Jun 20, 2010 - DSSS. Direct Sequence Spread Spectrum. DVB-H. Digital Video Broadcasting-Handheld. EDGE. Enhanced Data Rates for GSM Evolution ...
Un-coded versus Coded QPSK-OFDM Performance over Rayleigh Fading Channels and DL-PUSC Subchannelization for OFDMA
Leonardo O. A. Iheme
Submitted to the Institute of Graduate Studies and Research in partial fulfillment of the requirements for the Degree of
Master of Science in Electrical and Electronic Engineering
Eastern Mediterranean University June 2010 Gazimağusa, North Cyprus
Approval of the Institute of Graduate Studies and Research
Prof. Dr. Elvan Yılmaz Director (a)
I certify that this thesis satisfies the requirements as a thesis for the degree of Master of Science in Electrical and Electronic Engineering.
Assoc. Prof. Dr. Aykut Hocanın Chair, Department of Electrical Electronic and Engineering
We certify that we have read this thesis and that in our opinion it is fully adequate in scope and quality as a thesis for the degree of Master of Science in Electrical and Electronic Engineering.
Asst. Prof. Dr. Hassan Abou Rajab Co-Supervisor
Assoc. Prof. Dr. Erhan A. İnce Supervisor
Examining Committee 1. Assoc. Prof. Dr. Hüseyin Bilgekul 2. Assoc. Prof. Dr. Aykut Hocanın 3. Assoc. Prof. Dr. Erhan A. İnce 4. Assoc. Prof. Dr. Hasan Demirel 5. Asst. Prof. Dr. Hassan A. Rajab
ABSTRACT
In this thesis, a comprehensive study of the IEEE 802.16 physical (PHY) layer was carried out. An implementation of this standard is Wireless Interoperability for Microwave Access (WiMAX). Using the MATLAB programming environment, some of the mandatory parts of the PHY layer of WiMAX were simulated. Basic blocks of the PHY layer include: A convolutional encoder and a corresponding Viterbi decoder, a constellation mapper and an Orthogonal Frequency Division Multiplexing (OFDM) or Orthogonal Frequency Division Multiple Access (OFDMA) transmitter/receiver. The transmission was simulated over an Additive White Gaussian Noise (AWGN) channel and two Rayleigh multipath fading channel models. In order to generate small scale fading, the Jakes’ fading simulator was adopted.
A study of subchannel permutations is un-avoidable when OFDMA is involved so a comprehensive study of the Down Link Partial Usage of Sub-Carriers (DL-PUSC), permutation based non-adjacent subchannelization was carried out and MATLAB codes were written to simulate the subcarrier allocation process.
The performance of the system was assessed by link level simulations in form of Bit Error Rate (BER) versus Signal to Noise Ratio (SNR) curves. Doppler effect as a result of relative motion between the receiver and the transmitter was observed to degrade the performance and also develop an error floor in multipath fading channels. Improvement of the performance was observed after the inclusion of a rate ½ convolutional coder of constraint length iii
and generator polynomials
and
. The simulation with the convolutional encoder
yielded a coding gain over the AWGN channels and a lower error floor over the Rayleigh multipath fading channel.
Keywords: OFDM, OFDMA, DL-PUSC, Convolutional Coding, Rayleigh Fading Channel.
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ÖZ
Bu tezde geniş bant kablosuz iletişim standardı olan IEEE 802.16’nın fiziksel katmanı etraflı bir şekilde incelenmektedir. Bu standardın gerçek hayata uyarlanmış hali bugün Mikrodalga Erişim için Telsiz Birlikte İşlerlik (METBİ) sistemidir. Bu çalışmada MATLAB programlama dili kullanılarak METBİ’nin fiziki katmanındaki zorunlu bölümlerin benzetimleri gerçekleştirilmiştir. Fiziki katmanı oluşturan temel bloklar; evrişimsel kodlayıcı, kodlayıcıya uygun bir Viterbi kod çözücü, bir işaret kümesi eşleştiricisi, bir Dikgen Frekans Bölüşümlü Çoğullama (DFBÇ) veya çok kullanıcılı DFBÇ alıcı/verici bloğu olarak sıralanabilir. Benzetim sonuçları hem Toplanır Beyaz Gauss Gürültülü kanal hem de Jake’in sönümlemeli kanal modelini baz alan iki farklı çokyollu sönümlemeli kanal üzerinde elde edilmiştir.
Çok kullanıcılı DFBÇ benzetimleri esnasında alt kanal permütasyon methodlarının incelenmesi kaçınılmazdır. Bundan dolayı bu çalışmada telsiz erişim terminali yer yönündeki alt-taşıyıcıların kısmi kullanım yöntemi (DL-PUSC) etraflı bir şekilde incelenmiş
ve alt-taşıyıcıları farklı
alt-kanallara tahsis
edecek MATLAB
fonksiyonları geliştirilmiştir.
Sistem başarımı link seviyesinde bit hata oranı (BHO) na karşı sinyal gürültü oranı (SGO) eğrileri kullanılarak gösterilmiştir. Gönderici ve alıcı arasındaki bağıl devinimden kaynaklanan Doppler etkisinin arttığı oranda çok yollu sönümlemeli kanal üzerinde elde edilecek başarımı negatif yönde etkilediği gösterilmiştir. Bu durumlarda hızı ½ ve kısıt uzunluğu K= 7 olan bir evrişimsel kodlayıcı kullanıldığı takdirde (Üreteç polinomlar G1= 171oct ve G2 = 133oct) benzetim sonuçlarında
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iyileşme elde edilebilmektedir. Evrişimsel kodlayıcı ve Viterbi kod çözücülü benzetimler TBGG kanala göre yüksek kazanç göstermiş Rayleigh çokyollu sönümlemeli kanal üzerinde ise kodsuz benzetim sonuçlarına göre daha alçak bir hata zeminine neden vermiştir.
Anahtar Kelimeler: Dikgen Frekans Bölüşümlü Çoğullama (DFBÇ), çok kullanıcılı DFBÇ, telsiz erişim terminali yer yönündeki alt-taşıyıcıların kısmi kullanımı (DLPUSC), evrişimsel kodlayıcı, Rayleigh Sönümlemeli çokyollu kanal.
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DEDICATION
To my family:
Andee, Moji, Ije and Reni
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ACKNOWLEDGEMENTS
I would like to start by expressing my sincere gratitude to my supervisor, Assoc. Prof. Dr. Erhan A. İnce for his advice and assistance all through the period of this work. In times when I did not believe in myself he was there to encourage me and make me believe I can do what I set my mind to. He proved to be a true supervisor all through, showing excellent scientific and analytical skills. Words alone cannot express how grateful and privileged I am to be his student.
I feel indebted to my instructors who impacted me with knowledge throughout my studies here. I want to especially thank Assoc. Prof. Dr. Aykut Hocanın for challenging me and exposing me to Mobile Communications as a subject and also as a field of study. I acknowledge Prof. Dr. Şener Uysal and Prof. Dr. Hüseyin Özkaramanli for their vital contributions to the successful completion of my studies in EMU.
Thanks to my friends and colleagues for being sources of inspiration to me. Babani, Azadeh, Mustafa and everyone else I have not mentioned, I say a big thanks. To my family who stood by me through thick and thin, may you be richly rewarded.
To Elahi, for standing by me all the way and for her comforting words when I was at my low states; I say thank you. You truly are my custom made love.
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TABLE of CONTENTS
ABSTRACT ................................................................................................................ iii ÖZ ................................................................................................................................ v DEDICATION ........................................................................................................... vii ACKNOWLEDGEMENTS ...................................................................................... viii LIST of TABLES ...................................................................................................... xiv LIST of FIGURES ..................................................................................................... xv LIST of SYMBOLS ................................................................................................ xviii LIST of ABBREVIATIONS ...................................................................................... xx 1 INTRODUCTION ................................................................................................... 1 1.1 Background ...................................................................................................... 2 1.1.1 IEEE 802.16 Standards ............................................................................. 3 1.1.2 WiMAX PHY............................................................................................ 5 1.1.3 Jakes’ Model ............................................................................................. 7 1.2 Thesis Review .................................................................................................. 7 2 OVERVIEW OF WIRELESS COMMUNICATION SYSTEMS .......................... 9 2.1 Introduction ...................................................................................................... 9 2.2 Wireless and Mobile Networks ...................................................................... 11 2.3 IEEE 802.11 ................................................................................................... 12 2.4 Broad Band Wireless Access (BWA) ............................................................ 13 2.4.1 Broadband Wireless Frequency Spectrum .............................................. 15
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2.5 CDMA2000 .................................................................................................... 16 2.5.1 CDMA2000 Frequency Spectrum ........................................................... 17 2.5.2 CDMA Technology ................................................................................. 18 2.6 Third Generation Partnership Project (3GPP) ................................................ 20 2.6.1 3GPP Releases......................................................................................... 21 2.7 Long Term Evolution (LTE) .......................................................................... 22 2.7.1 3G LTE Technologies ............................................................................. 24 2.8 Wireless Broadband Deployment and Industry Trends ................................. 25 2.8.1 Fixed Broadband Wireless Access .......................................................... 26 2.8.2 Mobile Broadband Wireless Access ....................................................... 27 2.9 WiMAX .......................................................................................................... 28 2.10 Channel and Bandwidth Classes for WiMAX ............................................... 30 2.11 WiMAX Certification Profiles ....................................................................... 31 3 THE WIRELESS CHANNEL............................................................................... 33 3.1 Introduction .................................................................................................... 33 3.2 Additive White Gaussian Noise Channel ....................................................... 34 3.3 Fading Channel .............................................................................................. 35 3.4 Frequency Selective Fading ........................................................................... 36 3.5 Rayleigh Fading Channel ............................................................................... 37 3.6 Generating Fading (Jakes’ Model) ................................................................. 40 3.7 Channel Models.............................................................................................. 42 3.7.1 Tapped-Delay-Line Parameters............................................................... 43 x
4 ORTHOGONAL FREQUENCY DIVISION MULTIPLEXING ......................... 45 4.1 Introduction .................................................................................................... 45 4.2 Inter-Symbol (ISI) and Inter-Channel Interference (ICI) ............................... 46 4.3 Multicarrier Modulation ................................................................................. 46 4.4 OFDM Basics ................................................................................................. 48 4.4.1 FEC Encoder ........................................................................................... 49 4.4.2 QAM Mapper .......................................................................................... 50 4.4.3 Discrete Fourier Transform ..................................................................... 50 4.4.4 The Cyclic Prefix .................................................................................... 51 4.5 Mathematical Description of OFDM ............................................................. 53 5 CHANNEL CODING AND DECODING ............................................................ 56 5.1 Introduction .................................................................................................... 56 5.2 Convolutional Coding .................................................................................... 56 5.2.1 Structure of the Convolutional Code....................................................... 56 5.2.2 States of a Code ....................................................................................... 57 5.2.3 Trellis Diagram ....................................................................................... 58 5.2.4 Decoding ................................................................................................. 59 6 THE WIMAX PHYSICAL LAYER ..................................................................... 61 6.1 Introduction .................................................................................................... 61 6.2 Symbol Mapper .............................................................................................. 62 6.3 OFDM Symbol Structure ............................................................................... 63 6.3.1 Symbol Parameters .................................................................................. 63 xi
6.4 OFDMA and Subchannelization .................................................................... 64 6.5 Multiple Access Schemes............................................................................... 65 6.6 OFDMA ......................................................................................................... 65 6.6.1 OFDMA Symbol Structure ..................................................................... 67 6.7 Subchannelization in WiMAX ....................................................................... 67 6.7.1 DL PUSC................................................................................................. 69 6.8 OFDMA Frame .............................................................................................. 76 6.8.1 OFDMA Frame Parameters .................................................................... 78 6.8.2 Data Burst Formation via Vertical Mapping ........................................... 79 7 UN-CODED vs. CODED OFDM PERFORMANCE over MULTIPATH FADING CHANNELS.......................................................................................... 81 7.1 Introduction .................................................................................................... 81 7.2 Simulation of OFDM ..................................................................................... 82 7.2.1 Un-coded OFDM over AWGN Channel ................................................. 83 7.2.2 Coded OFDM over AWGN Channel ...................................................... 84 7.2.3 Un-coded OFDM over Multipath Rayleigh Fading Channels ................ 85 7.2.4 Coded OFDM over Multipath Rayleigh Fading Channel ....................... 91 8 CONCLUSION AND FUTURE WORK .............................................................. 93 8.1 Conclusion ...................................................................................................... 93 8.2 Future Work ................................................................................................... 94 8.2.1 Interleaved Codes .................................................................................... 94 8.2.2 MIMO...................................................................................................... 94
xii
8.2.3 IEEE 802.16m ......................................................................................... 94 REFERENCES........................................................................................................... 95 Appendix .................................................................................................................. 104 Appendix A: DL Subcarrier Permutation Functions ............................................ 105
xiii
LIST of TABLES
Table 1.1: IEEE 802.16 projects and standards ........................................................... 4 Table 2.1: 3GPP releases[2] ....................................................................................... 21 Table 2.2: Targets for LTE......................................................................................... 23 Table 2.3: 3G LTE specification ................................................................................ 25 Table 2.4: WiMAX Channel and Bandwidth Classes ................................................ 30 Table 3.1: Vehicular test environment, tapped-delay-line parameters[18] ................ 43 Table 3.2:Winner tapped delay-line model for scenario 2.8 (RS MS, NLOS) .......... 44 Table 6.1: Primitive parameters for OFDM symbol .................................................. 64 Table 6.2: DL PUSC Parameters ............................................................................... 69 Table 6.3: Permutation sequence ............................................................................... 74 Table 6.4: Parameters for DL PUSC example ........................................................... 75 Table 6.5: Cluster numbering(Major Group 3, DL PermBase = 10) ......................... 75 Table 6.6: Subcarrier Allocation ................................................................................ 76 Table 6.7: TDD OFDMA frame parameters .............................................................. 78 Table 7.1: OFDM Simulation Parameters .................................................................. 82 Table 7.2: Winner scenario 2.8 channel ..................................................................... 88 Table 7.3: ITU Vehicular-A channel parameters ....................................................... 89
xiv
LIST of FIGURES
Figure 1.1: Evolution for 3G CDMA/UMTS Systems ................................................ 3 Figure 2.1: Basic Communication System ................................................................... 9 Figure 2.2: Anticipated Growth of Wireless Users Worldwide (Source: UMTS Forum) .................................................................................................. 12 Figure 2.3: Typical Wireless LAN ............................................................................. 13 Figure 2.4: Channel Access Schemes ........................................................................ 19 Figure 2.5: 3GPP Arrow [3] ....................................................................................... 21 Figure 2.6: Strategic Inclination of Telecom Vendors [38] ....................................... 28 Figure 2.7: Mobile WiMAX Roadmap ...................................................................... 31 Figure 2.8: Release 1 certification profiles in Mobile WiMAX [22] ......................... 32 Figure 3.1: Multipath Scattering and Shadowing ...................................................... 34 Figure 3.2: Doppler power spectral density of Rayleigh fading with a maximum Doppler shift of 10Hz. .......................................................................... 36 Figure 3.3: L Tap Channel Model .............................................................................. 37 Figure 3.4: PDF of Rayleigh Fading Envelope .......................................................... 39 Figure 3.5: Jakes’ Fading Simulator .......................................................................... 42 Figure 4.1: A Basic Multicarrier Transmitter ............................................................ 47 Figure 4.2: A Basic Multicarrier Receiver ................................................................. 48 Figure 4.3: OFDM Transmitter Block Diagram ........................................................ 49 Figure 4.4: Constellation Maps: (a) BPSK, (b) QPSK and (c) 16-QAM ................... 50 Figure 4.5: The OFDM Cyclic Prefix ........................................................................ 52 Figure 4.6: Examples of OFDM Spectrum (a)Five Subcarriers (b) A Single Subcarrier ........................................................................................... 53
xv
Figure 5.1: Convolutional Encoder CC (1, 3, 2) ........................................................ 57 Figure 5.2: Example of a Trellis Diagram Adopted from [1] .................................... 58 Figure 5.3: Rate ½ Binary Convolutional Encoder .................................................... 59 Figure 5.4: Viterbi Decoder Data Flow...................................................................... 60 Figure 6.1: Functional stages of WiMAX PHY ......................................................... 61 Figure 6.2: Subcarrier Structure in Frequency ........................................................... 63 Figure 6.3: Multiple Access Schemes. (a) FDMA (b) TDMA (c) CDMA ................ 65 Figure 6.4: OFDMA Transmission. Ref (6) ............................................................... 66 Figure 6.5: (a) OFDM (b) OFDMA ........................................................................... 67 Figure 6.6: Subchannels in the Subcarrier Structure .................................................. 67 Figure 6.7: Illustration of OFDMA Frame with Multiple Zones ............................... 69 Figure 6.8: Example of an OFDMA DL Frame ......................................................... 71 Figure 6.9: PUSC Subchannel Allocation Procedure ................................................ 72 Figure 6.10: PUSC DL Slot ....................................................................................... 73 Figure 6.11: TDD Frame Structure ............................................................................ 77 Figure 6.12: Data Burst Formation ............................................................................ 79 Figure 6.13: Data Region Showing Data Bursts for Four Users ................................ 80 Figure 7.1: OFDM Performance over AWGN Channel ............................................ 83 Figure 7.2: Coded OFDM Performance over AWGN Channel ................................. 84 Figure 7.3: Theoretical Un-coded OFDM Performance over .................................... 87 Figure 7.4: Un-coded OFDM Performance over Rayleigh Multipath Fading Channel (Winner Scenario 2.8 Channel) ............................................................... 89 Figure 7.5: Un-coded OFDM Performance over Rayleigh Multipath Fading Channel (ITU Vehicular-A)................................................................................... 90
xvi
Figure 7.6: Un-coded OFDM Performance over Rayleigh Multipath Fading Channels (ITU-Vehicular A and Winner Scenario 2.8) .......................................... 91 Figure 7.7: Coded and Un-coded OFDM-QPSK over a Multipath ........................... 92
xvii
LIST of SYMBOLS
Amplitude of carrier Bandwidth Coherence bandwidth Doppler spread Carrier frequency Doppler shift Maximum Doppler frequency Rayleigh probability density function Ratio of cyclic prefix time to useful symbol time Total number of subcarriers Number of paths AWGN term Received signal Transmitted signal Delay spread Symbol duration Velocity Multiplicative gain of the kth path Subcarrier frequency spacing Phase shift of the kth path Wavelength of carrier frequency Phase of carrier
xviii
̂
Random phase Channel delay spread Delay of kth path
xix
LIST of ABBREVIATIONS
2G
2nd Generation
3G
3rd Generation
3GP
3rd Generation Project
3GPP
3rd Generation Partnership Project
4G
4th Generation
ADSL
Asymmetric Digital Subscriber Line
AMC
Adaptive Modulation and Coding
AWGN
Additive White Gaussian Noise
BER
Bit Error Rate
BPSK
Binary Phase Shift Keying
BS
Base Station
BWA
Broadband Wireless Access
CC
Convolution Code
CDMA
Code Division Multiple Access
CISPR
Comite International Special des Perturbations Radioelectriques
CP
Cyclic Prefix
CSI
Channel State Information
DFT
Discrete Fourier Transform
DL
Downlink
DSL
Digital Subscriber Line
DSSS
Direct Sequence Spread Spectrum
DVB-H
Digital Video Broadcasting-Handheld
EDGE
Enhanced Data Rates for GSM Evolution
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ETSI
European Telecommunications Standards Institute
Ev-DO
Evolution-Data Optimized
FCH
Frame Correction Header
FDD
Frequency Division Duplexing
FDM
Frequency Division Multiplexing
FDMA
Frequency Division Multiple Access
FEC
Forward Error Correction
FFT
Fast Fourier Transform
FUSC
Full Usage of SubCarriers
GPRS
General Packet Radio Service
GSM
Global System for Mobile
HSDPA
High Speed Downlink Packet Access
HSPA
High Speed Packet Access
HSUPA
High Speed Uplink Packet Access
ICI
Inter Carrier Interference
IDFT
Inverse Discrete Fourier Transform
IEEE
Institute of Electrical and Electronics Engineers
IFFT
Inverse Fast Fourier Transform
IMT
International Mobile Telecommunications
IP
Internet Protocol
IQ
In-phase and Quadrature-phase
ISI
Inter Symbol Interference
ITU
International Telecommunications Union
LAN
Local Area Network
LN
Logical Number
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LOS
Line Of Sight
LTE
Long Term Evolution
MAC
Media Access Control
MAN
Metropolitan Area Network
MAP
Memory Allocation Processor
MG
Major Group
MIMO
Multiple Input Multiple Output
MS
Mobile Station
NLOS
Non Line Of Sight
OFDM
Orthogonal Frequency Division Multiplexing
OFDMA
Orthogonal Frequency Division Multiple Access
PAN
Personal Area Network
PAPR
Peak to Average Power Ratio
PCS
Personal Communications Service
PHY
Physical
PN
Physical Number
PUSC
Partial Usage of SubCarriers
QAM
Quadrature Amplitude Modulation
QoS
Quality of Service
QPSK
Quadrature Phase Shift Keying
RS
Reed Solomon
RTG
Receive Transmission Gap
SAE
Switched Access Evolution
SC
Single Carrier
SFBC
Space Frequency Block Coding
xxii
SNR
Signal to Noise Ratio
SS
Spread Spectrum
STBC
Space Time Block Coding
TDD
Time Division Duplexing
TDMA
Time Division Multiple Access
TTG
Transmit Transition Gap
TUSC
Tile Usage of SubCarriers
UL
Up Link
UMTS
Universal Mobile Telecommunications System
UTRA
UMTS Terrestrial Radio Access
VoIP
Voice over IP
WAN
Wide Area Network
W-CDMA Wideband Code Division Multiple Access WiBro
Wireless Broadband
WiFi
Wireless Fidelity
WiMAX
Worldwide Interoperability for Microwave Access
WLL
Wireless Local Loop
WSSUS
Wide-Sense Stationary Uncorrelated Scattering
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Chapter 1
1 INTRODUCTION
Communication systems seek to transmit information from source to destination at high data rates regardless of the channel through which the signal is transmitted. Several schemes have been designed to combat channel impairments; these schemes could be either wired or wireless. Wireless communication systems are applied mostly in mobile communication systems. The need for broadband access today has gone beyond urban areas; in fact it has extended to the rural areas as well. Deployment of wired networks that extend to hundreds of kilometres is not economically feasible and also stands a lot of dangers in terms of natural and manmade disasters. For this reason, wireless deployments of various size networks have fast become the trend for realisation of broadband access around the world. This growing demand for wireless broadband systems has brought forward many technologically feasible solutions from different vendors.
WiMAX is a system that is resilient to channel impairments and thus provides relatively high data rates in hostile channel conditions. Other competing technologies like the 3GP family of broadband wireless access schemes also provide such high data rates in similar channel conditions. There is however an intersection in the underlying technology of these broadband wireless access schemes: mostly, OFDM is the backbone of their various physical layer implementations.
1
Due to its popularity, OFDM has gained tremendous attention as an area of study for researchers and developers. Using OFDM as a multiple access scheme in form of OFDMA has proved to be more efficient and also perform better. OFDMA is the underlying technology in mobile WiMAX which is an implementation of the IEEE 802.16e standard. Unlike OFDM, OFDMA allows multiple users to share each frame worth of data that is to be transmitted through the channel. This is achieved by a technique known as subchannelization in the downlink. A clear distinction between the two technologies is made later in the thesis.
1.1 Background The availability of a variety of solutions to the issue of high data rate delivery to wireless subscribers has fast become a matter of the choice of technology, as there are now a number of broadband wireless access schemes in the world. The term "3G" is now synonymous with high speed wireless access worldwide. 3G, meaning 3rd Generation, is a family of standards for mobile communications including Universal Mobile Telecommunications System (UMTS) and Code Division Multiple Access (CDMA) 2000. UMTS, sometimes referred to as WCDMA is currently the most popular variant of cellular mobile phones even though it is widely criticized for its large frequency spectrum usage. To improve the downlink and uplink capacity of UMTS systems, the 3rd Generation Partnership Project (3GPP) has developed the High Speed Downlink Packet Access (HSDPA) and High Speed Uplink Packet Access (HSUPA) enhancements for the downlink and uplink respectively. The latest improvement to the CDMA2000 technology is the 1×EvolutionData Optimized 1×EVDO technology.
2
3G technologies continue to evolve in order to meet the high demand for high data rates and a generally good Quality of Service (QoS) demanded by users. Figure 1.1 shows the evolution of 3G CDMA systems from 2004 up till 2008/9.
Figure 1.1: Evolution for 3G CDMA/UMTS Systems 1.1.1
IEEE 802.16 Standards
This group was established by the IEEE in 1998 to look at the wide area broadband wireless access issues and to recommend air interfaces and modulation techniques. The group gave its first recommendation in June 2001 specifying the 802.16 standard [22]. The air interface of 802.16 was accordingly designated as wireless MAN-SC, SC standing for Single Carrier.
There has been much development and improvement in the 802.16 standard over the years. The first 802.16 standard was 802.16 2001. This was a fixed wireless broadband connection which operated at a frequencies between 10 and 63GHz. 802.16.2 2001 was merely an extension to its legacy. 802.16c 2002 was used for system profiles. 802.16a 2003 described the physical layer and MAC applications. This standard used the 2 to 11 GHz frequency band. Some other standards and
3
projects which were withdrawn and merged overtime were P802.16b, P802.16d, and P802.162a. The802.16 2004 and 802.16e 2005 are some superseded standards along with 802.16f 2005 which is used as management information base for the 802.16 2004. 802.16 2004/Cor 1-2005 was published as corrections for fixed operations and was co-published with 802.16e 2005 which is a standard for wireless broadband access. Some other standards include 802.16K 2007, 802.16g2007 and 802.16 2009 which specifies an air interface for fixed and mobile broadband wireless access systems.P802.16m is currently in progress and is the most recent of the 802.16 standards. Table 1.1 provides a chronological summary of the fixed and mobile IEEE 802.16 standards and projects to date.
Table 1.1: IEEE 802.16 projects and standards Standard Description Fixed Broadband Wireless Access (10– 802.16-2001 63 GHz) 802.16.2-2001 Recommended practice for coexistence 802.16c-2002 System profiles for 10–63 GHz Physical layer and MAC definitions for 2– 802.16a-2003 11 GHz License-exempt frequencies P802.16b (Project withdrawn) Maintenance and System profiles for 2– P802.16d 11 GHz (Project merged into 802.16-2004) Air Interface for Fixed Broadband Wireless Access System 802.16-2004 (rollup of 802.16-2001, 802.16a, 802.16c and P802.16d) Coexistence with 2–11 GHz and 23.5– P802.16.2a 43.5 GHz (Project merged into 802.16.2-2004) Recommended practice for coexistence 802.16.2-2004 (Maintenance and rollup of 802.16.2-2001 and P802.16.2a) Management Information Base (MIB) for 802.16f-2005 802.16-2004 802.16Corrections for fixed operations 2004/Cor 1(co-published with 802.16e-2005) 2005
4
Status Superseded Superseded Superseded Superseded Withdrawn Merged
Superseded
Merged
Current Superseded Superseded
802.16e-2005 802.16k-2007 802.16g-2007 P802.16i
802.16-2009 802.16j-2009 P802.16h P802.16m
1.1.2
Mobile Broadband Wireless Access System Bridging of 802.16 (an amendment to IEEE 802.1D) Management Plane Procedures and Services Mobile Management Information Base (Project merged into 802.16-2009) Air Interface for Fixed and Mobile Broadband Wireless Access System (rollup of 802.16-2004, 802.16-2004/Cor 1, 802.16e, 802.16f, 802.16g and P802.16i) Multihop relay Improved Coexistence Mechanisms for License-Exempt Operation Advanced Air Interface with data rates of 100 Mbit/s mobile & 1 Gbit/s fixed
Superseded Current Superseded Merged
Current Current in progress Current
WiMAX PHY
WiMAX is a Broadband Wireless Access scheme based on the IEEE 802.16 standard. The name "WiMAX" was created by the WiMAX Forum, which was formed in June 2001 to promote conformity and interoperability of the standard. The forum describes WiMAX as a ―standards-based technology‖ enabling the delivery of last mile wireless broadband access as an alternative to cable and Digital Subscriber Line (DSL) [48]. The IEEE specified physical layer of WiMAX is very flexible so it has received a lot of attention from developers. It is based on the much researched OFDM/OFDMA which can be easily implemented using the Discrete Fourier Transform (DFT) algorithm known as Fast Fourier Transform (FFT).
Different aspects of the WiMAX physical layer have been analysed, discussed and simulated with propositions to improve on various areas of the entire system. For example:
In [21], a basic WiMAX physical layer model is described. In the work, they implemented the functional stages of a fixed WiMAX model with
5
concatenated Reed Solomon and convolutional encoders rather than just a convolutional encoder alone.
By exploiting the layered FFT structure, [51] showed that better performance can be achieved by using a novel Quadrature OFDMA system rather than the conventional OFDMA systems.
The capacity of a WiMAX system, like in any communication system depends on the available channel bandwidth; in WiMAX however, the flexibility of the physical layer extends to the fact that the channel bandwidth is scalable so that it is proportional to the size of the FFT used during the OFDM/OFDMA block stage. Capacity evaluation and analysis of data rate performance in [25], [40] and [13] show the dependence of capacity and data rate on frame overhead. [25] and [40] stress the importance of proper overhead analysis in the evaluation of capacity for WiMAX. 1.1.2.1 Channel Coding and Decoding in WiMAX Channel coding is an essential ingredient in communication systems especially in multipath channel scenarios. To achieve Forward Error Correction (FEC), extra parity bits are added to the original message to recover the corrupted information. The results shown in [42] indicate significant improvements when FEC is applied to the system. The WiMAX standard specifies several FEC schemes but it points out binary convolutional coding as a mandatory scheme. The WiMAX standard specifies an adaptive FEC scheme so that the code size adapts to the given channel condition at that instant. In [5], a comprehensive literature review of adaptive FEC is discussed.
6
1.1.2.2 OFDM and OFDMA OFDM dates as far back as over forty years ago [7] but the concept has only become very popular in the past decade. OFDM was initially used as a single user transmission scheme but over years of development, it can now be used in conjunction with Frequency Division Multiple Access (FDMA) or Time Division Multiple Access (TDMA) so that it forms a multi user access scheme. In WiMAX, one of the allowed transmission mode uses OFDM-TDMA. An OFDM-TDMA transmission system, assumes that the total bandwidth is exclusively allocated to each user, i.e. all subcarriers, inside a single TDMA frame, which covers some OFDM symbols [37]. OFDM is identified as the underlying technology in the PHY layer of the 802.16 standards. It is used as a multiple access scheme in the form of OFDMA starting from the 802.16e 2005 standard where mobility is taken into full consideration. In OFDMA, both time and/or frequency resources are used to separate the multiple user signals. 1.1.3
Jakes’ Model
The Jakes’ model for generating fading has proved over years to be an effective method for Rayleigh fading channel modelling[19] [33] [12]. It is based on summing the sinusoids of fading waveforms with equal strength and uniformly distributed arrival angles. Even with its wide spread use, the model has received several revisitations [12], [33] and [34] because it does not produce some important properties of physical fading channels. Specifically, [12] pointed out that it is difficult to create multiple uncorrelated fading waveforms with the classic model.
1.2 Thesis Review In Chapter 2, an overview of wireless communication systems will be discussed. Highlighted in Chapter 2 are the various technologies that are similar to WiMAX and
7
compete with it. The chapter will focus more on wireless broadband with WiMAX as an implementation. Chapter 3 will focus on the wireless channel and how Rayleigh fading can be generated using the Jakes sum of sinusoids model. A brief description of the channel models used for simulation in this thesis will wrap up Chapter 3.
OFDM will be introduced in Chapter 4 and detailed discussion will follow, giving descriptions of the various blocks that make up a basic OFDM system. The chapter will end with a mathematical description of OFDM with supporting equations. Chapter 5 will talk about channel coding using FEC in the form of convolutional coding. The Viterbi decoder which is the most effective way of decoding short convolutional codes will be used in this thesis and its description will conclude Chapter 5.
The stages involved in the implementation of the physical layer of WiMAX (IEEE 802.16e 2005) will be presented in Chapter 6. Detailed discussion of the OFDMA frame structure and DL PUSC subcarrier permutation will appear in later parts of Chapter 6. An integral aspect of the frame structure and the DL PUSC permutation is the data burst formation and this will be discussed in the concluding section of the chapter.
Chapters 7 and 8 will present the results of simulation and conclusion to the thesis respectively.
8
Chapter 2
2 OVERVIEW OF WIRELESS COMMUNICATION SYSTEMS
2.1 Introduction The goal of any communication system is to successfully transmit data to a receiver with minimal errors in the received data. The case is not different for wireless communication systems; however the channel through which the data is transmitted may differ depending on the application of the communication system. A common definition of wireless communication is: the transfer of information over a distance without the use of enhanced electrical conductors [49].
A basic communication system, wireless or not is made up of three main functional blocks, namely: transmitter, channel and receiver. The distinguishing factor in the type of communication system is the channel; it refers to the medium through which information or data travels from the transmitter to the receiver.
Figure 2.1: Basic Communication System
9
The challenge of a wireless communication system is in overcoming the effects of the channel on the transmitted signal. Wireless communication, like other modes of communication finds application in various areas such as:
Security systems
Television remote control
Cellular telephone (phones and modems)
WiFi
Wireless energy transfer
Computer Interface Devices
The most common application of wireless communication today is in the cellular telephone system. Otherwise known as mobile phone or cell phone, cellular telephone has been a tremendous success ever since its discovery in 1945. Statistics show that the world's largest individual mobile operator is China Mobile with over 500 million mobile phone subscribers. The world's largest mobile operator group by subscribers is UK based Vodafone. There are over 600 mobile operators and carriers in commercial production worldwide. Over 50 mobile operators have over 10 million subscribers each, and over 150 mobile operators had at least one million subscribers by the end of 2008 (source: wireless intelligence). We can broadly classify wireless systems as either Line Of Sight (LOS) or Non-Line of Sight (NLOS). The types of wireless communication include:
Radio transmission
Microwave transmission
10
Infrared and Millimetre waves
Light wave transmission
The above mentioned are distinguished by their frequencies of operation and thus their transmission range.
2.2 Wireless and Mobile Networks Wireless network refers to any type of computer network that is wireless, and is commonly associated with a telecommunications network whose interconnections between nodes is implemented without the use of wires [50]. Various types of these wireless networks exist, some of which are:
Wireless PAN
Wireless LAN
Wireless MAN
Wireless WAN
The focus of this thesis however is on the Wireless MAN (Metropolitan Area Network) and is sometimes referred to as WiMAX covered in IEEE 802.16d and IEEE 802.16e standards. In simple terms, a Wireless MAN can be defined as a wireless network which connects various other wireless LANs.
The development of a WiFi chip in 2003 heralded a new dimension to the move toward wireless services. The number of WiFi users rose to 120 million by 2005, 200 million by 2006, and was estimated to top a billion in 2008[22]
11
Figure 2.2: Anticipated Growth of Wireless Users Worldwide (Source: UMTS Forum) As a result of this rapid growth, WiFi which uses the IEEE 802.11 set of standards has become synonymous with Wireless LAN. A wireless local area network (WLAN) links devices via a wireless distribution method (typically spread-spectrum or OFDM), and usually provides a connection through an access point to the wider internet.
2.3 IEEE 802.11 IEEE 802.11 is a set of standards carrying out wireless local area network (WLAN) computer communication in the 2.4, 3.6 and 5 GHz frequency bands. The 802.11 family includes over-the-air modulation techniques that use the same basic protocol. The most popular are those defined by the 802.11b and 802.11g protocols, which are amendments to the original standard [16].
Wi-Fi is increasingly used as a synonym for 802.11 WLANs, although it is technically a certification of interoperability between 802.11 devices. The Wi-Fi Alliance, a global association of companies, promotes WLAN technology and certifies products if they conform to certain standards of interoperability. Among the 12
uses of Wi-Fi, the most important today is for internet access; another use is for computer-to-computer communications.
Figure 2.3: Typical Wireless LAN The relative ease of implementation of wireless LANs make them attractive but also it has its limitations and disadvantages, the most prominent being security and range of transmission. Among numerous limitations, some of the most obvious can be experienced in the data rate and interference from other devices operating in the 2.4GHz frequency band. These limitations make it difficult and sometimes impossible to implement wireless networks in nomadic rural areas. With the development various wireless broadband schemes, it has become possible to deploy wireless LANs as a last mile resort with a broad band wireless scheme as back haul.
2.4 Broad Band Wireless Access (BWA) The term broadband, depending on the context of usage can have different meanings. In telecommunication however, broadband is a signalling method that includes or handles a relatively wide range (or band) of frequencies, which may be divided into channels or frequency bins. Broadband is always a relative term, understood according to its context. In data communications for example, a digital modem will
13
transmit a data rate of 56 kilobits per second (Kbit/s) over a 4 kilohertz wide telephone line (narrowband). However when that same line is converted to a standard twisted-pair wire (no telephone filters), it becomes hundreds of kilohertz wide (broadband) and can carry several megabits per second (ADSL). Broadband access not only provides faster Web surfing and quicker file downloads but also enables several multimedia applications, such as real-time audio and video streaming, multimedia conferencing, and interactive gaming. Broadband connections are also being used for voice telephony using voice-over-Internet Protocol (VoIP) technology.
Broadband wireless is about bringing the broadband experience to a wireless context, which offers users certain unique benefits and convenience. Wireless Broadband is a fairly new technology that provides high-speed wireless internet and data network access over a wide area. According to the 802.16-2004 standard, broadband means 'having instantaneous bandwidth greater than around 1 MHz and supporting data rates greater than about 1.5 Mbit/s. This means that Wireless Broadband features speeds roughly equivalent to wired broadband access, such as that of ADSL or a cable modem.
Both wireless and broadband have on their own enjoyed rapid mass-market adoption. Wireless mobile services grew from 11 million subscribers worldwide in 1990 to more than 2 billion in 2005. During the same period, the Internet grew from being a curious academic tool to having about a billion users. This staggering growth of the Internet is driving demand for higher-speed Internet-access services, leading to a parallel growth in broadband adoption. In less than a decade, broadband subscription worldwide has grown from virtually zero to over 200 million [7]. 14
The International Telecommunications Union (ITU) has recognized three types of wireless access (F.1399 recommendations).
Fixed access: Wireless access application in which the location of the enduser termination and the network access point to be connected to the end user are fixed.
Nomadic wireless access: Wireless access application in which the location of the end-user termination may be in different places but it must be stationary while in use.
Mobile wireless access: Wireless access application in which the location of the end-user termination is mobile.
Fixed wireless broadband can be thought of as a competitive alternative to ADSL or cable modem and it seeks to provide services similar to that of the traditional fixedline broadband but using wireless as the medium of transmission. The mobile wireless broadband access on the other hand caters for portable, high speed devices such as mobile phones, notebook computers, etc. 2.4.1
Broadband Wireless Frequency Spectrum
In many cases, the frequency assignment is as important as the broadband technology selection; but like all other aspects of the physical world, the radio frequency electromagnetic spectrum is subject to usage limitations. Use of radio frequency bands of the electromagnetic spectrum is regulated by governments in most countries, in a Spectrum management process known as frequency allocation or spectrum allocation. A number of forums and standards bodies work on standards for frequency allocation, including:
15
•
International Telecommunication Union (ITU)
•
European Conference of Postal and Telecommunications Administrations (CEPT)
•
European Telecommunications Standards Institute (ETSI)
•
International Special Committee on Radio Interference (Comité International Spécial des Perturbations Radioélectriques - CISPR)
Using the lower frequency bands is preferable for broadband-intensive network deployments. The propagation characteristics of the lower frequency bands enable RF transmissions to travel greater distances. The increased range provides larger coverage areas. Fewer cell sites require fewer backhaul connections, which leads to lower costs. The lower frequency bands also enable better in-building penetration, better mobile performance, less power consumption and higher average data throughputs in a NLOS environment. This is becoming progressively more important as the bandwidth for the backhaul connections must increase to keep up with the growing demand for mobile broadband services.
This chapter will introduce broadband wireless access schemes and take a shallow dive into technologies implementing them. I will discuss the industry trends and worldwide deployment of broadband wireless access solutions. The chapter will end with an in-depth discussion about WiMAX, the IEEE 802.16 standard and how WiMAX competes with other broadband wireless solutions.
2.5 CDMA2000 CDMA2000 represents a family of IMT-2000 (3G) standards providing high-quality voice and broadband data services over wireless networks. CDMA2000 builds on the
16
inherent advantages of CDMA technologies and introduces other enhancements, such as Orthogonal Frequency Division Multiplexing (OFDM), advanced control and signalling mechanisms, improved interference management techniques, end-to-end Quality of Service (QoS), and new antenna techniques such as Multiple Inputs Multiple Output (MIMO) and beam forming to increase data throughput rates and quality of service, while significantly improving network capacity and reducing delivery cost.
Currently, CDMA2000 includes CDMA2000 1X (1X) and CDMA2000 EV-DO (Evolution-Data Optimized) standards. CDMA2000 1X (IS-2000) supports circuitswitched voice up to and beyond 35 simultaneous calls per sector and high-speed data of up to 153 kbps in both directions. It was recognized by the ITU as an IMT2000 standard in November 1999. CDMA2000 EV-DO introduces new high-speed packet-switched transmission techniques that are specifically designed and optimized for a data-centric broadband network that can deliver peak data rates beyond 3 Mbps in a mobile environment. CDMA2000 EV-DO was approved as an IMT-2000 standard (cdma2000 High Rate packet Data Air Interface, IS-856) in 2001.
CDMA2000 1X was deployed in 2000, as the first IMT-2000 standard to be commercially available, and today, along with EV-DO, it is the leading 3G technology serving around a half billion users worldwide. CDMA2000 systems provide a family of related services including cellular, PCS, WLL and fixed wireless. [9]. 2.5.1
CDMA2000 Frequency Spectrum
CDMA2000 operates in a relatively small amount of spectrum, 1.25 MHz, in most of the frequency bands designated by the International Telecommunication Union (ITU) 17
for the IMT-2000 systems. The smaller 1.25 MHz channel size enables greater spectrum assignment flexibility to
a. incrementally assign channels as the demand for capacity increases, and b. to facilitate in-band migration deployments which require the clearing of spectrum
CDMA2000 1X, EV-DO Rel. 0 and Rev. A operate in a paired 2 x 1.25 MHz FDD channel - compared to other 3G technologies which require a much larger 2 x 5 MHz channel. By using a narrower radio channel, operators benefit from greater flexibility and improved cost efficiencies in managing their scarce spectrum resources. EV-DO Rev. B enables operators to aggregate multiple 1.25 MHz channels, up to 15 channels in 20 MHz of spectrum, to deliver the next-generation multi-mega-bits-persecond data connectivity and bandwidth intensive applications more economically.
Currently, CDMA2000 network infrastructure and user devices are available in most of the IMT-2000 frequency bands designated by the ITU, including the 450 MHz, 700 MHz, 800 MHz, 1700 MHz, 1900 MHz, AWS and 2100 MHz bands. 2.5.2
CDMA Technology
Code Division Multiple Access is the channel access method used by the CDMA2000 standards. Unlike frequency and time access methods (FDMA & TDMA), CDMA allocates the entire spectrum to a user and uses codes to identify connections.
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Figure 2.4: Channel Access Schemes The CDMA is a digital modulation and radio access system that employs signature codes (rather than time slots or frequency bands) to arrange simultaneous and continuous access to a radio network by multiple users.
CDMA is a form of Direct Sequence Spread Spectrum (DSSS) communications. In general, Spread Spectrum (SS) communications is distinguished by three key elements:
1. The signal occupies a bandwidth much greater than that which is necessary to send the information. This results in many benefits, such as immunity to interference and jamming and multi-user access. 2. The bandwidth is spread by means of a code which is independent of the data. The independence of the code distinguishes this from standard modulation schemes in which the data modulation will always spread the spectrum somewhat. 3. The receiver synchronizes to the code to recover the data. The use of an independent code and synchronous reception allows multiple users to access the same frequency band at the same time.
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In order to protect the signal, the code used is pseudo-random. It appears random, but is actually deterministic, so that the receiver can reconstruct the code for synchronous detection. This pseudo-random code is also called pseudo-noise (PN) [47].
Contribution to the radio channel interference in mobile communications arises from multiple user access, multipath radio propagation, adjacent channel radiation and radio jamming. The spread spectrum system’s performance is relatively immune to radio interference; however, CDMA still has a few drawbacks, the main one being that capacity (number of active users at any instant of time) is limited by the access interference. Furthermore, Near-far effect requires an accurate and fast power control scheme. More detailed information about CDMA Technology can be found in [47] & [45].
2.6 Third Generation Partnership Project (3GPP) 3GPP is collaboration between groups of telecommunications associations, to make a globally applicable third generation (3G) mobile phone system specification within the scope of the International Mobile Telecommunications-2000 project of the ITU. The original scope of 3GPP was to produce Technical Specifications and Technical Reports for a 3G Mobile System based on evolved GSM core networks and the radio access technologies that they support (i.e., Universal Terrestrial Radio Access (UTRA) both frequency division duplex and time division duplex modes).
The scope was subsequently amended to include the maintenance and development of the Global System for Mobile communication (GSM) Technical Specifications
20
and Technical Reports including evolved radio access technologies (e.g. General Packet Radio Service (GPRS) and Enhanced Data rates for GSM Evolution (EDGE).
Figure 2.5: 3GPP Arrow [3] 3GPP was created in December 1998 by the signing of the "The 3rd Generation Partnership Project Agreement". The latest 3GPP Scope and Objectives document has evolved from this original Agreement [3] 2.6.1
3GPP Releases
3GPP uses a system of parallel "releases" - to provide developers with a stable platform for implementation and to allow for the addition of new features required by the market. So far, the group has nine releases with the tenth release in the works.
Table 2.1: 3GPP releases[2] Version Info Release 98 This and earlier releases specify pre-3G GSM networks Specified the first UMTS 3G networks, incorporating a CDMA Release 99 air interface Originally called the Release 2000 - added features including an Release 4 all-IP Core Network Release 5 Introduced IMS and HSDPA Integrated operation with Wireless LAN networks and adds Release 6 HSUPA, MBMS, enhancements to IMS such as Push to Talk over Cellular (PoC), GAN
21
Release 7
Release 8 Release 9 Release 10
Focuses on decreasing latency, improvements to QoS and realtime applications such as VoIP. This specification also focus on HSPA+ (High Speed Packet Access Evolution), SIM high-speed protocol and contactless front-end interface (Near Field Communication enabling operators to deliver contactless services like Mobile Payments), EDGE Evolution. LTE, All-IP Network (SAE). Release 8 constitutes a refactoring of UMTS as an entirely IP based fourth-generation network. SAES Enhancements, WiMAX and LTE/UMTS Interoperability LTE Advanced
Current 3GPP standards incorporate the latest revision of the GSM standards. 3GPP's plans for the future beyond Release 7 are in the development under the title Long Term Evolution (LTE).
2.7 Long Term Evolution (LTE) With services such as WiMAX offering very high data speeds, work on developing the next generation of cellular technology has started. The UMTS cellular technology upgrade has been dubbed LTE - Long Term Evolution. The idea is that 3G LTE will enable much higher speeds to be achieved along with much lower packet latency (a growing requirement for many services these days), and that 3GPP LTE will enable cellular communications services to move forward to meet the needs for cellular technology to 2017 and well beyond.
HSPA (High Speed Packet Access), a combination of HSDPA and HSUPA, and HSPA+ are now being deployed, the 3G LTE development is being dubbed 3.99G as it is not a full 4G standard, although in reality there are many similarities with the cellular technologies being touted for the use of 4G. However, regardless of the terminology, it is certain that 3G LTE will offer significant improvements in performance over the existing 3G standards [32].
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LTE core specifications are included in release 8. In terms of actual figures, targets for LTE included download rates of 100Mbps, and upload rates of 50Mbps for every 20MHz of spectrum. In addition to this LTE was required to support at least 200 active users in every 5MHz cell (i.e. 200 active phone calls). Targets have also been set for the latency in IP packet delivery. With the growing use of services including VoIP, gaming and many other applications where latency is of concern, figures need to be set for this. As a result a figure of sub-10ms latency for small IP packets has been set. The LTE is an evolution of the UMTS/3GPP 3G standards and is thus backward compatible in the sense that it:
Works with GSM/EDGE/UMTS systems
Utilizes existing 2G and 3G spectrum and new spectrum
Supports hand-over and roaming to existing mobile networks.
Unlike the earlier forms of 3G architecture, LTE uses OFDMA/SC-FDMA instead of CDMA. This singular property of LTE makes it very similar to WiMAX.
Table 2.2: Targets for LTE Max downlink speed (bps) Max uplink speed (bps) Latency round trip time approx.
100M 50 M ~10 ms
3GPP releases
Rel 8
Approx. years of initial roll out
2009 / 10
Access methodology
OFDMA / SC-FDMA
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2.7.1
3G LTE Technologies
LTE has introduced a number of new technologies when compared to the previous cellular systems. They enable LTE to be able to operate more efficiently with respect to the use of spectrum, and also to provide the much higher data rates that are being required.
OFDM (Orthogonal Frequency Division Multiplex): OFDM technology has been incorporated into LTE because it enables high data bandwidths to be transmitted efficiently while still providing a high degree of resilience to reflections and interference. The access schemes differ between the uplink and downlink: OFDMA (Orthogonal Frequency Division Multiple Access is used in the downlink; while SC-FDMA (Single Carrier - Frequency Division Multiple Access) is used in the uplink. SC-FDMA is used in view of the fact that its peak to average power ratio is small and the more constant power enables high RF power amplifier efficiency in the mobile.
Multiple Input Multiple Output (MIMO): One of the main problems that previous telecommunications systems have encountered is that of multiple signals arising from the many reflections that are encountered. By using MIMO, these additional signal paths can be used to an advantage so that the throughput is increased. When using MIMO, it is necessary to use multiple antennas to enable the different paths to be distinguished. Accordingly schemes using 2 × 2, 4 × 2, or 4 × 4 antenna matrices can be used. While it is relatively easy to add further antennas to a base station, the same is not true of mobile handsets, where the dimensions of the user equipment limit the number of antennas which should be placed at least a half wavelength apart.
24
System Architecture Evolution (SAE): With the very high data rate and low latency requirements for 3G LTE, it is necessary to evolve the system architecture to achieve the desired improvement in. One change is that a number of the functions previously handled by the core network have been transferred out to the periphery. Essentially this provides a much "flatter" form of network architecture. In this way latency times can be reduced and data can be routed more directly to its destination.
Table 2.3: 3G LTE specification Parameter Peak downlink speed 64QAM (Mbps) Peak uplink speeds (Mbps) Data type
Details 100 (SISO), 172 (2x2 MIMO), 326 (4x4 MIMO) 50 (QPSK), 57 (16QAM), 86 (64QAM) All packet switched data (voice and data). No circuit switched.
Channel bandwidths (MHz)
1.4, 3, 5, 10, 15, 20
Duplex schemes
FDD and TDD
Mobility Latency Spectral efficiency Access schemes Modulation types supported
0 - 15 km/h (optimised), 15 - 120 km/h (high performance) Idle to active less than 100ms Small packets ~10 ms Downlink: 3 - 4 times Rel 6 HSDPA Uplink: 2 -3 x Rel 6 HSUPA OFDMA (Downlink) SC-FDMA (Uplink) QPSK, 16QAM, 64QAM (Uplink and downlink)
2.8 Wireless Broadband Deployment and Industry Trends Driven by the demand for high data rates, flexible and easy-to-implement schemes have been developed. Various companies with their expertise have been working to achieve the best possible implemented standards and technologies. Perhaps the most challenging aspect of BWA deployment from an engineering point of view is in the
25
indoor NLOS. This poses the problem of penetration through walls and other obstacles. Given the wide variety of solutions developed and deployed for broadband wireless in the past, a full historical survey of these is beyond the scope of this thesis. Wireless Broadband can be deployed either as fixed or mobile broadband access 2.8.1
Fixed Broadband Wireless Access
Services provided using fixed broadband could include high-speed Internet access, telephony services using voice over IP, and a host of other Internet-based applications. Fixed wireless communication offer several advantages over traditional wired solutions such as lower entry and deployment costs; faster and easier deployment and revenue realization; ability to build out the network as needed; lower operational costs for network maintenance, management, and operation; and independence from the incumbent carriers [7].
In the United States and other developed countries with good wired infrastructure, fixed wireless broadband is being used in rural or underserved areas, where traditional means of serving them is more expensive. A potentially larger market for fixed broadband exists outside the United States, particularly in urban and suburban locales in developing economies—China, India, Russia, Indonesia, Brazil and several other countries in Latin America, Eastern Europe, Asia, and Africa—that lack an installed base of wire line broadband networks. National governments that are eager to quickly catch up with developed countries without massive, expensive, and slow network rollouts could use WiMAX to leapfrog ahead. A number of these countries have seen sizable deployments of legacy WLL systems for voice and narrowband data. Vendors and carriers of these networks will find it easy to promote the value of WiMAX to support broadband data and voice in a fixed environment.
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2.8.2
Mobile Broadband Wireless Access
By adding nomadic capabilities to fixed broadband wireless, it can be seen as a first step towards mobility. Nomadic access may not allow for seamless roaming and handover at vehicular speeds but would allow pedestrian-speed mobility and the ability to connect to the network from any location within the service area. Existing mobile operators are less likely to adopt WiMAX and more likely to continue along the path of 3G evolution for higher data rate capabilities. Korea Telecom, however, has begun deploying WiBro service in metropolitan areas to complement its ubiquitous CDMA2000 service by offering higher performance for multimedia messaging, video, and entertainment services [7]. WiBro (Wireless Broadband) is a wireless broadband Internet technology developed by the South Korean telecoms industry. WiBro can be seen as the South Korean service name for IEEE 802.16e (mobile WiMAX) international standard. As operators move into entertainment with the development of IP-TV, schemes for mobile broadband wireless access become imperative. Figure 2.6 is a rough illustration of where different vendors are strategically aiming, not necessarily where they are today.
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Figure 2.6: Strategic Inclination of Telecom Vendors [38] Despite the strategic inclinations, pretty much all vendors seem to be playing both sides of the game. See [38] for examples of vendors’ strategies.
2.9 WiMAX The name "WiMAX" was created by the WiMAX Forum, which was formed in June 2001 to promote conformity and interoperability of the standard. The forum describes WiMAX [39] as "a standards-based technology enabling the delivery of last mile wireless broadband access as an alternative to cable and DSL". ("WiMAX Forum-Technology").
WiMAX refers to interoperable implementations of the IEEE 802.16 wirelessnetworks standard (ratified by the WiMAX Forum), in similarity with Wi-Fi, which refers to interoperable implementations of the IEEE 802.11 Wireless LAN standard (ratified by the Wi-Fi Alliance). The WiMAX Forum certification allows vendors to sell their equipment as WiMAX (Fixed or Mobile) certified, thus ensuring a level of interoperability with other certified products, as long as they fit the same profile [48].
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The IEEE 802.16 standard forms the basis of 'WiMAX' and is sometimes referred to colloquially as WiMAX. Fixed WiMAX and Mobile WiMAX are respectively known as802.16d and 802.16e [26]. Clarifications of the formal names are as follows:
802.16-2004 is also known as 802.16d, which refers to the working party that has developed that standard. It is sometimes referred to as "Fixed WiMAX," since it has no support for mobility.
802.16e-2005, often abbreviated to 802.16e, is an amendment to 802.162004. It introduced support for mobility, among other things and is therefore also known as "Mobile WiMAX".
Mobile WiMAX is the WiMAX incarnation that has the most commercial interest to date and is being actively deployed in many countries. Mobile WiMAX is also the basis of future revisions of WiMAX. As such, references to and comparisons with WiMAX henceforth means Mobile WiMAX except otherwise stated.
WiMAX promises to substitute other broadband technologies competing in the same segment and will become an excellent solution for the deployment of the well-known last mile infrastructures in places where it is very difficult to get with other technologies such as cable or DSL, and where the costs of deployment and maintenance of such technologies would not be profitable. This way, WiMAX will connect rural areas in developing countries as well as underserved metropolitan areas. It can even be used to deliver backhaul for carrier structures, enterprise campus, and Wi-Fi hot-spots. WiMAX offers a good solution for these challenges because it provides a cost-effective, rapidly deployable solution.
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2.10 Channel and Bandwidth Classes for WiMAX The WiMAX Forum™ specifies the channel and FFT size combinations. The frequency range depends on the geographical region of operation as various regions have their operational frequency bands. For example, the Korean WiBro operates with a nominal channel bandwidth of 7MHz and an FFT size of 1024 operating in the 2.3 - 2.4 GHz band. WiMAX however has several band classes as shown in Table 2.4
Table 2.4: WiMAX Channel and Bandwidth Classes
Frequency Range (GHz)
Channel Bandwidth(s) (MHz)
FFT Size
1
2.3-2.4
5 10 8.75
512 1024 1024
3.5
512
2
2.305-2.320, 2.345-2.360
3
2.496-2.69
4
3.3-3.4
5 10 5 10 5 7 10 5 7 10 5 7 10 5 7 10
512 1024 512 1024 512 1024 1024 512 1024 1024 512 1024 1024 512 1024 1024
Band Class Index
3.4-3.8
5
3.4-3.6
3.6-3.8
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2.11 WiMAX Certification Profiles The IEEE 802.16e-2005 had prescribed the frequency band of 2 to 6 GHz for Mobile WiMAX and various options for bandwidths as well as multiplexing. The WiMAX Forum has, however, selected a subset of these parameters for mobile WiMAX certification profiles in Release 1 (Figure 2.8) [22].
Mobile WiMAX Rel 1 (802.16e)
Mobile WiMAX Rel 1.5 (802.16e Rev2)
Mobile Broadband 70+ Mbps
Mobile Broadband 125+ Mbps
2008
2009/2010
Mobile WiMAX Rel 2 (802.16m)
Mobile Broadband 300+ Mbps 2010/2011
Figure 2.7: Mobile WiMAX Roadmap Mobile WiMAX uses 512 OFDM carriers for a bandwidth of 5MHz and 1024 subcarriers for bandwidths of 7 and 10MHz. For initial certification profiles, the WiMAX Forum has selected an FFT size of 512 carriers and a guard band of 1/8. The frame size selected is 5ms.
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3.3-2.8 GHz
2.3-2.7 GHz Frequency
Bandwidth
5MHz
2.3-2.4 GHz
FFT Size
512
8.75MHz
1024
10MHz
1024
5MHz
Frequency
Bandwidth
FFT Size
5MHz
3.3-3.4 GHz
512
7MHz
1024
10MHz
1024
512
2.469-2.69 GHz
10MHz
1024
5MHz
512
3.4-3.8 GHz
512
3.5MHz 3.4-3.6 GHz 2.305-2.32 GHz
7MHz
1024
10MHz
1024
1024
3.6-3.8 GHz
5MHz 2.345-2.36 GHz 1024
10MHz
Figure 2.8: Release 1 certification profiles in Mobile WiMAX [22] Release 2 (IEEE 802.16m) of WiMAX is yet to be finalized, a revision of Release 1 (Release 1.5) is in progress and is set to be completed by the end of this year. Chip giant Intel, a major supporter of the movement to provide mobile WiMAX wireless broadband to Internet users around the world, expects the next major release of the technology to be deployed starting in 2012 [30].
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Chapter 3
3 THE WIRELESS CHANNEL
3.1 Introduction The rapid fluctuation of the amplitude of a signal over a relatively small distance is referred to as fading. Interference between two or more versions of the transmitted signal can result in different propagation delays at the receiver and this is known as multipath. Some of the causes of multipath as pointed out in [28] are: atmospheric ducting, ionospheric reflection and refraction, and reflection from water bodies and terrestrial objects such as mountains and buildings. Due to the relative motion between the mobile and the base station, each multipath wave experiences an apparent shift in frequency. The shift in received signal frequency due to motion is called the Doppler shift, and is directly proportional to the velocity and direction of motion of the mobile with respect to the direction of arrival of the received multipath wave [36].
The factors influencing small scale fading are:
1. Multipath propagation 2. Speed of the mobile 3. Speed of surrounding objects 4. The transmission bandwidth of the signal
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Figure 3.1: Multipath Scattering and Shadowing The classification of fading is based on the relationship between the signal parameters and the channel parameters. The channel is typically characterized by its impulse response which contains all the necessary information required to analyse or simulate any type of radio transmission through the channel [36].
3.2 Additive White Gaussian Noise Channel This is a channel model in which the only impairment to communication is a linear addition of wideband or white noise with a constant spectral density and a Gaussian distribution of amplitude. The model does not account for fading, frequency selectivity, interference, nonlinearity or dispersion. However, it produces simple and tractable mathematical models which are useful for gaining insight into the underlying behaviour of a system before these other phenomena are considered [4].
Wideband Gaussian noise comes from many natural sources, such as the thermal vibrations of atoms in conductors, shot noise, black body radiation from the earth and other warm objects, and from celestial sources such as the Sun.
34
Due to the limitation of this model, it is safe to say that it is not a realistic channel model for simulating a mobile wireless communication system.
3.3 Fading Channel The measure of how quickly the channel response de-correlates is called the coherence time. When the coherence time is large compared to the symbol duration of the signal, then the channel is referred to as slow fading. Fast fading is the opposite of slow fading and occurs when the coherence time is small or comparable to the symbol duration. Another classification of the fading process depends on the relationship between the delay spread of the channel which is a measure of its time depressiveness and the symbol duration. When the delay spread is much smaller than the symbol duration the fading is classified as flat and when it is not it is termed as frequency selective fading [35].
Doppler shift is caused by the relative motion between the receiver and the transmitter. Doppler spread
is a measure of the spectral broadening caused by the
time rate of change of the mobile radio channel and is defined as the range of frequencies over which the received Doppler spectrum is essentially non-zero. When a pure sinusoidal tone of frequency
is transmitted, the received signal spectrum,
called the Doppler spectrum, will have components in the range where on
to
is the Doppler shift. The amount of spectral broadening depends
which is a function of the relative velocity of the mobile and the angle
between the direction of motion of the mobile and the direction of arrival of the scattered waves [36].
35
Figure 3.2: Doppler power spectral density of Rayleigh fading with a maximum Doppler shift of 10Hz.
3.4 Frequency Selective Fading Fading is considered to be flat when the symbol duration of the signal is much larger than the delay spread of the channel. This is desirable for communication, unfortunately, for high data rate applications the signal bandwidth increases and the symbol period is on the order of a few microseconds.
The frequency selective fading channel can be modelled as an Figure 3.3.
tap filter depicted in
is the number of resolvable paths provided by the channel and is a
measure of the diversity available in the channel.
36
.... 0
Ts
2Ts
3Ts
4Ts
L-1(Ts)
Time
Figure 3.3: L Tap Channel Model [
Where
]
is the delay spread of the channel and
is the symbol duration. The
impulse response of the channel can be then expressed as:
∑
The usual model assumed for frequency selective fading is Wide Sense Stationary with Uncorrelated Scattering (WSSUS). This implies that the tap gains are uncorrelated [35].
3.5 Rayleigh Fading Channel The equivalent complex baseband received signal expressed as:
∑
37
in a multipath channel can be
Where path,
,
and
are the multiplicative gain, phase shift and the delay of the
denotes the number of paths
is the transmitted signal and
is
theAdditive White Gaussian Noise term.
When the path delays are small compared to the symbol duration and the received signal can be expressed as:
∑
∑
∑
From the above equation we can see that the original transmitted signal is modulated by a random time varying scale factor
.
is the in-phase component and
is the quadrature component of the gain. When the number of paths is large we can use the Central Limit Theorem to show that
38
and
are independentGaussian
random processes. This type of fading is known as Rayleigh fading as the envelope of the scale factor
follows a Rayleigh distribution shown in Figure 3.4.
Figure 3.4: PDF of Rayleigh Fading Envelope The phases
are uniformly distributed in the interval [
] and independent for
each path. This type of fading is the most commonly dealt with type of fading in the literature and is a good model for urban areas where there is no dominant or line-ofsight path available between the transmitter and the receiver.
Frequency selective channels present opportunities as well as problems. The delay spread in the channel being comparable or larger than a symbol period causes Inter Symbol Interference (ISI) and additional complexity in the signal processing is required at the receiver. On the other hand because the resolvable paths are
39
independent it is unlikely that all of them will be in a deep fade simultaneously. If the receiver is somehow able to exploit this availability of independent signal paths and utilize the frequency diversity in the channel it could provide a much more reliable system than what could be achieved in a flat fading channel without frequency diversity at the same average signal to noise ratio. This gain is called the diversity gain achieved by the system and can be measured by the negative slope of the error probability curve when both the error probability and the signal to noise ratio are in a logarithmic scale of the same base [44]. There are three common approaches to extract frequency diversity and mitigate ISI on the frequency selective channel. They are:
•
Single Carrier with Equalization
•
Direct-sequence Spread-Spectrum
•
Multi-carrier Systems
3.6 Generating Fading (Jakes’ Model) From the definition of Rayleigh fading given above, it is possible for one to generate this model by generating two independent Gaussian random variables namely: . However, sometimes only the amplitude fluctuations are of interest. Note that this is for link level simulations of wireless communication only. The aim of generating Rayleigh fading is to produce a signal that has the same Doppler spectrum shown in Figure 3.2.
Jakes’ model is based on summing sinusoids as defined by the following equations:
40
√ {[ ∑
]
√ [ ∑
]}
√
̂
̂
̂
̂
̂ ̂
⁄
, .
From the above development, the fading simulator shown in Figure 3.5 can be constructed. There are ⁄
low frequency oscillators with frequency (
where
) where
is the number of
sinusoids. The amplitudes of the oscillators are all unity except for the oscillator at frequency
which has amplitude ⁄√
Note that Figure 3.5 implements
except for the scaling factor of √ . It is desirable that the phase of be uniformly distributed. This can be accomplished using time averaging described in [43].
41
Offset oscillators cosω1t 2cosβ1
2sinβ1
cosωMt 2sinβM
2cosβM
2sinα
2cosα
1/√2cosωmt
+ x(t)
+ y(t)
g(t) = x(t) + jy(t)
Figure 3.5: Jakes’ Fading Simulator
3.7 Channel Models A channel can be modelled by trying to calculate the physical processes which modify the transmitted signal. Statistically, communication channels are modelled as a triple consisting of an input alphabet, an output alphabet, and for each pair of input and output elements a transition probability [10]. A realistic model will be a combination of both physical and statistical modelling. A typical example is a wireless channel modelled by a random attenuation (fading) followed by AWGN. The statistics of the random attenuation are decided by previous measurements or physical simulations.
In this work, a combination of a noise model (AWGN) and a radio frequency propagation model is used for the simulations.
42
The power delay profile gives the statistical power distribution of the channel over time for a signal transmitted for just an instant. Similarly, Doppler power spectrum gives the statistical power distribution of the channel for a signal transmitted at just one frequency. While the power delay profile is caused by multipath, the Doppler spectrum is caused by motion of the intermediate objects in the channel [19]. 3.7.1
Tapped-Delay-Line Parameters
There are commonly used empirical channel models available for simulation purposes. For the purpose of this work, two models are employed in the simulations. These are: the ITU-A Vehicular test Environment and the Winner Scenario 2.8. In both cases, the relative delay and the average power are the parameters of concern. 3.7.1.1 ITU-A Vehicular Test Environment There are six taps in this model; each tap with its corresponding relative delay in (ns) and average power in (dB). Table 3.1 shows the tapped-delay-line parameters up to six taps.
Table 3.1: Vehicular test environment, tapped-delay-line parameters[18] Relative Average Tap Delay Power Index (ns) (dB) 1 0 0 2 310 -1 3 710 -9 4 1090 -10 5 1730 -15 6 2510 -20
3.7.1.2 Winner Multipath Fading Model Table 3.2 shows the 20-tap Winner multipath channel model with corresponding delays and powers.
43
Table 3.2:Winner tapped delay-line model for scenario 2.8 (RS MS, NLOS) Relative Average Tap Delay Power index (ns) (dB) 1 0 -1.25 2 10 0 3 40 -0.38 4 60 -0.1 5 85 -0.73 6 110 -0.63 7 135 -1.78 8 165 -4.07 9 190 -5.12 10 220 -6.34 11 245 -7.35 12 270 -8.86 13 300 -10.1 14 325 -10.5 15 350 -11.3 16 375 -12.6 17 405 -13.9 18 430 -14.1 19 460 -15.3 20 485 -16.3
44
Chapter 4
4 ORTHOGONAL FREQUENCY DIVISION MULTIPLEXING
4.1 Introduction Although the principle of OFDM has been around for several decades, it was only in the last two decades that it started to be used in commercial systems [14]. OFDM has developed into a popular scheme for wideband digital communication, used in applications such as digital television, audio broadcasting, wireless networking and broadband internet access. This is as a result of its high data rate transmission capability with high bandwidth efficiency and its robustness to multi-path delay.
In [11] it was shown that a cellular mobile radio system based on OFDM using pilot based correction would provide a large improvement in BER performance in a Rayleigh fading environment. The flexibility and ease of equalization in OFDM systems has also been one of the driving factors in the introduction of OFDM to the cellular world.
The two disadvantages associated with OFDM are high Peak to Average Power Ratio (PAPR) and frequency synchronization issues. A study of any of these disadvantages would be out of the scope of this thesis. The next section of this chapter would give some information about multi-carrier modulation which is a prerequisite for understanding OFDM and OFDMA.
45
4.2 Inter-Symbol (ISI) and Inter-Channel Interference (ICI) The delay spread can cause inter-symbol interference (ISI) when adjacent data symbols overlap and interfere with each other due to different delays on different propagation paths. The number of interfering symbols in a single-carrier modulated system is given by
[ ]
The maximum Doppler spread in mobile radio applications using single-carrier modulation is typically much less than the distance between adjacent channels, such that the effect of interference on adjacent channels due to Doppler spread is not a problem for single-carrier modulated systems. For multi-carrier modulated systems, the sub-channel spacing
can become quite small, such that Doppler effects can
cause significant ICI. As long as all subcarriers are affected by a common Doppler shift
, this Doppler shift canbe compensated for in the receiver and ICI can be
avoided. However, if Doppler spread in the order of several per cent of the subcarrier spacing occurs, ICI may degrade the system performance significantly [15].
4.3 Multicarrier Modulation The principle of multi-carrier transmission is to convert a serial high-rate data stream onto multiple parallel low-rate sub-streams. The motivation for the development of multicarrier modulation lies in the daunting problem of ISI and the desire for high data rates. In order to have an ISI-free channel, the symbol rate
has to be
significantly larger than the channel delay spread . As a solution to this problem, multicarrier modulation divides the high-rate transmit stream into
46
lower rate
substreams, each of which has a symbol duration of
and is hence ISI free.
The number of interfering symbols in a multi-carrier modulated system is given by
[
]
It is obvious from the above relationship that the condition for minimal ISI is a symbol duration which is significantly larger than the delay spread of the channel.
The individual sub-streams can then be sent over
parallel subchannels, maintaining
the total desired data rate. As a correspondence in the frequency domain, the number of substreams is chosen to ensure that each subchannel has a bandwidth less than the coherence bandwidth of the channel, so the subchannels experience relatively flat fading [7].
cos(2πfc)
R/L bps
+
R/L bps R bps
...
S/P
x(t)
cos(2πfc+Δf) R/L bps
cos(2πfc+(L-1)Δf)
Figure 4.1: A Basic Multicarrier Transmitter Figure 4.1 depicts a high rate stream of with rate
is broken into
parallel streams, each
. Each individual stream is then modulated by a respective frequency.
47
In the time domain, the symbol duration on each subcarrier has increased to, so letting spread,
grow larger ensures that the symbol duration exceeds the channel-delay , which is a requirement for ISI-free communication. In the frequency
domain, the subcarriers have bandwidth
, which ensures flat fading, the
frequency domain equivalent to ISI-free communication.
cos(2πfc)
Demod 1
LPF
Demod 2
LPF
P/S
y(t)
R bps
cos(2πfc+Δf)
... Demod L
LPF
cos(2πfc+(L-1)Δf)
Figure 4.2: A Basic Multicarrier Receiver Figure 4.2 shows the block diagram for the decoder of a multi-carrier system where each subcarrier is decoded separately, requiring
independent demodulators.
4.4 OFDM Basics OFDM is a frequency-division multiplexing (FDM) scheme and it gets its name from the fact that the subcarrier frequencies are chosen such that the subcarriers are orthogonal to each other. The orthogonality allows for efficient modulator and demodulator implementation using the FFT algorithm on the receiver side, and IFFT on the sender side [31]. In order to totally get rid of ISI, OFDM employs the use of a cyclic prefix which increases the length of the symbol period so that it is much
48
greater than the delay spread of the channel. Figure 4.3 shows a block diagram of an OFDM transmitter.
Constellation Mapper
FEC Encoder
Subcarrier Mapping & Pilot Insertion
Serial to Parallel
IFFT
Binary input Data
Add Cyclic Prefix
Figure 4.3: OFDM Transmitter Block Diagram On the receiver side, the inverse is done in order to recover the transmitted signal. In what follows explanations are given for each block in the OFDM transmitter. 4.4.1
FEC Encoder
FEC stands for Forward Error Correction and is a scheme used for the correction of bit errors caused by the wireless channel. FEC improves the small scale link performance by adding redundant data bits in the transmitted message so that if an instantaneous fade occurs in the channel, the data may still be recovered at the receiver. The traditional role for error-control coding was to make a troublesome channel acceptable by lowering the frequency of error events. The error events could be bit errors, message errors, or undetected errors. The addition of FEC or coding to an OFDM system is essential [14], especially if the transmission bandwidth is large compared to the coherence bandwidth. Various error-coding methods can be applied on the incoming bit stream: block codes like Reed Solomon codes and convolutional codes are the most common ones. Also, a concatenation of a block coder, an interleaver and a convolutional encoder is often used. Concatenating RS and CC has the advantage of mitigating the output burst errors that are typical for convolutional Viterbi decoders [14].
49
4.4.2
QAM Mapper
Once the signal has been coded, it enters the constellation mapper block. All wireless communication systems use a modulation scheme to map coded bits to a form that can be effectively transmitted over the communication channel. Thus, the bits are mapped to a subcarrier amplitude and phase, which is represented by a complex in-phase and quadrature-phase (IQ) vector. The IQ plot for a modulation scheme shows the transmitted vector for all data word combinations. Types of digital modulation include BPSK, QPSK, 16-QAM, etc. The constellation maps for BPSK, QPSK, and 16-QAM modulations are shown in Figure 4.4.
Figure 4.4: Constellation Maps: (a) BPSK, (b) QPSK and (c) 16-QAM The constellation mapped data is subsequently modulated onto all allocated data carriers in order of increasing frequency offset index. 4.4.3
Discrete Fourier Transform
The Fast Fourier Transform (FFT) is an effective algorithm for the implementation of the DFT. Forward FFT takes a random signal, multiplies it successively by complex exponentials over the range of frequencies, sums each product and plots the results as a coefficient of that frequency. The coefficients are called a spectrum and represent ―how much‖ of that frequency is present in the input signal. 50
FFT can be written in sinusoids as:
∑
Here,
(
*
∑
(
*
are coefficients of the sines and cosines of frequency
the index of the frequencies over the the value of the spectrum for the
frequencies and frequency and
, where
is the time index.
is is
is the value of the signal at
time . The IFFT takes a frequency spectrum and converts it to a time domain signal by again successively multiplying it by a range of sinusoids. The equation for an IFFT is:
∑
(
*
∑
(
*
The IFFT is used to produce a time domain signal, as the symbols obtained after modulation can be considered the amplitudes of a certain range of sinusoids. This means that each of the discrete samples before applying the IFFT algorithm corresponds to an individual subcarrier. Besides ensuring the orthogonality of the OFDM subcarriers, the IFFT represents also a rapid way for modulating these subcarriers in parallel, and thus, the use of multiple modulators and demodulators, which spend a lot of time and resources to perform this operation, is avoided. 4.4.4
The Cyclic Prefix
The key to making OFDM realizable in practice is the use of the FFT algorithm, which has low complexity. In order for the IFFT/FFT to create an ISI-free channel, the channel must appear to provide a circular convolution [7]. By having a long
51
symbol period, the robustness of an OFDM transmission against multipath delay spread can be achieved. Figure 4.5 depicts one way to perform the cited long symbol period, creating a cyclically extended guard interval where each OFDM symbol is preceded by a periodic extension of the signal itself. This guard interval that is actually a copy of the last portion of the data symbol is known as the cyclic prefix (CP) and thus results in a longer symbol time [7].
XL-v XL-v+1 ... XL-1 X0 X1 X2 ... XL-v-1 XL-v XL-v+1 ... XL-1
Copy and pre-append last v symbols
Figure 4.5: The OFDM Cyclic Prefix Representing such an OFDM symbol in the time domain as a length
[
vector gives
]
After applying a cyclic prefix of length , the transmitted signal is
[
]
The cyclic prefix, although elegant and simple, is not entirely free. It comes with both a bandwidth and power penalty. Since required bandwidth for OFDM increases from additional
redundant symbols are sent, the to
. Similarly, an
symbol must be counted against the transmit-power budget [7].
52
There is a trade-off between the length of the cyclic prefix, the bandwidth and the transmitted energy. However, the length of the cyclic prefix is in the range of onefourth to one-sixteenth of the symbol duration. More detail on this in [14].
4.5 Mathematical Description of OFDM A mathematical treatment of OFDM involves
The Fourier transform
The use of the Fast Fourier Transform in OFDM
The guard interval and its implementation
1.5
1.5
1
1
0.5
0.5
0
0
-0.5 -8
-6
-4
-2
0 frequency
2
4
6
8
-0.5 -8
-6
-4
-2
0 frequency
2
4
6
8
Figure 4.6: Examples of OFDM Spectrum (a) Five Subcarriers (b) A Single Subcarrier Mathematically, each carrier can be described as a complex wave:
(
The real signal is the real part of
)
. Both
and
, the amplitude and
phase of the carrier, can vary on a symbol by symbol basis. The values of the parameters are constant over the symbol duration period .
53
Since OFDM consists of many carriers, the modulated signal,
in Figure 4.6
can be represented a:
∑
(
)
This is of course a continuous signal. If we consider the waveforms of each component of the signal over one symbol period, then the variables
and
take on fixed values, which depend on the frequency of that particular carrier, and so can be rewritten:
If the signal is sampled using a sampling frequency of
, then the resulting signal
is represented by:
∑
[
]
At this point, we have restricted the time over which we analyse the signal to samples. It is convenient to sample over the period of one data symbol. Thus we have a relationship:
54
If we now simplify
, without a loss of generality by letting
, then the
signal becomes:
∑
Now
can be compared with the general form of the inverse Fourier transform:
∑
In
, the function
sampled frequency domain, and
(
)
is no more than a definition of the signal in the is the time domain representation.
and
are equivalent if:
This is the condition that is required for orthogonality. Thus, one consequence of maintaining orthogonality is that the OFDM signal can be defined by using Fourier transform procedures [27].
55
Chapter 5
5 CHANNEL CODING AND DECODING
5.1 Introduction Channel coding is used extensively in communications field in order to achieve reliable data transfer, including digital video, mobile communication and satellite communications. This chapter provides some brief explanation on the encoding and decoding procedures for convolutional codes which are used in this thesis to asses coded OFDM performance over fading channels.
5.2 Convolutional Coding Convolutional codes are a family of error correcting codes which add redundant information based on the block of data they are processing. Convolutionally encoding data is basically accomplished using shift registers and associated combinatorial logic that perform modulo-two addition. A convolutional code is specified by
, in which each
is transformed into an
information symbol to be encoded
symbol, where
transformation is a function of the last
is the code rate
and the
information symbols, where
is the
constraint length of the code [21]. 5.2.1
Structure of the Convolutional Code
In simple terms, the structure of a convolutional encoder can be described as follows: first, (
) boxes are drawn to represent the memory registers then
modulo-two
adders to represent the output bits. The memory registers are then connected to the
56
adders using the generator polynomial. As an example, consider a convolutional encoder specified by
, the structure of this coder is shown inFigure 5.1
(1, 1, 1)
+
u1
u1
u0
v1
u-1
+
v2
(1, 0, 1)
+
v3
(0, 1, 1)
Figure 5.1: Convolutional Encoder CC (1, 3, 2) This is a rate 1/3 code. Each input bit is coded onto 3 output bits. The constraint length of the code is 2. The three output bits are produced by the 3 modulo-2 adders by adding up certain bits in the memory registers. The selection of which bits are to be added to produce the output bit is called the generator polynomial for that output bit. The polynomials give the code its unique error protection capacity. 5.2.2
States of a Code
In Figure 5.1, the number of combinations of bits in the shaded registers are called the states of the states of the code and are defined by example has
states which are:
. The
code in our
. Note here that the number of
states is independent of the rate of the code.
57
5.2.3
Trellis Diagram
A convolutional encoder is often seen as a finite state machine. Each state corresponds to some value of the encoder's register. Given the input bit value, from a certain state the encoder can move to two other states. These state transitions constitute a diagram which is called a trellis diagram [1].
Figure 5.2: Example of a Trellis Diagram Adopted from [1] Each path on the trellis diagram corresponds to a valid sequence from the encoder's output. Conversely, any valid sequence from the encoder's output can be represented as a path on the trellis diagram. As an example, Figure 5.2 shows a possible path in red.
The binary convolutional encoder, which as specified by the Release 1WiMAX standard has a native rate of
and a constraint length of . The generator polynomials used to
derive its two output code bits, denoted expressions:
58
and
, are specified in the following
1
1
1
1
+
+
+
T
1
T
0
T
0
T
+
+
1
1
0
+
X=171o
+
+
Y=133o
1
1
T
0
1
T
Figure 5.3: Rate ½ Binary Convolutional Encoder The block diagram for the binary convolutional encoder that implements the described code is shown in Figure 5.3. 5.2.4
Decoding
There are several methods of decoding convolutional codes but they are all categorized into two types:
1) Sequential decoding
Fano algorithm
2) Maximum likelihood decoding
Viterbi decoding
Unlike Viterbi decoding, sequential decoding has the advantage that the decoding complexity is virtually independent of the code constraint length. For this reason, sequential decoders are used mainly with very long codes. The main disadvantage of sequential decoding is the unpredictable decoding latency. The decoding complexity of Viterbi decoders grows exponentially with the code length, which makes it suitable only for relatively short codes.
59
5.2.4.1 Viterbi Decoding This decoder uses Viterbi algorithm for decoding a bit stream that has been encoded using a convolutional code. It was developed by Andrew J. Viterbi and was published in an IEEE transaction in 1967 [46]. The use of the Viterbi algorithm for decoding covolutionally coded data has become very popular since then. According to [1], the Viterbi algorithm consists of three major parts:
I.
Branch matric calculation Calculation of a distance between the input pair of bits and the four possible ―ideal‖ pairs (―00‖, ―01‖, ―10‖, ―11‖)
II.
Path matric calculation For every encoder state, calculate a metric for the survivor path ending in this state (a survivor path is a path with the minimum metric).
III.
Back Tracing This step is necessary for hardware implementations that don't store full information about the survivor paths, but store only one bit decision every time when one survivor path is selected from the two.
These parts are depicted in Figure 5.4
encoded stream
Branch metric calculation
Path metric calculation
Trackback
Figure 5.4: Viterbi Decoder Data Flow
60
decoded stream
Chapter 6
6 THE WIMAX PHYSICAL LAYER
6.1 Introduction The physical (PHY) layer of WiMAX was designed with much influence from WiFi, especially IEEE 802.11a. Although many aspects of the two technologies are different due to the inherent difference in their purpose and applications, some of their basic constructs are very similar. The WiMAX physical layer is based on OFDM. OFDM is the transmission scheme of choice to enable high-speed data, video, and multimedia communications and is used by a variety of commercial broadband systems, including DSL, WiFi, Digital Video Broadcast-Handheld (DVBH), and MediaFLO, besides WiMAX.
Figure 6.1 shows the functional stages of the WiMAX PHY layer.
Cyclic Prefix Input Bit Sequence
Channel Encoder
Symbol Mapper
Subcarrier Allocation + Pilot Insertion
Figure 6.1: Functional stages of WiMAX PHY
61
IFFT
The first set of functional stages is related to FEC, and includes channel encoding, rate matching (puncturing or repeating), interleaving, and symbol mapping. The next set of stages is related to the construction of the OFDM symbol in the frequency domain. During this stage, data is mapped onto the appropriate sub-channels and subcarriers. Pilot symbols are inserted into the pilot subcarriers, which allow the receiver to estimate and track the channel state information (CSI). This stage is also responsible for any space/time encoding for transmit diversity or MIMO, if implemented. The final set of functions is related to the conversion of the OFDM symbol from the frequency domain to the time domain and eventually to an analogue signal that can be transmitted over the air.
The rest of this thesis discusses the various mandatory functional stages of the PHY layer of WiMAX as defined by the IEEE 802.16d/e standards.
6.2 Symbol Mapper The symbol mapping stage basically refers to a digital modulation scheme which is used to convert the sequence of binary bits from the convolutional encoder into a sequence of complex valued symbols. The mandatory constellations according to the standard are QPSK and 16QAM with an optional 64QAM also defined in the standard.
Each modulation constellation is scaled by a number c, such that the average transmitted power is unity, assuming that all symbols are equally likely. The value of is √ ⁄ , √ ⁄
and √ ⁄
for the QPSK, 16 QAM, and 64 QAM modulations,
respectively.
62
6.3 OFDM Symbol Structure Each OFDM symbol consists of three types of subcarriers as depicted in Figure 6.2:
1. Data subcarriers: used for carrying data symbols 2. Pilot subcarriers: used for various estimation purposes such as channel tracking and are known a priori 3. Null subcarriers: this is further divided into two, namely the DC and the guard subcarriers. These subcarriers have no power allocated to them; the guard subcarriers have no power allocated to them in order to reduce the interference with adjacent symbols.
Pilot subcarriers
Data subcarriers
DC subcarrier
Guard subcarriers
Guard subcarriers
Figure 6.2: Subcarrier Structure in Frequency 6.3.1
Symbol Parameters
The primitive parameters of an OFDM symbol as defined by the standard are:
Total number of subcarriers or the FFT size
Nominal channel bandwidth,
Oversampling factor,
Ratio of cyclic prefix time to useful symbol time,
63
Table 6.1 shows a summary of these parameters with their possible values for different scenarios
Table 6.1: Primitive parameters for OFDM symbol Parameter Value (MHz) Definition Variable: 1.25, 1.75, 3.5, 5, 7, Nominal channel bandwidth 8.75, 10, 14, 15 256 for OFDM; Number of subcarriers, including the DC 128, 512, 1,024, subcarrier pilot subcarriers and the guard 2,048 for subcarriers SOFDMA 8/7, 28/25 Oversampling factor 1/4, 1/8, 1/16, Ratio of cyclic prefix time to useful symbol and 1/32 time
The OFDM symbol time duration is given as:
⁄
6.4 OFDMA and Subchannelization OFDMA consists of assigning one or several subchannels to each user with the constraint that the subcarrier spacing is equal to the OFDM frequency spacing [15]. A subchannel is defined as a group of subcarriers. Sub-channelization refers to the process of grouping the subcarriers into subchannels. Various sub-channelization schemes which have been defined by the WiMAX standard exist. In OFDMA, subchannels rather than subcarriers are allocated to different users based on some
64
subcarrier permutation schemes which will be discussed later in the chapter. This is in contrast to OFDM where all the subcarriers are allocated to a single user at a time. OFDMA can be seen as the multiple access scheme of OFDM.
6.5 Multiple Access Schemes Multiple access schemes provide ways in which multiple users can access the channel. The most common way to divide the available dimensions among the multiple users is through the use of frequency, time, or code division multiplexing. In Frequency Division Multiple Access (FDMA), each user receives a unique carrier frequency and bandwidth. In Time Division Multiple Access (TDMA), each user is given a unique time slot, either on demand or in a fixed rotation. Code Division Multiple Access (CDMA) systems allow each user to share the bandwidth and time slots with many other users and rely on orthogonal binary codes to separate out the users [7].
power
frequency
power
frequency
power
frequency
User 1 (a)
time
time
(b)
(c)
time
User 2 User 3
Figure 6.3: Multiple Access Schemes. (a) FDMA (b) TDMA (c) CDMA
6.6 OFDMA Like OFDM, OFDMA employs multiple closely spaced subcarriers, but the subcarriers are divided into groups of subcarriers. Each group is named a subchannel. The subcarriers that form a subchannel need not be adjacent. In the downlink, a subchannel may be intended for different receivers. In the uplink, a transmitter may
65
be assigned one or more subchannels. Subchannelization defines subchannels that can be allocated to mobile stations (MSs) depending on their channel conditions and data requirements. Using subchannelization, within the same time slot a Mobile WiMAX Base Station (BS) can allocate more transmit power to MSs with lower SNR (Signal-to-Noise Ratio), and less power to user devices with higher SNR.
Figure 6.4: OFDMA Transmission. Ref (6) This is illustrated in Figure 6.4. Subchannelization also enables the BS to allocate higher power to sub-channels assigned to indoor SSs resulting in better in-building coverage.
OFDMA is essentially a hybrid of FDMA and TDMA: Users are dynamically assigned subcarriers (FDMA) in different time slots (TDMA) as depicted in Figure 6.5
66
Figure 6.5: (a) OFDM (b) OFDMA 6.6.1
OFDMA Symbol Structure
The OFDMA symbol structure is similar to that of OFDM. The difference lies in the fact that subchannels rather than all subcarriers are allocated to users. Since OFDMA is a multiple access scheme, the data for the various users is contained within a symbol. Depending on the subcarrier permutation used, subcarriers may be adjacent or distributed across the available channel bandwidth. Figure 6.6 is a depiction of an OFDMA symbol showing subcarriers from different subchannels within the same symbol.
DC Subchannel 1
Subchannel 2
Subchannel 3
Subchannel 4
Figure 6.6: Subchannels in the Subcarrier Structure For full OFDMA symbol specification refer to [17].
6.7 Subchannelization in WiMAX Subchannelization refers to the process of grouping subcarriers to subchannels. The WiMAX standard defines various types of subchannelization schemes that can be used both in the up-link and in the down-link. A subchannel, as defined in the IEEE 802.16e-2005 standard, is a logical collection of subcarriers. The number and distribution of the subcarriers that make up a subchannel depends on the subcarrier 67
permutation that is used. The subcarrier permutations allowed in IEEE 802.16e-2005 are:
Down-link Full Usage of Subcarriers (DLFUSC)
Down-link Partial Usage of Subcarriers (DL PUSC)
Up-link Partial Usage of Subcarriers (UL PUSC)
Tile Usage of Subcarriers (TUSC)
Band Adaptive Modulation and Coding (Band AMC)
The aforementioned subcarrier permutation schemes can be broadly classified into two categories namely:
1. Distributed subcarrier permutation: the subcarriers are distributed pseudo-randomly. The advantages of this type of permutation are the exploration of frequency diversity and interference averaging [29]. On the other hand, this type of permutation makes channel estimation difficult since the subcarriers are distributed over the available bandwidth. PUSC, FUSC and TUSC use the distributed subcarrier permutation. 2. Adjacent subcarrier permutation: in this mode, a subchannel is made up of subcarriers that are adjacent in the available frequency band. It has the advantage of easier channel estimation. This mode is used in the band AMC permutation.
The mandatory permutation modes for up-link and downlink defined by the WiMAX standard are:
68
PUSC, FUSC and AMC for the downlink
PUSC and AMC for the uplink
The focus of this thesis is on the Downlink PUSC. As a justification notice that in Figure 6.7the only mandatory part of the frame is the downlink PUSC zone.
AMC
Optional PUSC
PUSC
TUSC 2
TUSC 1
AMC
UL Subframe
Optional FUSC
FUSC (DL-PermBase Z)
FUSC (DL-PermBase Y)
PUSC (DL-PermBase X)
PUSC (first zone contains FCH and DL-MAP)
Preamble
DL Subframe
Must appear in every frame May appear in a frame
Zone switch Ies in DL-MAP
Figure 6.7: Illustration of OFDMA Frame with Multiple Zones 6.7.1
DL PUSC
As an introduction to this section, I will start with some basic definitions. The DL PUSC parameters are tabulated in Table 6.2
Table 6.2: DL PUSC Parameters Parameter Null Subcarriers Pilot Subcarriers Data Subcarriers Subchannels
Value 184 120 720 30
Slot: this is the minimum possible data allocation unit. It is expressed as number of subchannels per number of OFDM symbols.
Data Region: it is a two-dimensional rectangular allocation of a group of subchannels in a group of OFDMA symbols. 69
Segment: the set of available subchannels form a segment. There are three segments in a frame. The concept of segmentation is used in sectorization where each segment is allocated to one sector.
Physical Cluster: it is a set of 14 adjacent subcarriers (12 data + 2 Pilot). These clusters are contiguous in the frequency band.
Logical Cluster: it is formed by renumbering physical clusters according to some renumbering sequence. Adjacent logical clusters are not contiguous in the frequency band.
Group: it is a set of logical clusters. Odd numbered groups contain half the number of logical clusters as compared to even numbered groups. There are six groups in total.
Perm Base: this has separate meanings in the uplink and the downlink. In the downlink it is called DL Perm Base and is an integer ranging from 0 to 31. It identifies the particular BS segment and is specified by the MAC layer.
Inner Permutation: this is the process of forming subchannels from the subcarriers of the logical clusters of a group.
Outer Permutation: this is the process of renumbering physical clusters to form logical clusters.
70
OFDM Symbol Index K+1
Subchannel Index
Segment 0
Segment 1
Segment 2
K+2
K+3
K+4
K+5
K+6
K+7
K+8
K+9
K+10 K+11
0 1 2 3 4 5 6 7 8 9
. . . . . . . . . . . . . . . . . . . .
PUSC Slot
Data Region
Figure 6.8: Example of an OFDMA DL Frame The process of allocating subcarriers to subchannels can be summarized as follows: the guard and dc subcarriers are first removed after which the remaining subcarriers (data + pilot) are renumbered and partitioned into groups of 14 subcarriers. These groups are called physical clusters. The physical clusters are then renumbered according to a renumbering sequence (outer permutation) so that the logical subcarriers are formed. Pilot positions are marked for even and odd symbols then the clusters are put into major groups according to the parity of the groups. The remaining data subcarriers within each group are then renumbered (0 to 143 or 95) depending on the parity of the groups. The subchannel allocation is done by allocating subcarriers from each group to subchannels according to a permutation formula. Figure 6.9 illustrates the steps involved in the permutation process.
71
Physical Cluster (PN) 0-59
PN PN PN PN PN PN
PN
. . . . . . . .
LN LN LN LN LN LN LN LN LN
59
LN
30 33 54 18 10 15 50 51 58 46
. . . . . . .
32 47
Step 3: Gather clusters in six major groups (MG) LN 0 – LN 11
PN
LN
MG 0 (even)
LN 12 – LN 19
PN
Step 2: Renumber the clusters. (in this example DL Perm Base=10)
MG 1 (odd)
LN 20 – LN 31
PN
0 1 2 3 4 5 6 7 8 9
MG 2 (even)
...
PN
Logical Cluster (LN)
Step 1: Divide the subcarriers into clusters of 14 subcarriers each
Step 4: Allocate subcarriers to subchannels
Allocate data subcarriers to subchannels. No. Of subchannels depends on the parity of each MG
Allocate pilots in each group depending on the parity of the symbol
MG X
Figure 6.9: PUSC Subchannel Allocation Procedure PUSC is best explained in a stepwise manner:
Step 1: All the subcarriers are portioned as right guard band, left guard band, DC, data and pilot. The data and pilot subcarriers are then grouped into sets of 14 adjacent subcarriers each. Where each set represents a physical cluster. For 1024 point FFT, there are 60 clusters (0-59).
Step 2: logical clusters are formed by renumbering physical clusters using Step two is essentially the outer permutation defined earlier in this section.
72
.
where the Renumbering sequence(j) is the jth entry of the following vector
{6, 48, 37, 21, 31, 40, 42, 56, 32, 47, 30, 33, 54, 18, 10, 15, 50, 51, 58, 46, 23, 45, 16, 57, 39, 35, 7, 55, 25, 59, 53, 11, 22, 38, 28, 19, 17, 3, 27, 12, 29, 26, 5, 41, 49, 44, 9, 8, 1, 13, 36, 14, 43, 2, 20, 24, 52, 4, 34, 0} Step 3: the logical clusters are gathered to form six major groups (numbered 0-5). Even numbered groups (0, 2 and 4) contain 12 logical clusters each; while odd numbered groups (1, 3 and 4) contain 6 logical clusters.
Step 4: pilot subcarriers are separated from the data subcarriers in this step. The position of the pilot subcarriers depends on if the OFDM symbol is odd or even as seen in Figure 6.10.
P
Even OFDMA Symbol
P
P
P
P
Pilot subcarrier Data subcarrier
Figure 6.10: PUSC DL Slot
73
Odd OFDMA Symbol
Step 5: this is the final step of the subcarrier allocation. After marking the pilot subcarrier positions, the remaining data subcarriers are numbered from 0 to 143 or 95 depending on the parity of the major group. Subcarrier allocation is done using
,
it is worth noting however that the formula is only applied to subcarriers of a major group.
{ [
] }
where
is the number of subchannels in the particular major group, equal
to 4 or 6, depending on the parity of the major group;
is the
subcarrier index of subcarrier
whose
varying between 0 and 23, in subchannel
value ranges between 0 and 143 or 95.
is the subchannel index varying between 0
and 29.
where
is the number of data subcarriers allocated to a subchannel in
each OFDMA symbol;
[ ] is the series obtained by rotating the basic permutation
sequence (Table 6.3) cyclically to the left times.
Table 6.3: Permutation sequence Permutation Base Sequence [3 0 2 1] 4 [3 2 0 4 5 1] 6
74
Major Group Parity Even odd
For a 1024 point FFT, there are: 1024 subcarriers, 184 null subcarriers (92 + 91 + 1), 120 pilot subcarriers and 720 data subcarriers. As an example, I will use DL PUSC permutation to find the 24 physical (data) subcarriers of subchannel 16.
Table 6.4: Parameters for DL PUSC example Parameter
Value
DL PermBase
10
OFDMA Symbol
Odd
Major Group
16
Permutation Sequence
[3 0 2 1] 4
The correspondence between the logical number and the physical number of the clusters is depicted in Table 6.5. The table also shows a correspondence between the logical subcarrier index and the original physical subcarrier index. Table 6.5: Cluster numbering(Major Group 3, DL PermBase = 10) Cluster Logical Subcarrier Cluster PN Cluster Physical LN Index Equation (6.1) Subcarrier Index 32
302-315
5
162-175
33
288-301
41
666-679
34
92-105
49
778-791
35
372-385
44
708-721
36
736-749
9
218-231
37
904-917
8
204-217
38
554-567
1
106-119
39
890-903
13
274-287
75
Table 6.6 depicts the logical subcarrier indexes with respect to the subchannel; values of
, logical subcarrier index in the major group. The last column in the table
shows the original physical subcarrier indexes with respect to the absolute subcarrier scale (0-1024).
Table 6.6: Subcarrier Allocation Logical Subcarrier Index in subchannel 16 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
Logical subcarrier index in the major group 16 17 18 19 20 21 22 23 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
100 104 111 119 121 126 136 140 3 11 13 18 28 32 39 47 49 54 64 68 75 83 85 90
Physical subcarrier index with respect to the absolute subcarrier scale 199 862 864 871 873 444 446 453 317 322 324 891 893 898 900 641 643 648 650 587 589 594 190 197
6.8 OFDMA Frame In IEEE 802.16e-2005, both frequency division duplexing and time division duplexing are allowed. In the case of FDD, the uplink and downlink sub-frames are transmitted simultaneously on different carrier frequencies; in the case of TDD, the
76
uplink and downlink sub-frames are transmitted on the same carrier frequency at different times. Figure 6.11 shows the frame structure for TDD [7]. Each DL subframe and UL sub-frame in IEEE 802.16e-2005 is divided into various zones, each using a different subcarrier permutation scheme as shown in Figure 6.7. The relevant information about the starting position and the duration of the various zones being used in a UL and DL sub-frame is provided by control messages in the beginning of each DL sub frame.
.
.
UL Burst 2
UL Burst 4
UL Burst 1
DL Burst 4 DL Burst 3
.
UL Burst 3
OFDMA Symbols k+30
.
DL Burst 5
. DL Burst1
DL-MAP UL-MAP
.
DL Burst 2
FCH
k+1 k+3
DL-MAP
DL Frame Preamble
Subchannels
k
Ranging Subchannels TTG DL Subframe
UL Subframe
Figure 6.11: TDD Frame Structure The first OFDM symbol in the downlink sub-frame is used for transmitting the downlink preamble. The downlink preamble is mainly used for time and frequency synchronization and channel estimation. Following the preamble, occupied by the initial subchannels is the Frame Correction Header (FCH). The FCH is used for carrying system control information such as the subchannels used for ranging, the length of the DL-MAP message and the subcarriers used (in case of segmentation). After the FCH come the DL-MAP and UL-MAP messages respectively. They
77
specify the data regions of the various users in the DL and UL sub-frames of the current frame. By listening to these messages, each SS can identify the subchannels and the OFDM symbols allocated in the DL and UL for its use [7]. The gap between the downlink and uplink sub-frames is called the Transmit Transition Gap (TTG). 6.8.1
OFDMA Frame Parameters
Table 6.7shows that at 10MHz, the OFDMA symbol time is 102.9 microseconds and so there are 48 symbols in a 5 millisecond frame. Of these, 1 symbol is used for TTG and RTG leaving 47 symbols. If
of these are used for DL, then
are
available for UL. The sub-division of the UL and DL sub-frames is done according to the DL/UL ratio. The standard defines various ratios but for the purpose of this study, a
ratio is used. In the DL sub-frame, the overhead consists of preamble,
FCH, DL-MAP and UL-MAP [40]. The rest of the OFDMA symbols in the frame are used to carry the data of the users. Table 6.7 shows specific values of the parameters discussed.
Table 6.7: TDD OFDMA frame parameters Parameters Channel Bandwidth Frame duration Number of OFDMA Symbols/Frame Total Number of OFDMA Overhead Symbols Number of OFDMA symbols for TTG and RTG Total Number of OFDMA Data Symbols Symbol Duration DL:UL DL OFDMA Data Symbols 3:1 UL OFDMA Data Symbols
78
Values 10 MHz 5 ms 48 10 1 37 102.9 μs 28 9
6.8.2
Data Burst Formation via Vertical Mapping
The data burst(s) in the PUSC zone of the DL sub-frame is formed by allocating slot by slot downwards across the subcarriers of the subchannels until all the subchannels of that time period are filled; then the same process is repeated for the adjacent OFDMA symbols until the entire DL sub-frame fills up or when the data is exhausted. The allocation is done user by user so that each user’s data is contained within that user’s data burst. Figure 6.12 depicts this process.
OFDM Symbol Index
Subchannel Index
Segment 0
Segment 1
0 1 2 3 4 5 6 7 8 9
. . . . . . . . . . .
Figure 6.12: Data Burst Formation This is illustrated with an example. Assume that there are four users with data symbols from the QAM mapper that are to fit into segment 0 of the DL sub-frame. There are 10 subchannels in each segment and assume the length of the DL subframe data region is 10 OFDMA symbols (5 slots). Each slot will contain 56 bits of data. The data regions of the DL sub-frame is depicted in Figure 6.13
79
OFDMA Symbols Slot
0 1 2
Data exhausted
Subchannels
3 4 5 6 7 8 9 Time interval
User 1 User 2 User 3 User 4
Figure 6.13: Data Region Showing Data Bursts for Four Users
80
Chapter 7
7 UN-CODED vs. CODED OFDM PERFORMANCE OVER MULTIPATH FADING CHANNELS
7.1 Introduction Link level (LL) simulations, model the behaviour of a link over a short period of time and usually involve modelling parts of the physical layer and some aspects of the MAC layer. The simulations are then used to arrive at theoretical results that model the behaviour of the single link under given channel conditions. The results are generally presented in terms of Bit Error Rate (BER) as a function of the Signal to Noise Ratio (SNR). The aim of this chapter is to show the BER performance of un-coded and coded OFDM over non-fading and fading channels. The two fading channel models used are the Winner Scenario 2.8 channel model and the ITU-A Vehicular channel. The Winner channel model has been structured for indoor and outdoor environments for the 5 GHz frequency range. The Winner model is based on the widely accepted modelling approach presented in [53]. Another commonly used set of empirical channel models is that specified in ITU-R recommendation [18]. The recommendation specifies three different test environments: indoor office, outdoor to indoor pedestrian and vehicular to high antenna. Since the delay spread can vary significantly, the recommendation specifies two different delay spreads for each test environment: low delay spread (ITU-A) and medium delay spread (ITU-B). In all
81
there are 6 different scenarios and for each of these cases, a multipath tap delay profile is specified [18]. In all ITU channel models each multipath component is modelled as an independent Rayleigh fading, and the correlation in the time domain is due to the Doppler shift that is related to the speed the mobile is moving with.
7.2 Simulation of OFDM The parameters used in the simulation of OFDM in this thesis are summarized in Table 7.1. The performance of OFDM was simulated over different channel conditions. The effect of the speed of the receiver was also taken into consideration while simulating under multipath conditions.
Table 7.1: OFDM Simulation Parameters Parameter Value FFT Size 1024 Constellation Mapping QPSK Symbol Duration 102.4µs Length of Cyclic Prefix 1/8 of Symbol duration (12.8µs) Channel Coding R ½ CC and Viterbi Decoding ITU A Vehicular Channel Multipath Channels Winner Channel (Scenario 2.8)
Theoretical and simulated results were compared in order to show conformance of the simulation to already developed theory. The BER is the number of received bits that have been altered due to noise, interference and distortion, divided by the total number of transferred bits during a studied time interval [8]. The BER is expressed as a function of the normalized carrier-to-noise ratio measure denoted (energy per bit to noise power spectral density ratio).
82
,
7.2.1
Un-coded OFDM over AWGN Channel
The performance of OFDM-QPSK over an AWGN channels is shown in Figure 7.1. The graph shows the theoretical as well as the experimental performance of the system plotted as BER against
. For QPSK the theoretical BER is given by:
√
⁄
Performance of QPSK modulated OFDM Transmission over an AWGN Channel
-1
10
experimental ber theoretical ber
-2
10
-3
BER
10
-4
10
-5
10
-6
10
0
1
2
3
4
5 Eb/N0 (dB)
6
7
8
9
10
Figure 7.1: OFDM Performance over AWGN Channel Figure 7.1 shows conformity of the simulated performance to the theoretically obtained BER performance in terms of the shape of the curves. The observed SNR loss of approximately
in the experimental BER curve is as a result of the
cyclic prefix introduced by OFDM [14]. The SNR loss is given by: ( where
*
denotes the length of the cyclic prefix and
the transmitted symbol. With
μ and
83
is the length of μ , using equation (7.2)
is found to be
. This loss is uniform throughout the performance
and can be seen as one of the costs of OFDM. For a longer cyclic prefix, it is expected that there will be a greater
. The result obtained is in parallel to
what is shown on page 45 of [14]. 7.2.2
Coded OFDM over AWGN Channel
In this simulation FEC is added to the system in order to improve its performance. The data is coded using a rate ½ convolutional encoder with a constraint length of 7 and decoded using a corresponding Viterbi decoder with a track back length of 32 (approximately 5 times the constraint length).
Performance of Rate 1/2 Convolutionally Coded OFDM-QPSK OFDM Transmission over an AWGN Channel
0
10
Coded BER Uncoded BER -1
10
-2
BER
10
-3
10
-4
10
-5
10
-6
10
0
1
2
3
4
5 Eb/N0 (dB)
6
7
8
9
10
Figure 7.2: Coded OFDM Performance over AWGN Channel The simulation was repeated 300 times for 15 OFDM symbols and the results were averaged. Note from Figure 7.2 that, the system BER performance for coded QPSKOFDM would reach a much lower bit error rate at an earlier (lower) signal to noise
84
ratio. For example the coded system will achieve a target BER of whereas the un-coded system will achieve the same BER at
at
.
In order to have a lower BER one must further increase the number of bits or symbols in the frame to transmit. However, since
is a good BER, this was not
done in this study. The significant reduction in the SNR in order to achieve a required BER is known as coding gain [20]. Figure 7.2 shows that with convolutional coding of rate R = ½ and constraint length of k = 7, at a BER of coding gain of 7.2.3
there is a
over the un-coded performance.
Un-coded OFDM over Multipath Rayleigh Fading Channels
Again OFDM-QPSK was simulated and presented as BER as a function of the SNR. It was expected that in a multipath channel, the performance of the system as compared to that in an AWGN channel would be worse. Since in a real life situation the receiver is mobile, mobility was also taken into consideration. The relationship between Doppler frequency and velocity was used for this purpose. The simulations in this section compare the performance of the system in the Winner and ITU-R specified (ITU-Vehicular A) channel models at different Doppler frequencies while using theoretical results as a benchmark. The performance was observed to degrade with increasing Doppler frequencies. The simulated BER is in close conformity with theoretical results obtained in [14]. The plots in Figure 7.3 show what is obtainable theoretically for various speeds of the receiver. Even though the profile information is not specified in [14], it has been made clear that the channel taps are approximately Rayleigh distributed. Thus, equation (7.3) and the curve obtained by equation (7.6) have been used for comparison. In a multipath Rayleigh fading channel, the probability of symbol error is given by:
85
√ ̅
̅ ̅
√
(
̅ ̅
)
where ̅
is the signal to noise ratio,
is the maximum Doppler frequency and
is the
subcarrier frequency spacing. According to page 84 of [52], the relationship between Symbol Error Rate (SER) and Bit Error Rate (BER) is:
where
is the number of bits per symbol. For QPSK, there are two bits per symbol.
Therefore equation (7.5) becomes:
Then the BER is:
The expression for the probability of bit error can therefore be derived from equation (7.3) and is given by:
̅
(
√
̅ ̅
√
(
̅ ̅
))
For detailed development of equation (7.3), refer to [14]. For multipath channels which have high delay spreads compared to the symbol duration, the channel coefficients might not be constant over neighbouring subcarriers. Therefore, the orthogonality of adjacent subcarriers is no longer
86
preserved. This causes an error floor in the BER performance due to the interference which comes from the neighbouring symbols. The resulting inter-symbol interference creates an irreducible error floor which is clearly visible in the curves of Figure 7.3. Theoretical OFDM-QPSK performance over a multipath Rayleigh fading channel
0
10
fd = 100 Hz fd = 400 Hz fd = 833 Hz -1
10
-2
BER
10
-3
10
-4
10
-5
10
0
5
10
15
20 25 Eb/N0 (dB)
30
35
40
Figure 7.3: Theoretical Un-coded OFDM Performance over Rayleigh Multipath Fading Channel In the following sections, a comparison was made between two channel models: ITU Vehicular-A channel model and the Winner Scenario 2.8 channel model. The Winner channel models were developed before the ITU channel models and they were used for evaluation of 3G systems but the ITU channels which present more adverse conditions were developed in order to be used for evaluation of IMT-Advance systems (4G). It was expected that the performance of OFDM will be better in the Winner channel when compared to the ITU channel because the ITU channel has larger relative delays.
87
The OFDM parameters specified in Table 7.1 earlier were used for simulating both channels. Each simulation was repeated 3000 times for 15 OFDM symbols and the results were averaged. For fair comparison of the performance between the two channels, the same length of cyclic prefix was used. 7.2.3.1 Un-coded OFDM performance over Winner Scenario 2.8 Channel Using the relative delay and power values in Table 7.2 and Jakes sum of sinusoids model earlier discussed in section 3.6, the following performance curves were obtained for Doppler shifts of of approximately
,
,
and and
corresponding to speeds respectively. Again it is in
agreement (in terms of the shape of the curve) with the performance curves obtained after plotting equation (7.8).
Table 7.2: Winner scenario 2.8 channel Relative Tap Delay index (ns) 1 0 2 10 3 40 4 60 5 85 6 110 7 135 8 165 9 190 10 220 11 245 12 270 13 300 14 325 15 350 16 375 17 405 18 430 19 460 20 485 88
Average Power (dB) -1.25 0 -0.38 -0.1 -0.73 -0.63 -1.78 -4.07 -5.12 -6.34 -7.35 -8.86 -10.1 -10.5 -11.3 -12.6 -13.9 -14.1 -15.3 -16.3
Performance of Uncoded OFDM-QPSK Transmission over Winner Sc. 2.8 multipath Rayleigh fading Channel
0
10
fd = 100Hz fd = 400Hz fd = 833Hz fd = 100 Hz fd = 400 Hz fd = 833 Hz Theoretical Experimental
-1
10
-2
BER
10
-3
10
-4
10
0
5
10
15
20 25 Eb/N0 (dB)
30
35
40
Figure 7.4: Un-coded OFDM Performance over Rayleigh Multipath Fading Channel (Winner Scenario 2.8 Channel) 7.2.3.2 Un-coded OFDM performance over ITU Vehicular-A Channel The same Doppler shifts and thus MS velocities were used with the delay and power values in Table 7.3 to obtain the performance curves in Figure 7.5.
Table 7.3: ITU Vehicular-A channel parameters Relative Tap Delay Index (ns) 1 0 2 310 3 710 4 1090 5 1730 6 2510
Average Power (dB) 0 -1 -9 -10 -15 -20
It is clear from the performance curves of Figure 7.5 that as the velocity of the MS increases so does the Doppler shift. The observed error floors for the various Doppler
89
frequencies also increased with the Doppler frequency as expected. Therefore, for a mobile observing a maximum Doppler shift of
, the error floor is significantly
lower than that of one observing a Doppler shift of
. This is attributed to the
fact that communication is more reliable when there is no relative motion between the transmitter and the receiver.
Performance of Uncoded OFDM-QPSK Transmission over ITU-Vehicular A multipath Rayleigh FadingChannel
0
10
fd = 100Hz fd = 400Hz fd = 833Hz fd = 100 Hz fd = 400 Hz fd = 833 Hz Experimental Theoretical
-1
10
-2
BER
10
-3
10
-4
10
0
5
10
15
20 25 Eb/N0 (dB)
30
35
40
Figure 7.5: Un-coded OFDM Performance over Rayleigh Multipath Fading Channel (ITU Vehicular-A) From the performance curves in Figure 7.6, it can be seen that OFDM has a better performance in the Winner Scenario 2.8 channel than in the ITU-Vehicular A channel. This is as a result of the large delays found in the ITU-Vehicular A channel: the maximum delay in the ITU-Vehicular A channel is Winner Scenario 2.8 channel is
while that in the
. This observation has also shown that the
error floor is dependent on the delay spread of the channel. For a Doppler frequency of
, the error floor of the OFDM performance over the Winner channel started
90
to form at
while for the ITU channel the error floor formation started at
. Performance of Uncoded OFDM-QPSK Transmission over ITU-Vehicular A and Winner Scenario 2.8 Multipath Rayleigh Fading Channels
0
10
fd = 833 Hz fd = 400 Hz fd = 100 Hz fd = 100Hz fd = 400Hz fd = 833Hz ITU-Vehicular A Channel Winner Scenario 2.8 Channel
-1
10
-2
BER
10
-3
10
-4
10
0
5
10
15
20 25 Eb/N0 (dB)
30
35
40
Figure 7.6: Un-coded OFDM Performance over Rayleigh Multipath Fading Channels (ITU-Vehicular A and Winner Scenario 2.8) 7.2.4
Coded OFDM over Multipath Rayleigh Fading Channel
As indicated in [14], coding is essential in order to mitigate the effects of the multipath channel in a wireless OFDM transmission. The same convolutional code configuration was applied to analyse the improved performance of the system in a fading channel. The channel used for this simulation is the ITU-Vehicular A channel (parameters are shown in Table 7.3) and a Doppler frequency of (corresponds to speed of
).
91
Performance of Uncoded and Rate 1/2 Convolutionally Coded OFDM-QPSK transmission over ITU-Vehicular A multipath Rayleigh fading Channel (fd = 400 Hz)
0
10
Coded BER Uncoded BER
-1
BER
10
-2
10
-3
10
-4
10
0
5
10
15
20 25 Eb/N0 (dB)
30
35
40
Figure 7.7: Coded and Un-coded OFDM-QPSK over a Multipath Rayleigh Fading Channel (ITU-Vehicular A) Figure 7.7 shows the improved performance of the system when coding was applied. Notice that the error floor of the transmission was lowered from about around
to
as a result of coding. There would be significant improvement in
the performance if the convolutional encoder is concatenated with a Reed Solomon encoder; where the Reed Solomon encoder is an outer encoder and the convolutional encoder will be an inner encoder.
92
Chapter 8
8 CONCLUSION AND FUTURE WORK
8.1 Conclusion Although a complete system level simulation is beyond the scope of this thesis, a comprehensive study and analysis of the mandatory parts of the PHY layer of IEEE 802.16e was carried out. Particular attention was paid to OFDM, OFDMA, convolutional coding and Viterbi decoding and the structure of the DL frame of the standard. The performance of the system seen in Chapter 7 agrees with theoretical results and I have shown in my simulations that improvement can be made by the inclusion of FEC in the system.
Real life channel model parameters were used for the simulation in order to obtain realistic performance figures. An error floor of about
was obtained for OFDM-
QPSK transmission in a multipath Rayleigh fading channel. The small scale fading was heralded by the use of sums of sinusoids in Jakes’ fading channel model.
A successful simulation of the DL PUSC permutation in Chapter 6 showed how frequency diversity is exploited in the DL OFDMA frame. This permutation and allocation of subcarriers to users within the same frame is the main distinguishing factor between OFDM and OFDMA. The various building blocks of the system, when put together for the mandatory parts of the PHY layer of WiMAX.
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8.2 Future Work 8.2.1
Interleaved Codes
It is possible to improve the performance of the FEC scheme by interleaving and puncturing the coded data before sending it to the constellation mapper. The interleaver serves to reduce the correlation between the fades experienced by successive source symbols that are transmitted over the channel (Stüber, 2002). 8.2.2
MIMO
The addition of multiple antennas to both the transmitter and receiver has proved to improve performance of OFDM and OFDMA systems. This can be done by incorporating Space Time or Frequency Block coding (SFBC or STBC) to the system. Space time block coding has emerged as an efficient means of achieving near optimal transmitter diversity gain [6]. SFBC outperforms STBC in a fast fading channel as seen in [24]. 8.2.3
IEEE 802.16m
The IEEE 802.16m will build upon the existing IEEE 802.16e standard technology. It promises to deliver higher data rates and a generally better performance than the present standard. A 2048 FFT size and a nominal channel bandwidth of 20 MHz will be used in this system. It also has support for scalability and multiple antennas at both the transmitter and receiver. It is expected to compete with the 3GPP LTE technology (4G) with data rates of up to 100 Mbit/s for mobile and 1 Gbps for fixed applications.
94
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9 Appendix
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Appendix A: DL Subcarrier Permutation Functions This appendix presents the subcarrier permutation MATLAB functions developed for this thesis. All the functions are self-explanatory and there is an example to illustrate how the functions work.
(1)
function out = nk(k,s) % k is the subcarrier index wrt subchannel between 0 & 27 (with pilots) % s is the subchannel index between 0 & 29 for 1024pt fft % Written By: Leonardo Obinna A. Iheme % Date: 12-04-2010 % Supervised by: Dr. Erhan Ince data_subcarrier_subchannel_index = 0:27; subchannel_index = 0:29; Nsubcarriers = 28; k = data_subcarrier_subchannel_index([k+1]); s = subchannel_index([s+1]); out = mod((k+13*s),Nsubcarriers);
(2) The outer permutation described in Chapter 6. This function does the renumbering of the physical clusters
function CL_Logical_No = Outer_permutation(CL_PHY_No, DL_PermBase) % this function gives an output of the cluster logical number % it is possible to input CL_PHY_No as a vector of maximum length 60 for
105
% 1024pt fft % the physical numbered clusters are renumbered according to the % renumbering sequence and the DL_PermBase % Written By: Leonardo Obinna A. Iheme % Date: 12-04-2010 % Supervised by: Dr. Erhan Ince
Re_num_sequence = [6 48 37 21 31 40 42 56 32 47 30 33 54 18 10 15 50 51 58 ... 46 23 45 16 57 39 35 7 55 25 59 53 11 22 38 28 19 17 3 27 12 29 26 5 41 49 44 9 8 1 13 36 14 43 2 20 24 52 4 34 0]; if CL_PHY_No ~= 0:59 error ('CL_PHY_No must be between 0 and 59') end Nclusters = 60; CL_Logical_No = Re_num_sequence([mod(((CL_PHY_No)+13*DL_PermBase),Nclusters)]+1);
(3) function phy_indexes = subcarrier_indexes(CL_PHY_No) % this function gives the subcarrier index (given the physical cluster number) % wrt absolute subcarrier index for 1024pt fft % Written By: Leonardo Obinna A. Iheme % Date: 12-04-2010 % Supervised by: Dr. Erhan Ince subcarrier_index = 92:931; if CL_PHY_No ~= 0:59 error ('CL_PHY_No must be between 0 and 59') end [phy_indexes] = subcarrier_index((14*CL_PHY_No)+1:(14*CL_PHY_No+13)+1)
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(4) Reshuffles the Subcarriers function subcarriers = reshufled_Sc(CL_PHY_No,DL_PermBase) % reshuffles the subcarriers according to the renumbering sequence and % outputs subcarrier indexes wrt the absolute subcarrier index % Written By: Leonardo Obinna A. Iheme % Date: 12-04-2010 % Supervised by: Dr. Erhan Ince for ii = Outer_permutation(CL_PHY_No,DL_PermBase) subcarriers = subcarrier_indexes(ii); end
(5) The inner permutation described in Chapter 6
{ [
]
}
function out = Inner_permutation(k,s,group_index,DL_PermBase) % this function gives the output of the subcarrier index wrt % the group indexes. % it is possible to specify k as a vector of subcarrier indexes % k = the subcarrier index within the subchannel s % s = the subchannel index % Written By: Leonardo Obinna A. Iheme % Date: 12-04-2010 % Supervised by: Dr. Erhan Ince P_s_even = [3 0 2 1]; P_s_odd = [3 2 0 4 5 1]; ifgroup_index == (1|3|5) % if the group is even Nsubchannels = 4;
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P_s = P_s_even; else Nsubchannels = 6; P_s = P_s_odd; end n_k = nk(k,s); Ps = shiftleft(P_s,s); Pj = Ps([mod(n_k,Nsubchannels)+1]); out = Nsubchannels*n_k+mod(Pj+DL_PermBase,Nsubchannels);
(6) function out = PHY_Sc_indexes(s,DL_PermBase) % this function gives an output of the physical reshuffled subcarrier % indexes. % s is the subchannel index from 0-29 for 1024pt fft % Written By: Leonardo Obinna A. Iheme % Date: 12-04-2010 % Supervised by: Dr. Erhan Ince sclist =[]; for n = 0:59 subcarriers = reshufled_Sc(n,1); sclist = [sclist subcarriers]; end % Physical subcarrier indexes in groups group0 group1 group2 group3 group4 group5
= = = = = =
sclist([1:168]); sclist([169:280]); sclist([281:448]); sclist([449:560]); sclist([561:728]); sclist([729:840]);
m = 28; % no. of subcarriers in a subchannel (0:(m-1)) % permutation based on the parity of the groups
108
% *******Checking which group s belongs to********** if s
