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COMMUNICATIONSYSTEMS (1st module)

Lecturer: Claudio Sacchi, Ph.D

University of Trento, International Master in

Telecommunications Enineerin, !cademic "ear#$%&'#$%(

!ssistant lecturer: CosimoStallo, Ph.D

)isitin *rofessor: Prof. Luc)andendor*e

PART 2: NOISE INCOMMUNICATION SYSTEMS

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TABLE OF CONTENTS

TECHNICAL INTROUCTION TO THERMALNOISE

Thermal noise measured PSD+

hite a**ro-imation+

Euivalent model for am*lifier thermal noise.

THERMAL NOISE PARAMETERI!ATION INTELECOMMUNICATION SYSTEMS

/oise fiure+ Some cases of technical interest a0out noise *arameters

com*utation.

Telecommunication SystemsUniversity of Trento

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TABLE OF CONTENTS

MAN"MAE NOISE AN INTERFERENCE Introduction+

Man'made noise features+

Man'made noise modelin+

Co'channel interference and ad1acent channel interference+

Phase noise.


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TECHNICAL INTROUCTION TOTHERMAL NOISE


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THERMAL NOISE MEASURE PS

#HAT$S THERMAL NOISE % Thermal noise is the electronic noise enerated 0y thermal

aitation of electrons inside an electrical conductor+

It is also 3no4n as 5ohnson'/yuist noise, 0ecause it 4asmeasured 0y 5.6. 5ohnson at 6ell La0s in %7#8 and

descri0ed in details 0y 9. /yuist 6ell La0s; in %7&$+ The t&ue thermal noise PSD has the follo4in e-*ression:

( )2

1( )

2 1 2

n h

h

RkT hS f

kTf

= =

+

7?%$'#& @9A;B Bolt'm$s *ostt

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#HAT$S THERMAL NOISE %


-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1

x 1012

1

1.1

1.2

1.3

1.4

1.5

1.6

1.7

1.8

1.9

2x 10

-21

frequency (Hz)

ThermalnoisePSD

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#HITE APPRO,IMATION (1) If the freuency is lo4 enouh, in *articular:

e can a**ro-imate very 4ell the a0ove mentioned PSD4ith a constant, i.e.:

The 4hiteF a**ro-imation of the PSD is -ull. &eso/lein most cases of technical interest it is very difficult tothin3 a0out communication systems 4hose *ass0and is of

the order of T9A;.


1 @ 2902

kTf THz T K

h

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#HITE APPRO,IMATION (2) Thermal noise can 0e assumed to 0e 0uss"

dst&/uted 0y invo3in the Central Limit Theorem+

Thermal noise is 'e&o"me+

Thermal noise sam*les are u*o&&elted 0y the 4ayconsiderin the 4hiteF assum*tion;+

THEREFORE:!G/ modelin is deute for thermalnoise. e can use it, e-*loitin all its intrinsic advantaes H

The *ro0lem is to find a *arameteriAation of this model thatsoundsF ood from an enineerin vie4*oint+

The idea is to *arameteriAe the !G/ model of thermalnoise as a function of the tem3e&tu&e.


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E4UI5ALENT MOEL FORAMPLIFIER THERMAL NOISE

#HY AMPLIFIERS ARE INTERESTIN0 FROM A

6NOISE7 5IE#POINT % It is 3no4n that the 0iestF and most e-*ensive;

com*onents of a communication system are am*lifiers+

Po4er am*lifiers and lo4'noise am*lifiers are made 0ysaladsF of electronic com*onents semiconductors, ca*acities,resistors, etc.;+

It is easy to understand that am*lifiers are &ele8t t9e&mlose sou&*es+

or this reason, 4e ta3e a *articular attention to thesecom*onents. or this reason, 4e 4ill sho4 a s*ecific model fornoisy am*lifiers, 0ased on tem*erature.


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E4UI5ALENT NOISE TEMPERATURE The eu8let ose tem3e&tu&e of a eneric

0andlimited !G/ source is defined as follo4s:

It is actually the t9e&mod.m* tem3e&tu&e of aresistor *rovidin the same thermal noise *o4er of theconsidered source.

eq nP kB k = =

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%%


NOISELESS AMPLIFIER MOEL In the follo4in, a noiseless am*lifier model is sho4n.

It is characteriAed 0y an in*ut resistance ri, an out*ut

resistance roand a transfer function 9:f;freuency'selective ain;


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A5AILABLE PO#ER AT THE OUTPUT OFTHE NOISELESS AMPLIFIER

The 8l/le 3oe&; at the out*ut of thenoiseless am*lifier model is iven as follo4s:

?; 4e are considerin here the hy*othesis of im*edancematchin JL=ro; that allo4s the o*timal *o4er transfer.

( ) ( ) ( ) ( )

( )

2 2 222

2

4 4 4

io io s

o o o s i

H f V H fV f rP f V f

r r r R r

= = =

+


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A5AILABLE PO#ER 0AIN e define the availa0le *o4er ain of the

am*lifier as follo4s:

e are considerin the im*edancematchin condition also for the in*ut Js=ri.

( ) ( )

( )

( )

( )

( ) 22

2

io o s SA

S S o s i o

H f rP f V f R Rg f

P f V f r R r r

= = =

+


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PO#ER SPECTRAL ENSITY AT THEOUTPUT OF A NOISELESS AMPLIFIER

LetKs su**ose that the in*ut sinal to the am*lifier is a4hite Gaussian noise *rocess 4ith euivalent noisetem*erature eual to s+

The e-*ression of the PSD of the coloredF noise at theout*ut of the noisless am*lifier is the follo4in one:

( )( ) ( ) ( ) ( )o A S A snoiselessf g f f g f k = =


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PO#ER SPECTRAL ENSITY AT THEOUTPUT OF A NOISY AMPLIFIER

!s *reviously mentioned, am*lifiers are the mostrelevant thermal noise sources of a communicationsystem+

Therefore, am*lifiers dd t9e&ml ose that isinternally enerated. Therefore:


( )( ) ( ) int ( )o A snoisyf g f k f = +

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A5AILABLE PO#ER AT THE OUTPUT OF A NOISYAMPLIFIER (1)

The 8l/le ose 3oe& at the out*ut of the noisy am*lifier isiven 0y the follo4in e-*ression:

Usually am*lifiers are characteriAed 0y t4o *arameters: the

m

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A5AILABLE PO#ER AT THE OUTPUT OF ANOISY AMPLIFIER (2)

Therefore, 4e can 4rite:

/o4 4e can define the e--e*t8e ose tem3e&tu&e

of the am*lifier as:

( ) ( )int0 0

o o s N N f df k gB f df

+ +

= = +

( )+

=

0

int

1 dff

gkBNe


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%8


AITI5E MOEL FOR NOISY AMPLIFIERS inally 4e can 4rite:

e can derive a 8e&. use-ul ddt8e model of the noisyam*lifier see fiure 0elo4;, 4here the internal noise is 0rouht

at the in*utF of the device. This 4ill ma3e easier the com*utationof sinal to'noise ratios.

( ) ( )0

o o s N N e s e N N f df k gB gkB gk B

+

= = + = +


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SI0NAL"TO"NOISE RATIO AT THE OUTPUT OF ANOISY AMPLIFIER (1) LetKs consider the system de*icted in the fiure 0elo4:

The 8l/le s=l sou&*e 3oe& is Ss+

LetKs su**ose that the sinal is 0and'limited and its J0and4idth is eual to a fraction of 6/.


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SI0NAL"TO"NOISE RATIO AT THE OUTPUTOF A NOISY AMPLIFIER (2)

Considerin the euivalent model of a noisy am*lifier,

4e can 4rite that:

e can conventionally define also the sinal'to'noiseratio t t9e 3ut of the am*lifier as:

( ) ( )S s s

O o s e N s e N

gS gS S S

N N gk B k B

= = =

+ +

Ns

s

S Bk

S

N

S

=


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SI0NAL"TO"NOISE RATIO AT THE OUTPUT OF ANOISY AMPLIFIER (>)

/o4 4e can e-*loit the *revious euation in order toderive an e-*ression of the sinal'to'noise ratio at the

out*ut of the am*lifier as a function of the sinal'to'noiseratio at the in*ut of the am*lifier, i.e.:

( ) ( ) SseNsses

O N

S

Bk

S

N

S

+

=

+

=

1

1

1

NoteO S

S S

N N

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THERMAL NOISE PARAMETERI!ATIONIN TELECOMMUNICATION SYSTEMS


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NOISE FI0URE

EFINITION OF NOISE FI0URE The ose -=u&e of an am*lifier is defined in the follo4in

4ay:

Given the *revious euations, 4e can derive a formulation of thenoise fiure de*endin on the euivalent noise tem*erature:

0

1@ 290

sO S

S SK

N F N

= = =

0

1 eF

= +


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#(

NOISE FI0URE

#HAT OES FREPRESENT % e can note from the *revious euation that:

Therefore a noisy am*lifier is characteriAed 0y a noise fiure% enerally e-*ressed in d6;. This means that it is

hotterF from a noise vie4*oint; than the surroundinenvironment+

! lo"ose m3l-e& has a noise tem*erature lo4er thanenvironmental tem*erature. This means that it is colderF thanthe surroundin environment. Therefore: %#.

( ) 01 = Fe


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#2

NOISE FI0URE

NOISE AN 0AIN PARAMETERS OFAMPLIFIERS


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NOISE PARAMETERS COMPUTATION:SOME CASES OF INTEREST

CASE 1: CASCAE OF AMPLIFIERS LetKs consider the cascade of t4o am*lifier staes. 6oth staes

are noisy+

LetKs su**ose that 0oth staes are linear and time'invariant

LTI;+ Moreover, letKs su**ose that the 0and*ass of the second stae

falls 4ithin the 0and*ass of the first stae 6#6%;.


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CASE 1: CASCAE OF AMPLIFIERS (2)

Under this hy*othesis 4e can say that the 0and*ass of thecascade 6/ is eual to 6#+

The availa0le noise *o4er at the out*ut of the t4o staes can0e e-*ressed 0y the sum of three terms:

( ) NNNsO BkgBkggBkggN 2211221 ++=

Nose t t9e =&ess o-t9e *s*de (m3l-ed

/. /ot9 st=es)

Nose te&ll.=ee&ted /. t9e 1?

st=e m3l-ed /. t9ese*od st=e

Nose te&ll.=ee&ted /.t9e 2? st=e


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#8


CASE 1: CASCAE OF AMPLIFIERS (>) If 4e define as the total ain of the cascade, 4e can e-*ress the

*o4er availa0le at the out*ut of the cascade as follo4s:

Therefore, t9e eu8let ose tem3e&tu&e of the cascade

can 0e iven as follo4s:

NsO Bg

gkN

++=

1

21

1

21

ge

+=


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#7


CASE 1: CASCAE OF AMPLIFIERS (@) The total noise fiure of the cascade is iven 0y:

e can iterate this formula for the eneric case of /am*lifiers*ut in cascade. e o0tain the so'called F&s$s -o&mul:

1 2 21

0 1 0 1

11

FF F

g g

= + + = +

12121

3

1

21

...

1...

11

++

+

+=

N

N

ggg

F

gg

F

g

FFF


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CASE 2: RECEI5ER (1) Let us consider no4 *om3lete &e*e8e& s*9eme consistin of

t4o staes: a first J stae, namely: 3&ede*to ut and asecond 0ase0and stae, namely dete*to&:

The first stae usually contains an am*lifier characteriAed 0y 9=9= d 9=9 ose -=u&e. Considerin the riisKs formula 4ecan say that:

21 1 1

1

1ric ric ric

FF F F F

g

= +


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CASE 2: RECEI5ER (2) Under this hy*othesis, the m os. st=e of the

system is the J *redetection unit+

The detector *ut in cascade *erforms some nonlinear

demodulation tas3s analo or diital; on the0ase0and am*lified sinal+

Therefore, 4e can reasona0ly su**ose that thedetector *ot s=-*tl. dd ose to the

system+ Moreover, /e= t t9e &=9t 3&t o- t9e *s*de,

its noise contri0ution is reduced 0y the am*lifier ain.


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CASE 2: RECEI5ER (>) /o4, 4e can com*ute the 3&e"dete*to s=l"to"

ose &to that is 0y definition;:

( ) R TRS N S B=

( ) NeR kk =+=

S.stem osetem3e&tu&e

( )( )

RR

R e T

SS N

k B =

+


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&&

CASE >: CABLE REPEATER SYSTEMS (1)

In a C!T) net4or3, the sinal transmitted throuh the ca0le isstronly attenuated 4ith distance. or this reason, it ismandatory to *ut some am*lifiers throuh the line+

The most efficient solution is to em*loy &e3ete& m3l-e&s

that e-actly com*ensate the ca0le attenuation in the considerednet4or3 sement see fiure 0elo4;:



( )1 1cr c r g L g= =

N:t; % # & m ":t;

( )0

TX

c c T

SS

N k L B

=

0

1 1cc c cF L L

= + = +

1 1( 1)

(1/ )

r rcr c c c c r c r

c c

F FF F L L L F L F

g L

= + = + = +

1cL >> 1rF >

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CASE >: CABLE REPEATER SYSTEMS (2) The o8e&ll ose -=u&e for the mcascaded

sections can 0e com*uted as follo4s:

If straihtfor4ardly follo4s the eu8let osetem3e&tu&e of the cascade:

( ) ( )2 1

1 1 1 ( 1)cr cr cr cr cr cr mcr cr cr

F F FF F mF m mF g g g

= + + + + = +

00)1( cre mFF =


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&2


CASE >: CABLE REPEATER SYSTEMS (>) e can reasona0ly *resume that the noise tem*erature at the

transmitter 4ill 0e small com*ared to the euivalent noisetem*erature of the entire cascaded system+

Under these conditions, the *redetection sinal'to'noise ratio can0e com*uted as follo4s:

( ) 10

1

=

N

S

mBkFm

S

Bk

S

N

S

Tcr

T

Te

T

R


( )1 0

T

cr T

SS

N kF B

=

Sinal'to'noise ratio at theout*ut of the first re*eater

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MAN"MAE NOISE ANINTERFERENCE


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MAN"MAE NOISE SOURCES

INTROUCTION Thermal noise is not the only distur0ance added to a sinaltransmitted onto a real channel+

Thermal noise is rearded as the natural or internal noise of atelecommunication system+

It is naturally in o**osition to the man'made noise+

Man'made noise is enerated 0y a variety of emissions fromelectrical dischares and other source, i.e.: /oise from electrical machinery+

/oise from s*ar3 inition in *etrol enines+ S4itchin transients+

Dischare lihtin, etc.


5.J. 9erman, Electromanetic !m0ients and Man'Made /oiseF, in: Multi')olume EMCEncyclo*edia Series, %7>7.

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MAN"MAE NOISE FEATURES (tmedom)

Im3uls18eo1seA

*9&*te&1'ed/. m.outl.e&s (ot0uss1)

(8 M9A vehicular

man'made noise


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MAN"MAE NOISE FEATURES(-&eue*. dom)

T9e s3e*t&um 1s

-&e2ue*."sele*t18e (ot#91te o1se)

/oise enerated 0ya hih'voltae

electric line


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MAN"MAE NOISE MOELIN0

MOEL OF A SIN0LE"NOISE IMPULSE! reasona0le model for a sinle noise im*ulse

is the follo4in:


0( ) ( ) ( )z t p t t u t=

Pulse function offinite duration

/oise'li3e 4aveform

!. Shu3la, easi0ility study of measurement of man'made noiseF, DEJ! re*ort, London U;:March #$$% htt* availa0le;.

f

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MOEL OF A TRAIN OF NOISE PULSES Man'made noise may not com*rise a sinle

im*ulse 0ut a train of *ulses e.. inress'

noise in ca0le lines;+ The corres*ondin model is iven as follo4s:


( ) ( ) ( )n nnz t p t u t=

4here:( ) n

n n

n

t tp t a p

=

Pulse duration

T l i ti S tU i it f T t

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SIN0LE NOISE IMPLUSE (E,AMPLE)


a; The envelo*e is a0uss 3ulse+

0; The noise 4aveform is aseuence of randomnum0er u-o&ml.dst&/uted in O'%,%.

T l i ti S tU i it f T t

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TRAIN OF NOISE PULSES (E,AMPLE)


a; e have 0uss 3ulses4ith different am*litudesand durations+

0; The noise 4aveform is aseuence of randomnum0er u-o&ml.dst&/uted in O'%,%+

c; 9ere, 4e have a 3e&od*emission of noise *ulses. Inmany cases, the emissions ot 3e&od*.


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((

CO"CHANNEL AN AACENTCHANNEL INTERFERENCE

CO"CHANNEL INTERFERENCE (CCI) It is 3no4n also as *&osstl++

It is an interference due to telecommunication sinalssmulteousl. transmitted t t9e sme-&eue*. of the 4anted sinal+

This ty*oloy of interference can 0e encountered onthe tele39oe les /ENT, ENT; and *ellul&

eto&+s ty*ically in GSM;+ Co'channel interference is dest&u*t8e. It must 0e

controlled in order to save system *erformances.

yy


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E,AMPLES OF CCI Tele*hone lines Cellular /et4or3s

yy

Cells mar3ed 4ith the same letter transmitat the same freuency :freuency reuse;

Physically ad1acent co**er *airs interfereone 4ith another

1

s

N

I

i

PC

IP

=

=

C&&1e& to1te&-e&e*e

&t1o


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(


AACENT CHANNEL INTERFERENCE(ACI)

The ad1acent channel interference arises 4hen asinal is transmitted at a freuency very close to theone of the 4anted sinal+

!CI is ty*ical of DM! systems. It can 0e reduced 0yusin front'end filters 4ith selective 0and*ass

characteristics and adeuate uard'0ands+ The effects of !CI can 0e uite nasty es*ecially in

lo= FM &do and T5 /&od*st.


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(>


AACENT CHANNEL INTERFERENCE(ACI): PARAMETERI!ATION

( )10 1 2log 20.3

ACIK f f BI

=

= filter slo*e factor d6@dec;

6= sinal 0and4idth 4anted;

S. Ta00ane, 9and0oo3 of Mo0ile Jadio /et4or3sF,!rtech'9ouse: #$$$.


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PHASE NOISE

#HAT PHASE NOISE IS % Phase noise is a sto*9st* 3e&tu&/to of the

freuency of an analo or diital oscillator+

Phase noise is involved 0y the *resence ofm3e&-e*tos d ose in the oscillator circuit+

!ctually, *hase noise is oe o- t9e most &ele8td&-ts in hih'freuency analo J circuitry for

telecommunication a**lications+ Phase noise im*act on system *erformance is often

critical. It must 0e reduced.


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PHASE NOISE

PHASE NOISE MOELIN0 Phase noise is modeled as follo4s:

n:t;is a SS Gaussian random *rocess 4hose*o4er s*ectral density is iven 0y:

( )( ) cos ( )c c nc t A t t = + +

( ) 2 2cS f f f

is a *ostt usually re*orted in data'sheets e-*ressed in d6carrier@9A;

:LaurentKs a**ro-imation;


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PHASE NOISE

PHASE NOISE SPECTRAL ANALYSIS

Phase'noiseeffect on

the carrier

ro4

Rel os*llto&out3utmeasured 0y as*ectrumanalyAer;

.S. undert, Introduction to J Simulation and Its !**lication, IEEE 5ournal of Solid'StateCircuits, )ol. &(, /o.7, **. %#78'%&%7, Se*t. %777.


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2%

PHASE NOISE

PHASE NOISE PO#ER SPECTRAL ENSITYPhase Noise Mask for 92.6 GHz solid state Oscillator

-140

-130

-120

-110

-100

-90

-80

-70

-60

-50

-40

1.E+03 1.E+04 1.E+05 1.E+06 1.E+07 1.E+08

Freq. [Hz]


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2#

PHASE NOISE

PHASE NOISE REALI!ATION


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2&

PHASE NOISE

PHASE NOISE EFFECTS (1)

Phase noise im*acts on the most critical tas3 in coherentdemodulation, i.e.: carrier recovery+

Carrier recovery is *erformed 0y a circuit called P9se"Lo*+ed"Loo3 PLL;+

In the *resence of *hase noise a eneric PLL converes 4ith aresidual 39se d&-t iven 0y:

( )

2

2

T

L

B

BS f d f =

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2(

PHASE NOISE

PHASE NOISE EFFECTS (2)

It is 4orth notin that the *hase drift due to *hase noise isadded to the *hase drift due to the !G/ noise+

It is easy to understand that *hase noise can 0e lmostlet9l in diital communications+

In fact, a &ele8t &esdul 39se d&-t e.. #$B; involvesa rotation of the constellation that may render demodulationim*ossi0le+

! small *hase drift e.. %$B; * s=-*tl. *&ese the0it'error'rate u* to t4o orders of manitude;+

or this reason, oscillator 4ith &edu*ed 39se ose arealmost advisa0le. Unfortunately, they are uite e-*ensive.


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PHASE NOISE

PHASE NOISE EFFECTS (>)

Some 6EJ curves, as e-am*le:

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