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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
CNU Dept. of Electronics
D. J. Kim2
Lecture on Communication Theory
- 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
CNU Dept. of Electronics
D. J. Kim3
Lecture on Communication Theory
< 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
CNU Dept. of Electronics
D. J. Kim4
Lecture on Communication Theory
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
CNU Dept. of Electronics
D. J. Kim5
Lecture on Communication Theory
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
CNU Dept. of Electronics
D. J. Kim6
Lecture on Communication Theory
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
CNU Dept. of Electronics
D. J. Kim7
Lecture on Communication Theory
t)
2
Wf(2sin)t(nt)
2
Wf(2cos)t(n)t(n CQCI π-π
CNU Dept. of Electronics
D. J. Kim8
Lecture on Communication Theory
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
CNU Dept. of Electronics
D. J. Kim9
Lecture on Communication Theory
- 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
CNU Dept. of Electronics
D. J. Kim10
Lecture on Communication Theory
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
CNU Dept. of Electronics
D. J. Kim11
Lecture on Communication Theory
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
CNU Dept. of Electronics
D. J. Kim12
Lecture on Communication Theory
- 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
CNU Dept. of Electronics
D. J. Kim13
Lecture on Communication Theory
- 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
CNU Dept. of Electronics
D. J. Kim14
Lecture on Communication Theory
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
CNU Dept. of Electronics
D. J. Kim15
Lecture on Communication Theory
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
CNU Dept. of Electronics
D. J. Kim16
Lecture on Communication Theory
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