s-72.245 transmission methods in telecommunication systems (4 cr)

14
S-72.245 Transmission Methods in Telecommunication Systems (4 cr) Review

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S-72.245 Transmission Methods in Telecommunication Systems (4 cr). Review. 25. Filt. Phase detector. VCO. Divide by 10. PLL based frequency synthesizer. Reference signal f in is locked for instance to the fundamental frequency of a crystal oscillator. By adjusting the - PowerPoint PPT Presentation

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Page 1: S-72.245 Transmission Methods in Telecommunication Systems (4 cr)

S-72.245 Transmission Methods in Telecommunication Systems (4 cr)

Review

Page 2: S-72.245 Transmission Methods in Telecommunication Systems (4 cr)

2 Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen25

Page 3: S-72.245 Transmission Methods in Telecommunication Systems (4 cr)

3 Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen

Page 4: S-72.245 Transmission Methods in Telecommunication Systems (4 cr)

4 Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen

Page 5: S-72.245 Transmission Methods in Telecommunication Systems (4 cr)

5 Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen

Page 6: S-72.245 Transmission Methods in Telecommunication Systems (4 cr)

6 Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen

PLL based frequency synthesizer

VCOVCO

Filt.Filt.Phasedetector

Phasedetector

Divide by10

Divide by10

10out in

f f

inf

By adjusting thedivider differentfrequencies can be producedwhose phase is locked into fin

Reference signal fin

is locked for instanceto the fundamental frequency of a crystal oscillator

Page 7: S-72.245 Transmission Methods in Telecommunication Systems (4 cr)

7 Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen

Detecting DSB using PLL-principle

An important application for PLLs is in synchronization of receiver local oscillator in synchronous detection

In the Costas PLL (below) two phase discriminators are used to:– cancel out DSB modulation x(t) in the driving signal– synchronize the output frequency to the center frequency of the

DSB spectra (the suppressed carrier)– to detect the DSB signal

Cos

tas

PL

L d

etec

tor

for

DS

B

PD: phase detector (=multiply+LPF)

Loop drives phase error to zero

LPF yields constant (zero) output when loop is locked to carrier

1sin cos sin 2 sin 02ss ss ss ss

Page 8: S-72.245 Transmission Methods in Telecommunication Systems (4 cr)

8 Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen

PAM Power Spectral Density (PSD) PSD for PAM can be determined by using a general expression

For uncorrelated message bits

and therefore

on the other hand and

21( ) ( ) ( )exp( 2 )

x an

G f P f R n j nfDD

Amplitude autocorrelation

2 2

2

, 0( )

, 0

a a

a

a

m nR n

m n

2 2( )exp( 2 ) exp( 2 )

a n an n

R n nfD m j nfD

1exp( 2 )

n n

nj nfD f

D D

2 22 2 2( ) ( ) ( ) ( )

x a an

G f r P f m r P nr f nr

1/r D

Total power

DC power

Page 9: S-72.245 Transmission Methods in Telecommunication Systems (4 cr)

9 Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen

PAM Power Spectral Density (PSD) PSD for PAM can be determined by using a general expression

For uncorrelated message bits

and therefore

on the other hand and

21( ) ( ) ( )exp( 2 )

x an

G f P f R n j nfDD

Amplitude autocorrelation

2 2

2

, 0( )

, 0

a a

a

a

m nR n

m n

2 2( )exp( 2 ) exp( 2 )

a n an n

R n nfD m j nfD

1exp( 2 )

n n

nj nfD f

D D

2 22 2 2( ) ( ) ( ) ( )

x a an

G f r P f m r P nr f nr

1/r D

Total power

DC power

Page 10: S-72.245 Transmission Methods in Telecommunication Systems (4 cr)

10 Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen

Example For unipolar binary RZ signal:

Assume source bits are equally alike and independent, thus

1( ) sinc

2 2

b b

fP f

r r

/ 22 2 2 2 2

0

(1/ 2 ) / 4,bT

a b a aT A dt A m

2 2

2 2( ) sinc ( )sinc16 2 16 2x b

nb b

A f A nG f f nr

r r

22

22 2

( ) ( )

( ) ( )

x a

an

G f r P f

m r P nr f nr

22 1

4 2b

b

Ar

r

Page 11: S-72.245 Transmission Methods in Telecommunication Systems (4 cr)

11 Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen

Equalization: Removing Residual ISI Consider a tapped delay line equalizer with

Search for the tap gains cN such that the output equals zero at sample intervals D except at the decision instant when it should be unity. The output is (think for instance paths c-N, cN or c0)

that is sampled at yielding

( ) ( ) N

eq nn N

p t c p t nD ND

( ) ( ) ( )N N

eq n nn N n N

p kD ND c p kD nD c p D k n

k

t kD ND

( ) ( 2 )N N

p t c p t ND

( ) ( )N N

p t c p t

0( ) ( )

Np t c p t ND

Page 12: S-72.245 Transmission Methods in Telecommunication Systems (4 cr)

12 Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen

Tapped Delay Line: Matrix Representation

At the instant of decision:

That leads into (2N+1)x(2N+1) matrix where (2N+1) tap coefficients can be solved:

1, 0

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

N N

eq k n nn N n N k n

kp t c p D k n c p

k N

0 2

1 1 1

0

1 1 1

2 0

... 0

...

... 0

... 1

... 0

... 0

N N

N N

N N

N N

N N

p p c

p p c

p p c

p p c

p p c

0 1 1 2

1 0 1 2 1

1 1

2 2 1 1 0

... 0

... 0

... 1

... 0

n n n n

n n n n

n n n n n n

n n n n n

p c p c p c

p c p c p c

p c p c p c

p c p c p c

0 1 2

1

n

n n n

p p p

c c c

+( )

eqp t

( )p t

Page 13: S-72.245 Transmission Methods in Telecommunication Systems (4 cr)

13 Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen

Example of Equalization

Read the distorted pulse values into matrix from fig. (a)

and the solution is

1

0

1

1.0 0.1 0.0 0

0.2 1.0 0.1 1

0.1 0.2 1.0 0

c

c

c

1

0

1

0.096

0.96

0.2

c

c

c

Zero forced values

0p

1p

2p

1p

2p

Question: what does thesezeros help because they don’texist at the sampling instant?

Page 14: S-72.245 Transmission Methods in Telecommunication Systems (4 cr)

14 Helsinki University of Technology,Communications Laboratory, Timo O. Korhonen

Monitoring Transmission Quality by Eye Diagram

Required minimum bandwidth is

Nyqvist’s sampling theorem:

/ 2T

B r

Given an ideal LPF with thebandwidth B it is possible totransmit independent symbols at the rate:

/ 2 1/(2 )T b

B r T