CNU Dept. of Electronics D. J. Kim1 Lecture on Communication Theory Chapter 5. Noise in CW...

CNU Dept. of Electronics

D. J. Kim1

Lecture on Communication Theory

Chapter 5. Noise in CW Modulation System

5.1 Introduction - Receiver Noise (Channel Noise) :

additive, White, and Gaussian 으로 가정

5.2 Receiver Model

1. RX Model

N0 = KTe where K = Boltzmann’s constant

Te = equivalent noise Temp.

Average noise power per unit bandwidth

Sw(f)

Rw()

)(2

N 0

2

N 0

f

2

N density spectral power Gaussian, and white,additive, : )t(w - 0


D. J. Kim2


- Band Pass Filter (Ideal case)

w(t) n(t)

- filtered noise as narrow-band noise

n(t) = nI(t)cos(2fCt) - nQ(t)sin(2fCt)

where nI(t) is inphase, nQ(t) is quadrature component

- filtered signal x(t)

x(t) = s(t) + n(t)

- Average Noise Power = N0BT

BPF

outputreceiver

O

I

noise the of power average

signal message ddemodulate the of power average)SNR( -

n(t) noise filtered the of power average

s(t) signal modulated the of power average)SNR( -

2B

2B

N0

SNI, SNQ


D. J. Kim3


< DSB 와 SSB 의 Signal 과 Noise Power Spectral Density 정리 >

- DSB

- SSB

1SM(f)

f

SS(f)

2

1

41

f f

SY(f)

)ff(S)ff(S4

1)f(S )fCtm(t)cos(2s(t) -

2P

)4P

(2t)fm(t)cos(2 P)t(m

CMCMS

C

Θπ

π

2

N0

f

SS(f)

f

2

N0

(t)n2

1 m(t)

2

1

WN22

NW4 WN

2

NW2

I

00

00

4

P

2

P

2

P

4

1 t)f(t)sin(2m̂

2

1 t)fm(t)cos(2

2

1 CC

ππ

)Wtsin()t(n2

1)Wtcos()t(n

2

1)t(m

4

1

WN2

NW2 WN

2

NW2

QI

00

00

ππ

1

f

4

1

f

2

N0

f f

2

N0


D. J. Kim4


2. 변복조간의 비교1) 서로 다른 변복조 system 을 비교하기 위한 조건

- s(t) by each system has the same average power

- noise w(t) has the same average power measured in the message

BW =W

2) Channel SNR

3)

5.3 Noise in DSB-SC Receivers

1. Model of DSB-SC Receivers

inputreceiveratC BW message the in noise the of power average

signal modulated the of power average)SNR(

C

O

(SNR)

(SNR) = merit of Figure


D. J. Kim5


2. (SNR)O

NW2

PAC)SNR( -

(baseband)

NW2

N2W power noise Average-

2

PAC s(t) of power Average-

df (f)S P

power signal Average-

bandwidth message : W

(f)S : m(t) ofdensity spectral Power

factor scaling :C re whe

)t(m)tf2cos(CA)t(s -

0

2C

2

DSB,C

00

2C

2

WW- M

M

CC

∫

π

)t(n2

1)t(mCA

2

1 y(t)

)tf4sin()t(nA2

1)tf4cos()t(n)t(mCA

2

1)t(n

2

1)t(mCA

2

1

)tf2cos()t(x)t(v -

)tf2sin()t(n)tf2cos()t(n)t(m)tf2cos(CA

)t(n)t(s)t(x -

IC

CQCCICIC

C

CQCICC

∴

ππ

π

πππ


D. J. Kim6


5.4 Noise in SSB Receivers - SSB Modulated wave

1)SNR(

)SNR(

merit of Figure

NW2

PAC

2NW

4PAC)SNR( -

NW2n(t) noise filtered pass band of Power(t))Power(n

(passband) NW2

1(2W)N

4

1 power noise Average-

4

PAC power signal Average-

SCDSBC

O

0

2C

2

0

2C

2

O

0I

00

2C

2

∴

∴

0

2C

2

SSB,C

0

2C

22C

22C

2

CCCC

NW4

PAC)SNR(

(baseband) Noise) BW message( NW power noise Average-

DSB) of (half 4

PAC

2

P

4

AC

2

P

4

AC power Message -

density spectral power same the has (t)m̂ and m(t)

additive are densities spectral power their

eduncorrelat are (t)m̂ and m(t)

0E[m(t)] othogonal, are (t)m̂ and m(t)

)t(m̂)tf2sin(CA2

1)t(m)tf2cos(CA

2

1)t(s

안의

⇒

⇒

ππ


D. J. Kim7


t)

2

Wf(2sin)t(nt)

2

Wf(2cos)t(n)t(n CQCI π-π


D. J. Kim8


SC-DSB as same 1)SNR(

)SNR( merit of Figure -

NW4

PAC)SNR( -

(passband) NW4

1

2

NW

4

1

2

NW

4

1 power noise Average-

PAC16

1 power signal Average-

Wt)(sin(t)n2

1Wt)(cos(t)n

2

1m(t)CA

4

1 y(t)

output Combined -

SSBC

O

0

2C

2

SSB,O

000

2C

2

QIC

ππ

5.4 Noise in AM Receiver

t)f(t)sin(2n-t)f(t)]cos(2nm(t)kA[A

n(t) s(t) x(t)

signal Filtered -

NW2

P)k(1A (SNR)

)2

N(2W NW power noise Average-

2P)k(1A power signal Average-

t)fm(t)]cos(2k[1 A s(t)

signal AM -

CQCIaCC

0

2a

2C

AMC,

00

2a

2C

CaC

ππ

←

π


D. J. Kim9


- By envelope detector

ex1) Single-Tone Modulation

1Pk1

Pk

)SNR(

)SNR( merit of Figure -

1 k

power noise Avg power carrier Avg

NW2

PkA (SNR) -

(t)nm(t)kAA y(t)

(t)n(t),n m(t)]k1[ AAssume

(t)n(t)]nm(t)kA[A

x(t)of envelop )t(y

2a

2a

AMC

O

a

0

2a

2C

AMO,

IaCC

QIaC

2

12Q

2IaCC

≤조건

(max)3

1F.O.M 1, if

2Ak1

Ak

)SNR(

)SNR(

wheret)ft)]cos(2f2cos(1[A)t(s2

AP t)fcos(2 A )t(m

2

2

2m

2a2

1

2m

2a2

1

AMC

O

CmC

2m

mm

μ

μ

μ

Akμππμ

→π

ma


D. J. Kim10


Threshold Effect

Carrier-to-noise < 1

narrow-band noise n(t)

Threshold Effect : loss of message in an envelope detector that

operates at a low CNR.

ninformatio of loss complete

] [0,2 over ddistributeuniformly is (t) where

(t)]m(t)cos[kA(t)]cos[Ar(t)

(t)]m(t)]cos[k[1Ar(t)y(t)

(t))tfr(t)cos(2t)fm(t)]cos(2k[1 A

n(t)s(t)x(t)

phase is (t) envelope, is r(t) re whe

(t)] (t)fr(t)cos[2 n(t)

aCC

aC

CCaC

C

⇒

πψ

ψψ

ψ

ψππ

ψ

ψπ


D. J. Kim11


5.6 Noise in FM Receivers

w(t) : zero mean white Gaussian noise with psd = No/2s(t) : carrier =fc, BW = BT 즉 (fC BT/2)

- BPF : [fC - BT/2 ~ fC + BT/2]

- Amplitude limiter : remove amplitude variations

by clipping and BPF

- Discriminator slope network or differentiator : varies linearly with frequency envelope detector

- Baseband LPF : message BW 에 맞추어서 .

- FM signal

- Filtered noise n(t)

)]t(tf2cos[A)t(s

dt)t(mk2)t(

]dt)t(mk2tf2cos[A)t(s

CC

t0f

t0fCC

φπ

πφ

ππ

∫

∫

)t(n

)t(ntan)t(

))t(n())t(n(r(t)

where

)]t(tf2r(t)cos[

)tf2sin()t(n)tf2cos()t(n)t(n

I

Q1

2Q

2I

C

CQCI

ψ

ψπ

ππ


D. J. Kim12


- Discriminator output

)]t()t(sin[A

)t(rdt)t(mk2

)]t()t(sin[A

)t(r(t)(t)

r(t) AAssume

)]t()t(cos[)t(rA

)]t()t(sin[)t(rtan(t)(t) where

)]t(tf2cos[)t(r)]t(tf2cos[A

n(t)s(t) x(t)

C

t0f

C

C

C

1-

CCC

φψπ

φψφθ

φψ

φψφθ

ψπφπ

∴

∫

dt

)t(dn

πA2

1)t(n

)]}t(sin[)t(r{dt

d

πA2

1

)]}t()t(sin[)t(r{dt

d

πA2

1)t(n

where

)t(n)t(mkdt

d

2

1)t(v

Q

Cd

C

Cd

df

ψ

φψ

θ(t)

π

at discriminator output

at Rx output


D. J. Kim13


- Figure of merit of FM

where P = message power

W = message bandwidth

kf = frequency sensitivity

< 결론 > BT Noise Performance

ex) Single-tone modulation

T

f

ff

22f

FMC

O

B D

ratio deviation : W

Pk

W

fD

deviationfrequency : PkAmkf

D3W

P3k

)SNR(

)SNR(

Δ

Δ

trade off

2WSC-DSB c.f.

4W2 0.5

471.03

2

2

3

3

1 AM

index modulation : W

f e wher

2

3

W

f

2

3

W

ff3k

)SNR(

)SNR(

)tf2cos(f

f)t(m

)tf2sin(f

fdt)t(m2

)tf2sin(f

ftf2cosA)t(s

max

2

22

2212

m2f

FMC

O

mm

mm

t0f

mm

CC

ηβ

ββ

Δβ

βΔΔ

πΔ

πΔ

πk

πΔ

π

때는같을과


D. J. Kim14


5.7 Pre-emphasis and de-emphasis in FM

P.S.D. of noise at FM Rx output

P.S.D. of typical message signal

=> 모든 band 를 효과적으로 사용 못함

Commercial FM radio 에서 사용

signal

noise

otherwise 0

2f

A

fN

(f)S

output tordiscrimina the at (t)n noise of P.S.D

WfW- , )(

1)(

2

C

2

0

Nd

d

T

pe

de

B

fHfH


D. J. Kim15


Applications) FM radio, audio-tape-recording

Dolby-A, Dolby-B, DBX : filtering+dynamic range compression

df)f(Hf3

W2I

factor tImprovemen -

A3

WN2dff

A

N

noise output

of power Average

df)f(HfA

N

emphasis-de with

power noise output Average

2de

WW

2

3

2C

30W

W2

2C

0

2de

WW

22C

0

63dB~53 : emphasis-de & emphasis-pre Rx with

50dB~40 : emphasis-de & emphasis-pre Rx without

13

22I 15kHz W2.1kHz,

WtanW3

W

3

2I

fjf

1

1(f)H

f

jf1(f)H )

1

3

ff1f

3

O

de

O

pe

2O

2

FM

FM

dB

f

ff

f

df

W

ex

O

OO

OWW


D. J. Kim16


5.8 Summary and Discussion

13dBI IV & III

5 FM, IV.

(SNR)23

(SNR) 2 FM, III.

SNR)((SNR) SSB SC,-DSB II.

sinusoidal for (SNR)2

(SNR) AMI.

C

2

O

CO

C2

2

O

는

<H.W.> chap 5. 5.7 chap 6. 6.2, 6.7, 6.15, 6.17

CNU Dept. of Electronics D. J. Kim1 Lecture on Communication Theory Chapter 5. Noise in CW...

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Transcript of CNU Dept. of Electronics D. J. Kim1 Lecture on Communication Theory Chapter 5. Noise in CW...