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ANALYSIS PERFORMANCE OF 256 AND 1024 QAM BY USING REED
SOLOMON CODES APPLY IN DIGITAL VIDEO BROADCASTING
THROUGH ADDITIVE WHITE GHAUSSIAN NOISE CHANNEL
INSTITUT PENGURUSAN PENYELIDIKAN
UNIVERSITI TEKNOLOGI MARA
40450 SHAH ALAM, SELANGOR
MALAYSIA
DISEDIAKAN OLEH :
SUZI SEROJA SARNIN
NORFISHAH AB WAHAB
NOOR HAFIZAH ABDUL AZIZ
NOVEMBER 2009
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Tarikh : 1 November 2009
No. Fail Projek : 600-RMI/ST/DANA 5/3/Dst (124/2008)
Penolong Naib Canselor (Penyelidikan)
Institut Pengurusan Penyelidikan
Universiti Teknologi MARA
40450 Shah Alam
Ybhg. Prof.,
LAPORAN AKHIR PENYELIDIKAN “ANALYSIS PERFORMANCE OF
256 AND 1024 QAM BY USING REED SOLOMON CODES APPLY IN
DIGITAL VIDEO BROADCASTING THROUGH ADDITIVE WHITE
GHAUSSIAN NOISE CHANNEL”
Merujuk kepada perkara di atas, bersama-sama ini disertakan 2 (dua) naskah
Laporan Akhir Penyelidikan bertajuk “Analysis Performance Of 256 and 1024
QAM By Using Reed Solomon Codes apply in Digital Video Broadcasting
through Additive White Ghaussian Noise Channels”.
Sekian, terima kasih.
Yang benar,
SUZI SEROJA SARNIN
Ketua
Projek Penyelidikan
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PROJECT TEAM MEMBERS
SUZI SEROJA SARNIN
Project Leader
………………………………………………………………
NORFISHAH AB WAHAB
Project Member
……………………………………………………..
NOOR HAFIZAH ABDUL AZIZ
Project Member
……………………………………………………..
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DECLARATION
I hereby pledge this thesis is my original writing except the quotations and summaries
that I had clearly quoted the sources.
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ACKNOWLEDGEMENT
First and foremost, I praised God the Almighty for the blessings endowed upon
me. My deep sense of gratitude to the group members, madam Norfishah Ab Wahab
and miss Noor Hafizah Abdul Aziz for their support and commitment throughout this
research.
I would also like to thank all of the persons who have directly or indirectly
involved and contributed for the success of the project.
Finally, my special gratitude is dedicated to my husband, children and family
members for their endless support that make this research possible.
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TABLE OF CONTENTS
CHAPTER PAGE
DECLARATION
ACKNOWLEDGEMENT
ABSTRACT
TABLE OF CONTENTS
LIST OF FIGURES
LIST OF TABLES
LIST OF ABREVIATIONS
1. INTRODUCTION
Background
Objective
Scope of project
Thesis Organization
2. LITERATURE RIVIEW
Quadrature Phase Shift Keying (QPSK)
QPSK Modulator
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QPSK Bandwidth
QPSK Demodulator
Minimum Shift Keying (MSK) modulation
Cyclic Codes
Coding Process (Cyclic Codes)
Procedure of Obtaining the Transmitted Polynomial
Systematic Encoding of a Cyclic Code
Error Correction
Additive white Gaussian Noise (AWGN) channel
3. METHODOLOGY
4. RESULTS AND DISCUSSION
Flowchart of the simulation
Result and analysis from the simulation
Input message
Encoding process
Modulation process
Transmission medium
Demodulation process
Decoding process
BER error performance
5. CONCLUSION
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6. REFERENCES
7. APPENDIX
LIST OF FIGURES
FIGURE TITLE PAGE
2.1 QPSK modulator block diagram 7
2.2 QPSK scatter diagram 8
2.3 MSK signal 10
2.4 QPSK demodulator block diagram 13
2.5 MSK encoding signal 14
2.6 Encoding circuit 21
2.7 Example of syndrome calculation with an (n-k)-stage shift
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24
3.1 Cyclic code encoder 27
4.1 Flow chart of simulation 31
4.2(a) QPSK input message 33
4.2(b) MSK input message 33
4.3(a) QPSK encoded signal 35
4.3(b) Output signal QPSK 36
4.4(a) QPSK modulated signal 37
4.4(b) MSK modulated signal 37
4.5(a) QPSK modulated signal added with noise 38
4.5(b) MSK modulated signal added with noise 38
4.6(a) Demodulated signal 39
4.6(b) Demodulated signal 39
4.7 MSK output signal
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41
4.8(a) QPSK Bit error rate performance 42
4.8(b) MSK Bit error rate performance 43
4.9 Performance of QPSK and MSK Modulation 44
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LIST OF ABBREVIATIONS
AWGN - Additive White Gaussian Noise
CRC - Cyclic Redundancy Check
ECC - Error Control Coding
Ex-OR - Exclusive OR
FCS - Frame Check Sequence
FEC - Forward Error Correction
FSK - Frequency Shift Keying
MSK - Minimum Shift Keying
QPSK - Quadrature Phase Shift Keying
MOD-2 - Modulo-2
PISO - Parallel in Serial Out
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PSK - Phase Shift Keying
S/N - Signal to Noise
SISO - Serial In Serial Out
Tb - Bit Period
Ts - Time Symbol
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ABSTRACT
This project is highlight about the performance of 256-Quadrature Amplitude
Modulation (QAM) and 1024-QAM applying in Digital Video Broadcasting (DVB)
through Additive White Gaussian Noise (AWGN) channel. Besides, this project using
Reed-Solomon (R-S) code as the decode/encode technique in order to act as a forward
error correcting code. Furthermore, this project is basically deal with one transmit
antenna and one receive antenna at the transmission part and receiving part respectively.
There are some comparison will be made between the 256-QAM and 1024-QAM
purposefully to get the best performance when applying in DVB through AWGN
channel in which both of them is using the same forward error correcting code (Reed-
Solomon code) technique. Basically, the best performance is determined in term of Bit
Error Rate (BER) and Signal Energy to Noise Power Density Ratio (Eb/No). It is
observed that as the constellation order of QAM increase the performance will be
degraded. Thus, 256-QAM will give the best performances either in term of Eb/No or
BER. In the mean time, both of the QAM (256-QAM and 1024-QAM) also being
compared in term of the symbol-error correcting capability that is known as t in which it
is observed that the performance is graded in response to the increasing of the value of t.
During this project, all the simulation process that presented the performances of both of
the QAM is done by using software that is known as MATLAB version 7.6.0.
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ANALYSIS PERFORMANCE OF 256 AND 1024 QAM BY USING REED
SOLOMON CODES APPLY IN DIGITAL VIDEO BROADCASTING
THROUGH ADDITIVE WHITE GHAUSSIAN NOISE CHANNEL
DISEDIAKAN OLEH :
SUZI SEROJA SARNIN
NORFISHAH AB WAHAB
NOOR HAFIZAH ABDUL AZIZ
NOVEMBER 2009
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1
CHAPTER 1
INTRODUCTION
1.1 BACKGROUND
It is well known that the QAM has been widely used as a modulation technique for
digital communication system due to its simple detection [1] and the ability to achieve
high rate transmission without increasing the bandwidth [2]. In response to this fact,
QAM become a suitable modulation technique in order to fulfill the requirement that
needs high speed transmission in DVB. However, there is a need for efficient process or
techniques of implementation of QAM to make sure that QAM can operate in maximum
or optimize performance. This is because by moving to a higher-order constellation, it is
possible to transmit more bits per symbol but on the other hands, if the mean energy of
the constellation is remain the same thus more susceptible to noise and other corruption
[3]. The fact that increasing the order of the QAM constellation will degrade the QAM
performance will be study in this project.
In digital communication, one of the most important technical issues that might be
occurred which are synchronization problem and the forward error correction used in
this project which is R-S code has a unique advantage that suited to modify this
problem. This is because this R-S code has the ability to recover the synchronization
problem since this code is self-synchronizable [4]. Owing to this reasons, the R-S code
has been choose in order to study the performance of QAM apply in DVB. Nevertheless,
the R-S code is affected with its Symbol-Error Correcting Capability (t) in which the R-
S code will perform better in higher value of t. This fact also will be discuss during this
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project in order to study the performance of both 256-QAM and 1024-QAM apply in
DVB through AWGN channel for various value of t.
Since, this project is study the performance of QAM in DVB, it is necessary to find the
most suitable channel that use to propagate the signal. Basically, channel is fall into
three types which are fading channels, channels in which the noise stems from the others
and AWGN channel. As the author compared all the three type of channels, the best
suite channel for DVB is AWGN channel. This is because in the practical world is that
AWGN never infinite in bandwidth. Thus, the destruction process is successfully safe
since the receiver or measuring instrument has finite bandwidth [5].
1.2 OBJECTIVE
This project has several objectives such as to analysis and simulates the performance
between 256-QAM and 1024-QAM using Reed-Solomon code applying in DVB
through AWGN channel. Besides, this project also purposefully to compare both
constellation order of QAM (256-QAM and 1024-QAM) in order to yield the best
performances when applying in DVB in term of BER as well as Eb/No. Furthermore, the
performance of Reed-Solomon code also being highlight in term of symbol-error
correcting capability (t) for both of the constellation order of QAM. Lastly, this project
also guides me to have the ability in using the MATLAB 7.6.0.
1.3 SCOPE OF PROJECT
This project focusing on the analysis performance of 256 QAM as well as 1024 QAM
when applying in DVB. AWGN channel and Reed –Solomon code have been choose in
this project in which the Reed-Solomon code is act as the decode/encode technique or
also can be describe as forward error correction and on the other hands, AWGN is act as
the medium for signal propagation. Basically, this project makes a comparison between
both of the constellation order of QAM (256-QAM and 1024-QAM) in order to find
which one of them can yield the best performance in DVB through AWGN channel.
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Besides, the performance comparison for both constellation order of QAM also being
done in term of symbol-error correcting capability (t) as the value of t will determined
the capability of Reed-Solomon code to correct error. All the comparison during this
project is represented using the graph of BER versus Eb/No as the performance for both
order of QAM applying in DVB is analyze in term of BER and Eb/No using MATLAB
version 7.6.0.
1.4 PROBLEM STATEMENT
Modulation and demodulation process is the important process that involved in this
project in which modulation process is modulated the information signal with carrier
signal in order to make the signal compatible to the transmission channel. On the other
hands, demodulation process is the reverse process of the modulation process since it is
responsible to convert the modulated signal back to the original information signal
(remove the carrier signal from the information signal). Thus, it is important to
determine what type of modulation that is suitable applying in DVB. Since QAM has
ability due to its simple detection and the ability to achieve high rate transmission
without increasing the bandwidth, QAM become a suitable modulation technique in
order to fulfill the requirement that needs high speed transmission in DVB. This is
because QAM allowing two digital carrier signals to get transmitted on the same
bandwidth that will give QAM an advantage of conservation of bandwidth. Furthermore,
with QAM, amplitude and phase shift keying are combined so that can optimized the
distance between the point in the constellation diagrams and will reduced the probability
of one point to misinterpreted with neighbour point as compared to other digital
modulation technique. All of these facts lead to make the QAM being chosen as the
modulation technique for this project.
The synchronization problem which is one of the most important technical issues in
digital communication required the best coding/decoding technique in order to make the
information or signal successfully received at the receiving part. Since the Reed-
Solomon code have an ability to provide self-synchronization, this type of code being
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selected to act as the code/decode technique or also can be known as the forward error
correcting code. In the mean time, the Reed-Solomon is a powerful class of code and
extremely flexible in use since Reed-Solomon code is a good choice for a variety of
channel condition as has low redundancy overhead. Besides, with Reed-Solomon code,
one code can be use both to detect and correct errors in which depends to the redundant
message being added.
Furthermore, the other problem that causes the author to study in this project is about the
most suite channel for yield the good performance of DVB. This is because it is difficult
to eliminate of all the noise of the received signal at the receiver part in order to get the
original input signal. As a result, the author is decided to study about the best channel in
DVB. Basically, channel is fall into three types which are fading channels, channels in
which the noise stems from the others and AWGN channel. As the author compared all
the three type of channels, the best suite channel for DVB is AWGN channel. This is
because in the practical world is that AWGN never infinite in bandwidth. Thus, the
destruction process is successfully safe since the receiver or measuring instrument has
finite bandwidth.
1.5 THESIS ORGANIZATION
This thesis has been divided into five chapters. Chapter 1 covers the introduction of this
thesis, the objective of this project, the scope of work and the thesis organization. In
Chapter 2, the basic theory has been discussed and this basic theory included Quadrature
Amplitude Modulation (QAM), Reed-Solomon (R-S) code, Additive White Gaussian
Noise (AWGN) channel and Digital Video Broadcasting (DVB). Chapter 3 presents the
methodology of this project and also contains the explanation about the simulation steps
that being used during this project using MATLAB version 7.6.0. Then, Chapter 4 is
focusing on the result obtained and all of the result has been discussed in this chapter.
Finally, Chapter 5 is provide the conclusion for the whole project and also provide the
idea for future development in order to improve the project in future
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CHAPTER 2
LITERATURE REVIEW
2.1 MODULATION AND DEMODULATION
Modulation and demodulation process are the important processes that involved in this
project and both of them play a specific utility applying at different part in this project’s
process in which modulation is takes place at transmission part and the demodulation is
requires at the receiving part. In order to propagate the information signal over standard
transmission media, it is necessary to modulate the information signal onto higher
frequency analog signal called a carrier. Thus, the modulation process can be define as a
process of impressing low frequency information signals onto a high frequency carrier
signal due to make the signal compatible to the transmission channel [6] .
On the other hands, the demodulation process is the reverse process of the modulation
process since it is responsible to convert the modulated carrier signal back to the original
signal (remove the information signal from the carrier signal). Furthermore, in digital
communication, there are several types of modulation process might be involves. For
instance:
Amplitude Shift Keying (ASK) – amplitude of the carrier is modulated.
Frequency Shift Keying (FSK) – frequency of the carrier is modulated.
Phase Shift Keying (PSK) – phase of the carrier is modulated.
Quadrature Amplitude Modulation (QAM) – amplitude and phase are
modulated.
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All of these types of digital communication as their own pros and contras and QAM
have been chosen as the modulation technique for this project as it has the ability that
fulfilled the DVB requirement. In respond to this, the theoritical part of QAM has been
further discussed later.
2.2 QUADRATURE AMPLITUDE MODULATION (QAM)
As a modulation technique in this project, QAM modulated the information signal due to
make it compatible to the channel then lead to successfully being transmitted to the
receiver. QAM is a modulation scheme which conveys data by changing or modulating
the amplitude and the phase of two carrier waves as QAM process involves two input
signal that is classified as in phase component, I-channel and quadrature component Q-
channel [2]. The process of QAM can best be described using QAM block diagram [6]:
Figure 2.1: (a) QAM Modulator; (b) QAM Demodulator
According to the QAM block diagram, the input signal is divided into two channels (I-
channel and Q-channel) as being state before in which both of them will added together
at linear summer in order to produce the QAM output. Basically, the balance modulator
is act as a multiplier that multiplied one channel by sine wave (I-channel) and the other
channel is multiplied by a cosine wave (Q-channel). Actually, the sine and cosine wave
is the carrier signal that being produced by carrier oscillator but one of them undergoes
90o phase shifter that make them differ by 90
o out of phase. Owing to this reason that
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cause both of the channel (I-channel and Q-channel) also 90o out of phases and lead to
bandwidth conservation (higher data rate without require increasing of bandwidth) as
one of the advantage for QAM. Then, when the signal is captured at the receiver, the
filter at the QAM demodulator will removes the high frequency terms leaving only the
independently modulated signal (independently of the quadrature component for I-
channel and independently of the in phase component for Q-channel) [7].
Digital signal is being represented using constellation diagram. Similarly with QAM that
also represented using constellation diagram that purposefully to graphically represent
the quality of the signal as well as the distortion of the digital signal. There are many
types of constellation diagram which is depending on the constellation order of QAM,
. For instance, Square constellation is created when the order of QAM is a power of 4.
Besides, the Cross constellation diagram can be constructed when the order of QAM is
not equal to the power of 4. This statement can be summarized as [8]:
Square Constellation
M = 4n
(2.1)
Where n =1, 2, 3, …
Figure 2.2: Square Constellation Diagram
Cross Constellation
M ≠ 4n (2.2)
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Where n =1, 2, 3, …
Figure 2.3: Cross Constellation Diagram
However, it also can be other type of QAM constellation diagram:
Figure 2.4: Constellation Diagram Of 8-QAM
In digital telecommunication, the data is usually binary and the number of points in the
grid is usually a power of two (2, 4, 8, …). Thus, the Square Quadrature Amplitude
Modulation is produce and widely used as a modulation technique that has the number
of bits per symbol is even. This modulation technique is suitable for this project since
involves 256-QAM and 1024-QAM that have the number of bit is equal to eight and ten
respectively (even). On the other hands, for the odd number of bits per symbol, the most
suitable modulation technique is Cross Quadrature Amplitude Modulation [7].
Furthermore, the QAM technique is being development in order to improve its
performance. As a result, the new technique of QAM is yield such as Triangular
Quadrature Amplitude Modulation [1] and Rectangular Quadrature Amplitude
Modulation [2]. During this project, there are two constellation orders of QAM that has
been studied which are 256-QAM and also 1024-QAM.
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In mathematically, QAM represented as [9]:
;
; (2.3)
Where ε is represent the signal energy, is equal to the signal amplitude for the
information conveyed by the cosine of the carrier and the signal amplitude for the
information conveyed by the sine of the carrier is denoted as
2.2.1 256-QAM
256-QAM is one type of QAM that constructed with 256 as the constellation order
(M=256). Beside, the bit rate of input data of 256-QAM is denoted as . This
statement can best be described using the 256-QAM block diagram below:
Figure 2.5: 256-QAM Block Diagram at Transmission Part
Referring to the 256-QAM block diagram at the transmission part, it is shows that he
input data is divided into two channels which are I-channel and Q-channel and both of
them consists of bit rate that is equal to the original input data divided by eight. Then,
both of the channel is undergoes 2-to-16 level converter in order to produce 16 level
PAM signal. Next, I-channel is multiplied with the carrier signal that is denoted as sin
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wct. On the other hands, Q-channel also multiplied with carrier signal but the carrier
signal is undergoes 90o phase shifter first that make the carrier signal is in cosine
function (cos wct) and lead both channel are 90o out of phase. Lastly, the linear summer
will add both of them in order to yield the QAM output.
256-QAM has a capability to transmit only smaller data rate as the 256-QAM
constructed with number of bits is equal to eight. By mathematically:
(2.4)
Where is represent the constellation order of QAM and is equal to the number of
bits.
In respond to this, 256-QAM has less susceptible to noise. This is because the error
performance of QAM depends primarily on the minimum distance among points in its
constellation [5] and this distance is determined by the constellation order of QAM as
higher order will yield minimum distance of points in the constellation diagram. Its can
be proved using formula [5]:
(2.5)
Where represent the nearest-neighbour distance in the constellation, is the
number of distinct pairs at the distance and is represent the number of points in the
constellation.
Thus, the probability of error is decline as the point distance in the constellation is
increase since the probability for one point to misinterpret to the neighbour point is
reduced. Oppositely for large value of M, it causes in decreasing value of point distance
in the constellation, hence the probability for one point to misinterpret to others is
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