Analog Communication Systems

EC-413-F

Lecture No 4,5

Topics To be Covered

Noise in CW Modulation System

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

N0

2

N0

f

2

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

• - 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

- DSB

- SSB

1 SM(f)

f

SS(f)

2

1

4

1

f f

SY(f)

)ff(S)ff(S4

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

2

P)

4

P(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

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

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

• BW =W

• 1) Channel SNR

• 2)

•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

• 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

• 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

t)

2

Wf(2sin)t(nt)

2

Wf(2cos)t(n)t(n CQCI π-π

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

• 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(s

2

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

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

•Noise in FM Receivers

• w(t) : zero mean white Gaussian noise with psd = No/2

• s(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 :

• - 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

)]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

• Pre-emphasis and de-emphasis in FM

• P.S.D. of noise at FM Rx output

• P.S.D. of typical message signal

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