simulation in digital communication

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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