chapter 3 digital communication 1 - 0 - kyunghee university chapter 3: baseband...

Chapter 3 Chapter 3 Digital Communication 1

- 1 -

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Chapter 3: Baseband

Demodulation/Detection


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풍선효과풍선효과

Idiots, it’s trade-off!!

Bit error Bit error PPBB

PowerEb/No

Bandwidth

W

Bitrate R


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White NoiseWhite Noise

ACS PSD

( Ex ) Thermal noise : 0 ~ 1012 Hz

AWGN ( Additive White Gaussian Noise ) Channel

- Infinite Bandwidth :

- Pass through a specific channel

- If AWGN is correlated with one of a set of orthonormal functions

Bandlimited AWGN channel

0( )2n

NG f 0( ) ( )

2 n

NR

2 0var[ ( ) ] ( )2

Nn t df

( ) , j t

2 2 0

0var( ) [ ( ) ( ) ]

2

T

j j

Nn E n t t

the variance of the correlator output is given by

( Why ? Appendix C )


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Three Major Functions of Digital ReceiverThree Major Functions of Digital Receiver

Filtering : - Reduce unwanted noise and interference

- Recover a baseband pulse with the best possible

SNR, free of any ISI (Inter-Symbol Interference

- Matched filter or Correlator

- Equalizing filter for channel – induced ISI

Sampling : Get the best signal components

Decision : Reduce the probability of error

( Note ) Detection : Decision – making process


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Functional Block for DigitalFunctional Block for Digital Demodulation / Detection Procedure Demodulation / Detection Procedure

Frequencydown-

conversion

Receivingfilter

Equalizingfilter( )is t

AWGN

( )r t

Transmittedwaveform

Receivedwaveform

( ) ( ) ( ) ( )i cr t s t h t n t

Thresholdcomparison

H1

H2

Sampleat t = T

Demodulate & sample

For bandpasssignal

Compensation forchannel induced

ISI

Baseband pulse( possibly distorted )

( )z t

Baseband pulse

0( ) ( ) ( )iz t a t n t

( )z T

Sample ( teststatistic )

0( ) ( ) ( )iz T a T n T

Predetectionpoint

Detect

orim

iu

Message symbolor

channel symbol iu

im

Step 1waveform - to - sample transformation

Step 2decision making

( )z T

Optional

Essential


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Vectorial Representation of Signal Waveforms (1)Vectorial Representation of Signal Waveforms (1)

N-dimensional orthogonal space

Orthogonal and orthonormal functions

–

, Kronecker delta function

Dfn : A space characterized by a set of N linearly independent functions , called basis function.

{ ( )}j t

1( )

0

for j kj k

otherwise

–

– If , then are called orthonormal functions. 1jK { ( )}j t

NkjforkjKdttt j

T

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

NkjforkjdtT

kt

T

jt

T

T,,2,1,][

2cos

2cos

20

Cf)


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Any arbitrary function in the space can be expressed as a linear combination of N orthogonal waveforms, such that

– Compact form

1

( ) ( ) , 1, , ,N

i ij jj

S t a t i M N M

0

1( ) ( ) , 1, , , 0

T

ij i jj

a S t t dt i M t TK

– Coefficient form

– 1 11 1 12 2 1N N

2 21 1 22 2 2N N

M M1 1 M 2 2 MN N

( ) ( ) ( ) ( )

( ) ( ) ( ) ( )

( ) ( ) ( ) ( )

S t a t a t a t

S t a t a t a t

S t a t a t a t

1, ,j N

M symbols


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Observation :

– The set of signal waveforms , can be viewed as a set of vectors

3 31 1 32 2 33 3 3 31 32 33( ) ( ) ( ) ( ) ( , , )S t a t a t a t a a a S

{ ( )}iS t

(Ex.)

The task of the receiver is to decide whether has a close “resemblance”

to the prototype .

r

jS

The analysis of all demodulation of detection schemes involves this concept of distance

between a received waveform and a set of possible transmitted waveforms.

Refer to Fig. 3.4

},,,{)}({ 11 iNiii aaats


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Example of Vector Representation

)(1 t

)(2 t

E

E

E

)2

cos(2

)( 0 M

it

T

EtSi

)(tSi

M

i2


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Waveform EnergyWaveform Energy

Energy of the waveform over a symbol duration( )jS t

If , then

Average symbol energy :

sT

22

0 0

0

0

( ) ( ) ( )

( ) ( )

( ) ( )

T T

i i ij i

T

ij i ik kj k

T

ij ik i kj k

j k

E S t dt a t dt

a t a t dt

a a t t dt

Eq. (3.13) ~ Eq.(3.17)

1jK 2

1

N

i ijj

E a

1

1 M

s ii

E EM

Average bit energy : / ( / )b sE E k k bits symbol

][ kjKaa jikij


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Variance of White Noise

▷ white Gaussian noise process, n(t), with zero mean and two-sided power spectral density,

▷ Noise variance is infinite, filtered AWGN is finite

▷ The output of each correlator, , t=T

▷ mean of

jn

jn


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▷ variance of

▷ n(t) is zero-mean process

▷ The autocorrelation function

▷ If n(t) is assumed stationary, then Rn(t,s) is only a function of the time difference,

jn

)}()({),( sntnEstRn

st


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▷ For a stationary random process, the power spectral density, Gn(f), and the autocorrelation function,Rn( ), form a Fourier transform pair.

▷ Since n(t) is white noise,

So,

2/)( 0NfGn

Inverse FT

1)() cf)(

22)( 020 N

dfeN

R fjn

1

2 0

2

N


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Signal RepresentationSignal Representation

Transmitted signal : 1

2

( ) , 0 1( )

( ) , 0 0i

s t t T fors t

s t t T for

Received signal : ( ) ( ) ( ) ( ) 1, 2, ,i cr t s t h t n t i M

Output of receiving filter : ( ) ( ) ( )iz t a t n t

( )

( )

n T

z T

Output of sampler at t = T : ( ) ( ) ( )iz T a T n T

: Gaussian random variable ( n0 = n(T) )

: Gaussian random variable ( a1 = a1(T) , a2 = a2(T) )

convolution


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Conditional pdf : -2

200 0

00

1 1( ) exp[ ] : 0 , var

22

np n mean iance

- : Likelihood function of s11

2

1

00

1 1( ) exp[ ]

22

zs

z ap

-2

2

2

00

1 1( ) exp[ ]

22

zs

z ap

Conditional pdf p ( z/s )Conditional pdf p ( z/s )

- If s1(t) is transmitted , then 1 0 z a n

- If s2(t) is transmitted , then 2 0 z a n

Fig. 3. 2.

: Likelihood function of s2

o no

σo

a1 a2


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EEbb / N / N00

Analog communications : S/N ( or SNR ) figure of merit ( power signal )

0

sec

/ / sec

b bE S T S W Joule W

N N W N R W Hz W

Digital communications : Eb/N0 figure of merit

- Eb : bit energy , - N0 : one – sided PSD - S : signal power

Why Eb/N0 is a natural figure of merit ?

- Focusing on one symbol , the power ( averaged over all time ) goes to zero .

- Hence , power is not a useful way to characterize a digital waveform .- The symbol energy ( power integrated over Ts ) is a more useful parameter

for characterizing digital waveforms .

- Tb : bit duration[sec] - S : signal power[Watt] - N : noise power[Watt]


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Demodulation and Detection

• The received signal over Gaussian channel


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is equal

a1 a2

H1

H2

Decision-making criterion


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Minimum error criterion

ln 1 = 0


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▷ Error Probability

and because of the symmetry of the probability density function

a1 a2

BER


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Complementary error functionComplementary error function

212

( ) exp( )2x

uQ x du

212

( ) exp( ) 32x

xQ x for x

12(0)Q

(1) 0.1587Q

(2) 0.0228Q

( ) 0Q

x

Right half of N(0,1)


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Matched Filter ( MF ) ( 1 )Matched Filter ( MF ) ( 1 )

A linear filter designated to provide the maximum SNR at its output for a given transmitted symbol waveform .

AWGN Channel , transmitted signal ( ) , 0s t t T

Matched Filter

h(t) , H(f)

Detector z(T)

1 or 0

threshold

sampleat t = T

PCM wavess(t)

WGN n(t)


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KyungHeeUniversityMatched Filter

)()(

)()()()('

)(2

)()(

:)(

)(2

,)()()(

*21

2

2

2

1

2

21

20

2

2

2020

2

20

2

xkfxfifholdsequalityThe

dxxfdxxfdxxfxfinequalitysSchwarz

dffHN

dfefSfH

N

S

functiontransferfilterfHwhere

dffHN

dfefSfHta

a

N

S

ftj

T

ftji

i

T

Linear Filter designed to provide the maximum SNR at its output


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elsewhere

TttTksth

efkSfH

FilterMatchedFunctionTransferOptimal

N

EdffS

NN

S

dffSdffHdfefSfH

fTj

T

ftj

0

0)()(

)()(

)(

2)(

2

)()()()(

2*

0

2

0

22

2

2

0 T

0 T

s(t)

h(t)

Matched filter 일 때 , S/N 이 최대값이 됨을 증명했다 .


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Correlator Realization of the MFCorrelator Realization of the MF

0

( ) ( ) ( ) ( ) ( ) ( ( ) ( ) ) t

z t r t h t r h t d h t s T t

0 0( ) [ ( ) ] ( ) ( )

t tr s T t d r s T t d

At t = T , : Cross – correlation of with0

( ) ( ) ( )T

z T r s d ( )r t ( )s t

( Observation ) Integration – and – Dump Filter

For NRZ Waveform , ( ) 1 0s t for t T

0( ) ( )

Tz T r d

( Note ) The correlator output and the matched filter output are the same only at time t = T . ( Refer to Fig. 3.7 )


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▷ Correlation Realization of the Matched Filter

MF output

Matched Filter

When t=T

0( ) ( )* ( ) ( ) ( )

tz t r t h t r h t d

0( ) ( ) [ ]

Tz T r S d

0( ) [ ( )]

tr S T t d


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Equivalence of Matched Filter and CorrelatorEquivalence of Matched Filter and Correlator

h( T - t )r(t) = si (t) + n(t) z (T)

Matched tos1(t) - s2(t)

0T

r(t) = si (t) + n(t) z (T)

s1(t) - s2(t)

Matched Filter

Correlator


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Probability of Bit Error ( PProbability of Bit Error ( PB B ))

for Binary Signaling (1)for Binary Signaling (1)

1 2

0 0 0

(1 )

2 2d b

B

E Ea aP Q Q Q

N N

( ) Output SNR at time t = T :

21 2 1 2

20 0

( )

/ 2 2 2d d

T o

E Ea a a aS

N N N

22 2

1 2 1 2 1 20 0 0 0

1 20

( ) ( ) ( ) ( ) ( ) ( )

12 ( ) ( ) cos

2 1

T T T T

d

T

b b bb

b

E s t s t dt s t dt s t dt s t s t dt

E E E s t s t dtE

E

Cross-correlation coefficient -

1<ρ<1 ρ =0 if uncorrelated

a1 a2


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Probability of Bit Error ( PProbability of Bit Error ( PB B ))

for Binary Signaling (2)for Binary Signaling (2)

0

(1 )bB

EP Q

N

for antipodal signaling 0

2 bB

EP Q

N

( 1 )

for orthogonal signaling 0

bB

EP Q

N

( 0)

1 1 2 1

01 2 0

( ) ( ) , ( ) ( )

2 ,2

b b

b b b

s t E t s t E t

Na a E E E

s1s2

s1

s2

bE bE

bE

bE

2

1

bd EE 4

2)2( bd EE

)2

(0N

EQP d

B


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Comparison of Binary SignalingComparison of Binary Signaling

At the same bit energy Eb and noise condition No,

)2

(0N

EQP d

B

Compare

21 20

( ( ) ( ) )T

dwhere E s t s t dt


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Unipolar Signaling (1)Unipolar Signaling (1)

1( ) , 0 for binary 1 ( 0)s t A t T A

Signal

–

0 ( ) 0 , 0 for binary 0s t t T –


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Unipolar Signaling (1)Unipolar Signaling (1)

Detection Process

)()()( 1 tntstr

TAAdttnAEtsTzETaT 2

011 }))(({)}(|)({)(

Atsts )]()([ 21

0})({)}(|)({)(022 T

AdttnEtsTzETa

22

221

0

TAaa

)()2

()2

(00

2

0 N

EQ

N

TAQ

N

EQP bd

B

2

2TAEb


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Bipolar Signaling (1)Bipolar Signaling (1)

– for binary 1

– for binary 0

1( ) 0s t A t T

2 ( ) 0s t A t T

– 2 2 21 20 0

( ( ) ( ) ) (2 ) 4T T

dE s t s t dt A dt A T

A

-A

T 2T 4T t Decision

T

0

T

0

)(1 ts

)(2 ts

)(2 Tz

)(1 Tz

)(tr


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0 0 0

4 2

2 2d b b

B

E E EP Q Q Q

N N N

Refer to Fig. 3.14

Average bit energy :2 2

2

2 4d

b

EA T A TE A T

Bipolar Signaling (2)Bipolar Signaling (2)

)(0N

EQP b

B

)2

(0N

EQP b

B

3dB

10-2

10-4

)(0

dBN

Eb14-1


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3.2.5.3 Signaling Described with Basis Functions (1)3.2.5.3 Signaling Described with Basis Functions (1)

Unipolar Signaling

–

1 11 1 11

1( ) ( ) ( )s t a t A T A a A T

T

21 1 1 10 0

1( ) ( ) ( ) 1 ) ( )

T Tt t dt t dt ex t

T

2 21 1 21

1( ) ( ) 0 0 ( 0)s t a t a

T

–

–

Basis functions Basis functions orthonormal functions orthonormal functions


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Detection process

1 1 11 1 1 110 0( ) ( ) ( ) ( ) ( ) ( ) 2

T T

ba T E r t t dt E a t n t t dt a E

2 1 21 1 1 210 0( ) ( ) ( ) ( ) ( ) ( ) 0

T Ta T E r t t dt E a t n t t dt a

2 20

2 2b

A T A TE

2 bA T E

1( )t

21

0

a 11

2 bE

a



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Bipolar Signaling

–1 11 1 11

1( ) ( ) ( )s t a t A T A a A T

T

2 21 1 21

1( ) ( ) ( )s t a t A T A a A T

T

2 22

2b b

A T A TE A T A T E

Detection process

1 11 2( ) , ( )b ba T a E a T E


–


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Observations on Binary SignalingObservations on Binary Signaling

We can see that a 3-dB error performance improvement for bipolar

signaling compared with unipolar signaling .

Bandpass antipodal signaling ( e.g. , BPSK ) has the same PB

performance as baseband antipodal signaling ( e.g. , bipolar pulses )

with MF detection .

Bandpass orthogonal signaling ( e.g. , orthogonal FSK ) has the same

PB performance as baseband orthogonal signaling ( e.g. , unipolar pulses )

s1s2

bE bE

bd EE 4

s1

s2

bE

bE

2

1

2)2( bd EE


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Bandlimited ChannelBandlimited Channel

So far , digital communication over on AWGN channel

– No bandwidth requirement and/or channel distortion

Now , digital communication over a bandlimited baseband channel

– Bandwidth constraint and/or channel distortion

– Modeled as a linear filter channel with a limited bandwidth

– Telephone channels , microwave , satellite etc.


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Linear Filter ChannelLinear Filter Channel

More stringent requirements on the design of modulation signals

Preclude the use of rectangular pulses at the modulator output

Distort the transmitted signal

Cause the intersymbol interference ( ISI ) at the demodulator

Frequency responses of channel are distorted , thus non-flat or frequency selective channels .

Increase PB

Requires channel equalizers to compensate for the distortion caused by the transmitter and the channel .


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FT

FT

Inter-symbol interference

Infinite bandwidth

Our dilemma!!

양쪽에서 조금씩 타협

Infinite duration and non-causal

t

tf

f


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Typical Baseband Digital System

System Transfer function :( ) ( ) ( ) ( )t c rH f H f H f H f

(a)

H ( f )h ( t )

Detector

T T

k{ x }

1x 2x

3xt = kT

k{ x }

(b)

Noise

Pulse 1 Pulse 2

Trasmittingfilter

ChannelReceiving

filterDetector

T T

k{ x }

1x 2x

3x

Noise

t = kT

k{ x }

Transmit Channel Receiving

Equivalent model with two pulses


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3.3 Inter-symbol Interference ( ISI )

ISI : Due to the effects of system filtering , the

received pulses can overlap one another.

The tail of a pulse can smear into adjacent symbol

Interfere with the detection process

Degrade the error performance

Even in the absence of noise, the effects of filtering

and channel-induced distortion lead to ISI.

( ) ( )t cH f H f


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Ideal Nyquist Filter for Zero ISI (1)

Theoretical Minimum Nyquist BW =

Ideal Nyquist pulse :

infinite tail find practical one

sR

s

1R / 2

2T

: Symbol rate [ symbols / sec ]

h(t) sin c( t / T )

f

(a)

H(f)

T

t

h(t)

01

2

T

1

2T

1

0

-T T(b)

h(t - T)

–


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Ideal Nyquist Filter ( apulse ) for Zero ISI (2)

Nyquist filters are not realizable

since they have the infinite filter length.

Observation : (i) Even though has long tails, a tail pass through zero amplitude at t = T when is to be sampled. (ii) If the sample timing is perfect, thee will be no ISI degradation introduced.

Among the class of Nyquist filters, the most popular ones are the raised cosine and the square root-raised cosine filters.

h( t - T ) h(t)


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Pulse shape to Reduce ISI

Nyquist filters provide zero ISI only when the sampling is performed at exactly the correct sampling time. When the tails are large, small timing errors will result in ISI

One frequently used transfer function belonging to the Nyquist close ( zero ISI at the sampling points) is called the raised-cosine filter.

H(f)


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Raised – Cosine Filter ( R-C Filter )

Wffor

WfWWforWW

WWf

WWffor

fH

||0

||22||

4cos

2||1

)( 00

02

0

00 /)( WWWr

)( 0WWbandwidthexcess T

WbandwidthNyquist2

1min 0

2cos~0cos

2

)~0cos(1

0W0W W

r =1

r =0.5

r =0

fTRrateSymbol /1


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Raised – Cosine Filter ( R-C Filter ) (2)

Impulse Response :

: Minimum Nyquist Filter0

1w

2T

0

0

w wr

w

: roll-off factor ( 0 r 1 )

s

1R [Hz]

T : symbol rate

s

1w (1 r )R

2 DSB sw (1 r )R

20

000

)(41

)(2cos)2(2)(

tWW

tWWtWncsiWth

Baseband bandwidth

Double-sided bandwidth


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Baseband and double-sideband bandwidth

Baseband bandwidth

)(tx tftxtx cc 2cos)()(

tfc2cos Local oscillator

|)(| fX

mfmf f

|)(| fX c

mc ff mc ff fmc ff

double-sideband bandwidth

mc ff


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Spectrum of Raised Cosine Pulse• r=0 corresponds to sinc(.) function

f (Hz)

1.0

0.5

(1 )Wo r Wo W

Wo r Wo r

sDSB RrW )1( T

Rs

1

|)(| fH


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Raised Cosine Pulse - Time Domain

r=0r=0.35r=0.5r=1.0

-4 -3 -2 -1 0 1 2 3 4-0.5

0

0.5

1

1.5

2

t (us)

x(t)

Raised Cosine Pulses for Several Different Rolloff Factors

Sync fn

sec2

1 T


- 53 -

KyungHeeUniversityRaised Cosine Pulse - Frequency Domain

r=0r=0.35r=0.5r=1.0

-5 0 5-120

-100

-80

-60

-40

-20

0

20

40

f (MHz)

|X(f)|^2 (dB)

Energy Spectrum of Raised Cosine Pulses

MHzW 10


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Implementation of Raised Cosine Pulse

• Can be digitally implemented with an FIR filter

• Analog filters such as Butterworth filters may approximate the tight shape of this spectrum

• Practical pulses must be truncated in time– Truncation leads to sidelobes - even in RC pulses

• Sometimes a “square-root” raised cosine spectrum is used when identical filters are implemented at transmitter and receiver– We will discuss this more for “matched filtering.”


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Bandwidth of Raised Cosine Pulses

• For PCM system: 2n=L (1 sample = n bits)

– is a parameter called “roll-off factor”

• Special cases:– r = 0 is just an Sa(.) function

– r = 1 is the largest possible value

– r = 0.35 is used in U.S. Digital Cellular (IS-54/136) standard

– r = 0.22 is used in WCDMA (3G) standard

0 1 r

1Hz

2SSB s

rBW f n

SSB s

1W (1 r )R

2 SSB

Sampling rate


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(i) When r = 1, the required excess bandwidth is

100% and the tails are quite small. (ii) Bandpass - modulated signals ( chap. 4 ), such as

Amplitude-Shift Keying (ASK) and Phase-Shift

Keying (PSK), require twice the transmission

bandwidth of the equivalent baseband signals. WDSB

(iii) The larger the filter roll-off, the shorter will be

the pulse tails ( which implies smaller tail amplitudes ).


SSB s

1W (1 r )R

2


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(v) The smaller the filter roll-off is,

the smaller the excess BW will be.

Increase the signaling rate or the number of users

that can simultaneously use system.

The greater sensitivity to timing errors.

(iv) large r Small tail’s exhibit less sensitivity to timing error’s and thus make for small degradation due to ISI.


SSB s

1W (1 r )R

2


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FT

FT

Inter-symbol interference

Infinite bandwidth

Recall our dilemma!!

양쪽에서 조금씩 타협

Infinite duration and non-causal

t

tf

f

r=0


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Raised Cosine (R-C) Filter ( 2 - ASK , r = 0 )Raised Cosine (R-C) Filter ( 2 - ASK , r = 0 )

©

Roll-off Factor : r = 0

Filter Duration = [-4Ts,4Ts]

No. of Oversampling = 8

[8 samples/Ts]

Output of Matched Filter

[1,-1,-1,1,-1,1,1,-1,1,-1]

Large ISI


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Raised Cosine Filter ( 2 - ASK , r = 0.5 )Raised Cosine Filter ( 2 - ASK , r = 0.5 )

©

Roll-off Factor : r = 0.5



Output of Matched Filter

[1,-1,-1,1,-1,1,1,-1,1,-1]


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Raised Cosine Filter ( 2 - ASK , r = 1 )Raised Cosine Filter ( 2 - ASK , r = 1 )

©

Roll-off Factor : r = 1.0



Small ISI


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3.3.2 Two types of Error-performance Degradation

Without ISI

– theoretical

practical

0/ 10bE N dB

With ISI – More may not help the ISI problem.

0/bE N

– Equalization will help.

510BP

dBNEb 12/ 0

10 12

510BP

0/ NEb

10 12

510BP

0/ NEb

110BP

110BP


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Example of Bandwidth Requirements (1)Example of Bandwidth Requirements (1)

Example 3.3 (a) Find minimum required bandwidth for 4-ary PAM baseband modulation (R = 2400 bps , r = 1) (b)Find minimum required bandwidth for 4-ary PAM bandpass modulation

( Answer ) (a) M = 4 k = 2 bits symbol rate

(b)

12002s

RR Hz

1(1 ) 1200

2 sW r R Hz

(1 ) 2400DSB sW r R Hz


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Ex 3.4) Digital Telephone Circuits ( PCM Waveform )

– 3 kHz analog voice 8 bit ADC fs = 8kHz – Bit rate : R = 8000 8 bits = 64 kHz – For ideal Nyquist Filtering ,

Note) Binary signaling with a PCM waveform requires at least eight times the BW required for the analog channel . needs speech codec, 10kbps

(analog BW : guard-band + 3 kHz = 4 kHz )

132

2 2PCM

RW kHz

T

Example of Bandwidth Requirements (2)Example of Bandwidth Requirements (2)


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3.3.3 Demodulation/Detection of shaped pulse3.3.3 Demodulation/Detection of shaped pulse

Conventional : filter-out unwanted spectrum Matched : maximize energy at the sample points T.

• Optimal under AWGN

* =

* =

No ISI

with ISI Nyquist pulse

2TT

T

t

t t

t t

t

Sample point

Sample point


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KyungHeeUniversity

3.3.3 Demodulation/Detection of shaped pulse3.3.3 Demodulation/Detection of shaped pulse

Nyquist waveform observation (i) The square-root raised cosine filter non zero ISI (ii) transmitter output not exact original samples (iii) MF(matched filter) output zero ISI at the sample points.

[+1 +1 -1 +3 +1 +3] [+1 +1 -1 +3 +1 +3]

transmitter output Matched filter output Channel

correlator


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Eye PatternEye Pattern

Oscilloscope display for the received signalon the vertical input with the horizontal sweep

rate 1/Ts

The optimum sampling time corresponds tothe maximum eye opening , yielding the greatest

protection against noise .

If there were no filtering in the system , thenthe system response would yield ideal rectangular

pulse shapes . ( no filtering BW corresponding to the transmission of the data pulse is infinite )

As the eye closes , ISI is increasing ; as the eyeopens , ISI is decreasing .

DA : Measure of distortion caused by ISI

JT : Measure of the timing jitter

MN : Measure of noise margin

ST : Sensitivity-to timing error


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Practical Eye Pattern for ASK (or PAM)


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KyungHeeUniversity

Type of Eye Pattern


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KyungHeeUniversity

Eye Pattern ( 4 – ASK ) with Roll-off FactorEye Pattern ( 4 – ASK ) with Roll-off Factor

©

r = 0

r = 0.5

r = 0.25

r = 1.0

chapter 3 digital communication 1 - 0 - kyunghee university chapter 3: baseband...

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