Chapter 5. Noise in CW Modulation System

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

Chapter 5. Noise in CW Modulation System

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Transcript of Chapter 5. Noise in CW Modulation System