Carrier-Amplitude modulation
In baseband digital PAM:
(2(2d - the Euclidean distance between two adjacent points)d - the Euclidean distance between two adjacent points)
the transmitted signal waveforms:
special case:
rectangularpulse
the Amplitude modulated Carrier
signal is usually called
amplitude shift keying (ASK)
0r
G fr ( )2
WW-
Figure 7.1: Energy density spectrum of the transmitted signal
gT(t).
Carrier
f tccos( )2
Baseband
signal sm
Bandpass
s t tm
signal
cos 2 fc( )
Figure 7.2: amplitude modulation of a sinusoidal carrier by the baseband PAM signal
0r
G fr ( )2
WW-
1
)a(
f
U fm ( )1
2
0)b(
- fc + W- fc - W - fc fc + Wfcfc - W
Figure 7.3: Spectra of (a) baseband and (b) amplitude-modulated signal.
0-5d d-d-3d 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:
Figure 7.5: Demodulation of bandpass digital PAM signal.
X
X
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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
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.
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110
M=2
EE
01
10
00
11
Es
M=4
Es
100
101111
010011 001
000
M=8 Figure 7.8:PSK signal constellations
Phase Demodulation and Detection
the two quadrature components of the additive noise
The correlation metrics
the received signal vector r is projected onto eachof the M possible transmitted signal vector {Sm}and select the vector corresponding to the largest projection.
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.
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Uniform random number generator
compare
4-PSK
MAPPERDetector
Bit-error counter
Symbol-error
counter
2-bit symbol
ncrc
ns rs
Figure 7.11:Block diagram of an M=4 PSK system for Monte Carlo simulation
++
Gaussian RNG
Gaussian RNG
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.
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Example 7.5: Perform a Monte Carlo simulation of an M=4 DPSK communication
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Figure 7.15: Block diagram of m=4 DPSK system for the Monte Carlo simulation
Uniform random number generator
compare
4-DPSK
MAPPERDelay
Symbol-error
counter
2-bit output
ncrc
ns rs++
Gaussian RNG
Gaussian RNG
M=4DPSK
Detector
Quadrature Amplitude Modulation
the transmitted signal waveform
the combined digital amplitude and digital-phase modulation form
Transmitting
filter gT(t)
Binary data
Serial-to- parallel converter
Transmitting
filter gT(t)
Oscillator
Balanced modulator
Balanced modulator
90 Phase shift Transmitted QAM signal
+
Functional block diagram of modulator for QAM
Quadrature Amplitude demodulation
X
X
X
XDemodulation 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.
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Amc
Ams
Figure:Block diagram of an M=16-QAM system for the Monte Carlo simulation
Uniform random number generator
compare
M=16-QAM
signal selectorDetector
Bit-error counter
Symbol-error
counter
4-bit symbol
nc rc
nsrs
++
Gaussian RNG
Gaussian RNG
Carrier-Frequency Modulation
Frequency-Shift Keying
Demodulation and detection of FSK signals
the filter received signal at the input
The additive bandpass noise
phase shift
Sample at t=T
PLL1
Sample at t=T
Sample at t=T
Received signal
Output decision
Figure 7.26: Phase-coherent demodulation of M-ary FSK signals.
PLL1
PLL1
Figure 7.26: Demodulation of M-ary signals for noncoherent detection .
Sample at t=T
Rec
eive
d si
gnal
cos2f tc
Sample at t=T
Detector
Sample at t=T
sin 2f tc
cos ( )2 f f tc
Sample at t=T
sin ( )2 f f tc
cos [ ( ) ]2 1 f M f tc
cos [ ( ) ]2 1 f M f tc
Output decision
( )dr0
t
r1c
r1c
r1c
r1c
r1c
r1c
( )dr0
t
( )dr0
t
( )dr0
t
( )dr0
t
( )dr0
t
Example 7.7:Consider a binary communication system that employs the two FSK signal waveforms given as
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u t c os f t
u t f t
b1 1
1 2
2
2
( ) ,
( ) cos ,
0 t 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 f ti b( ) ( ), 24
0 t T
Numerically implement the correlation-type demodulator for FSK signals.
Probability of Error for Noncoherent Detection of FSK
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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 square-law detector. The block diagram of the the binary FSK system to be simulated is shown in Figure 7.30.
Uniform RNG
FSK signal selector
( )
r s1
( )
Detector
( )2( )
r c2
Gaussian RNG
compare
Bit-error counterFigure7.30: Block diagram of a binary FSK system for the Monte Carlo simulation
Output
bit
Gaussian RNG
s2r
c2r
r s1
c1rc1r
s2r 2r
1r2
2
2
Uniform RNG
Uniform RNG
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 sysfor controlling the phase of the local oscillator .
the input tothe 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.
-
+
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Example 7.9: [First-order PLL] Assuming that
G ss
s( )
.
1 0 01
1
And K=1, determine and plot the response of thePLL to an abrupt change of height 1 to the input phase.
Clock Synchronizationearly-late gate: A simple implementation of clock synch based on the fact that in a PAM communicationsys the output of the matched filter is the autocorrlationfunction 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 theirrelative values,generates a signal to correct the sampling time.
Late sampleEarly sample
T- T T+
Matched filter output
Optimum sample
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 raised-cosine 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
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