the standard, this book will discuss the mathematical formulation of many enabling technologies (such as OFDM and MIMO) in the context of the overall performance of the system. Furthermore, by including chapters dedicated to simulation, performance evaluation, and implementation, the book broadens its appeal to a much larger readership composed of both academicians and practitioners.
Through an intuitive and pedagogic approach, we will build up components of the LTE PHY progressively from simple to more complex using MATLAB programs. Through simulation of the MATLAB programs, the reader will feel confident that he or she has learned not only all the details necessary to fully understand the standard but also the ability to implement it.
We aim to clarify technical details related to PHY modeling of the LTE standard. Therefore, knowledge of the basics of communication theory (topics such as modulation, coding, and estimation) and digital signal processing is a prerequisite. These prerequisites are usually covered by the senior year of most electrical engineering undergraduate curricula. It also aims to teach through simulation with MATLAB. Therefore a basic knowledge of the MATLAB language is necessary to follow the text. This book is intended for professors, researchers, and students in electrical and computer engineering departments, as well as engineers, designers, and implementers of wireless systems. What they learn from both a technical and a programming point of view may be quite applicable to their everyday work. Depending on the reader's function and the need to implement or teach the LTE standard, this book may be considered introductory, intermediate, or advanced in nature.
The book is conceptually composed of two parts. The first deals with modeling the PHY of the LTE standard and with MATLAB algorithms that enable the reader to simulate and verify various components of the system. The second deals with practical issues such as simulation of the system and implementation and prototyping of its components. In the first chapter we provide a brief introduction to the standard, its genesis, and its objective, and we identify four enabling technologies (OFDM, MIMO, turbo coding, and dynamic link adaptations) as the components responsible for its remarkable performance. In Chapter 2, we provide a quick and sufficiently detailed overview of the LTE PHY specifications. Chapter 3 introduces the modeling, simulation, and implementation capabilities of MATLAB and Simulink that are used throughout this book. In Chapters 4–7 we treat each of the enabling technologies of the LTE standard (modulation and coding, OFDM, MIMO, and link adaptations) in detail and create models in MATLAB that iteratively and progressively build up LTE PHY components based on these. We wrap up the first part of the book in Chapter 8 by putting all the enabling technologies together and showing how the PHY of the LTE standard can be modeled in MATLAB based on the insight obtained in the preceding chapters.
Chapter 9 includes a discussion on how to accelerate the speed of our MATLAB programs through the use of a variety of techniques, including parallel computing, automatic C code generation, GPU processing, and more efficient algorithms. In Chapter 10 we discuss some implementation issues, such as target environments, and how they affect the programming style. We also discuss fixed-point numerical representation of data as a prerequisite for hardware implementation and its effect on the performance of the standard. Finally, in Chapter 11 we summarize what we have discussed and provide some directions for future work.
Any effort related to introducing the technical background of a complex communications system like LTE requires addressing the question of scope. We identify three conceptual elements that can combine to provide a deep understanding of the way the LTE standard works:
The theoretical background of the enabling technologies
Details regarding the standard specifications
Algorithms and simulation testbenches needed to implement the design
To make the most of the time available to develop this book, we decided to strike a balance in covering each of these conceptual elements. We chose to provide a sufficient level of discussion regarding the theoretical foundations and technical specifications of the standard. To leverage our expertise in developing MATLAB applications, we decided to cover the algorithms and testbenches that implement various modes of the LTE standard in further detail. This choice was motivated by two factors:
In this sense, the insight and understanding obtained by delving into simulation details are invaluable as they provide a better mastery of the subject matter. Even more importantly, they instill a sense of confidence in the reader that he or she can try out new ideas, propose and test new improvements, and make use of new tools and models to help graduate from a theoretical knowledge to a hands-on understanding and ultimately to the ability to innovate, design, and implement.
It is our hope that this book can provide a reliable framework for modeling and simulation of the LTE standard for the community of young researchers, students, and professionals interested in mobile communications. We hope they can apply what they learn here, introduce their own improvements and innovations, and become inspired to contribute to the research and development of the mobile communications systems of the future.
List of Abbreviations
ASIC
Application-Specific Integrated Circuit
BCH
Broadcast Channel
BER
Bit Error Rate
BPSK
Binary Phase Shift Keying
CP
Cyclic Prefix
CQI
Channel Quality Indicator
CRC
Cyclic Redundancy Check
CSI
Channel State Information
CSI-RS
Channel State Information Reference Signal
CSR
Cell-Specific Reference
CUDA
Compute Unified Device Architecture
DM-RS
Demodulation Reference Signal
DSP
Digital Signal Processor
eNodeB
enhanced Node Base station
E-UTRA
Evolved Universal Terrestrial Radio Access
FDD
Frequency Division Duplex
FPGA
Field-Programmable Gate Array
HARQ
Hybrid Automatic Repeat Request
HDL
Hardware Description Language
LTE
Long Term Evolution
MAC
Medium Access Control
MBMS
Multimedia Broadcast and Multicast Service
MBSFN
Multicast/Broadcast over Single Frequency Network
MIMO
Multiple Input Multiple Output
MMSE
Minimum Mean Square Error
MRC
Maximum Ratio Combining
MU-MIMO
Multi-User Multiple Input Multiple Output
OFDM
Orthogonal Frequency Division Multiplexing
PBCH
Physical Broadcast Channel
PCFICH
Physical Control Format Indicator Channel
PCM
Pulse Code Modulation
PDCCH
Physical Downlink Control Channel
PDSCH
Physical Downlink Shared Channel
PHICH
Physical Hybrid ARQ Indicator Channel
PHY
Physical Layer
PMCH
Physical Multicast Channel
PRACH
Physical Random Access Channel
PSS
Primary Synchronization Signal
PUCCH
Physical Uplink Control Channel
PUSCH
Physical Uplink Shared Channel
QAM
Quadrature Amplitude Modulation
QPP
Quadratic Permutation Polynomial
QPSK
Quadrature Phase Shift Keying
RLC
Radio Link Control
RMS
Root Mean Square
RRC
Radio Resource Control
RTL
Register Transfer Level
SC-FDM
Single-Carrier Frequency Division Multiplexing
SD
Sphere Decoder
SFBC
Space–Frequency Block Coding
SINR
Signal-to-Interference-plus-Noise Ratio
SNR
Signal-to-Noise Ratio
SSD
Soft-Sphere Decoder
SSS
Secondary Synchronization Signal
STBC
Space–Time Block Coding
SFBC
Space-Frequency Block Coding
SU-MIMO
Single-User MIMO
TDD
Time-Division Duplex
UE
User Equipment
ZF
Zero Forcing
Chapter 1
Introduction
We live in the era of a mobile data revolution. With the mass-market expansion of smartphones, tablets, notebooks, and laptop computers, users demand services and applications from mobile communication systems that go far beyond mere voice and telephony. The growth in data-intensive mobile services and applications such as Web browsing, social networking, and music and video streaming has become a driving force for development of the next generation of wireless standards. As a result, new standards are being developed to provide the data rates and network capacity necessary to support worldwide delivery of these types of rich multimedia application.
LTE (Long Term Evolution) and LTE-Advanced have been developed to respond to the requirements of this era and to realize the goal of achieving global broadband mobile communications. The goals and objectives of this evolved system include higher radio access data rates, improved system capacity and coverage, flexible bandwidth operations, significantly improved spectral efficiency, low latency, reduced operating costs, multi-antenna support, and seamless integration with the Internet and existing mobile communication systems.
In some ways, LTE and LTE-Advanced are representatives of what is known as a fourth-generation wireless system and can be considered an organic evolution of the third-generation predecessors. On the other hand, in terms of their underlying transmission technology they represent a disruptive departure from the past and the dawn of what is to come. To put into context the evolution of mobile technology leading up to the introduction of the LTE standards, a short overview of the wireless standard history will now be presented. This overview intends to trace the origins of many enabling technologies of the LTE standards and to clarify some of their requirements, which are expressed in terms of improvements over earlier technologies.
1.1 Quick Overview of Wireless Standards
In the past two decades we have seen the introduction of various mobile standards, from 2G to 3G to the present 4G, and we expect the trend to continue (see Figure 1.1). The primary mandate of the 2G standards was the support of mobile telephony and voice applications. The 3G standards marked the beginning of the packet-based data revolution and the support of Internet applications such as email, Web browsing, text messaging, and other client-server services. The 4G standards will feature all-IP packet-based networks and will support the explosive demand for bandwidth-hungry applications such as mobile video-on-demand services.
Figure 1.1 Evolution of wireless standards in the last two decades
Historically, standards for mobile communication have been developed by consortia of network providers and operators, separately in North America, Europe, and other regions of the world. The second-generation (2G) digital mobile communications systems were introduced in the early 1990s. The technology supporting these 2G systems were circuit-switched data communications. The GSM (Global System for Mobile Communications) in Europe and the IS-54 (Interim Standard 54) in North America were among the first 2G standards. Both were based on the Time Division Multiple Access (TDMA) technology. In TDMA, a narrowband communication channel is subdivided into a number of time slots and multiple users share the spectrum at allocated slots. In terms of data rates, for example, GSM systems support voice services up to 13 kbps and data services up to 9.6 kbps.
The GSM standard later evolved into the Generalized Packet Radio Service (GPRS), supporting a peak data rate of 171.2 kbps. The GPRS standard marked the introduction of the split-core wireless networks, in which packet-based switching technology supports data transmission and circuit-switched technology supports voice transmission. The GPRS technology further evolved into Enhanced Data Rates for Global Evolution (EDGE), which introduced a higher-rate modulation scheme (8-PSK, Phase Shift Keying) and further enhanced the peak data rate to 384 kbps.
In North America, the introduction of IS-95 marked the first commercial deployment of a Code Division Multiple Access (CDMA) technology. CDMA in IS-95 is based on a direct spread spectrum technology, where multiple users share a wider bandwidth by using orthogonal spreading codes. IS-95 employs a 1.2284 MHz bandwidth and allows for a maximum of 64 voice channels per cell, with a peak data rate of 14.4 kbps per fundamental channel. The IS-95-B revision of the standard was developed to support high-speed packet-based data transmission. With the introduction of the new supplemental code channel supporting high-speed packet data, IS-95-B supported a peak data rate of 115.2 kbps. In North America, 3GPP2 (Third Generation Partnership Project 2) was the standardization body that established technical specifications and standards for 3G mobile systems based on the evolution of CDMA technology. From 1997 to 2003, 3GPP2 developed a family of standards based on the original IS-95 that included 1xRTT, 1x-EV-DO (Evolved Voice Data Only), and EV-DV (Evolved Data and Voice). 1xRTT doubled the IS-95 capacity by adding 64 more traffic channels to achieve a peak data rate of 307 kbps. The 1x-EV-DO and 1x-EV-DV standards achieved peak data rates in the range of 2.4–3.1 Mbps by introducing a set of features including adaptive modulation and coding, hybrid automatic repeat request (HARQ), turbo coding, and faster scheduling based on smaller frame sizes.
The 3GPP (Third-Generation Partnership Project) is the standardization body that originally managed European mobile standard and later on evolved into a global standardization organization. It is responsible for establishing technical specifications for the 3G mobile systems and beyond. In 1997, 3GPP started working on a standardization effort to meet goals specified by the ITU IMT-2000 (International Telecommunications Union International Mobile Telecommunication) project. The goal of this project was the transition from a 2G TDMA-based GSM technology to a 3G wide-band CDMA-based technology called the Universal Mobile Telecommunications System (UMTS). The UMTS represented a significant change in mobile communications at the time. It was standardized in 2001 and was dubbed Release 4 of the 3GPP standards. The UMTS system can achieve a downlink peak data rate of 1.92 Mbps. As an upgrade to the UMTS system, the High-Speed Downlink Packet Access (HSDPA) was standardized in 2002 as Release 5 of the 3GPP. The peak data rates of 14.4 Mbps offered by this standard were made possible by introducing faster scheduling with shorter subframes and the use of a 16QAM (Quadrature Amplitude Modulation) modulation scheme. High-Speed Uplink Packet Access (HSUPA) was standardized in 2004 as Release 6, with a maximum rate of 5.76 Mbps. Both of these standards, together known as HSPA (High-Speed Packet Access), were then upgraded to Release 7 of the 3GPP standard known as HSPA+ or MIMO (Multiple Input Multiple Output) HSDPA. The HSPA+ standard can reach rates of up to 84 Mbps and was the first mobile standard to introduce a 2 × 2 MIMO technique and the use of an even higher modulation scheme (64QAM). Advanced features that were originally introduced as part of the North American 3G standards were also incorporated in HSPA and HSPA+. These features include adaptive modulation and coding, HARQ, turbo coding, and faster scheduling.
Another important wireless application that has been a driving force for higher data rates and spectral efficiency is the wireless local area network (WLAN). The main purpose of WLAN standards is to provide stationary users in buildings (homes, offices) with reliable and high-speed network connections. As the global mobile communications networks were undergoing their evolution, IEEE (Institute of Electrical and Electronics Engineers) was developing international standards for WLANs and wireless metropolitan area networks (WMANs). With the introduction of a family of WiFi standards (802.11a/b/g/n) and WiMAX standards (802.16d/e/m), IEEE established Orthogonal Frequency Division Multiplexing (OFDM) as a promising and innovative air-interface technology. For example, the IEEE 802.11a WLAN standard uses the 5 GHz frequency band to transmit OFDM signals with data rates of up to 54 Mb/s. In 2006, IEEE standardized a new WiMAX standard (IEEE 802.16m) that introduced a packet-based wireless broadband system. Among the features of WiMAX are scalable bandwidths up to 20 MHz, higher peak data rates, and better special efficiency profiles than were being offered by the UMTS and HSPA systems at the time. This advance essentially kicked off the effort by 3GPP to introduce a new wireless mobile standard that could compete with the WiMAX technology. This effort ultimately led to the standardization of the LTE standard.
1.2 Historical Profile of Data Rates
Table 1.1 summarizes the peak data rates of various wireless technologies. Looking at the maximum data rates offered by these standards, the LTE standard (3GPP release 8) is specified to provide a maximum data rate of 300 Mbps. The LTE-Advanced (3GPP version 10) features a peak data rate of 1 Gbps.
Table 1.1 Peak data rates of various wireless standards introduced over the past two decades
Technology
Theoretical peak data rate (at low mobility)
GSM
9.6 kbps
IS-95
14.4 kbps
GPRS
171.2 kbps
EDGE
473 kbps
CDMA-2000 (1xRTT)
307 kbps
WCDMA (UMTS)
1.92 Mbps
HSDPA (Rel 5)
14 Mbps
CDMA-2000 (1x-EV-DO)
3.1 Mbps
HSPA+ (Rel 6)
84 Mbps
WiMAX (802.16e)
26 Mbps
LTE (Rel 8)
300 Mbps
WiMAX (802.16m)
303 Mbps
LTE-Advanced (Rel 10)
1 Gbps
These figures represent a boosts in peak data rates of about 2000 times above what was offered by GSM/EDGE technology and 50–500 times above what was offered by the W-CDMA/UMTS systems. This remarkable boost was achieved through the development of new technologies introduced within a time span of about 10 years. One can argue that this extraordinary advancement is firmly rooted in the elegant mathematical formulation of the enabling technologies featured in the LTE standards. It is our aim in this book to clarify and explain these enabling technologies and to put into context how they combine to achieve such a performance. We also aim to gain insight into how to simulate, verify, implement, and further enhance the PHY (Physical Layer) technology of the LTE standards.
1.3 IMT-Advanced Requirements
The ITU has published a set of requirements for the design of mobile systems. The first recommendations, released in 1997, were called IMT-2000 (International Mobile Telecommunications 2000) 1. These recommendations included a set of goals and requirements for radio interface specification. 3G mobile communications systems were developed to be compliant with these recommendations. As the 3G systems evolved, so did the IMT-2000 requirements, undergoing multiple updates over the past decade 2.
In 2007, ITU published a new set of recommendations that set the bar much higher and provided requirements for IMT-Advanced systems 3. IMT-Advanced represents the requirements for the building of truly global broadband mobile communications systems. Such systems can provide access to a wide range of packet-based advanced mobile services, support low- to high-mobility applications and a wide range of data rates, and provide capabilities for high-quality multimedia applications. The new requirements were published to spur research and development activities that bring about a significant improvement in performance and quality of services over the existing 3G systems.
One of the prominent features of IMT-Advanced is the enhanced peak data for advanced services and applications (100 Mbps for high mobility and 1 Gbps for low mobility). These requirements were established as targets for research. The LTE-Advanced standard developed by 3GPP and the mobile WiMAX standard developed by IEEE are among the most prominent standards to meet the requirements of the IMT-Advanced specifications. In this book, we focus on the LTE standards and discuss how their PHY specification is consistent with the requirements of the IMT-Advanced.
1.4 3GPP and LTE Standardization
The LTE and LTE-Advanced are developed by the 3GPP. They inherit a lot from previous 3GPP standards (UMTS and HSPA) and in that sense can be considered an evolution of those technologies. However, to meet the IMT-Advanced requirements and to keep competitive with the WiMAX standard, the LTE standard needed to make a radical departure from the W-CDMA transmission technology employed in previous standards. LTE standardization work began in 2004 and ultimately resulted in a large-scale and ambitious re-architecture of mobile networks. After four years of deliberation, and with contributions from telecommunications companies and Internet standardization bodies all across the globe, the standardization process of LTE (3GPP Release 8) was completed in 2008. The Release 8 LTE standard later evolved to LTE Release 9 with minor modifications and then to Release 10, also known as the LTE-Advanced standard. The LTE-Advanced features improvements in spectral efficiency, peak data rates, and user experience relative to the LTE. With a maximum peak data rate of 1 Gbps, LTE-Advanced has also been approved by the ITU as an IMT-Advanced technology.
1.5 LTE Requirements
LTE requirements cover two fundamental components of the evolved UMTS system architecture: the Evolved Universal Terrestrial Radio Access Network (E-UTRAN) and the Evolved Packet Core (EPC). The goals of the overall system include the following:
Improved system capacity and coverage
High peak data rates
Low latency (both user-plane and control-plane)
Reduced operating costs
Multi-antenna support
Flexible bandwidth operations
Seamless integration with existing systems (UMTS, WiFi, etc.).
As a substantial boost in mobile data rates is one of the main mandates of the LTE standards, it is useful to review some of the recent advances in communications research as well as theoretical considerations related to the maximum achievable data rates in a mobile communications link. We will now present some highlights related to this topic, inspired by an excellent discussion presented in Reference 4.
1.6 Theoretical Strategies
Shannon's fundamental work on channel capacity states that data rates are always limited by the available received signal power or the received signal-to-noise-power ratio 5. It also relates the data rates to the transmission bandwidths. In the case of low-bandwidth utilization, where the data rate is substantially lower than the available bandwidth, any increase of the data rate will require an increase in the received signal power in a proportional manner. In the case of high-bandwidth utilization, where data rates are equal to or greater than the available bandwidth, any increase in the data rate will require a much larger relative increase in the received signal power unless the bandwidth is increased in proportion to the increase in data rate.
A rather intuitive way to increase the overall power at the receiver is to use multiple antennas at the receiver side. This is known as receive diversity. Multiple antennas can also be used at the transmitter side, in what is known as transmit diversity. A transmit diversity approach based on beamforming uses multiple transmit antennas to focus the transmitted power in the direction of the receiver. This can potentially increase the received signal power and allow for higher data rates.
However, increasing data rates by using either transmit diversity or receive diversity can only work up to a certain point. Beyond this, any boost in data rates will start to saturate. An alternative approach is to use multiple antennas at both the transmitter and the receiver. For example, a technique known as spatial multiplexing, which exploits multiple antennas at the transmitter and the receiver sides, is an important member of the class of multi-antenna techniques known as MIMO. Different types of MIMO technique, including open-loop and closed-loop spatial multiplexing, are used in the LTE standard.
Beside the received signal power, another factor directly impacting on the achievable data rates of a mobile communications system is the transmission bandwidth. The provisioning of higher data rates usually involves support for even wider transmission bandwidths. The most important challenge related to wider-band transmission is the effect of multipath fading on the radio channel. Multipath fading is the result of the propagation of multiple versions of the transmitted signals through different paths before they arrive at the receiver. These different versions exhibit varying profiles of signal power and time delays or phases. As a result, the received signal can be modeled as a filtered version of the transmitted signal that is filtered by the impulse response of the radio channel. In the frequency domain, a multipath fading channel exhibits a time-varying channel frequency response. The channel frequency response inevitably corrupts the original frequency-domain content of the transmitted signal, with an adverse effect on the achievable data rates. In order to adjust for the effects of channel frequency selectivity and to achieve a reasonable performance, we must either increase the transmit power, reduce our expectations concerning data rates, or compensate for the frequency-domain distortions with equalization.
Many channel-equalization techniques have been proposed to counter the effects of multipath fading. Simple time-domain equalization methods have been shown to provide adequate performance for transmission over transmission bandwidths of up to 5 MHz. However, for LTE standards and other mobile systems that provision for wider bandwidths of 10, 15, or 20 MHz, or higher, the complexity of the time-domain equalizers become prohibitively large. In order to overcome the problems associated with time-domain equalization, two approaches to wider-band transmission have been proposed:
The use of multicarrier transmission schemes, where a wider band signal is represented as the sum of several more narrowband orthogonal signals. One special case of multicarrier transmission used in the LTE standard is the OFDM transmission.
The use of a single-carrier transmission scheme, which provides the benefits of low-complexity frequency-domain equalization offered by OFDM without introducing its high transmit power fluctuations. An example of this type of transmission is called Single-Carrier Frequency Division Multiplexing (SC-FDM), which is used in the LTE standard as the technology for uplink transmission.
Furthermore, a rather straightforward way of providing higher data rates within a given transmission bandwidth is the use of higher-order modulation schemes. Using higher-order modulation allows us to represent more bits with a single modulated symbol and directly increases bandwidth utilization. However, the higher bandwidth utilization comes at a cost: a reduced minimum distance between modulated symbols and a resultant increased sensitivity to noise and interference. Consequently, adaptive modulation and coding and other link adaptation strategies can be used to judiciously decide when to use a lower- or higher-order modulation. By applying these adaptive methods, we can substantially improve the throughput and achievable data rates in a communications link.
1.7 LTE-Enabling Technologies
The enabling technologies of the LTE and its evolution include the OFDM, MIMO, turbo coding, and dynamic link-adaptation techniques. As discussed in the last section, these technologies trace their origins to well-established areas of research in communications and together help contribute to the ability of the LTE standard to meet its requirements.
1.7.1 OFDM
As elegantly described in Reference 6, the main reasons LTE selects OFDM and its single-carrier counterpart SC-FDM as the basic transmission schemes include the following: robustness to the multipath fading channel, high spectral efficiency, low-complexity implementation, and the ability to provide flexible transmission bandwidths and support advanced features such as frequency-selective scheduling, MIMO transmission, and interference coordination.
OFDM is a multicarrier transmission scheme. The main idea behind it is to subdivide the information transmitted on a wideband channel in the frequency domain and to align data symbols with multiple narrowband orthogonal subchannels known as subcarriers. When the frequency spacing between subcarriers is sufficiently small, an OFDM transmission scheme can represent a frequency-selective fading channel as a collection of narrowband flat fading subchannels. This in turn enables OFDM to provide an intuitive and simple way of estimating the channel frequency response based on transmitting known data or reference signals. With a good estimate of the channel response at the receiver, we can then recover the best estimate of the transmitted signal using a low-complexity frequency-domain equalizer. The equalizer in a sense inverts the channel frequency response at each subcarrier.
1.7.2 SC-FDM
One of the drawbacks of OFDM multicarrier transmission is the large variations in the instantaneous transmit power. This implies a reduced efficiency in power amplifiers and results in higher mobile-terminal power consumption. In uplink transmission, the design of complex power amplifiers is especially challenging. As a result, a variant of the OFDM transmission known as SC-FDM is selected in the LTE standard for uplink transmission. SC-FDM is implemented by combining a regular OFDM system with a precoding based on Discrete Fourier Transform (DFT) 6. By applying a DFT-based precoding, SC-FDM substantially reduces fluctuations of the transmit power. The resulting uplink transmission scheme can still feature most of the benefits associated with OFDM, such as low-complexity frequency-domain equalization and frequency-domain scheduling, with less stringent requirements on the power amplifier design.
1.7.3 MIMO
MIMO is one of the key technologies deployed in the LTE standards. With deep roots in mobile communications research, MIMO techniques bring to bear the advantages of using multiple antennas in order to meet the ambitious requirements of the LTE standard in terms of peak data rates and throughput.
MIMO methods can improve mobile communication in two different ways: by boosting the overall data rates and by increasing the reliability of the communication link. The MIMO algorithms used in the LTE standard can be divided into four broad categories: receive diversity, transmit diversity, beamforming, and spatial multiplexing. In transmit diversity and beamforming, we transmit redundant information on different antennas. As such, these methods do not contribute to any boost in the achievable data rates but rather make the communications link more robust. In spatial multiplexing, however, the system transmits independent (nonredundant) information on different antennas. This type of MIMO scheme can substantially boost the data rate of a given link. The extent to which data rates can be improved may be linearly proportional to the number of transmit antennas. In order to accommodate this, the LTE standard provides multiple transmit configurations of up to four transmit antennas in its downlink specification. The LTE-Advanced allows the use of up to eight transmit antennas for downlink transmission.
1.7.4 Turbo Channel Coding
Turbo coding is an evolution of the convolutional coding technology used in all previous standards with impressive near-channel capacity performance 7. Turbo coding was first introduced in 1993 and has been deployed in 3G UMTS and HSPA systems. However, in these standards it was used as an optional way of boosting the performance of the system. In the LTE standard, on the other hand, turbo coding is the only channel coding mechanism used to process the user data.
The near-optimal performance of turbo coders is well documented, as is the computational complexity associated with their implementation. The LTE turbo coders come with many improvements, aimed at making them more efficient in their implementation. For example, by appending a CRC (Cyclic Redundancy Check) checking syndrome to the input of the turbo encoder, LTE turbo decoders can take advantage of an early termination mechanism if the quality of the code is deemed acceptable. Instead of following through with a fixed number of decoding iterations, the decoding can be stopped early when the CRC check indicates that no errors are detected. This very simple solution allows the computational complexity of the LTE turbo decoders to be reduced without severely penalizing their performance.
1.7.5 Link Adaptation
Link adaptation is defined as a collection of techniques for changing and adapting the transmission parameters of a mobile communication system to better respond to the dynamic nature of the communication channel. Depending on the channel quality, we can use different modulation and coding techniques (adaptive modulation and coding), change the number of transmit or receive antennas (adaptive MIMO), and even change the transmission bandwidth (adaptive bandwidth). Closely related to link adaptation is channel-dependent scheduling in a mobile communication system. Scheduling deals with the question of how to share the radio resources between different users in order to achieve more efficient resource utilizations. Typically, we need to either minimize the amount of resources allocated to each user or match the resources to the type and priority of the user data. Channel-dependent scheduling aims to accommodate as many users as possible, while satisfying the best quality-of-service requirements that may exist based on the instantaneous channel condition.
1.8 LTE Physical Layer (PHY) Modeling
In this book we will focus on digital signal processing in the physical layer of the Radio Access networks. Almost no discussion of the LTE core networks is present here, and we will leave the discussion of higher-layer processing such as Radio Resource Control (RRC), Radio Link Control (RLC), and Medium Access Control (MAC) to another occasion.
Physical layer modeling involves all the processing performed on bits of data that are handed down from the higher layers to the PHY. It describes how various transport channels are mapped to physical channels, how signal processing is performed on each of these channels, and how data are ultimately transported to the antenna for transmission.
For example, Figure 1.2 illustrates the PHY model for the LTE downlink transmission. First, the data is multiplexed and encoded in a step known as Downlink Shared Channel processing (DLSCH). The DLSCH processing chain involves attaching a CRC code for error detection, segmenting the data into smaller chunks known as subblocks, undertaking channel-coding operations based on turbo coding for the user data, carrying out a rate-matching operation that selects the number of output bits to reflect a desired coding rate, and finally reconstructing the codeblocks into codewords. The next phase of processing is known as physical downlink shared channel processing. In this phase, the codewords first become subject to a scrambling operation and then undergo a modulation mapping that results in a modulated symbol stream. The next step comprises the LTE MIMO or multi-antenna processing, in which a single stream of modulated symbols is subdivided into multiple substreams destined for transmission via multiple antennas. The MIMO operations can be regarded as a combination of two steps: precoding and layer mapping. Precoding scales and organizes symbols allocated to each substream and layer mapping selects and routes data into each substream to implement one of the nine different MIMO modes specified for downlink transmission. Among the available MIMO techniques implemented in downlink transmission are transmit diversity, spatial multiplexing, and beamforming. The final step in the processing chain relates to the multicarrier transmission. In downlink, the multicarrier operations are based on the OFDM transmission scheme. The OFDM transmission involves two steps. First, the resource element mapping organizes the modulated symbols of each layer within a time–frequency resource grid. On the frequency axis of the grid, the data are aligned with subcarriers in the frequency domain. In the OFDM signal-generation step, a series of OFDM symbols are generated by applying inverse Fourier transform to compute the transmitted data in time and are transported to each antenna for transmission.
Figure 1.2 Physical layer specifications in LTE
In my opinion, it is remarkable that such a straightforward and intuitive transmission structure can combine all the enabling technologies so effectively that they meet the diverse and stringent IMT-Advanced requirements set out for the LTE standardization. By focusing on PHY modeling, we aim to address challenges in understanding the development of the digital signal processing associated with the LTE standard.
1.9 LTE (Releases 8 and 9)
The introduction of the first release of the LTE standard was the culmination of about four years of work by 3GPP, starting in 2005. Following an extensive study of various technologies capable of delivering on the requirements set for the LTE standard, it was decided that the air interface transmission technology of the new standard would be based on OFDM in downlink and SC-FDM in uplink. The full specifications, including various MIMO modes, were then incorporated in the standard. The first version of the LTE standard (3GPP version 8) was released in December 2008. Release 9 came in December 2009; it included relatively minor enhancements such as Multimedia Broadcast/Multicast Services (MBMS) support, location services, and provisioning for base stations that support multiple standards 4.
1.10 LTE-Advanced (Release 10)
The LTE-Advanced was released in December 2010. LTE-Advanced is an evolution of the original LTE standard and does not represent a new technology. Among the technologies added to the LTE standard to result in the LTE-Advanced were carrier aggregation, enhanced downlink MIMO, uplink MIMO, and relays 4.
1.11 MATLAB® and Wireless System Design
In this book, we use MATLAB to model the PHY of the LTE standard and to obtain insight into its simulation and implementation requirements. MATLAB is a widely used language and a high-level development environment for mathematical modeling and numerical computations. We also use Simulink, a graphical design environment for system simulations and model-based design, as well as various MATLAB toolboxes – application-specific libraries of components that make the task of modeling applications in MATLAB easier. For example, in order to model communications systems we use functionalities from the Communication System Toolbox. The toolbox provides tools for the design, prototyping, simulation, and verification of communications systems, including wireless standards in both MATLAB and Simulink.
Among the functionalities in MATLAB that are introduced in this book are the new System objects. System objects are a set of algorithmic building blocks suitable for system design available in various MATLAB toolboxes. They are self-documented algorithms that make the task of developing MATLAB testbenches to perform system simulations easier. By covering a wide range of algorithms, they also eliminate the need to recreate the basic building blocks of communications systems in MATLAB, C, or any other programming language. System objects are designed not only for modeling and simulation but also to provide support for implementation. For example, they have favorable characteristics that help accelerate simulation speeds and support C/C++ code generation and fixed-point numeric, and a few of them support automatic HDL (Hardware Description Language) code generation.
1.12 Organization of This Book
The thesis of this book is that by understanding its four enabling technologies (OFDMA, MIMO, turbo coding, and link adaptation) the reader can obtain an adequate understanding of the PHY model of the LTE standard. Chapter 2 provides a short overview of the technical specifications of the LTE standard. Chapter 3 provides an introduction to the tools and features in MATLAB that are useful for the modeling and simulation of mobile communications systems. In Chapters 4–7, we treat each of the OFDM, MIMO, modulation, and coding and link adaptation techniques in detail. In each chapter, we create models in MATLAB that iteratively and progressively build up components of the LTE PHY based on these techniques. Chapter 8, on system-level specifications and performance evaluation, discusses various channel models specified in the standard and ways of performing system-level qualitative and quantitative performance analysis in MATLAB and Simulink. It also wraps up the first part of the book by putting together a system model and showing how the PHY of the LTE standard can be modeled in MATLAB based on the insight obtained in the preceding chapters.
The second part deals with practical issues such as simulation of the system and implementation of its components. Chapter 9 includes discussion on how to accelerate the speed of our MATLAB programs using a variety of techniques, including parallel computing, automatic C code generation, GPU (Graphics Progressing Unit) processing, and the use of more efficient algorithms. In Chapter 10, we discuss related implementation issues such as automatic C/C++ code generation from the MATLAB code, target environments, and code optimizations, and how these affect the programming style. We also discuss fixed-point numerical representation of data as a prerequisite for hardware implementation and its effect on the performance of various modeling components. Finally, in Chapter 11, we summarize our discussions and highlight directions for future work.
References
[1] ITU-R (1997) International Mobile Telecommunications-2000 (IMT-2000). Recommendation ITU-R M.687-2, February 1997.
[2] ITU-R (2010) Detailed specifications of the radio interfaces of international mobile telecommunications-2000 (IMT-2000). Recommendation ITU-R M.1457-9, May 2010.
[3] ITU-R (2007) Principles for the Process of Development of IMT-Advanced. Resolution ITU-R 57, October 2007.
[4] Dahlman, E., Parkvall, S. and Sköld, J. (2011) 4G LTE/LTE-Advanced for Mobile Broadband, Elsevier.
[5] Shannon, C.E. (1948) A mathematical theory of communication. Bell System Technical Journal, 379–423, 623–656.
[6] Ghosh, A. and Ratasuk, R. (2011) Essentials of LTE and LTE-A, Cambridge University Press, Cambridge.
[7] Proakis, J.G. (2001) Digital Communications, McGraw-Hill, New York.
Chapter 2
Overview of the LTE Physical Layer
The focus of this book is the LTE (Long Term Evolution) radio access technology and particularly its PHY (Physical Layer). Here, we will highlight the major concepts related to understanding the technology choices made in the design of the LTE PHY radio interface. Focusing on this topic will best explain the remarkable data rates achievable by LTE and LTE-Advanced standards.
LTE specifies data communications protocols for both the uplink (mobile to base station) and downlink (base station to mobile) communications. In the 3GPP (Third Generation Partnership Project) nomenclature, the base station is referred to as eNodeB (enhanced Node Base station) and the mobile unit is referred to as UE (User Equipment).
In this chapter, we will cover topics related to PHY data communication and the transmission protocols of the LTE standards. We will first provide an overview of frequency bands, FDD (Frequency Division Duplex) and TDD (Time Division Duplex) duplex methodologies, flexible bandwidth allocation, time framing, and the time–frequency resource representation of the LTE standard. We will then study in detail both the downlink and uplink processing stacks, which include multicarrier transmission schemes, multi-antenna protocols, adaptive modulation, and coding schemes and channel-dependent link adaptations.
In each case, we will first describe the various channels that connect different layers of the communication stacks and then describe in detail the signal processing in the PHY applied on each of the downlink and uplink physical channels. The amount of detail presented will be sufficient to enables us to model the downlink PHY processing as MATLAB® programs. In the subsequent four chapters we will iteratively and progressively derive a system model from simpler algorithms in MATLAB.
2.1 Air Interface
The LTE air interface is based on OFDM (Orthogonal Frequency Division Multiplexing) multiple-access technology in the downlink and a closely related technology known as Single-Carrier Frequency Division Multiplexing (SC-FDM) in the uplink. The use of OFDM provides significant advantages over alternative multiple-access technologies and signals a sharp departure from the past. Among the advantages are high spectral efficiency and adaptability for broadband data transmission, resistance to intersymbol interference caused by multipath fading, a natural support for MIMO (Multiple Input Multiple Output) schemes, and support for frequency-domain techniques such as frequency-selective scheduling 1.
The time–frequency representation of OFDM is designed to provide high levels of flexibility in allocating both spectra and the time frames for transmission. The spectrum flexibility in LTE provides not only a variety of frequency bands but also a scalable set of bandwidths. LTE also provides a short frame size of 10 ms in order to minimize latency. By specifying short frame sizes, LTE allows better channel estimation to be performed in the mobile, allowing timely feedbacks necessary for link adaptations to be provided to the base station.
2.2 Frequency Bands
The LTE standards specify the available radio spectra in different frequency bands. One of the goals of the LTE standards is seamless integration with previous mobile systems. As such, the frequency bands already defined for previous 3GPP standards are available for LTE deployment. In addition to these common bands, a few new frequency bands are also introduced for the first time in the LTE specification. The regulations governing these frequency bands vary between different countries. Therefore, it is conceivable that not just one but many of the frequency bands could be deployed by any given service provider to make the global roaming mechanism much easier to manage.
As was the case with previous 3GPP standards, LTE supports both FDD and TDD modes, with frequency bands specified as paired and unpaired spectra, respectively. FDD frequency bands are paired, which enables simultaneous transmission on two frequencies: one for the downlink and one for the uplink. The paired bands are also specified with sufficient separations for improved receiver performance. TDD frequency bands are unpaired, as uplink and downlink transmissions share the same channel and carrier frequency. The transmissions in uplink and downlink directions are time-multiplexed.
Release 11 of the 3GPP specifications for LTE shows the comprehensive list of ITU IMT-Advanced (International Telecommunications Union International Mobile Telecommunication) frequency bands 2. It includes 25 frequency bands for FDD and 11 for TDD. As shown in Table 2.1, the paired bands used in FDD duplex mode are numbered from 1 to 25; the unpaired bands used in TDD mode are numbered from 33 to 43, as illustrated in Table 2.2. The band number 6 is not applicable to LTE and bands 15 and 16 are dedicated to ITU Region 1.
Table 2.1 Paired frequency bands defined for E-UTRA
Table 2.2 Unpaired frequency bands defined for E-UTRA
Operating band index
Uplink and downlink operating band frequency range (MHz)
Duplex mode
33
1900–1920
TDD
34
2010–2025
TDD
35
1850–1910
TDD
36
1930–1990
TDD
37
1910–1930
TDD
38
2570–2620
TDD
39
1880–1920
TDD
40
2300–2400
TDD
41
2496–2690
TDD
42
3400–3600
TDD
43
3600–3800
TDD
2.3 Unicast and Multicast Services
In mobile communications, the normal mode of transmission is known as a unicast transmission, where the transmitted data are intended for a single user. In addition to unicast services, the LTE standards support a mode of transmission known as Multimedia Broadcast/Multicast Services (MBMS). MBMS delivers high-data-rate multimedia services such as TV and radio broadcasting and audio and video streaming 1.
MBMS has its own set of dedicated traffic and control channels and is based on a multicell transmission scheme forming a Multimedia Broadcast Single-Frequency Network (MBSFN) service area. A multimedia signal is transmitted from multiple adjacent cells belonging to a given MBSFN service area. When the content of a single Multicast Channel (MCH) is transmitted from different cells, the signals on the same subcarrier are coherently combined at the UE. This results in a substantial improvement in the SNR (signal-to-noise ratio) and significantly improves the maximum allowable data rates for the multimedia transmission. Being in either a unicast or a multicast/broadcast mode of transmission affects many parameters and components of the system operation. As we describe various components of the LTE technology, we will highlight how different channels, transmission modes, and physical signals and parameters are used in the unicast and multicast modes of operations. The focus throughout this book will be on unicast services and data transmission.
2.4 Allocation of Bandwidth
The IMT-Advanced guidelines require spectrum flexibility in the LTE standard. This leads to scalability in the frequency domain, which is manifested by a list of spectrum allocations ranging from 1.4 to 20 MHz. The frequency spectra in LTE are formed as concatenations of resource blocks consisting of 12 subcarriers. Since subcarriers are separated by 15 kHz, the total bandwidth of a resource block is 180 kHz. This enables transmission bandwidth configurations of from 6 to 110 resource blocks over a single frequency carrier, which explains how the multicarrier transmission nature of the LTE standard allows for channel bandwidths ranging from 1.4 to 20.0 MHz in steps of 180 kHz, allowing the required spectrum flexibility to be achieved.
Table 2.3 illustrates the relationship between the channel bandwidth and the number of resource blocks transmitted over an LTE RF carrier. For bandwidths of 3–20 MHz, the totality of resource blocks in the transmission bandwidth occupies around 90% of the channel bandwidth. In the case of 1.4 kHz, the percentage drops to around 77%. This helps reduce unwanted emissions outside the bandwidth, as illustrated in Figure 2.1. A formal definition of the time–frequency representation of the spectrum, the resource grid, and the blocks will be presented shortly.
Table 2.3 Channel bandwidths specified in LTE
Channel bandwidth (MHz)
Number of resource blocks
1
.
4
6
3
15
5
25
10
50
15
75
20
100
Figure 2.1 Relationship between channel bandwidth and number of resource blocks
2.5 Time Framing
The time-domain structure of the LTE is illustrated in Figure 2.2. Understanding of LTE transmission relies on a clear understanding of the time–frequency representation of data, how it maps to what is known as the resource grid, and how the resource grid is finally transformed into OFDM symbols for transmission.
Figure 2.2 LTE time-domain structure
In the time domain, LTE organizes the transmission as a sequence of radio frames of length 10 ms. Each frame is then subdivided into 10 subframes of length 1 ms. Each subframe is composed of two slots of length 0.5 ms each. Finally, each slot consists of a number of OFDM symbols, either seven or six depending on whether a normal or an extended cyclic prefix is used. Next, we will focus on the time–frequency representation of the OFDM transmission.
2.6 Time–Frequency Representation
One of the most attractive features of OFDM is that it maps explicitly to a time–frequency representation for the transmitted signal. After coding and modulation, a transformed version of the complex-valued modulated signal, the physical resource element, is mapped on to a time-frequency coordinate system, the resource grid. The resource grid has time on the x-axis and frequency on the y-axis. The x-coordinate of a resource element indicates the OFDM symbol to which it belongs in time. The y-coordinate signifies the OFDM subcarrier to which it belongs in frequency.
Figure 2.3 illustrates the LTE downlink resource grid when a normal cyclic prefix is used. A resource element is placed at the intersection of an OFDM symbol and a subcarrier. The subcarrier spacing is 15 kHz and, in the case of normal cyclic prefix, there are 14 OFDM symbols per subframe or seven symbols per slot. A resource block is defined as a group of resource elements corresponding to 12 subcarriers or 180 kHz in the frequency domain and one 0.5 ms slot in the time domain. In the case of a normal cyclic prefix with seven OFDM symbols per slot, each resource block consists of 84 resource elements. In the case of an extended cyclic prefix with six OFDM symbols per slot, the resource block contains 72 resource elements. The definition of a resource block is important because it represents the smallest unit of transmission that is subject to frequency-domain scheduling.
Figure 2.3 Resource elements, blocks, and grid
As we discussed earlier, the LTE PHY specification allows an RF carrier to consist of any number of resource blocks in the frequency domain, ranging from a minimum of six resource blocks up to a maximum of 110 resource blocks. This corresponds to transmission bandwidths ranging from 1.4 to 20.0 MHz, with a granularity of 15 kHz, and allows for a very high degree of LTE bandwidth flexibility. The resource-block definition applies equally to both the downlink and the uplink transmissions. There is a minor difference between the downlink and the uplink regarding the location of the carrier center frequency relative to the subcarriers.
In the uplink, as illustrated in Figure 2.4, no unused DC subcarrier is defined and the center frequency of an uplink carrier is located between two uplink subcarriers. In the downlink, the subcarrier that coincides with the carrier-center frequency is left unused. This is shown in Figure 2.5. The reason why the DC subcarrier is not used for downlink transmission is the possibility of disproportionately high interference.
Figure 2.4 Resource blocks and DC components of the frequency in uplink transmission
Figure 2.5 Resource blocks and DC components of the frequency in downlink transmission
The choice of 15 kHz as subcarrier spacing fits perfectly with the OFDM mandate that turns a frequency-selective channel into a series of frequency-flat subchannels with fine resolution. This is turn helps the OFDM to efficiently combat frequency-selective fading by using a bank of low-complexity equalizers that apply to each of the flat-faded subchannels in the frequency domain.
2.7 OFDM Multicarrier Transmission
In the LTE standard, the downlink transmission is based on an OFDM scheme and the uplink transmission is based on a closely related methodology known as SC-FDM. OFDM is a multicarrier transmission methodology that represents the broadband transmission bandwidth as a collection of many narrowband subchannels.
There are multiple steps involved in OFDM signal generation. First, modulated data are mapped on to the resource grid, where they are organized and aligned in the frequency domain. Each modulated symbol ak is assigned to a single subcarrier on the frequency axis. With N subcarriers occupying the bandwidth with a subcarrier spacing of Δf, the relationship between the bandwidth and subcarrier spacing is given by:
2.1
Each subcarrier fk can be considered an integer multiple of subcarrier spacing:
2.2
The OFDM modulator consists of a bank of N complex modulators, where each modulator corresponds to a single subcarrier. The OFDM modulated output x(t) is thus expressed as:
2.3
2.4
The OFDM modulation lends itself naturally to an efficient implementation based on Inverse Fast Fourier Transform (IFFT). After the OFDM modulation, an OFDM symbol is generated and a cyclic prefix is added to the modulated signal. Insertion of a cyclic prefix is essentially copying of the last part of the OFDM symbol to its beginning.
