To Study The Phase Noise Effect In

OFDM Based Communication System

A THESIS

submitted by

Ashutosh Maithani

for the award of the degree

of

Master of Technology

Department of Electronics & Communication Engineering

Graphic Era University, Dehradun, India.

August , 2012

ii

DEDICATED TO,

My parents

iii

ACKNOWLEDGEMENTS

I would like to acknowledge the contribution of all those people who have been blessed

to be associated with me. I would like to thank my guide and mentor Er. Navita Sajwan ,

Assistant Professor, Department of Electronics and Communication Engineering, GEU

Dehradun Uttrakhand, for her supervision, knowledge, support and persistent

encouragement during my research work. She steered me through this journey with her

invaluable advice, positive criticism, stimulating discussions and consistent

encouragement.

With a grateful heart, I acknowledge the noble and gentle hand of support lent to me by

Dr. Anamika Bhatia, HOD, Department of Electronics and Communication Engineering,

, GEU Dehradun Uttrakhand, , for her valuable guidance at every step and cooperation to

carry out simulations. Her enthusiasm and engagement in giving guidance and sharing

knowledge cannot be valued.

I also express my deep sense of gratitude to Dr. Rajarshi Mahapatra , Project Coordinator

Department of Electronics and Communication Engineering, GEU Dehradun

Uttrakhand. He provided me continuous help and guidance to complete my dissertation.

I also express my deep sense of gratitude to other staff members of the department have

given me help and valuable advice during this period. My studies would not have been

complete without the help and friendship of colleagues. They will always have a place in

my fond memories.

Date : Ashutosh Maithani

iv

DECLARATION

I certify that,

a) the work contained in this thesis is original and has been done by me under the guidance of my supervisor.

b) the work has not been submitted to any other institute for any degree or diploma. c) I have followed the guidelines provided by the institute in preparing the thesis.

d) I have conformed to the norms and guidelines given in the ethical code of conduct of the institute.

e) whenever I have used materials (data, theoretical analysis, figures, and text) from other sources, I have given due credit to them by citing them in the text of the thesis and giving their details in the references. Further, I have taken permission from the copyright owners of the sources, whenever necessary.

Name of the student

Ashutosh Maithani

v

THESIS CERTIFICATE

This is to certify that the thesis titled TITLE submitted to the Graphic Era University,

Dehradun, by Author, for the award of the degree of Master of Technology (Full

time/Part time), is a bona fide record of the research work done by him under my

supervision. The contents of this thesis, in full or in parts, have not been submitted to any

other Institute or University for the award of any degree or diploma.

Name of the Prof. Dr. Rajarshi Mahapatra Research Guide- Navita Sajwan Designation-Asistant Professor

Department- ECE GEU-Dehradun, 248 002 Place: Dehradun Date:

vi

CERTIFICATE OF APPROVAL

16th Aug. 2012

Certified that the thesis entitled Title submitted by name to Graphic Era University, Dehradun for the award of the degree of Master of Technology has been accepted by the external examiners and that the student has successfully defended the work carried out, in the final examination.

Signature: Name: Er. Navita Sajwan (Supervisor) Signature: Name: Dr. Rajarshi Mahapatra. (Internal examiner) Signature: Name: (External Examiner) Signature: Name: Dr. Anamika Bhatia (Head of the department)

vii

ABSTRACT Orthogonal frequency division multiplexing (OFDM) is being successfully used in many

applications. It was chosen for IEEE 802.11a wireless local area network (WLAN)

standard, and it is being considered for the fourth-generation mobile communication

systems. Along with its many attractive features, OFDM has some principal drawbacks.

Sensitivity to frequency errors and phase noise between the transmitted and received

signals is the most dominant of these drawbacks. In this thesis, phase noise effects on

OFDM based communication systems are investigated under Rayleigh fading

environment. Phase noise has two main effects. First, it causes a random phase variation

common to all sub-carriers. The effects of this common phase error(CPE) are minimized

by employing phase tracking techniques or differential decoding. Second, it introduces

Inter carrier interference (ICI).In OFDM system, when subjected to fading extremely

high signal to noise ratio(SNR) are required to achieve resonable error probability.Coding

becomes obvious choice to achieve higher possible rate in presence of crosstalk,

impulsive and other interferences. This form of OFDM is called coded OFDM

(COFDM). Reed-Solomon codes can compensate these two dimensional errors.

Channel estimation in OFDM based communication system is a technique use to

minimize common phase error(CPE) occurred due to phase noise. Least square with

averaging (LSA) is block-type pilot symbol aided channel estimation technique used to

multiplex reference symbols, so-called pilot symbols, into the data stream. The receiver

estimates the channel state information based on the received, known pilot symbols. The

pilot symbols can be scattered in time and/or frequency direction in OFDM frames.

This thesis analyzed Uncoded, Reed-Solomon coded and Reed-Solomon coded with LSA

channel estimated OFDM based communication system in presence of phase noise by

using MATLAB Simulink. Various Simulink modal of OFDM based communication

system is developed in this thesis.The LSA channel estimation scheme is use to remove

common phase error (CPE) occured due to phase noise and then Reed-Solomon coding is

use to improve BER performance of OFDM system with phase noise.The simulation

performance results of the OFDM system for Rayleigh fading with QPSK modulation is

discuss in this thesis.

viii

ix

TABLE OF CONTENTS

DEDICATION ii

ACKNOWLEDGEMENTS iii

DECLARATION BY THE CANDIDATE iv CERTIFICATE BY THE SUPERVISOR v

CERTIFICATE OF APPROVAL vi

ABSTRACT vii

LIST OF TABLES ix

LIST OF FIGURES x

ABBREVIATIONS xi

NOTATIONS xii

1. INTRODUCTION 1

1.1. MS Word features………………………………….……………….......... 2

1.2. MS Word figures………………………………………………………… 2

1.3. MS Word options………………………………………………………… 2

BRIEF BIO DATA OF THE CANDIDATE

PUBLICATIONS OUT OF THIS WORK

REFERENCES

A. A SAMPLE APPENDIX

x

LIST OF TABLES

TABLE NO.

TITLE PAGE NO.

5.1 Simulation Parameters 52

5.2 Uncoded OFDM with Rayleigh fading in absence of PHN 54 5.3 Uncoded OFDM system with Rayleigh fading at different values

of PHN 56

5.4 Comparison table between R-S coded and uncoded OFDM system at different values of phase noise

59

5.5 Comparison table between R-S coded OFDM and R-S coded with LSA channel Estimated OFDM system

62

xi

LIST OF FIGURES

FIGURE NO.

TITLE PAGE NO.

2.1 Delayed Signals 11

2.2 Representation of a Symbol in a Frequency Selective Channel 11

2.3 Illustration of ISI 12

2.4 Representation of a Symbol in Flat Fading Channel 12

2.5 OFDM Splits a Data Stream into N Parallel Data Streams 13

2.6 Frequency spectrum of OFDM transmission 14

2.7 Carrier signals in an OFDM transmission 15

2.8 OFDM Transmitter 17

2.9 Serial to Parallel conversion 18

2.10 Parallel to Serial conversion 19 2.11 Guard period insertion in OFDM 20 2.12 OFDM Receiver 21

2.13 Constellation Diagram 25

2.14 Constellation Diagram for QPSK 28 2.15 Timing diagram for QPSK 30

3.1 Oscillator Phase Noise 35

3.2 Phase Noise 36

4.1 Channel Estimation 39

4.2 R-S System 43 4.3 R-S codeword 44 4.4 Architecture of a R-S (n – k) Encoder 47

4.5 Architecture of a R-S(n-k) Decoder 48

5.1 Uncoded OFDM System 53

5.2 BER vs. Eb/No plot of uncoded OFDM 54

xii

5.3 Uncoded OFDM with PHN 55

5.4 BER performance curve of uncoded OFDM system at different PHN

57

5.5 R-S coded OFDM system with PHN 58

5.6 Comparision curve between R-S coded and uncoded at PHN=

-70 dBc/Hz

60

5.7 R-S coded with LSA channel estimated OFDM system

61

5.8 Comparison curve between uncoded, R-S coded and , R-S coded with LSA channel Estimated OFDM system at PHN=

-70 dBc/Hz

63

xiii

ABBREVIATIONS

ADSL Asymmetric Digital Subscriber Line

ADC Analog to Digital Converter

BER Bit Error Rate

BPSK Binary Phase Shift Keying

CP Cyclic Prefix

CIR Carrier to Interference Power Ratio

CPE Common Phase Error

CDMA Code Division Multiple Access

DAB Digital Audio Broadcast

DVB-T Digital Video Broadcasting-Terrestrial

DAC Digital To Analog Converter

DSP Digital Signal Processing

DFT Discrete Fourier Transform

DUT Device Under Test

EDGE Enhanced Data Rates for Global Evolution

FFT Fast Fourier Transform

FDM Frequency Division Multiplexing

GMSK Gaussian Minimum Shift Keying

GSM Global System for Mobile Communication

GPRS General packet Radio Service

HDSL High speed Digital Subscriber Line

HDTV High Definition Television

xiv

ICI Inter Carrier Interference

ISI Inter Symbol Interference

IFFT Inverse Fast Fourier Transform

IEEE Institute for Electrical and Electronic Engineers.

IDFT Inverse Discrete Fourier Transform

LSA Least Square With Averaging

MCM Multi Carrier Modulation

MC Multicarrier Communication

NTT Nippon Telephone and Telegraph

OFDM Orthogonal Frequency Division Multiplexing

PSK Phase Shift Keying

PHN Phase Noise

PSD Power Spectral Density

QPSK Quadrature Phase Shift Keying

QAM Quadrature Amplitude Modulation

R&D Research and Development

R-S OR RS Reed Solomon

SNR Signal to Noise Ratio

SIR Signal to Interference Ratio

TACS Total Access Communications system

TDMA Time Division Multiple Access

UMTS Universal Mobile Telecommunication System

VLSI Very Large Scale Integration

WLAN Wireless Local Area Network

xv

xvi

SYMBOLS & NOTATIONS

Ts- Symbol Period

Td- Delay Spread

Bc- Coherence Bandwidth

Bs- Symbol Bandwidth

M- number of points in the constellation

CHAPTER 1

INTRODUCTION

1.1 INTRODUCTION

Orthogonal frequency division multiplexing (OFDM) is successfully used in various

applications, such as European digital audio broadcasting and digital video broadcasting

systems [1,2]. In 1999, the IEEE 802.11a working group chose OFDM for their 5-GHz

band wireless local area network (WLAN) standard, which supports a variable bit rate

from 6 to 54 Mbps. OFDM was also one of the promising candidates for the European

third-generation personal communications system (universal mobile telecommunication

system). However, it was not approved since the code division multiple access(CDMA)

based proposals received more support. OFDM is now being considered for the fourth-

generation mobile communication systems [3]. Therefore, OFDM’s performance in

mobile and fading environments is the topic of many current studies.

Orthogonal Frequency Division Multiplexing (OFDM) is a special form of multi carrier

modulation technique which is used to generate waveforms that are mutually orthogonal.

In an OFDM scheme, a large number of orthogonal, overlapping, narrow band sub-

carriers are transmitted in parallel. These carriers divide the available transmission

bandwidth. The separation of the sub-carriers is such that there is a very compact spectral

utilization. With OFDM, it is possible to have overlapping sub channels in the frequency

domain, thus increasing the transmission rate. In order to avoid a large number of

modulators and filters at the transmitter and complementary filters and demodulators at

the receiver, it is desirable to be able to use modern digital signal processing techniques,

such as fast Fourier transform (FFT). After more than forty years of research and

development carried out in different places, OFDM is now being widely implemented in

high-speed digital communications. OFDM has been accepted as standard in several wire

line and wireless applications. Due to the recent advancements in digital signal

processing (DSP) and very large-scale integrated circuits (VLSI) technologies, the initial

obstacles of OFDM implementations do not exist anymore. In a basic communication

2

system, the data are modulated onto a single carrier frequency. The available bandwidth

is then totally occupied by each symbol. This kind of system can lead to inter-symbol-

interference (ISI) in case of frequency selective channel. The basic idea of OFDM is to

divide the available spectrum into several orthogonal sub channels so that each

narrowband sub channels experiences almost flat fading. The attraction of OFDM is

mainly because of its way of handling the multipath interference at the receiver.

Multipath phenomenon generates two effects

(a) Frequency selective fading and

(b) Intersymbol interference (ISI).

The "flatness" perceived by a narrowband channel overcomes the frequency selective

fading. On the other hand, modulating symbols at a very low rate makes the symbols

much longer than channel impulse response and hence reduces the ISI. Use of suitable

error correcting codes provides more robustness against frequency selective fading. The

insertion of an extra guard interval between consecutive OFDM symbols can reduce the

effects of ISI even more. The use of FFT technique to implement modulation and

demodulation functions makes it computationally more efficient. OFDM systems have

gained an increased interest during the last years. It is used in the European digital

broadcast radio system, as well as in wired environment such as asymmetric digital

subscriber lines (ADSL). This technique is used in digital subscriber lines (DSL) to

provides high bit rate over a twisted-pair of wires.

1.2 HISTORY OF MOBILE WIRELESS COMMUNICATIONS

The history of mobile communication [4,5] can be categorized into 3 periods:

(1) The pioneer era

(2) The pre-cellular era

(3) The cellular era 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

3

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. 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.

The cellular zone 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. 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 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

4

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

[6,7].

1G analog cellular systems were actually 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.

The first commercial analog cellular systems include Nippon Telephone and Telegraph

(NTT) Cellular – Japan, Advanced Mobile Phone Service (AMPS) – US, Australia,

China, Southeast Asia, Total Access Communications system (TACS) - UK, and Nordic

Mobile Telephone (NMT) – Norway, Europe.

2G digital systems use digital radio channels for both voice (digital voice) and digital

control channels. 2G digital systems typically use more efficient modulation

technologies, including Global System for Mobile communications (GSM), which uses a

standard 2-level Gaussian Minimum Shift Keying (GMSK). Digital radio channels offer a

universal data transmission system, which can be divided into many logical channels that

can perform different services. 2G also uses multiple access (or multiplexing)

technologies to allow more customers to share individual radio channels or use narrow

channels to allow more radio channels into a limited amount of radio spectrum band.

The 3 basic types of access technologies used in 2G are:

(1) Frequency division multiple access (FDMA)

(2) Time division multiple access (TDMA)

(3) Code division multiple access (CDMA)

The technologies either reduce the RF channel bandwidth (FDMA), share a radio channel

by assigning users to brief time slot (TDMA), or divide a wide RF channel into many

different coded channels (CDMA). Improvements in modulation techniques and multiple

access technologies amongst other technologies inadvertently led to 2.5G and 3G. For

example, EDGE can achieve max 474 kbps by using 8-PSK with the existing GMSK.

This is 3x more data transfer than GPRS.

5

1.3 GENERATIONS OF TELECOMMUNICATION

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

analog cellular systems were actually 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.

The first commercial analog cellular systems include Nippon Telephone and Telegraph

(NTT) Cellular – Japan, Advanced Mobile Phone Service (AMPS) – US, Australia,

China, Southeast Asia, Total Access Communications system (TACS) - UK, and Nordic

Mobile Telephone (NMT) – Norway, Europe. 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. 2G digital systems typically use more efficient modulation technologies,

including Global System for Mobile communications (GSM), which uses a standard 2-

level Gaussian Minimum Shift Keying (GMSK). 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. 2G also uses multiple access (or multiplexing)

technologies to allow more customers to share individual radio channels or use narrow

channels to allow more radio channels into a limited amount of radio spectrum band. The

3 basic types of access technologies used in 2G are: frequency division multiple access

(FDMA), time division multiple access (TDMA), and code division multiple access

(CDMA). The technologies either reduce the RF channel bandwidth (FDMA), share a

radio channel by assigning users to brief timeslot (TDMA), or divide a wide RF channel

into many different coded channels (CDMA).

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 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.

6

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 probable the 4G

network would be a network which is a combination of different technologies, for

example, current cellular networks, 3G cellular network and wireless LAN, working

together using suitable interoperability protocols.

1.4 MOTIVATION

OFDM is robust in adverse channel conditions and allows a high level of spectral

efficiency. Multiple access techniques which are quite developed for the single carrier

modulations (e.g. TDMA, FDMA) had made possible of sharing one communication

medium by multiple number of users simultaneously. The sharing is required to achieve

high capacity by simultaneously allocating the available bandwidth to multiple users

without severe degradation in the performance of the system. FDMA and TDMA are the

well known multiplexing techniques used in wireless communication systems.

While working with the wireless systems using these techniques, various problems

encountered are

(1) Multi-path fading

(2) Time dispersion which lead ISI

(3) Lower bit rate capacity

(4) Requirement of larger transmit power for high bit rate and

(5) Less spectral efficiency

Disadvantage of FDMA technique is its Bad Spectrum Usage. Disadvantages of TDMA

technique is Multipath Delay spread problem. In a typical terrestrial broadcasting, the

7

transmitted signal arrives at the receiver using various paths of different lengths. Since

multiple versions of the signal interfere with each other, it becomes difficult to extract the

original information.

Orthogonal Frequency Division Multiplexing (OFDM) has recently gained fair degree of

prominence among modulation schemes due to its intrinsic robustness to frequency

selective Multipath fading channels. OFDM system also provides higher spectrum

efficiency and supports high data rate transmission. This is one of the main reasons to

select OFDM a candidate for systems such as Digital Audio Broadcasting (DAB), Digital

Video Broadcasting (DVB), Digital Subscriber Lines (DSL), and Wireless local area

networks (HiperLAN/2), and in IEEE 802.11a, IEEE 802.11g. The focus of future fourth-

generation (4G) mobile systems is on supporting high data rate services such as

deployment of multi-media applications which involve voice, data, pictures, and video

over the wireless networks. At this moment, the data rate envisioned for 4G networks is 1

GB/s for indoor and 100Mb/s for outdoor environments.Orthogonal frequency division

multiplexing (OFDM) is a promising candidate for 4G systems because of its robustness

to the multipath environment.

1.5 RELATED RESEARCH

Due to its many attractive features, OFDM has received much attention in the wireless

communications research communities. Numerous studies have been performed to

investigate its performance and applicability to many different environments. Below are

some of the many studies conducted concerning the effect of frequency errors and Phase

Noise on OFDM systems.

Weinstein and Ebert proposed a modified OFDM system [8] in which the discrete Fourier

Transform (DFT) was applied to generate the orthogonal subcarriers waveforms instead

of the banks of sinusoidal generators. Their scheme reduced the implementation

complexity significantly, by making use of the inverse DFT (IDFT) modules and the

digital-to-analog converters. In their proposed model, baseband signals were modulated

by the IDFT in the transmitter and then demodulated by DFT in the receiver. Therefore,

8

all the subcarriers were overlapped with others in the frequency domain, while the DFT

modulation still assures their orthogonality.

Cyclic prefix (CP) or cyclic extension was first introduced by Peled and Ruiz in 1980 [9]

for OFDM systems. In their scheme, conventional null guard interval is substituted by

cyclic extension for fully-loaded OFDM modulation. As a result, the orthogonality

among the subcarriers was guaranteed. With the trade-off of the transmitting energy

efficiency, this new scheme can result in a phenomenal ISI (Inter Symbol Interference)

reduction. Hence it has been adopted by the current IEEE standards. In 1980, Hirosaki

introduced an equalization algorithm to suppress both inter symbol interference (ISI) and

ICI [10], which may have resulted from a channel distortion, synchronization error, or

phase error. In the meantime, Hirosaki also applied QAM modulation, pilot tone, and

trellis coding techniques in his high-speed OFDM system, which operated in voice-band

spectrum.

Many of the published studies about the frequency errors use two main references.The

first is the study of Pollet on sensitivity of OFDM systems to frequency offset and

Wiener phase noise [11], and the second is the study of Moose on a technique for OFDM

frequency offset correction [12].

Other related studies include the study of Armada on the phase noise and subcarrier

spacing effects on OFDM system’s performance [13], the study of Xiong about the effect

of Doppler frequency shift, frequency offset, and phase noise on OFDM receiver’s

performance [14] and the study of Zhao on the sensitivity of OFDM systems to Doppler

shift and carrier frequency errors [15].

Other related studies include the study of Mohammad Reza Gholami on the phase noise.

In his paper [16] he discussed about the LS Filter approach to suppress phase noise in

OFDM system.

Other related studies include the study of Ana Garcia Armada on the Phase Noise. In the

paper [17] Author Analyzes the performance of OFDM system under phase noise and

its dependence on the no of sub-carriers both in the presence and absence of a phase

correction mechanism.

9

1.6 OBJECTIVE AND OUTLINE OF THESIS

The main objective of this thesis is to compensate the effects of phase noise in OFDM

based communication system and enhanced the performance of the system in terms of

bit error rate (BER) by using R-S coding with LSA channel estimation technique. Some

other objectives are

(1) To analysis the BER Performance of Uncoded OFDM System without considering

phase noise.

(2) To analysis the BER Performance of Uncoded OFDM System at different values of

phase noise.

(3) To analysis the Comparison between Uncoded OFDM and R-S Coded OFDM

System at different values of phase noise .

(4) To analysis the Comparison between R-S Coded OFDM and R-S coded with LSA

Channel Estimated OFDM System at different values of phase noise.

This report is organized as follows:

In Chapter 2, the basics of OFDM, its transmitter and receiver,its advantages and

application are discussed. Digital modulation, quadrature phase-shift keying ,radio

propagation,rayleigh fading and doppler shift are also present in this chapter.

In Chapter 3, phase noise problem in OFDM based communication system is discussed.

Its theortical analysis is also present in this chapter.

In Chapter 4, Reed-Solomon coding and decoding process, least square with averaging

channel estimation technique is discussed.

In Chapter 5, simulation parameters and steps, Simulation results is discussed. Differents

simulink models of OFDM based communication system and results in tabular as well as

graphical form is also present in this chapter .

In Chapter 6, conclude the report and future works are also outline.

10

CHAPTER 2

ORTHOGONAL FREQUENCY DIVISION MULTIPLEXING

2.1 INTRODUCTION

The rapid growth of the applications utilizing digital communication systems increased

the need for high-speed data transmission. New multi-carrier modulation techniques are

being proposed and implemented to keep up with the demand of higher data rates. Of

these multi-carrier techniques, OFDM is the method of choice for high-speed

communication due to its many attractive features. This chapter attempts to justify the

choice of OFDM among other communication techniques.

Orthogonal Frequency Division Multiplexing (OFDM) is a multicarrier transmission

technique, which divides the bandwidth into many carriers, each one is modulated by a

low rate data stream [18, 19]. In term of multiple access technique, OFDM is similar to

FDMA in that the multiple user access is achieved by subdividing the available

bandwidth into multiple channels that are then allocated to users. However, OFDM uses

the spectrum much more efficiently by spacing the channels much closer together. This is

achieved by making all the carriers orthogonal to one another, preventing interference

between the closely spaced carriers.

2.2 FUNDAMENTALS OF OFDM

2.2.1 Multi-path ( Delay-spread or time dispersion )

In general, high data rate means short symbol time compared to the delay spread

(TSYMBOL<TDELAY) . Delay-spread greatly affects the communication system and the

signal might not be recovered at the receiver.

This section addresses the effects of delay spread which occurs as the surfaces between a

transmitter and a receiver reflect a transmitted signal. The receiver obtains the transmitted

signals with random phase offsets and this causes random signal fades as reflected signals

destructively or constructively affect each other [20], as seen in Figure (2.1).

11

Figure (2.1)-Delayed Signals [21]

When TSYMBOL< TDELAY (BC<BS) as in Figure (2.2), the signal faces frequency selective

fading and this causes time dispersion. The effect of this is intersymbol interference (ISI),

where the energy of one symbol leaks into another symbol, as can be viewed from Figure

(2.3). As a result, the bit error rate (BER) increases, this in turn degrades the

performance. ISI is one of the biggest problems of digital communication and OFDM

deals with this problem very effectively.

(a) (b)

Figure (2.2)-Representation of a Symbol in a Frequency Selective Channel

12

(a) Time domain (b) Frequency domain

Figure (2.3)-Illustration of ISI [22]

A way to deal with frequency selective fading is to decrease the data rate and thus change

the frequency selective fading to flat fading. The desired scheme is illustrated in Figure

(2.4). OFDM systems mitigate the ISI by changing the frequency selective fading channel

to flat fading channel as discussed below

(a) (b)

13

Figure (2.4)-(a) Time Domain Representation, (b) Frequency Domain

Representation of a Symbol in Flat Fading Channel.

OFDM modulates user data onto tones by using either phase shift keying (PSK) or

quadrature amplitude modulation (QAM). An OFDM system takes a high data rate

stream, splits it into N parallel data streams and transmits them simultaneously. As can be

observed from Figure (2.5), each of these parallel data streams has a rate of R N, where R

is the original data rate. The data streams are modulated by different carriers and

combined together by inverse fast Fourier transform (IFFT) to generate the time-domain

signal to be transmitted [20]

Figure(2.5)-OFDM Splits Data Stream into N Parallel Data Streams[23]

By creating a slower data stream, the symbol duration becomes larger than the channel’s

impulse response. In this way, each carrier is subject to flat fading

2.2.2 Orthogonality

OFDM is simply defined as a form of multi-carrier modulation where the carrier spacing

is carefully selected so that each sub carrier is orthogonal to the other sub carriers. Two

signals are orthogonal if their dot product is zero. That is, if you take two signals multiply

them together and if their integral over an interval is zero, then two signals are orthogonal

14

in that interval. Orthogonality can be achieved by carefully selecting carrier spacing, such

as letting the carrier spacing be equal to the reciprocal of the useful symbol period. As the

sub carriers are orthogonal, the spectrum of each carrier has a null at the centre frequency

of each of the other carriers in the system. This results in no interference between the

carriers, allowing them to be spaced as close as theoretically possible. Mathematically,

suppose we have a set of signals ψ then

(2.1)

The signals are orthogonal if the integral value is zero over the interval [a a+T], where T

is the symbol period. Since the carriers are orthogonal to each other the nulls of one

carrier coincides with the peak of another sub carrier. As a result it is possible to extract

the sub carrier of interest.

Figure (2.6)-Frequency spectrum of OFDM transmission

OFDM transmits a large number of narrowband sub channels. The frequency range

between carriers is carefully chosen in order to make them orthogonal each another. In

15

fact, the carriers are separated by an interval of 1/T, where T represents the duration of an

OFDM symbol. The frequency spectrum of an OFDM transmission is illustrated in

Figure (2.6). This Figure indicates the spectrum of carriers significantly over laps over

the other carrier. This is contrary to the traditional FDM technique in which a guard band

is provided between each carrier. Each sinc of the frequency spectrum in the Figure (2.6)

corresponds to a sinusoidal carrier modulated by a rectangular waveform representing the

information symbol.

Figure (2.7)-Carrier signals in an OFDM transmission

It is easily notice that the frequency spectrum of one carrier exhibits zero-crossing at

central frequencies corresponding to all other carriers. At these frequencies, the

intercarrier interference is eliminated, although the individual spectra of subcarriers

overlap. It is well known that orthogonal signals can be separated at the receiver by

correlation techniques. The receiver acts as a bank of demodulators, translating each

carrier down to baseband, the resulting signal then being integrated over a symbol period

to recover the data. If the other carriers beat down to frequencies which, in the time

domain means an integer number of cycles per symbol period (T), then the integration

16

process results in a zero contribution from all these carriers. The waveforms of some of

the carriers in an OFDM transmission are illustrated in Figure (2.7).

2.3 INTERSYMBOL AND INTERCARRIER INTERFERENCE

In a multipath environment, a transmitted symbol takes different times to reach the

receiver through different propagation paths. From the receiver‘s point of view, the

channel introduces time dispersion in which the duration of the received symbol is

stretched. Extending the symbol duration causes the current received symbol to overlap

previous received symbols and results in intersymbol interference (ISI).

In OFDM, ISI usually refers to interference of an OFDM symbol by previous OFDM

symbols. For a given system bandwidth the symbol rate for an OFDM signal is much

lower than a single carrier transmission scheme. For example for a single carrier BPSK

modulation, the symbol rate corresponds to the bit rate of the transmission. However for

OFDM the system bandwidth is broken up into N subcarriers, resulting in a symbol rate

that is N times lower than the single carrier transmission. This low symbol rate makes

OFDM naturally resistant to effects of Inter-Symbol Interference (ISI) caused by

multipath propagation. Multipath propagation is caused by the radio transmission signal

reflecting off objects in the propagation environment, such as walls, buildings,

mountains, etc. These multiple signals arrive at the receiver at different times due to the

transmission distances being different. This spreads the symbol boundaries causing

energy leakage between them.

In OFDM, the spectra of subcarriers overlap but remain orthogonal to each other. This

means that at the maximum of each sub-carrier spectrum, all the spectra of other

subcarriers are zero. The receiver samples data symbols on individual sub-carriers at the

maximum points and demodulates them free from any interference from the other

subcarriers. Interference caused by data symbols on adjacent sub-carriers is referred to

intercarrier interference (ICI).

The orthogonality of subcarriers can be viewed in either the time domain or in frequency

domain. From the time domain perspective, each subcarrier is a sinusoid with an integer

number of cycles within one FFT interval. From the frequency domain perspective, this

17

corresponds to each subcarrier having the maximum value at its own center frequency

and zero at the center frequency of each of the other subcarriers. The orthogonality of a

subcarrier with respect to other subcarriers is lost if the subcarrier has nonzero spectral

value at other subcarrier frequencies. From the time domain perspective, the

corresponding sinusoid no longer has an integer number of cycles within the FFT

interval. ICI occurs when the multipath channel varies over one OFDM symbol time.

When this happens, the Doppler shift on each multipath component causes a frequency

offset on the subcarriers, resulting in the loss of orthogonality among them.This situation

can be viewed from the time domain perspective, in which the integer number of cycles

for each subcarrier within the FFT interval of the current symbol is no longer maintained

due to the phase transition introduced by the previous symbol. Finally, any offset

between the subcarrier frequencies of the transmitter and receiver also introduces ICI to

an OFDM symbol.

2.4 OFDM TRANSMITTER

A block diagram of the OFDM transmitter module is presented in Figure (2.8). Each of

the blocks is explained in detail in the following subsections.

Figure (2.8)-OFDM Transmitter

2.4.1 Channel Coding

A sequential binary input data stream is first encoded by the channel coder. Error

correction coding is important for OFDM systems used for mobile communications.

18

When channel coding is used to improve its performance, OFDM is referred to as coded

OFDM (COFDM).

2.4.2 Signal Mapping

A large number of modulation schemes are available allowing the number of bits

transmitted per carrier per symbol to be varied. Digital data is transferred in an OFDM

link by using a modulation scheme on each subcarrier. A modulation scheme is a

mapping of data words to a real (In phase) and imaginary (Quadrature) constellation, also

known as an IQ constellation. For example 256-QAM (Quadrature Amplitude

Modulation) has 256 IQ points in the constellation constructed in a square with 16 evenly

spaced columns in the real axis and 16 rows in the imaginary axis.

The number of bits that can be transferred using a single symbol corresponds to

where M is the number of points in the constellation, thus 256-QAM transfers

8 bits per symbol. Increasing the number of points in the constellation does not change

the bandwidth of the transmission, thus using a modulation scheme with a large number

of constellation points, allows for improved spectral efficiency. For example 256-QAM

has a spectral efficiency of 8 b/s/Hz, compared with only 1 b/s/Hz for BPSK. However,

the greater the number of points in the modulation constellation, the harder they are to

resolve at the receiver.

2.4.3 Serial to Parallel and Prallel to Serial conversion

19

Figure (2.9)-Serial to Parallel conversion

Data to be transmitted is typically in the form of a serial data stream. In OFDM, each

symbol transmits a number of bits and so a serial to parallel conversion stage is needed to

convert the input serial bit stream to the data to be transmitted in each OFDM symbol.

The data allocated to each symbol depends on the modulation scheme used and the

number of subcarriers. At the receiver the reverse process takes place, with the data from

the subcarriers being converted back to the original serial data stream.

20

Figure (2.10)-Parallel to Serial conversion

2.4.4 Inverse Fast Fourier Transform

The OFDM message is generated in the complex baseband. Each symbol is modulated

onto the corresponding subcarrier using variants of phase shift keying (PSK) or different

forms of quadrature amplitude modulation (QAM).The data symbols are converted from

serial to parallel before data transmission. The frequency spacing between adjacent

subcarriers is Nπ/2, where N is the number of subcarriers. This can be achieved by using

the inverse discrete Fourier transform (IDFT), easily implemented as the inverse fast

Fourier transform (IFFT) operation [26].

The OFDM baseband sub-carrier is

(2.3)

Where 푓 is the 푘 sub-carrier frequency An OFDM symbol consists of N modulated

sub-carriers. The OFDM signal not including a cyclic prefix is given by [24]

(2.4)

Where is the complex data symbol and NT is the OFDM symbol duration. The

sub-carriers in Eq. (2.3) and (2.4) have frequencies

(2.5) In the sense that ensures orthogonality

(2.6)

21

If the signal s (t) is sampled with a sampling period of T, the following is obtained:

(2.7)

This Eq. (2.7) is IDFT { } and was proposed by [25]. As can be seen from Eq. (2.7), a

baseband OFDM transmission symbol is an N-point complex modulation sequence. It is

composed of N complex sinusoids, which are modulated with z (k)

2.4.5 Guard Period

The effect of ISI on an OFDM signal can be reduced by the addition of a guard period to

the start of each symbol. This guard period is a cyclic copy that extends the length of the

symbol waveform. Each subcarrier, in the data section of the symbol, (i.e. the OFDM

symbol with no guard period added, which is equal to the length of the IFFT size used to

generate the signal) has an integer number of cycles.

Figure (2.11)-Guard period insertion in OFDM

Figure (2.11) shows the insertion of a guard period. The total length of the symbol is TS=

TG+TFFT, where TS is the total length of the symbol in samples, TG is the length of the

guard period in samples, and TFFT is the size of the IFFT used to generate the OFDM

signal. In addition to protecting the OFDM from ISI, the guard period also provides

protection against time-offset errors in the receiver.

A Guard time is introduced at the end of each OFDM symbol in form of cyclic prefix to

prevent Inter Symbol Interference (ISI).

22

The Guard time is cyclically extended to avoid Inter-Carrier Interference (ICI) - integer

number of cycles in the symbol interval. Guard Time > Multipath Delay Spread, to

guarantee zero ISI & ICI.

2.5 OFDM RECEIVER

A block diagram of the OFDM RECEIVER module is presented in Figure (2.12).

Figure (2.12)-OFDM Receiver

2.5.1 Removing Guard Interval and FFT Processing

At the OFDM receiver end, the first step is to remove the guard interval to obtain the

information portion of the symbol for further processing. Next, the time domain samples

are transformed into the frequency domain by the FFT process. This also makes it

possible to recover the OFDM frequency tones.

2.5.2 Decoding

The next step in the receiver is the time or frequency differential decoding. Following the

differential decoding, the inverse mapping of each received complex modulation value

into a corresponding N-ary symbol is accomplished.

2.6 ADVANTAGES OF OFDM

23

(1) OFDM Is less sensitive to sample timing offsets than single carrier systems.

(2) It Provides good protection against co channel interference and impulsive

parasitic noise.

(3) Eliminates ISI through use of a cyclic prefix.

(4) By dividing the channel into narrowband flat fading sub channels, OFDM is more

resistant to frequency selective fading than single carrier systems are. i.e.

robustness to frequency selective fading channels.

(5) Channel equalization becomes simpler than by using adaptive equalization

techniques with single carrier systems.

(6) Using adequate channel coding and interleaving one can recover symbols lost due

to the frequency selectivity of the channel.

(7) It is possible to use maximum likelihood decoding with reasonable complexity.

(8) OFDM is computationally efficient by using FFT techniques to implement the

modulation and demodulation functions.

2.7 APPLICATIONS OF OFDM

(1) OFDM is used in European Wireless LAN Standard – HiperLAN/2.

(2) OFDM is used in IEEE 802.11a and 802.11g Wireless LANs.

(3) OFDM is used in IEEE 802.16 or WiMax Wireless MAN standard.

(4) OFDM is used in IEEE 802.20 or Mobile Broadband Wireless Access (MBWA)

standard.

(5) OFDM is used in Digital Audio Broadcasting (DAB).

(6) OFDM is used in Digital Video Broadcasting (DVB) & HDTV.

(7) OFDM is used in Used for wideband data communications over mobile radio

channels such as

(7.1) High-bit-rate Digital Subscriber Lines (HDSL at 1.6Mbps).

(7.2) Asymmetric Digital Subscriber Lines (ADSL up to 6Mbps).

(7.3) Very-high-speed Digital Subscriber Lines (VDSL at 100 Mbps).

(7.4) ADSL and broadband access via telephone network copper wires.

(8) OFDM is used in Point-to-point and point-to-multipoint wireless applications .

24

(9) OFDM is under consideration for use in 4G Wireless systems.

2.7 MODULATION

In communication, modulation is the process of varying a periodic waveform, in order to

use that signal to convey a message over a medium. Normally a high frequency

waveform is used as a carrier signal. The three key parameters of a sine wave are

frequency, amplitude, and phase, all of which can be modified in accordance with a low

frequency information signal to obtain a modulated signal. There are 2 types of

modulations

(1) Analog modulation.

(2) 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.

2.8.1 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. The aim of digital modulation is to transfer a digital bit stream over

an analog band pass channel or a radio frequency band. The changes in the carrier signal

are chosen from a finite number of alternative symbols. Digital modulation schemes have

greater capacity to convey large amounts of information than analog modulation

schemes. There are three major classes of digital modulation techniques used for

transmission of digitally represented data

(1) Amplitude-shift Keying (ASK).

(2) Frequency-shift keying (FSK).

(3) Phase-shift keying (PSK).

25

All convey data by changing some aspect of a base-band signal, the carrier wave, (usually

a sinusoid) in response to a data signal. In the case of PSK, the phase is changed to

represent the data signal. There are two fundamental ways of utilizing the phase of a

signal in this way

(1) 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 or

(2) 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)

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

2.9 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) [27]. 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.

A convenient way to represent PSK schemes is on a constellation diagram (as shown in

figure (2.13) 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.

26

Figure (2.13)-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 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. Notably absent from these various schemes is 8-PSK. This is because its error-rate

performance is close to that of 16-QAM it is only about 0.5 dB better but its data rate is

only three-quarters that of 16-QAM. Thus 8-PSK is often omitted from standards and, as

seen above, schemes tend to 'jump' from QPSK to 16-QAM (8-QAM is possible but

difficult to implement).

Any digital modulation scheme uses a finite number of distinct signals to represent digital

data. PSK uses a finite number of phases,each assigned a unique pattern of binary bits.

27

Usually, each phase encodes an equal number of bits. Each pattern of bits forms the

symbol that is represented by the particular phase. The demodulator, which is designed

specifically for the symbol set used by the modulator, determines the phase of the

received signal and maps it back to the symbol it represents, thus recovering the original

data. This requires the receiver to be able to compare the phase of the received signal to a

reference signal such a system is termed coherent (and referred to as CPSK).

Alternatively, instead of using the bit patterns to set the phase of the wave, it can instead

be used to change it by a specified amount. The demodulator then determines the

changes in the phase of the received signal rather than the phase itself. Since this scheme

depends on the difference between successive phases, it is termed differential phase-shift

keying (DPSK). DPSK can be significantly simpler to implement than ordinary PSK

since there is no need for the demodulator to have a copy of the reference signal to

determine the exact phase of the received signal (it is a non-coherent scheme). In

exchange, it produces more erroneous demodulations. The exact requirements of the

particular scenario under consideration determine which scheme is used.

Applications of PSK

Owing to PSK's simplicity, particularly when compared with its competitor quadrature

amplitude modulation, it is widely used in existing technologies.

The wireless LAN standard, IEEE 802.11b-1999, uses a variety of different PSKs

depending on the data-rate required. At the basic-rate of 1 Mbit/s, it uses DBPSK

(differential BPSK). To provide the extended-rate of 2 Mbit/s, DQPSK is used. In

reaching 5.5 Mbit/s and the full-rate of 11 Mbit/s, QPSK is employed, but has to be

coupled with complementary code keying. The higher-speed wireless LAN standard,

IEEE 802.11g-2003 has eight data rates: 6, 9, 12, 18, 24, 36, 48 and 54 Mbit/s. The 6 and

9 Mbit/s modes use OFDM modulation where each sub-carrier is BPSK modulated. The

12 and 18 Mbit/s modes use OFDM with QPSK. The fastest four modes use OFDM with

forms of quadrature amplitude modulation.

Because of its simplicity BPSK is appropriate for low-cost passive transmitters, and is

used in RFID standards such as ISO/IEC 14443 which has been adopted for biometric

28

passports, credit cards such as American Express's ExpressPay, and many other

applications. IEEE 802.15.4 (the wireless standard used by ZigBee) also relies on PSK.

IEEE 802.15.4 allows the use of two frequency bands: 868–915 MHz using BPSK and at

2.4 GHz using OQPSK.

For determining error-rates mathematically, some definitions will be needed

퐸 = Energy-per-bit

퐸 = Energy-per-symbol = k퐸 with k bits per symbol

푇 = Bit duration

푇 = Symbol duration

N0 / 2 = Noise power spectral density (W/Hz)

푃 = Probability of bit-error

푃 = Probability of symbol-error

Q(x) will give the probability that a single sample taken from a random process with

zero-mean and unit-variance Gaussian probability density function will be greater or

equal to x. It is a scaled form of the complementary Gaussian error function

Q(x) = ퟏ √ퟐ흅

∫ 풆 풕ퟐ/ퟐ 풅풕풙 = ퟏퟐ

풆풓풇풄 풙√ퟐ

, x≥0 (2.8)

The error-rates quoted here are those in additive white Gaussian noise (AWGN).

QPSK digital modulation schemes for OFDM system is use in this thesis . Hence a study

on QPSK has been carried out in next section.

2.9.1 Quadrature Phase Shift Keying (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.

29

Fig (2.14)-Constellation Diagram for QPSK

Figure (2.14) shows the constellation diagram for QPSK with Gray coding. Each adjacent

symbol only differs by one bit. Sometimes known as quaternary or quadric phase 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. Analysis shows that QPSK

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. 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.

The implementation of QPSK is more general than that of BPSK and also indicates the

implementation of higher-order PSK. Writing the symbols in the constellation diagram in

terms of the sine and cosine waves used to transmit them:

30

(2.9)

This yields the four phase‘s π/4, 3π/4, 5π/4 and 7π/4 as needed. This results in a two-

dimensional signal space with unit basis functions.

∅ퟏ(풕) = √ퟐ/√푻풔 퐜퐨퐬 (2흅풇풄 풕)

∅ퟐ(풕) = √ퟐ/√푻풔 퐬퐢퐧 (2흅풇풄 풕) (2.10)

The first basis function is used as the in-phase component of the signal and the second as

the quadrature component of the signal. Hence, the signal constellation consists of the

signal-space 4 points ± 퐄퐬√ퟐ

, ± 퐄퐬√ퟐ

The factors of 1/2 indicate that the total power is split equally between the two carriers.

QPSK can be viewed as two independent BPSK signals.

Bit error rate

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:

퐏퐛 = 퐐( √ ퟐ퐄퐛퐍퐎

) (2.11)

However, in order to achieve the same bit-error probability as BPSK, QPSK uses

twice the power (since two bits are transmitted simultaneously). The symbol error rate is

given by:

푷풔 = ퟏ − (ퟏ − 푷풃)ퟐ = 2푸 √푬풃푵푶

−푸ퟐ √푬풃푵푶

(2.12)

31

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

probability of symbol error may be approximated.

푷푺 ≈ 2푸 √푬풃푵푶

(2.13)

The modulated signal is shown below for a short segment of a random binary data-

stream. The two carrier waves are a cosine wave and a sine wave, as indicated by the

signal-space analysis above. Here, the odd-numbered bits have been assigned to the in-

phase component and the even-numbered bits to the quadrature component (taking the

first bit as number 1)

The total signal ,the sum of the two components is shown at the bottom. Jumps in phase

can be seen as the PSK changes the phase on each component at the start of each bit-

period.

Figure (2.15)-Timing diagram for QPSK

In figure (2.15) binary data stream is shown on the time axis. The two signal components

with their bit assignments are shown the top and the total, combined signal at the bottom.

Note the abrupt changes in phase at some of the bit-period boundaries.

The binary data that is conveyed by this waveform is: 1 1 0 0 0 1 1 0.

The odd bits, highlighted here, contribute to the in-phase component: 1 1 0 0 0 1 1 0

The even bits, highlighted here, contribute to the quadrature-phase component:

32

1 1 0 0 0 1 1 0

2.10 RADIO PROPAGATION

In an ideal radio channel, the received signal would consist of only a single direct path

signal, which would be a perfect reconstruction of the transmitted signal. However in a

real channel, the signal is modified during transmission in the channel. The received

signal consists of a combination of attenuated, reflected, refracted, and diffracted replicas

of the transmitted signal [28]. On top of all this, the channel adds noise to the signal and

can cause a shift in the carrier frequency if the transmitter or receiver is moving (Doppler

Effect). Understanding of these effects on the signal is important because the

performance of a radio system is dependent on the radio channel characteristics

2.10.1 ATTENUATION

Attenuation is the drop in the signal power when transmitting from one point to another.

It can be caused by the transmission path length, obstructions in the signal path, and

multipath effects. Any objects that obstruct the line of sight signal from the transmitter to

the receiver can cause attenuation. Shadowing of the signal can occur whenever there is

an obstruction between the transmitter and receiver. It is generally caused by buildings

and hills, and is the most important environmental attenuation factor. Shadowing is most

severe in heavily built up areas, due to the shadowing from buildings. However, hills can

cause a large problem due to the large shadow they produce. Radio signals diffract off the

boundaries of obstructions, thus preventing total shadowing of the signals behind hills

and buildings. However, the amount of diffraction is dependent on the radio frequency

used, with low frequencies diffracting more than high frequency signals. Thus high

frequency signals, especially, Ultra High Frequencies (UHF), and microwave signals

require line of sight for adequate signal strength. To overcome the problem of shadowing,

transmitters are usually elevated as high as possible to minimize the number of

obstructions

2.11 FADING EFFECTS

33

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

channels refers to mathematical models for the distortion that a carrier modulated

telecommunication signal experiences over certain propagation media. Small scale fading

also known as multipath induced fading is due to multipath propagation. Fading results

from the superposition of transmitted signals that have experienced differences in

attenuation, delay and phase shift while travelling from the source to the receiver.

2.11.1 Rayleigh Fading

Rayleigh fading with AWGN is use in this thesis , so in this section we will discuss

about the Rayleigh fading

Rayleigh fading channel are useful models of real-world phenomena in wireless

communication. These phenomena include multipath scattering effects, time dispersion,

and Doppler shifts that arise from relative motion between the transmitter and receiver. It

is a statistical model for the effect of a propagation environment on a radio signal, such as

that used by wireless devices

Rayleigh fading models assume that the magnitude of a signal that has passed through

such a transmission medium (also called a communications channel) will vary randomly,

or fade, according to a Rayleigh distribution.

Rayleigh fading is viewed as a reasonable model for troposphere and ionospheric signal

propagation as well as the effect of heavily built-up urban environments on radio signals.

Rayleigh fading is most applicable when there is no dominant propagation along a line of

sight between the transmitter and receiver.

2.12 DOPPLER SHIFTS

When a wave source and a receiver are moving relative to one another the frequency of

the received signal will not be the same as the source. When they are moving toward each

other the frequency of the received signal is higher than the source, and when they are

moving away each other the frequency decreases. This is called the Doppler Effect. An

34

example of this is the change of pitch in a car‘s horn as it approaches then passes by. This

effect becomes important when developing mobile radio systems. The amount the

frequency changes due to the Doppler Effect depends on the relative motion between the

source and receiver and on the speed of propagation of the wave. The Doppler shift in

frequency can be written

∆풇 = ± 풇풗풄퐜퐨퐬휽 (2.14)

Where f is the change in frequency of the source seen at the receiver, f is the frequency of

the source, v is the speed difference between the source and receiver, c is the speed of

light and is the angle between the source and receiver. For example: Let

f = 1 GHz, and v = 60km/hr (16.67m/s) and = 0 degree, then the Doppler shift will be

풇 = ퟏퟎퟗ . ퟏퟔ.ퟔퟕퟑ×ퟏퟎퟖ

= ퟓퟓ.ퟓ 푯풛 (2.15)

This shift of 55Hz in the carrier will generally not affect the transmission. However,

Doppler shift can cause significant problems if the transmission technique is sensitive to

carrier frequency offsets (for example OFDM) or the relative speed is very high as is the

case for low earth orbiting satellites.

35

CHAPTER 3

PHASE NOISE PROBLEM IN OFDM SYSTEM

3.1 PHASE NOISE

Phase noise is the frequency domain representation of rapid, short-term, random

fluctuations in the phase of a waveform, caused by time domain instabilities ("jitter").

Generally speaking radio frequency engineers speak of the phase noise of an oscillator,

whereas digital system engineers work with the jitter of a clock.

Historically there have been two conflicting yet widely used definitions for phase noise.

The definition used by some authors defines phase noise to be the Power Spectral Density

(PSD) of a signal's phase the other one is based on the PSD of the signal itself. Both

definitions yield the same result at offset frequencies well removed from the carrier. At

close-in offsets however, characterization results strongly depends on the chosen

definition. Recently, the IEEE changed its official definition to ∅(푛) = 푠∅/2 where 푠∅ is

the (one-sided) spectral density of a signal's phase fluctuations.

An ideal oscillator would generate a pure sine wave. In the frequency domain, this would

be represented as a single pair of delta functions (positive and negative conjugates) at the

oscillator's frequency, i.e., all the signal's power is at a single frequency. All real

oscillators have phase modulated noise components. The phase noise components spread

the power of a signal to adjacent frequencies, resulting in noise sidebands. Oscillator

phase noise often includes low frequency flicker noise and may include white noise.

Consider the following noise free signal v (t) = Acos(2πf0t).

Phase noise is added to this signal by adding a stochastic process represented by φ to the

signal as v(t) = Acos(2πf0t + φ(t)).

Phase noise is a type of cyclostationary noise and is closely related to jitter. A particularly

important type of phase noise is that produced by oscillators.

36

Phase noise (∅(푛)) is typically expressed in units of dBc/Hz, representing the noise

power relative to the carrier contained in a 1 Hz bandwidth centered at a certain offsets

from the carrier. For example, a certain signal may have a phase noise of -80 dBc/Hz at

an offset of 10 kHz and -95 dBc/Hz at an offset of 100 kHz. Phase noise can be measured

and expressed as single sideband or double sideband values, but as noted earlier, the

IEEE has adapted as its official definition, one-half the double sideband PSD.

Phase noise cannot be removed by filtering without also removing the oscillation signal.

And since it is predominantly in the phase, it cannot be removed with a limiter. so phase

noise removing is a major problem in OFDM.

37

Figure (3.1)-Oscillator phase noise

Figure (3.1) shows that how the oscillator phase noise is introduced in the OFDM system.

A local oscillator produces common phase error (CPE). The signal transmit at transmitter

side have phase rotation at receiver side.

Phase noise can be measured using a spectrum analyzer if the phase noise of the device

under test (DUT) is large with respect to the spectrum analyzer's local oscillator.

Spectrum analyzer based measurement can show the phase-noise power over many

decades of frequency from 1 Hz to 10 MHz. The slope with offset frequency in various

offset frequency regions can provide clues as to the source of the noise.

38

Figure (3.2)-Phase Noise

Figure (3.2) shows the OFDM carriers in frequency domain and the effect of phase noise

on these carriers.

The phase noise in the local oscillator of transmitter and receiver affects on the

orthogonality between the adjacent subcarriers. This introduce two main effects First, it

causes a random phase variation common to all sub-carriers. Second, it introduces ICI.

This ICI degrades the bit error rate (BER) performance of the system.

Based on the model defined in [11], the degradation D in SNR, i.e., the required increase

in SNR to compensate for the phase noise is

퐃퐝퐁 ≅ ퟏퟏퟔ 퐥퐧 ퟏퟎ

(ퟒ훑퐍 훃퐑) 퐄퐒퐍퐎

(3.1)

Since R= N/T = NR , where N is the total number of sub-carriers and 푅 is the subcarrier

symbol rate, Equation (3.1) can be rewritten as

푫풅푩 ≅ ퟏퟏퟔ 풍풏 ퟏퟎ

(ퟒ흅 휷푹풔

) 푬푺푵푶

(3.2)

3.2 THEORTICAL ANALYSIS OF PHASE NOISE

A theoretical analysis of phase noise effects in OFDM signals can be found in [29]. The

complex envelope of the transmitted OFDM signal for a given OFDM symbol sampled

with sampling frequency 푓 = B

S(n)=∑ 풁풌 푵 ퟏ풌 ퟎ 풆풋(ퟐ흅/푵)풌풏 (3.3)

with This symbol is actually extended with a Time Guard in order to cope with multipath

delay spread, For the sake of simplicity, we will not consider this prefix since it is

eliminated in the receiver. Assuming that the channel is flat, the signal is only affected by

phase noise ∅(푛)

r(n)= S(n) .풆풋 ∅(풏) (3.4)

39

The received signal is Orthogonal Frequency Division Demultiplexed (OFDD) by means

of a Discrete Fourier Transform. In order to separate the signal and noise terms, let us

suppose that ∅(푛) is smaller so that

퐞퐣∅퐧 ≈ ퟏ + 퐣∅(퐧) (3.5)

In this case, the demultiplexed signal is

퐘퐊 ≈ 풁풌 + 풋푵

∑ 풁풓 ∑ ∅(푛) 푵 ퟏ풏 ퟎ

푵 ퟏ풓 ퟎ 풆풋

ퟐ흅푵 (풓 풌)풏

퐘퐊 = 풁풌 + 풆풌 (3.6)

Thus we have an error term 푒 for each sub-carrier which results from some

combination of all of them and is added to the use signal.

If r=k: Common Phase Error

퐣퐍

∑ 퐙퐫 ∑ ∅(퐧) = 퐣. 퐙퐤. ∅퐍 ퟏ퐧 ퟎ

퐍 ퟏ퐫 ퟎ (3.7)

If r≠k : Inter-Carrier Interference

퐣퐍

∑ 퐙퐫 ∑ ∅(퐧) 퐞퐣ퟐ훑퐍 (퐫 퐤)퐧퐍 ퟏ

퐧 ퟎ퐍 ퟏ퐫 ퟎ (3.8)

40

CHAPTER 4

METHODOLOGY USED TO COMPENSATE PHASE NOISE

4.1 LEAST SQUARE WITH AVERAGING CHANNEL ESTIMATION

TECHNIQUE

A wideband radio channel is normally frequency selective and time variant. For an

OFDM mobile communication system, the channel transfer function at different

subcarriers appears unequal in both frequency and time domains. Therefore, a dynamic

estimation of the channel is necessary. Pilot-based approaches are widely used to

estimate the channel properties and correct the received signal.

There are two types of pilot-based channel estimation

(1) Block-type pilot channel estimation

(2) Comb-type pilot channel estimation

Figure (4.1)-Channel Estimation ([30])

In Figure (4.1) the first kind of pilot arrangement is block-type pilot arrangement. The

pilot signal assigned to a particular OFDM block, which is sent periodically in time-

domain. This type of pilot arrangement is especially suitable for slow-fading radio

channels. Because the training block contains all pilots, channel interpolation in

41

frequency domain is not required. Therefore, this type of pilot arrangement is relatively

insensitive to frequency selectivity.

The second kind of pilot arrangement is comb-type pilot arrangement. The pilot

arrangements are uniformly distributed within each OFDM block. Assuming that the

payloads of pilot arrangements are the same, the comb-type pilot arrangement has a

higher re-transmission rate. Thus the comb-type pilot arrangement system is provides

better resistance to fast-fading channels. Since only some sub-carriers contain the pilot

signal, the channel response of non-pilot sub-carriers will be estimated by interpolating

neighboring pilot sub-channels. Thus the comb-type pilot arrangement

is sensitive to frequency selectivity when comparing to the block-type pilot arrangement

system.

LS with averaging channel estimation technique is use in this thesis to remove common

phase error. It is a block-type channel estimation technique. In this channel estimation

technique we consider the data carried by the k subcarrier of an OFDM symbol is

X = c + p where c is the information symbol with varience σ and p is the

superimposed pilot symbol with varience σ defined

훈 = 훔퐜ퟐ / 훔퐜ퟐ + 훔퐩ퟐ (4.1)

is the ratio of information symbol power to total transmitted symbol power. In the

superimposed pilot scheme, the power ratio η can take values 0<η < 1whereas in a

conventional scheme η = 1 when information symbols are transmitted ( X = c ) and

η = 0 for pilot transmission ( X = p ) Consider a frequency-selective channel with

memory L, and channel tap value vector h=[ h … … . h ]. The received OFDM sample

y is given by

퐲퐧 = ∑ 퐡퐥 퐱퐧 퐥 퐞퐣∅(풏) + 퐰퐧퐋 ퟏ퐥 ퟎ (4.2)

where ∅(푛) is the time domain phase error due to phase noise introduced at the receiver

and w is the channel noise which is gaussian distributed N(0,σ ) in Eq.(4.2)

42

x=[x , x , x … . . x ] is the IFFT of the data symbol X=[X , X , X … … X ]. The

post FFT signal at the receiver (FFT of y , 0 ≤ n ≤ N − 1) is

퐘퐊 = 퐇퐊 퐗퐊 퐒ퟎ + ∑ 퐇퐥 퐗퐥 퐒퐥 퐤 + 퐖퐤퐍 ퟏ퐥 ퟎ (4.3)

Where H and S are the channel frequency response and intercarrier interference (ICI),

respectively. The ICI term 푆 is a function of the phase noise ∅(푛) given by

푺풍 = ퟏ푵

∑ 풆풋ퟐ흅풏풍/푵 풆∅(풏) 푵 ퟏ풏 ퟎ , 풍=0……N-1 (4.4)

From Eq. (4.3) it can be seen that the phase noise cause common phase error as well as

ICI. The received post-FFT signal given in (4.3) can be written as

퐘퐊 = 퐇퐊 퐂퐊 퐒ퟎ + 퐇퐊 퐏퐊 퐒ퟎ + 퐖퐤 + 퐈퐤 (4.5)

Where I is the ICI term . the effect of S on the post-FFT data symbol C′ s is a common

phase rotation. The least squares estimation with averaging scheme treats the contribution

of the unknown information symbol C in the received signal (post-FFT) Y as noise.

This means that the term H C S is the noise term in Eq. (4.5) thus Y can be

expressed as

퐘퐊 = 퐇퐊 퐏퐊 퐒ퟎ + 퐙퐤 (4.6)

Where Z = H C S + W + I is the total noise The least squares (LS) estimate of the

phase rotation term S based on k subcarrier signal is

푺풐⋀(k) = 풀풌푯푲푷푲 (4.7)

Substitute Eq. (4.5) in Eq. (4.7)

푺풐⋀(k) = 푺ퟎ + 푪풌 푺ퟎ푷풌

+ 푽풌푯풌 푷풌

(4.8)

43

Where V = I + W In Eq. (4.8), S⋀(k) is the initial estimate obtained only using

k post-FFT signal. In a frequency selective channel, different subcarriers experience

different fading according to the channel conditions. In the conventional techniques of

phase estimation, if a dedicated pilot subcarrier falls in deep fade, the phase estimation

accuracy would be adversely affected. However, in superimposed pilot scheme since

pilots are present in all the subcarriers, it is advantageous to use subcarriers that have

better channel response for phase estimation instead of using all the subcarriers. This can

be effectively implemented as the channel state information is present at the receiver

(Since the preamble can be used to estimate the channel). Thus we can use subcarrier

selection for phase estimation as follows:

Compute Ω = {|퐻 | | 0 ≤ 푖 ≤ 푁 − 1} and select set of Indices I={퐾 ,퐾 , …퐾 }

corresponding to the 푁 highest elements of Ω. Some assumptions about the noise terms

in Eq. (4.8) can be made in the presence of above mentioned subcarrier selection. The

second and the third terms in Eq. (4.8) are noise terms and it is valid to assume that the

variance of third term in Eq. (4.8),

is negligible compared to the variance of the

second term due to following reasons.

(i) With the subcarrier selection the lower values of |H | are eliminated and

(ii) The variance of the transmitted symbols C , which is contributing towards the

noise term, is higher than the sum of variances of the ICI term and channel

noise,V . With this assumption, it can be noted that the variance of the noise

term in Eq. (4.8) is approximately constant irrespective of channel and the

subcarrier.

Since variance of the noise terms is constant over the subcarriers, an equal weight

averaging scheme is proposed to improve the estimate of S as

푺⋀ = ퟏ푵ퟎ

∑ 푺풐⋀(퐤)풌∈푰 (4.9)

Substituting for 푆⋀(k) in Eq. (4.9) gives

푺풐⋀ = 푺ퟎ + ퟏ푵ퟎ

∑ 푪풌 푺ퟎ푷풌풌∈푰 + ퟏ

푵ퟎ ∑ 푽풌

푯풌 푷풌풌∈푰 (4.10)

= 푺ퟎ + 푺ퟎ휶 + 휷 (4.11)

44

Here α = ∑ ∈ β = ∑

∈

And 푆 훼 + 훽 denotes the total estimation error.

4.2 REED-SOLOMON CODING

Reed-Solomon codes are block-based error correcting codes with a wide range of

applications in digital communications and storage. Reed-Solomon codes are used to

correct errors in many systems including:

(1) Storage devices (including tape, Compact Disk, DVD, barcodes, etc).

(2) Wireless or mobile communications (including cellular telephones, microwave

links, etc).

(3) Satellite communications.

(4) Digital television / DVB.

(5) High-speed modems such as ADSL, xDSL, etc.

An R-S code was invented by Irving S. Reed and Gustave Solomon. They described a

systematic way of building codes that could detect and correct multiple random symbol

errors. By adding t check symbols to the data, an R-S code can detect any combination of

up to t erroneous symbols, and correct up to ⌊t/2⌋ symbols. In Reed-Solomon coding,

source symbols are viewed as coefficients of a polynomial

over a finite field. The original idea was to create n code symbols from k source symbols

by oversampling at n > k distinct points, transmit the sampled points, and use

interpolation techniques at the receiver to recover the original message.

A typical system is shown here:

45

Figure (4.2)-R-S System

4.2.1 Properties of Reed-Solomon Codes

Reed Solomon codes are a subset of BCH codes and are linear block codes. A Reed-

Solomon code is specified as R-S (n,k) with s-bit symbols. This means that the encoder

takes k data symbols of s bits each and adds parity symbols to make an n symbol

codeword. There are n-k parity symbols of s bits each. A Reed-Solomon decoder can

correct up to t symbols that contain errors in a codeword, where 2t = n-k.

Figure (4.3) shows a typical Reed-Solomon codeword (this is known as a Systematic

code because the data is left unchanged and the parity symbols are appended):

Figure (4.3)-R-S codeword

For example a popular Reed-Solomon code is R-S (15, 11) with 4-bit symbols. Each

codeword contains 15 code word bytes, of which 11 bytes are data and 4 bytes are parity.

For this code:

n = 15, k = 11, s = 4 , 2t = 4, t = 2

The decoder can correct any 2 symbol errors in the code word: i.e. errors in up to 2 bytes

anywhere in the codeword can be automatically corrected.

Given a symbol size s, the maximum codeword length (n) for a Reed-Solomon code is n

= 2s – 1

For example, the maximum length of a code with 4-bit symbols (s=4) is 15 bytes.

Symbol error

46

One symbol error occurs when 1 bit in a symbol is wrong or when all the bits in a symbol

are wrong. for example R-S (15,11) can correct 2 symbol errors. In the worst case, 2 bit

errors may occur, each in a separate symbol (byte) so that the decoder corrects 2 bit

errors. In the best case, 2 complete byte errors occur so that the decoder corrects 2 x 4 bit

errors.

Decoding

Reed-Solomon algebraic decoding procedures can correct errors and erasures. An erasure

occurs when the position of an erred symbol is known. A decoder can correct up to t

errors or up to 2t erasures. Erasure information can often be supplied by the demodulator

in a digital communication system, i.e. the demodulator "flags" received symbols that are

likely to contain errors.

When a codeword is decoded, there are three possible outcomes:

(1) If 2s + r < 2t (s errors, r erasures) then the original transmitted code word will always

be recovered,

(2) Otherwise the decoder will detect that it cannot recover the original code word and

indicate this fact.

(3) OR the decoder will mis-decode and recover an incorrect code word without any

indication

Coding Gain

The advantage of using Reed-Solomon codes is that the probability of an error remaining

in the decoded data is (usually) much lower than the probability of an error if Reed-

Solomon is not used. This is often described as coding gain

4.2.2 Reed-Solomon Encoding and Decoding Process

(1) Encoding Process

The amount of processing "power" required to encode and decode Reed-Solomon codes

is related to the number of parity symbols per codeword. A large value of t means that a

47

large number of errors can be corrected but requires more computational power than a

small value of t. In digital communication systems that are both bandwidth-limited and

power-limited, error-correction coding (often called channel coding) can be used to save

power or to improve error performance at the expense of bandwidth [31]. The R-S

encoding and decoding require a considerable amount of computation and arithmetical

operations over a finite number system with certain properties, i.e. algebraic systems,

which in this case is called fields. R-S’s initial definition focuses on the evaluation of

polynomials over the elements in a finite field (Galois field GF) [32]. The k information

symbols that form the message to be encoded as one block can be represented by a

polynomial M(x) of order k – 1, so that:

푴(풙) = 푴풌 ퟏ 풙풌 ퟏ + ………푴ퟏ풙 + 푴ퟎ (4.12)

where each of the coefficients M ,…….. M , M is an m-bit message symbol, that is an

element of GF(2 ). M is the first symbol of the message. To encode the message, the

message polynomial is first multiplied by X and the result is divided by the generator

polynomial, g(x). Division by g(x) produces a quotient q(x) and a remainder r(x), where

r(x) is of degree up to n – k– 1.Thus

퐌(퐱) × 퐱퐧 퐤

퐠(퐱)퐫(퐱)퐠(퐱) +

퐫(퐱)퐠(퐱) (4.13)

Having produced r(x) by division, the transmitted code word T(x) can then be formed by

combining M(x) and r(x) as follows

퐓(퐱) = 퐌(퐱) × 퐱퐧 퐤 + 퐫(퐱)

= 퐌퐤 ퟏ 퐱퐧 ퟏ + ⋯ +퐌ퟎ 퐱퐧 퐤 + 퐫퐧 퐤 ퟏ + ⋯ +퐫ퟎ (4.14)

Which shows that the code word is produced in the required systematic form. Adding the

remainder, r(x), ensures that the encoded message polynomial will always be divisible by

the generator polynomial without remainder. This can be seen by multiplying Eq. (4.13)

by g(x)

M(x)× 퐱퐧 퐤 = 퐠(퐱) × 퐪(퐱) + 퐫(퐱) (4.15)

48

and rearranging

M(x)× 퐱퐧 퐤 + 퐫(퐱) = 퐠(퐱) × 퐪(퐱) (4.16)

Here we, note that the left-hand side is the transmitted code word, T(x), and that the

right-hand side has g(x) as a factor. Also, because the generator polynomial. The code

generator polynomial takes the form

g(x)= (x+휶풃) (x+ 휶풃 ퟏ)………..(x+휶풃 ퟐ풕 ퟏ) (4.17)

Eq. (4.17), has been closer to consist of a number of factors, each of these is also a factor

of the encoded message polynomial and will divide it without remainder. Thus, if this is

not true for the received message, it is clear that one or more errors have occurred [33].

To visualize hardware that implements Eq. (4.13), one must understand the operations

M(x)× x and r(x). As known, for systematic encoding, the information symbols must

be placed as the higher power coefficients.

So means that information symbols toward the higher powers of x, from n

– 1 down n – k. The remaining positions from power n – k – 1 to 0 fill with zeros.

Consider, for example, the same polynomial as above:

(4.18)

Multiplying the above equation by yields

(4.19)

The second term of Eq. (4.13), r(x) is the remainder when it divides polynomial

by the polynomial g(x). Therefore, it needs designing a circuit that

performs two operations: a division and a shift to a higher power of x. Linear-feedback

shift registers enable one to easily implement both operations. Figure (4.4) shows a

general diagram of the encoder for Reed-Solomon (n,k) code. The main design task is to

49

implement the GF( ) multiplication and addition circuits, apart from some control

circuitry or logic. It can add any two elements from the GF( ) field by modulo 2

adding their binary notations, which resembles the XOR hardware operation [34].

Figure (4.4)-Architecture of a R-S (n – k) Encoder

(2) Decoding Process

A general architecture for decoding Reed-Solomon codes is shown in the Figure (4.5)

Figure (4.5)-Architecture of a R-S(n-k) Decoder

50

Here

C(x) Received codeword

Syndromes

Λ(x) Error locator polynomial

Error locations

Error magnitudes

Recovered code word

The received codeword C(x) is the original (transmitted) codeword plus errors:

C(x) = + e(x) A Reed-Solomon decoder attempts to identify the position and

magnitude of up to t errors (or 2t erasures) and to correct the errors or erasures.

Peterson decoder

Peterson developed a practical decoder based on syndrome decoding. Peterson decoder

contains the following processes,

Syndrome decoding

The transmitted message is viewed the coefficients of a polynomial M(x) that is divisible

by a generator polynomial g(x)

퐌(퐱) = ∑ 퐌퐢퐤 ퟏ퐢 ퟎ 퐱퐢 (4.20)

퐠(퐱) = ∏ (퐱 + 훂퐢)퐛 ퟐ퐭 ퟏ 퐢 ퟏ (4.21)

where 훼 is a primitive root. Since M(x) is divisible by generator g(x), it follows that

M(α )=0, i=1, 2,….n-k

The transmitted polynomial is corrupted in transit by an error polynomial e(x) to produce

the received polynomial C(x).

51

C(x) = M(x) + e(x) (4.22)

e(x)=∑ 퐞퐢퐱퐢퐧−ퟏ퐢=ퟎ (4.23)

where ei is the coefficient for the i power of x. Coefficient ei will be zero if there is no

error at that power of x and nonzero if there is an error. If there are ν errors at distinct

powers ik of x, then

e(x)= ∑ 퐞퐢퐤퐱퐢퐤퐧 ퟏ

퐢 ퟎ (4.24)

The goal of the decoder is to find ν, the positions i and the error values at those

positions. The syndromes s are defined as

퐬퐣 = 퐂(훂퐣) + 퐞(훂퐣) = ퟎ + 퐞(훂퐣) = 퐞(훂퐣) , 퐣 = ퟏ,ퟐ, … . .퐧 − 퐤

= ∑ 퐞퐢퐤훂퐣 퐢퐤퐯

퐤 ퟏ (4.25)

The advantage of looking at the syndromes is that the message polynomial drops outs

Error locators and error values

For convenience, define the error locators X and error values Y as

X = α , Y = e

Then the syndromes can be written in terms of the error locators and error values as

퐬퐣 = ∑ 퐘퐤 퐯퐤 ퟏ 퐗퐤

퐣 (4.26)

The syndromes give a system of n-k ≥ 2ν equations in 2ν unknowns, but that system of

equations is nonlinear in the X and does not have an obvious solution. However, if the

X were known (see below), then the syndrome equations provide a linear system of

52

equations that can easily be solved for the Yk error values

⎣⎢⎢⎢⎢⎢⎡ 퐗ퟏ

ퟏ 퐗ퟐퟏ … … … . .퐗퐯ퟏ

퐗ퟐퟏ 퐗ퟐퟐ … … … … .퐗퐯ퟐ ...

퐗ퟏ퐧 퐤 퐗ퟐ퐧 퐤 … …퐗퐯퐧 퐤⎦⎥⎥⎥⎥⎥⎤

⎣⎢⎢⎢⎢⎡퐘ퟏ퐘ퟐ...퐘퐯⎦⎥⎥⎥⎥⎤

=

⎣⎢⎢⎢⎢⎡퐒ퟏ퐒ퟐ...

퐒퐧 퐤⎦⎥⎥⎥⎥⎤

(4.27)

Error locator polynomial

Peterson found a linear recurrence relation that gave rise to a system of linear equations.

Solving those equations identifies the error locations. Define the Error locator polynomial

Λ(x) as

Λ(x) = ∏ (ퟏ − 풙풗풌 ퟏ 퐗퐤) = ퟏ + 횲ퟏ풙ퟏ + 횲ퟐ 풙ퟐ + … … … …횲풗풙풗 (4.28)

The zeros of Λ(x) are the reciprocals X

Λ(푿풌ퟏ) = 0

Λ(푿풌ퟏ) =ퟏ + 횲ퟏ푿풌

ퟏ + 횲ퟐ 푿풌ퟐ + … … … …횲풗푿풌

풗 =0 (4.29)

Multiply both sides by Yk X and it will still be zero

풀풌 푿풌풋 풗Λ(푿풌

ퟏ)= 풀풌 푿풌풋 풗 + 횲ퟏ풀풌 푿풌

풋 풗푿풌ퟏ + 횲ퟐ 풀풌 푿풌

풋 풗 푿풌ퟐ

… . +횲풗풀풌 푿풌풋 풗푿풌

풗 =0 (4.30)

= 풀풌 푿풌풋 풗 +횲ퟏ풀풌 푿풌

풋 풗 ퟏ +횲ퟐ 풀풌 푿풌풋 풗 ퟐ +………+ 횲풗풀풌 푿풌

풋

=0 (4.31) ∑ 풀풌 푿풌

풋 풗풗풌 ퟏ + 횲ퟏ ∑ 풀풌 푿풌

풋 풗 ퟐ 풗푲 ퟏ + … … … … + 횲풗 ∑ 풀풌 푿풌

풋 풗풌 ퟏ

= ퟎ (4.32)

Which reduces to

53

퐬퐣 퐯 + 횲ퟏ 퐬퐣 퐯 ퟏ + … … … … . +횲풗 ퟏ 퐬퐣 ퟏ + 횲풗 퐬퐣 = 0 (4.33)

퐬퐣 횲풗+ 퐬퐣 ퟏ횲풗 ퟏ + … … . . 퐬퐣 퐯 ퟏ 횲ퟏ + = − 퐬퐣 퐯 (4.44)

Now have system of linear equations that can be solved for the coefficients Λi of the error

location polynomial

⎣⎢⎢⎢⎢⎡풔ퟏ 풔ퟐ … . . 풔풗풔ퟐ 풔ퟑ … 풔풗 ퟏ.

.

.풔풗 풔풗 ퟏ … 풔ퟐ풗 ퟏ⎦

⎥⎥⎥⎥⎤

⎣⎢⎢⎢⎢⎡횲풗횲풗 ퟏ

.

.

.횲ퟏ ⎦

⎥⎥⎥⎥⎤

=

⎣⎢⎢⎢⎢⎡ −풔풗 ퟏ− 풔풗 ퟐ

.

.

.− 풔풗 풗⎦

⎥⎥⎥⎥⎤

(4.45)

Obtain the error locations from the error locator polynomial

Use the coefficients Λi found in the last step to build the error location polynomial. The

roots of the error location polynomial can be found by exhaustive search. The error

locators (and hence the error locations) can be found from those roots. Once the error

locations are known, the error values can be determined and corrected.

54

CHAPTER 5

SIMULATION RESULTS AND DISCUSSION

5.1 SIMULATION PARAMETERS AND STEPS

This chapter presents simulation of an OFDM communication system with phase noise ,

operating under Rayleigh channel conditions. The Simulation parameters of an OFDM

system are shown in Table (5.1)

Table (5.1)-Simulation Parameters

PARAMETERS VALUE

Modulation type QPSK

FFT length nFFT 128

Number of data subcarriers 102

Number of guard and pilot carriers 22

Doppler Shift 200 Hz

Frequency offset 100 Hz

Samples per frame 44

R-S code rate 0.73

SIMULATION’S STEPS

(1) Generate the information bits randomly.

(2) Encode the information bits using a R-S encoder.

(3) Use QPSK to convert the binary bits 0 and 1, into complex signals.

(4) Insert pilot training bits for channel estimation.

(5) Perform serial to parallel conversion.

(6) Use IFFT to Generate OFDM signals, zero padding has been done before IFFT.

(7) Use parallel to serial convertor to transmit signal serially.

55

(8) Introduce phase noise.

(9) Introduce noise to simulate channel errors.

(10)At the receiver side, perform reverse operation to decode the received sequence.

(11)Estimate the channel by using LSA technique.

(12)Calculate BER and plot it.

5.2 BER PERFORMANCE OF UNCODED OFDM SYSTEM WITHOUT

CONSIDERING PHASE NOISE

Figure (5.1)-Uncoded OFDM System

Figure(5.1) shows the MATLAB Simulink model of uncoded OFDM System. Bernoulli

Binary has been used as a signal generator and samples per frame=44. Rayleigh fading

has been used as a channel fading and AWGN used as a channel Noise. Maximum

OFDM Transmitter

OFDM Receiver

BER Multipath Channeland AWGN

.

BER

To Workspace

QPSK Mapping

QPSK Demapping

guard intervalinsertion

. S/P

P/S

OFDM BasebandDemodulator

Remove Zero & CP

OFDM BasebandModulator

Add Zero & CP

BERCalculation

.

RemoveZero

Selector

Mul tipathRayleigh Fading

0.03363

Display2

BernoulliBinary

AWGN

56

dopper shift=200 Hz and sample time = ( 8e-5)/180. On simulating this model the

following Results has been obtained.

Table (5.2)-Uncoded OFDM with Rayleigh fading in absence of PHN

SNR 0 2 4 6 8 10 12 14 16 18 20

BER of uncoded OFDM without PHN

.2818 .2111 .1488 .0995 .0643 .0423 .0261 .0158 .0104 .0070 .0042

Table (5.2) shows the BER performance of uncoded OFDM system at different values of

SNR (Eb/No).

57

Figure (5.2)-BER vs. Eb/No plot of uncoded OFDM

Figure (5.2) shows the graphical representation of BER performance of uncoded OFDM.

This is the BER plot of OFDM system when effect of phase noise and frequency offset is

not considered.

5.3 BER PERFORMANCE OF UNCODED OFDM SYSTEM AT DIFFERENT

VALUES OF PHASE NOISE

Figure (5.3) shows the MATLAB Simulink model of uncoded OFDM system with

phase noise. Bernoulli Binary is use as a signal generator.

0 2 4 6 8 10 12 14 16 18 2010

-3

10-2

10-1

100

Eb/No

BER

BER vs Eb/No plot for rayleigh fading in OFDM system

Uncoded OFDM without PHN

58

Figure (5.3)-Uncoded OFDM with PHN

Here also Rayleigh fading used as a channel fading and AWGN used as a channel Noise.

Frequency offset is fixed to 100Hz .On simulation of this model at different values of

phase noise following results has been obtained.

Table (5.3)-Uncoded OFDM system with Rayleigh fading at different values of PHN

OFDM Transmitter

OFDM Receiver

BER Multipath Channeland AWGN

BER

To Workspace

QPSK Mapping

QPSK Demapping

.

. S/P

P/S

OFDM BasebandDemodulator

Remove Zero & CP

OFDM BasebandModulator

Add Zero & CP

SERCalculation

.

RemoveZero

Selector

PhaseNoise

PhaseNoise

MultipathRayleigh Fading

0.3492

Display2

Bernoul l iBinary

AWGN

59

SNR 0 2 4 6 8 10 12 14 16 18 20

BER AT PHN=

-90 dBc/Hz

.3502 .2729 .2030 .1431 .0951 .0630 .0389 .0240 .0143 .0078 .0048

BER AT PHN=

-80 dBc/Hz

.3509 .2731 .2035 .1435 .0957 .0636 .0395 .0244 .0150 .0084 .0054

BER AT PHN=

-70 dBc/Hz

.3510 .2735 .2040 .1440 .0961 .0642 .0400 .0251 .0153 .0091 .0064

BER AT PHN=

-60

dBc/Hz

.3577 .2822 .2111 .1518 .1029 .0690 .0430 .0274 .0176 .0103 .0070

BER AT PHN=

-55

dBc/Hz

.3692 .2968 .2284 .1670 .1237 .0847 .0548 .0369 .0246 .0170 .0119

BER AT PHN=

-50

dBc/Hz

.4070 .3438 .2825 .2326 .1914 .1567 .1286 .1083 .0970 .0861 .0777

BER AT PHN=

-45

.4984 .4547 .4193 .3839 .3622 .3399 .3277 .3173 .3074 .3025 .2982

60

dBc/Hz

Table(5.3) shows that, uncoded OFDM system without phase noise have better BER

performance in comparatively with uncoded OFDM system with phase noise.On

increasing the value of phase noise in OFDM system, its BER performance degrade

respectively.The reason behind it is that due to phase noise, common phase error(CPE)

occurred in the OFDM system and this breaks the orthogonallity of the OFDM symbols

and produce inter carrier interference (ICI).

Table (5.4) also shows that, BER performance of uncoded OFDM system at PHN =

-70 dBc/Hz, -80 dBc/Hz, -90 dBc/Hz have approximately same. So ,at the simulation

parameters shown in Table (5.1), PHN= -70 dBc/HZ is considered as the optimum value

of phase noise. It means, effect of phase noise on OFDM system is consider negligible at

the PHN< -70 dBc/Hz .This limit may varied on varying the simulation parameters

especially the guard interval, number of OFDM sub-carriers and frequency offset.

61

Figure (5.4)-BER performance curve of uncoded OFDM system at different PHN

Figure (5.4) shows the graphical representation of BER performance of uncoded OFDM

system at different values of phase noise.The effect of phase noise may de reduced by

using some methods ,who have already disccus in previous chapters.

0 2 4 6 8 10 12 14 16 18 2010

-3

10-2

10-1

100

Eb/No

BER

BER vs Eb/No plot for OFDM system with different phase noise at frequency offset=100Hz

Uncoded OFDM without PHNcurve at PHN= -70 dBc/Hz curve at PHN= -60 dBc/Hzcurve at PHN= -55 dBc/Hzcurve at PHN= -50 dBc/Hz curve at PHN= -45 dBc/Hz

62

5.4 COMPARISON ANALYSIS BETWEEN UNCODED OFDM SYSTEM AND

REED-SOLOMON CODED OFDM SYSTEM AT DIFFERENT VALUES OF

PHASE NOISE

Figure (5.5) shows the MATLAB Simulink model of coded OFDM System. In this

model Reed-Solomon coding having code rate of 0.73 is use as a channel coding. QPSK

mapping is use as a symbol mapping. In Reed-Solomon coding, code rate is the ratio of

message length (K) and codeword length (N). Here K=11 and N=15 is use to achieve

code rate of 0.73, Rayleigh fading is use as a channel fading and AWGN used as a

channel noise.

Figure (5.5)-R-S coded OFDM system with PHN

BER

OFDM Transmitter

OFDM Receiver

BER Multipath Channeland AWGN

BER1

To Workspace1 BER

To Workspace

QPSK Mapping

QPSK Demapping

.

.

BERCalculation

S/P

P/S

OFDM BasebandDemodulator

Remove Zero & CP

OFDM BasebandModulator

Add Zero & CP

BERCalculation

RS(15,11) Decoder

RS(15,11) Encoder

RemoveZero

Selector1

Selector

PhaseNoise

PhaseNoise Multipath

Rayleigh Fading

0.06007

Display2

0.0569

Display1

Bernoull iBinary

AWGN

63

On simulation of this model at different values of phase noise following Results has been

obtained.

Table (5.4)-Comparison table between R-S coded and uncoded OFDM system at

different values of phase noise

SNR

(dB)

0 2 4 6 8 10 12 14 16 18 20

BI

T E

RR

OR

R

ATE

OFDM without PHN

.2818 .2111 .1488 .0995 .0643 .0423 .0261 .0158 .0104 .0070 .0042

OFDM with PHN= -70 dBc/Hz

.3510 .2735 .2040 .1440 .0961 .0642 .0400 .0251 .0153 .0091 .0064

OFDM with PHN= -60 dBc/Hz

.3577 .2822 .2111 .1518 .1029 .0690 .0430 .0274 .0176 .0103 .0070

OFDM with PHN= -55 dBc/Hz

.3692 .2968 .2284 .1700 .1237 .0847 .0548 .0369 .0246 .0170 .0119

OFDM with PHN= -50 dBc/Hz

.4070 .3438 .2825 .2326 .1914 .1567 .1286 .1083 .0970 .0861 .0777

OFDM with PHN= -45 dBc/Hz

.4984 .4547 .4193 .3839 .3622 .3399 .3277 .3173 .3074 .3025 .2982

OFDM with RS coding at PHN=

-70 dBc/Hz

.3656 .2811 .2115 .1516 .0983 .0603 .0328 .0201 .0094 .0037 .0025

OFDM with RS coding at PHN=

-60 dBc/Hz

.3745 .2962 .2192 .1587 .1057 .0646 .0371 .0217 .0122 .0041 .0025

64

OFDM with RS coding at PHN=

-55 dBc/Hz

.3882 .3123 .2381 .1767 .1299 .0800 .0513 .0348 .0185 .0092 .0046

OFDM with RS coding at PHN=

-50 dBc/Hz

.4251 .3654 .2986 .2441 .2013 .1609 .1309 .1076 .0946 .0790 .0679

OFDM with RS coding at PHN=

-45 dBc/Hz

.5138 .4746 .4401 .4081 .3831 .3619 .3490 .3344 .3224 .3169 .3116

From the Table (5.4) it has been analyzed that, R-S coding gives the better BER

performance on high values of SNR but it give worst performance on PHN ≥ -45

dBc/Hz.

Figure (5.6) shows the comparison between uncoded OFDM system verses R-S coded

OFDM system at PHN= -70 dBc/Hz.

65

Figure (5.6)-Comparison curve between R-S coded and uncoded OFDM at PHN=-70

dBc/Hz Figure (5.6) shows that the performance of the OFDM system is improved by using R-S

code especially when SNR(Eb/No) is increased to more than 10 dB. It is clear from

Figure (5.6) that an R-S coded OFDM gains 2dB improvement at the BER level of 0.009

when PHN= -70 dBc/Hz.

0 2 4 6 8 10 12 14 16 18 2010

-3

10-2

10-1

100

Eb/No

BER

BER vs Eb/No performance plot for OFDM system with phase noise= -70dBc/Hz and frequency offset=100 Hz

curve for uncoded OFDM system curve for RS coded OFDM system

66

5.5 COMPARISON ANALYSIS BETWEEN R-S CODED OFDM AND R-S

CODED WITH LSA CHANNEL ESTIMATED OFDM SYSTEM AT DIFFERENT

VALUES OF PHASE NOISE

Figure (5.7)-R-S coded with LSA channel estimated OFDM system Figure (5.7) shows MATLAB Simulink model of coded OFDM system. In this model

Reed-Solomon coding having code rate of 0.73 is used as a channel coding. Here pilot

training bits are inserted with OFDM symbols at transmitter end for channel estimation,

these bits are separated at the receiver end. Number of data subcarrier used =102 and

BER

OFDM Transmitter

OFDM Receiver

Multipath Channeland AWGN

BER1

To Workspace1

QPSK Mapping

QPSK Demapping

.

.

LSAChannelEstimator

CPECompensation S/P

P/S

OFDM BasebandDemodulator

Remove Zero & CP

OFDM BasebandModulator

Add Zero & CP

BERCalculation

Training

RS(15,11) Decoder

RS(15,11) Encoder

RemoveZero

Selector1

PhaseNoise

PhaseNoise

MultipathRayleigh Fading

0.01983

Display1

Bernoull iBinary

AWGN

67

numbers of pilot subcarriers=22. On simulating this model the following results has been

obtained.

Table (5.5)-Comparison table between R-S coded OFDM and R-S coded with LSA channel Estimated OFDM system

SNR

(dB)

0 2 4 6 8 10 12 14 16 18 20

BIT

ER

RO

R

RA

TE

OFDM with RS coding at PHN= -70 dBc/Hz

.3656 .2811 .2115 .1516 .0983 .0603 .0328 .0201 .0094 .0037 .0025

OFDM with RS coding at PHN= -60 dBc/Hz

.3745 .2962 .2192 .1587 .1057 .0646 .0371 .0217 .0122 .0041 .0025

OFDM with RS coding at PHN= -55 dBc/Hz

.3882 .3123 .2381 .1767 .1299 .0800 .0513 .0348 .0185 .0092 .0046

OFDM with RS coding at PHN= -50 dBc/Hz

.4251 .3654 .2986 .2441 .2013 .1609 .1309 .1076 .0946 .0790 .0679

OFDM with RS coding at PHN=-45 dBc/Hz

.5138 .4746 .4401 .4081 .3831 .3619 .3490 .3344 .3224 .3169 .3116

OFDM with RS coding +LSA channel estimation at PHN=

-70 dBc/Hz

.2397 .1716 .1188 .0715 .0408 .0233 .0147 .0055 .0024 .0022 .0007

OFDM with RS coding +LSA channel estimation at

.2470 .1826 .1252 .0769 .0491 .0263 .0171 .0080 .0024 .0021 .0007

68

PHN=

-60 dBc/Hz

OFDM with RS coding +LSA channel estimation at PHN=

-55 dBc/Hz

.2688 .2013 .1452 .0955 .0599 .0382 .0243 .0125 .0058 .0042 .0025

OFDM with RS coding +LSA channel estimation at PHN=

-50 dBc/Hz

.3220 .2628 .2147 .1683 .1399 .1129 .0963 .0805 .0717 .0615 .0579

OFDM with RS coding +LSA channel estimation at PHN=

-45 dBc/Hz

.4536 .4157 .3905 .3669 .3469 .3343 .3243 .3157 .3096 .3063 .3045

Table (5.5) shows that with the application of least square with averaging channel

estimation technique on R-S coded OFDM system, its BER performance is improved

this is because LSA channel estimation technique compensate the effect of phase noise

and save the orthogonality between the sub-carriers.

It has been studied in previous section that R-S coding is not so effective on higher values

of phase noise and it give the worst result on or above the PHN= -45 dBc/Hz. it is

observed by the comparision of Table (5.4) and Table (5.5) that LSA channel estimation

technique on R-S coded OFDM system work efficiently on or above the PHN= -45

dBc/Hz.

69

Figure (5.8)-Comparison curve between uncoded, R-S coded and , R-S coded

with LSA channel Estimated OFDM system at PHN= -70 dBc/Hz Figure (5.8) shows the comparative analysis between uncoded, R-S coded and R-S coded

with LSA channel estimated OFDM system. It also shows that LSA channel estimation

technique on R-S coded OFDM system work effectively on low as well as high values of

SNR(Eb/No).

It has been analyzed from Figure (5.8) that at SNR=12 dB and PHN= -70 dBc/Hz, BER

of uncoded OFDM is= 0.0400, BER of R-S coded OFDM is= 0.0328 and BER of R-S

coded with LSA channel estimated OFDM system is= .0147. It means that BER

0 2 4 6 8 10 12 14 16 18 2010

-4

10-3

10-2

10-1

100

Eb/No

BER

BER vs Eb/No performance plot for OFDM with phase noise= -70dBc/Hz and frequency offset=100Hz

curve for uncoded OFDM curve for RS coded OFDMcurve for RS coded with LSA channel estimated OFDM

70

performance of the R-S coded OFDM system is improved when LSA channel estimated

technique use with it.

It is clear from Figure (5.8) that an R-S coded with LSA channel estimated OFDM gains

3dB improvement at the BER level of 0.009 with respect to the R-S coded OFDM, and

gains 5dB improvement at the BER level of 0.009 with respect to uncoded OFDM.

71

CHAPTER 6

CONCLUSION AND FUTURE SCOPE

6.1 CONCLUSION

The objective of this thesis was to investigate the phase noise effects on OFDM based

communication systems and compensate it to improve BER performance.

This objective has been accomplished by investigating the effect of phase noise on the

performance of the system through a comprehensive simulation study.

A comprehensive background of OFDM based communication systems has been

presented, including the sub-carrier orthogonality requirement and IFFT/FFT processes.

A theoretical analysis of phase noise and their effects on overall system performance has

examined based on the work reported in the literature.

MATLAB Simulink model of an OFDM based communication system has been

developed and discussed in this thesis. According to simulation results it concluded that

phase noise degrade the BER performance of the OFDM system, when phase noise

increased BER also increased.The effect of phase noise on OFDM system has negligible

at the PHN< -70 dBc/Hz. The BER performance of the OFDM system has improved by

using R-S coding especially when the SNR(Eb/No) increased to more than 10dB. R-S

coded OFDM gains 2dB improvement at BER level of 0.009 when PHN= -70 dBc/Hz

with respect to uncoded OFDM.

R-S coded with LSA channel estimated OFDM gains 3dB improvement at the BER level

of 0.009 with respect to the R-S coded OFDM, and gains 5dB improvement at the BER

level of 0.009 with respect to uncoded OFDM.

The least square with averaging channel estimation technique removed common phase

error (CPE) which occurred in OFDM system due to phase noise, and improved BER

performance of the OFDM system.

6.2 SCOPE OF FUTURE WORK

72

1. This R-S coding with least square with averaging channel estimation technique

can also be applied under different multipath propagation mobile conditions such

as Nakagami –m fading channel, weibull fading channel etc.

2. This R-S coding with least square with averaging channel estimation technique

can be extended to Multiple input and Multiple output (MIMO) OFDM systems.

3. QPSK was used in this thesis. The effects of other signaling schemes on the

system performance may be studied to find an optimum signaling scheme. Also of

interest would be a study of the effects of changing the OFDM system parameters

used in this thesis, especially the guard interval and the number of OFDM sub-

carriers on the performance of the system.

73

REFERENCES

[1] European Telecommunications Standards Institute (ETSI), Radio Broadcasting Systems;

Digital Audio Broadcasting (DAB) to Mobile, Portable and Fixed Receivers, European Telecommunication Standard ETS 300 401, 1st edition, reference DE/JTC-DAB, February 1995. Available from the ETSI Secreteriat, F-06921 Sophia Antipolis Cedex, France.

[2] European Telecommunications Standards Institute (ETSI), Digital Video Broadcasting (DVB); Framing Structure, Channel Coding and Modulation for Digital Terrestrial Television, European Telecommunications Standard, ETS 300 744 1st edition, reference DE/JTC-DVB-8, March 1997. Available from the ETSI Secreteriat,F-06921 Sophia Antipolis Cedex, France.

[3] J.J. van de Beek, P.A. Odling, S.K. Wilson, and P.O. Borjesson, “Orthogonal Frequency- Division Multiplexing (OFDM)”, Review of Radio Science 1996-1999, W.R. Stone (ed.), International Union of Radio Science (URSI), Oxford University Press, Sweden, pp. 26-38, 1999

[4] H. Harada and R. Prasad, Simulation & Software Radio for Mobile Communications, Artech house Publisher, London, 2002.

[5] V.N. Richard and R. Prasad, OFDM for Wireless Multimedia Communication, Artech house Publisher, London, 2000

[6] Wikipedia the Free encyclopedia: http://www.wikipedia.org/

[7] T. S. Rappport, Wireless Communications, principles and practice, 2nd Edition, prentice- Hall publications, 2002.

74

[8] S .Weinstein and P. Ebert, ―Data Transmission by Frequency Division Multiplexing Using the Discrete Fourier Transform, IEEE Trans. On Communication , vol.19, Issue: 5, pp. 628–634, October.1971

[9] A . Peled and A. Ruiz, ― Frequency domain data transmission using reduced computational complexity algorithms, Acoustics, Speech, and Signal Processing, IEEE International Conference on ICASSP '80, vol. 5, pp.964 –967, April. 1980

[10] B. Hirosaki, ―An analysis of automatic equalizers for orthogonally multiplexed QAM systems, IEEE Trans. Commun , vol. COM-28, pp.73-83, January.1980.

[11] T. Pollet, M.V. Bladel and M. Moeneclaey, “BER Sensitivity of OFDM systems to carrier frequency offset and Wiener phase noise,” IEEE Trans. on Communication , vol. 43, no. 2/3/4, pp. 191-193, February./March./April. 1995.

[12] P.H. Moose, “A technique for orthogonal frequency division multiplexing frequency offset correction,” IEEE Trans. on Communication, vol. 42, no. 10, pp. 2908-2914, October. 1994

[13] A.G. Armada and M. Calvo, “Phase Noise and Sub-Carrier Spacing Effects on the Performance of an OFDM Communication System,” IEEE Commun Letters, vol.2, no. 1, January 1998.

[14] Fuqin Xiong “The Effect of Doppler Frequency Shift, Frequency Offset of the Local Oscillators, and Phase Noise on the Performance of Coherent OFDM Receivers,” prepared by Ohio Monty Andro Glenn Research Center, Cleveland,Ohio, NASA/TM—2001-210595, 2001.

[15] Y. Zhao and S.G. Haggman, “Sensitivity to Doppler shift and carrier frequency errors in OFDM systems-The consequences and solutions”, Proceedings of IEEE, Vehicular Technology Conference, pp. 2474-2478, 1996.

75

[16] Mohammad Reza Gholami , Said Nader-Esfahani and A.A Eftekhar “A New method of Phase Noise compensation in OFDM” IEEE Commun Letters, pp 3443-3446, 2003

[17] Ana Garcia Armanda “Understanding the effects of Phase Noise in orthogonal frequency division multiplexing (OFDM)”IEEE Transactions on Broadcasting ,Vol 47.2,June 2001

[18] Charan Langton, Orthogonal frequency division multiplexing (OFDM) tutorial. http://www.complextoreal.com/chapters/ofdm2.pdf

[19] L. Hanzo, M. Munster, B. J. Choi and T. Keller, OFDM and MC-CDMA for broadband multi-user Communications, New York, IEEE press, 2000

[20] The International Engineering Consortium, Web Forum Tutorials, OFDM for Mobile Data Communication, http://www.iec.org/

[21] Klaus Witrisal, “Orthogonal Frequency Division Multiplexing (OFDM) for Broadband Communications and Digital Audio Broadcasting (DAB)” Presented in Graz University of Technology, Graz, Austria, 21 March 2002, http://spsc.inw.tugraz.at/courses/dat2/OFDM_handout.pdf,

[22] Charan J. Langton, “Signal Processing & Simulation Newsletter”, http://www.complextoreal.com/ISI.htm

[23] K.T. Peh, “Orthogonal Frequency Division Multiplexing (OFDM) and Carrier Interferometry OFDM (CI/OFDM)” presented at Wireless Communications Seminar in Michigan Technological University, December 2003 FDM (CI/OFDM), http://www.ece.mtu.edu/faculty/ztian/ee5950/Teh_seminar.pdf

76

[24] J.J. van de Beek, P.A. Odling, S.K. Wilson, and P.O. Borjesson, “Orthogonal Frequency-Division Multiplexing (OFDM)”, Review of Radio Science 1996-1999, W.R. Stone (ed.), International Union of Radio Science (URSI), Oxford University Press, Sweden, pp. 26-38, 1999

[25] S.B. Weinstein and P.M. Ebert, “Data transmission by frequency-division multiplexing using the discrete Fourier transform,” IEEE Transactions on Communications, vol. 19, no. 5, pp. 628-634, October 1971.

[26] T. S. Rappport, Wireless Communications, principles and practice, 2nd Edition, prentice- Hall publications, 2002

[27] Simon Haykin, Digital Communications, Wiley Publications Ltd, Singapore, 1988

[28] Jochen Schiller, Mobile Communications, Pearson Education Ltd, Singapore, 2003

[29] A. G. Armada and M. Calvo, “Phase noise and sub-carrier spacing effects on the performance of an OFDM communication system,” IEEE Commun. Lett., vol. 2, no.1, pp. 11–13, Jan. 1998

[30] http://code.ucsd.edu/~yushen/publications_files/Yushi%20Shen-Jan06-Freescale-OFDM.pdf

[31] S.B Wicker, and V.K. Bhargava, Reed-Solomon Codes and their Applications, Piscataway, NJ: IEEE Press, 1994

[32] R. E. Blahut, “Theory and Practice of Error Control Codes. Reading”, MA: Addison-Wesley, 1983

77

[33] C.K.P. Clark, Reed-Solomon Error Correction, Research & Development British Broadcasting, Corporation, BBC 2002

[34] S. Peter, “Error Control Coding: An Introduction”. Prentice Hall, 1991