chapter 8. digital passband transmission 8.1 introduction

CNU Dept. of Electronics

D. J. Kim1

Lecture on Communication Theory

Chapter 8. Digital Passband Transmission

8.1 Introduction

Analog Digital Passband

Amplitude Mod. ASK ( Amplitude Shift Keying )Freq. Mod FSK ( Frequency Shift

Keying )Phase Mod PSK ( Phase Shift

Keying )

keying means switching

Coherent RX : phase locked Noncoherent RX : Phase unlocked

8.2 Passband Transmission Model


D. J. Kim2


- Symbol (with duration T) mi alphabet {m1,m2,,

mM}

(ex) Quaternary : alphabet { 00, 01, 10, 11}

- Prior probability { P(m1), P(m2), , P(mm) }

Equally likely

- Output of signal TX encoder

- Modulator :

Energy of

- ASK, FSK, PSK

iM

mPp ii all for 1)(

)MNNi ( elements real with Vector s

(t) sii signal distinct Vector s

MidttsET

ii ,,3,2,1)(0

2

(t) si


D. J. Kim3


- Channel : Bandpass communication channel, additive

white

Gaussian noise (AWGN) channel

Channel is linear with wide bandwidth

w(t) : additive, zero-mean, stationary, white, Gaussian

noise

- Average probability of symbol error

를 minimize 하는 receiver : optimum in the minimum

probability of error sense

- Time synchronized

-

M

iiie mPmmPP

1

ˆ

eP

Phase locked, coherent detection, coherent RX

Phase unlocked, non-coherent detection, non-coherent RX


D. J. Kim4


8.3 Gram-Schmidt Orthogonalization Procedure: Representation of any set of M energy signals { si(t) } as a linear combinations of N orthogonal basis functions where N M.

- Real-valued energy signals s1(t), s2(t),, sM(t) is

in the form

where

- Real valued basic functions are orthonormali.e.

Mi

Tttsts

N

jjiji ,,2,1

0 )()(

1

NjMi

dtttssT

jiij ,,2,1,,2,1

)()(0

jiji

dtttT

ji if 0 if 1

)()(0


D. J. Kim5


Gram-Schmidt orthogonalization procedure ; Basis functions 을 구하는 방법

Input s1(t), s2(t),, sM(t)

Let

Def

Then

Def

so

1

11

)()(

Ets

t

111111111 e wher )()()( EststEts

T

dtttss0 1221 )()(

)()()( 12122 tststg

orthogonal ; 0)()( 21210 12 ssdtttgT

normalize ;

Tdttg

tgt

0

22

22

)(

)()(

221

22

1212 )()(

sE

tsts

TT

dtttdtt0 210

22 0)()( ,1)(


D. J. Kim6


In general form

where

Def

-

Examples

- Fourier series expansion of a periodic signal

- Representation of a band-limited signal in terms of its

samples taken at the Nyquist rate

1

1

)()()(i

jjijii tststg

1,,2,1,1)()(0

ijdtttssT

jiij

Ndttg

tgtT

i

ii ,1,2, i

0

2 )(

)()(

for and tindependenlinearly not areThey

set tindependenlinearly a form signal The

NitgMN

MNtststs

i

Mi

0)(

)(,),(),( 2


D. J. Kim7


Example

Ex1) Gram-Schmidt Orthogonality Procedure


D. J. Kim8


and

T TdttsE0

211 3

)(

otherwise 0, 0 3,3)()(

1

11

TtTEtst

T T TdtT

dtttss0

3

01221 33)1()()(

T TdttsE0

222 3

2)(

otherwise

,03233)()()(

221

22

12122

TtTT

sE

tstst

031 s

32

332 33)1(

T

T

TdtT

s

)()()()( 232131313 tststst

otherwise 0

1 TtTtstststg

32)()()()( 23213133

otherwise ,

,0323

)(

)()(

0

23

33

TtTT

dttg

tgtT


D. J. Kim9


for 0)(g ,4 4 ti


D. J. Kim10


8.4 Geometric Interpretation of signalsIn a vector form of signal

where

Mi

s

ss

iN

i

i

i ,,2,12

1

s

N

jjiji tsts

1

)()(


D. J. Kim11


- :signal vector

- Signal space : N-dimensional Euclidean space

- Length or absolute value or norm :

Squared-length

- Cosine of angle between vector and

- Euclidean distance

is

is

N

jiji

Tii s

1

22 sss

is js

ji

jTi

ij ss

sscos

jiikd ss

N

jkjijkiik ssd

1

222 ss

T

ki dttsts0

2)()(


D. J. Kim12


8.5 Response of bank of correlators to noisy input

Received signal

Output of correlator j

11 wsi

)(tx22 wsi

NiN ws

,M,,i

Tttwtstx i 21

0 )()()(

T

jj

T

jiij

T

jijjj

dtttww

dtttss

Njwsdtttxx

0

0

0

)()(

)()( where

,,2,1 )()(


D. J. Kim13


Statistical Characterization of the Correlator Output

Let

Mean

Covariance

, of fct sample with x(t)prtX ..:)(

jj wvrW value sample with..:

jijjX WsEXEj

μ

ijjij sWEs

222 varσ jijjjX WEsXEXj

jN

duuuWdtttWET

j

T

j

all for 2

)()()()(

0

00

)]μ)(μ[(]cov[kj XkXjkj XXEXX

kj

WWE kj

for 0

][

)(2

0 tWN process noise the ofdensity spectral power : where


D. J. Kim14


NX

XX

2

1

X

NXXX ,,, 21

x

Mimxfmf ij

N

jXi j

,,2,1 , 1

xX

yprobabilit transition channel

fcts likelihood

element nobservatio vector nobservatio

:

::

i

j

mf

x

x

x

X

2

00

1exp1ijjijX sx

NNmxf

j

MisxN

NmfN

jijj

Ni ,,2,11exp

1

2

0

20

xX

Define the vector of N random variables

are statistically independent

Conditional probability density fct of

위 식을 만족하는 channel : memoryless channel

여기서


D. J. Kim15


8.6 Coherent Detection of Signals in Noise

- M possible signals :

- Received signal

- Receiver’s job : “best estimate” of TXed signal

- Represent as appropriate set of N orthonormal basis functions

represent by a point in N-dimensional Euclidean space

i.e. , transmitted signal point or message point

- Signal Constellation : Set of message points

- Decision making process : Given observation vector x,

Pe 를 최소화 하도록 x 를 mi 의 estimate 으로

mapping

)(,),(),( 21 tststs M

Mi

Tttwtstx i ,,2,1

0)()()(

2)( 0Ntw psd where 의

)(tsi

)(tsi

)(tsi

Miwi ,,2,1 , sx

m


D. J. Kim16


1. Maximum Likelihood Decoder

1) MAP (Maximum a Posteriori) rule

Optimal decision

Select which minimize

Select which maximize

In other words, select i

: prior probability of occurrence of symbol mi

: likelihood fct that results when symbol mk

is transmitted

imm ˆ

xx sentnot , iie mPmP

xsent 1 imP

im

)(x

xx

X

X

fmfP

mP iii sent

)(

maxmaxxx

xX

X

fmfp

mP ii

iiisent

ip

kmf xX

im


D. J. Kim17


MAP 의 예

2) ML Decoder

From MAP

is independent of the transmitted signal,

Assume with equal probability

Then

xXf im

ik pp

Decoder ML select

iimf

ixXmax

21

11 PP if

31

32

1

1

P

P


D. J. Kim18


In other wordsSet if is maximum for k=i

Likelihood fct

So, is a monotone increasing fct.

Called the metric

ML rule

3) Graphical interpretation of ML decision rule

Let Z denote the N-dimensional space of all possible

observation vector x

i.e. Z : observation space

Z is partitioned into M decision regions

Decision rule :

observation vector x lies in region Z i

if is maximum for k=i

imm ˆ kmf xX

0imf xX

imf xXln

iimf

ixXln

selectmax

MZZZ ,,, 21

kmf xXln


D. J. Kim19


Consider AWGN Channel

Metric

Decision rule :

Observation vector x lies in region Zi

if is maximum for k=i

or if is minimum for k=i

or if is minimum for k=i

Conclusion : ML decision rule is simply to choose

the message point closest to the received

signal point

MksxN

NmfN

jkjj

Nk ,,2,11expπ

1

2

0

20

xX

MksxN

NNmfN

jkjjk ,,2,1 1ln

2ln

1

2

00

xX

N

jkjj sx

N 1

2

0

1

N

jkjj sx

1

2

ksx


D. J. Kim20


Examples

boundary Decision

)( axf X

aa

)( axf X


D. J. Kim21


8.A Constellation ( 성상도 )

1. Example of constellations

The alphabet is the set of symbols that are available for transmission

- Binary antipodal (BPSK)

- a a

}A{I km

}A{R ke

Figure 1. Two popular constellations for passband PAM transmission. The constants b and c affect the power of the transmitted signal


D. J. Kim22


2. Slicer

- makes the decision about the intended symbol.

- selects that minimizes

- ML : maximum likelihood MAP : maximum a - posteriori detector

3. Minimum Distance

- Euclidean distance 두점 사이의 거리

- dmin 성상도에서 가장 가까운 두점 사이의 거리

8PSK 4VSB

kA2ˆ kk A-Q

-3 -1 1 3


D. J. Kim23


4. Decision Regions

Figure 2 . Received samples perturbed by additive Gaussian noise form a Gaussian cloud around each of the points in the signal constellation

Figure 3. The ML detectors for the constellations in Figure 1 have the decision regions shown.


D. J. Kim24


5. Power constraintsex)

Telephone channel : average power is constrained by regulation P(voiceband data signal) P(voice signal) to limit crosstalk interference.

Radio channel : Power regulation to avoid interference with other radio SVC to avoid nonlinearity in the RF circuitry

Transmitted power

where T : symbol interval

power constraint ;

sets an upper bound on the minimum distance dmin

for any given constellation design.

221gAX T

P

whiteis sequence symbol assume )(σ 2 jwTAA eS

dwjwGg

22 )(21σ

PσσT

P gAX 221

22

gA

PT


D. J. Kim25


6. Constellation Design

1) objective : maximize the distance btw symbols

while not exceeding the power constraint

2) 방법

zero mean

모든 점들간의 거리가 똑같이

모든 점들이 동일 원 내에 분포

3) QAM

Figure 4. Some QAM constellations.

Figure 5. Cross constellations.


D. J. Kim26


4) AM-PM( 복잡 )

5) Hexagonal constellations ( 복잡 )

6) Higher Dimensions ; 3rd, 4th-order

Figure 6. Constellations using phase-shift keying and amplitude modulation.


D. J. Kim27


8.7 Probability of Error

- Observation space Z is partitioned, in accordance with ML

decision rule, into a set of M regions

- Suppose symbol mi (signal vector Si) is TXed.

- Observation vector : x

Average probability of symbol error Pe

< Problem > Numerical computation of integral is impractical

MiZ i ,,2,1

sent sent in lie not does i

M

iiie mPmZPP

1

x

M

iii mZP

M 1

1 sent in lie not does x

M

iii mZP

M 1

11 sent in lies x

M

iZ i

i

dmxfM 1

11 xx


D. J. Kim28


1. Union Bound on the Probability of Error Example of QPSK

In General

확률가까울에보다가

는

vector nobservatio

where

k

k

e

ss

ssPssPssPssPsP

1

12

4123122121

,,,,

x

MiPmPM

ikk

kiie ,,2,1,1

2

ss

sent is when, than to closer is iikki PP sssxss ,2

2 0

2

0

exp1ikd du

Nu

N


D. J. Kim29


where

Thus

Avg. Probability of symbol error

For symmetric geometry

Consider

Thus

kiikd ss where

0221

Ndikerfc

u

dzzu 2exp2)

erfc(

MiN

dmP ikie ,,2,1

221

0

erfc

erfc1

M

i

M

ikk

ikM

iiee N

dM

mPM

P1 01 22

11

all for erfc iN

dmPPM

ikk

ikiee

1 0221

-exp1erfc

0

2

0 22 Nd

Nd ikik

all for iN

dPM

ikk

ike

1 0

2

2exp

π21


D. J. Kim30


If TXed signal power >> noise spectral density No

Approximation of the bound

Mmin : # of TXed signals that attain the minimum Euclidean distance for each mi

0

2

,

min

2minexp

π2 NdMP ik

kikie

2min M 4min M


D. J. Kim31


2. Bit Versus Symbol Error Probabilities

BER ( Bit Error Rate ) or Probability of bit errorm bits 1 symbol

1) Case 1Gray code : 옆 심볼과는 1 bit 만 차이 나게 design

옆 심볼과 error 가 날 경우 1 bit error 만 나게 함

In general

Mm 2log

MPe

2log BER

ee PM

P BER 2log


D. J. Kim32


2) Case 2

Let M=2K, where K is an integer

Assume that all symbol errors are equally likely and occur with

probability

where Pe is avg. probability of symbol error

Error 가 있는 symbol 에서 번째 i bit 가 error 일 확률 (2K-1

경우의 수 )

121

Kee P

MP

eeK

K-

PM

MP

12

122BER

1

2BER lim e

M

P


D. J. Kim33


8.8 Correlation Receiver

- ML Decision rule


if is minimum for k=i

- Consider

- Other form of ML Decoder


if is maximum for k = i

where ; energy

ksx

N

jkj

N

jkjj

N

jj

N

jkjj ssxxsx

1

2

11

2

1

2 2

k

N

jkjjkkk

Esx21maxmin

1

sx

k

N

jkjj Esx

21

1

N

jkjk sE

1

2


D. J. Kim34


- Implementation


D. J. Kim35


8.9 Detection of signals with unknown phase

noiseUncertaninty

phase

Synchronization with the phase of the carrier : costly

Noncoherent receiver : phase information 무시

( 조건 ) Information 이 phase 에 실려 있지 않을 경우만 가능

ex) FSK, non-negative ASK O.K.

PSK 적용 안됨

Consider FSK

where

Received signal (AWGN channel)

where

)

정수는kTkf

TttfTEts

i

ii

(2

0,π2cos2)(

π..:

0),(π2cos2)(

0,2 over

vr

TttwtfTEtx i

TttwtftfTEtx ii 0),(2sinsin2coscos2)(


D. J. Kim36


Correlator output of

Correlator output of

So,

tfTE

i2cos2

RI wEy cos

tfTE

i2sin2

IQ wEy sin

wE

wEyy QI

2222 sincos

Figure 8.12 Noncoherent receivers. (a) Quadrature receiver usingcorrelators. (b) Quadrature receiver using matched filters.(c) Noncoherent matched filter.


D. J. Kim37


Noncoherent matched filter

= matched filter + envelope detector

dfxtTfT

dfxtTfT

dtTfxT

ty

T

ii

T

ii

T

i

0

0

0

2sin)(2sin2

2cos)(2cos2

2cos)(2)(

-


D. J. Kim38


8.10 Hierarchy of Digital Modulation Techniques

CoherentBinary, M-ary

ASK, PSK, FSK

Ex) QPSK, MSK, QAM( Hybrid )

Non-coherentASK, FSK

DPSK : noncoherent form of binary PSK

8.11 Coherent binary PSK


D. J. Kim39


Only one basis fct

Signals

Euclidean distance

Avg. probability of symbol error = BER

Implementation :

bcb

TTtfT

t 0 , 2cos2)(1

tfTE

ts cb 2cos

2)(1

tfTE

ts cb 2cos

2)(2

bEd 212

00

12 erfc21

2erfc

21

NE

NdP b

e


D. J. Kim40


8.12 Coherent Binary FSK

FSK

CPFSK(Sunde’s FSK)

For Binary CPFSK

Orthonomal basis function

bib

bi Tttf

TEts 0π2cos2)( ,

b

ci T

inf

,3,2,1integer fixed:

inc

)( 0)( 1

2

1

tsts

0 1 0 1

bib

i TttfT

t 0 , 2cos2)(


D. J. Kim41


Euclidean distance (BPSK 와 3 dB 차이 )

Avg. prob. of symbol error = BER

Implementation

bEd 212

02erfc

21

NE

P be


D. J. Kim42


8.13 Coherent QPSK

Orthonormal basis fct

TttfT

t c 0 2cos2)(1

TttfT

t c 0 2sin2)(2

bTT 2 where


D. J. Kim43


Symbol error

BER with gray coding

(Observation) BPSK 와 BER 동일

그러나 사용

따라서 Coherent detection 경우 BPSK 보다 QPSK 가

좋다 .

Edd 21412

b

e

EE

NE

NEP

2

2erfc

22erfc

212

00

0

erfcNE

P be

0

erfc21

NE

BER b

BW21


D. J. Kim44


Implementation


D. J. Kim45


8.14 Coherent MSK

1. Consider CPFSK

In the form of an angle-modulated signal

bTt 0

0 symbol for

1 symbol for

)0(2sin2

)0(2cos2

)(

2

1

tfTE

tfTE

ts

b

b

b

b

)(2cos2)( ttfTEts cb

b

bb

TttTht 0)0()( ,

0 symbol 1 symbol

::

ratio deviation ;

carrier ;

21

21

2

1

21

2

2

ffTh

fff

fThf

fThf

b

c

bc

bc


D. J. Kim46


2. Phase Trellis

at t = Tb

Sunde’s FSK, h=1 change

MSK, change for Tb

0 symbol for - 1 symbol for

hh

Tb ππ

)0(

h2π

21

Symbol 1

Symbol 0


D. J. Kim47


3. Signal-space diagram

For k 는 integer

tftTE

tftTE

ts cb

bc

b

b 2sin)(sin2

2cos)(cos2

)(

0 symbol - 1 symbol

TttT

tb

02

)0()(

bbbb TtTTktTk or 1212

or 0)0(

pulse cosine cycle half ;

tTT

E

tTT

EtTEts

bb

bbb

bI

2cos2

2cos)0(cos2)(cos2)(

0 0 0 1 0 1 1


D. J. Kim48


4 가지 경우

Orthonormal basis fct

2 0 For bbb TktkTTt 222

2)( bT

bbb

b

bb

bb

bQ

TttTT

E

tT

TTEt

TEts

22

sin2

2sin)(sin2)(sin2)(

0 ;

0 symbol of ontransmissi (




2)0)0(

2))0(

2))0(

2)0)0(

b

b

b

b

T

T

T

T

bcbb

bcbb

TttftTT

t

TttftTT

t

0 2sin2

sin2)(

0 2cos2

cos2)(

2

1


D. J. Kim49


MSK signal

bTttststs 0 )()()( 2211

b

T

bb

bb

T

T b

TtTEdtttss

TtTEdtttss

b

b

b

20 )(sin)()(

)0(cos)()(

2

0 22

11

systemMSK for diagram space-Signal 8.23 Figure

1


D. J. Kim50


Ex3)2

2

2

2

0 0


D. J. Kim51


4. Average PE

AWGN channel

same as BPSK , QPSK

Good performance observation over 2Tb seconds

)()()( twtstx

bb TtT

)0(ˆ0x

0)0(ˆ0x )()(

1

11111

b

b

T

Twsdtttxx

bTt 20

2)(ˆ0x

2)(ˆ0x

)()(

2

22

0 2222

b

bT

T

Twsdtttxx b

0

erfc21BER

NEb


D. J. Kim52


5. Generation and Detection of MSK signals

tT

tftT

tfT

tftTT

t

bc

bc

b

cbb

22cos

22cos2

2cos2

cos2)(1

tT

tftT

tfT

tftTT

t

bc

bc

b

cbb

22cos

22cos2

2sin2

sin2)(2


D. J. Kim53


8.15 Noncoherent, Nonorthogonal Modulation

Noncoherent : 수신단에서 carrier phase 를 모른다 .

For orthogonal signals s1(t) and s2(t)

g1(t), g2(t) phase-shifted version of s1(t) and s2(t)

Received signal

Receiver

TttwtgTttwtg

tx0)()(0)()(

)(2

1


D. J. Kim54


Average Probability of error

02exp

21

NEPe density spectral noise

symbolenergy signal :

:

0NE


D. J. Kim55


8.16 Noncoherent Binary FSK

Binary FSK

Implementation

Probability of error = BER

bib

bi Tttf

TEts 0π2cos2)(

0 symbol 1 symbol

2

1

fffi

integer is ib

ii n

Tnf

02exp

21

NEP b

e


D. J. Kim56


8.17 Differential Phase-Shift Keying (DPSK)

symbol 0 Phase change of

symbol 1 No phase change

수신단에서는 두개의 symbol 사이에서만 phase

fluctuation 이 constant 가 되면 phase change 로서

symbol 0 과 1 을 구분

i.e. relative phase difference

symbol 1 for

symbol 0 for

s1(t) and s2(t) are orthogonal

bb TtT 2

bbcb

b

bcb

b

TtTtfT

E

TttfT

E

ts

2π2cos2

0π2cos2

)(1

bb TtT 2

bbcb

b

bcb

b

TtTtfT

E

TttfT

E

ts

2ππ2cos2

0π2cos2

)(2


D. J. Kim57


Avg. PE = BER

Thus

gain of 3dB over noncoherent FSK for the same

1. Generation of DPSK

b

b

EETT

22

0

exp21

NEP b

e

o

bN

E

2modulo

1 k k kd b d


D. J. Kim58


Ix

Qx

)(tx

1 0 0 1 0 0 1 1kk dd 1

2. Optimum Receiver

{dk}


D. J. Kim59


bQ

I Ttxx

at

0

00x

bQ

I Ttxx

21

11

at x


D. J. Kim60


change

change 0

πθsinθcos

θsinθcos

2222

22

101010AA

AA

xxxxxx QQIIT

θsinθcos

0

0

AxAx

Q

I

θsinθcos

1

1

AxAx

Q

I

θsinθcos

1

1

AxAx

Q

I


D. J. Kim61


8.18 Comparison of Binary and Quaternary Modulation Schemes

Table 8.4 summary of Formulas for the Bit Error Rate of Different Digital Modulation schemes

Figure 8.32Comparison of the noiseperformances of different PSK and FSK schemes


D. J. Kim62


(Observations)

BER

Coherent binary PSK, QPSK 와 MSK 가 같은 성능을

가지고 다른 system 보다 smaller BER

Coherent PSK 가 Coherent RSK 보다 3dB 우수

DPSK 가 noncoherent binary RSK 보다 3dB 우수

For high

BER of DPSK Coherent binary PSK

BER of noncoherent FSK Coherent binary FSK

o

bN

E

o

bN

E


D. J. Kim63


8.19 M-ary Modulation Techniques

1. M-ary PSK

M possible signals

Basic function

))1(22cos(2)( iM

tfTEtS ci

Mi ~1

)2cos(21 tf

Tc

Binary M-ary

Bit duration Tb Tb

Symbol duration Tb T =(log2 M)Tb

Throughput 1 배 log2M 배

Required SNR Low High

SNR Required throughput Therefore off trade

)2sin(22 tf

Tc


D. J. Kim64


d12 =d18 =

where E : signal energy per symbol

Average probability of symbol ever for coherent M-ary

PSK

For M-ary DPSK

)sin(2M

E

MN

EerfcN

derfcPoo

eπsin

2212 12

MNEerfcPo

esin2


D. J. Kim65


2. M-ary QAM : square lattice of message points

Transmitted signal

where Eo is the energy of the signal with the lowest amplitude

Basis functions

Coordinates of the i th message point are

where

)π2cos(2)π2cos(2)( tfbTEtfa

TEtS ci

oci

oi

)π2cos(2)(Φ1 tfT

t c

)π2sin(2)(Φ2 tfT

t c

),( oioi EbEa

)1,1..().........1,3()1,1(

)3,1..().........1,3()3,1()1,1..().........1,3()1,1(

),(

LLLLLL

LLLLLLLLLLLL

ba ii

ML


D. J. Kim66


ex) 16 QAM

Probability of symbol error : minimum distance

for

large M

for small & large M

Average energy

So,

For QPSK M=4

oEd 2

o

o

oe

NEerfc

NderfcP 2

2214

o

oe

NEerfc

MP 112

ooav EMELE

312

312 2

o

ave NM

EerfcM

P12

3112

o

ave N

EerfcP2

)3,3()3,1()3,1()3,3()1,3()1,1()1,1()1,3()1,3()3,1()1,1()1,3()3,3()3,1()3,1()3,3(

),(

ii ba


D. J. Kim67


3. M-ary FSK

Signals

Signals are orthogonal

Probability of symbol error for coherent

Pe for noncohernet detection

4. Comparison of M-ary Digital Mod Techniques

QAM : High throught, linear

PSK : nonlinear

FSK : increasing BW, reduced power

tinTT

Ets ciπcos2 Tt 0 Mi ~1

j idttstsT

ji ,00

oe N

EerfcMP2

121

oe N

EMP2

exp2

1


D. J. Kim68


8.20 Power spectra

Passband signal

where is complex envelope; baseband signal

1.Binary PSK

tftStftStS cQcI π2sinπ2cos

fctjtS π2exp~Re

)( fG

f

f

PSD

bT1

bT1

DAC

)(tg

2bT

2bT

tS~

binary

)(tg

bT twc cos twc cos


D. J. Kim69


실제의 구성도

xxDAC sin

xx

sin

RC

bT1

bT21

bT21

bT1

binary

data

구현필터로하나의

filter RCx

xsin

twc cos twc cos

RC


D. J. Kim70


b

b

T1 BW FSK binary

T1 null first PSK binary


D. J. Kim71


T0.5 BW MSK

T1 null first QPSK

b

bT21


D. J. Kim72


bTM2log1

T1 null first ;PSK ary -M


D. J. Kim73


bTM 5.0logBW deviation) (freq 0.5 2 h forFSK ary -M ;


D. J. Kim74


8.21 BW Efficiency

1. BW efficiency of M–ary PSK

Nyquist minimum BW theorem :

실수 data 전송 시 1 sec 동안 1hz 에 2 개의 symbol

을 보낼 수 있다

복소수 data 전송 시 1Hz 에 1 개의 symbol / sec 가

가능

SSB 로 2 배 , = 0 로 2 배 성능 증가

2ρ

2

ρ

MM

2

2

b

b

log

logRT

2B

BR

M 2 4 8 16 32 640.5 1 1.5 2 2.5 3

M 2 4 8 16 32 642 4 6 8 10 12

사용로에서의경우사용

의또는경우사용안할

DSB BW passband RC

1 filter RC

bandwidthT2B rate bit

T1 R whereb

b

,α,

::

ρ

ρ


D. J. Kim75


2. Bandwidth Efficiency of M-ary FSK signals

To maintain orthogonality: freq difference = 2T1

bits/s/Hz M

M2log BR

M2logMR

TMlog2M

2TM Bandwidth

2b

2

b

b2

ρ

M 2 4 8 16 32 641 1 0.75 0.5 0.3125 0.1875

잘 안 쓴다

ρ


D. J. Kim76


8.22 Synchronization

1) Carrier recovery = carrier synchronization :

carrier 의 frequency 와 phase 를 recover

coherent detection

noncoherent detection

2) Clock recovery =symbol synchronization: timing (or sampling ) instant 를 recover ,

individual symbol 의 starting 과 finishing time 을 알기 위해 ,

individual symbol 의 정확한 중간 점을 알기 위해

3) Packet or cell 동기

4) Frame 동기

5) Network 동기

1.Carrier synchronization

1) 작은 양의 discrete component(dc component ) pilot 을 전송 수신기에서 Narrowband PLL 을 사용하여 carrier 복조

dc 부근의 신호성분은 random 하므로 average out

됨

문제점 : waste of power

ex) Analog(AM), Digital ( 미국 DTV 전송방식 8VSB)


D. J. Kim77


2) Power of M Carrier Recovery, M th-power loop

Received signal

여기서 for M-ary PSK

문제점 ) M phase ambiguities in (0,2) for BPSK , M=2, 0˚ , 180˚ phase ambiguities

M

signals reference M

.....................

kkc A j k

KT jk eA e X argω

122

k

kπl

M

Mπl

j ee

MπljAj

k

k e e2

arg

cM ω at line spectral strong

k

θkT jMMk A e X c k ω


D. J. Kim78


3) Costas Loop

Real 신호만 전송 시 In-phase 에 data output

Quadrature path will be zero

0º, 180º phase ambiguity problem

M-ary PSK 에 적용하면 M Phase ambiguities


D. J. Kim79


4) Differential encoding

phase ambiguity 없애는 방법중의 하나

Coherent detection of differentially encoded binary PSK

Coherent detection of differentially encoded QPSK

2. Symbol Synchronization

1) Clock 을 전송 별도의 선

data-bearing signal 과

multiplexing 해서

2) Baseband waveform 에서 추출

동일와나가 MSK QPSK eP 1 E for

21 - EP

b

be

o

o

b

o

N

NEerfc

Nerfc 2

QPSK coherent NE large for

NEerfc

NEerfc

NE2erfc -

NEerfcP

ob

o

b4

o

b3

o

b2

o

b e

동일와,

2


D. J. Kim80


ex) Early–gate Late–gate clock recovery

Raised – cosine filter 의 경우

2T

2T

21

nx

nx21

nx

21

21

nnxx detector phase

21n

xnx

21n

x

21

21

nnxx detector phase


D. J. Kim81


<HW> 8.1, 8.6, 8.10, 8.16, 8.18, 8.17, 8.22

chapter 8. digital passband transmission 8.1 introduction

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