A comparative study and performance analysis of different modulation techniques which shows graphically and comparative results Channel Noise with Bit Error Rate of ASK, FSK, PSK and QPSK.

1. Problem:
Make a comparative study and performance analysis of different modulation
techniques which shows graphically and comparative results Channel Noise
with Bit Error Rate of ASK, FSK, PSK and QPSK.
Write a report on your analysis and justification of your results.
Abstract:
Digital communication is a transfer of information from source to destination in the form of discrete
signals. These signals are manipulated by electronic circuits (analog or digital) for making it possible
to transmit and receive the data or information. Digital transmission is the physical transfer of data
over a point-to-point or point-to-multipoint communication channel such as copper wires (guided and
unguided channels), optical fibres, wireless communication channels, and storage media. The data is
represented as an electromagnetic signal, such as an electrical voltage, radio wave, microwave, or
infrared signal. This paper presents a comparison between the different basic digital modulation
techniques which are amplitude shift keying (ASK), frequency shift keying (FSK), phase shift keying
(PSK) and quadrature phase shift keying (QPSK). These modulation schemes can be characterized by
their transmitted symbols which consist of a discrete set of values occurring at gradually spaced
intervals. The selection of a digital modulation technique for a specific application depend not only the
bandwidth efficiency and implementation complexity but also error rate occurred in a bit (BER) and
signal to noise ratio. Binary modulation methods use two level symbols and are facile to implement,
provide good error substantiation. BER is a key parameter that used for assessing systems that transmit
signal data from one location to another. SNR is well known measure of how the signal and noise
power compare against each other. It directly affects the probability of error performance of a system.
The objective is to make a comparative study and performance analysis of different modulation
techniques. The method used is to make this comparison based on Channel Noise with Bit Error Rate.
Using graphs of the different modulations obtained, we have presented the variations of these two
criteria. The results show that the error probabilities of phase-shift keying and frequency-shift keying
are small compared with amplitude-shift keying. A more practical simulation on an image transmission
using these modulation techniques has made it possible to see more clearly the efficiencies of these
modulation techniques. Thus, we can say that phase-shift keying is the optimal modulation.
Keywords:
Modulation, ASK, FSK, PSK, QPSK, Bit Error Ratio (BER), Signal to Noise Ratio (SNR)
Introduction:
At present age is the day of communication. The biggest part of communication is growing by wireless
technologies. The performance of the good transmitting and receiving systems is very important. For
good performance, attenuation, distortion, noise must be avoided from transmitting signal as long as
possible. For that measurement of transmitting signal and receiving signal should be accurate. With
some digital modulation techniques (ASK, FSK, PSK), parameters, coding and filtering can affect the
transmission quality and accuracy of the received signal. Digital modulation is the modulation
techniques that are used to discrete signals to modulate a carrier wave. In digital modulation, high

2. carrier frequencies are used so that signals can transmit over long distances with the help of criterion
long distance communication media such as radio channel [1]. Noise in the channel does not have the
deleterious effect on the received of demodulated signal is the main advantages. However, small, if an
analog signal has some noise, the demodulated signal is corrupted. For example, if the modulating
signal were in the range of 0 to 1 V, the specific value 0.58 V were sent, a small amount of noise might
the change the value of demodulated signal 0.60 V, the receiver would believe the correct value was
0.60 V. The main advantage of ASK modulation for generation of ASK is that it's relatively easy to
implement. It offers high bandwidth efficiency. Both ASK modulation and demodulation processes are
relatively cheap. The ASK modulation technique is commonly used in transmitting digital data. In
FSK, the implementation is easier than AM technique. PSK modulation has good noise rejection
capability and the system generates a smaller noise bandwidth. Coding and modulation are the process
of optimizing the performance of digital communication systems. In communication, parameters are
used for the purpose of controlling error of communication system. BER and SNR parameters are used
here for digital modulation technique.
Fig 1: Block Diagram of Digital Communication System.

3. Methodology:
Amplitude Shift Keying (ASK): It is a form of modulation that represents digital data as variations in
the amplitude of a carrier wave. The amplitude of an analog carrier signal varies in accordance with
the bit stream (modulating signal), keeping frequency and phase constant. This digital modulation
scheme is used to transmit digital data over optical fiber, point to point military communication.
applications, etc. Binary 1 is represented by a short pulse of light and binary 0 by the absence of light.
The ASK is obtained by the alteration of the amplitude of the carrier wave. It is a coherent modulation
technique hence the concept of the co-relation between the signals, number of basic functions. It has
very poor bandwidth efficiency. The basic merit of this technique is its simple implementations but is
highly prone to noise. The combination with PSK yields derivatives like QAM and Mary ASK, which
have much important application with improved parameters. The binary signal when ASK modulated,
gives zero value for low input and it gives the carrier output for high input. ASK can be expressed by
S(t) = dAcosωct
ωc = 2πfc
or, S(t) = dAcos2πfct 0<=t<=T
Here fc = frequency of the carrier wave and A = constant, d(t)= 1 or 0, T = bit duration. For d=0, S(t)=
0 and for d=1, S (t) = Acos2πfct.
Fig 2: ASK Generation Circuit Block Diagram
Fig 3: ASK Modulated Waveform

4. Frequency Shift Keying (FSK): Frequency Shift Keying is the method of transmitting digital signals
in which the frequency of carrier signal varies according to the digital signal changes. In frequency
shift keying (FSK), the frequency of the carrier is shifted between two discrete values, one representing
binary “1” and representing binary “0” but the carrier amplitude does not change. With this scheme the
one is called the mark frequency and the zero is called the space frequency. The simple form of FSK
is BFSK. The instantaneous vale of the FSK signal is given by:
S1(t) = A cos (ω1t + θ1); for bit 1
S2(t) = A cos (ω2t + θ2); for bit 0
As ω = 2πf, So
S1(t) = A cos (2πf1t + θ1); for bit 1
S2(t) = A cos (2πf 2t + θ2); for bit 0
Here, A = Constant and f = frequency of the carrier wave. 𝑓1 and 𝑓2 are the frequencies corresponding
to binary “1” and “0” respectively and 𝑓1>𝑓2. From above equation, it is clear that the FSK signal can
be considered to be comprising of two ASK signal with carrier frequencies 𝑓1 and 𝑓2.
Fig 4: FSK Generation Circuit Block Diagram
Fig 5: FSK Modulated Waveform

5. Phase Shift Keying (PSK): Phase shift keying is a digital modulation process which carries data by
changing the phase of the carrier wave. There are several methods that can be used accomplish PSK.
The binary phase shift keying technic is simpler than quadrature phase shift keying. In binary phase
shift keying to opposite signal phases are used because there are two possible wave phases. The digital
signal is separated time wise into individual bits. For the different bits phase will be changed for the
two same values phases will be unchanged. Binary phase shift keying is sometimes called as phase
modulation. For the input binary sequence, binary input from 1 to 0 output modulated wave will change
its phase at 1800. Binary input from 0 to 1 output modulated wave will change its phase at 180˚. At the
time of same binary input output modulated wave remain unchanged (from 0 to 0 or 1 to 1) or changed
by 00. It is widely used for wireless LANs, RFID and Bluetooth communication. The problem with
phase shift keying is that the receiver cannot know the exact phase of the transmitted signal to
determine whether it is in a mark or space condition. This would not be possible even if the transmitter
and receiver clocks were accurately linked because the path length would determine the exact phase of
the received signal. The binary phase shift keying signal can be defined by:
S(t) = Am(t)cosωt; 0<=t<=T
S(t) = Am(t)cos2πfct; 0<=t<=T
Here, m(t) = +1 or -1, A = Constant, fc = frequency of the carrier wave, T= bit duration.
Fig 6: PSK Generation Circuit Block Diagram Fig 7: PSK Modulated Waveform

6. Quadrature Phase Shift Keying (QPSK): Quadrature Phase Shift Keying (QPSK) is a form of Phase
Shift Keying in which two bits are modulated at once, selecting one of four possible carrier phase shifts
(0, 90, 180, or 270 degrees). QPSK allows the signal to carry twice as much information as ordinary
PSK using the same bandwidth. QPSK is used for satellite transmission of MPEG2 video, cable
modems, videoconferencing, cellular phone systems, and other forms of digital communication over
an RF carrier. In QPSK the original data stream dk(t) = d0, d1, d2, …. is divided into an in-phase stream,
dI(t), and a quadrature stream, dq(t).
dI(t) = d0, d2, d4, …….
dq(t) = d1, d3, d5, …….
dI(t) and dq(t) each have half the bit rate of dk(t). A convenient orthogonal realization of a QPSK
waveform, S(t), is achieved by amplitude modulating the in-phase and quadrature data streams onto
the cosine and sine functions of a carrier wave as follows:
S(t) = 1/√2 * dI(t) cos (2πf0t + π/4) + 1/√2 * dq(t) sin (2πf0t + π/4) – (1)
Using trigonometric identities, this equation can also be written as:
S(t) = cos [ 2πf0t + Θ(t)]
The value of Θ(t) will correspond to one of the four possible combinations of dI(t) and dq(t) in the
equation (1). Θ(t) = 0o
, ± 90o
, or 180o
.
Fig 8: QPSK Generation Circuit Block Diagram
Fig 9: QPSK Modulated Waveform

7. Bit Error Rate (BER): Bit error rate refers to the number of bit errors in per unit time. It is the ratio of
total number of error bit to the total number of transmitted bits. It is very important way to determine
the quality of transmission. It is often expressed as a percentage.
BER = Total number of error bits / Total number of transmitted bits.
As an example, let the transmitted bit sequence:
0 1 0 1 0 0 0 1 1 0
And the following received bit sequence:
0 1 1 1 0 1 0 0 1 1
In this case the number of bit errors is 4.
BER= (4 / 10) × 100% = 40% error.
Signal Noise Ratio (SNR): Signal to noise ratio means the ratio between the power of carrier signals
to the power of noise signal in a wave. It is a measure used to compares the level of a desired signal to
the level of background noise. It is expressed in logarithmic scale (dB). SNR also expressed by μ0/2μ.
SNR = Signal Power / Noise Power.

8. Code for Output Waveforms of ASK, FSK, PSK, QPSK:
Amplitude Shift Keying (ASK):
clc;
clear all;
close all;
%GENERATE CARRIER SIGNAL
Tb=1; fc=10;
t=0:Tb/100:1;
c=sqrt(2/Tb)*sin(2*pi*fc*t);
%generate message signal
N=8;
m=rand(1,N);
t1=0;t2=Tb
for i=1:N
t=[t1:.01:t2]
if m(i)>0.5
m(i)=1;
m_s=ones(1,length(t));
else
m(i)=0;
m_s=zeros(1,length(t));
end
message(i,:)=m_s;
%product of carrier and message
ask_sig(i,:)=c.*m_s;
t1=t1+(Tb+.01);
t2=t2+(Tb+.01);
%plot the message and ASK signal
subplot(5,1,2);axis([0 N -2 2]);plot(t,message(i,:),'r');
title('message signal');xlabel('t--->');ylabel('m(t)');grid on
hold on
subplot(5,1,4);plot(t,ask_sig(i,:));
title('ASK signal');xlabel('t--->');ylabel('s(t)');grid on
hold on
end
hold off
%Plot the carrier signal and input binary data
subplot(5,1,3);plot(t,c);
title('carrier signal');xlabel('t--->');ylabel('c(t)');grid on
subplot(5,1,1);stem(m);
title('binary data bits');xlabel('n--->');ylabel('b(n)');grid on

9. Phase Shift Keying (PSK):
clc;
clear all;
close all;
%GENERATE CARRIER SIGNAL
Tb=1;
t=0:Tb/100:Tb;
fc=2;
c=sqrt(2/Tb)*sin(2*pi*fc*t);
%generate message signal
N=8;
m=rand(1,N);
t1=0;t2=Tb
for i=1:N
t=[t1:.01:t2]
if m(i)>0.5
m(i)=1;
m_s=ones(1,length(t));
else
m(i)=0;
m_s=-1*ones(1,length(t));
end
message(i,:)=m_s;
%product of carrier and message signal
bpsk_sig(i,:)=c.*m_s;
%Plot the message and BPSK modulated signal
subplot(5,1,2);axis([0 N -2 2]);plot(t,message(i,:),'r');
title('message signal(POLAR form)');xlabel('t--->');ylabel('m(t)');
grid on; hold on;
subplot(5,1,4);plot(t,bpsk_sig(i,:));
title('BPSK signal');xlabel('t--->');ylabel('s(t)');
grid on; hold on;
t1=t1+1.01; t2=t2+1.01;
end
hold off
%plot the input binary data and carrier signal
subplot(5,1,1);stem(m);
title('binary data bits');xlabel('n--->');ylabel('b(n)');
grid on;
subplot(5,1,3);plot(t,c);
title('carrier signal');xlabel('t--->');ylabel('c(t)');
grid on;

10. Frequency Shift Keying (FSK):
clc;
clear all;
close all;
%GENERATE CARRIER SIGNAL
Tb=1; fc1=2;fc2=5;
t=0:(Tb/100):Tb;
c1=sqrt(2/Tb)*sin(2*pi*fc1*t);
c2=sqrt(2/Tb)*sin(2*pi*fc2*t);
%generate message signal
N=8;
m=rand(1,N);
t1=0;t2=Tb
for i=1:N
t=[t1:(Tb/100):t2]
if m(i)>0.5
m(i)=1;
m_s=ones(1,length(t));
invm_s=zeros(1,length(t));
else
m(i)=0;
m_s=zeros(1,length(t));
invm_s=ones(1,length(t));
end
message(i,:)=m_s;
%Multiplier
fsk_sig1(i,:)=c1.*m_s;
fsk_sig2(i,:)=c2.*invm_s;
fsk=fsk_sig1+fsk_sig2;
%plotting the message signal and the modulated signal
subplot(3,2,2);axis([0 N -2 2]);plot(t,message(i,:),'r');
title('message signal');xlabel('t---->');ylabel('m(t)');grid on;hold on;
subplot(3,2,5);plot(t,fsk(i,:));
title('FSK signal');xlabel('t---->');ylabel('s(t)');grid on;hold on;
t1=t1+(Tb+.01); t2=t2+(Tb+.01);
end
hold off
%Plotting binary data bits and carrier signal
subplot(3,2,1);stem(m);
title('binary data');xlabel('n---->'); ylabel('b(n)');grid on;
subplot(3,2,3);plot(t,c1);
title('carrier signal-1');xlabel('t---->');ylabel('c1(t)');grid on;
subplot(3,2,4);plot(t,c2);
title('carrier signal-2');xlabel('t---->');ylabel('c2(t)');grid on;

11. Quadrature Phase Shift Keying (QPSK):
clc;
clear all;
close all;
%GENERATE QUADRATURE CARRIER SIGNAL
Tb=1;t=0:(Tb/100):Tb;fc=1;
c1=sqrt(2/Tb)*cos(2*pi*fc*t);
c2=sqrt(2/Tb)*sin(2*pi*fc*t);
%generate message signal
N=8;m=rand(1,N);
t1=0;t2=Tb
for i=1:2:(N-1)
t=[t1:(Tb/100):t2]
if m(i)>0.5
m(i)=1;
m_s=ones(1,length(t));
else
m(i)=0;
m_s=-1*ones(1,length(t));
end
%odd bits modulated signal
odd_sig(i,:)=c1.*m_s;
if m(i+1)>0.5
18
m(i+1)=1;
m_s=ones(1,length(t));
else
m(i+1)=0;
m_s=-1*ones(1,length(t));
end
%even bits modulated signal
even_sig(i,:)=c2.*m_s;
%qpsk signal
qpsk=odd_sig+even_sig;
%Plot the QPSK modulated signal
subplot(3,2,4);plot(t,qpsk(i,:));
title('QPSK signal');xlabel('t---->');ylabel('s(t)');grid on; hold on;
t1=t1+(Tb+.01); t2=t2+(Tb+.01);
end
hold off
%Plot the binary data bits and carrier signal
subplot(3,2,1);stem(m);
title('binary data bits');xlabel('n---->');ylabel('b(n)');grid on;
subplot(3,2,2);plot(t,c1);
title('carrier signal-1');xlabel('t---->');ylabel('c1(t)');grid on;
subplot(3,2,3);plot(t,c2);
title('carrier signal-2');xlabel('t---->');ylabel('c2(t)');grid on;

12. Bit Error Rate of ASK, FSK, PSK, QPSK:
Amplitude Shift Keying (ASK):
d1,2 = √2Eb; Pe =Q √(Eb/No)
Frequency Shift Keying (FSK):
d1,2 = √2Eb; Pe =Q √(Eb/No)
Phase Shift Keying (PSK):
d1,2 = 2 √Eb; Pe =Q √(2Eb/No)
Quadrature Phase Shift Keying (QPSK):
d1,2 = 2 √Eb; Pe =Q √(2Eb/No)

13. Calculation of Channel Noise and Bit Error Rate of ASK, FSK, PSK, QPSK:
Amplitude Shift Keying (ASK):
Fig 10: BER Performance for ASK
Phase Shift Keying (PSK):
Fig 11: BER Performance for PSK

14. Frequency Shift Keying (FSK):
Fig 12: BER Performance for FSK
Quadrature Phase Shift Keying (QPSK):
Fig 13: BER Performance for QPSK

15. Results:
The basic research work carried out in the field of communication lead to the development of new
modulation techniques, coding techniques, error rate performances analysis but the ever increasing
demand of the faster communication system with large bandwidth requirements has again generated a
new requirement towards the development of newer techniques, so many modulation techniques like
BPSK, DPSK, QPSK, MSK, GMSK, M-ary QAM have been developed.
The comparison table for various parameters for ASK, FSK, PSK, and QPSK is shown below:
Parameters ASK FSK PSK QPSK
Variable
Characteristics
Amplitude Frequency Phase Phase
Complexity Simple
Moderately
Complex
Complex Very Complex
Bandwidth
Is proportional to
signal rate (B
=(1+d) S), d is due
to modulation &
filtering, lies
between 0 & 1.
B=(1+d)
×S+2Δf
B=(1+d) ×S B=2× (1+d) ×S
Noise
Immunity
Low High High Very High
Error
Probability
High Low Low Low
Performance
in presence of
noise
Low
Better than
ASK
Better than FSK
Better than
FSK
Bitrate
(bits/sec)
Suitable up to 100
bits/sec
Suitable up to
about 1200
bits/sec
Suitable for high bit
rates
Suitable for
higher bit rates
Spectral
Efficiency
(bits/s/Hz)
1
<1 (depends
upon
modulation
index)
1 2
Merits
Low cost,
Simple
implementation
Low cost,
Simple
implementation
Robust, simple
implementation, used
for satellite
communication,
power advantage over
ASK
BW efficient
and spectrally
efficient
scheme
Demerits
More prone to
noise, BW
inefficient scheme
Design
complexity
BW inefficient
scheme, non-linear
modulation scheme
Complex
receiver design
Table 1: Comparison of various parameters of ASK, FSK, PSK and QPSK

16. Conclusion:
An analysis of the digital modulation technique carried out in this article reveals that the selection of a
digital modulation technique is solely dependent on the type of application. This is because of the fact
that some of the technique provide lesser complexities in the design of the modulation and
demodulation system and prove to be economic like the ASK, FSK, PSK techniques and can be
visualized for the systems which really does not require high amount of precisions or when economy
is the major aspect and the BER performances can be tolerated. The search for a better modulation
technique doesn’t end here as the criterion for higher data rate communication is taking the lead in
almost every area of communication and thus the BER realization becomes very important and crucial
aspect for any future digital modulation technique.
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