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ABSTRACT
Three types of digital modulation techniques, namely Amplitude
shift keying (ASK), Frequency
shift keying (FSK) and phase shift keying (FSK) are observed and
investigated in this experiment. ASK,FSK
and M-PSK modulated signals are produced using MATLAB software
and Simulink. The coding for
MATLAB are troubleshoot from the questions given to produce
modulated signals. For ASK, FSK and PSK
amplitude, frequency and phase of carrier signal is varied to
represent binary 1 and 0 respectively.
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INTRODUCTION
Modulation is one of a technique of converting digital data to
an analog signal. Analog signal takes a
discrete number of signal level. Discrete analog signals operate
with a discrete number of levels like
digital signals. Discrete modulation technique begins with
simple modulation technique(shift keying) and
ends with more complex techniques used for systems (quadrature
amplitude modulation).
The simplest modulation technique is amplitude shift keying. ASK
imparts to a sinusoid two or more
discrete amplitude level. By modulating a high-frequency
sinusoid or carrier, a spectrum of a signal can
be shifted to a higher frequency range. s(t)=A cos 2 for binary
=1 and s(t)=0 for binary=0. A data
value 1 (higher amplitude) and a data value 0 (lower amplitude)
represented by two different
amplitudes of a signal as shown in figure 1. During each period,
amplitude of the signal is constant. The
amplitude levels can also be represented in 2 bits (Figure 2).
Every time amplitude changes, 2 bits are
transmitted. It is more efficient than one that require two
signal changes every bit. ASK is susceptible to
sudden noise impulses. The signal will experience significant
increase in amplitude. Hence, ASK is least
efficient in systems that require high transmission rate.
0,0
1),2cos()(
binary
binarytfAts
c
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Frequency shift keying (FSK) uses two different frequency ranges
to represent data values of 0
and 1 as in figure. The lower frequency might represent a 1 and
the higher frequency might represent a
0. The frequency of signal is controlled by baseband signal. FSK
does not affected by noise impulses.
However, it is subjected to intermodulation distortion which
will create new frequencies when the
frequencies of two or more signals mix together.
Phase shift keying is the third modulation technique. It
represents 0s and 1s by different
changes in the phase of a waveform. A 0 cannot be a phase change
, while a 1 can be phase change of
180 degrees. It does not affected by amplitude changes or
intermodulation distortion. PSK can be used
at a high frequency. PSK is accurate that the signal transmitter
can increase efficiency by introducing
multiple phase shift angle.
0),2cos(
1),2cos()(
2
1
binarytfA
binarytfAts
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In MPSK, the data bits to be modulated is grouped into symbols 2
M bits and take m possible
values 0,1,..,m-1. The modulator shifts the carrier to one m
possible values of the input symbol during
each interval.
1)(),2cos()(
0),2cos(
1),2cos(
0),2cos(
1),2cos()(
tdtftAd
binarytfA
binarytfA
binarytfA
binarytfAts
c
c
c
c
c
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Results
TASK 1
Matlab program for ASK modulated signal before troubleshoot
%b is the input binary bit stream
%f is the frequency of the carrier
n= length(b); %determine the length of bit stream
t=0:0.01: n-0.01; %time axis
for i=1:n
bw(((i-1)*100+1:i*100)=b(i); %loop
end
carrier= cos(2*pi*f*t); %carrier signal
modulated = bw.*carrier; %modulated signal
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Matlab program for ASK modulated signal after
troubleshooting:
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Enter binary bit stream=[1 -1 1 -1 1]
Enter carrier frequency=0.8 Hz
Enter binary bit stream= [1 -1 1 -1 1]
Enter carrier frequency=10Hz
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Discussions:
In ASK modulation, the amplitude of carrier is varied to create
signal elements. In this lab, the input
of binary bit stream is entered by users. In this case the input
is [1 -1 1 -1]. This is because as in the
question wants the graph to be plotted for amplitude of binary
code A=1V and A=-1V. In ASK, the
amplitude of carrier assumes one of the two amplitudes dependent
on the logic stream of the input bit
stream. When the message signal is 1 or high, the modulated
signal will show and high frequency, but
when message signal is 0 or low, the modulated signal will still
remain at zero.Next, when
troubleshooting, a change is made that the value of x is added
so that, x = 1:1:(n+1)*100.
This is to complete the formula for binary bit stream in the
y-axis which is incomplete in this coding.
Hence the formula declared in the loop is bw(x(i*100:(i+1)*100))
= b(i). So it will loop to get the signal
value for ASK. The output graphs show that the first waveform is
a message which initiates the second
waveform is an ASK signal. The third waveform is modulated
signal. In this lab, two values carrier
frequencies are entered to compare the outputs waveforms of
different values. The first carrier
frequency entered is 0.9 Hz. Digital signal is transmitted,
modulates a carrier signal and varies its
amplitude in such a way as to make it coincide with the logical
1 and the logical 0, two different
amplitudes of the carrier. When the carrier frequency is change
to a bigger value, which is 10 Hz. The
value of carrier frequency is higher than the amplitude of
modulating signal. The modulation index,
m>1. Hence, overmodulation occur which in turns causing
distortion. Both frequency and phase remains
constant while amplitude changes. The bandwidth required is two
times the highest frequency content
including any harmonics for binary pulse modulating signals.
Conclusions
ASK is generated using matlab program. The most important
characteristic of ASK signal is that the two binary values, 1 and 0
are represented by two different amplitudes of the carrier
frequency. When changes from 1 to 0, the amplitude of modulated
frequency also changes. In matlab, if the input carrier
frequency is high, modulation index,m will be greater than 1.
Then distortion occurs.The source signals are generally referred to
as baseband signals. It sends analogue and digital signals directly
over a medium. The low-frequency signal is often
frequency-translated to a higher frequency range for
efficient transmission. . The three basic ways of modulating a
sine wave carrier for binary digital modulation, 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. ASK is more susceptible to
noise and inefficient to use for modulation technique. Instead, it
is used typically used only up to 1200 bps for voice-grade
lines.The ASK technique is used to transmit digital data over
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optical fiber, where one signal element is represented by a
light pulse while the other signal element is represented by the
absence of light.
TASK 2
Frequency shift keying (FSK)
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Enter binary bit stream to [1 0 1 0 1]
Enter carrier frequency = 0.8 Hz
Enter binary bit stream [1 0 1 0 1]
Enter carrier frequency=10 Hz
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Discussions:
In FSK, frequency of carrier signal is varied to represent
binary signal 1 or 0. A frequency shift keyed transmitter has its
frequency shifted by the message. In this lab, the input of binary
bit stream is entered
by users. In this case the input is [1 0 1 0 1]. In FSK, two
frequencies are transmitted which is one
corresponding to binary 1(mark) and another one is 0 (space). In
this lab, two values of carrier frequencies
are entered. Frequency is shifted while amplitude and phase
remains constant in each bit interval. The
first value is 0.8Hz. The results of modulated signal shows that
the frequency is shifted when data is
transfer from binary signal 1 to 0. There is difference in
frequency in the modulated signal when going
from 1 to 0.The two possible carriers with different frequencies
that are coupled to logical binary
values 1 and 0 .When the frequency of carrier entered is 10Hz,
it can be seen that there is distortion or
noise presence in carrier signal 1 and carrier signal 2. The
modulation index, m>1. Hence, overmodulation
occur which in turns causing distortion. However it still can be
seen that at modulated signal there is
difference in frequency in the modulated signal when going from
1 to 0.
Conclusions:
Matlab code obtained for ASK modulated signal can be altered to
produce Matlab code for FSK signal. Higgher frequency of carrier
will produce distortion and noise, however the FSK modulated signal
is still can be seen when it is shifted from 1 to 0. The most
common form of FSK is binary FSK (BFSK), in which the two binary
values are represented by two different frequencies near the
carrier frequency. There are three common form of FSK, that is
Binary Frequency Shift Keying, BFSK, Multiple Frequency Shift
Keying, BFSK. BFSK literally implies using a pair of discrete
frequencies to transmit binary (0s and 1s) information. With this
scheme, the "1" is called the mark frequency and the "0" is called
the space frequency.
BFSK is less susceptible to error than ASK. On voice-grade
lines, it is typically used up to 1200 bps. It is also commonly
used for high-frequency (3 to 30 MHz) radio transmission, also be
used at even higher frequencies on local area networks that use
coaxial cable.
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TASK 3
M-PSK
Simulink Block Diagram:
Graph Results:
i)Noise ii)
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Results After Troubleshooting:
Changes that have been made
i)Change Bernoulli Binary Generator to Random Integer
Generator
Change sample time to 1e-7
ii)AWGN Channel
Change symbol period to
Symbol period=log2(M)*1e-7
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iii)Error Rate Calculation
Change maximum number of symbols=1e8
Simulink block diagram:
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Graph Results:
Discussions
PSK is a modulation where there is only one carrier so that two
numerical values 1 and 0 are coupled to two different phases of the
same frequency 0 and 180 respectively. In this lab, the Simulink is
triggered to produce a 8-PSK modulator. When troubleshooting, the
Bernoulli Binary Generator is changed to Random Integer Generator.
Also the value of sample time is changed to 1e-7. The reasons
Random Integer Generator is used instead of Bernoulli Binary
Generator is because it generates random integers in the range [0,
M-1], where M is the M-ary number defined in the dialog box. As in
this lab, 8-ary is need to be generated. Meanwhile, Bernoulli
Binary Generator only can generate m binary numbers using a
Bernoulli distribution. That is why before we troubleshoot, the
results is only 2-PSK instead of 8-PSK. This is generally because
it could not produce other than m-binary numbers. Next the sample
time is changed to 1e-7 because a smaller sample time can produce a
more precise result. This is also the same as in AWGN Channel and
Error Rate Calculation where the sample time/ maximum number of
symbols is changed. The output at discrete time plot shows a 8
plotted M-PSK. This plot refers as 8 phase. The
phase start with 0 degree, and it changes every 45 degree. M-ary
number refers to the 8-PSK. In PSK,
the phase of the carrier is shifted to represent data. It use
two phase (0 and 180) to represent the two
binary digits. When M=8, so the output of binary bit is equal to
3 bit. This 3 bit encoded, formatting
titbits and producing 3 different output phase. The data next to
the scatter plot is Gaussian Noise that
presents to process zero mean and single-side power density
spectral.
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Conclusions:
Using Simulink can create a Phase Shift Keying modulation. In
PSK, the phase of the carrier signal is shifted to represent data.
M-PSK where M=8 is popular on straight-forward extension of QPSK.
8=2^3. Hence,3 bits fit into every symbol. If M>8, the distance
between constellation point is small and Eb/No ratio has to become
larger to attain target BER. The mapping from the data bits
arbitrary but generally some data bits are used. In M-PSK
constellation, every constellation point is always has two
neighbors with equal probabilities of an error to either neighbor.
BER is for every symbol error there is one bit error assumed but
there are 4 bits per symbol. In PSK, the demodulator must be able
to determine the phase of received sinusoid with respect to some
reference phase. PSK is less susceptible to errors than ASK, while
it requires the same bandwidths as ASK. Besides, it is more
efficient to use bandwidth which is a high data rate. One of the
disadvantages of PSK includes it is more complex signal detection
or recovery process than ASK and FSK.
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) Blake: Electronics Communications System 2nd Edition, CENGAGE
Learning, Delmar, 2002
4) N Vlajic:
www.cse.yorku.ca/course...11/.../CSE3213_07_ShiftKeying_F2010.pdf
,
ASK,FSK,PSK,QAM, Fall 2010.
5) Harjot Kaur: www.iject.org/vol2issue3/2/harjot.pdf
Comparative Performance Analysis of M-ary
PSK Modulation Schemes using Simulink, September 2011