Un-coded versus Coded QPSK-OFDM Performance...

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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

Transcript of Un-coded versus Coded QPSK-OFDM Performance...

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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

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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

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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 and generator polynomials

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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 (DL-

PUSC), 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

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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

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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

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8.2.3 IEEE 802.16m ......................................................................................... 94

REFERENCES ........................................................................................................... 95

Appendix .................................................................................................................. 104

Appendix A: DL Subcarrier Permutation Functions ............................................ 105

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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

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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

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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

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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

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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

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Random phase

Channel delay spread

Delay of kth

path

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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

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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 man-

made 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.

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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.

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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

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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 Status

802.16-2001 Fixed Broadband Wireless Access (10–

63 GHz) Superseded

802.16.2-2001 Recommended practice for coexistence Superseded

802.16c-2002 System profiles for 10–63 GHz Superseded

802.16a-2003 Physical layer and MAC definitions for 2–

11 GHz Superseded

P802.16b License-exempt frequencies

(Project withdrawn) Withdrawn

P802.16d

Maintenance and System profiles for 2–

11 GHz

(Project merged into 802.16-2004)

Merged

802.16-2004

Air Interface for Fixed Broadband Wireless

Access System

(rollup of 802.16-2001, 802.16a, 802.16c and

P802.16d)

Superseded

P802.16.2a

Coexistence with 2–11 GHz and 23.5–

43.5 GHz

(Project merged into 802.16.2-2004)

Merged

802.16.2-2004

Recommended practice for coexistence

(Maintenance and rollup of 802.16.2-2001 and

P802.16.2a)

Current

802.16f-2005 Management Information Base (MIB) for

802.16-2004 Superseded

802.16-

2004/Cor 1-

2005

Corrections for fixed operations

(co-published with 802.16e-2005) Superseded

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802.16e-2005 Mobile Broadband Wireless Access System Superseded

802.16k-2007 Bridging of 802.16

(an amendment to IEEE 802.1D) Current

802.16g-2007 Management Plane Procedures and Services Superseded

P802.16i Mobile Management Information Base

(Project merged into 802.16-2009) Merged

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)

Current

802.16j-2009 Multihop relay Current

P802.16h Improved Coexistence Mechanisms for

License-Exempt Operation in progress

P802.16m Advanced Air Interface with data rates of 100

Mbit/s mobile & 1 Gbit/s fixed Current

1.1.2 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

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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.

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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 re-

visitations [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

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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.

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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

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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

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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]

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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

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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

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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].

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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 end-

user 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 fixed-

line 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:

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• 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

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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 circuit-

switched 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 IMT-

2000 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)

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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-per-

second 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

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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

Release 99 Specified the first UMTS 3G networks, incorporating a CDMA

air interface

Release 4 Originally called the Release 2000 - added features including an

all-IP Core Network

Release 5 Introduced IMS and HSDPA

Release 6

Integrated operation with Wireless LAN networks and adds

HSUPA, MBMS, enhancements to IMS such as Push to Talk

over Cellular (PoC), GAN

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Release 7

Focuses on decreasing latency, improvements to QoS and real-

time 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.

Release 8

LTE, All-IP Network (SAE). Release 8 constitutes a refactoring

of UMTS as an entirely IP based fourth-generation network.

Release 9 SAES Enhancements, WiMAX and LTE/UMTS Interoperability

Release 10 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) 100M

Max uplink speed

(bps) 50 M

Latency

round trip time

approx.

~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.

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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 Details

Peak downlink speed

64QAM

(Mbps)

100 (SISO), 172 (2x2 MIMO), 326

(4x4 MIMO)

Peak uplink speeds

(Mbps)

50 (QPSK), 57 (16QAM), 86

(64QAM)

Data type 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 0 - 15 km/h (optimised),

15 - 120 km/h (high performance)

Latency Idle to active less than 100ms

Small packets ~10 ms

Spectral efficiency Downlink: 3 - 4 times Rel 6 HSDPA

Uplink: 2 -3 x Rel 6 HSUPA

Access schemes OFDMA (Downlink)

SC-FDMA (Uplink)

Modulation types supported 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

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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 wireless-

networks 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 802.16-

2004. 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

Band Class

Index

Frequency Range

(GHz)

Channel

Bandwidth(s)

(MHz)

FFT Size

1 2.3-2.4

5 512

10 1024

8.75 1024

2 2.305-2.320,

2.345-2.360

3.5 512

5 512

10 1024

3 2.496-2.69 5 512

10 1024

4 3.3-3.4

5 512

7 1024

10 1024

5

3.4-3.8

5 512

7 1024

10 1024

3.4-3.6

5 512

7 1024

10 1024

3.6-3.8

5 512

7 1024

10 1024

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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 2(802.16m)

Mobile WiMAX Rel 1.5(802.16e Rev2)

Mobile WiMAX Rel 1(802.16e)

Mobile Broadband 70+ Mbps

2008

Mobile Broadband 125+ Mbps

2009/2010

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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2.3-2.4 GHz

5MHz

8.75MHz

10MHz

512

1024

1024

2.469-2.69 GHz

5MHz

10MHz

512

1024

2.305-2.32 GHz

2.345-2.36 GHz

3.5MHz

5MHz

10MHz

512

1024

1024

3.3-3.4 GHz

5MHz

7MHz

10MHz

512

1024

1024

5MHz

7MHz

10MHz

512

1024

1024

3.4-3.8 GHz

3.4-3.6 GHz

3.6-3.8 GHz

Frequency Bandwidth FFT Size Frequency Bandwidth FFT Size

2.3-2.7 GHz 3.3-2.8 GHz

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.

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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 to

where is the Doppler shift. The amount of spectral broadening depends

on 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].

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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 tap filter depicted in

Figure 3.3. is the number of resolvable paths provided by the channel and is a

measure of the diversity available in the channel.

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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 in a multipath channel can be

expressed as:

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Where , and are the multiplicative gain, phase shift and the delay of the

path, 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 and are independentGaussian

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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-of-

sight 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

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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:

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√ {[ ∑ √

]

[ ∑

√ ]}

⁄ ,

.

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].

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2sinβ1 2cosβ1

cosω1t

2sinβM 2cosβM

cosωMt

2sinα 2cosα

1/√2cosωmt

++

g(t) = x(t) + jy(t)

y(t)x(t)

Offset oscillators

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.

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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]

Tap

Index

Relative

Delay

(ns)

Average

Power

(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.

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Table 3.2:Winner tapped delay-line model for scenario 2.8 (RS MS, NLOS)

Tap

index

Relative

Delay

(ns)

Average

Power

(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

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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.

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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 lower rate

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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].

S/P

R/L bps

R/L bps

R/L bps

+...

cos(2πfc)

cos(2πfc+Δf)

cos(2πfc+(L-1)Δf)

R bps

x(t)

Figure 4.1: A Basic Multicarrier Transmitter

Figure 4.1 depicts a high rate stream of is broken into parallel streams, each

with rate . Each individual stream is then modulated by a respective frequency.

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In the time domain, the symbol duration on each subcarrier has increased to,

so letting grow larger ensures that the symbol duration exceeds the channel-delay

spread, , 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.

Demod 1

Demod 2

Demod L

LPF

LPF

LPF

P/S R bpsy(t)

...

cos(2πfc)

cos(2πfc+Δf)

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

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greater than the delay spread of the channel. Figure 4.3 shows a block diagram of an

OFDM transmitter.

FEC EncoderConstellation

Mapper

Subcarrier Mapping &

Pilot Insertion

Serial to Parallel

IFFT Add Cyclic Prefix

Binary input Data

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].

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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.

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FFT can be written in sinusoids as:

∑ (

*

∑ (

*

Here, are coefficients of the sines and cosines of frequency , where is

the index of the frequencies over the frequencies and is the time index. is

the value of the spectrum for the frequency and 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

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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 redundant symbols are sent, the

required bandwidth for OFDM increases from to . Similarly, an

additional symbol must be counted against the transmit-power budget [7].

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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 one-

fourth 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

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 .

-8 -6 -4 -2 0 2 4 6 8-0.5

0

0.5

1

1.5

frequency

-8 -6 -4 -2 0 2 4 6 8-0.5

0

0.5

1

1.5

frequency

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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:

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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 is no more than a definition of the signal in the

sampled frequency domain, and 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].

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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 information symbol to be encoded

is transformed into an symbol, where is the code rate and the

transformation is a function of the last 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

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adders using the generator polynomial. As an example, consider a convolutional

encoder specified by , the structure of this coder is shown inFigure 5.1

u1 u0 u-1

+

+

+

v1

v3

v2

(1, 1, 1)

(0, 1, 1)

(1, 0, 1)

u1

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 . The code in our

example has states which are: . Note here that the number of

states is independent of the rate of the code.

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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 and , are specified in the following

expressions:

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T T T T T T

+ + + +

+ + ++

1 1 1 1 1

11111

0 0

00

X=171o

Y=133o

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.

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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

Branch metric calculation

Path metric calculation

Trackbackencoded stream

decoded stream

Figure 5.4: Viterbi Decoder Data Flow

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Chapter 6

6 THE WIMAX PHYSICAL LAYER

6.1 Introduction

The physical (PHY) layer of WiMAX was designed with much influence from Wi-

Fi, 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 (DVB-

H), and MediaFLO, besides WiMAX.

Figure 6.1 shows the functional stages of the WiMAX PHY layer.

Channel Encoder

Symbol Mapper

Subcarrier Allocation

+ Pilot Insertion

IFFT

Cyclic Prefix

Input BitSequence

Figure 6.1: Functional stages of WiMAX PHY

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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.

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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.

Guard subcarriers

Pilot subcarriers

DC subcarrierGuard subcarriers

Data 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,

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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,

8.75, 10, 14, 15

Nominal channel bandwidth

256 for OFDM;

128, 512, 1,024,

2,048 for

SOFDMA

Number of subcarriers, including the DC

subcarrier pilot subcarriers and the guard

subcarriers

8/7, 28/25 Oversampling factor

1/4, 1/8, 1/16,

and 1/32

Ratio of cyclic prefix time to useful symbol

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

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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].

User 1

User 2

User 3

frequencypower

time

frequencypower

time

frequencypower

time(a) (b) (c)

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

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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

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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.

Subchannel 1 Subchannel 2 Subchannel 3 Subchannel 4

DC

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

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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:

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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.

Pre

amb

le

PU

SC(f

irst

zo

ne

con

tain

s FC

H a

nd

DL-

MA

P)

PU

SC(D

L-P

erm

Bas

e X

)

FUSC

(DL-

Per

mB

ase

Y)

FUSC

(DL-

Per

mB

ase

Z)

Op

tio

nal

FU

SC

AM

C

TUSC

1

TUSC

2

PU

SC

Op

tio

nal

PU

SC

AM

C

Must appear in every frame

May appear in a frameZone switch Ies in DL-MAP

DL Subframe UL Subframe

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 Value

Null Subcarriers 184

Pilot Subcarriers 120

Data Subcarriers 720

Subchannels 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.

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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.

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0

1

2

3

4

5

6

7

8

9...............

Sub

chan

ne

l In

de

x

Segment 0

Segment 1

Segment 2 .....

OFDM Symbol Index

K+1 K+2 K+3 K+4 K+5 K+6 K+7 K+8 K+9 K+10 K+11

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.

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Step 1: Divide the subcarriers into clusters of 14 subcarriers each

Ph

ysic

al C

lust

er (

PN

) 0

-59

PN 0

PN 1

PN 2

PN 3

PN 4

PN 5

PN 6

PN 7

PN 8

PN 9.......

PN

.59

Step 2: Renumber the clusters. (in this example DL Perm Base=10)

LN 30

LN 33

LN 54

LN 18

LN 10

LN 15

LN 50

LN 51

LN 58

LN 46.......

LN

32

47

Logi

cal C

lust

er (

LN)

Step 3: Gather clusters in six major groups (MG)

LN 0

– L

N 1

1LN

12

– L

N 1

9LN

20

– L

N 3

1..

.

MG 0 (even)

MG 1 (odd)

MG 2 (even)

Step 4: Allocate subcarriers to subchannels

MG X

Allocate pilots in each group

depending on the parity of the symbol

Allocate data subcarriers to

subchannels. No. Of subchannels depends on the parity of each

MG

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.

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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 P

P P

P Pilot subcarrier

Data subcarrier

Even OFDMA Symbol

Odd OFDMA Symbol

Figure 6.10: PUSC DL Slot

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74

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 varying between 0 and 23, in subchannel whose

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 Major Group Parity

4 [3 0 2 1] Even

6 [3 2 0 4 5 1] odd

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75

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

LN

Logical Subcarrier

Index

Cluster PN

Equation (6.1)

Cluster Physical

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

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76

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

Logical subcarrier index in the

major group

Physical

subcarrier index

with respect to

the absolute

subcarrier scale

0 16 100 199

1 17 104 862

2 18 111 864

3 19 119 871

4 20 121 873

5 21 126 444

6 22 136 446

7 23 140 453

8 0 3 317

9 1 11 322

10 2 13 324

11 3 18 891

12 4 28 893

13 5 32 898

14 6 39 900

15 7 47 641

16 8 49 643

17 9 54 648

18 10 64 650

19 11 68 587

20 12 75 589

21 13 83 594

22 14 85 190

23 15 90 197

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

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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 sub-

frame 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.

DL

Fram

e P

ream

ble

FCH

DL-

MA

P

DL-

MA

PU

L-M

AP

DL

Bu

rst1

DL

Bu

rst

4D

L B

urs

t 5

DL

Bu

rst

3

DL

Bu

rst

2

UL

Bu

rst

1

UL

Bu

rst

3U

L B

urs

t 4

UL

Bu

rst

2

Ranging Subchannels

DL Subframe UL Subframe

Sub

chan

nel

s

OFDMA Symbols

TTG

k k+1 k+3 . . . k+30 . ..

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

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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 Values

Channel Bandwidth 10 MHz

Frame duration 5 ms

Number of OFDMA Symbols/Frame 48

Total Number of OFDMA Overhead

Symbols 10

Number of OFDMA symbols for TTG

and RTG 1

Total Number of OFDMA Data

Symbols 37

Symbol Duration 102.9 μs

DL:UL

3:1

DL OFDMA Data Symbols 28

UL OFDMA Data Symbols 9

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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.

0

1

2

3

4

5

6

7

8

9...........

Sub

chan

ne

l In

de

x

Segment 0

Segment 1

OFDM Symbol Index

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 sub-

frame 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

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OFDMA Symbols

0

1

2

3

4

5

6

7

8

9

Sub

chan

nel

s

User 1User 2User 3User 4

Slot

Time interval

Data exhausted

Figure 6.13: Data Region Showing Data Bursts for Four Users

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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

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82

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

Multipath Channels ITU A Vehicular Channel

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).

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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:

√ ⁄

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 is the length of

the transmitted symbol. With μ and μ , using equation (7.2)

0 1 2 3 4 5 6 7 8 9 1010

-6

10-5

10-4

10-3

10-2

10-1

Eb/N0 (dB)

BE

R

Performance of QPSK modulated OFDM Transmission over an AWGN Channel

experimental ber

theoretical ber

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84

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).

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 QPSK-

OFDM would reach a much lower bit error rate at an earlier (lower) signal to noise

0 1 2 3 4 5 6 7 8 9 1010

-6

10-5

10-4

10-3

10-2

10-1

100

Eb/N0 (dB)

BE

R

Performance of Rate 1/2 Convolutionally Coded OFDM-QPSK OFDM Transmission over

an AWGN Channel

Coded BER

Uncoded BER

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85

ratio. For example the coded system will achieve a target BER of at

whereas the un-coded system will achieve the same BER 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 there is a

coding gain of over the un-coded performance.

7.2.3 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:

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86

(

)

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

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87

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.

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.

0 5 10 15 20 25 30 35 4010

-5

10-4

10-3

10-2

10-1

100

Eb/N0 (dB)

BE

R

Theoretical OFDM-QPSK performance over

a multipath Rayleigh fading channel

fd = 100 Hz

fd = 400 Hz

fd = 833 Hz

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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 , and corresponding to speeds

of approximately , and 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

Tap

index

Relative

Delay

(ns)

Average

Power

(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

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89

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

Tap

Index

Relative

Delay

(ns)

Average

Power

(dB)

1 0 0

2 310 -1

3 710 -9

4 1090 -10

5 1730 -15

6 2510 -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

0 5 10 15 20 25 30 35 40

10-4

10-3

10-2

10-1

100

Eb/N0 (dB)

BE

R

Performance of Uncoded OFDM-QPSK Transmission over

Winner Sc. 2.8 multipath Rayleigh fading Channel

fd = 100Hz

fd = 400Hz

fd = 833Hz

fd = 100 Hz

fd = 400 Hz

fd = 833 Hz

Theoretical

Experimental

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90

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.

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 while that in the

Winner Scenario 2.8 channel is . 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

0 5 10 15 20 25 30 35 40

10-4

10-3

10-2

10-1

100

Eb/N0 (dB)

BE

R

Performance of Uncoded OFDM-QPSK Transmission over

ITU-Vehicular A multipath Rayleigh FadingChannel

fd = 100Hz

fd = 400Hz

fd = 833Hz

fd = 100 Hz

fd = 400 Hz

fd = 833 Hz

Experimental

Theoretical

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91

to form at while for the ITU channel the error floor formation started at

.

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 ).

0 5 10 15 20 25 30 35 40

10-4

10-3

10-2

10-1

100

Eb/N0 (dB)

BE

R

Performance of Uncoded OFDM-QPSK Transmission over

ITU-Vehicular A and Winner Scenario 2.8 Multipath Rayleigh Fading Channels

fd = 833 Hz

fd = 400 Hz

fd = 100 Hz

fd = 100Hz

fd = 400Hz

fd = 833Hz

ITU-Vehicular A Channel

Winner Scenario 2.8 Channel

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92

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 to

around 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.

0 5 10 15 20 25 30 35 4010

-4

10-3

10-2

10-1

100

Eb/N0 (dB)

BE

R

Performance of Uncoded and Rate 1/2 Convolutionally Coded OFDM-QPSK transmission over

ITU-Vehicular A multipath Rayleigh fading Channel (fd = 400 Hz)

Coded BER

Uncoded BER

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93

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.

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95

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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

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% 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 = sclist([1:168]); group1 = sclist([169:280]); group2 = sclist([281:448]); group3 = sclist([449:560]); group4 = sclist([561:728]); group5 = sclist([729:840]);

m = 28; % no. of subcarriers in a subchannel (0:(m-1))

% permutation based on the parity of the groups

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% *******Checking which group s belongs to********** if s <= 5

group_index = 0;

subcarrier_logical_indexes = Inner_permutation(0:(m-

1),s,group_index,DL_PermBase);

out = group0(subcarrier_logical_indexes+1);

elseif 6<=s<=9

group_index = 1;

subcarrier_logical_indexes = Inner_permutation(0:(m-

1),s,group_index,DL_PermBase);

out = group1(subcarrier_logical_indexes+1);

elseif 10<=s<=15

group_index = 2;

subcarrier_logical_indexes = outer_permutation(0:(m-

1),s,group_index,DL_PermBase);

out = group2(subcarrier_logical_indexes+1);

elseif 16<=s<=19

group_index = 3;

subcarrier_logical_indexes = outer_permutation(0:(m-

1),s,group_index,DL_PermBase);

out = group3(subcarrier_logical_indexes+1);

elseif 20<=s<=25

group_index = 4;

subcarrier_logical_indexes = outer_permutation(0:(m-

1),s,group_index,DL_PermBase);

out = group4(subcarrier_logical_indexes+1);

else 26<=s<=29;

group_index = 5;

subcarrier_logical_indexes = outer_permutation(0:(m-

1),s,group_index,DL_PermBase);

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out = group5(subcarrier_logical_indexes+1); end end

(7)

This was used for circularly shifting the basic permutation sequence to the left

depending on the group number. The detailed explanation is in Chapter 6

function [out] = shiftleft(X,k)

% shifts elements of X circularly k times

out = X( mod((1:end)+k-1, end)+1 );

(8)

This script is an example that demonstrates the usage of the functions.

% Example illustrating how the function, PHY_Sc_indexes, works

% Written By: Leonardo Obinna A. Iheme % Date: 12-04-2010

Clear all clc

subcarrier_phy_numbers = [];

n = 30; % number of subchannels

DL_PermBase = input ('What is your DL _PermBase? ');

if DL_PermBase ~= 0:31 error ('DL_PermBase must be between 0 and 31') end

subchannel_range = input('What is the range of subchannels?

');

for s = subchannel_range sub = PHY_Sc_indexes(s,DL_PermBase); subcarrier_phy_numbers = [subcarrier_phy_numbers sub]; end

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display('Concatenated PHY indexes for n subchannels'); disp(subcarrier_phy_numbers)