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
Since the s
affected by
no Line of
other side w
channel.
Fading is c
which arriv
waves whic
widely in a
propagation
Fad
Scale fadin
forests, bil
3
ding in a wi
signal leave
y many phys
Sight betw
would have
caused by in
ve at the re
ch combine
amplitude a
n time of
ding can be
ng. Large-s
lboards, etc
. MULT
ireless envi
es the trans
sical and en
ween the tra
been chara
nterference
eceiver at s
e in the rece
and phase,
the waves
F
defined into
cale fading
c. Small-sc
1
TIPATH
ironment
smitter and
nvironmenta
nsmitter an
acterized de
between tw
slightly diff
eiver antenn
depending
s and the
ig 3.1 Multipa
o two major
g results fro
cale fading
17
H PROP
propagate
al distortion
nd the receiv
eeply by the
wo or more
ferent times
na and gives
on the dist
bandwidth
ath propogatio
r categories
om promine
occurs wh
POGATI
through the
ns. Even, m
ver and the
e multiple p
versions of
s. These wa
s result to a
tribution of
h of the tr
on
of Large-S
ent terrain
hen the heig
ION
e receiver i
most of the ti
e received s
phenomena
f the transm
aves are th
a signal whi
f intensity a
ransmitted
Scale fading
counter su
ght of the
it would be
ime there is
ignal in the
of the radio
mitted signal
e multipath
ch can vary
and relative
signal [8]
g and Small-
uch as hills
antennas is
e
s
e
o
l
h
y
e
.
-
,
s
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
Fa
h er d
CoTimo
.5 Small-Scale
Fig 3.6 Smal
ider in this
the OFDM
Fading
DeSpread
pe
ast Fading
oherence me<Symbol Period
Vf
v
2
e Fading base
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.