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Implementation of Digital Communication using Matlab (Graduation project for
B.Sc. degree)
Thesis · May 2015
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University of Technology, Iraq
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Ministry of Higher Education and scientific Research
University of Technology
Computer Engineering Department
Information Technology Branch
Implementation of Digital Communication using
Matlab
Graduation project submitted to the department of
Computer Engineering in partial fulfillment of requirement
for the degree of B.Sc.
By
Zena Mohammed
Ali Kamal
Supervised By
Dr.Eng.Riyadh J.S
May-2015
Supervisor’s Certificates
I certify that this project entitled
“Implementation of Digital Communication
Using Matlab” was prepared by (Zena
Mohammed, Ali Kamal) under my supervision
at the Computer Engineering Department,
University of Technology Iraq, Baghdad. In
partial fulfillment of the requirement for B.Sc.
Degree
Signature:
Name: Dr.Eng.Riyadh J.S
Scientific Degree:
Date: 2015-5-
‫‪Dedication‬‬
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Abstract
With the increasing demand in communication, it has
become necessary to give better and efficient service to
users by using better technique. This project
demonstrate different modulation technique including
Amplitude Shift Keying (ASK), Frequency Shift Keying
(FSK), Phase Shift Keying (PSK) and analyze the Bit
Error Rate (BER) for different modulation schemes such
as Binary Phase Shift Keying (BPSK), Quadrature Phase
Shift Keying (QPSK), Octal Phase Shift Keying (8PSK),
and Trellis Coded Modulation (TCM). By Choosing a
reliable modulation scheme and better coding
technique the enhancement of the performance can be
obtained in transmitter and receiver of the system.
Simulated result is shown to analyze and compare the
performance of these systems by using additive white
Gaussian noise channel (AWGN). Finally the different
modulation schemes are compared on the basis of BER
and best modulation scheme is determined. From
analysis of modulation techniques, the system could use
more appropriate modulation technique to suit the
channel quality, thus we can deliver the optimum and
efficient system parameters. Both Matlab Code and
Simulink have been used for simulation.
List of Contents
Subject
Page No.
Chapter One: General Introduction
1.1 Introduction
1.2 Digital commutation System
1
2
Chapter Two: Related Theory
2.1 Amplitude-Shift Keying (ASK) Modulation
2.2 Frequency-Shift Keying (FSK) Modulation
2.3 Phase-Shift Keying (PSK) Modulation
4
10
17
Chapter Three: Modeling of Digital Communication System
3.1 Modeling using Matlab M-File
22
3.2 Modeling using Matlab Simulink
27
3.4 Integrating Matlab with C# GUI
37
Chapter Four: Conclusion
41
3.3 Convolutional Encoder TCM
References
32
42
Chapter One
Introduction
Chapter One
1.1 Introduction
In the simplest form, a transmission-reception system is a three-block system,
consisting of a) a transmitter, b) a transmission medium and c) a receiver. If we
think of a combination of the transmission device and reception device in the form
of a ‘transceiver’ and if (as is usually the case) the transmission medium allows
signal both ways, we are in a position to think of a both-way (bi-directional)
communication system. For ease of description, we will discuss about a one-way
transmission-reception system with the implicit assumption that, once understood,
the ideas can be utilized for developing / analyzing two-way communication
systems. So, our representative communication system, in a simple form, again
consists of three different entities, viz. a transmitter, a communication channel and a
receiver. A digital communication system has several distinguishing features when
compared with an analog communication system. Both analog (such as voice signal)
and digital signals (such as data generated by computers) can be communicated
over a digital transmission system. When the signal is analog in nature, an
equivalent discrete-time discrete-amplitude representation is possible after the
initial processing of sampling and quantization. So, both a digital signal and a
quantized analog signal are of similar type, i.e. discrete-time-discrete-amplitude
signals. A key feature of a digital communication system is that a sense of
‘information’, with appropriate unit of measure, is associated with such signals. This
visualization, credited to Claude E. Shannon, leads to several interesting schematic
description of a digital communication system. For example, consider Fig.1.1 which
shows the signal source at the transmission end as an equivalent ‘Information
Source’ and the receiving user as an ‘Information sink’. The overall purpose of the
digital communication system is ‘to collect information from the source and carry
out necessary electronic signal processing such that the information can be
delivered to the end user (information sink) with acceptable quality’. One may take
note of the compromising phrase ‘acceptable quality’ and wonder why a digital
transmission system should not deliver exactly the same information to the sink as
accepted from the source. A broad and general answer to such query at this point is:
well, it depends on the designer’s understanding of the ‘channel’ (Fig. 1.1) and how
the designer can translate his knowledge to design the electronic signal processing
algorithms / techniques in the ’Encoder’ and ‘decoder’ blocks in Fig. 1.1 We hope to
pick up a few basic yet good approaches to acquire the above skills. However,
pioneering work in the 1940-s and 1950-s have established a bottom-line to the
search for ‘a flawless (equivalently, ‘error-less’) digital communication system’
bringing out several profound theorems (which now go in the name of Information
1
Chapter One
Theory) to establish that, while error-less transmission of information can never be
guaranteed, any other ‘acceptable quality’, arbitrarily close to error-less
transmission may be possible. This ‘possibility’ of almost error-less information
transmission has driven significant research over the last five decades in multiple
related areas such as, a) digital modulation schemes, b) error control techniques, c)
optimum receiver design, d) modeling and characterization of channel and so forth.
As a result, varieties of digital communication systems have been designed and put
to use over the years and the overall performance have improved significantly.
Figure 1.1: Basic block diagram of a digital communication system
1.2 Digital Communication System
It is possible to expand our basic ‘three-entity’ description of a digital
communication system in multiple ways. For example, Fig. 1.2 shows a somewhat
elaborate block diagram explicitly showing the important processes of ‘modulation
demodulation’, ‘source coding-decoding’ and ‘channel encoding – decoding’. A
reader may have multiple queries relating to this kind of abstraction. For example,
when ‘information’ has to be sent over a large distance, it is a common knowledge
that the signal should be amplified in terms of power and then launched into the
physical transmission medium. Diagrams of the type in Figs. 1.1 and 1.2 have no
explicit reference to such issues. However, the issue here is more of suitable
representation of a system for clarity rather than a module-by-module replication of
an operational digital communication system.
2
Chapter One
Figure 1.2: A possible breakup of the pervious diagram (following Shannon’s ideas)
To elaborate this potentially useful style of representation, let us note that we have
hardly discussed about the third entity of our model, viz. the ‘channel’. One can
define several types of channel. For example, the ‘channel’ in Fig. 1.2 should more
appropriately be called as a ‘modulation channel’ with an understanding that the
actual transmission medium (called ‘physical channel’), any electromagnetic (or
otherwise) transmission- reception operations, amplifiers at the transmission and
reception ends and any other necessary signal processing units are combined
together to form this ‘modulation channel’. We will see later that a modulation
channel usually accepts modulated signals as analog waveforms at its inputs and
delivers another version of the modulated signal in the form of analog waveforms.
Such channels are also referred as ‘waveform channels’. The ‘channel’ in Fig. 1.1, on
the other hand, appears to accept some ‘encoded’ information from the source and
deliver some ‘decoded’ information to the sink. Both the figures are potentially
useful for describing the same digital communication system. On comparison of the
two figures, the reader is encouraged to infer that the ‘channel’ in Fig. 1.1 includes
the ‘modulation channel’ and the modulation- demodulation operations of Fig. 1.2.
The ‘channel’ of Fig. 1.1 is widely denoted as a ‘discrete channel’, implying that it
accepts discrete-time-discrete-amplitude signals and also delivers discrete-time
discrete-amplitude signals.
3
Chapter Two
Related Theory
Chapter Two
2.1 Amplitude-Shift Keying (ASK) Modulation
U
The transmission of digital signals is increasing at a rapid rate. Low-frequency analogue
signals are often converted to digital format (PAM) before transmission. The source
signals are generally referred to as baseband signals. Of course, we can send analogue
and digital signals directly over a medium. From electro-magnetic theory, for efficient
radiation of electrical energy from an antenna it must be at least in the order of
magnitude of a wavelength in size; c = fλ, where c is the velocity of light, f is the signal
frequency and λ is the wavelength. For a 1kHz audio signal, the wavelength is 300 km.
An antenna of this size is not practical for efficient transmission. The low-frequency
signal is often frequency-translated to a higher frequency range for efficient
transmission. The process is called modulation. The use of a higher frequency range
reduces antenna size.
In the modulation process, the baseband signals constitute the modulating signal and
the high-frequency carrier signal is a sinusiodal waveform. There are three basic ways
of modulating a sine wave carrier. For binary digital modulation, they are called binary
amplitude-shift keying (BASK), binary frequency-shift keying (BFSK) and binary phaseshift keying (BPSK). Modulation also leads to the possibility of frequency multiplexing.
In a frequency-multiplexed system, individual signals are transmitted over adjacent,
non-overlapping frequency bands. They are therefore transmitted in parallel and
simultaneously in time. If we operate at higher carrier frequencies, more bandwidth is
available for frequency-multiplexing more signals.
2.1.1 Binary Amplitude-Shift Keying (BASK)
U
A binary amplitude-shift keying (BASK) signal can be defined by
s(t) = A m(t) cos2πf c t,
R
0<t<T
R
Where A is constant, m(t)=1 or 0 , f c is the carrier frequency, and T is the bit
R
R
duration. It has a power P= 𝐴2 /2 , so tha A=√2𝑃 this equation( ) can be written as
S(t)= √2𝑃 cos2πf c t
R
R
0<t<T
= √𝑃𝑇�2/𝑇 cos2πf c t 0 < t < T
R
R
=√𝐸 �2/𝑇cos2πf c t 0 < t <
R
R
4
Chapter Two
constellation diagram of the BASK signals is shown in Figure 2.1.
Figure 2.1: BASK signal constellation diagram.
Figure 2.2 shows the BASK signal sequence generated by the binary sequence
0 1 0 1 0 0 1. The amplitude of a carrier is switched or keyed by the binary signal
m(t). This is sometimes called on-off keying (OOK).
Figure 2.2: (a) Binary modulating signal and (b) BASK signal.
5
Chapter Two
The Fourier transform of the BASK signal s(t) is
S(f)=(A/2)*M(f-fc)+(A/2)*M(f+fc)
The effect of multiplication by the carrier signal Acos 2πf c t is simply to shift the
spectrum of the modulating signal m (t) to f c . Figure shows the amplitude spectrum
of the BASK signals when m(t) is a periodic pulse train.
Figure 2.3: (a) Modulating signal, (b) spectrum of (a), and (c) spectrum of BASK
signals.
Since we define the bandwidth as the range occupied by the baseband signal m(t)
from 0 Hz to the first zero-crossing point, we have B Hz of bandwidth for the
baseband signal and 2B Hz for the BASK signal. Figure shows the modulator and a
possible implementation of the coherent demodulator for BASK signals.
6
Chapter Two
Figure 2.4: (a) BASK modulator and (b) coherent demodulator.
2.1.2 M-ary Amplitude-Shift Keying (M -ASK)
An M-ary amplitude-shift keying (M-ASK) signal can be defined by
Where
s(t) =
A i cos 2π f c t
0
0<t <T
elsewhere
A i = A[2i - (M - 1)]
E i = P i T is the energy of s(t) contained in a symbol duration for i = 0, 1, ...,
M - 1. Figure 2.5 shows the signal constellation diagrams of M -ASK and 4-ASK signals
Figure 2.5: (a) M-ASK and (b) 4-ASK signal constellation diagrams.
7
Chapter Two
Figure shows the 4-ASK signal sequence generated by the binary sequence 00 01 10 11.
Figure 2.6: 4-ASK modulation: (a) binary sequence, (b) 4-ary signal, and (b) 4-ASK
signal.
8
Chapter Two
Figure 2.7 shows the modulator and a possible implementation of the coherent
demodulator for M-ASK signals.
Figure 2.7: (a) M-ASK modulator and (b) coherent demodulator.
9
Chapter Two
2.2 Frequency-Shift Keying (FSK) Modulation
U
Frequency-shift keying (FSK) is a frequency modulation scheme in which digital
information is transmitted through discrete frequency changes of a carrier wave.
The simplest FSK is binary FSK (BFSK). BFSK uses a pair of discrete frequencies to
transmit binary (0s and 1s) information
0T
0T
0T
0T
0T
0T
0T
0T
0T
0T
0T
0T
0T
0T
0T
0T
0T
0T
0T
0T
2.2.1 Binary Frequency-Shift Keying (BFSK)
U
A binary frequency-shift keying (BFSK) signal can be defined by
where A is a constant, f 0 and f 1 are the transmitted frequencies, and T is the bit
R
R
R
R
duration. The signal has a power P = A2/2, so that A = 2P . Thus equation can be
written as
P
P
where E = PT is the energy contained in a bit duration. For orthogonality, f 0 = m/T
R
R
and f 1 = n/T for integer n > integer m and f 1 - f 0 must be an integer multiple of
th
2
2
1 / 2 T. We can take φ 1 ( t) =
cos 2π f 0 t and φ 2 ( t ) =
sin 2π f 1 t as e
T
T
orthonormal basis functions . The applicable signal constellation diagram of the
orthogonal BFSK signal is shown in Figure 2.8.
R
R
R
R
R
R
R
10
R
R
R
R
R
R
Chapter Two
Figure 2.8: Orthogonal BFSK signal constellation diagram.
Figure 2.9: (a) Binary sequence, (b) BFSK signal, and (c) binary modulating and
BASK signals.
11
Chapter Two
It can be seen that phase continuity is maintained at transitions. Further, the BFSK
signal is the sum of two BASK signals generated by two modulating signals m
0 (t)
An alternative representation of the BFSK signal consists of letting f 0 = f c - f
and f 1
and m 1 (t). Therefore, the Fourier transform of the BFSK signal s(t) is
= f c + f. Then
and
f1 - f0 = 2 f
s(t) = Acos2π( f c + f)t
deviation, β is the
where f c is the carrier frequency, f = β B is the frequency
modulation index, and B = 1/T is the bandwidth of the modulating signal.
When
f >> 1/T, we have a wideband BFSK signal. The bandwidth is approximately equal
to 2 f. When f << 1/T , we have a narrowband BFSK signal. The bandwidth is
approximately equal to 2B.
12
Chapter Two
Figure 2.10 shows the modulator and coherent demodulator for BFSK signals.
Figure 2.10: (a) BFSK modulator and (b) coherent demodulator
13
Chapter Two
1.2.2M-ary Frequency-Shift Keying (M -FSK)
An M-ary frequency-shift keying (M-FSK) signal can be defined by
for i = 0, 1, ..., M - 1. Here, A is a constant, f i is the transmitted frequency, θ' is the
initial phase angle, and T is the symbol duration. It has a power P = A2/2, so that
A = 2P. Thus equation (24.6) can be written as
where E = PT is the energy of s(t) contained in a symbol duration for i = 0, 1, ...,
M - 1. For convenience, the arbitrary phase angle θ' is taken to be zero. functions.
Figure 2.11 shows the signal constellation diagram of an orthogonal 3-FSK signal.
Figure 2.11: Orthogonal 3-FSK signal constellation diagram.
14
Chapter Two
Figure 2.12 shows the 4-FSK signal generated by the binary sequence 00 01 10 11.
Figure 2.12: 4-FSK modulations: (a) binary signal and (b) 4-FSK signal.
15
Chapter Two
Figure 2.13: (a) M-FSK modulator and (b) coherent demodulator.
16
Chapter Two
2.3 Phase-Shift Keying (PSK) Modulation
Phase-shift keying (PSK) is a digital modulation scheme that conveys data by
changing, or modulating, the phase of a reference signal (the carrier wave). Any
digital modulation scheme uses a finite number of distinct signals to represent
digital data
2.3.1Binary Phase-Shift Keying (BPSK)
A binary phase-shift keying (BPSK) signal can be defined by
s(t) = A m(t) cos 2πf c t,
0<t<T
where A is a constant, m (t) = +1 or -1, f c is the carrier frequency, and T is the bit
duration. The signal has a power P = A2/2, so that A = 2P .
Figure 2.14: BPSK signal constellation diagram.
17
Chapter Two
Figure 2.15: (a) Binary modulating signal, and (b) BPSK signal.
Figure 2.16 (a) Modulating signal, (b) Spectrum of (a), and (c) spectrum of BPSK
signals.
18
Chapter Two
2.3.2 M-ary Phase-Shift Keying (M - PSK)
An M-ary phase-shift keying (M-PSK) signal can be defined by
for i = 0, 1, ..., M - 1. Here, A is a constant, f c is the carrier frequency, θ' is the initial
phase angle, and T is the symbol duration. By expanding equation (23.3), we have
where E = PT is the energy of s(t) contained in a symbol duration for i = 0, 1, ...,
M - 1. For convenience, the arbitrary phase angle θ' is taken to be zero. If we take
2 cos 2πf c t and φ 2 (t) = - 2 sin 2πf c t as the orthonormal basis functions,
T
T
the applicable signal constellation diagrams of the M-PSK and 4-PSK signals are
shown in Figure 2.17.
φ 1 (t) =
Figure 2.17: (a) M-PSK and (b) 4-PSK signal constellation diagrams.
Figure 2.18 shows the 4-PSK signal sequence generated by the binary sequence 00
01 10 11.
19
Chapter Two
Figure 2.18: 4-PSK modulation: (a) binary sequence and (b) 4-PSK signal.
20
Chapter Two
Figure 2.19 shows the modulator and a possible implementation of the coherent
demodulator for M-PSK signals [3, 4].
Figure 2.19: (a) M-PSK modulator, and (b) coherent demodulator.
21
Chapter Three
Modeling of Digital
Communication System
Chapter Three
3.1. Modeling using Matlab m-file
Using Matlab Code for modeling the modulation process and Bit Error Rate performance
3.1. BASK Modulation
The output of the Matlab code for BASK modulation shown in figure (3.1) has the following
parameters: Carrier frequency=8 with Message frequency=4
3.1.2. BFSK Modulation
Figure 3.1: BASK Modulation
The output of the Matlab code for BFSK modulation shown in figure (3.2) has the following
parameters: 1st Carrier frequency=16, 2nd Carrier frequency=8 with Message frequency=4
Figure 3.2: BFSK Modulation
22
Chapter Three
3.1.3. BPSK Modulation
The output of the Matlab code for BPSK modulation shown in figure (3.3) has the following
parameters: Carrier frequency=8 with Message frequency=4
3.1.4. QPSK Modulation
Figure 3.3: BPSK Modulation
The output of the Matlab code for QPSK modulation shown in figure (3.4) has the following
parameters: Carrier frequency=8
Figure 3.4: QPSK Modulation
23
Chapter Three
3.1.5. 8PSK Modulation
The output of the Matlab code for 8PSK modulation shown in figure (3.5) has the following
parameters: Carrier frequency=8 with Message input= [0 2 5 1 6 3 4 7]
Figure 3.5: 8PSK Modulation
24
Chapter Three
Bit Error Rate (BER) Using Matlab m-file
3.1.6. BPSK BER
The output of the Matlab code for BPSK BER shown in figure (3.6) has the following
parameters: SNR from 1 to 20, Number of Bit=1000000 and Energy Bit=1
3.1.7. QPSK BER
Figure 3.6: BPSK Bit Error Rate
The output of the Matlab code for QPSK BER shown in figure (3.7) has the following
parameters: SNR from 1 to 20 , Number of Bit=1000000 and Energy Bit=1
Figure 3.7: QPSK Bit Error Rate
25
Chapter Three
3.1.8. 8PSK BER
The output of the Matlab code for 8PSK BER shown in figure (3.8) has the following
parameters: SNR from 1 to 20 , Number of Bit=1000000 and Energy Bit=1
Figure 3.8: 8PSK Bit Error Rate
26
Chapter Three
3.2 . Modeling using Matlab Simulink
Using Matlab Simulink for modeling the modulation process and Bit Error Rate
performance by using the following block parameter showing in table 3.1
Name of the block
Name of the parameter
BPSK | QPSK | PSK
Random Integer
Generator
M-ary Number
Initial Seed
Sample Time
Sample per Frame
Output data type
2|4|8
37
1
1e6
Double
BPSK modulator
Baseband
M-ary Number
Phase offset (rad)
Constellation ordering
Input Type
Output Type
2 | 4| 8
Pi/2 | Pi/4 | Pi/8
Binary
Integer
Double
AWGN Channel
Initial Seed
Mode
Eb/No (dB)
Number of bit per Symbol
Input Signal Power (Watt)
Symbol Period
37
Signal to Noise Ratio
(Eb/No)
EbNodB
1
1
MPSK Demodulator
Baseband
M-ary Number
Phase offset (rad)
Constellation ordering
Output Type
2|4|8
Pi/2 | Pi/4 | Pi/8
Binary
Integer
Error Rate
Calculation
Receive Delay
Computation Delay
Computation Mode
Output Data
Variable Name
Stop Simulation
Target Number of Errors
Maximum Number of
Symbols
0
0
Entire Frame
Workspace
BER_DATA
Checked
Inf
1e6
Table 3.1: Input Parameter Table of the Matlab Simulink Block
27
Chapter Three
3.2.1. BPSK Simulink
The Matlab Simulink block diagram of the for BPSK shown in figure (3.9) with transmitted
and received bits in figure (3.10) and the BER performance in figure (3.11)
Figure 3.9: BPSK Block Diagram
Figure 3.10: BPSK Transmitted and Received Bits
Figure 3.11: BPSK BER Performance
28
Chapter Three
3.2.2. QPSK Simulink
The Matlab Simulink block diagram of the for QPSK shown in figure (3.12) with transmitted
and received bits in figure (3.13) and the BER performance in figure (3.14)
Figure 3.12: QPSK Block Diagram
Figure 3.13: QPSK Transmitted and Received Bits
Figure 3.14: QPSK BER Performance
29
Chapter Three
3.2.3. 8PSK Simulink
The Matlab Simulink block diagram of the for QPSK shown in figure (3.15) with transmitted
and received bits in figure (3.16) and the BER performance in figure (3.17)
Figure 3.15: 8PSK Block Diagram
Figure 3.16: 8PSK Transmitted and Received Bits
Figure 3.17: 8PSK BER Performance
30
Chapter Three
3.2.4. TCM
The Matlab Simulink block diagram of the for TCM shown in figure (3.18) with the BER
performance in figure (3.19)
Figure 3.18: TCM Block Diagram
Figure 3.19: TCM BER Performance
31
Chapter Three
3.3. Convolutional Encoder TCM
A Convolutional encoder accepts a sequence of n bits and it produces at its output 𝑙
binary coded digits at any time. In general, a convolutional encoder with a memory
of L bits may be considered as a finite-state machine (or finite memory system
rather than memory less system, as in the case of the block encoder) with 2𝑙
possible states. The state of the encoder at any time instant is determined by the
contents of its store (delay unit) at that time instant.
Let the n input digits form the n-component vector
𝑎𝑖 = [𝑎𝑖,1 𝑎𝑖,2 . . . . . . . . . 𝑎𝑖,𝑛 ]
. . . . . . (3.1)
And let the 𝑙 output digits form the 𝑙-component vector
𝛽𝑖 =[ 𝛽𝑖,0 𝛽𝑖,1 . . . . . . . . .𝛽𝑖,𝑙−1]
. . . . . . (3.2)
𝜇𝑖 =[ 𝜇𝑖,0 𝜇𝑖,1 . . . . . . . . .𝜇𝑖,𝐿−1 ]
. . . . . . (3.3)
Also let the state of the encoder be defined as the L-component vector
Where the binary digits 𝛼𝑖,ℎ ,𝛽𝑖,ℎ and 𝜇𝑖,ℎ may take any one of their two possible
values 0 and 1.
The operation of the convolutional encoder may now be described as follows: for
each input sequence 𝛼𝑖 ,the encoder generates the sequence 𝛽𝑖 at its output ,while
changing its state from 𝜇𝑖 to its next state 𝜇𝑖+1 .since for every n input bits , 𝑙 bits are
produced by the encoder ,so the rate of the convolutional encoder is R=n/ 𝑙.
As an example, Figure (3.20) shows a 4-state convolutional the minimum squared
Euclidean distance sometime called the free Euclidean distance is defined as
𝑑12 =𝑀𝑖𝑛𝑖=𝑗 . |𝑆𝑖 -𝑆𝑗 |2
for all I,j
. . . . . .(3.4)
Where 𝑆𝑖 and 𝑆𝑗 assume all valid pairs of coded sequences that the convolutional
encoder/modulator combination can produce and excludes all the cases whrer the
two sequences are identical . and |𝑆𝑖 -𝑆𝑗 | is the unitary distance between the two
sequences 𝑆𝑖 and 𝑆𝑗
The asymptotic coding gain of the coded system over the corresponding uncoded
system is given by
2
𝐺𝑐 (dB)=10𝐿𝑜𝑔10 (𝑑𝑓2 /𝑑𝑢𝑛
)
32
. . . . . . (3.5)
Chapter Three
Where 𝑑𝑓 is given by Eq. 3.4, and 𝑑𝑢𝑛 is the minimum Euclidean distance of the
uncoded system .Here Eq.3.5 assume that the average transmitted signal energy of
the coded and uncoded system is the same.
For an example to find the 𝑑𝑓 and 𝐺𝑐 for a coded 4-PSK signal with signal
constellation (M=4) .let us consider the encoder in Figure (3.21) and its statetransition diagram in Figure(3.22).
The 𝑑𝑓 can be calculated by assuming the correct state as the all-zero state.
𝑑𝑓2 =𝑑 2 (0,3)+ 𝑑 2 (0,0)+ 𝑑 2 (0,2)
. . . . . . (3.6)
=2+0+4=6
Where 𝑑2 (i,j) is the square Euclidean distance between the signal points i and j ,
and I (or j) is the decimal representation of the output coded digits.
The asymptotic coding gain of the coded 4-PSK ( in this example) over the uncoded
2
2-PSK with 𝑑𝑢𝑛
=4 is
𝐺𝑐 = 10 𝐿𝑜𝑔10 (6/4)=1.7609 dB
. . . . . . (3.7)
Thus an advantage of about 1.76 dB in tolerance to AWGN can be obtain with coding
3.3.2. Viterbi Decoder
The Viterbi decoding technique is one approach to the maximum likelihood
detection of convolutional codes In general, the Viterbi decoder operates by tracing
through a trellis identical to that at the encoder in an attempt to emulate the
encoder’s behavior. At any given instant the decoder does not know the state of the
encoder and does not try to decode this immediately . The decoder examines all
possible branches to each state in the trellis stage. For each state .it computes a
likelihood score, known as the branch cost (branch metric), from the received data
and the data corresponding to each branch.
Each state has associated with it accost, which is the sum of the surviving
branches cost up to that state (the surviving branches are the branches which
produce the smallest new state cost). To determine the surviving branches, the
branches cost is added to the state cost in the previous stage of the trellis.
After evaluating a number of stages of the trellis the surviving paths in the
latest stage will originate (with a high probability) from a single state in the first
33
Chapter Three
stage of the trellis. After this. The most likely state of the encoder in the first stage
will be known, and hence it can be deduced the original input data, even though a
decision has not yet been made for the latest
Figure 3.20: Four-State, rate ½ convolutional encoder
Figure3.21: General Structure of TCM
34
Chapter Three
State at
time iT
𝜇𝑖
0
1
2
3
Input at
time iT
𝛼𝑖
Output at
time iT
𝛽𝑖
0
1
0
1
0
1
0
1
0
3
0
3
1
2
1
2
State at
Time(i +1)T
𝜇𝑖+1
Table3.2: Truth Table of the convolutional encoder
Figure 3.22: State-transition diagram of the encoder i
Figure 3.23: Model of combined encoding and modulation
35
0
1
2
3
1
0
3
2
Chapter Three
Figure3.24: calculation the minimum free distance of the encoder in Figure (3.20)
Figure 3.25: Trellis diagram of the encoder assuming the initial and terminal states
are zero
36
Chapter Three
3.4. Integrating Matlab with C# GUI
37
Chapter Three
38
Chapter Three
39
Chapter Three
40
Chapter Four
Conclusion
Chapter Four
Conclusion
In this project presents, error performance of modulation
techniques with AWGN channel are analyzed and BER is
calculated. Based on numerical calculation, the BER of BPSK,
QPSK, 8PSK and TCM was graphically plotted and compared.
The real measurements have achieved the results which have
accepted. According to this work, a performance of different
modulation techniques and channel coding is analyzed on the
basis of BER over AWGN channel. From the analysis of
different modulation techniques, we can say BPSK gives better
performance with compared to QPSK and 8PSK over AWGN
channel. Also we have limitation to increase Eb/No ratio.
Hence, for a fixed value of Eb/No, we have to use some kind of
coding to improve quality of the transmitted signal by using
Trellis Coded Modulation TCM which gives better BER
performance compared to uncoded modulation methods.
41
References
[1] B.P. Lathi: Modern Digital and Analog Communication, Oxford University
Press, New York, 1998
[2] Wayne Tomasi: Electronics Communications System, Prentice Hall, New
Jersey, 2004
[3] Madhow: Fundamentals of Digital Communication, Cambridge University
Press, New York, 2008
[4] Amos Gilat: MATLAB Introduction with Applications, Third Edition,
Department of Mechanical Engineering, The Ohio State University, Third
Edition,2008
[5] O. Beucher and M.Weeks. Introduction to MATLAB & Simulink: A Project
Approach, Third Edition, 2006
[6] Data transmission by trellis coded modulation using convolution codes
ISBN: 978-960-474-316-2, Martin Papez and Matej Cico,The Tomas Bata
University
42
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