Carrier-Amplitude modulation
In baseband digital PAM:
(2d - the Euclidean distance between two adjacent points)
the transmitted signal waveforms:
special case:
rectangular
pulse
the Amplitude modulated Carrier
signal is usually called
amplitude shift keying (ASK)
Gr ( f )
W-
2
W
0
r
Figure 7.1: Energy density spectrum of the transmitted signal
g (t).
T
Baseband
signal sm

Bandpass signal
sm ( t ) cos 2f c t
Carrier
cos( 2f c t )
Figure 7.2: amplitude modulation of a sinusoidal carrier by the
baseband PAM signal
1
W-
Gr ( f )
2
W
0
(a)
r
Um ( f )
1
2
f
- fc - W
- fc
- fc + W
0
fc - W
fc
fc + W
(b)
Figure 7.3: Spectra of (a) baseband and (b) amplitudemodulated signal.
-5d
-3d
-d
0
d
3d
5d
Figure 7.4: Signal points that take M values on the real line
The baseband PAM signal waveforms in general:
Demodulation of PAM Signal
when we cross correlate the signal r(t)
with the signal waveform we get:
the variance can expressed as:
X
X
Figure 7.5: Demodulation of bandpass digital PAM signal.
Example 7.1:
In an amplitude-modulated digital PAM system, the
transmitter filter with impulse response gT(t) has a square-root
raised-cosine spectral characteristic as described in Illustrative
problem 6.7, with a roll-off factor a=0.5. The carrier frequency
is fc=40/T. evaluate and graph the spectrum of baseband
signal and the spectrum of the amplitude-modulated signal
Answer
ip_07_01
Carrier-Phase Modulation
This type of digital phase modulation is called
Phase-Shift-Key
where gT(t) is the transmitting filter pulse shape.
when gT(t) is a rectangular pulse we expressed
the transmitted signal waveform (at 0 < t <T) as:
Example 7.2:
Generate the constant-envelope PSK signal waveforms given
by (1.3.4) for M=8. For convenience, the signal amplitude is
normalized to unity.
Answer
ip_07_02
00
01
Es
E
E
11
M= 2
10
M= 4
011
001
010
Es
110
100
111
M=8
000
101
Figure 7.8:PSK signal
constellations
Phase Demodulation and Detection
the two quadrature components of the additive noise
the received signal vector r is projected onto each
of the M possible transmitted signal vector {Sm}and
select the vector corresponding to the largest projection.
The correlation metrics
we select the {Sm} signal whosh phase is the closet
Example 7.3: We shall perform a Monte Carlo simulation of M=4 PSK
communication system that models the detector as the one that computes
the correlation metrics given in (7.3.15). The model for the system to be
simulated is shown in Figure 7.11.
Uniform random
number generator
Gaussian RNG
nc
4-PSK
MAPPER
rc
+
Detector
ns + rs
2-bit
symbol
Gaussian RNG
compare
Bit-error
counter
Symbol-error
counter
Figure 7.11:Block diagram of an M=4 PSK system for
Monte Carlo simulation
Answer
ip_07_03
Differential Phase Modulation and
Demodulation
X
X
Block diagram of DPSK demodulator
Example 7.4: implement a differential encoder for the case of
m=8 DPSK.
Answer
ip_07_04
Example 7.5:
Perform a Monte Carlo simulation of an M=4 DPSK
communication
Answer
ip_07_05
Uniform random
number generator
Gaussian RNG
nc
4-DPSK
MAPPER
rc
+
ns + rs
Delay
M=4DPSK
Detector
2-bit
output
Gaussian RNG
compare
Symbol-error
counter
Figure 7.15: Block diagram of m=4 DPSK system for the Monte Carlo
simulation
Quadrature Amplitude Modulation
the transmitted signal waveform
the combined digital amplitude
and digital-phase modulation form
Transmitting
filter gT(t)
Binary Serial-todata parallel
converter
Balanced
modulator
Oscillator
+
90 Phase shift
Transmitting
filter gT(t)
Transmitted
QAM signal
Balanced
modulator
Functional block diagram of modulator for QAM
Quadrature Amplitude demodulation
X
X
X
X
Demodulation and detection of QAM signals
Probability of Error for QAM in an
AWGN Channel
Example 7.6: perform a Monte Carlo simulation of am M=16-QAM
communication system using a rectangular signal constellation. The
model of the system to be simulated is shown in figure 7.22.
Uniform random
number generator
Gaussian RNG
nc
A
mc
M=16-QAM
+
A
ms
signal selector
ns +
rc
Detector
rs
4-bit
symbol
Gaussian RNG
compare
Bit-error
counter
Symbol-error
counter
Figure:Block diagram of an M=16-QAM system for
the Monte Carlo simulation
Answer
ip_07_06
Carrier-Frequency Modulation
Frequency-Shift Keying
Demodulation and detection of FSK signals
the filter received signal at the input
phase
shift
The additive bandpass noise

PLL1

Received
signal
Sample at t=T
Sample at t=T
PLL1
Output
decision

Sample at t=T
PLL1
Figure 7.26: Phase-coherent demodulation of M-ary FSK signals.
  ( )dr
cos2f t
t
0
c
sin 2f c t
r1c
Sample at t=T
  ( )dr
r1c
 
r1c
t
Received signal
0
cos 2 ( f c  f )t
t
( )dr
0
Detector
sin 2 ( f c  f )t
  ( )dr
t
0
r1c
Output
decision
Sample at t=T
cos 2 [ f c  ( M  1) f ]t


t
( )dr
0
cos 2 [ f c  ( M  1) f ]t
  ( )dr
t
0
r1c
Sample at t=T
r1c
Sample at t=T
Figure 7.26: Demodulation of M-ary signals for noncoherent detection .
Example 7.7:Consider a binary communication system that employs
the two FSK signal waveforms given as
u1 (t )  c os2f 1t , 0  t  Tb
u1 (t )  cos 2f 2 t , 0  t  Tb
Where f1 =1000/Tb and f2= f1+1/Tb. The channel imparts a phase shift of 
=45 on each of the transmitted signals, so that the received signal in the
absence of noise is

r (t )  c os(2f i t  ), 0  t  Tb
4
Numerically implement the correlation-type demodulator for FSK
signals.
Answer
ip_07_07
Probability of Error for Noncoherent
Detection of FSK
Example 7.8: perform a Monte Carlo simulation of a binary FSK communication system in
which the signal waveforms are given by(7.5.1) where f2 = f2 +1/ Tb and the detector is a squarelaw detector. The block diagram of the the binary FSK system to be simulated is shown in Figure
7.30.
Uniform
RNG
Uniform
RNG
r1c
FSK
signal
selector
Uniform
RNG

r1s


r2 c
r2s

Gaussian
RNG
r1c ( ) 2
r1s
2
r2 c
()
( )2
r2s 2
()

r1
Output
Detector

bit
r2
Gaussian
RNG
compare
Bit-error counter
Figure7.30: Block diagram of a binary FSK system for the Monte
Carlo simulation
Answer
ip_07_08
Synchronization in Communication Systems
Carrier Synchronization: A local oscillator whose
phase is controlled to be synch with the carrier signal.
Phase-Locked Loop: A nonlinear feedback control sys
for controlling the phase of the local oscillator .
the input to
the PLL
the input of the loop filter
( e(t) has a high and a low frequency component. )
The role of the loop filter is to remove
the high frequency component.

Figure 7.32: The
Input signal
r(t)
+
-
Figure 7.33: The phase-locked loop after removal of high-frequency
components

+
-
Figure 7.34: The linearized model for a phase-locked loop.
Example 7.9: [First-order PLL] Assuming that
1  0.01s
G ( s) 
1 s
And K=1, determine and plot the response of thePLL to an
abrupt change of height 1 to the input phase.
Answer
ip_07_09
Clock Synchronization
early-late gate: A simple implementation of clock
synch based on the fact that in a PAM communication
sys the output of the matched filter is the autocorrlation
function of the basic pulse signal used in the PAM sys.
The autocorrlation function is MAX and symmetric
when we are not sampling at the optimal sampling time:
in this case the correct sampling time is before
the assumed sampling time, and the sampling
should be done earlier / be delayed.
The early-late gate synch sys therefore takes
three samples at T1, T-, T+ and then compares
|y(T-) | and |y(T+) | and, depending on their
relative values,generates a signal to correct
the sampling time.
Matched filter output
Early
sample
Optimum
sample
Late
sample
TT-
T
T
T+
T+
Figure 7.36: The matched filter output and early and late
samples
Example 7.10:[clock synchronization]
A binary PAM communication systems uses a raisedcosine waveform with a roll-off factor of 0.4. The system
transmission rate is 4800 bits/s. write a MATLAB file that
simulates the operation of an early-late gate for this
system
Answer
ip_07_10