MODULASI PSK (PHASE SHIFT KEYING)

Sistem Komunikasi

Prodi D3 TT

Yuyun Siti Rohmah, ST.,MT

BINARY SHIFT KEYING

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Binary Shift Keying (BPSK)

Perubahan Parameter Fasa dari sinyal pembawa sesuai dengan

sinyal informasi.

Menggunakan alternatif-alternatif fasa gelombang sinus utk

mengkodekan bit-bit dimana Fasa dipisahkan 180 derajat

Sederhana utk diimplementasikan, tidak efisien dalam

penggunaan bandwidth.

Sangat kokoh, sering digunakan secara extensif pada

komunikasi satelit.

3

Blok Sistem BPSK

4

"0")( ; )2cos(

"1")( ; )02cos()(

tbtfA

tbtfAts

c

c

Data

Carrier

Carrier+

BPSK waveform

1 1 0 1 0 1

Contoh Sinyal BPSK

5

Konstelasi sinyal BPSK

Fasa dipisahkan 180 derajat.

6

'0' binary )2cos()(

'1' binary )2cos()(

2

1

tfAts

tfAts

cc

cc

Q

0

State 1

State

7

f

S(f)

fc fc+ Rfc- R fc+ 2Rfc- 2R

BWmin

BWmin=2BN

= 2.Rb/2

BN=Bandwidth Nyquist

Spektrum Sinyal BPSK

MODULASI QPSK (QUADRATURE SHIFT KEYING)

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Quadrature Phase Shift Keying

• Teknik modulasi multilevel : 2 bit per symbol

• Lebih efisien spektrum, lebih kompleks

receiver.

• Dua kali lebih efisien bandwidth daripada

BPSK Q

00 State

11 State 10 State

01 State

Phase of Carrier: /4, 3/4, 5/4, 7/4 9

4 bentuk gelombang berbeda:

-1.5

-1

-0.5

0

0.5

1

1.5

0 0.2 0.4 0.6 0.8 1 -1.5

-1

-0.5

0

0.5

1

1.5

0 0.2 0.4 0.6 0.8 1

-1.5

-1

-0.5

0

0.5

1

1.5

0 0.2 0.4 0.6 0.8 1 -1.5

-1

-0.5

0

0.5

1

1.5

0 0.2 0.4 0.6 0.8 1

00 01

11 10

cos+sin -cos+sin

cos-sin -cos-sin

10

Bentuk Sinyal

QPSK

Blok Sistem QPSK

11

Bandpass modulation: Signal Space & Vector

Bandpass modulation: The process of converting data signal to a sinusoidal waveform where its amplitude, phase or frequency, or a combination of them, is varied in accordance with the transmitting data.

Bandpass signal (General Condition):

where is the baseband pulse shape with energy .

We assume here (otherwise will be stated):

is a rectangular pulse shape with unit energy.

Gray coding is used for mapping bits to symbols.

denotes average symbol energy given by

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TtttitT

Ethts ic

ii 0 )()1(cos

2)()(

)(thhE

sE

M

i is EM

E1

1

)(th

Phase Shift Keying (PSK)

I. PSK signal waveform (transmitted signal):

Phase (examples):

Symbol energy and symbol interval

0 , phase: , 2

( ) cos[ ( )] 0 , 1( ,2

) , ,ii iE

s ti

tt tT

tM

T i M

13

7 / 2

1/ 2

3 53, , ,0

2

7, , ,

BPSK( 2) : ,0

QPSK( 44 4 4

) : o 2

r4

i

ii

M

M

2

0

is symbol energy. is symbol inter .

Can you show that

va

( ?

l

)T

i

E

s t dt

T

E

II. Signal space representation

Note: decomposition of PSK signal waveform:

1) Orthonormal basis:

2) Signal vector:

3) Constellations:

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2 2cos , si( ) : , 1, ,ni i

i iE Es t i

M MM

s

1 0 2 02 2

( ) cos( ), ( ) sin( )t t t tT T

0 02 2

( ) cos[ ( )]cos( ) sin[ ( )]sin( )i i iE E

s t t t t tT T

(examples)

Signal space representation (cont.)

4) A proof of signal space representation

Bases are orthonormal

Signal space vector for each waveform si(t)

15

20

2 22

2

0 0 0

1 0 0

1 2 0 0

00 0

0

0( ) 2 sin ( ) 2 [1 cos(

( ) 2 2

cos( )sin( ) sin(2 ) /

1.

.

( ) ( ) 2

cos ( ) [1 cos

2

2 )]/ 2 1

(2 )]

2 0.

/ 2T

T

T

T

T

Tt dt T t dt T t

t dt T dt T

t t t

dt

t t dt T

t t

d

d

d

t

t T t

1 1 0 0 0

2 2 0 00

0

0

0

0

( ) ( ) 2 T

T c cos[ ( )]

( ) ( ) 2 T cos[ ( )]sin( )

T sin[ ( )] sin[2 (

cos[ ( )]cos( )

os[ ( )] cos[2 (

] n

)

) i

]

s [

Ti i

Ti i i

Ti i i

i iiT

i

a s t t dt

a s t t dt E dt

E dt

E t t t dt

E t t t d

E t

t

t E

t t

t t t

( )]t

Signal space representation (cont.)

5) What happens if baseband pulse-shaping h(t) is considered?

Signal waveform:

Use basis (note that h(t) can be assumed normalized):

Signal space vector is still:

Conclusion: there is no difference in signal space whether pulse-shaping is considered. We can study only PSK instead of the more general PM.

1 0 2 02 2

( ) ( )cos( ), ( ) ( )sin( )t h t t t h t tT T

2 2cos , si( ) : , 1, ,ni i

i iE Es t i

M MM

s

16

02

( ) ( )cos[ ( )]i iE

s t h t t tT

PSK modulator

Special case: BPSK modulator

General case: M-ary PSK modulator

17

ia E ( )h t

02 cos( )T t

( )is t

binary

bits

1ia

2ia

( )h t

( )h t

02 cos( )T t

02 sin( )T t

( )is tNote:

Inputs are signal-

space vector.

Carriers are in basis

form.

1 0 2 0

1 2

( ) 2 cos( ) 2 sin( )

( , ) cos(2 ), sin(2 )

i i i

i i i

s t a T t a T t

a a E i M E i M

s

Symbol

map

Bandwidth of PSK signal waveform Just like DSB modulation:

Exercise : Consider QPSK transmission with date rate 2000 bps. The magnitude of the signal si(t) is √2E/T =1 volt.

a) What is the minimum PSK signal bandwidth?

b) Find the signal space points

c) Draw the constellation

d) Find signal waveform for transmitting {1001}.

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PSK baseband2W W

2 PSK baseband,min

3

1 0

a) (log ) 2000 / 2 1000. 2 2 2 1000Hz.

b) ( cos 2 4, sin 2 4), where / 2 0.5 10 , 1, ,4

d) Define mapping as: {00:0, 01: , 10: 2, 11: 3 2}.

Then {10} ( ) cos(

s b s

i

R R M W W R

E i E i E T i

s t t

s

2 02). {01} ( ) cos( )s t t

Phase ( ) in ( ) is

different from phase of

(phase in signal space)

i i

i

t s t

s

Demodulation and detection

Demodulation: The receiver signal is converted to baseband, filtered and sampled.

Detection: Sampled values are used for detection using a decision rule such as ML detection rule.

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Nz

z

1

z

T

0

)(1 t

T

0

)(tN

)(tr

1z

Nz

z Decision

circuits

(ML detector) m

Demodulation Detection

Demodulations type:

Some notations

Carrier:

Modulation types with respect to carrier parameters

Modulation

Varying parameter

Demodulation

PSK Coherent or

noncoherent

QAM Coherent or

noncoherent

FSK Coherent or

Noncoherent

( )t

20

0

both ( ) and ( )A t t

0 0 0( ) ( )cos[ ( )], 2s t A t t t f

Two dimensional modulation, demodulation and detection (M-PSK)

M-ary Phase Shift Keying (M-PSK)

21

M

it

T

Ets c

si

2cos

2)(

2

21

21

2211

2

sin 2

cos

sin2

)( cos2

)(

,,1 )( )()(

iis

sisi

cc

iii

EE

M

iEa

M

iEa

tT

ttT

t

Mitatats

s

Two dimensional mod… (MPSK)

22

)(1 t

2s1s

bE

“0” “1”

bE

)(2 t

3s

7s

“110”

)(1 t

4s2s

sE“000”

)(2 t

6s 8s

1s

5s

“001” “011”

“010”

“101”

“111” “100”

)(1 t

2s 1s

sE

“00”

“11”

)(2 t

3s4s

“10”

“01”

QPSK (M=4)

BPSK (M=2)

8PSK (M=8)

Demodulation BPSK

BPSK with coherent detection:

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T

0

)(1 t

)(trDecision

Circuits Compare z

with threshold.

mz

)(1 t

2s1s

bE

“0” “1”

bE

bE221 ss

Error probability …

BPSK with coherent detection (with perfect carrier synchronization):

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2

0

N

EQP b

B

2/

2/

0

21

NQPB

ss

)(1 t

bEbE0

1s2s

)|( 1mp zz

)|( 2mp zz

Demodulation M-PSK

Coherent detection of Q-PSK

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Decision Region QPSK

s2

s4

decide s1

s1

decide s2

decide s3

decide s4

s3 )(1 t

)(2 t

0

00

2

0

2

2

2

2

11

221

211

N

EQp

N

EQ

N

EQpp

N

EQpp

be

bbce

bIBPSKC

Power Spectra of M-Ary PSK

MfTcMEfS

TfcEfS

bbB

B

2

2

2

logsinlog2

sin2

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QPSK vs. BPSK

Let’s compare the two based on BER and bandwidth

BER Bandwidth

BPSK QPSK BPSK QPSK

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Rb Rb/2

EQUAL

2

0

N

EQP b

B 2

0

N

EQP b

B

Error probability …

Coherent detection

of M-PSK

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8-PSK

3s

7s

“110” )(1 t

4s2s

sE

“000”

)(2 t

6s 8s

1s

5s

“001” “011”

“010”

“101”

“111” “100”

Decision variable

r z

Compute

Choose

smallest X

Yarctan

|ˆ| i

T

0

)(1 t

T

0

)(2 t

)(tr

T

dtttrXr0

11 )().(

m

T

dtttrYr0

22 )().(

is a noisy estimate of the transmittedi

Error probability …

Coherent detection of MPSK …

The detector compares the phase of observation vector to M-1 thresholds.

Due to the circular symmetry of the signal space, we have:

where

It can be shown that (for M > 4)

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dpPP

MMPMP

M

Mc

M

m

mcCE )(1)(1)(1

1)(1)(/

/ˆ1

1

ss

MN

EQMP s

E

sin

22)(

0

MN

EMQMP b

E

sin

log22)(

0

2

or

2|| ;sinexp)cos(

2)( 2

00

ˆ

N

E

N

Ep ss

Probability of symbol error for M-PSK

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EP

dB / 0NEb

Note!

• M = 2k

• “The same average symbol energy for different sizes of signal space”

THANK YOU

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