Lec13 Bandpass Modulation I

8/10/2019 Lec13 Bandpass Modulation I

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Introduction

Points to be discussed in this lecture

Introduction

Coherent Binary Amplitude Shift Keying

Coherent Binary Phase Shift Keying

Coherent Binary Frequency Shift Keying


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IntroductionReading Assignment

Simon Haykin, Digital Communications,John Wiley & Sons, Inc., 1988, Chapter 7.

K. Sam Shanmugam, Digital and AnalogCommunication Systems, John Wiley &

Sons, Inc., 1979, Chapter 8.


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Introduction

Passband modulation shifts the basebandsignal spectrum to a carrier frequency

cf .

It converts the baseband signal to a band-pass signal for transmission through a band-pass channel using a sinusoidal carrier.

Band-pass signals propagate well throughthe atmosphere with reduced antenna size.

(Antenna size is proportional to thewavelength of the signal to be transmitted

8/ , 3 10 m/scc f c= = .).


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Introduction

Passband data transmission allows manymessage signals to share the spectrum bytransmitting at different carrier frequencies(frequency division multiplexing).

Passband data transmission provides for

transmitting digital information in conformityto channel limitations imposed by thecommunications authorities. (e.g.TCRA, ITU)

What is the frequency spectrum for cellularsystems?


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Introduction

Digital passband modulation schemes areclassified as: -

Binary vs M-ary

Binary Amplitude Shift Keying (BASK)

Binary Phase Shift Keying (BPSK)Binary Frequency Shift Keying (BFSK)M-ary ASK, M-ary PSK, M-ary FSK

M-ary QAM

Coherent vs Noncoherent


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Introduction

Different digital passband modulationschemes are compared in terms of

1. Probability of bit error performance ep .2. Spectral characteristics.3. Transmission bandwidth (bandwidth

efficiency /b TR B= ).4. Complexity.5. Immunity to nonlinear channel

distortions.


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Introduction

A band-pass signal ( )s t with carrier

frequencyc

f can be expressed in terms of its

quadrature components( )

andI

m t

( )Qm t as

( ) ( ) ( ) ( ) ( )

( ) ( )

cos 2 sin 2

Re exp 2

I c Q c

c

s t m t f t m t f t

s t j f t

=

=

( ) ( ) ( )I Qs t m t jm= + t is baseband equivalent (or

complex envelope) of bandpass signal

( )s t .


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Introduction

( )Im t is the baseband in-phase component.

( )Qm t is the baseband quadrature component.

Let be the power spectral density

(PSD) of (

( )SS

f

)s t

. Then the PSD of ( )s t ( )SS f

isrelated to ( )by

SS f

( ) ( ) ( )14SS c cSS SS f f f f f = + + Prove


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A signal ( )is t 1,2i= for transmission of a

binary symbol 1,2im i= during each signaling

interval for a BASK system is defined byb

T

( )

( )1

1

2cos 2 0

0 elsewhere

c b

b

Ef t t T

s t T

=

( )2 0s t =

1E is the energy of the transmitted signal ( )1s t

andb

T for a fixed integer is the

carrier frequency.

/c c

f n= cn


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An orthonormal basis function 1( )t for theBASK signal set is therefore defined by

( ) ( )

1

2cos 2 0

0 elsewhere

c b

b

f t t Tt T

=

Transmitted signal1( )s t is expressed in terms

of1( )t as

( ) ( )1 1

1

0

0 elsewhere

bE t t T

s t

=


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Same as forthe unipolarNRZ line codeconstellation.

Also calledOn-Off Keying(OOK).

2Z

2 0=s 1 1E=s

1 / 2T E=

1Z

( )1 t

For an AWGN channel with coherent

detection, bit error probability ep isexpressed as


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b1

2e

o o

EEp Q Q

N N

= =

,

1

b

0

2

EE

+= is the average energy per bit.

The BASK signal can be expressed as

( ) ( ) ( ) ( ) ( )

( ) 1

cos 2 2

1, bit 1 2 / , 0 ,

0, bit 00, elsewhere

bI c k ck

k b b

k

k

coss t m t f t a f t

b E T t T a g t

b

g t kT

=

= =

= = =

=


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UnipolarNRZ

encoder

( )1 t ( )Im t BinaryData Binary

ASKsequence

{ }kb signal

( )s t

BASK TRANSMITTER

( ) ( )1 2 / cos 2b ct T f t =

1r Decisiondevice 1

1

bit 1 ifbit 0 if

r Tbr T

>=


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PSD of the BASK signal is equal to that ofthe unipolar NRZ line code shifted to

cf

( ) ( ) ( )

( ) ( ) ( )2b

1=4

1

sinc 14

ss c cSS SS

bSSb

f f f f f

E

f fT fT

+ +

= +

0 c b

f R+

2T bB R= ( )ss f

cf cf c bf R

f


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Binary Phase Shift Keying (BPSK)

A signal ( )is t 1,2i= used to represent a binary

symboli

m 1,2i= during each signaling

interval for a BPSK system is defined byb

T

( )

( )2

cos 2 1 0

0 elsewhere

bc b

i b

Ef t i t T

s t T

+ =

bE is the average energy of the transmittedsignal per bit and is the carrier frequency.

cf


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An orthonormal basis function 1( )t for theBPSK signal set is defined by

( ) ( )

1

2cos 2 0

0 elsewhere

c b

b

f t t Tt T

=

1( )s t and )2 ( are expressed in terms of 1( )t ass t

( ) ( )

( ) ( )1 1

1 2

, 0 , 0,

0, elsewhere 0, elsewhere

b b b bE t t T E t t Ts t s t

= =


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2 2E=s

2Z

Same as for thepolar NRZ linecode signal spacediagram. Also

called antipodalsignaling.

1 1E=s

0T=

1Z

( )1 t

For an AWGN channel with coherent

detection, ep is expressed as

2b

e

o

Ep Q

N

=


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Binary Phase Shift Keying

In general, the BPSK signal can be expressed as

( ) ( ) ( ) ( ) ( )

( )

cos 2 2

1, bit 1 2 / , 0 ,

1, bit 0 0, elsewhere

I c k c

k

k b b b

k

b

k

coss t m t f t a f t

b E T ta g t

b

g t kT

T

=

= =

+ = = =

=

Polar

NRZencoder

( )1 t ( )Im t

BinaryData Binary

PSKsequence

{ }kb signal

( )s t

BPSK TRANSMITTER


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( ) ( )1 2 / cos 2b ct T f t =

1r Decision

device 11

bit 1 if

bit 0 if

r Tb

r T

>=


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( ) ( ) ( )

( ) ( )2b

1=4

2 sinc

ss c cSS SS

bSS

f f f f f

f E fT

+ +

=

( )ss f

cf cf c bf R+ c bf R 0 f

2T b

B R=


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Binary Frequency Shift Keying (BFSK)

A signal ( )is t 1,2i= used to represent a binarysymbol

im 1,2i= during each signaling

interval is defined byb

T

( )2

cos 2 0

0 elsewhere

b cb

i b b

E n it t T

s t T T

+ =

bE is the energy of the transmitted signal ( )is t and is an integer.c

n


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Note that ( )1s t and ( )2s t are orthogonal. Note

also that 2 1 1/ bf f T = (Sundes FSK) which

results in a continuous-phase frequency-shift keying (CPFSK) signal.

Orthonormal basis functions ( ), 1,2i t i = for

the BFSK signal set is defined by

( ) ( )2

cos 2 0

0 elsewhere

i b

i bf t t Tt T

=


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Signal1( )s t and 2 ( )s t are expressed in terms of

1( )t and 2 ( )t as

( ) ( )

( ) ( )1 2

1 2

, 0 , 0,

0, elsewhere 0, elsewhere

b b b bE t t T E t t T

s t s t

= =

The signal constellation of BFSK is thereforetwo-dimensional ( 2N= ) with 2 message

points.


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Binary Frequency Shift Keying

2 (0, )bEs

1( ,0)bEs

1Z

2Z

( )2 t

( )1 t

For an AWGN channel with coherentdetection,

ep is expressed as

be

o

Ep Q

N

=


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Binary Frequency Shift Keying (BFSK)( )t

( )m t

BFSK TRANSMITTER

BinaryData

1

( )2 t

Inverter

BinaryFSK

sequence

{ }kb

Unipolar

NRZencoder signal

( )s t

( )1 t

0

bT

dt

l +

Decisiondevice

0

bT

dt

1r BFSK COHERENT RECEIVER

( )r t

bit 1 ifbit 0 if

k

l Tb

l T

>=


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The BFSK signal can in general beexpressed in terms of the in-phase andquandrature components as

( ) ( ) ( ) ( ) ( )

( ) ( ) ( )

( )

cos 2 sin 2

2

cos ,

1, bit 1 2 / sin , 0

,1, bit 00, elsewhere

I c Q c

b

I Q k bkb b

k b b b

k b

k

s t m t f t m t f t

E t

m t m t a g t kT T T

tb E T t T

a g t Tb

=

=

= =

=

= = + =


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Binary Frequency Shift Keying

PSD of the BFSK signal is the sum of PSDsof the quandrature components.

( ) ( ) ( )

( ) ( )

( )

2

22 2 2

1=4

8 cos1 1

2 2 2 4 1

ss c cSS SS

b bb

SS b b bb

f f f f f

E T fEf f f

T T T T f

=

+ +

+ + +

0c

fc

f

2b

c

Rf +

2b

c

Rf

( )ss f

cf 3

2b

c

Rf

3T b

B R=

3

2b

c

Rf +

f

Lec13 Bandpass Modulation I

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