PPSS ZZ 11 99 ::11 66 ((PPiinn dd.. 11 //99 77 )) UUnniivveerrss iittii TTeekknnoollooggii MMaallaayyss iiaa

BORANG PENGESAHAN STATUS TESIS¨

JUDUL : BER PERFORMANCE STUDY OF ORTHOGONAL FREQUENCY DIVISION

MULTIPLEXING (OFDM)

SESI PENGAJIAN : 2006 / 2007

Saya

(HURUF BESAR) mengaku membenarkan tesis (PSM/Sarjana/Doktor Falsafah)* ini disimpan di Perpustakaan Universiti Teknologi Malaysia dengan syarat-syarat kegunaan seperti berikut:

1. Tesis adalah hakmilik Universiti Teknologi Malaysia. 2. Perpustakaan Universiti Teknologi Malaysia dibenarkan membuat salinan untuk tujuan

pengajian sahaja. 3. Perpustakaan dibenarkan membuat salinan tesis ini sebagai bahan pertukaran antara

institusi pengajian tinggi. 4. ** Sila tanda ( )

SULIT (Mengandungi maklumat yang berdarjah keselamatan atau kepentingan Malaysia seperti yang termaktud di dalam AKTA RAHSIA RASMI 1972)

TERHAD (Mengandungi maklumat yang TERHAD yang telah ditentukan

oleh organisasi/badan di mana penyelidikan dijalankan)

TIDAK TERHAD

Disahkan oleh

(TANDATANGAN PENULIS) (TANDATANGAN PENYELIA)

Alamat Tetap:

NO 7, JALAN 40, PROF DR THAREK ABDUL

DESA JAYA, KEPONG, RAHMAN

52100 KUALA KUMPUR Nama Penyelia

Tarikh: 01 DISEMBER 2006 Tarikh: 01 DISEMBER 2006

CATATAN: * Potong yang tidak berkenaan. ** Jika tesis ini SULIT atau TERHAD, sila lampirkan surat daripada pihak berkuasa/organisasi

berkenaan dengan menyatakan sekali sebab dan tempoh tesis ini perlu dikelaskan sebagai SULIT atau TERHAD.

¨ Tesis dimaksudkan sebagai tesis bagi ijazah Doktor Falsafah dan Sarjana secara penyelidikan, atau disertai bagi pengajian secara kerja kursus dan penyelidikan, atau Laporan Projek Sarjana Muda (PSM).

ANIS SALWA OSMAN

“I hereby declare that I have read this project report and in my opinion this project is

sufficient in terms of scope and quality for the award of the degree of Master of

Engineering (Electrical – Electronics & Telecommunication) by taught course.”

Signature : ………………………………………

Name of Supervisor : PROF DR THAREK ABD RAHMAN

Date : 01 DECEMBER 2006

BER PERFORMANCE STUDY OF ORTHOGONAL FREQUENCY DIVISION

MULTIPLEXING (OFDM)

ANIS SALWA OSMAN

A project report submitted in partial fulfillment of the

requirements for the award of the degree of

Masters of Engineering (Electrical – Electronics & Telecommunication)

Faculty of Electrical Engineering

Universiti Teknologi Malaysia

DECEMBER 2006

ii

I declare that this thesis entitled “BER Performance Study of Orthogonal Frequency

Division Multiplexing” is the result of my own research except as cited in the

references. The thesis has not been accepted for any degree and is not concurrently

submitted in candidature of any other degree.

Signature : ................................................................

Name : ANIS SALWA OSMAN

Date : 01 DECEMBER 2006

iii

ACKNOWLEDGEMENTS

My sincere thanks goes to my supervisor, Prof. Dr Tharek bin Abd Rahman,

for his guidance in the execution of the project, for keeping me on my toes, and for

his kind understanding. I am especially grateful for all the help he provided and

resources he made available without which the project would not have reached its

current stage. I am also indebted to thank Dr Zaharuddin bin Mohamed, for being

most efficient in coordinating the project. Many thanks also goes out to the project

presentation assessors, Dr Sevia Mahdaliza binti Idrus Sutan Nameh and Dr. Razali

Ngah, who have given me much advice and guidance during the project presentation.

Finally, I would like to thank my beloved family for just being there, giving me the

strength, love and much needed moral support.

iv

ABSTRACT

A mobile radio channel is characterized by a multipath fading environment.

The signal is offered to the receiver contains not only line of sight of radio wave, but

also a large number of reflected radio waves that arrive at the receiver at different

times. Delayed signals are a result of reflections from terrain features such as trees,

hills, mountains, vehicles or building. These reflected delayed waves interfere with

the direct wave and cause intersymbol interference (ISI), which causes significant

degradation of the network performance. In order to overcome a multipath fading

environment and achieve a wireless broadband multimedia communication system

(WBMCS), it is possible to use OFDM transmission scheme. OFDM is based on

parallel data transmission scheme that reduces that effects of multipath fading and

renders complex equalizers unnecessary. OFDM is expected to be used in wireless

LAN (WLAN) systems. In this project will study and identify t h e Orthogonal

Frequency Division Multiplexing (OFDM) technology that gives the best BER

performance in a multipath fading environment using computer simulation.

Essentially, ideal and worst case communication channel models were studied and

the simulation programs were written to simulate that channels. Orthogonal

Frequency Division Multiplexing is modeled and simulated under different channel

conditions such as AWGN and Rayleigh fading. Subsequently, a comparison study

is carried out to obtain the BER performance for Orthogonal Frequency Division

Multiplexing under under 1-path multipath fading conditions and to identify which

channel gives the best BER performance. The comparison study showed that BER

for AWGN channel gives the best BER performance compared to Rayleigh channel.

v

ABSTRAK

Saluran radio bergerak dikategorikan di dalam persekitaran “multipath

fading”. Di bahagian penerimaan, isyarat diterima daripada pelbagai sudut dan

waktu yang berbeza. Kelewatan isyarat berlaku apabila terdapatnya halangan

daripada pokok, bukit, gunung, kenderaan ataupon bangunan. Hasil pembalikkan

kelewatan isyarat dengan isyarat sebenar akan terhasilnya “intersymbol interference

(ISI)”, yang akan menyebabkan pencapaian rangkaian menurun. Untuk mengatasi

masalah “multipath fading” dan mencapai tahap “wireless broadband multimedia

communication system (WBMCS)”, skim penghantaran OFDM diperkenalkan.

OFDM menggunakan konsep penghantaran data digital secara selari untuk

mengatasi masalah “multipath fading”. OFDM dijangka digunakan di dalam sistem

komunikasi tanpa wayar rangkaian tempatatan. Di dalam projek ini akan

mempelajari dan mengenalpasti teknologi “Orthogonal Frequency Division

Multiplexing (OFDM)” yang akan yang memberikan nilai BER yang terbaik dalam

persekitaran “multipath fading” menerusi simulasi komputer. Model saluran

komunikasi yang “ideal” dan “worst” dijadikan sumber untuk dipelajari dan

program ditulis untuk tujuan simulasi. Seterusnya, “Orthogonal Frequency

Division Multiplexing” model direka dan disimulasi untuk setiap saluran yang

berbeza seperti “AWGN” dan “Rayleigh”. Satu perbandingan kajian dilaksanakan

untuk memperolehi tahap BER bagi “Orthogonal Frequency Division Multiplexing”

di bawah keadaan saluran “Multipath Fading” untuk menentukan saluran yang dapat

memberikan tahap BER yang terbaik. Hasil perbandingan menunjukkan BER di

bawah saluran AWGN memberikan BER yang terbaik berbanding BER di bawah

saluran Rayleigh.

vi

TABLE OF CONTENT

CHAPTER TITLE PAGE

DECLARATION ii

ACKNOWLEDGEMENTS iii

ABSTRACT iv

ABSTRAK v

TABLE OF CONTENTS vi

LIST OF TABLES xi

LIST OF FIGURES xii

LIST OF MATLAB CODES xiii

LIST OF APPENDICES xiv

1 INTRODUCTION 1

1.1 History of Mobile Wireless Communications 2

1.2 Objectives of the project 7

1.3 Scope of the project 8

1.4 Motivations 8

1.5 Problem statement 9

1.6 Methology and Report Structure 10

2 ORTHOGORNAL FREQUENCY DIVISION MULTIPLEXING

(OFDM) TRANSMISSION TECHNOLOGY 12

2.1 Introduction 12

2.2 Evolution of OFDM 13

2.2.1 Frequency Division Multiplexing (FDM) 13

2.2.2 Multicarrier Communication (MC) 13

2.2.3 Orthogonal Frequcny Division Multiplexing 14

vii

2.3 Orthogonal Frequency Division Multiplexing Technology 14

2.4 Concept of Paralle Transmission Scheme 15

2.5 Concept of OFDM Transmission Technology 19

2.5.1 Transmitter Configuration 19

2.5.1 Guard Interval 21

2.5.2 Receiver Configuration 23

2.6 Advantages of OFDM 24

2.7 Disadvantages of OFDM 25

3 DIGITAL MODULATION SCHEME 26

3.1 Modulation 26

3.2 Digital Modulation 27

3.3 Phase Shift Keying (PSK) 27

3.4 Bit Rate and Symbol Rate 29

3.3 QPSK 30

4 COMMUNICATION CHANNEL 33

4.1 Communication Channel 33

4.2 Multipath 34

4.3 Fading 36

4.4 Multipath Fading 36

4.5 Multipath Fading Characteristic 36

4.6 Diversity scheme 38

5 COMMUNICATION CHANNEL MODELLING AND

SIMULATION 39

5.1 Additive White Gaussian Noise (AWGN) Channel 39

5.1.1 Matlab Implementation 40

5.2 Rayleigh Fading Channel 41

5.2.1 Matlab Implementation 46

6 QUADRATURE PSK (QPSK) MODELLING AND

SIMULATION 55

6.1 QPSK Transmission Scheme 55

viii

6.1.1 Basic Configuration of Quadratue modulation scheme 55

6.1.2 Basic configuration of QPSK Transmission Scheme 57

6.2 Matlab Implementation 59

6.2.1 Matlab code QPSK modulation 59

6.2.2 Matlab code QPSK demodulation 60

7 ORTHOGORNAL FREQUENCY DIVISION MULTIPLEXING

(OFDM) MODELLING AND SIMULATION 62

7.1 Orthogornal Frequency Division Multiplexing (OFDM)

configuration using computer simulation 62

8 RESULT AND DISCUSSION 68

8.1 OFDM under AWGN channel 68

8.1.1 OFDM under AWGN channel (Theory) 68

8.1.2 OFDM under AWGN channel after matlab simulation 69

8.1.3 Comparison OFDM under AWGN channel theory and

after matlab simulation 70

8.2 OFDM under one path Rayleigh fading 71

8.2.1 OFDM under one path Rayleigh fading (Theory) 71

8.2.2 OFDM under one path Rayleigh fading after matlab

simulation 72

8.2.3 Comparison between theory and simulation (OFDM

under one path Rayleigh) 73

8.3 Comparison OFDM under two different channels: AWGN and

one path Rayleigh 74

9 CONCLUSION AND FURTHER WORK 77

9.1 Positive Conclusion 78

9.2 Further Improvement for this project 78

9.3 Future Research 79

9.4 Final Note 79

REFERENCES 80

APPENDICESA – G 81 - 101

ix

LIST OF TABLES

TABLE NO. TITLE PAGE

1.1 History of mobile communication 3

x

LIST OF FIGURES

FIGURE NO. TITLE PAGE

1.1 Evolution of mobile wireless communications 2

1.2 Flowchart to calculate BER performance 10

2.1 Typical impulse response of multipath fading: (a) time domain, (b)

frequency domain 16

2.2 Parallel Transmission scheme: multicode transmission 18

2.3 Parallel Transmission scheme: multicarrier transmission 18

2.4 OFDM transmission system: Transmitter 19

2.5 OFDM transmission signal in each subcarrier 20

2.6 Guard Interval 23

2.7 OFDM radio transmission system: Receiver 23

3.1 Constellation diagram 28

3.2 Bit rate and symbol rate 29

3.3 Constellation diagram for QPSK 30 3.4 Four symbols that represents the four phases in QPSK 31

4.1 Effect of multipath on a mobile station 37

5.1 Received signal corrupted by AWGN 39

5.2 Principle of multipath channel 42

5.3 Delayed wave with incident angle nq 43

5.4 Configuration of multipath fading channel 49

5.5 Flowchart to obtain multipath faidng channel 50

6.1 Basic configuration of quadrature modulation scheme 56

6.2 Mapping circuit function for QPSK 58

7.1 Computer simulation to calculate the BER of an OFDM system 62

7.2 Frame format of the simulation model 64

7.3 Input and Output of IFFT 65

8.1 Theoretical AWGN 69

xi

8.2 AWGN after matlab simulation 70

8.3 Comparison between AWGn theory and simulation 71

8.4 OFDM under one path Rayleigh (Theory) 72

8.5 OFDM under one path Rayleigh after simulation 73

8.6 Comparison OFDM under one path Rayleigh between theory and

simulation 74

8.7 OFDM comparison between AWGN and one path Rayleigh 75

xii

LIST OF MATLAB CODES

CODE NO. TITLE PAGE

5.1 AWGN 40

5.2 AWGN with variable noise power 41

5.3 Subfunction for fading 46

5.4 Generate delayed waves 50

5.5 Frequency selecting fading 51

6.1 QPSK modulation 59

6.2 QPSK demodulation 60

xiii

LIST OF APPENDICES

APPENDIX TITLE PAGE

A Timeline for Project 1 105

B Timeline for Project 2 106

C MATLAB Codes for OFDM under AWGN channes 108

D MATLAB Codes for OFDM under one path Rayleigh fading 109

E MATLAB Codes to plot AWGN 110

F MATLAB Codes

G MATLAB Codes for Subfunction

CHAPTER 1

INTRODUCTION

This project studies the Bit Error Rate (BER) for Orthogonal Frequency

Division Multiplexing under different channels condition.

Digital multimedia applications as they are getting common lately create an

ever increasing demand for broadband communications systems. Orthogonal

Frequency Division Multiplexing (OFDM) has grown to be the most popular

communications system in high speed communications in the last decade. In fact, it

has been said by many industry leaders that OFDM technology is the future of

wireless communications.

The prosperous progress of mobile communications has built the main road

of the history of wireless communication. The mobile wireless communications

progressed from Personal Communication Services/Network (PCS/PCN) to Global

System for Mobile Radio Channel (GSM) to General Packet Radio Service (GPRS)

to Enhanced Data for Global Evolution (EDGE) to Universal Mobile

Telecommunication Systems (UMTS) (better known as 3G) and will continue to

evolve to 4G which is under active research. The evolution is depicted in the

following figure.

2

Figure 1.1: Evolution of mobile wireless communications

A step back into the history of wireless communications will reveal how this

evolution was made possible.

1.1 History of Mobile Wireless Communications

The history of mobile communication can be categorized into 3 periods:

§ the pioneer era

§ the pre-cellular era

§ the cellular era

3

Time Significant Pioneer Era 1860s James Clark Maxwell’s electromagnetic (EM) wave postulates 1880s Proof of the existence of EM waves by Heinrich Rudolf Hertz 1890s First use of wireless and forst patent of wireless communications

by Gugliemo Marconi 1905 First transmission of speech and music via a wireless link by

Reginald Fessenden 1912 Sinkng of the Titanic highlights the importance of wireless

communication on the seaways; in the following years marine radio telegraphy is established

Precellular Era 1921 Detroit Police Department conducts field test with mobile radio 1933 In the United States, four channels in the 30-40 MHz range 1938 In the United States, rules for regular services 1940 Wireless Communication is stimulated by World War II 1946 First commercial mobile telephone system operated by the Bell

system and deployed in St Louis 1948 First commercial fully automatic mobile telephone system is

deployed in Richmond, Virgina, in the United States 1950s Microwave telephone and communication links are developed 1960s Introduction of trunked radio systems with automatic channel

allocation capabilities in the United States 1970 Commercial mobile telephone system operated in many countries

(e.g: 100 million moving vehicles on U.S highways, “B-Netz” in West Germany)

Cellular Era 1980s Deployment of analog cellular systems 1990s Digital cellular development and dual mode operation of digital

systems 2000s Future public land mobile communication systems (FPLMTSs) /

International mobile telcommunications-2000 (IMT-200 0 ) / Universal mobile telecommunication systems (UMTS) will be deployed with multimedia services

2010s Fixed point (FP) – based wireless broadband communications and software radio will be available over the Internet

2010s Radio over fiber (such as fiber optic microcells) will be available

Table 1.1: History of Mobile Communications

4

In the pioneer era, a great deal of the fundamental research and development

in the field of wireless communications took place. The postulates of

electromagnetic (EM) waves by James Clark Maxwell during the 1860s in England,

the demonstration of the existence of these waves by Heinrich Rudolf Hertz in 1880s

in Germany and the invention and first demonstration of wireless telegraphy by

Guglielmo Marconi during the 1890s in Italy were representative examples from

Europe. Moreover, in Japan, the Radio Telegraph Research Division was

established as a part of the Electro technical Laboratory at the Ministry of

Communications and started to research wireless telegraph in 1896.

From the fundamental research and the resultant developments in wireless

telegraphy, the application of wireless telegraphy to mobile communication systems

started from the 1920s. This period, which is called the pre-cellular era, began with

the first land-based mobile wireless telephone system installed in 1921 by the

Detroit Police Department to dispatch patrol cars, followed in 1932 by the New

York City Police Department. These systems were operated in the 2MHz frequency

band. Unfortunately, during World War II, the progress of radio communication

technologies was drastically stimulated.

In 1946, the first commercial mobile telephone system, operated in the

150MHz frequency band, was set up by Bell Telephone Laboratories in St. Louis.

The demonstration system was a simple analog communication system with a

manually operated telephone exchange.

Subsequently, in 1969, a mobile duplex communication system was realized

in the 450MHz frequency band. The telephone exchange of this modified system

was operated automatically. The new system, called the Improved Mobile

Telephone System (IMTS), was widely installed in the United States. However,

because of its large coverage area, the system could not manage a large number of

users or allocate the available frequency bands efficiently.

5

The cellular zone was concept was developed to overcome this problem by

using the propagation characteristics of radio waves. The cellular zone concept

divided a large coverage area into many smaller zones. A frequency channel in one

cellular zone is used in another cellular zone. However, the distance between the

cellular zones that use the same frequency channels is sufficiently long to ensure that

the probability of interference is quite low. The use of the new cellular zone concept

launched the third era, known as the cellular era.

The first generation of cellular mobile communication was developed from

1980 to 1990. In this period, research and development (R&D) centered on analog

cellular communication systems.

In the United States, an analog cellular mobile communication service called

Advanced Mobile Phone Service (AMPS) was started in October 1983 in Chicago.

In Europe, several cellular mobile communication services were started. In

Norway, Nordic Mobile Telephone (NMT) succeeded in the development of an

analog cellular mobile communication system.

In the United Kingdom, Motorola developed an analog cellular mobile

communication system called the total access communication system (TACS) based

on AMPS in the 1984-1985 periods. In 1983, NMT started a modified NMT-450

called NMT-900. Moreover, C-450, RTMS and Radiocom-2000 were, respectively,

introduced in Germany, Italy and France.

Meanwhile, in Japan, Nippon Telephone and Telegraph (NTT) developed a

cellular mobile communication system in the 800 MHz frequency band and started

service in Tokyo in December 1979. Furthermore, a modified TACS that changed

the frequency band to adjust for Japanese frequency planning and was called JTACS

was also introduced in July 1989. Subsequently, narrowbakd TACS (NTACS),

which introduced the required frequency band in half, started service in October

1991.

6

So far, the evolution of the analog cellular mobile communication system is

described. There were many problems and issues, for example, the incompatibility

of the various systems in each country or region, which precluded roaming. In

addition, analog cellular mobile communication systems were unable to ensure

sufficient capacity for the increasing number of users, and the speech quality was

not good.

To solve these problems, the R&D of cellular mobile communication

systems based on digital radio transmission schemes was initiated. These new

mobile communication systems became known as the second generation (2G) of

mobile communication systems, and the analog cellular era is regarded as the first

generation (1G) of mobile communication systems.

In Europe, the global system for mobile communication (GSM), a new

digital communication system that allowed international roaming and using 900

MHz frequency band had been introduced in 1992.

First Generation (1G) is described as the early analogue cellular phone

technologies. Actually, 1G is a hybrid of analog voice channels and digital control

channels. The analog voice channels typically used Frequency Modulation (FM)

and the digital control channels used simple Frequency Shift keying (FSK)

modulation. NMT and AMPS cellular technologies fall under this categories.

Second Generation (2G) described as the generation first digital fidely used

cellular phones systems. 2G digital systems use digital radio channels for both voice

(digital voice) and digital control channels. GSM technology is the most widely

used 2G technologies. This gives digital speech and some limited data capabilities

(circuit switched 9.6kbits/s). Other 2G technologies are IS-95 CDMA, IS-136

TDMA and PDC.

Two and Half Generation (2.5G) is an enhanced version of 2G technology.

2.5G gives higher data rate and packet data services. GSM systems enhancements

7

like GPRS and EDGE are considered to be in 2.5G technology. The so-called 2.5G

technology represent an intermediate upgrade in data rates available to mobile users.

Third Generation (3G) mobile communication systems often called with

names 3G, UMTS and WCDMA promise to boost the mobile communications to the

new speed limits. The promises of third generation mobile phones are fast Internet

surfing, advanced value-added services and video telephony. Third-generation

wireless systems will handle services up to 384 kbps in wide area applications and

up to 2 Mbps for indoor applications.

Fourth Generation (4G) is intended to provide high speed, high capacity, low

cost per bit, IP based services. The goal is to have data rates up to 20 Mbps. Most

propable the 4G network would be a network which is a combination of different

technologies, for example, current celluart networks, 3G celluar network and

wireless LAN, working together using suitable interoperability protocols.

1.2 Objectives of the project § To study a concept of Orthogonal Frequecy Division Multiplexing (OFDM)

Tranmission Technology in WLAN enviroment

§ To design and evaluate Orthogonal Frequency Division Multiplexing (OFDM)

in a Multipath Fading Channel using computer simulation (MATLAB)

§ To obtain and compare between the theoretical and simulation result for

Orthogonal Division Multiplexing (OFDM) under different communication

channel

§ To obtain and compare the Bit Error Rate (BER) Performance for different

communication channel

8

1.3 Scope of the project

In this project, I focused on designing the matlab code for two different

channel conditions that affects the BER performance for Orthogonal Frequency

Divison Multiplexing (OFDM) in WLAN environment. Both channels are:

§ AWGN Channel

§ Rayleigh Channel

Digital modulation that has been used in this project is QPSK modulation.

1.4 Motivations

OFDM is expected to be used in future broadcasting and wireless LAN

(WLAN) systems. IEEE802.11a is the technology that used OFDM concept. Since

wireless technologies become a very high demand nowadays, OFDM is chosen to be

a subject study.

By learning to design and evaluate the Orthogonal Frequecny Division

Multiplexing (OFDM) system using computer simulation, I will be able to establish

my position in the research and development of wireless communications and

further design and simulate more complex systems.

In this project, I ’ m using the MATLAB computer-simulation software,

which is produced by MathWork Inc. MATLAB, a sophisticated language for

matrix calculation, and stands for MATrix LABoratory. MATLAB is chosen as the

computer language to design the Orhtogonal Frequency Division Multiplexing

(OFDM) systems because it is one of the most popular computer simulation

languages in the world. MATLAB is used throughout this project to:

§ model and simulate the communication channel (AWGN and Rayleigh)

§ model and simulate of the transmission system for OFDM using QPSK

modulation

9

§ compute and compare the BER.

1.5 Problem statement

Mobile wireless systems operate under harsh and challenging channel

conditions. The wireless channel is distinct and much more unpredictable than the

wireline channel because of factors such as multipath and shadow fading, Doppler

spread, and delay spread or time dispersion. These factors are all related to

variability that is introduced by the mobility of the user and the wide range of

environments that may be encountered as a result.

In wireless communications, multipath is the propagation phenomenon that

results in radio signals reaching the receiving antenna by two or more paths. Causes

of mutipath include atmospheric, ducting, ionospheric reflection and refraction and

reflection from terrestrial objects such as mountains and buildings. The reflected

signals arrive at the receiver with random phase offsets, because each reflection

generally follows a different path to reach the user’s receiver. The result is random

signal fades as the reflections destructively (and constructively) superimpose on one

another, which effectively cancels part of the energy signal for brief periods of time.

The degree of cancellation or fading will depend on the delay spread of the reflected

signals, as embodied by their relative phases and their relative power.

The project studies and identifies the Orthogonal Frequency Divison

Multiplexing (OFDM) that gives the best BER performance in a multipath fading

environment using QPSK modulation system. This project will identify the best

BER performance between different types of communication channel. The outcome

from the BER vs Signal Energy per bit over noise power density ratio (Eb/No) will

be shown in the graph format.

10

1.6 Methodology and Report Structure

This is a simulation project which studied the BER performance for

Orthogonal Frequency Division Multiplexing (OFDM) under different

communication channels. This study involves four main procedures to achieve its

ob jec t ives . The procedures involved modeling and simulations o f t he

communication channel between ideal and worst case, OFDM transmission system,

QPSK transmission system and calculation and comparison of BER. The following

flowchart summarizes the procedures:

Figure 1.2 Flowchart to calculate BER performance

In Chapter 1, there is an introduction of this project, where it contained

history of mobile communication, objectives, scope, motivations and problem

statements.

The second chapter, more concentrate on the subject matter which is

Orthogonal Frequency Division Multiplexing (OFDM). Extensive research is

Step 0 Initial study & research on wireless communications

Step 1 Communication Channel Model

Ideal Channel

Worst Case Channel

Step 2 OFDM Transmission

System Model

Step 3 GPSK Transmission

System Model

Step 4 Calculate BER and compare results

Project 1

Project 2

11

carried out on the existing wireless communications system and its underlying

modulation schemes.

In Chapter 3, concept of the digital modulation scheme is discussed. In this

chapter, concentrate more on quadrature PSK since this modulation has been chosen

as a digital modulation in OFDM.

Subsequently, the next chapter, Chapter 4, we will focus on communication

channel that exists in wireless communication, how the communication channels

contribute in the BER performance of OFDM.

The fifth chapter outlines the modeling and simulation of communication

channel using MATLAB. Two channels are modeled; they are the ideal

communication channel and the worst case communication channel.

In chapter 6, outlines the modeling and simulation of quadrature PSK

(QPSK).

While in chapter 7, outline the modeling and simulation of the Orthogonal

Frequency Division Multiplexing (OFDM) under different communications

channels.

The second last and last chapter will conclude on the results from all the

simulations. Discussions and analysis on the results are included in this section.

CHAPTER 2

ORTHOGONAL FREQUENCY DIVISION MULTIPLEXING

TRANSMISSION TECHNOLOGY

Focus of this project is on Orthogonal Frequency Division Multiplexing

(OFDM) Transmission Technology. A study is carried out on OFDM and drilled

down further on concept of the parallel transmission scheme that has been used in

OFDM.

2.1 Introduction

Orthogonal Division Multiplexing (OFDM) has grown to be the most

popular communications systems in high speed communications in the last decade.

In fact, it has been said by many industry leaders that OFDM technology is the

future of wireless communications.

The root of OFDM dates back in the lter 1950s, with the technology gaining

popularity when it became the standard for digital audi broadcasting (DAB). Using

16 independent channels, each carrying a 256kbps data rat, OFDM enables

transmission to be sent and received simultenously. Terrestial digital video

briadcasting (DVB-T) in Europe was also an early OFDM application. However,

these broadcasting systems did not offer much promise for two way communications

in a typical broadcasting environment; transmitters are a rather expensive option.

13

Late 1997, Lucent and NTT submittec proposals to the IEEE for a high speed

wireless standard for local are networks (LAN). Eventually, the two companies

combined their proposals and it was accepted as a draft stanadard in 1998 and as a

standard now known as IEEE802.11a standard, in 1999.

2.2 Evolution of OFDM

The evolution of OFDM [2] can be divided into three parts. There are

consists of Frequency Division Multiplexing (FDM), Multicarrier Communication

(MC) and Orthogonal Frequency Division Multiplexing.

2.2.1 Frequency Division Multiplexing (FDM)

Frequency Division Multiplexing (FDM) has been used for a long time to

carry more than one signal over a telephone line. FDM is the concept of using

different frequency channels to carry the information of different users. Each

channel is identified by the center frequency of transmission. To ensure that the

signal of one channel did not overlap with the signal from an adjacent one, some gap

or guard band was left between different channels. Obviously, this guard band will

lead to inefficiencies which were exaggerated in the early days since the lack of

digital filtering is made it difficult to filter closely packed adjacent channels.

2.2.2 Multicarrier Communication (MC)

The concept of muticarrier (MC) communications uses a form of FDM

technologies but only between a single data source and a single data receiver. As

multicarrier communications was introduced, it enabled an increase in the overall

capacity of communications, thereby increasing the overall throughput. Referring to

14

MC as FDM, however, is somewhat misleading since the concept of multiplexing

refers to the ability to add signals together. MC is actually the concept of splitting a

signal into a number of signals, modulating each of these new signals over its own

frequency channel; multiplexing these different frequency channels together in an

FDM manner; feeding the received signal via a receiving antenna into a

demultiplexer that feeds the different frequency channels to different receivers and

combining the data output of the receivers to form the received signal.

2.2.3 Orthogonal Frequency Division Multiplexing

OFDM is the concept of MC where the different carriers are orthogonal to

each other. Orthogonal in this respect means that the signals are totally independent.

It is achieved by ensuring that the carriers are placed exactly at the nulls in the

modulation spectra of each other. Source for OFDM spectral efficiency is the fact

that the drop off of the signal at the band is primarily due to a single carrier which is

carrying a low data rate. OFDM allows for sharp rectangular shape of the spectral

power density of the signal.

2.3 Orthogonal Frequency Division Multiplexing Technology

Orthogonal Frequency Division Multiplexing (OFDM) also known as

discrete multitone modulation (DMT), is based upon the principle of requency

division multiplexing (FDM), but it utilized as a digital modulation scheme. The bit

stream that is to be transmitted is split into several parallel bit streams, typically

dozens to thousands. The available frequency spectrum is divided into sub-channels

and each low rate bit stream is transmitted over one sub channel by modulating sub-

channel by ,odulating a sub-carrier using a standard modulation scheme, for

example: PSK, QAM. The sub-carrier frequencies are chosen so that the modualted

data streams are orthogonal to each other, meaning that cross talk between the sub-

channels is eliminated.

15

Channel equalization is simplified by using many slowly modulated

narrowband signals instead of one fastly modulated wideband signal. The primary

advantage of OFDM is its ability to coop with severe channel conditions, for

example multipath and narrowband interference without complex equalization filters.

2.4 Concept of the Parallel Transmission Scheme

The multipath fading environment in which not only a direct transmission

signal but also many reflected signals arrive at the receiver at different timues in the

time domain is characterized by a channel impulse response, which includes the

information about the relative time when the delayed signal arrived at receiver, the

power of the signal and its phase as compared to the power and phase of the direct

wave. Figure 2.1 shows a typical impulse response of multipath fading in the time

and frequency domains.

From the time domain point of view, many signals with different arrival

times, signal power and phases are reveived at receiver. From the frequecny point of

view, the multipath fading environment is characterized by the enhancement of

some frequencies and the attenuation of others. If there is mobile reception the the

relative power levels and attenuations of various reception path will change with

time. A narrowband signal will vary in quality as the peaks and the frequency

response move around in the frequency domain. There will also be a noticeable

variation in the phase response which will affect all systems using the phase as a

means of signalling.

Let us consider the situation where single carrier serial high speed wireless

data is transmitted in a multipath fading environment. If digital data are transmitted

at a rate of several megabits per second, and the maximum delay time of delayed

waves caused by multipath fading is larger than 1 µs, the maximum delay time of

the delayed waves is greater than 1 symbol time. Figure 2.1 illustrates the

waveforms of a single carrier serial high speed wireless data transmission scehme in

16

the time domain and the 1 symbol time. Both the waveforms and the spectrum are

distorted and need to to equalize the distorted signal.

Figure 2.1: Typical impulse response of multipath fading:

(a) time domain

(b) frequency domain

One way to equalie the signal is by using adaptive equalization techniques

that estimate the channel impulse response at the received data signal at the receiver.

However, there are practical difficulties associated with operating this equalization

at several megabits per second with high speed, compact and low cost hardware

because if the transmitted data wanted to be recovered from the received data,

several successive symbols must to be stored in order to equalize the received data

sequentially.

17

From the frequency domain point of view, when a transmitted signal suffers

from multipath fading, some part of the signal may suffer from constructive

interference and be enhanced in level, whereas some other parts of the signal may

suffer from destructive interference and be attenuated, sometimes to the point of

extinction. In general, frequency bands that are close together will suffer from the

same variation in the signal strength, which is well correlated. The width of the

frequency bands that have high correlation value is called the coherent bandwidth.

For a narrowband signal, distortion is usually minimized if the bandwidth of the

signal is less than the coherent bandwidth. There is, however, a significant chance

that the signal will be subjected to severe attenuation in some occasions. A signal

that occupies a bandwidth greater than the coherent bandwidth will be subjected to

more distortion but will suffer from less variation in the total received power even if

it is subjected to significant levels of multipath fading.

In order to prevent the problems caused by the multipath fading environment

and achieve broadband mobile communications, it is necessary to use parallel

transmission, in which the transmitted high speed data is converted to slow parallel

data in several channels. These data are multiplexed using several multiplexing

techniques to distinguish between the subchannels.

Figure 2.1 shows the effects of the effect of the parallel transmission scheme.

For a given overall data rate, increasing the number of parallel transmission channels

reduce the data rate that each individual subchannels mus convey or in other words,

lengthen the symbol period. AS a result, the delay time of the delayed waves is

suppressed to within 1 symbol time.

In order to distinguish the subchannels, frequency division multiplexing

(FDM) and code division multiplex (CDM) are often used. Sometimes, the first

method will refer to multicarrier transmission and the second method referred to

multicode transmission. OFDM is a multicarrier transmission technology and the

most efficient one.

18

Figure 2.2 : Parallel transmission scheme : Multicode transmission scheme

Figure 2.3 : Parallel Transmission scheme : Multicarrier transmission scheme

19

2.5 Concept of OFDM Transmission Technology

In this section, focus on the development and applications of the OFDM

transmission scheme.

2.5.1 Transmitter Configuration

Figure 2.4 : OFDM transmission system : Transmitter

Figure 2.4 shows the configuration of an OFDM transmitter. In the

transmitter, the transmitted high speed data is first converted into parallel data of N

subchannels. Then, the transmitted data of each parallel subchannel is modulated by

PSK based modulation.

Consider a quadrature modulated data sequence of the N channels (d0, d1,

d2, .., dN-1) and dIn and dQn are {1,-1} in QPSK and {±1,±3} in 16-QAM. These

modulated data are fed into an inverse fast Fourier transform (IFFT) circuit and an

OFDL signal is generated. The transmitted data is given by

s(t) = ΣΣdi (k) exp (j2πfi(t-kTs))f(t-kTs)

= ΣΣ (dIi (k) + jdQi (k))(cos(2πfi(t-kTs)) + j sin (2πfi(t-kTs))) f(t-kTs)

= ΣΣ (dIi (k) cos(2πfi(t-kTs)) - dQ i (k)sin (2πfi(t-kTs))) f(t-kTs)

+j ΣΣ (dIi (k) sin(2πfi(t-kTs)) - dQ i (k)cos (2πfi(t-kTs))) f(t-kTs) (2.1)

S/P

IFFT

Binary low speed data

d1

d2

dN-1

Guard time

insertion

S’(t) S(t)

Binary high speed data

20

Where Ts is the symbol duration of the OFDM signal and fi (i=0, 1, 2, …) is

the frequency of the ith subcarrier given by

fi = f0 + i/ Ts (2.2)

Here, f(t) is the pulse waveform of each of the symbols and it is defined as

f(t) = 1 (0 t Ts )

0 (otherwise) (2.3)

Figure below shown that the waveforms of real part and an imaginary part of

an OFDM signal in each subchannel when i = 0, 1, 2, …, N-1. The OFDM signal

includes many carrier signals with their own frequencies. This OFDM signal is fed

into a guard time insertion circuit to reduce ISI.

Figure 2.5 : OFDM transmission signal in each subcarrier

21

2.5.1.1 Guard Interval

One key principle of OFDM is that since low rate modulation scheme, where

the symbols are relatively long compared to the channel time characteristics suffer

less from intersymbol interference caused by multipath. It is the advantageous to

transmit a number of low rate streams in parallel instead of a single high rate stream.

Since the duration of each symbol is long, it can be affordable to insert a guard

interval between the OFDM symbols and thus the intersymbols interference can be

eliminated. The transmitter sends s cyclic prefix during the guard interval. The guard

interval also reduces the sensitivity to time synchronization problems.

The orthogonality of subchannels in OFDM can be maintained and

individual subchannels can be completeky separated by using an FFT circuit at the

receiver when there are no ISI and intercarrier interference (ICI) introduced by

transmission channel distortion. The spectra of OFDM signal are not strictly band

limited, the distortion due to mutipath fading causes each subchannel to spread the

power into tha adjacent channel. Moreover, the delayed wave with the delay time

larger than 11 symbol time contaminates the next symbol. In order to reduce this

distortion, a simple solution is to increase the symbol duration or the number of

carriers. However, this method may be difficult to implement in terms of carrier

stability against Doppler frequency and FFT size.

Another way to eliminate ISI is to create a cyclically extended guard interval,

where each OFDM symbol is preceded by a periodic extension of the signal itself.

The total symbol duration:

Ttotal = Tg + Tn (2.4)

Where,

Tg = guard time interval

Each symbol is made of two parts. The whole signal is contained in the

active symbol, the last part of which is also repeated at the start of the symbol and is

called a guard interval. When the guard interval is longer than the channel impulse

response or the multipath delay, the effect of ISI can be eliminated. However, the

22

ICI or in band fading still exists. The ratio of the guard interval to the useful symbol

duration is application dependent. The insertion of guard interval will reduce the

data throughput; Tg is usually smaller than Ts/4.

After the insertion of a guard interval, the OFDM signal is given by

s’(t) = ΣΣdi (k) exp (j2πfi(t-kTtotal))f’(t-kTtotal) (2.5)

where f’(t) is the modified pulse waveform of each symbol defined as

f(t) = 1 ( Tg t Ts )

0 (t<-Tg, t > Ts) (2.6)

The OFDM signal is transmitted to the receiver; however, the transmitted

data, s’(t) is contaminated by multipath fading and AWGN. At the receiver, the

received signal is given by

r(t) = h(τ, t)s(t-τ)dτ + n(t) (2.7)

where h(τ, t) is the impulse response of the radio channel at time t, and n(t) is

the complex AWGN.

23

Figure 2.6: Guard Interval Insertion

2.5.2 Receiver Configuration

Figure 2.7: OFDM radio transmission system : Receiver

Guard time removal

FFT

P/S

Binary high speed data

r(t)

d’1

d’2

d’N-1

24

At the receiver, received signal r(t) is filtered by a bandpass filter, which is

assumed to have sufficiently wide passband to introduce only negligible distortion in

the signal. An orthogonal detector is then applied to the signal where the signal is

downconverted to IF band. Then, an FFT circuit is applied to the signal to obtain

Fourier coefficients of the signal in observation periods [iTTotal , iTTotal + Ts]. The

output, di’(k), of the FFT circuit of the ith OFDM subchannel is given by

di’(k) = 1/Ts r(t) exp (-j2πfi(t-kTtotal))dt (2.8)

If he characteristics of delayed wave, hi’(k) in a multipath fading

environment can be estimated, therefore the received data also can be equalized as

follows:

di’’ (k) = (hi’ * (k)) / (hi’(k)hi’ * (k) )) (di’(k)) (2.9)

where * indicates the comples conjugate.

By comparing dk and di’’ (k), the BER performance can be calculated. The

BER depends on the level of the receiver’s noise. In OFDM transmission, the

orthogonal is preserved and the BER performance depends on the modulation

scheme in each subchannel.

2.6 Advantages of OFDM

§ Can easily be adopted to severe channel conditions without complex

equalization

§ Robust to narrowband co channel interference

§ Robust to intersymbil interference and fading caused by multipath

propagation

§ High spectral efficiency

§ Efficient implementation by FFTs

25

§ Low sensitivity to time synchronization errors

§ Tuned sub channel receiver filter are not required

§ Facilitates Single Frequency Network; i.e: transmitter macrodiversity

2.7 Disadvantages of OFDM

§ Sensitive to Doppler shift

§ Sensitive to frequency synchronization problems

§ Inefficient transmitter power consumption since linear power amplifier is

required

26

CHAPTER 3

DIGITAL MODULATION SCHEMES

In this project, Quadrature PSK (QPSK) is selected to be a digital

modulation in OFDM. Hence, before proceed to design and evaluate OFDM in

computer simulation, a study on QPSK has been carried out.

3.1 Modulation

Modulation is the process of facilitating the transfer of information over a

medium. Voice cannot be sent very far by screaming. To extend the range of sound,

we need to transmit it through a medium other than air, such as a phone line or radio.

The process of converting information (voice in this case) so that it can be

successfully sent through a medium (wire or radio waves) is called modulation.

There are 2 types of modulations: Analog modulation and digital modulation.

In analog modulation, an information-bearing analog waveform is impressed on the

carrier signal for transmission whereas in digital modulation, an information-bearing

discrete-time symbol sequence (digital signal) is converted or impressed onto a

continuous-time carrier waveform for transmission. 2G wireless systems are realized

using digital modulation schemes.

27

3.2 Digital Modulation

Nowadays, digital modulation is much popular compared to analog

modulation. The move to digital modulation provides more information capacity,

compatibility with digital data services, higher data security, better quality

communications, and quicker system availability. Developers of communications

systems face these constraints:

§ available bandwidth

§ permissible power

§ inherent noise level of the system

The RF spectrum must be shared, yet every day there are more users for that

spectrum as demand for communications services increases. Digital modulation

schemes have greater capacity to convey large amounts of information than analog

modulation schemes.

3.3 Phase Shift Keying (PSK)

PSK is a modulation scheme that conveys data by changing, or modulating,

the phase of a reference signal (i.e. the phase of the carrier wave is changed to

represent the data signal). A finite number of phases are used to represent digital

data. Each of these phases is assigned a unique pattern of binary bits; usually each

phase encodes an equal number of bits. Each pattern of bits forms the symbol that is

represented by the particular phase.

There are two fundamental ways of utilizing the phase of a signal in this

way:

§ By viewing the phase itself as conveying the information, in which case the

demodulator must have a reference signal to compare the received signal's

phase against; (PSK) or

28

§ By viewing the change in the phase as conveying information - differential

schemes, some of which do not need a reference carrier (to a certain extent)

(DPSK).

A convenient way to represent PSK schemes is on a constellation diagram

(as shown in figure 2 below). This shows the points in the Argand plane where, in

this context, the real and imaginary axes are termed the in-phase and quadrature

axes respectively due to their 90° separation. Such a representation on

perpendicular axes lends itself to straightforward implementation. The amplitude of

each point along the in-phase axis is used to modulate a cosine (or sine) wave and

the amplitude along the quadrature axis to modulate a sine (or cosine) wave.

Figure 3.1 Constellation Diagram

In PSK, the constellation points chosen are usually positioned with uniform

angular spacing around a circle. This gives maximum phase-separation between

adjacent points and thus the best immunity to corruption. They are positioned on a

circle so that they can all be transmitted with the same energy. In this way, the

moduli of the complex numbers they represent will be the same and thus so will the

amplitudes needed for the cosine and sine waves. Two common examples are

binary phase-shift keying (BPSK) which uses two phases, and quadrature phase-

shift keying (QPSK) which uses four phases, although any number of phases may be

29

used. Since the data to be conveyed are usually binary, the PSK scheme is usually

designed with the number of constellation points being a power of 2.

3.4 Bit rate and symbol rate

To understand and compare different PSK modulation format efficiencies, it

is important to first understand the difference between bit rate and symbol rate. The

signal bandwidth for the communications channel needed depends on the symbol

rate, not on the bit rate.

EachSymbolmittedWithfBitsTransTheNumbero

BitRateSymbolRate = (2.1)

Bit rate is the frequency of a system bit stream. Take, for example, a radio

with an 8 bit sampler, sampling at 10 kHz for voice. The bit rate, the basic bit

stream rate in the radio, would be eight bits multiplied by 10K samples per second,

or 80 Kbits per second. (For the moment we will ignore the extra bits required for

synchronization, error correction, etc.).

Figure 3.2 Bit Rate and Symbol Rate

30

Figure above is an example of a state diagram of a Quadrature Phase Shift

Keying (QPSK) signal. The states can be mapped to zeros and ones. This is a

common mapping, but it is not the only one. Any mapping can be used. The

symbol rate is the bit rate divided by the number of bits that can be transmitted with

each symbol. If one bit is transmitted per symbol, as with BPSK, then the symbol

rate would be the same as the bit rate of 80 Kbits per second. If two bits are

transmitted per symbol, as in QPSK, then the symbol rate would be half of the bit

rate or 40 Kbits per second. Symbol rate is sometimes called baud rate. Note that

baud rate is not the same as bit rate. These terms are often confused. If more bits

can be sent with each symbol, then the same amount of data can be sent in a

narrower spectrum. This is why modulation formats that are more complex and use

a higher number of states can send the same information over a narrower piece of

the RF spectrum.

3.5 QPSK

QPSK is a multilevel modulation techniques, it uses 2 bits per symbol to

represent each phase. Compared to BPSK, it is more spectrally efficient but requires

more complex receiver.

Figure 3.3 Constellation Diagram for QPSK

31

Figure above shows the constellation diagram for QPSK with Gray coding.

Each adjacent symbol only differs by one bit. Sometimes known as quaternary or

quadriphase PSK or 4-PSK, QPSK uses four points on the constellation diagram,

equispaced around a circle. With four phases, QPSK can encode two bits per

symbol, shown in the diagram with Gray coding to minimize the BER - twice the

rate of BPSK. Figure below depicts the 4 symbols used to represent the four phases

in QPSK. Analysis shows that this may be used either to double the data rate

compared to a BPSK system while maintaining the bandwidth of the signal or to

maintain the data-rate of BPSK but halve the bandwidth needed.

Figure 3.4 Four symbols that represents the four phases in QPSK

Although QPSK can be viewed as a quaternary modulation, it is easier to see

it as two independently modulated quadrature carriers. With this interpretation, the

even (or odd) bits are used to modulate the in-phase component of the carrier, while

the odd (or even) bits are used to modulate the quadrature-phase component of the

carrier. BPSK is used on both carriers and they can be independently demodulated.

As a result, the probability of bit-error for QPSK is the same as for BPSK:

32

÷÷

ø

ö

çç

è

æ=

0

2

N

EQP b

b (3.1)

However, with two bits per symbol, the symbol error rate is increased:

2)1(1 bs PP --=

÷÷

ø

ö

çç

è

æ-÷

÷

ø

ö

çç

è

æ=

0

2

0

2N

EQ

N

EQ ss (3.2)

If the signal-to-noise ratio is high (as is necessary for practical QPSK

systems) the probability of symbol error may be approximated:

(3.3)

As with BPSK, there are phase ambiguity problems at the receiver and

differentially encoded QPSK is more normally used in practice.

33

CHAPTER 4

COMMUNICATION CHANNEL

In wireless communications, a practical communication channel is

often modeled by a random attenuation of the transmitted signal, followed by

additive noise. The attenuation captures the loss in signal power over the course of

the transmission, and the noise in the model captures external interference and/or

electronic noise in the receiver. Hence, depending on the application, the

mathematical model for the communication system includes a model for the

distortion introduced by the transmission medium, and termed the communication

channel, or channel for short. Types of communications channels:

§ 1. Simplex communication (1 way)

§ Duplex communication (2 ways)

4.1 Communication Channel

Channel, in communications (sometimes called communications channel),

refers to the medium through which information is transmitted from a sender (or

transmitter) to a receiver. In practice, this can mean many different methods of

facilitating communication, including:

1. A connection between initiating and terminating nodes of a circuit.

2. A path for conveying electrical or electromagnetic signals, usually

distinguished from other parallel paths.

34

3. The portion of a storage medium, such as a track or a band, that is

accessible to a given reading or writing station or head.

4. In a communications system, the part that connects a data source to a data

sink.

4.2 Multipath

In wireless communications, mutipath is the propagation

phenomenon that results on radio signals reaching the receiving antenna by two or

more paths. Causes of mutipath include atmospheric ducting, ionospheric refelction

and refraction and reflection from terrestrial object such as mountains and buildings.

The effects of multipath include constructive and destructive interference and

phase shifthing of the signal. This causes Rayleigh Fading named after Lord

Rayleigh. Rayleigh fading with a strong line of sight is said to have a Rician

distributuion or tobe Rician fading.

In digital radio communications such as GSM Multipath can cause errors and

affect the quality of communications. The errors are due to Intersymbol Interference

(ISI). Equalizers are often used to correct the ISI. Alternatively, techniques such as

orthogonal frequency division modulation and Rake receivers may be used.

4.3 Fading

Fading is about the phenomenon of loss of signal in telecommunications.

Fading or fading channels refers to mathematical models for the distortion that a

carrier modulated telecommunication signal experiences over certain propagation

media. Short team fading also known as mutipath induced fading is due to mutipath

propagaration. Fading results from the superposition of transmitted signals that have

35

experienced differences in attenuation, delay and phase shift while travelling from

the source to the receiver. It may be caused by attenuation of a single signal.

The most common types of fading known as “slow fading” and “fast fading”

as they apply to a mobile radio environment. Fading refers to the time variation of

the received signal power caused by changes in the transmission medium or path.

Slow fading: Shadowing or Large Scale Fading is a kind of fading caused by larger

movements of a mobile or obstructions within the peropagation environment. Fast

fading also known as Multipath fading or small scale fading is a kind of faidng

occuring with small movements of a mobile.

The best way to combat fading is to ensure that multiple versions of the same

signal are transmitted, received and coherently combined. This is usually termed

diversity and is sometimes acquired through multiple antennas. Mathematically, the

simplest model for the fading phenomenon is multiplication of the signal waveform

with a time dependent coefficient which is often modeled as a random variable,

making the received signal to noise ratio a random quantity.

Fading channel models are often used to model electromagnetic transmission

of information over wireless meida such as with cellular phones and in broadcast

communication. Small scale fading is usually divided into fading based on multipath

time delay spread and that based on Doppler spread.

There are two typer of fading based on multipath time delay spread:

§ Flat fading: the bandwidth of the signal is less than the coherence

bandwidth of the channel or the delay spread is less than the symblo

period.

§ Frequnecy selective fading: the bandwidth of the signal is greater

than the coherence bandwidth of the channel or the delay spread si

greater than the symbol period

There are two types of fading based on doppler spread:

36

§ Fast Fading: has a high doppler spread and the coherence time is less

than the symbol time and the channel variations are faster than

baseband signal variation

§ Slow Fading: has a low Doppler spread. The coherence time is

greater than the symbol period and the channel variations are slower

than the baseband signal variation

4.4 Multipath Fading

Multipath Fading is simply a term used to describe the multiple paths a radio

wave may follow between transmitter and receiver. Such propagation paths include

the ground wave, ionospheric refraction, reradiation by the ionospheric layers,

reflection from the earth’s surface or from more than one ionospheric layer, and so

on.

Multipath fading occurs when a transmitted signal divides and takes more

than one path to a receiver and some of the signals arrive out of phase, resulting in a

weak or faidng signal. Some transmission losses that effect radio wave propagation

are ionospheric absorption, ground reflection and free space losses. Electromagnetic

interference (EMI) both natural and man made, interfere with radio communications.

The maximum useable frequency (MUF) is the highest frequecy that can be used for

communications between two locations at a given angle of incidence and time of day.

The lowest usable frequency (LUF) is the lowest frequency that can be used for

communications between two locations.

4.5 Multipath Channel Characteristics

Because there are obstacles and reflectors in the wireless propagation

channel, the transmitted signal arrivals at the receiver from various directions over a

37

multiplicity of paths. Such a phenomenon is called multipath. It is an unpredictable

set of reflections and/or direct waves each with its own degree of attenuation and

delay.

Multipath is usually described by: Line-of-sight (LOS): the direct connection

between the transmitter (TX) and the receiver (RX). Non-line-of-sight (NLOS): the

path arriving after reflection from reflectors. The illustration of LOS and NLOS is

shown in Figure 4.1.

Figure 4.1 Effect of multipath on a mobile station.

Characteristics of a Multipath Channel are:

§ Delay spread – this is the interval for which a symbol remains inside

a multipath channel

§ Channel can be modeled as a FIR filter with one line of sight (LOS)

path & several multipaths, the signals from the multipaths being

delayed and attenuated version of the signal from the LOS path

Multipath will cause amplitude and phase fluctuations, and time delay in the

received signals.

38

4.6 Diversity Schemes A diversity scheme is a method that is used to develop information from

several signals transmitted over independent fading paths. This means that the

diversity method requires that a number of transmission paths be available, all

carrying the same message but having independent fading statistics. The mean

signal strengths of the paths should also be approximately the same. The basic

requirement of the independent fading is received signals are uncorrelated.

Therefore, the success of diversity schemes depends on the degree to which the

signals on the different diversity branches are uncorrelated.

Multipath fading may be minimized by practices called spaced diversity and

frequency diversity. In space diversity, two or more receiving antennas are spaced

some distance apart. Fading does not occur at both antennas. Therefore, enough

output is almost always available from one of the antennas to provide a useful signal.

In frequency diversity, two transmitter and two receivers are used, each pair tuned to

a different frequency, with the same information being transmitted simultaneously

over both frequencies. One of the two receivers will almost always produce a useful

signal.

Proper combining the multiple signals will greatly reduce severity of fading

and improve reliability of transmission. Because deep fades seldom occur

simultaneously during the same time intervals on two or more paths. The simplest

combining scheme is selection combining, which is based on the principle o f

selecting the best signal (the largest energy or SNR) among all of the signals

received from different branches.

39

CHAPTER 5

COMMUNICATION CHANNEL MODELING AND SIMULATION 5.1 Additive White Gaussian Noise (AWGN) Channel

In the study of communication systems, the classical (ideal) additive white

Gaussian noise (AWGN) channel, with statistically independent Gaussian noise

samples corrupting data samples free of intersymbol interference (ISI), is the usual

staring point for understanding basic performance relationships. An AWGN channel

adds white Gaussian noise ti the signal that passes through it.

In constructing a mathematical model for the signal at the input of the

receiver, the channel is assumed to corrupt the signal by the addition of white

Gaussian noise as shown in Figure 5.1 below, therefore the transmitted signal, white

Gaussian noise and received signal are expressed by the following equation with s(t),

n(t) and r(t) representing those signals respectively:

)()()( tntstr += (5.1)

Figure 5.1 Received signal corrupted by AWGN

+ s(t) r(t)

n(t)

40

Where n(t) is a sample function of the AWGN process with probability density

function (pdf) and power spectral density as follows:

]/[2

1)( 0 HzWNfnm =F (5.2)

Where N0 is a constant and called the noise power density.

5.1.1 Matlab Implementation

In Matlab, added white Gaussian noise is simulated by using a built- in

function randn, which generates random numbers and matrices whose elements are

normally distributed with mean 0 and variance 1.

AWGN noise is added to the digital modulated signal with in-phase channel

(I-channel) and quadrature-phase (Q-channel) data vectors, idata a n d qdata,

respectively, thus giving the output of I-channel and Q-channel as iout and qout.

)()()(

)()()(

trandntqdatatqout

trandntidatatiout

+=

+=

Matlab code 5.1: AWGN

The above code produced AWGN noise of noise power 1. For the

computation of BER performance, the noise power is varied. Noise power is

defined as a variable, npow and since idata and qdata are voltages, not powers, the

notation of npow is changed from power to voltage. This is defined as attn.

npowattn2

1= (5.3)

41

The code above is revised after it is contaminated by noise with a power of

npow become:

)()()(

)()()(

trandnattntqdatatqout

trandnattntidatatiout

´+=

´+=

Matlab code 5.2: AWGN with variable noise power

The Matlab code above is used for BER performance evaluation under the

ideal communication channel where the attn, idata and qdata are the inputs to set the

noise contaminated signal.

5.2 Rayleigh Fading Channel

Rayleigh fading is a statistical model for the effect of a propagation

environment on a radio signal such as that used by wireless devices. It assumes that

the power of a signal that has passed through such a transmission medium (also

called a communications channels will vary randomly or fade according to a

Rayleigh distributuion – the radial component of the sum of two uncorrelated

Gaussian random variables. It is reasonable model for tropospheric and ionospheric

signal propagation as well as the effect of heavily built up urban environment on

radio signals. Rayleigh fading is most applicable when there is no line of sight

between the transmitter and receiver.

42

Figure 5.2 Principle of multipath channel

As shown in the model above, the path between base station and mobile

stations of terrestrial mobile communications is characterized by various obstacles

and reflections. The radio wave transmitted from the base station radiates in all

directions. These radio waves, including reflected waves that are reflected off of

various objects, diffracted waves, scattering waves, and the direct wave from the

base station to the mobile station. Therefore the path lengths of the direct, reflected,

diffracted, and scattereing waves are different, the time each takes to reach the

mobile station is different. The phase of the incoming wave also varies because of

the reflection. As a result, the receiver receives a superposition consisting of several

waves having different phase and time of arrival. The generic name of a radio wave

in which the time of arrival is retarded in comparison with this direct wave is called

a delayed wave. Then, the reception environment characterized by a superposition

of delayed waves is called multipath propaation environment [1].

In a multipath propagation environment, the received signal is sometimes

weakened or intesified. The signal level of the received wave changes from moment

to moment. Multipath fading raises the error rate of the received data.

43

The delayed wave with incident angle nq is given by the following equation

(5.4) and corresponding to Figure 5.2, when a continuous wave of single frequency

cf (Hz) is transmitted from the base station.

)]2(exp)(Re[)( tfjtetr cnn p= (5.4)

where Re[] indicates the real part of a complex number that gives the

complexenvelope of the incoming wave from the direction of the number n.

Figure 5.3 Delayed wave with incident angle nq

Moreover, j is a complex number. )(ten is given in (5.5) by using

propagation path length from the base station of the incoming waves: )(mLn , the

speed of the mobile station, v (m/s), and the wavelength, l (m).

)()(

)cos(2(exp)()(

tjytx

vtLjtRte

nn

nnn

nn

+=

+-

-= fl

qp

(5.5)

where nR and nf are the envelope and phase of the nth incoming wave.

)(txn and )(tyn are the in-phase and quadrature phase factors of )(ten , respectively.

The incoming nth wave shifts the carrier frequency as lq nv cos (Hz) by the

Doppler effect (Hz). This is called the Doppler shift, which described as df , has a

maximum value of lv , when the incoming wave comes from the running direction

nq

Mobile station

44

of the mobile station in 1cos =nq . Then this maximum is the largest Doppler shift.

The delayed wave that comes from the rear of the mobile station also has a

frequency shift of - df (Hz).

It is shown by (5.4), since received wave )(tr received in the mobile station

is the synthesis of the above-mentioned incoming waves, when the incoming wave

number is made to be N.

å=

=N

nn trtr

1

)()(

( )( )[ ]tftytftx

tfjtftjytx

tfjte

cc

cc

c

N

nn

pp

pp

p

2sin)(2cos)(

2sin2cos)()(Re

)2(exp)(Re1

-=

++=

úû

ùêë

é÷ø

öçè

æ= å

=

(5.6)

where x(t) and y(t) are given by

å

å

=

=

=

=

N

nn

N

nn

tyty

txtx

1

1

)()(

)()(

(5.7)

and x(t) and y(t) are normalized random processes, having an average value

of 0 and dispersion of s , when N is large enough. The combination probability

density p(x,y) is then given by (5.8), where x=x(t), y=y(t)

÷÷ø

öççè

æ +=

2

22

2 2exp

2

1),(

sps

yxyxp (5.8)

In addition, it can be expressed as r(t) using the amplitude and phase of the

received wave.

))(2cos()()( ttftRtr c qp += (5.9)

45

R(t) and )(tq are given by

[ ]xyt

yxRtR1

2

tan)(

)(-==

+==

qq (5.10)

By using a transformation of variables, p(x,y) can be converted into ),( qRp

÷÷ø

öççè

æ-=

2

2

2 2exp

2),(

spsq

RRRp (5.11)

By integrating ),( qRp over q from 0 to 2, the probability density function

)(Rp is obtained (5.12).

÷÷ø

öççè

æ-=

2

2

2 2exp)(

ss

RRRp (5.12)

By integrating ),( qRp overR from 0 to ¥ , the probability density function

)(qp is obtained (5.13).

p2

1)( =Rp (5.13)

From these equations, the envelope fluctuation follows a Rayleigh

distribution, and the phase fluctuation follows a uniform distribution on the fading in

the propagation path.

An expression for simulations of this Rayleigh fading is found. Here, the

mobile station receives the radio wave as shown in Figure 5.2, the arrival angle of

the receiving incoming wave is uniformly distributed, and the wave number of the

incoming waves is N.

)()()( tyjtxtr ×+=

46

( )

å

å

=

=

þýü

îíì

÷÷ø

öççè

æ÷÷ø

öççè

æ+

úúû

ù

êêë

é

++

þýü

îíì

÷÷ø

öççè

æ÷÷ø

öççè

æ

+=

1

1

1 111

1 1111

2cos2cossin

2

2cos1

12cos2cossin

1

2

N

nd

N

ndd

tN

nf

N

n

Nj

tfN

tN

nf

N

n

N

pp

p

pp

pp

(5.14)

where 1N is an odd number and 1N is given by

÷ø

öçè

æ-= 1

22

11

NN (5.15)

In this case, the following relations are satisfied

[ ] [ ]0)]()([

2

1)()(

22

=

==

tytxE

tyEtxE

QI

QI (5.16)

5.2.1 Matlab Implementation The following Matlab code is written based on the equation (5.14):

% fade.m

% generate rayleigh fade

function [iout,qout,ramp,rcos,rsin] = fade (idata,qdata,nsamp,tstp,fd,no,counter,flat)

% Input variables

% idata : input i channel data

% qdata : input q channel data

% nsamp : number of samples to be simulated

% tstp : minimum time resolution

% fd : maximum doppler frequency

% no : number of waves in order to generate fading

47

% counter : fading counter

% flat : flat fading or not

% (1-flat (only amplitude is fluctuated), 0-normal (phase and amplitude

% are fluctuated))

% Output variables

% iout : output i channel data

% qout : output q channel data

% ramp : amplitude contaminated by fading

% rcos : cosine value contaminated by fading

% rsin : sine value contaminated by fading

if fd ~= 0.0

ac0 = sqrt(1.0 ./ (2.0.*(no + 1)));

% power normalized constant (ich)

as0 = sqrt(1.0 ./ (2.0.*(no)));

% power normalized constant (qch)

ic0 = counter;

% fading counter

pai = 3.14159265;

wm = 2.0.*pai.*fd;

n = 4.*no + 2;

ts = tstp;

wmts = wm.*ts;

paino = pai./no;

xc=zeros(1,nsamp);

xs=zeros(1,nsamp);

ic=[1:nsamp]+ic0;

for nn = 1 : no

cwn = cos( cos(2.0.*pai.*nn./n).*ic.*wmts );

xc = xc + cos(paino.*nn).*cwn;

48

xs = xs + sin(paino.*nn).*cwn;

end

cwmt = sqrt(2.0).*cos(ic.*wmts);

xc = (2.0.*xc+cwmt).*ac0;

xs = 2.0.*xs.*as0;

ramp=sqrt(xc.^2+xs.^2);

rcos=xc./ramp;

rsin=xs./ramp;

if flat == 1

iout = sqrt(xc.^2 + xs.^2).*idata(1:nsamp);

% output signal (ich)

qout = sqrt(xc.^2 + xs.^2).*qdata(1:nsamp);

% output signal (qch)

else

iout = xc.*idata(1:nsamp) - xs.*qdata(1:nsamp);

% output signal (ich)

qout = xs.*idata(1:nsamp) + xc.*qdata(1:nsamp);

% output signal (qch)

end

else

iout=idata;

qout=qdata;

end

% end of file

Matlab code 5.3: Subfunction for fading

49

Figure 5.4: Configuration of multipath fading channel

In the multipath propagation environment, the mobile station not only the

direct wave but also delayed waves caused by refelction, diffarction and scattering

that reach the time later tha the direct wave. The model of the relationship between

this direct wave and the delayed wave is shown in Figure 5.4.

It is clear that the amplitude has a Rayleigh distribution and that the phase

has a uniform distribution when the received signal is observed at the arrival time. It

is also clear that there are fixed ratios of the average electric powers of the direct and

delayed waves. Therefore, in simulating multipath fading environment, only the

relative signal level and relative delay time of the delayed waves need to be given in

comparison with the direct wave [1]. The flowchart is shown as follows:

Transmitter

Receiver

1

2

3

4 1

2

3

4

Delayed Waves

Normalized time

Direct Waves

50

Figure 5.5 Flowchart to obtain multipath fading channel

Based on the flowchart, the following Matlab codes are written for the

multipath fading. The first code in this section (Matlab code 5.3) i s the fading

subfunction to shift the input data by the specified delayed time. Matlab code 5.4

performs the entire flowchart above and calls two subfuctions – delay.m (Matlab

code 5.4) and fade.m (Matlab code 5.3) to achieve the multipath fading channel.

% delay.m

% gives delay to input signal

function [iout,qout] = delay (idata,qdata,nsamp,idel)

% Input variables

Shift of input data by delayed time

Fade for the shifted signal by subfunction

For delayed

wave #j

Start j=0

j = the number of

delayed wave

j = j + 1

end

n

y

Output Ich data : iout

Output Qch data: qout

Output data

Input Parameter

Input Ich data : idata Input Qch data : qdata Delayed time : itau Signal power of delayed waves : dlvl Time resolution : tstp Simulation time in one simulation : nsamp Fading counter : itn

51

% idata : input i channel data

% qdata : input q channel data

% nsamp : number of samples to be simulated

% idel : number of samples to be delayed

% Output variables

% iout : output i channel data

% qout : output q channel data

iout = zeros(1,nsamp);

qout = zeros(1,nsamp);

if idel ~= 0

iout(1:idel)=zeros(1,idel);

qout(1:idel)=zeros(1,idel);

end

iout(idel+1:nsamp)=idata(1:nsamp-idel);

qout(idel+1:nsamp)=qdata(1:nsamp-idel);

% end of file

Matlab code 5.4 Generate delayed waves

% sefade.m

% generates frequency selecting fading

function[iout,qout,ramp,rcos,rsin]=sefade(idata,qdata,itau,dlvl,th,n0,itn,n1,nsamp,

tstp,fd,flat)

% Input variables

% idata : input i channel data

% qdata : input q channel data

% itau : delay time for each multipath fading

52

% dlvl : attenuation level for each multipath fading

% th : initialized phase for each multipath fading

% n0 : number of waves in order to generate each multipath fading

% itn : fading counter for each multipath fading

% n1 : number of summation for direct and delayed waves

% nsamp : total number of symbols

% tstp : minimum time resolution

% fd : maximum doppler frequency

% flat : flat fading or not

% (1-flat (only amplitude is fluctuated), 0-normal (phase and amplitude

% are fluctuated))

% Output variables

% iout : output i channel data

% qout : output q channel data

% ramp : amplitude contaminated by fading

% rcos : cosine value contaminated by fading

% rsin : sine value contaminated by fading

iout=zeros(1,nsamp);

qout=zeros(1,nsamp);

total_attn=sum(10.^(-1.0.*dlvl./10.0));

for k = 1 : n1

atts = 10.^( -0.05 .* dlvl(k));

if dlvl (k) == 40.0

atts = 0.0;

end

theta = th(k) .* pi ./ 180.0;

53

[itmp,qtmp]=delay(idata,qdata,nsamp,itau(k));

[itmp3,qtmp3,ramp,rcos,rsin]=fade(itmp,qtmp,nsamp,tstp,fd,n0(k),itn(k),flat);

iout = iout + atts.*itmp3./sqrt(total_attn);

qout = qout + atts.*qtmp3./sqrt(total_attn);

end

% end of file

Matlab code 5.5 Frequency selecting fading

In the above code, the inputs are the time resolution, relative signal levels

and relative delay times of the direct and delayed waves, a complex modulating

signal formed by the transmitter and expressed in an equivalent lowpass system, and

the simulation time for one simulation loop.

The simulation time at one simulation loop and a minimum time resolution

of simulation use sm50 and sm5.0 , respectively. The three delayed waves are

assumed to have mean power of 10 dB, 20 dB and 25 dB smaller than the direct

wave, respectively, and that the relative arrival times were retarded with respect to

the direct wave by 1, 1.5 and 2 sm , respectively. Therefore, the input variable for

the multipath fading simulator is

tstp = 0.5.*10.^(-6);

itau = [0, floor(1.*10.^(-6)/tstp), floor(1.5.*10.^(-6)/tstp), floor(2.*10.^(-

6)/tstp)];

= [0, 2, 3, 4];

dlvl = [0, 10, 20, 25];

nsamp = 50.*10.^(-6)/tstp = 100;

The Frequency selecting fading code begins by delaying the input signal by

using the above input parameters. Next, Rayleigh fading is added to the delayed

signals. Only the number of delayed waves set in the parameter repeats this process.

54

All are added afterwards. As a result, the output signal taken from the multipath

Rayleigh fading is obtained.

A fading counter method is used here for generating an independently fading

delay time. The fading counter gives the start time of fading generation to a fading

generator such as fade.m. Different start times of fading generation must be set to all

direct and delayed waves to simulate an independently distributed Rayleigh fading

environment.

The initial value of the fading counter, itnd, is set during the initial set up

phase for each PSK based transmission scheme. The size of the vector of this fading

counter is equal to the size of the vector that expresses the delay time of the delayed

wave and the size os the vector that shows the relative power level of the delayed

wave.

The fading counter is then updated after each simulation loop by adding a

value, itnd0, corresponding to the simulation time to it. One hundred points are

added after each simulation loop in the case of a minimum time resolution of

sm5.0 and an observation time of sm50 . The added value is called the update time.

The update time could be adjusted to reduce the simulation time. By making the

update time larger than the observation time, the transmission performance under

Rayleigh fading can be evaluated with a small number of simulation loops.

However, the simulation result may not be precise.

CHAPTER 6

QUADRATURE PSK (QPSK) MODELING AND SIMULATION 6.1 QPSK TRANSMISSION SCHEME 6.1.1 Basic Configuration of Quadrature Modulation Scheme A QPSK signal is generated by two BPSK signal. Two orthogonal carrier

signals are used to distinguish the two signals. One is given by tf cp2cos and the

other is given by tf cp2sin . The two carrier signals remain orthogonal in the area of

a period.

02sin2cos0

=´ò tftf c

T

c

c

pp (6.1)

where cT is the period of the carrier signals and c

cT

f1

= .

By using tf cp2cos and tf cp2sin , the QPSK signals can be represented by:

)2sin()(2

1)2cos()(

2

1)( tftdtftdts cQcI pp += (6.2)

A channel in which tf cp2cos is used as a carrier signal is generally called an

in-phase channel, or Ich, and a channel in which tf cp2sin is used as a carrier signal

is generally called quadrature-phase channel, or Qch. Therefore, )(td I and )(tdQ

are the data in Ich and Qch, respectively. Modulation schemes that use Ich and Qch

56

are called quadrature modulation schemes. The basic configuration is shown in

Figure 6.1.

Figure 6.1 Basic configuration of quadrature modulation scheme

In the system shown above, the input digital data, ( )K,2,1: =kdd kk is first

converted into parallel data with two channels, Ich and Qch. The data are

represented as )(td I and )(tdQ . The conversion or data allocation is done using a

mapping circuit block. Then, the data allocated to Ich is filtered using a pulse

shaping filter in Ich. The pulse shaped signal is converted in analog signal by a D/A

converter and multiplied by a tf cp2cos carrier wave. The same process is carried

out on the data allocated to Qch but it is multiplied by a tf cp2sin carrier wave

instead. Then, the Ich and Qch signals are added and transmitted to the air.

Data

Generator

Pulse Shaping

Filter

D/A

Band Pass Filter (BPF)

å )2sin( ttc Ttf

s(t)

r(t)

tf cp2cos

Mapping

Circuit

Pulse Shaping

Filter

D/A

π/2 phase

shifter

Pulse

Compensator

Pulse Shaping

Filter

A/D

Band Pass Filter (BPF)

data

tf cp2cos

Demapping

Circuit

Pulse Shaping

Filter

A/D

π/2 phase

shifter

Pulse

Compensator

Decision Circuit

Decision Circuit

57

At the receiver, the received wave passes through a BPF to eliminate any

sprurious signals. Then, it is downconverted to the baseband by multiplying by the

RF carrier frequency. )](2cos[ 1 ttf c qp + and )](2sin[ 1 ttf c qp + are used for Ich and

Qch respectively, where )(1 tq is the phase noise of the frequency source, the

difference between the frequency sources of the transmitter and receiver. Then, in

both the Ich and Qch channels, the downcoverted signal is digitally sampled by an

A/D converters, and the digital data is fed to a DSPH. In the DSPH, the sampled

data is filtered with pulse shaping filter to eliminate ISI. The signals are then

synchronized and the transmitted digital data is recovered.

6.1.2 Basic Configuration of QPSK Transmission Scheme [1] As mentioned in the previous section, QPSK is basically a type of quadrature

modulation scheme. Its basic operations generally follow the configuration shown

in Figure 6.1 with some blocks specialized for QPSK. These blocks include the

mapping, demapping and pulse shaping functions.

For the mapping function, a simple circuit is used to allocate the data as

illustrated in the following figure. This mapping function basically allocates all

even bits to Ich and all odd bits to Qch. And demapping is just the opposite

operation.

58

Figure 6.2: Mapping circuit function for QPSK

For pulse shaping, the root Nyquist filter is used. The theoretical BER values

with AWGN and one-path Rayleigh fading are shown below:

( )obAWGNQPSK NEerfcBER2

1=- (6.3)

úú

û

ù

êê

ë

é

+-=-

0

11

11

2

1

NE

FADINGQPSK

b

BER (6.4)

In the simulation under the Rayleigh fading environment, it has been

assumed that the frequency rotation is compensated for.

6.2 Matlab Implementation MATLAB code has been written for modulation and demodulation of QPSK.

d0 d1

d2 d3

d4

d5

d(t) Input data

d6 d7 t

0 T 2T 3T 4T 5T 6T 7T 8T

t d0

d2

d4

Ich(t) Ich data

d6

0 2T 4T 6T 8T

t d1

d3 d5

Qch(t) Qch data

d7

0 2T 4T 6T 8T d(t)

Ich data

Qch data

Block Diagram

59

6.2.1 Matlab code QPSK modulation %QPSK modulation

function [iout,qout] = qpskmod(paradata,para,nd,ml)

m2=ml./2;

paradata2=paradata.*2-1;

count2=0;

for jj=1:nd

isi = zeros(para,1);

isq = zeros(para,1);

for ii= 1:m2

isi = isi + 2.^(m2 -ii).* paradata2 ((1:para),ii+count2);

isq = isq + 2.^(m2 - ii).*paradata2((1:para), m2+ii+count2);

end

iout ((1:para),jj) = isi;

qout ((1:para),jj) =isq;

count2=count2+ml;

end

Matlab code 6.1 : QPSK Modulation

60

6.2.2 Matlab code QPSK demodulation %QPSK demodulation

function [demodata] =qpskdemod (idata,qdata,para,nd,ml)

demodata=zeros(para,ml*nd);

demodata((1:para),(1:ml:ml*nd-1))=idata((1:para),(1:nd))>=0;

demodata((1:para),(2:ml:ml*nd))=qdata((1:para),(1:nd))>=0;

Matlab code 6.2 : QPSK Demodulation

CHAPTER 7

ORTHOGONAL FREQUENCY DIVISION MULTIPLEXING (OFDM)

MODELLING AND SIMULATION

7.1 OFDM Configuration using computer simulation

A block diagram of the simulation is shown in Figure 7.1.

Pilot data Serial to

parallel converter

Data generator

Channel coding

Serial to Parallel

converter

Modulation

IFFT Radio

Channel (equivalent

lowpass System)

Power Level

detection

Noise Level

Decision circuit

Gaussian Noise

Generator

Synchronization

+

B A C

para x ml x nd (bit) ml x nd x R

(bit/parallel channel)

para x ml x nd x R

(bit) nd x R

(bit/parallel channel)

62

Figure 7.1 Computer simulations to calculate the BER of an OFDM system

The parameter for the simulation has been defined as follows:

para = 128 ; % Number of parallel channel

fftlen = 128; % FFT length

noc =128; % Number of carrier

nd = 6; %Number of OFDM symbol for one loop

ml = 2; %Modulation level : QPSK

sr = 250000; % Symbol rate

br = sr.*ml; % Bit rate per carrier

gilen = 32; %Length of guard interval

ebn0 = 100; %ebn0 : Eb/No

nloop = 100; % Number of simulation loops

noe = 0; % Number of error data

nod = 0; %Number of transmitted data

As shown in Figure 7.1 and the above parameters, the OFDM system can be

stimulated with 128 subcarriers, a 4-ms symbol time (tstp = 1./sr), and a ¼ tstp

guard interval.

A

B

Fading Compensator 1

Fading Compensator 2

FFT

Demodulator Parallel to serial

converter

Channel decoding

Decision

Compensator

C

BER

ml x nd x R

(bit/parallel channel)

ml x nd x R x para (bit)

para x ml x nd

(bit)

63

After defining all the variables, QPSK is chosen to be modulation techniques

in each channel.

To start the simulation, random serial data of 0 and 1 are generated

consisting of 1-by-para*nd*ml vector. This vector is called as “seridata”.

seridata =rand(1,para*nd*ml)>0.5;

Then, the serial data vector,”seridata” was converted into a parallel data

vector, “paradata”, consistiong of a para-by-nd*ml vector to transmit the data in

parallel in order to enable parallel transmission with 128 subchannels where each

channel was using a QPSK modulation scheme.

paradata = reshape9seridata, para, nd*ml);

Next, the vector “paradata” was fed into the mapping circuit. In the circuit,

the parallel data were converted into modulated parallel data of two channels, Ich

and Qch by a predefined mapping method.

[ich,qch] = qpskmod (paradata, para,nd,ml);

The frame format of the simulation is configured as shown in Figure 7.2.

64

Figure 7.2: Frame format of the simulation model

Then, these data were incrased kmod times to normalize the data as follows:

kmod=1/sqrt(2);

ich1=ich.*kmod;

qch2=qch.*kmod;

After the mapping, these parallel data on the frequency axis were fed into the

IFFT circuit. In this circuit, the parallel data were converted into serial data on the

time axis by using OFDM.

x=ich1+qch1.*I;

y=ifft (x);

ich2 =real (y);

qch2 = imag (y);

The input and output are shown in Figure 7.3. Then ich2 and qch2, guard

interval were inserted to eliminate ISI caused by multipath fading.

Guard Interval

Nd symbols

Frequency (para chann

el)

Information data

65

Figure 7.3: Input and Output of IFFT

At this point, fftlen2 was defined as the length of symbol including the guard

interval. After that the filtered signal was transmitted to the air. The transmitted

signal will passed through the radio channel (equivalent lowpass systems) and was

transmitted to the receiver.

At the receiver, the received signal was first contaminated by AWGN. The

noise function was introduced as a function comb.m. In this simulation, the variable

“attn” will vary in accordance with given Eb/No. Here, “spow” refers to the signal

power per carrier per symbol. For the OFDM system, “spow” had to be divided by

“para” which indicates the number of parallel subcarriers.

spow = sum(ich3.^qch3./nd./para;

attn = 0.5*spow*sr/br*10.^9-ebn0/10);

attn =sqrt(attn);

By using “attn” and comb.m, the transmitted data was contaminated by

AWGN.

[ich4,qch4] = comb (ich3,qch3,length(ich3), attn);

1 2 3 60 61 IFFT 62 124 125 126 127

Frequency

domain input

Time domain

output

66

Then, the guard interval was removed from received signal ich4 and qch4.

[ich5,qch5] = girem(ich4,qch4, fftlen2, gilen,nd);

These data, “ich5” and “qch5” on the time axis were fed into the FFT circuit.

In this circuit, the serial data were converted into parallel data on the frequency axis.

rx = ich5+qch5.8i;

ry = fft (rx);

ich6 = real (ry);

qch6 =imag(ry);

The converted data were divided by “kmod” in each channel to unnormalize

the data and were fed into the demodulation function.

ich7 = ich6./kmod;

qch7 = qch6./kmod;

[demodata] =qpskdemod(ich7,qch7,para,nd,ml);

After that, the demodulated data were converted into a 1-by-para*nd*ml

vector. The data were called “demodata1”.

demodata =reshape(demodata,1,para*nd*ml);

Since, in this project, we need to obtain the BER under different

communication channels. Therefore, the number of errors should be calculated. In

this simulation, the transmitted data are referred ti as ‘seridata” and the received data

are referred to as “demodata1”. The calculation will be performed as follows:

%instantaneous number of errors and data bits

noe2 = sum(abs(seridata-demodata1);

nod2 = length(seridata);

%cumulative number of errors and data bits in noe and nod

67

noe = noe +noe2;

nod=nod+nod2;

Then, BER under different communication channel can be obtained using the

following operation:

ber = noe/nod;

Then, for BER performance under one path flat Rayleigh, we need to

determine the fading parameters and the parameters to generate fading.

%Generated data are fed into a fading simulator

[ifade,qfade]=sefade(ich3,qch3,itau,dlv1,th1,n0,itnd1,now1,

length(ich3),tstp,fd,flat);

%Update fading counter

Itnd1 =itnd1 + itnd0

All the matlab codes for OFDM under AWGN and Rayleigh fading can be

referred at the Appendix.

CHAPTER 8

RESULTS AND DISCUSSION

8.1 OFDM under AWGN channel

Under this condition, the BER performance of OFDM under AWGN

channels are simulate two times. One for theoretically and another is with matlab

code simulation.

8.1.1 OFDM under AWGN channel (theory)

OFDM has been simulated under AWGN channel which is known as the

ideal communication channel. Below is the result of the theoretical AWGN. The

BER vs Eb/No graph is plotted.

69

Figure 8.1: Theoritical AWGN 8.1.2 OFDM under AWGN channel after matlab simulation

The BER vs Eb/No graph below shown that the result of OFDM under

AWGN channel after the simulation.

70

Figure 8.2: AWGN after matlab simulation

8.1.3 Comparison OFDM under AWGN channel theory and simulation

71

Figure 8.3: Comparison between AWGN theory and simulation

Discussion:

The result shown that AWGN under simulation gives 0.9691 db shifts from

the theoretical value. This shift was caused by the cutting off of the guard interval

power from the received signal. It can be calculated as follows:

shift value(dB) = -10log 10(gilen/fftlen2)

8.2 OFDM under one path Rayleigh fading

8.2.1 OFDM under one path Rayleigh fading (Theory)

Graph below shows the result of OFDM one path Rayleigh fading

theoretically.

72

Figure 8.4: OFDM under one path Rayleigh (Theory)

8.2.2 OFDM under one path Rayleigh after simulation

After designing and running the matlab code, the BER vs Eb/No graph can

be obtained under one path Rayleigh.

73

Figure 8.5: OFDM under one path Rayleigh after simulation

8.2.3 Comparison between theory and simulation (OFDM under one

path Rayleigh)

Figure 8.6 shows the result after simulation when comparing between theory

and simulation.

74

Figure 8.6: Comparison OFDM under one path Rayleigh between theory and

simulation

Discussion:

From the BER performance under one path Rayleigh fading, it shows that if we can

compensate for the amplitude and phase fluctuations caused by fading perfectly,

0.9691 dB shifted can be obtained from the theoretical value.

8.3 Comparison OFDM under two different channels: AWGN and One Path

Rayleigh Fading

After simulating all the matlab code individually, now is the time to make

the comparison OFDM under two different channels, AWGN and One path

75

Rayleigh Fading. Figure 8.7 shows the performance for both communication

channels.

Figure 8.7: OFDM Comparison between AWGN and One Path Rayleigh

Discussion:

From the graph, it shows that AWGN communication channel gives the best

and ideal performance as compared to Rayleigh fading. In other words, Rayleigh

fading is the worst communications model in wireless communications.

76

8.4 Summary of Results

§ OFDM BER performance for AWGN simulation is differed from the

AWGN theory with 0.9691 dB shift.

§ OFDM BER performance for one path Rayleigh simulation also

gives 0.9691dB shift as compared to theoritcal value.

§ OFDM BER performance for the AWGN communication channels is

the ideal communication channel model

§ OFDM BER performance for one path Rayleigh is the worst

communication channel model in wireless communication

CHAPTER 9

CONCLUSIONS AND FURTHER WORK

This thesis has outlined all the work done on studying the BER performance

of Orthogonal Frequency Division Multiplexing (OFDM) under two different types

of communication channels in wireless communications.

In order to achieve the objectives of this thesis, first, the concept of

Orthogonal Frequency Division Multiplexing (OFDM) is studied. Then,

communication channel models for ideal (AWGN) and worst case (multipath

fading) channels were studied. AWGN is fairly simple to implement in Matlab

using its built- in function. A simplified version of the multipath fading channel is

derived from a complex theoretical mathematical model i s found. This model is

then implemented in Matlab to simulate multipath fading channel. The digital

modulations are studied and the best modulation that suite with OFDM technology

is selected.

After selecting the entire main component in OFDM, the Matlab codes are

written respectively. Once, the programs are written, they are simulated and verified

by obtaining instantaneous waveforms of the transmission scheme. The output is

compared against the theoretical models and equations. The computer simulation

programs were established to behave as expected.

78

Lastly, a comparison study is carried out to obtain the BER performance for

Orthogonal Frequency Division Multiplexing (OFDM) under different types of

communications channel. The ideal and the worst communication are defined.

9.1 Positive Conclusion All the simulation as well as the project itself runs smoothly. All the

expected results are obtained. From the results, it’s showed that the OFDM BER

performance under AWGN channel gives 0.9691 db shift. The shift of the value was

caused by guard interval power for the received signals. The OFDM BER

performance for one path Rayleigh fading also gives 0.9691dB shift. This value can

be obtained if the amplitude and phase fluctuations caused by fading can be

compensated perfectly. Lastly, from the simulations, AWGN communications

channels give the best/ ideal communication as compared to one path Rayleigh

fading.

9.2 Further improvement for this Project

I would like to simulate up to higher N-path fading channel level to identify

at which N does the BER performance is no longer lowered and what is the lowest

(i.e. the best) BER performance that it would give. Besides that, I would like to

simulate under different digital modulations to identify the best modulation scheme

that can be used in OFDM.

79

9.3 Future research

Further study on wireless LAN that using OFDM as the platform. More

research can be carried out on realizing the application of OFDM in the future

wireless communications.

9.4 Final Note In this project, I have been exposed to the wireless communications worlds.

This project has increased my understanding on OFDM and the most important

thing MATLAB software. I have learned a lot and achieved the objectives of the

project. I hope this will be my stepping stone to embark in the R&D for the wireless

technologies.

80

REFERENCES

1. Hiroshima Harada, Ramjee Prasad, Simulation and Software Radio for Mobile

Communication, Artech House, 165-226, 2002

2. Ahmad R.S Bahai, Burion R.Saltzberg, Multi-Carrier Digital Communication

Theory and Applications of OFDM, Kluwer Academic/Plenum Publishing NY,

1999

3. http://www.wi- lan.com

4. B.P.Lathi, Modern Digital and Analog Communication Systems, 3rd Edition,

New York Oxford : Oxford University Press, 1998

5. Leon W.Couch II, Digital and Analog Communication Systems, 6 th Edition,

Prentice Hall, 2001

6. http://www.ert.rwth-aachen.de/Projekte/Theo/OFDM/www_ofdm.html

7. Jakes, W.C., Microwave Mobile Communications, NewYork:IEEE Press, 1994

8. Richard Van Nee, Ramjee Prasad, OFDM for Wireless Multimedia

Communications, Norwood, MA:Artech House, 2000

9. Juha Heiskala, John Terry, OFDM Wireless LANs : A Theoretical and Practical

Guide, Sams, 2001

10. http://en.wikipedia.org/wiki/Orthogonal_frequency-division_multiplexing

11. http://www.skydsp.com/publications/4thyrthesis/index.htm

81

APPENDIX A

TIMELINE FOR PROJECT 1

Task W1 W2 W3 W4 W5 W6 W7 W8 W9 W10 W11 W12 W13 W14 W15

Project proposal

First Project

Summary

Literature review

Research on

parallel scheme

transmission

Research on

OFDM

Research on

communication

channels

Research on BER

performance

Discussion with

supervisor

Matlab installation

Learning Matlab

Presentation draft

Presentation slide

preparation

82

Presentation

Report Writing

83

APPENDIX B

TIMELINE FOR PROJECT 2

Task W1 W2 W3 W4 W5 W6 W7 W8 W9 W10 W11 W12 W13 W14 W15

Model and

Simulate OFDM

tranmission

Model and

simulate OFDM

Receiver

Model and

simulate OFDM

under AWGN

channel

Model and

simulate OFDM

under one path

Rayleigh

Simulate OFDM

under AWGN

between theory

and simulation

Simulate OFDM

under one path

Rayleigh between

theory and

simulation

84

Simulate and

comparing OFDM

under AWGN and

one path Rayleigh

Presentation slide

preparation

Presentation

Thesis Writing

85

APPENDIX C

MATLAB CODES FOR OFDM UNDER AWGN COMMUNICATION

CHANNEL

% OFDM under AWGN channels

% Simulation program to realize OFDM transmission system

%************************preparation part********************

para=128; %Number of paralle channel to transmit

fftlen = 128; %FFT length

noc=128; %Number of carrier

nd=6; %Number of information OFDM symbol for one loop

ml=2; %Modulation level:QPSK

sr=250000; %Symbol rate

br=sr.*ml; %Bit rate per carrier

gilen =32; %Length of guar interval (points)

ebn0=3; %Eb/No

%***********************main loop part*******************

nloop=100; %Number of simulation loops

noe=0; %Number of error data

nod = 0; %Number of transmitted data

eop=0; %Number of error packet

86

nop=0; %Number of transmitted packet

for iii=1:nloop

%*********************transmitter******************

%*********************data generation **************

seldata=rand(1,para*nd*ml)>0.5; %rand:built in function

%*************Serial to parallel conversion****************

paradata =reshape(seldata,para,nd*ml); %reshape: built in function

%****************QPSK Modulation ***********************

[ich,qch]=qpskmod(paradata, para, nd,ml);

kmod = 1/sqrt(2); %sqrt: built in fucntion

ich1 = ich.*kmod;

qch1 = qch.*kmod;

%*******************IFFT****************************

x = ich1 +qch1.*i;

y = ifft (x); %ifft: built in function

ich2 = real (y); %real:built in function

qch2 = imag (y); %imag:built in function

%*******************Guard Interval Insertion****************

[ich3,qch3]= giins(ich2,qch2,fftlen,gilen,nd);

fftlen2 = fftlen +gilen;

%****************Attenuation Calculation******************

87

spow = sum (ich3.^2+qch3.^2)/nd./para; %sum:built in function

attn = 0.5*spow*sr/br*10.^(-ebn0/10);

attn = sqrt(attn);

%************************Receiver**********************

%**************AWGN addition*****************************

[ich4, qch4] = comb(ich3, qch3,attn);

%********************Guard Interval Removal*************

[ich5,qch5] = girem (ich4,qch4, fftlen2, gilen, nd);

%********************FFT********************************

rx = ich5+qch5.*i;

ry = fft (rx); %fft:built in function

ich6 = real (ry); %real:built in function

qch6 = imag (ry); %imag:built in function

%*********************demodulation*******************

ich7 = ich6./kmod;

qch7 = qch6./kmod;

[demodata]=qpskdemod(ich7,qch7,para, nd,ml);

%*****************parallel to serial conversion***************

demodata1 = reshape(demodata, 1,para*nd*ml);

%*************** Bit Error Rate (BER) *******************

88

%instantaneous number of error and data

noe2=sum (abs(demodata1-seldata));

nod2 = length(seldata);

%cumulative the number of error and data in noe and nod

noe = noe+noe2;

nod = nod +nod2;

%*************Output Result******************

ber=noe/nod;

fprintf('%f\t%e\t%d\t\n',ebn0,ber,nloop);

fid = fopen('BERofdm.dat','a');

fprintf (fid,'%f\t%e\t%d\t\n',ebn0,ber,nloop);

fclose (fid);

end

89

APPENDIX D

MATLAB CODES FOR OFDM UNDER ONE PATH RAYLEIGH FADING

% Program one path Rayleigh fading

% Simulation program to realize OFDM tranmission system (under one path

% fading)

%*******************Preparation part*******************************

para =128; %Number of parallel channel to transmit

fftlen = 128; %FFT length

noc =128; %Number of carrier

nd=6; %number of information OFDM symbol for one loop

ml =2; %Modulation level:QPSK

sr=250000; %Symbol rate

br=sr.*ml; %bit rate per carrier

gilen =32; %Length of guard interval (points)

%ebn0=50; %Eb/No

%********************Fading initialization***************************

%If you use fading function "sefade", you can intialize all of the

%parameters

%Otherwise you can comment out the following intialization

90

tstp = 1/sr/(fftlen+gilen); %time resolution

%Arrival time for each multipath normalized by tstp

%If you would like to simulate under one path fading model, you have only

%to set direct wave

itau = [0];

%Mean power for each multipath normalized by direct wave

%If you would like to simulate under one path fading model, you have only

%to set direct wave

dlvl = [0];

%Number of waves to generate fading for each muiltpath

%In normal caes, more than six waves are needed to generate Rayleigh Fading

n0 =[6];

%Initial phase of delayed wave

%In this simulation one-path Rayleigh fading is considered

th1 = [0.0];

%Number of fading counter to skip

itnd0 = nd*(fftlen+gilen)*10;

%Initial value of fading counter

%In this simulation one path Rayleigh fading is considered

%Therefore one fading counter is needed

itnd1 = [1000];

91

%Number of direct wave + Number of delayed wave

%In this simulation one path Rayleigh fading is considered

now1=1;

%Maximum Doppler frequency (Hz)

%You can insert your favourite value

fd=320;

%You can decide two modes to simulate fading by changing the variable flat

%flat : flat fading or not

%(1-flat(only amplitude is fluctuated), 0-normal(phase and amplitude are

%fluctuated)

flat=1;

%*******************main loop part***************************

nloop=500; %Number of simulation loops

noe = 0; %number of error data

nod =0; %Number of transmitted data

eop = 0; %Number of error packet

nop =0; %Number of transmitted packet

for iii=1:nloop;

%*******************transmitter********************************

%******************** Data generation **************************

seldata = rand(1,para*nd*ml)>0.5; %rand:built in function

%*********************Serial to parallel conversion**************

92

paradata=reshape(seldata, para, nd*ml); %reshape:built in function

%*****************QPSK Modulation************************

[ich, qch] = qpskmod(paradata, para, nd,ml);

kmod = 1/sqrt(2); %sqrt:built in function

ich1=ich.*kmod;

qch1=qch.*kmod;

%**************IFFT***********************************

x=ich1+qch1.*i;

y=ifft(x); %IFFT:built in function

ich2 = real(y); %real:built in function

qch2 = imag(y); %imag:built in function

%************************Guard Interval Insertion***************

[ich3,qch3]=giins(ich2,qch2,fftlen, gilen, nd);

fftlen2 = fftlen +gilen;

%************************Attenuation Calculation***************

spow=sum(ich3.^2+qch3.^2)/nd./para;

attn=0.5*spow*sr/br*10.^(-ebn0/10);

attn=sqrt(attn);

%*****************Fading Channel****************************

%Generated data are fed into a fading simulator

93

[ifade,qfade]=sefade(ich3,qch3,itau,dlvl,th1,n0,itnd1,now1, length(ich3), tstp,fd,

flat);

%Update fading counter

itnd1=itnd1+itnd0;

%****************Receiver***************************

%*******************AWGN addition************************

[ich4,qch4]=comb(ifade,qfade,attn);

%*****************Guard Interval Removal************************

[ich5,qch5] =girem(ich4, qch4, fftlen2, gilen, nd);

%********************FFT*************************************

rx=ich5+qch5.*i;

ry=fft(rx); %fft:built in function

ich6=real(ry); %real:built in function

qch6=imag (ry); %imag:built in function

%************************demodulation******************************

ich7=ich6./kmod;

qch7= qch6./kmod;

[demodata] =qpskdemod(ich7,qch7, para,nd,ml);

%*******************Parallel to Serial COnversion ********************

demodata1=reshape(demodata,1,para*nd*ml);

94

%**************************Bit Error Rate****************************

%instantaneous number of error and data

noe2 = sum (abs(demodata1-seldata)); %sum:built in function

nod2 = length(seldata); %length: built in function

%cumulative the number of error and data is noe and nod

noe = noe+noe2;

nod = nod+nod2;

%***********************Output Result**************************

ber=noe/nod;

fprintf('%f\t%e\t%e\t\n', ebn0,ber,nloop);

fid =fopen('BERofdmfad.dat','a');

fprintf(fid,'%f\t%e\t%e\t\n', ebn0,ber, nloop);

fclose(fid);

end

95

APPENDIX E

MATLAB CODES TO PLOT OFDM BER PERFORMANCE UNDER AWGN

CHANNEL

%Program to plot OFDM under AWGN channel

i=1

for ebn0=0:2:20

ber(i)=ofdm_awgn(ebn0)

i=i+1

end

ebn0=[0:2:20];

semilogy(ebn0,ber,'b+-');

legend('BER');

xlabel ('E_b/N_0'); ylabel ('BER');

grid on;

96

%Program to plot OFDM under AWGN (theory and simulation) bert=zeros(1,31); for ebn0=0:10 bert(1,ebn0+1)=erfc(sqrt(10^(ebn0/10)))/2; end for ebn0=0:30 bera(1,ebn0+1)=ofdm_awgn(ebn0); ebn1(1,ebn0+1)=ebn0; end semilogy(ebn1,bert,'-k'); hold on; semilogy(ebn1,bera,'-mo'); hold on; title('BER vs E_b/N_0'); legend('AWGN THEORY', 'AWGN '); xlabel ('E_b/N_0'); ylabel ('BER'); grid on;

97

APPENDIX F

MATLAB CODE TO PLOT OFDM UNDER ONE PATH RAYLEIGH

%Program to plot OFDM under one path Rayleigh

i=1

for ebn0=0:5:50

ber(i)=ofdm_fading(ebn0)

i=i+1

end

ebn0=[0:5:50];

semilogy(ebn0,ber,'b+-');

legend('1 path Rayleigh');

Title ('BER vs E_b/N_0');

xlabel ('E_b/N_0'); ylabel ('BER');

grid on;

98

%Program to plot OFDM under one path Rayleigh theory and simulation

for ebn0=0:30

berfad1t(1,ebn0+1)=0.5*(1-(1/sqrt(1+(1/(10^(ebn0/10))))));

berfad1s(1,ebn0+1)=ofdm_fading(ebn0);

ebn1(1,ebn0+1)=ebn0;

end

semilogy(ebn1,berfad1t,'-k');

hold on;

semilogy(ebn1,berfad1s,'-go');

hold on;

legend('1 path Rayleigh theory', '1 path Rayleigh');

title ('BER vs E_b/N_0');

xlabel ('E_b/N_0 (dB)'); ylabel ('BER');

grid on;

99

APPENDIX G

MATLAB CODE FOR SUBFUNCTION

% Function to generate awgn % comb.m function [iout,qout] = comb (idata,qdata,attn) % variables % idata : input i channel data % qdata : input q channel data % iout : output i channel data % qout : output q channel data % attn : attenuation level caused by Eb/No or C/N iout = randn(1, length(idata)).*attn; qout = randn(1, length(qdata)).*attn; iout = iout + idata(1:length(idata)); qout = qout + qdata(1:length(qdata));

100

%Function to insert guard interval into transmission signal %giins.m function [iout, qout]=giins(idata,qdata,fftlen, gilen,nd); %*********************Variables******************************* %idata: Input Ich data %qdata: Input Qch data %iout: Output Ich data %qout: Output Qch data %fftlen : Length of FFT(points) %gilen : Length of guard interval(points) %*************************************************************** idata1 = reshape(idata,fftlen, nd); qdata1 = reshape(qdata,fftlen, nd); idata2 = [idata1(fftlen-gilen+1:fftlen,:); idata1]; qdata2 = [qdata1(fftlen-gilen+1:fftlen,:); qdata1]; iout = reshape (idata2,1, (fftlen+gilen)*nd); qout = reshape (qdata2,1, (fftlen+gilen)*nd);

101

%Function to remove guard interval from received signal %girem.m function [iout,qout] = girem(idata,qdata, fftlen2,gilen, nd); %**************************Variables************************** %idata : Input Ich data %qdata : Input Qch data %iout : Output Ich data %qout : Output Qch data %fftlen2 : Length of FFT (points) %gilen : Length of guard interval (points) %nd : Number of OFDM symbols %************************************************************ idata2=reshape (idata,fftlen2,nd); qdata2=reshape (qdata, fftlen2, nd); iout = idata2 (gilen+1:fftlen2,:); qout = qdata2 (gilen+1:fftlen2,:);