Baseband Digital SystemAnalog to Digital Conversion

SamplingQuantizingEncoding

Digital Signal RepresentationOrthogonal conditionBandwidth

Line Codes and SpectrumISI and Eye PatternMatched FilterPerformance

1

Principles of Communication

BandpassDigital System (1)

LC 5-9

Lecture 19, 2008-11-25

3

Contents

Review of Digital Baseband System OOKBPSKDPSKFSK

4

Binary Modulated Bandpass SignalsDigitally modulated bandpass signals are generated by using the complex envelops for AM, PM, FM or QM (quadrature modulation) signaling.For digital modulated signals, the modulating signal m(t) is a binary or multilevel digital signal.The most common binary signaling techniques are as follows:

On-off keying (OOK), also called amplitude shift keying (ASK). Binary phase-shift keying (BPSK).Frequency-shift keying (FSK)

5

On-Off KeyingAlso called amplitude shift keying (ASK), which consists of keying (switching) a carrier sinusoid on and off with a unipolar binary signal. OOK is identical to unipolar binary modulation on a DSB-SC signal.

)()(cos)(})(Re{)(

tmAtgttmAetgts

c

cctj c

=== ωω

6

OOK Spectrum

{ }

2 22 2

2 22 2

( ) , ( ) ( )0 0

( )( ) [ ( ) ( )] [ ( ) ( )]4 2

1( ) [ ( ) ( )]4

[ ( ) ( )] [ ( ) ] [ ( ) ]8 8

cc

c cg b b b b

s g c g c

c c bc c c b c b

A A Am t g t A m t

A A AP f f T Sa fT f T Sa fT

P f P f f P f f

A A Tf f f f Sa f f T Sa f f T

δ π δ π

δ δ π π

⎧ ⎧= = =⎨ ⎨⎩ ⎩

= + = +

= − + +

− + + + − + +＝

RB

B

nullT

absT

2)(

)(

=

∞=

7

OOK Generation

Multiplier

cos

OOK( )

( )

cos

Switch

( )

OOK( )

( )

( )

8

OOK DemodulationOOK may be detected by using either an envelope detector (noncoherent detection) or a product detector (coherent detection).

9

Binary Phase-Shift Keying (BPSK)BPSK consists of shifting the phase of a carrier 0° or 180° with a unipolar binary signal. BPSK is equivalent to PM or DSB-SC with a polar binary modulation.

10

BPSK

( ) 1 polar baseband data signal( ) Re{ ( ) } cos[ ( )]

cos[ ( )]cos sin[ ( )]sin

cos( ) cos sin( ) ( )sin

cj tc c p

c p c c p c

c p c c p c

pilot carrier data

m ts t g t e A t D m t

A D m t t A D m t t

A D t A D m t t

ω ω

ω ω

ω ω

= ±

= = +

= −

= −144424443 144424443

The level of the pilot carrier term is set by the value of the peak deviation, Δθ=Dp

The digital modulation index h is defined by 2h θπΔ

=

The maximum signaling efficiency is obtained by letting90 / 2

( ) ( )sin( ) ( )

p

c c

c c

D

s t A m t tg t jA m t jA

θ π

ω

Δ = = ° =

= −

= = ±

11

Spectrum of BPSK

( )

{ }

22

2

1

2

22 2

( )( ) ( )

, 0( )

0, 0

( ) ( )

1( ) [ ( ) ( )]4

[ ( ) ] [ ( ) ]4

sj kfTg

ns

Ic

n n k iii

g c b b

s g c g c

cb c b c b

F fP f R k e

T

A kR k g g P

k

P f A T Sa fT

P f P f f P f f

A T Sa f f T Sa f f T

π

π

π π

∞

=−∞

∗+

=

=

⎧ == = = ⎨

≠⎩=

= − + +

= − + +

∑

∑ L

RB nullT 2)( =

12

BPSK Generation

( )Encoding

Bipolar NRZ

MultiplierBPSK( )

cos

( )

sin0

switch

BPSK( )

Phase Shifter ( )

( )

13

BPSK Demodulation

14

Differential Phase-Shift Keying (DPSK)

PSK signals cannot be detected incoherently.In differential encoding, the information is conveyed by phase shifts between any two successive signal intervals.

Message

Encoded

1 01 1 0 0 1 0

15

DPSK GenerationDifferential encoding and decoding:

Decoding is obtained by the simple rule:

that is realized by the circuit shownright.Note that no local oscillator is requiredHow would you construct the encoder?

1

1

start, say with 1if 1,set if 0,set

k

k k k

k k k

am a am a a

−

−

=

= =⎧⎨ = ≠⎩

1k k kd a a−= ⊕

mkak

A B Y0 0 10 1 01 0 01 1 1

XOR

16

DPSK Demodulation

In practice, DPSK is often used instead of BPSK, because the DPSK receiver does not require a carrier synchronizer circuit.

17

Frequency-Shift Keying (FSK)FSK consists of shifting the frequency of a carrier from a mark frequency to a space frequency according to the baseband binary signal. FSK is identical to FM with a binary modulation.

18

FSK Generation (1)

The FSK signal can be characterized as one of two different types, depending on the method used to generate it. One type is called discontinuous-phase FSK. It is generated by switching the output line between two different oscillators.

19

Discontinuous-Phase FSK

⎩⎨⎧

−+−+

=⇒⎩⎨⎧

++

=+

⎩⎨⎧

++

=+=

tttt

ttt

tt

ff

tAtA

ttAts

c

cc

c

ccc

ωθωωθω

θθωθω

θω

θθ

θωθω

θω

22

11

22

11

2

1

2

1

22

11

)()(

twooscillator of phase up-start :one oscillator of phase up-start :

frequency 0)(binary space :frequency 1)(bianry mark :

sent being is 0when ),cos(sent being is 1when ),cos(

)](cos[)(

20

FSK GenerationAnother type is called continuous-phase FSK. It is generated by feeding the data signal into a frequency modulator.

])(cos[)( ∫ ∞−+=

t

fcc dmDtAts λλω

21

Example

Spectrum of the Bell-Type 103 FSK Modem

22

10101010). (i.e.,pattern data galternatinan toingcorrespond signal,FSK bandwidth

- widest theof case for the evaluated be willspectrum TheHz 2002 :deviationpeak -to-Peak

/1 :intervalBit bits/s 300 :rateBit

=Δ=

=

FRT

R

b

23

bff

t

Tfb

fbb

f

t

fbb

t

f

ff

n b

b

TDtD

dDTDtTtT

tDdDtTtT

dmDt

DtmDF

TnTttmtm

TT

b

+−=

−+=≤≤

=+=≤≤−

=

=

==Δ

−−

Π=±=

=

∫

∫

∫

∑

∞−

∞

−∞=

2/

0

0

0

)1(2

)(,2/32/For

)1()(,2/2/For

0)0( Assume

)()(

2)](max[

21 :deviationfrequency Peak

1)(2)(or1)(

2 :signal modulating of period

λθ

λθ

θ

λλθ

ππ

24

25

2

22

)(,4/34/For

2)(,4/4/For

2

67.030020022

22 :index modulation Digital

2)](max[

00

00

00

00

00

0

00

hhtTT

htT

h

TDtDtTtT

httT

htDtTtT

ThD

RFFT

FTTDTD

h

TDt

bff

f

f

b

fbf

bf

πωππ

θ

ωπθ

π

πππθ

θθ

+−=+−=

+−=≤≤

===≤≤−

=

≈=Δ

=Δ=

Δ===Δ

=

==Δ

26

])()(

[

])()(

[

][

][

1)(1

)(

0

))(2/())(2/3(

0

))(2/())(2/(

0

4/3

4/0

)(4/

4/0

)(

0

4/3

4/

)(4/

4/

)(

0

4/3

4/

)(4/

4/0

4/3

4/

)(

0

4/3

4/0

)(

0

0

00

0

0

0

0

00

0

0

0

0

000

0

00

0

0

00

0

0

nhjeee

nhjee

TA

nhjee

nhje

TA

dteedteTA

dteedteeTA

dteeAT

dttgT

c

eceAtg

nhjnhjhj

nhjnhjc

T

T

tnhjhj

T

T

tnhjc

T

T

tnhjhjT

T

tnhjc

T

T

tjnhhtjT

T

tjnhtjc

T

T

tjntjc

T

Tn

tjnn

tjc

+−−

+−

−=

+−+

−=

+=

+=

==

==

+−+−−−−

+−

−

−

+−

−

−

−+−

−

−

−

−

−

∞

∞−

∫∫

∫∫

∫∫

∑

ωω

ωωππ

πππ

ωπ

ω

ωπω

ωπωωω

ωθ

ωθ

27

RhRRF

BFBBFBB

ffGffGfS

RnfcnffcfG

nhSanhSaAnhj

eeenhj

eeAnhj

eeenhj

eeA

fT

cc

nn

nn

nc

nhjnhjnj

nhjnhjc

nhjnhjnj

nhjnhj

c

222

22)1(2)1(2

)]()([)(

)2

()()(

)]})(2/[()1()])(2/[({2

]))(2/(2))(2/(2

[2

])(2)(2

[

21

0

))(2/())(2/())(2/())(2/(

))(2/())(2/())(2/())(2/(

+=+Δ≈

+Δ=+Δ

=+=

−−+−=

−=−=

+−+−=

++

+−

−=

+−−

+−

−=

∗

∞

−∞=

∞

−∞=

+−+−

−−−

++−−

−−−

∑∑

β

δδ

ππ

ππ

ππππ

πππ

πππ

ππ

28

29

30

31

PSD of FSK

The PSD for the complex envelope of the continuous-phase FSK signal is

spectrum) in the termsdiscrete also are there,,2,1,0(When ,2,1,0/2

)2cos()2cos(2)2(cos1])3(2cos[)2cos(})]3([2cos{

)(and

)]}32([{)(where

)}()()(2)](1)[()](1)[({2

)(

2

2112222211

21

2

K

K

=≠Δ=

Δ−Δ+−+ΔΔ−−+Δ−

=

−Δ−=

++++

=

hRFh

fTFTFTTmnFFTTmnFf

fB

nFfTSafA

fAfAfBfBfAfBfA

TAfP

bbb

bbb

nm

bn

bcg

ππππππ

π

32

PSD of FSK (con’t)

33

FSK DemodulationFSK can be detected by using either a frequency (noncoherent) detector or two product detectors (coherent detection).

34

HomeworkLC 5-46, 5-47, 5-52, 5-53