Modulation and Demodulation

Modulation and Demodulation 1
ABSTRACT.
In this report, Amplitude modulation demodulation, AM, have been dealt in details. The
theoretical background of the AM in comparison with other types of modulation ranging from
analogue to digital have been analyzed. In the Matlab Simulink environment, AM modulation
demodulation types have been implemented. In the first stage, Double Side Side Band with the
Carrier, DSB WC, AM modulation have been designed in Simulink and the modulated output
signals tested under different modulating index. The analysis of the output signals was derived
from the equivalent signals in continuous time and frequency domain. Second stage involves
demodulation of the DSB WC modulated signals were implemented in Matlab Simulink
applying the principle of envelope detector and coherent synchronous detector. The resultant
output message signals at the receiving end in both cases were compared with the actual message
at the sending end. In the last stage, the phase and frequency of the local oscillator in the
synchronous detector was altered in accordance with the given parameters and the effects on the
resultant demodulated signals were analyzed in the Matlab Simulink environment.
1: INTRODUCTION
Advancement and revolution in technology has resulted to a number of inventions that has
reduced vast global into a small nation as far as information transmission in concerned. For
instance, in 1876, Graham Bell invented transmission of voice message using electrical signals
(Encyclopedia.com, 2019). Wireless transmission medium that uses electromagnetic waves was
invented to curb limited of hardwired system. Electromagnetic transmission, commonly dubbed
as radio, transmits energy in the wave. There are two basic ends in the system namely;
transmitting end and receiving end. The transmitting end sends out radio waves through air using
transmitter and receiving end captures the transmitted radio waves using antenna of the receiver.
The receiver decodes the message into the actual message that can be easily understood
(Woodford, 2019). The figure below shows the basic transmission of the message from the
transmitter to the receiver.
Figure 1: Transmitter and Receiver. Courtesy (Woodford, 2019).
Transmitter and receiver used designed using electronic components. The electromagnetic wave
is basically a mixture of the electricity and magnetic as illustrated in the figure below.

Modulation and Demodulation 2
Figure 2: Electromagnetic waves. Courtesy (Techplayon, 2017)
In analog radios, the message is signal is imposed on carrier during modulation process for
transmission (Tait Radio Academy, 2019).
2: LITERATURE REVIEW
Importance of modulating and demodulating signals.
Signals are modulated so as to be transmitted over long distance by riding over the power of the
high frequency carrier signals. Transmitting signals at higher frequency drastically reduces the
size of the antenna required. Signals are also modulated to enhance multiplexing of message
signals within the same transmission medium (Web.mit.edu, 2012). Demodulation is the process
of retrieving message signal from the modulated signal. The recovery of the information is
executed at the receiving end where the demodulator decodes message into its equivalent sound,
image or binary data (BYJUS, 2019).
The difference between digital and analog modulation scheme.
Broad types of modulation include (Techplayon, 2017);
i. Analog modulation
ii. Digital modulation.

Modulation and Demodulation 3
Analog modulation involves transmission of the analog baseband low frequency message signal
using high frequency carrier signals (Spincore.com, 2019).
Types of analog modulation includes (BYJUS, 2019);
i. Frequency modulation
ii. Amplitude modulation
iii. Phase modulation
The digital modulation uses discrete message signal to modulate high frequency carrier signal
(Global, 2019).
Types of digital digital modulation includes;
i. Amplitude Shift Keying ASK
ii. Frequency Shift Keying FSK
iii. Phase Shift Keying PSK
In many aspects, analog modulation is dissimilar to digital modulation. In the analog modulation,
the signal is continuous while in the digital modulation, the signal is given as a set of discrete
values. The input data signal for digital modulation must be in binary numbers 1s and 0s as
opposed to the analog signal whose maximum and minimum values of the amplitude is
considered (ElProCus, 2019).
Theoretical performance of the digital modulation.
Types of digital modulation are discussed below.
1. Amplitude Shift Keying ASK
The nodulation signal consists of 1s and 0s which implies ON/OFF data signal. The sinusoidal
carrier signal is switched into ON/OFF amplitude variations with respect to the binary sequence
of the modulating data signal. The diagram below demonstrates ASK.
Figure 3: Amplitude Shift Keying ASK. Courtesy (ElProCus, 2019)

Modulation and Demodulation 4
ASK is applied in the IR remote control and in the transmitters and receivers of the fiber optic.
2. Frequency Shift Keying FSK
In the FSK, the modulating data signal is in digital form while the carrier wave is an analog
signal at high frequency. The modulating data signal switches the frequency of the carrier signal
into two frequencies with respect to the binary sequence. With LOW input, 0s, the frequency of
the carrier signal is switched to lower frequency, f 1 ,that the initial frequency. On contrary, when
the input binary of the data signal is HIGH, 1s, the corresponding frequency of the carrier signal
is maintained as the initial frequency f 2. The figure below shows the FSK (ElProCus, 2019).
Figure 4: Frequency Shift Keying FSK. Courtesy (ElProCus, 2019)
FSK is useful in applications such as in modems in telemetry system.
3. Phase Shift Keying PSK
Phase Shift Keying, PSK, modulation is basically phase variation of the carrier sinusoidal signal
with guidance of the binary sequence of the data signal. The phase shifts by +180 degrees as
shown in the figure below.

Modulation and Demodulation 5
Figure 5:Phase Shift Keying PSK. Courtesy (ElProCus, 2019)
Phase Shift Keying is very useful in modelling of the broadband modem (ADSL), mobiles
phones and communication of satellites (ElProCus, 2019).
Modulation and demodulation process of the AM signals.
AM modulation process
The baseband signal is represented by the equation below;
V mod =V t cos ( ωt t )=V t cos ( 2 π f t t ) (1)
Wheref t−¿Baseband frequency.
V t −Baseband amplitude.
Expression of the carrier signal is;
V car =V c cos ( ωc t )=V c cos ( 2 π f c t ) (2)
Where V c−is carrier signal amplitude
f c−is carrier signal frequency.
The modulated AM signal is the product of the baseband and the carrier signals.
V AM (t )= [ V t + V mod ] V car (3)
Where V AM (t )is the modulated signal. Substituting respective equation in equation (3).
V AM (t )= [ V c+V t cos ( ωt t ) ] cos ( ωc t ) (4)
Simplifying equation (4) by removing V c outside the bracket.
V AM (t )= [1+ V t
V c
cos ( ωt t ) ]V c cos ( ωc t ) (5)
From equation (5), the modulating index is given by;

Modulation and Demodulation 6
ma= V t
V c
(6)
Therefore, equation (5) becomes;
V AM (t )= [ 1+ma cos ( ωt t ) ] V c cos ( ωc t ) (7)
Using trigonometric identity, the simplified version of equation (7) is;
V AM (t )=V c cos ( ωc t ) + V c ma
2 cos ( ωc +ωm ) t+ V c ma
2 cos ( ωc−ωm ) t (8a)
V AM (t )=V C cos ( 2 π f c t ) + V c ma
2 cos {2 πt ( f c+f m ) }+ V c ma
2 cos {2 πt ( f c−f m ) } (8b)
On the spectrum, the modulated signal is a DSC WC as shown below.
Figure 6:Spectrum of DSBWC AM signal
The modulated signal is as shown below.
Figure 7: Under-modulation of AM signal.
AM demodulation process
AM demodulation in the process of retrieving back modulating signals that carry useful
information. The block diagram for the AM demodulation is as shown below.

Modulation and Demodulation 7
Figure 8: Demodulation Scheme. Courtesy (Electronic notes, 2019)
AM demodulation can be implemented in two ways namely;
i. Envelope detector.
ii. Synchronous demodulator.
Envelope detector demodulation.
Envelope detector is basically a low pass filter. It allows low frequencies to pass and impedes
high frequency component. The figure below shows implementation of Square Law and
Envelope detector scheme.
Figure 9: Square Law and Envelope detector scheme. Courtesy (Ecelabs.njit.edu, 2019)
The modulated signal as in equation (7) is squared as shown below.
V AM (t )
2= { [ 1+ ma cos ( ωt t ) ] V c cos ( ωc t ) }
2
(9)
Simplifying;
V AM (t )
2= 1
2 ( 1+ma cos [ωt t] )2+ 1
2 ( 1+ ma cos [ ωt t] ) 2 cos ( 2 ωc t ) (10)
The high frequency component (cos ( 2ωc t )) is filtered out and thus equation (10) becomes;
V mod (t )
2= 1
2 (1+ma cos [ωt t ] )2
(11)
Finding square root;

Modulation and Demodulation 8
V mod (t )= 1
4 ( 1+ ma cos [ωt t ] ) (12)
Synchronous detector demodulation.
The diagram below shows the architectural scheme of the synchronous demodulator.
Figure 10: Synchronous Demodulator. Courtesy (Ecelabs.njit.edu, 2019)
From equation (8b);
V AM (t )=V C cos ( 2 π f c t ) + V c ma
2 cos {2 πt ( f c+ f m ) }+ V c ma
2 cos {2 πt ( f c−f m ) } (13)
Equation (13) is multiplied by { sin ( 2 π f c t ) } resulting into
¿ {− 1
2 cos ( 2 π f m t ) sin ( 2 π f m t )− 1
2 sin ( 2 π f c t ) −¿ 1
2 cos ( 2 π f mt ) ( 4 π f c t−2 π f m t ) + 1
4 cos ( 2 π f m t ) sin ( 2 π f c t +2 π f m t
(14)
The low pass filter of the synchronous demodulator filters out high frequency component ( f c)
resulting into;
V mod (t )=−1
2 cos ( 2 π f m t ) sin ( 2 π f m t ) (15)
The demodulated signal is thus as shown in equation (15)

Modulation and Demodulation 9
Amplitude Quadrature Modulation.
Two carrier signals modulated by the baseband are of the same frequency but 90 degrees out of
phase. In other words, the carrier signals are sine and cosine waves of same frequency and
amplitude. The in-phase signal is designated as “I” and quadrature signal is denoted as “Q”. The
QAM utilizes two sidebands by planting two independent sidebands in the same spectrum (notes,
2019).
The expression for I and Q are as shown below.
I = A cos θ∧Q= A sin θ (16)
The figure below shows QAM modulation scheme.
Figure 11: QAM modulation scheme
QAM modulation entails amplitude and phase modulation. Two modulated signals are produced
in the baseband stage. Two modulated signals are summed and processed into required frequency
and amplitude.
QAM demodulator is the opposite of the QAM modulator. The signal is split as it penetrates into
the system. They are then applied to the mixers with “I” and “Q” oscillator.

Modulation and Demodulation 10
Figure 12: QAM demodulation scheme
QAM modulation is different from Phase Shift Keying in terms of application. In PSK, the phase
of the carrier signal is varied as per the binary sequence of the digital data signal. In the QAM
modulation, the amplitude and phase of the carrier signal is adjusted by the modulating data
signal (notes, 2019).
3: SIMULATION CONFIGURATION
Modulation of 500 kHz carrier using 50 kHz message signal
DSB AM amplitude modulation scheme was implemented in Matlab Simulink as illustrated in
the figure below. The carrier signal and message signal were initialized with 500 kHz and 50kHz
frequencies in radian per second as shown in the expression below.
n . rad /sec =2 πf (17)
For carrier signal at 500 kHz;
ncarrier=2 π ×500,000 rad /sec (18)
For Message signal at 50 kHz;
nmessage=2 π ×50,000 rad /sec (19)

Modulation and Demodulation 11
Figure 13: DSB AM modulation
The model was simulated and the output modulated signal observed in frequency and time
domain. Signal in frequency domain was observed on the spectrum analyzer while time, it was
observed on the oscilloscope. The modulating index was changed as 0.5, 1 and 2 as the output
plots analyzed on the next section.
Demodulating DSB AM modulated signal using Envelope Detector.
Demodulation of the modulated signal using the envelope detector implemented in Matlab
Simulink as shown in figure 14.

Modulation and Demodulation 12
Figure 14: Demodulation of AM modulated signal using the envelope detector
The type of demodulator implementation is a Square Law envelope detector scheme. The
stopband of the low pass filter was set to 50 kHz. The output of the demodulated signals was
observed in both time and frequency domain. The modulating index was set as 0.5, 1, and 2 as
the output of the demodulated signals using envelope detector were observed.
Demodulating DSB AM modulated signal using synchronous detector.
Using synchronous detector was implemented in Matlab Simulink to demodulate AM modulated
signal.

Modulation and Demodulation 13
Figure 15: Demodulation using the synchronous detector
The modulating index was varied as 0.5, 1 and 2 as demodulated signals were viewed both in
time and frequency domain.
Demodulation of the DSB AM modulated signals using synchronous demodulator with
non-coherent Local Oscillator
The local oscillator signal of the previous model was varied in accordance with the given
parameter, making the whole demodulating system non-coherent.

Modulation and Demodulation 14
Figure 16:Demodulation of AM modulated signal using the synchronous detector with non-
coherent oscillator.
The modulating index was set to relatively large value implying infinite depth of modulation.
1 stage: Offset frequency
In the first set, the frequency of the oscillator signal was adjusted with an offset of (∆ f ) of 1kH,
2kH, 3kH, and 4kH and an output signal tested at each instance. The frequencies were adjusted
using the expressions below.
f c−new=f c+ ∆ f (20)
The Simulink block of the oscillator was set as;
ncarrier={2 π ×(f c+∆ f ) }rad / sec (21)
Where
f c=500 kHz
∆ f ={1 kHz , 2kHz ,3 kHz∧4 kHz
The corresponding signals were plotted as shown in the next section.
2 stage: Phase offset.
In the second stage, the phase offset of (∆ φ) 0, 45, 90, 270, and 360 degrees was introduced. In
the Simulink block of the oscillator, the phase input was initialized in radians as shown by the
expressions below.

Modulation and Demodulation 15
C(R )= ∆ φ
180 × π (22)
Where
∆ φ={0 , 45 , 90 ,270∧360
The output of the non-coherent synchronous detector was plotted in both frequency and time
domain as shown in the next section.
4: SIMULATION RESULTS
Modulation of 500 kHz carrier using 50 kHz message signal Results
The results of the DSB modulated signals under varying modulating index are as shown in the
figures below.
When modulating index is 0.5
When the modulating index was set to 0.5, the output of the demodulator is as shown in figure
17.
Figure 17: DSB AM modulated signal at 0.5 modulating index.
As observed, the signal has undergone under-modulation. This implies that the ratio of amplitude
of the message signal over carrier signal is less than one as illustrated by the expression below.

Modulation and Demodulation 16
ma= V m
V C
<1 (23)
When the depth of modulation is less than 1, the original message in the modulated signal in still
intact, i.e, it is not distorted. The frequency domain of the modulated signal has three spikes as
observed in figure 18.
Figure 18: AM modulated signal spectrum at 0.5 modulating index
Two side spikes represents sidebands of the modulated signal and the center spike is the carrier
signal since the modulated signal is DSB with carrier.
Existence of sidebands denote that the modulated signal has two frequency components.
When modulating index in 1.
The resultant modulated signal when modulating index was adjusted to unit is as shown in the
figure below.

Modulation and Demodulation 17
Figure 19:Figure 17: DSB AM modulated signal at 1 modulating index.
The modulating index for this case is derived as;
ma= V m
V C
=1 (24)
This indicates that the carrier and modulating signal have the same amplitude. Under this case,
the modulation is said to be a perfect modulation. The spectrum for the modulated signal is as
shown in figure 20.
Figure 20: AM modulated signal spectrum at 1 modulating index
The modulated signal has two frequency components due to sidebands. Under perfect
modulation, the message embedded in the modulated signal is not interfered with.
When modulating index is 2.

Modulation and Demodulation 18
The modulating index of the modulator was set to 2 and the resultant output signal is as shown in
figure 21.
Figure 21:Figure 17: DSB AM modulated signal at 2 modulating index.
The depth of modulation is calculated as;
ma= V m
V C
>1 (25)
Modulating index of more than unit implies that the signal has been over-modulated. Over-
modulation has a negative impact on the original message as it is distorted. The frequency
domain of the over-modulated signal is as shown in figure 22.
Figure 22: AM modulated signal spectrum at 2 modulating index
The spectrum has three spikes of equal magnitude. Thus the message has been distorted as there
are no sidebands. Over-modulated signal has three frequency components.

Modulation and Demodulation 19
Results of demodulating DSB AM modulated signal using Envelope Detector.
The demodulation of the DSB AM modulated signal outputs are as shown in the figures below.
Inferences were made at modulating index of 0.5, 1 and 2.
When modulating index is 0.5
With modulating index of 0.5, the figure below shows demodulated signal alongside the original
message signal.
Figure 23: Modulating and Demodulated signal at 0.5 modulating index
As noted, message and demodulated signals have the same frequency and are in phase. In other
word, the demodulated signal is replica of the message signal.
The frequency domain of the demodulated signal is as shown in the figure below.

Modulation and Demodulation 20
Figure 24: Spectrum of demodulated signal at 0.5 modulating index
The spectrum has one spike crossing x-axis implying that it has one frequency component.
Therefore, during demodulation, the high frequency components of the carrier signals have been
filtered out during demodulation.
When modulating index is 1.
The demodulated signal in time domain when the modulating index was 1 is as shown below.
Figure 25: Modulating and Demodulated signal at 1 modulating index
The message signal compared with the demodulated signals is dissimilar. The demodulated
signal is not a pure sine wave as the original message signal.
The frequency domain of the demodulated signal is as shown in the figure below.

Modulation and Demodulation 21
Figure 26:Spectrum of demodulated signal at 1 modulating index
The spectrum has three spikes crossing x-axis implying that the demodulated signal is not a pure
sine wave. In other words, the message in the signal has been distorted.
When modulating index is 2.
The output signal at the output of the envelope detector when the modulating index is 2 is as
shown below.
Figure 27: Modulating and Demodulated signal at 2 modulating index
The demodulated signal is not a pure sinusoidal wave. The spectrum of the demodulated signal is
as shown in the figure below.

Modulation and Demodulation 22
Figure 28:Spectrum of demodulated signal at 2 modulating index
Three spikes have been observed to be crossing the x-axis suggesting that the signal is not a pure
sine wave as the message signal.
Results of demodulating DSB AM modulated signal using synchronous detector.
The demodulation of the DSB AM modulated signal outputs are as shown in the figures below.
Inferences were made at modulating index of 0.5, 1 and 2.
When modulating index is 0.5
The output of the synchronous detector at 0.5 modulating frequency is as shown in the figure
below.

Modulation and Demodulation 23
Figure 29: Modulating and Demodulated signal at 0.5 modulating index
The demodulated signal has the same frequency as the message signal. However, the only
difference between the two signal is that they are 180 degrees out of phase. The spectrum of the
demodulated signal is as shown below.
Figure 30:Spectrum of demodulated signal at 0.5 modulating index
The spectrum has one spike implying that the demodulated signal has one frequency component.
Therefore, the original message is still intact.
When modulating index is 1

Modulation and Demodulation 24
When the modulation index was set to 1, the demodulated signal at the output of the synchronous
demodulator is as shown in the figure below.
Figure 31: Modulating and Demodulated signal at 1 modulating index
Just like the previous case, the signals have the same frequency but 180 degrees out of phase.
The spectrum of the demodulated signal is as shown below.
Figure 32: Spectrum of demodulated signal at 1 modulating index
The demodulated signal has one frequency component thus the message of the original signal is
not distorted.

Modulation and Demodulation 25
When modulating index is 2.
The output of the synchronous demodulator is as shown below.
Figure 33: Modulating and Demodulated signal at 2 modulating index
Despite modulated signal having modulating index greater than one, the output of the
demodulator has the same frequency as the original message signal. The spectrum is as shown
below.
Figure 34: Spectrum of demodulated signal at 2 modulating index
From the spectrum, the demodulated signal has one frequency component.

Modulation and Demodulation 26
Results of demodulation of the DSB AM modulated signals using synchronous demodulator
with non-coherent Local Oscillator
The simulation was done in two stage involving frequency offset and phase offset.
1 stage: Results of frequency offset
When frequency offset is 1kHz
When the offset frequency was adjusted to 1kHz, the demodulated signal is not sinusoidal as
shown in the figure below.
Figure 35: Demodulated and Demodulating signal at 1kHz offset
In the frequency domain, the spectrum of the demodulated signal is as shown in figure 36.
Figure 36: Spectrum of the Demodulated signal at 1 kHz offset
The spectrum has an m-shaped spectrum suggesting that the signal is not a pure sine wave.

Modulation and Demodulation 27
When the frequency offset is 2kHz
The frequency offset of the local oscillator when adjusted to 2 kHz, the output of the
demodulator is as shown in figure 37.
Figure 37:Demodulated and Demodulating signal at 2kHz offset
The output of the demodulator with frequency offset in the local oscillator is not a sinusoidal
wave. The spectrum of the demodulated signal is as shown figure 38.
Figure 38: Spectrum of the Demodulated signal at 2 kHz offset
The spectrum has an m-shaped spike suggesting that the message of the original signal has been
distorted.
When the frequency offset is 3kH

Modulation and Demodulation 28
The frequency offset of the local oscillator when adjusted to 3 kHz, the output of the
demodulator is as shown in figure 39.
Figure 39: Demodulated and Demodulating signal at 3kHz offset
The output of the demodulator with frequency offset in the local oscillator is not a sinusoidal
wave. The spectrum of the demodulated signal is as shown below.
Figure 40:Spectrum of the Demodulated signal at 3kHz offset
The spectrum has an m-shaped spectrum suggesting that the signal is not a pure sine wave.
When the frequency offset is 4kHz

Modulation and Demodulation 29
The frequency offset of the local oscillator when adjusted to 4 kHz, the output of the
demodulator is as shown in figure 41.
Figure 41:Demodulated and Demodulating signal at 4kHz offset
The output of the demodulator with frequency offset in the local oscillator is not a sinusoidal
wave. The spectrum of the demodulated signal is as shown below.
Figure 42: Spectrum of the Demodulated signal at 4 kHz offset

Modulation and Demodulation 30
The spectrum has an m-shaped spectrum suggesting that the signal is not a pure sine wave.
Therefore, frequency offset at the local oscillator completely distorts the message of the
modulating carrier wave.
2 stage: Results of phase offset
When phase offset is 0 degrees
Zero degrees offset has not impact on the demodulated signal of the non-coherent oscillator as
far as the message of the carrier signal is concerned.
Figure 43:Demodulated and Demodulating signal at 0 degrees offset
As seen on the figure above, the frequency of the demodulated signal is similar to the frequency
of the modulating signal. The frequency domain of the demodulated signal is as shown in the
figure below.

Modulation and Demodulation 31
Figure 44: Spectrum of the demodulated signal at 0 degrees offset
The signal has one frequency component proving that the message in the signal has been
maintained as in the original modulating signal.
When phase offset is 45 degrees
The figure below shows demodulated signal alongside modulating signal.
Figure 45:Demodulated and Demodulating signal at 45 degrees offset
The demodulated signal has the same frequency as the modulating signal. The frequency domain
equivalent of the demodulated signal is as shown in the figure below.

Modulation and Demodulation 32
Figure 46: Spectrum of the demodulated signal at 45 degrees offset
The signal has one frequency component.
When phase offset is 90 degrees
When phase offset of 90 degrees was introduced, the demodulated signal in comparison with the
message signal is as shown in the figure below.
Figure 47:Demodulated and Demodulating signal at 90 degrees offset
The two signals are totally dissimilar implying that the original message have been distorted.
The spectrum of the demodulated signal is as shown in the figure below.

Modulation and Demodulation 33
Figure 48: Spectrum of the demodulated signal at 180 degrees offset
The signal has more than one frequency component hence the original information has been
distorted.
When offset is 270 degrees
When phase offset of 270 degrees was introduced, the demodulated signal in comparison with
the message signal is as shown in the figure below.
Figure 49: Demodulated and Demodulating signal at 270 degrees offset
The two signals are totally dissimilar implying that the original message have been distorted.
The spectrum of the demodulated signal is as shown in the figure below.

Modulation and Demodulation 34
Figure 50: Spectrum of the demodulated signal at 270 degrees offset
The signal has more than one frequency component hence the original information has been
distorted.
When offset is 360 degrees
When phase offset of 360 degrees was introduced, the demodulated signal in comparison with
the message signal is as shown in the figure below.
Figure 51: Demodulated and Demodulating signal at 360 degrees offset
The demodulated signal has the same frequency as the modulating signal. The frequency domain
equivalent of the demodulated signal is as shown in the figure below.

Modulation and Demodulation 35
Figure 52: Spectrum of the demodulated signal at 360 degrees offset
The demodulated signal has one frequency component thus the message of the original signal is
not distorted.
As from the analysis of the frequency offset and phase offset, all frequency offsets tested gave
distorted information. However, with the phase shift, 0 degrees and 360 phase shifts gave the
demodulated signal bearing the original information. Therefore, phase shift is more efficient and
reliable than frequency shift.
Comparison of performance of the Phase Shift Keying (PSK) and Quadrature Amplitude
Modulation (GAM)
Performance of PSK
In the PSK, there is phase variation of the carrier signal in M-ary PSK as the amplitude
remain unchanged. The modulated waveform in the MPSK is as shown in the expression
below.
Si (t )= √ 2 Es
T s
cos {2 π f c+ 2 π
M ( i−1 ) } (26)
For
0 ≤ t ≤T s
And

Modulation and Demodulation 36
i=1,2 , … M
The energy contained in each symbol is given as;
Es= ( log2
M ) Eb (27)
And the period of the symbol is determined by;
T s= ( log2
M ) T b (29)
The integral of equation (26) can be rewritten as;
si (t )= √ 2 Es
T s
cos { 2 π
M ( i−1 ) }cos ( 2 π f c t ) − √ 2 Es
T s
sin { 2 π
M ( i−1 ) }sin ( 2 π f c t ) (30)
Where
i=1,2 , … . M
Since the amplitude of the carrier signal is constant, the constellation diagram for PSK is
circular as shown in the figure below.
Figure 53: 16PSK Constellation
.
Thus, the M-ary signals are uniformly distributed at zero center. The radius of the 16PSK
constellation is equal to √ Es .
The Euclidean distance is given by;
d1=2 √ Es ( π
16 )=0.393 √ Es (31)
Performance of QAM
The QAM works by varying both frequency and amplitude of the carrier signal. The expression
describing QAM modulating is as shown below.

Modulation and Demodulation 37
si (t )= √ 2 Es
T s
ai cos ( 2 π f c t ) + √ 2 Es
T s
bi sin ( 2 π f c t ) (32)
For
0 ≤ t ≤T s
And
i=1,2 , … M
The constellation diagram for 16QAM is as shown in the figure below.
Figure 54: 16QAM Constellation
The Euclidean distance is given by;
d2= √ 2 Es
3 =0.471 √Es (34)
Comparing the Euclidean distance of 16PSK as in equation (31), and 16QAM as in equation
(34),
d2 >d1 (35)
Thus, it can be concluded that the performance of 16QAM is better when compared to the
performance of 16PSK (Tan and Chen, 2019).

Modulation and Demodulation 38
5: CONCLUSION
The study of the AM modulation has successfully been covered in this report. The theoretical
background of analog modulation and digital modulation was dealt with. It was seen that the
carrier signal in both types of modulation is continuous analog signal and the disparity is brought
about by the type of the message signal. The theory behind types of digital modulation utilizing
the three properties of the carrier signal have been discussed. DSB AM modulation and
demodulation was implemented in Matlab Simulink environment. During the implementation of
AM modulation in Simulink, under-modulated, over-modulated and perfectly modulated signals
were observed and analyzed. Various types of AM demodulation using Envelope detector and
Synchronous demodulator with coherent and non-coherent oscillator were also studied in the
Matlab Simulink environment. Also, QAM modulation was theoretically studied. Its
performance was compared to that of the PSK. It was found out that QAM is better in
performance that PSK.

Modulation and Demodulation 39
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