IMAGE TRANSMISSION OVER AWGN/ FADING

CHANNELS USING OFDM AND

PERFORMANCE ANALYSIS

Saina Lajevardi

Undergraduate Project Report

submitted in partial fulfillment of

the requirements for the

degree of Bachelor of Science (B.S.)

in

Electrical and Electronic Engineering Department

Eastern Mediterranean University

June 2008

2  

Approval of the Electrical and Electronic Engineering Department

______________________________

Assoc. Prof. Dr. Aykut Hocanin

Chairman

This is to certify that we have read this thesis and that in our opinion it is fully adequate, in cope and quality, as an Undergraduate Project.

______________________________

Assoc. Prof.Dr. Erhan INCE

Supervisor

Members of the examining committee

Name Signature

1. Prof. Dr. Dervis Deniz …….……………………………..

2. Assis. Prof. Dr. Hasan Demirel …….……………………………..

3. Assoc. Prof. Dr. Huseyin Ozkaramanli …….……………………………..

4. Assoc. Prof. Dr. Mostafa Uyguroglu …….……………………………..

Date: 16-June-2008.

3  

ABSTRACT

IMAGE TRANSMISSION OVER AWGN/ FADING

CHANNELS USING OFDM AND PERFORMANCE ANALYSIS

by

Saina Lajevardi

Electrical and Electronic Engineering Department

Eastern Mediterranean University

Supervisor: Assoc. Prof. Dr. Erhan INCE

Keywords: OFDM, AWGN channel, multipath fading, Flat slow/fast fading, Frequency selective slow/fast fading.

OFDM technique in multimedia transmission is the basis of this project. OFDM as a multicarrier transmission technique is a subject of high interest in wireless communications. The use of OFDM has increased greatly due to its numerous advantages: high data rate transmission, the quality of the reception and its ability to combat Intersymbol Interference (ISI) especially in fading channels.

The purpose of this project is to analyze the performance of OFDM technique over different channels under specific assumption. Two RGB images are the transmission data in this project.

The different channels exhibit different effects on the performance of image transmission using OFDM technique. Results from the simulation analysis are also viewed in comparison with theoretical results.

In the further steps, Clarke’s model for flat fading has been adopted to the simulation which includes the channel’s Delay Spread and Doppler Spread characteristics. By changing different parameters the channel behaves as flat slow/ fast fading or frequency selective slow/ fast fading.

4  

Acknowledgments My sincere thank and love to my mother who has always been the angel of my life. I

would like to thank my family who has always supported me and whose love and trust

was always my companion.

I am specially obliged to my supervisor Associate Professor Dr. Erhan Ince whose noble

thoughts have helped me to accomplish my project, and whose patience gave me enough

motivation and enjoyment. His genuine attempt in improving my confidence during my

whole project is really admirable.

I would like to thank the outstanding and hard working members of Electrical and

Electronic Engineering department from whom I learned a lot during my four years of

study. Not just in learning the scientific material, but also their way of behaving greatly

affected my life. Specifically, I would like to give my gratitude to the chairman of the

department, Dr. Aykut Hocanin who has helped me during the process of the project

through his numerous contributions.

At the end, I would like to appreciate Dr. Ozlem Caykent’s intellectual support and her

attention which had always guided me, and had a great influence on improving my

outlook toward life.

5  

Table of Contents

ABSTRACT ....................................................................................................................... 3

Acknowledgments ............................................................................................................. 4

Table of Contents .............................................................................................................. 5

LIST OF FIGURES .......................................................................................................... 7

LIST OF TABLES ............................................................................................................ 8

1. INTRODUCTION ..................................................................................................... 9

2. THE OFDM PRINCIPLE....................................................................................... 11

2.1 Orthogonal Frequency Division Multiplexing ............................................................... 11

2.2 Advantages and Drawback of OFDM ............................................................................ 13

2.3 The OFDM System Model ............................................................................................. 14

3. MULTIPATH PROPOGATION ........................................................................... 17

3.2 Small-Scale Fading ........................................................................................................ 19

3.3 Impulse Response Model of a Multipath Channel ......................................................... 19

3.3.1 Parameters of Mobile Multipath Channels: Delay Spread .................................... 21

3.3.2 Parameters of Mobile Multipath Channels: Doppler Spread ................................ 24

3.4 Types of small scale fading ............................................................................................ 26

3.4.1 Flat fading .............................................................................................................. 28

3.4.2 Frequency selective fading ..................................................................................... 28

3.4.3 Fast Fading and Slow Fading Due to Doppler Spread ......................................... 28

3.5 Rayleigh Distribution ..................................................................................................... 29

3.6 Clarke’s Model for multipath Fading Channels ............................................................. 31

6  

4. REULTS OF SIMULATION ................................................................................. 35

4.1 OFDM over AWGN channel ......................................................................................... 35

4.1.1 BER vs SNR in theory and simulation .................................................................... 37

4.2 OFDM over Multipath Fading Channel ......................................................................... 38

4.2.1 OFDM over Flat Slow/Fast Fading Channel ........................................................ 38

4.2.2 OFDM over Frequency Selective Slow/Fast fading channel ................................. 40

4.3 Analysis of the Simulation Results ................................................................................ 42

5. CONCLUSION AND FUTURE WORK ............................................................... 44

6. REFERENCES ........................................................................................................ 46

 

 

 

7  

 

List of Figures

Fig 2.1 spectrum of an OFDM signal (a) a single subchannel (b) 5 carriers at the central

frequency of each subchannel ........................................................................................... 11 

Fig 2.2 Basic OFDM system [7] ....................................................................................... 15 

Fig 3.1 Multipath propogation .......................................................................................... 17 

Fig 3.2 channel fading manifestation and degradations [9] .............................................. 18 

Fig 3.3 (a) Normalized exponential power-delay profile. (b) Normalized Gaussian power-

delay profile for 4 . ................................................................................................... 24 

Fig 3.4 The Doppler spectrum corresponding to uniformly distributed angles of arrivals25 

Fig 3.5 Small-Scale Fading based on multipath time delay spread .................................. 27 

Fig 3.6 Small-Scale Fading based on Doppler Spread ..................................................... 27 

Fig 3.7 Matrix illustrating type of fading experienced by a signal as a function of

baseband signal bandwidth [8].......................................................................................... 29 

Fig 3.8. PDF of Rayleigh distribution ............................................................................... 30 

Fig 3.9 Frequency domain implementation of a Rayleigh fading simulator at baseband.32 

Fig 3.10 multiple Rayleigh simulators to perform flat/ frequency selective fading ......... 33 

Fig 4.1 Original pictures ................................................................................................... 35 

Fig 4.2 Receievd pictures from AWGN channel using OFDM with SNR of 0dB,3dB,6dB

and 9dB ............................................................................................................................. 36 

Fig 4.3 Graph of theoretical and simulation comparison of OFDM performance over

AWGN channel with BPSK modulation .......................................................................... 37 

Fig 4.4 Results of OFDM over flat slow fading channel with different SNR .................. 39 

Fig 4.5 Results of OFDM over flat fast fading channel with different SNR .................... 39 

Fig 4.6 Results of OFDM over frequency selective slow fading channel with different

SNR ................................................................................................................................... 40 

Fig 4.7 Results of OFDM over frequency selective fast fading channel with different

SNR ................................................................................................................................... 41 

Fig 5.1 Forward error coding for OFDM (COFDM) ....................................................... 45 

8  

List of Tables

Table 4.1 PSNR results for different simulated channels ................................................. 43

9  

1. INTRODUCTION OFDM (Orthogonal Frequency Division Multiplexing) is a multicarrier technique

modulation which has come to consideration in the past 10 years. Although, the birth of

the idea goes back to 1960’s, the recent fast growth of wireless technology which

provides the high bit rate data for multimedia transmission has convinced the people to

look for more reliable transmission techniques [1]. The high bit rate in wireless

communication which is provided over one high bandwidth carrier frequency does not

usually get out from the channels’ changes victorious.

In [2] OFDM has been defined as a special case of Frequency Division

Multiplexing (FDM). It also gives an analogy saying a FDM channel is like water flow

out of a faucet, in contrast the OFDM signal is like a shower. This has made people to

think of sending the data’s in parallel subcarriers and also lower data rate so that Inter

symbol Interference (ISI) and the effect of multichannel fading decrease whereas the

overall data rate has remained the same [3]. The most important wireless application that

make use of OFDM are Digital Audio Broadcasting (DAB), Digital Video Broadcasting

(DVB), wireless local area networks (WLAN) and wireless local loop (WLL) [1,3].

In general, the existence of OFDM scheme in transceiver increases the

performance of the system and indeed the communication is based on OFDM in a 20

MHz bandwidth. Per subcarrier, the modulation scheme ranges from BPSK (Binary

Phase Shift Keying) up to 64-QAM. All these plus the information coding bring out a

system with data bit rate ranges from 6Mbit/s to 54Mbit/s which is an extensive increase

[1].

OFDM as a spread spectrum technology provides the wireless network with anew

physical (PHY) layer which is embedded to the chipset. In order to come up with

orthogonal subcarriers which are the main reason why we do not theoretically have

Interference Fast Fourier transform (FFT) processor are used. However, the main concept

of orthogonality comes from the linear relationship between IFFT and FFT which have

been implemented in transmitter and receiver, respectively. Jones goes on to say, "By the

use of the Fast Fourier Transform (FFT) algorithm, it can be better because it allows

10  

precise control of all those multiple simultaneous frequencies (carriers) used to

simultaneously carry many data bits in parallel on different frequencies." [4]

The report starts with the general and technical information of OFDM and then

goes to the next step which is a brief introduction to the multipath channel. In that

section, small-scale fading in multipath channels are introduced which are going to be

implemented as our channel in further investigation.

The last chapter devoted to the result of simulation. The codes have been written

for an image transmission using OFDM technique over different channels. The point is to

appreciate the performance rather than going through the solutions for compensation.

11  

2. THE OFDM PRINCIPLE 2.1 Orthogonal Frequency Division Multiplexing

Multicarrier modulation is the main idea in OFDM [1]. The basic idea has been

introduced and patented in the mid 60’s by Chang [5]: the available bandwidth W is

divided into a number of of subbands, commonly called subcarriers, each of

width ∆ . In fact instead of transmitting the data symbols in a serial way, at a

baud rate R, a multicarrier transmitter convert the data stream into parallel data and the

symbol duration for each multicarrier scheme is ⁄

Fig 2.1 spectrum of an OFDM signal (a) a single subchannel (b) 5 carriers at the central frequency of each subchannel

In fact, the multicarrier signal can be written as a set of modulated carriers:

, Ψ 2.1∞

∞

Where , is the data symbol modulating the subcarrier in the signaling

interval.

Normally, increasing reduces ISI and simplifies the equalizer into a single

multiplication. However, the performance in time variant channels is degraded by long

symbols. If the coherence time of the channel is small compared to Ts, the channel

frequency response changes significantly during the transmission of one symbol and a

reliable detection of the transmitted information becomes impossible. As a consequence,

12  

the coherence time of the channel defines an upper bound for the number of subcarriers.

A reasonable range for can be derived as

2.2

Orthogonality comes from the fact that we need to increase the spectral efficiency

as well as there should be no interference. Therefore the sub channels must overlap in

transmitter and receiver without interference. The multicarrier modulations that fulfill

these conditions are called orthogonal frequency division multiplex (OFDM) systems.

Ψ1

, 0,

0, 2.3

Where: 0, 1, … ,

The windowing of the orthogonal waveform of Ψ is a convulsion with

. exp . in the frequency domain. In deed, they are orthogonal as

shown as folloing:

Ψ Ψ 2.4

Accordingly, demodulation is consists of matched filter which satisfies the relation:

, Ψ 2.5

In fact, the implementation of an OFDM system which consists of oscillators in the

transmitter and a bank of matched filters in receiver are becoming very complex. As

Weinstein and Ebert mentioned in [2] an IDFT and DFT operation can replace the

baseband modulation and the bank of matched filter respectively ( should be power of

2).

13  

2.2 Advantages and Drawback of OFDM OFDM actually brings some specific advantages to the wireless communication.

The advantages would be listed as following [6]:

Multi-path Delay Spread Tolerance

As it has been already explained one of the main effects of the multicarrier

modulation is its robust against ISI which mostly comes from the multipath

delay spread. The increase in the symbol time of the OFDM symbol by N

times is the reason of this robustness. Further, using the cyclic extension

process and proper design, one can completely eliminate ISI from the system.

Effectiveness against Channel Distortion

Usually, there is variation in the channel and no ideal case of having

flatness amplitude distortion which gives rise to the ISI as explained before. In

single carrier transmission such as twisted pair in telephone lines, complex

equalizers are needed to mitigate the effect of the channel which does not

response effectively in some high frequencies.

However, in OFDM systems, the bandwidth of each carrier frequency is

relatively small so the amplitude response over this narrow bandwidth will be

basically flat and it can be assumed that the phase response is linear, too. Even

if the situation of the distorting channel is severe, then just a simple equalizer

is enough to solve the problem.

Throughput Maximization (Transmission at Capacity)

Subcarriers modulation improves the flexibility of OFDM to channel

fading and distortion. The technique which is called channel loading increases

the capacity of transmission. If the subcarrier with a particular frequency is

going to be distorted in the channel is known and the sample duration is

relatively greater than the channel changing then the system would be

designed somehow, so scale down/up the modulation and coding scheme for

the particular subcarrier. This attempt would result in an increase in the whole

capacity of the transmission system against the fading distortion.

14  

Robustness against Impulse Noise

Impulse noise is an interference caused by atmospheric phenomena such

as lightening in channels like twisted pair or wireless channels. To give an

example how a transmission system would come up with impulse noise, let’s

assume to have a 10Mbps system with the symbol duration of 0.1µs, then an

impulse noise waveform which last for a couple of micro seconds would be

able to cause a burst of errors which would not be corrected by the error-

correction coding.

However, in OFDM system, the symbol duration is much larger than the

corresponding single carrier one and it is not likely that impulse noise be a

treat in this case, all that make simplicity in the design and implementation of

OFDM systems.

Frequency Diversity

OFDM is the best technique in frequency diversity. In a combination of

FDM and CDMA which is called MC-CDMA transmission technique,

frequency diversity is already present in the system.

There are also some drawbacks in the OFDM system [7] and people are concentrating

their work on these drawbacks in order to optimize OFDM.

Peak-to-Average power ratio (PAPR) or the large dynamic range of the signal.

Clipping is used to overcome the problem.

Sensitivity to frequency errors.

2.3 The OFDM System Model In an OFDM system, the incoming data stream is grouped in blocks of data

symbols. These are OFDM symbols and would be represented by a vector

, , … , , and then an IDFT is performed on each subcarrier and a cyclic

prefix of length will be added. The resulting complex baseband discrete time signal

of OFDM-symbol can be written as

15  

1 ,

/ , 0, 1 2.6

0,

Where n is the discrete time index.

Fig 2.2 Basic OFDM system [7]

In general, the received signal is the sum of a linear convolution with the discrete channel

impulse response and additive white Gaussian noise . Therefore, we implicitly

assume that the channel fading is slow enough to consider it as constant during one

OFDM symbol. We also, assume that the transmitter and receiver are perfectly

synchronized which is in practice it is not very simple to be achieved. We have already

assumed that the channel impulse response will be accommodated, or in another word,

0 for 0 and 1, then can be written as [1];

2.7

In the receiver the incoming sequence is split into blocks and the cyclic

prefix associated with each block will be removed. This results in a vector

1 … 1 ,

IDFT

(IFFT)

Modulation

(BPSK, QPSK, QAM, etc)

 

S/P

Baseband

OFDM

signal

P/S

Demodulation

(BPSK, QPSK, QAM,

etc)

DFT

(FFT)

 

S/P

Baseband

OFDM

signal

Channel

AWGN/Fading

 

P/S

16  

And at the end, the received data symbol , is obtained by performing a -point DFT

on this vector and ,

, / 2.8

By substituting and , we are going to have sample of the -point and at

the same time DFT of the as , ∑ 10

2 / .

Therefore the inner part of the received signal which is shown in the equation (2.9) is the

IDFT and the outer part is DFT. This is a linear relation of IDFT and DFT which make

the orthogonality possible in OFDM.

,1

, , 2.9

In fact, Equation (2.9) demonstrates that the received data symbols are the transmitted

symbols multiplied by the corresponding frequency domain channel coefficient in

addition to the noise contribution.

 

3.1 Fad

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17 

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18  

below the height of the surrounding structure and then there is no single line of path

between the transmitter and the receiver. Even if the LOS exists the multipath still occurs

since the reflection and countering are always there. The signal received by the receiver

normally contains different plane waves which have randomly distributed amplitudes,

phases and angles of arrival. [9] explains that the short-term fluctuation in the signal

amplitude caused by the local multipath which is mostly observed over distance of about

half a wavelength is small-scale fading and long-term variation in the mean signal level is

large-scale fading.

Fig 3.2 channel fading manifestation and degradations [9]

However, small-scale fading is the one which has been considered in the implementation

of the second part of this particular project.

Signal (Time) 

Time variance of 

Large‐ Scale Fading 

Small‐Scale Fading 

Fading Manifestation 

Flat fading 

Frequency selective fading

Slow fading 

Fast fading 

19  

3.2 Small-Scale Fading There are four major physical factors which could influence on small-scale fading

[8]:

Multipath Propagation

The presence of different dissipates the signal energy into amplitude, phase and

time. I this case, multiple versions of the waveform arrives at the receiving

antenna, displaced with respect to time and spatial orientation. Multipath

propagation sometimes extends the time required for baseband propagation to

reach to receiver.

Speed of the Mobile

The relative motion between transmitter and receiver leads to Doppler shift.

Depending on if they move toward each other or away so that the Doppler shift

would be positive or negative respectively.

Speed of surrounding objects

The objects in the radio channel may be in motion. If they move faster than the

mobile then it dominates small dace fading. Otherwise, it can be ignored.

The transmission bandwidth of the signal

If the bandwidth of transmitted signal is greater than the bandwidth of the

channel then the signal will go under distortion. However, if the communication

is in local area then the strength of the signal would not be distorted

significantly. Basically, coherence bandwidth is defined as the bandwidth over

which the channel transfer function remains flat, meaning that the gain is

constant and phase response is linear [9].

3.3 Impulse Response Model of a Multipath Channel The impulse response is a good characterization of the channel since it may be

used to predict and compare the performance of many different mobile communication

systems and transmission bandwidths for a particular mobile channel condition.

In order to implement the filtering characteristic of the channel we assume that the only

condition which makes the channel vary in time is the receiver’s movement. Then the

20  

impulse response of the channel is going to be a function of position of the receiver.

Then, if represnet the transmitted signal, , the impulse response of the channel

and , the received signal, then

,∞

, 3.1

Also, we already know that, and then if we replace with , still the received

signal is going to be a function of time since is constant. This shows that we can

represent a mobile radio channel as a linear time varying channel.

In general, the received signal in multipath channel consists of a series of attenuated, time

delayed, phase shifted replicas of the transmitted signal, the baseband impulse response

of a multipath channel can be expressed as

, , exp 2 , 3.2

Where , and are the real amplitudes and excess delays, respectively, of th

multipath component at time . The phase term 2 , in … represents the

phase shift due to free space propagation of the th multipath component plus any

additional phase shifts which are encountered in the channel. For simplicity, the phase

term is just represented by a single variable , . Note that some excess delay bins

may have no multipath at some time and , [8].

However, if the channel impulse response is assumed to be time invariant, or is at least

wide sense stationary over a small–scale time or distance interval, the channel impulse

response would be simplified as

, exp 3.3

The assumption of time invariant over a local area is valid when the time delay

resolution of the channel impulse response model accurately and uniquely resolves every

21  

multipath component over the local area. The small-scale fading occurs when the

multipath phases are identically and independently distributed uniformly over [0, 2 ] or

when the path amplitudes are uncorrelated. It is an acceptable assumption to believe that

phases will be different since the waves travel hundred of wavelengths and probably get

there with different phases.

When the transmitted signal has a bandwidth much greater than the bandwidth of

the channel, then the multipath structure is completely resolved by the received signal at

any time, and the received power varies very little since the individual multipath

amplitudes do not change rapidly over a local area. However, if the transmitted signal has

a very narrow bandwidth (e.g. the baseband signal has a duration greater than the excess

delay of the channel), then multipath is not resolved by the received signal fluctuations

(fading) occur at the receiver due to the phase shifts of the many unresolved multipath

components.

3.3.1 Parameters of Mobile Multipath Channels: Delay Spread

Many multipath channel parameters are derived from the power delay profile.

Power delay profiles are found by averaging instantaneous power delay profile

measurements over a local area in order to determine an average small-scale power delay

profile. Depending on the time resolution of the probing pulse and the type of multipath

channels studied, researchers often choose to sample at spatial separation of a quarter of a

wavelength and over receiver movements no greater than 6 m in outdoor channels and no

greater than 2 m in indoor channels in the 450 MHz-6GHz range.

Parameters such as the mean excess delay, rms delay spread, and the excess delay

spread (X dB) are the multipath channel parameters which can be determined from a

power delay profile. Mostly, the time dispersive properties of wide band multipath

channels are quanifies by their mean excess delay ( ) and rms delay spread ( ). The

mean excess delay is the first moment of the power delay profile and is defined as

∑ ∑

∑∑ 3.4

22  

The rms delay spread is the square root of the second central moment of the power delay

profile and is defined as

3.5

It should be noted that the power delay profile and the magnitude frequency

response (the spectral response) of a mobile radio channel are related through the Fourier

transform. It is therefore possible to obtain an equivalent description of the channel in the

frequency domain using its frequency response characteristics. Similarly, coherence

bandwidth is used to characterize the channel in the frequency domain. The rms delay

spread and coherence bandwidths are inversely proportional to one another, although

their exact relationship is a function of the exact multipath structure.

In fact, the small-scale variations of a mobile radio signal can be directly related

to the impulse response of the mobile radio channel. Basically, the impulse response is a

wideband channel characterization and contains all the necessary information to simulate

or analyze any type of radio transmission through the channel. This results from the fact

that a mobile radio channel can be modeled as a linear filter with a time varying impulse

response, while the time variation is due to receiver motion is space. The filtering nature

of the model has been done by the summation of the amplitudes and delays of multiple

arriving waves at any instant of time.

In general, for a wireless digital communication system, the significance of channel delay

spread depends on the relationship between the rms delay-spread of the channel and the

symbol period of the digital modulation [10]. Since the power-delay profile is an

empirical quantity that depends on the operating environment, for computer simulation

purposes we can only postulate functional forms of the profile, and vary the parameters

of these functional forms in order to obtain results that are applicable to a broad spectrum

of wireless environment [11].

The first is the exponential power-delay profile which is given by:

 

The second

Where S is

d is the Gau

the rms del

exp0,

ssian power

√exp

0,

lay-spread,

2

p ,

r-delay prof

,

is the ave

(a

23 

0,

file which d

, 0,

erage delay

a)

defined as:

introduced

by the chan

3.6

3.7

nnel.

24  

(b)

Fig 3.3 (a) Normalized exponential power-delay profile. (b) Normalized Gaussian power-delay profile for 4 .

3.3.2 Parameters of Mobile Multipath Channels: Doppler Spread

Consider the reliever is moving with a constant velocity of , along a path of .

The difference in path lengths traveled by the wave from source , since we

assumed that S is very far away is going to be same for both positions of and .

Therefore, we evaluate the phase change in the received signal which is due to the

difference in path lengths is

∆ 2 ∆

2 ∆

3.8

Therefore, the Doppler frequency is going to be;

1

2 .∆∆ . 3.9

25  

This equation introduces a relationship between the mobile velocity and Doppler shift

and a spatial angle between the direction of the motion and the direction of the arrival of

the wave [8].

It can be seen from equation (3.2) that Doppler shift depends on the frequency. In

a multipath propagation environment in which multiple signal copies propagate to the

receiver with different angles of arrival, the Doppler shift will be different for various

propagation paths and the resulting signal is the addition of the multipath components.

Consequently, the frequency spectrum of the received signal would be wider than

the transmitted one. The amount of Doppler spread, then, characterizes the rate of

channel variations. Doppler spread can be quantitatively characterized by the Doppler

spectrum.

Fig 3.4 The Doppler spectrum corresponding to uniformly distributed angles of arrivals

26  

The Doppler spectrum is the power spectral density of the received signal when a

single-frequency sinusoid is transmitted over a multipath propagation channel. If the

environment is static then the power spectral density is just an impulse response at the

carrier frequency of transmitted signal.

Fig 3.4 shows the characteristic of channel variation when the mobile receiver moves at a

constant speed and the signal power received by the antenna arrives uniformly from all

incident angles in [0, 2 ], and the Doppler spectrum will have the form of:

1 3.10

The bandwidth of the Doppler spectrum, or equivalently the maximum Doppler Shift

, is a measure of the rate of channel variations. When the Doppler bandwidth is

small compared to the bandwidth of the signal, the channel variations are slow relative to

signal variations which are referred to slow fading. Otherwise, the variation called fast

fading.

3.4 Types of small scale fading Basically, the types of fading that the transmitted signal undergoes depend on the

nature of the signal with respect to the characteristic of the channel. The characteristic

such as the bandwidth and symbol period of the transmitted signal and channel

parameters such as rms delay spread and Doppler spread. Therefore the time delays

dispersion and frequency dispersion results in four types of fading in wireless

communication.

As multipath delay spread leads to time dispersion and frequency selective fading,

Doppler spread leads to frequency dispersion and time selective fading. The following

tree depicts the condition for each of four types of fading [8]:

 

Wh

spread. Me

BWSignal

cha

HighDoppleSprea

Fig 3.

at we cons

eaning that

Flat F

W of <BW of annel

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Fig 3.6 Smal

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Fading

DeSpread

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ast Fading

oherence me<Symbol Period

Vf

v

2

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l-Scale Fading

s project is

M system of

elay d<Symbol eriod

Channel Variations faster than baseband

signal variations

DoSp

27 

ed on multipat

g based on Do

the categor

f this projec

BWSigna

cha

Low oppler pread

th time delay s

oppler Spread

ry based on

ct has been

FreqSelFa

W of al>BW of annel

Slow Fading

CoherenTime>Symol Perio

spread

d

n multipath

n gone throu

quency ective ading

DSpread

pe

g

nce mbod

CVa

s

ba

va

time delay

ugh the flat

Delay d>Symbol eriod

Channel ariations slower than

aseband signal

ariations

y

t

28  

fading and fast fading channels. The result and closer view of the implementation will be

explained in chapter 4.

3.4.1 Flat fading

The signal undergoes flat fading if the radio channel has a constant gain and linear

phase response over a bandwidth which is greater than the bandwidth of the transmitted

signal. That is the most common types of fading in the literature.

In flat fading, the characteristic of the multipath channels is such that the spectral

characteristic of the transmitted signal are preserved in the receiver. The only difference

is the strength of the signal which has been modified through the fluctuations in the gain

of the multipath channel. Although, the amplitude changes over time but the shape of the

spectrum remains the same.

3.4.2 Frequency selective fading

In frequency selective fading, we have our channel with a constant gain and linear

phase response but over a bandwidth which is smaller than the bandwidth of the

transmitted signal. In the presence of these kinds of channels, receiver receives the

multiple versions of the signal which have been faded in amplitude and have been

delayed in time and so that have been distorted.

In another word, frequency selective fading channel is due to time dispersion of

the transmitted symbols within the channel. Thus channel induces intersymbol

interference (ISI).

3.4.3 Fast Fading and Slow Fading Due to Doppler Spread

When the channel is specified as fast or slow fading, there is no specification if it

is flat or frequency selective fading. In fact, the velocity of the mobile (receiver)

determines if the mobile undergoes fast fading or slow fading.

Depending on how rapidly the transmitted baseband signal changes as compared

to the rate of change of the channel, a channel may be classified either as a fast fading

channel or slow fading channel.

29  

In a fast fading channel, the channel impulse response changes rapidly within the

symbol duration. That is to say, the coherence time of the channel is smaller than the

symbol period of the transmitted signal. However, in a slow fading channel, the channel

impulse response changes at a rate much slower than the transmitted baseband signal.

The relation between the various multipath parameters and the type of the fading

experienced by the signal are summarized in figure 3.5.

Fig 3.7 Matrix illustrating type of fading experienced by a signal as a function of baseband signal bandwidth [8].

3.5 Rayleigh Distribution Rayleigh distribution is used to model the statistical characteristic of the mobile

radio channel in flat fading. As we know the envelope of the sum of in phase and

quadrature Gaussian noise results in a Rayleigh distribution with a pdf as following.

2 0 ∞

0 0 3.11

Frequency Selective

Fast Fading

Frequency Selective

Slow Fading

Flat Fast Faing

Flat SlowFading

30  

– We usually assume that there is no line of sight between the transmitter and

receiver or in another word there are several paths that signal can take in order to

get to the receiver. In phase and quadrature components of complex fading gain

are complex, zero mean Gaussian process. Thus the fading envelope follows a

Rayleigh fading distribution.

– Will only consider frequency-independent (flat) channel responses [channel

impulse response has only one tap; thus no inter-symbol interference]

In fact, several models have been proposed to explain the statistical nature of the

mobile channel. The one we are going to look at and use in our implementation is

clarke’s model.

Fig 3.8. PDF of Rayleigh distribution

31  

3.6 Clarke’s Model for multipath Fading Channels Several multipath models have been introduced to explain the observed statistical

nature of a mobile channel. First model has been suggested by Ossana which is based on

the reflected waves from the flat sides of randomly located buildings. This model

assumes line of sight and that is one of the reason why it is not very applicable in channel

modeling. In urban areas line of sight is been blocked by obstacles. Clarke’s model is

based on scattering and is widely used.

The statistical characteristics of the electromagnetic fields of the received signal

at the mobile are deduced from scattering. The model assumes a fixed transmitter with a

vertically polarized antenna. The filed incident on the mobile antenna is assumed to be

compromised of N azimuthally plane waves with arbitrary carrier phase, arbitrary

azimuthally angles of arrival and each wave having equal average amplitude. It should be

noted that since there is no direct line of sight, it is very likely that the scattered

components arriving at a receiver will experience similar attenuation over small scale

distances.

The assumption for flat fading case is that the receiver is moving and there is no excess

delay due to multipath and for the th wave arriving at the angle , the Doppler Shift is in

Hertz is given by

cos 3.12

where is the wavelength of the incident wave.

The spectrum is centered on the carrier frequency and is zero outside the range of

. each of the arriving waves has its own carrier frequency which is slightly offset

from the center frequency. For instance, in case of a vertical 4⁄ antenna with (

1.5) , and a uniform distribution 12 over 0 to 2 , the output spectrum is given

by

1.5

1 3.13

32  

Doppler components arriving at 0°and 180° have an infinite power spectral density. That

would not be a problem since is uniformly distributed and the probability that a single

component arrives at exactly those angle is zero.

The popular simulation uses the concept of in-phase and quadratures modulation.

Two independent Gaussian low pass noise sources are used to produce in-phase and

quadrature fading branches. Therefore, each Gaussian source is the summation of the in-

phase and quadrature once they are orthogonal to each other. To shape the random

signals in the frequency domain, it is proper to use the inverse fast Fourier transform

(IFFT) at the last stage of the simulator.

Fig 3.9 Frequency domain implementation of a Rayleigh fading simulator at baseband.

The simulator in Fig 3.9 is implemented by following the steps below [8];

∗

−12Ng

12−

Ng

2/Ng∗

2/Ng

mfmf−

)( fSE

mfmf−0IFFT

∗

−12Ng

12−

Ng

2/Ng∗

2/Ng

mfmf−

)( fSE

mfmf−0IFFT

∑

2⋅

2⋅

⋅ )(tr

Independent complex Gaussian samples from line spectra

33  

1. Specifying as the number of frequency domain points which should be a power

of 2 and would represent and maximum Doppler shift of .

2. 1 ∆⁄ defines the time duration of a fading waveform and comes from

∆ 2 1⁄

3. Generating complex Gaussian random variables for 2⁄ positive frequency

components of the noise source.

4. Constructing the negative frequency components by conjugating the positive

frequency values.

5. Multiplying two branches by fading spectrum of .

6. Perform IFFT on the two branches to get N point noise source in time domain.

The square root will be taken to have the real part of it.

7. Finally the square root of the summation gives a N point time series of a

simulated Rayleigh fading signal with the Doppler spread and time correlation.

In order to produce frequency selective fading, several Rayleigh fading simulators

may be used in conjunction with variables gains and time delays which are shown in

Fig 3.10.

This simulation still can be modified to model a multipath channel with a direct path

of line of sight. By making a single frequency component dominant in amplitude

within and at 0, the fading is changed from Rayleigh to Ricean.

To determine the impact of flat fading on applied signal , the applied signal must

be multiplied by the output of the simulator, . And to see the impact of more than

one multipath component, a convolution must be performed which can be seen in the

Fig 3.10.

34  

Rayleigh Fading

Simulator

Rayleigh Fading

Simulator

Rayleigh Fading

Simulator

)(ts

1τ Nτ0a

1a

Na

∑ )(tr

Signal under Test

Fig 3.10 multiple Rayleigh simulators to perform flat/ frequency selective fading

35  

4. REULTS OF SIMULATION

4.1 OFDM over AWGN channel As explained in chapter 2, OFDM technique would utilize the performance of

wireless communication especially in multimedia transmission. I have implemented a

MATLAB program in order to transmit an image over AWGN and fading channels using

OFDM.

In the first part of this section, I am going to compare the result of the RGB image

transmission with four different SNR. The system has implemented as explained in

chapter 2. I am using BPSK as my modulation technique and each subcarrier carries 2048

bits during the transmission.

In the next step I compare my result with the theoretical performance of the

OFDM transmission over AWGN channel. The graph would analyze the comparison

I have used two pictures with different sizes to discuss the performance.

Fig 4.1 Original pictures

36  

0 DB 3DB

6DB 9DB

0dB 3dB 6dB 9dB

Fig 4.2 Received pictures from AWGN channel using OFDM with SNR of 0dB,3dB,6dB and 9dB

37  

4.1.1 BER vs SNR in theory and simulation

Performance of OFDM with BPSK modulation in BER can be evaluated by the formula

given [12];

,12

4.1

While; 4.2

The graph of comparison is shown in Fig 3.4.

Fig 4.3 Graph of theoretical and simulation comparison of OFDM performance over AWGN channel with BPSK modulation

As it can be seen from the Fig 4.3 the simulator works quite similar to the theoretical

expectation and it works much better in 0dB.

38  

4.2 OFDM over Multipath Fading Channel In order to investigate OFDM performance over fading channel, I have used

Clarke’s model to simulate fading channel in four different types [1,13].

The model has been already explained in chapter 3 of this project.

In this simulation I have assumed that my receiver is moving once as a pedestrian

with the velocity of 4 miles/hour and once as a car with velocity of 120 miles/hour for

flat fading and 80 miles/hour for frequency selective fading [14].

Since Clarke’s model is using Rayleigh distribution it means that there is no line

of sight between the transmitter and receiver and in case of frequency selective fading

channel I have assumed 3 different paths with delays of 0, 8 and 16 samples, respectively.

4.2.1 OFDM over Flat Slow/Fast Fading Channel

The same images would be used as the transmission tool. Clarke’s model has been

adapted to the OFDM simulation program in order to model a multipath channel with flat

fading characteristic. For the small Doppler shift, a velocity of 4 Miles/ hour and for the

huge Doppler shift, 120 Miles/ hour have been devoted to the velocity of the mobile

receiver. In flat fading simulation, I just use my minimum and maximum SNR for Lena’s

picture.

0dB 9dB

39  

0dB 3dB 6dB 9dB

Fig 4.4 Results of OFDM over flat slow fading channel with different SNR

 

0dB 9dB

0dB 3dB 6dB 9dB

Fig 4.5 Results of OFDM over flat fast fading channel with different SNR

40  

4.2.2 OFDM over Frequency Selective Slow/Fast fading channel

I follow the same procedure for this simulation, too. However, I use the Clarke’s

model several times for different delayed version of the received image in order to model

frequency selective fading. In fast fading model of this channel model, 80 Miles/hour is

the maximum velocity of the receiver, since with higher than this velocity the affect of

Doppler shift prevents us from observing the improvement of the picture’s quality with

higher SNR transmission.

0dB 9dB

0dB 3dB 6dB 9dB

Fig 4.6 Results of OFDM over frequency selective slow fading channel with different SNR

41  

0dB 3dB

6dB 9dB

0dB 3dB 6dB 9dB

Fig 4.7 Results of OFDM over frequency selective fast fading channel with different SNR

42  

4.3 Analysis of the Simulation Results Table 1 is a good tool to come up with the comparison of the OFDM performance

over different channels.

It is obvious from PSNR results that, OFDM works quite well in AWGN channel

and by small increase of the power of signal, the picture would be received quite perfect.

As it can be seen from previous sections and the received pictures, the main

problem is the transmission over fading channels which are actually the main presence

channels in wireless communication. The results show that the quality of the received

pictures decrease by the fast motion of the receiver in addition to the change of the

channel characteristic from flat fading to frequency selective fading channels [15].

These results are quite flexible by having the picture of Lena which is in larger

size. However, in comparison there is no big different outcome.

It should be noted that OFDM already improves the performance of transmission

in fading channel. As it is shown from simulation results, the performance does not drop

highly in case of fading channels. Since OFDM technique is the main basis of this

simulation, the subcarriers have already overcome the fading problems.

In fact, since the data is transmitted in parallel in OFDM, we have longer symbol

periods. For example, for N parallel streams, symbol period is N times as long.

43  

Table 4.1 PSNR results for different simulated channels

Channel/

SNR AWGN

Flat Slow

Fading

Flat Fast

Fading

Frequency

Selective

Slow Fading

Frequency Selective

Fast Fading

0dB 15.94 dB 14.28 dB 13.74dB 13.13 dB 10.91 dB

3dB 21.24 dB 17.23 dB 16.30 dB 15.11 dB 11.58 dB

6dB 30.99 dB 21.41 dB 19.42 dB 17.29 dB 12.10 dB

9dB 50.83 dB 26.30 dB 23.00 dB 19.84 dB 12.54dB

44  

5. CONCLUSION AND FUTURE WORK In this project, I have studied the effect of the 3 different channels of AWGN, flat

fading and frequency selective fading as with effect of Doppler spread on image

transmission in a wireless transceiver model. The result has shown that using the same

SNR, AWGN channel gives the better result and flat fading and frequency selective

fading comes out with less efficient result, respectively.

In the simulation and analysis of OFDM performance, BPSK has been used as the

modulation technique. The multipath channel has been modeled by using Clarke’s mode

for flat fading channel.

There are numbers of future consideration specifically to this project and

generally in the study of OFDM. In this implementation, I have used MATLAB 7.5 for

the simulation. In the future, it can be implemented to a GNU radio with USRP hardware

support which brings out a practical simulator as well [16].

Here again, the modulation is BPSK which means the phase is the storage of our

image’s data. In the future, it would be a good comparison if QAM is also been employed

as the transmitter modulation. Different equalizer would be added in the receiver part to

decrease the nulls which result from fading channels.

Cyclic prefix would be considered in order to overcome fading problem in

addition to the usage of equalizer. The usage of cyclic prefix is common in today’s

OFDM communication while it has its disadvantage which is the waste of bandwidth.

Specifically in the model used as fading channel the line of sight is blocked. With

some modification to the structure, Ricean distribution would be generated which

represents the presence of Line of Sight (LOS) between the transmitter and receiver. That

would also be a good comparison to the found result.

In general, an OFDM scheme could be improved when the transceiver system use

error- coding theory on the incoming bit stream [1]. Various error-coding methods can be

applied such as: block codes, Reed Solomon codes and convolution codes. More recently

trellis coded modulation, which operates on symbols instead of bits, and turbo codes have

45  

been proposed. Also, to overcome multipath problem, Multi Input Multi Output (MIMO)

would be implemented in the system rather than Single Input Single Output (SISO) in

further study [5].

Fig 5.1 Forward error coding for OFDM (COFDM)

Since, synchronization of OFDM system is an issue in this field, there are many

attempts in order to overcome this problem. Therefore, study of synchronization to this

project would also add as a future work [17].

Forward Error Coder

Time Interleave

r

SerialTo

Paraller

Frequencyinterleaver

OFDM transmitt

er

46  

6. References [1] Engels. M., “Wireless OFDM systems”. 2 nd Ed. Boston: KLUWER Academic,

2002.

[2] Changton. L., “Orthogonal Frequency Division Multiplexing (OFDM) Tutorial”.

Intutuive Guide to Communication. www.complextoreal.com. 2004.

[3] Frederiksen, F.B, and Prasad, R., “An overview of OFDM and Related Techniques

Towards Development of Future Wireless Multimedia Communications”, IEEE

2002.

[4] S. J. Vaughan-Nichols. “OFDM: Old Technology for New Market”. November

14, 2002.

[5] Chang, R.W., “Orthogonal Frequency Division Multiplexing”, U.S. Patent

3,488,445, field 1966, issued Jan. 1970.

[6] Ramasami, V.C., “Orthogonal Frequency Division Multiplexing”, KUID 698659.

[7] Bolat, E., “Study of OFDM performance over AWGN channels”. BS thesis.

Eastern Mediterranean University. July 2003

[8] T. S. Rappaport, Wireless Communication, Chapters. 3 and 4,Upper Saddle River,

NJ: Prentice Hall, 1996.

[9] Gayatri S., Prabhu and P., and Shankar, M., “Simulation of Flat Fading Using

MATLAB for Classroom Instruction”, IEEE TRANSACTIONS ON

EDUCATION, VOL. 45, NO. 1, FEBRUARY 2002.

[10] D. C. Cox, “Universal Digital Portable Radio Communications”, IEEE

Proceedings. Vol 75, No.4, pp. 463-477, April 1987.

[11] J. C. –I. Chuang, “The Effects of Time Delay Spread on portable Radio

Communications Channels with Digital Modulation,” IEEE Journal on Selected

Areas in Communications, Vol.5, No. 5, pp. 879-889, June 1987.

[12] Lawrey, E. “OFDM as Modulation Technique”, Sky DSP, 2001

47  

[13] “OFDM transmission over Gaussian Channel”, CCU Wireless Comm. Lab.

[14] Al-Zuraiqi, F., “Analysis, Simulation and Modeling of mobile and fixed fading

channel”, B.S. thesis, Eastern Mediterranean University. June 2004

[15] Arauz, J. “Discrete Rayleigh Fading Channel Modeling”, University of Pittsburg,

March 2002.

[16] Xiang, W., Waters, D., Barry, J., and Walkenhorts, B. “Implementation and

Experimental Results of a Three-Transmitter Tree-Receiver OFDM/ BLAST

Testbed”, IEEE Communication Magazine, December, 2004.

[17] Laurenti, N., “Implementation Issues in OFDM”, M.S Thesis, Universit_a degli

studi di padova, 1998.

Note: All MATLAB codes used for the simulation in this project are included in a CD

with each copy.