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Digital modulation: the process by which digital symbols are transformed into

waveforms that are compatible with the characteristics of the channel

In baseband modulation the waveforms take the form of shaped pulses; In bandpass

modulation the shaped pulses modulate a sinusoid called carrier wave

The transmission of EM fields through space is accomplished with the use of

antennas. The size of antennas depends on the wavelength and the application

For cellular, the antenna are typically /4 in size while =c/f

Considering sending a baseband signal f = 3000 Hz by coupling it to an antenna

directly without a carrier wave. How large would the antenna have to be?

For the 3000 Hz baseband signal, /4 = 25000 m, so, to transmit a 3000 Hz baseband

signal without carrier-wave modulation, an antenna that spans 25000 m would be

required

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Modulation Benefits

Antenna dimension

Separate the different signal, such as FDM

Minimize the effect of interference, such asspread-spectrum modulation

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Demodulation vs Detection:

Sometimes interchangeably

Demodulation emphasizes waveform recovery

Detection entails the process of symbol decision

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2EA

T

!

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Channel Model

We use AWGN channel model to determine

probability of error

Additive: the noise gets added notmultiplied

White: the spectrum of the noise is flat for all

frequencies

Gaussian: the values of the noise follows the

Gaussian probability distribution function

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y Q(y) y Q(y) y Q(y)

0,05

0,10

0,150,20

0,25

0,4801

0,4602

0,44050,4207

0,4013

1,05

1,10

1,151,20

1,25

0,1469

0,1357

0,12510,1151

0,0156

2,10

2,20

2,302,40

2,50

0,0179

0,0139

0,01070,0082

0,0062

0,30

0,35

0,40

0,45

0,50

0,3821

0,3632

0,3446

0,3264

0,3085

1,30

1,35

1,40

1,45

1,50

0,0968

0,0885

0,0808

0,0735

0,0668

2,60

2,70

2,80

2,90

3,00

0,0047

0,0035

0,0026

0,0019

0,0013

0,55

0,60

0,65

0,70

0,75

0,2912

0,2743

0,2578

0,2420

0,2266

1,55

1,60

1,65

1,70

1,75

0,0606

0,0548

0,0495

0,0446

0,0401

3,10

3,20

3,30

3,40

3,50

0,0010

0,00069

0,00048

0,00034

0,00023

0,80

0,85

0,90

0,95

1,00

0,2119

0,1977

0,1841

0,1711

0,1587

1,80

1,85

1,90

1,95

2,00

0,0359

0,0322

0,0287

0,0256

0,0228

3,60

3,70

3,80

3,90

4,00

0,00016

0,00010

0,00007

0,00005

0,00003

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Use Gray Code

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Scheme S1 and s2 BW Pe

Coherent ASK

Noncoh. ASK Same as above

Coherent FSK

Noncoh. FSK Same as above

Coherent PSK

1 cos cs t A t[!

2 0s t !2

b

r;2

04

bA T

Q N

2b

r;2

0

1exp

2 16

bA T

N

1 cos c ds t A t[ [!

2 cos c ds t

At[ [

!

2 1.5d b

r[ T!

2b

r"2

0

0.61b

A T

Q N

2 2d bk r[ T!

2b

r" 2

0

1exp

2 8

bA T

N

1 cos cs t A t[! 2 cos cs t A t[!

2c b

k r[ T!

2 br; 2

0

bA T

QN

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Standard form of rectangularQAM

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Symbol error probability of M-ary QAM

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