simulation in digital communication
DESCRIPTION
Simulation in Digital communication. chapter # 7 Digital Transmission Via Carrier Modulation. Carrier-Amplitude modulation. In baseband digital PAM:. (2d - the Euclidean distance between two adjacent points). the transmitted signal waveforms:. special case:. rectangular pulse. - PowerPoint PPT PresentationTRANSCRIPT
![Page 1: Simulation in Digital communication](https://reader035.vdocuments.us/reader035/viewer/2022062500/5681586a550346895dc5ca54/html5/thumbnails/1.jpg)
![Page 2: Simulation in Digital communication](https://reader035.vdocuments.us/reader035/viewer/2022062500/5681586a550346895dc5ca54/html5/thumbnails/2.jpg)
![Page 3: Simulation in Digital communication](https://reader035.vdocuments.us/reader035/viewer/2022062500/5681586a550346895dc5ca54/html5/thumbnails/3.jpg)
Carrier-Amplitude modulation
In baseband digital PAM:
(2(2d - the Euclidean distance between two adjacent points)d - the Euclidean distance between two adjacent points)
![Page 4: Simulation in Digital communication](https://reader035.vdocuments.us/reader035/viewer/2022062500/5681586a550346895dc5ca54/html5/thumbnails/4.jpg)
the transmitted signal waveforms:
special case:
rectangularpulse
![Page 5: Simulation in Digital communication](https://reader035.vdocuments.us/reader035/viewer/2022062500/5681586a550346895dc5ca54/html5/thumbnails/5.jpg)
the Amplitude modulated Carrier
signal is usually called
amplitude shift keying (ASK)
![Page 6: Simulation in Digital communication](https://reader035.vdocuments.us/reader035/viewer/2022062500/5681586a550346895dc5ca54/html5/thumbnails/6.jpg)
0r
G fr ( )2
WW-
Figure 7.1: Energy density spectrum of the transmitted signal
gT(t).
![Page 7: Simulation in Digital communication](https://reader035.vdocuments.us/reader035/viewer/2022062500/5681586a550346895dc5ca54/html5/thumbnails/7.jpg)
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
![Page 8: Simulation in Digital communication](https://reader035.vdocuments.us/reader035/viewer/2022062500/5681586a550346895dc5ca54/html5/thumbnails/8.jpg)
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.
![Page 9: Simulation in Digital communication](https://reader035.vdocuments.us/reader035/viewer/2022062500/5681586a550346895dc5ca54/html5/thumbnails/9.jpg)
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:
![Page 10: Simulation in Digital communication](https://reader035.vdocuments.us/reader035/viewer/2022062500/5681586a550346895dc5ca54/html5/thumbnails/10.jpg)
Demodulation of PAM Signal
![Page 11: Simulation in Digital communication](https://reader035.vdocuments.us/reader035/viewer/2022062500/5681586a550346895dc5ca54/html5/thumbnails/11.jpg)
when we cross correlate the signal r(t) with the signal waveform we get:
the variance can expressed as:
![Page 12: Simulation in Digital communication](https://reader035.vdocuments.us/reader035/viewer/2022062500/5681586a550346895dc5ca54/html5/thumbnails/12.jpg)
Figure 7.5: Demodulation of bandpass digital PAM signal.
X
X
![Page 13: Simulation in Digital communication](https://reader035.vdocuments.us/reader035/viewer/2022062500/5681586a550346895dc5ca54/html5/thumbnails/13.jpg)
Answerip_07_01MATLAB.lnk
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
![Page 14: Simulation in Digital communication](https://reader035.vdocuments.us/reader035/viewer/2022062500/5681586a550346895dc5ca54/html5/thumbnails/14.jpg)
Carrier-Phase Modulation
This type of digital phase modulation is called Phase-Shift-Key
where gT(t) is the transmitting filter pulse shape.
![Page 15: Simulation in Digital communication](https://reader035.vdocuments.us/reader035/viewer/2022062500/5681586a550346895dc5ca54/html5/thumbnails/15.jpg)
when gT(t) is a rectangular pulse we expressed the transmitted signal waveform (at 0 < t <T) as:
![Page 16: Simulation in Digital communication](https://reader035.vdocuments.us/reader035/viewer/2022062500/5681586a550346895dc5ca54/html5/thumbnails/16.jpg)
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.
Answerip_07_02MATLAB.lnk
![Page 17: Simulation in Digital communication](https://reader035.vdocuments.us/reader035/viewer/2022062500/5681586a550346895dc5ca54/html5/thumbnails/17.jpg)
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
![Page 18: Simulation in Digital communication](https://reader035.vdocuments.us/reader035/viewer/2022062500/5681586a550346895dc5ca54/html5/thumbnails/18.jpg)
Phase Demodulation and Detection
the two quadrature components of the additive noise
![Page 19: Simulation in Digital communication](https://reader035.vdocuments.us/reader035/viewer/2022062500/5681586a550346895dc5ca54/html5/thumbnails/19.jpg)
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
![Page 20: Simulation in Digital communication](https://reader035.vdocuments.us/reader035/viewer/2022062500/5681586a550346895dc5ca54/html5/thumbnails/20.jpg)
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.
Answerip_07_03MATLAB.lnk
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
![Page 21: Simulation in Digital communication](https://reader035.vdocuments.us/reader035/viewer/2022062500/5681586a550346895dc5ca54/html5/thumbnails/21.jpg)
Differential Phase Modulation and Demodulation
![Page 22: Simulation in Digital communication](https://reader035.vdocuments.us/reader035/viewer/2022062500/5681586a550346895dc5ca54/html5/thumbnails/22.jpg)
![Page 23: Simulation in Digital communication](https://reader035.vdocuments.us/reader035/viewer/2022062500/5681586a550346895dc5ca54/html5/thumbnails/23.jpg)
X
X
Block diagram of DPSK demodulator
![Page 24: Simulation in Digital communication](https://reader035.vdocuments.us/reader035/viewer/2022062500/5681586a550346895dc5ca54/html5/thumbnails/24.jpg)
Example 7.4: implement a differential encoder for the case of m=8 DPSK.
Answerip_07_04MATLAB.lnk
![Page 25: Simulation in Digital communication](https://reader035.vdocuments.us/reader035/viewer/2022062500/5681586a550346895dc5ca54/html5/thumbnails/25.jpg)
Example 7.5: Perform a Monte Carlo simulation of an M=4 DPSK communication
Answerip_07_05MATLAB.lnk
![Page 26: Simulation in Digital communication](https://reader035.vdocuments.us/reader035/viewer/2022062500/5681586a550346895dc5ca54/html5/thumbnails/26.jpg)
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
![Page 27: Simulation in Digital communication](https://reader035.vdocuments.us/reader035/viewer/2022062500/5681586a550346895dc5ca54/html5/thumbnails/27.jpg)
Quadrature Amplitude Modulation
the transmitted signal waveform
the combined digital amplitude and digital-phase modulation form
![Page 28: Simulation in Digital communication](https://reader035.vdocuments.us/reader035/viewer/2022062500/5681586a550346895dc5ca54/html5/thumbnails/28.jpg)
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
![Page 29: Simulation in Digital communication](https://reader035.vdocuments.us/reader035/viewer/2022062500/5681586a550346895dc5ca54/html5/thumbnails/29.jpg)
![Page 30: Simulation in Digital communication](https://reader035.vdocuments.us/reader035/viewer/2022062500/5681586a550346895dc5ca54/html5/thumbnails/30.jpg)
![Page 31: Simulation in Digital communication](https://reader035.vdocuments.us/reader035/viewer/2022062500/5681586a550346895dc5ca54/html5/thumbnails/31.jpg)
Quadrature Amplitude demodulation
X
X
X
XDemodulation and detection of QAM signals
![Page 32: Simulation in Digital communication](https://reader035.vdocuments.us/reader035/viewer/2022062500/5681586a550346895dc5ca54/html5/thumbnails/32.jpg)
Probability of Error for QAM in an AWGN Channel
![Page 33: Simulation in Digital communication](https://reader035.vdocuments.us/reader035/viewer/2022062500/5681586a550346895dc5ca54/html5/thumbnails/33.jpg)
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.
Answerip_07_06MATLAB.lnk
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
![Page 34: Simulation in Digital communication](https://reader035.vdocuments.us/reader035/viewer/2022062500/5681586a550346895dc5ca54/html5/thumbnails/34.jpg)
Carrier-Frequency Modulation
![Page 35: Simulation in Digital communication](https://reader035.vdocuments.us/reader035/viewer/2022062500/5681586a550346895dc5ca54/html5/thumbnails/35.jpg)
Frequency-Shift Keying
![Page 36: Simulation in Digital communication](https://reader035.vdocuments.us/reader035/viewer/2022062500/5681586a550346895dc5ca54/html5/thumbnails/36.jpg)
Demodulation and detection of FSK signals
the filter received signal at the input
The additive bandpass noise
phase shift
![Page 37: Simulation in Digital communication](https://reader035.vdocuments.us/reader035/viewer/2022062500/5681586a550346895dc5ca54/html5/thumbnails/37.jpg)
![Page 38: Simulation in Digital communication](https://reader035.vdocuments.us/reader035/viewer/2022062500/5681586a550346895dc5ca54/html5/thumbnails/38.jpg)
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
![Page 39: Simulation in Digital communication](https://reader035.vdocuments.us/reader035/viewer/2022062500/5681586a550346895dc5ca54/html5/thumbnails/39.jpg)
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
![Page 40: Simulation in Digital communication](https://reader035.vdocuments.us/reader035/viewer/2022062500/5681586a550346895dc5ca54/html5/thumbnails/40.jpg)
Example 7.7:Consider a binary communication system that employs the two FSK signal waveforms given as
Answerip_07_07MATLAB.lnk
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.
![Page 41: Simulation in Digital communication](https://reader035.vdocuments.us/reader035/viewer/2022062500/5681586a550346895dc5ca54/html5/thumbnails/41.jpg)
Probability of Error for Noncoherent Detection of FSK
![Page 42: Simulation in Digital communication](https://reader035.vdocuments.us/reader035/viewer/2022062500/5681586a550346895dc5ca54/html5/thumbnails/42.jpg)
Answerip_07_08
MATLAB.lnk
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
![Page 43: Simulation in Digital communication](https://reader035.vdocuments.us/reader035/viewer/2022062500/5681586a550346895dc5ca54/html5/thumbnails/43.jpg)
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
![Page 44: Simulation in Digital communication](https://reader035.vdocuments.us/reader035/viewer/2022062500/5681586a550346895dc5ca54/html5/thumbnails/44.jpg)
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.
![Page 45: Simulation in Digital communication](https://reader035.vdocuments.us/reader035/viewer/2022062500/5681586a550346895dc5ca54/html5/thumbnails/45.jpg)
Figure 7.32: The
![Page 46: Simulation in Digital communication](https://reader035.vdocuments.us/reader035/viewer/2022062500/5681586a550346895dc5ca54/html5/thumbnails/46.jpg)
Input signal r(t) +
-
Figure 7.33: The phase-locked loop after removal of high-frequency components
![Page 47: Simulation in Digital communication](https://reader035.vdocuments.us/reader035/viewer/2022062500/5681586a550346895dc5ca54/html5/thumbnails/47.jpg)
Figure 7.34: The linearized model for a phase-locked loop.
-
+
![Page 48: Simulation in Digital communication](https://reader035.vdocuments.us/reader035/viewer/2022062500/5681586a550346895dc5ca54/html5/thumbnails/48.jpg)
Answerip_07_09MATLAB.lnk
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.
![Page 49: Simulation in Digital communication](https://reader035.vdocuments.us/reader035/viewer/2022062500/5681586a550346895dc5ca54/html5/thumbnails/49.jpg)
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
![Page 50: Simulation in Digital communication](https://reader035.vdocuments.us/reader035/viewer/2022062500/5681586a550346895dc5ca54/html5/thumbnails/50.jpg)
when we are not sampling at the optimal sampling time:
![Page 51: Simulation in Digital communication](https://reader035.vdocuments.us/reader035/viewer/2022062500/5681586a550346895dc5ca54/html5/thumbnails/51.jpg)
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.
![Page 52: Simulation in Digital communication](https://reader035.vdocuments.us/reader035/viewer/2022062500/5681586a550346895dc5ca54/html5/thumbnails/52.jpg)
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
![Page 53: Simulation in Digital communication](https://reader035.vdocuments.us/reader035/viewer/2022062500/5681586a550346895dc5ca54/html5/thumbnails/53.jpg)
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
Answerip_07_10MATLAB.lnk