Ch5 Analog
Transcript of Ch5 Analog
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NCCUWireless Comm. Lab.
Chapter 5Effect of Noise on Analog Communication
Systems
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Outline)Chapter 5 Effect of Noise on Analog Communication Systems
A5.1 Effect of Noise on linear-Modulation Systems
5.1.1 Effect of noise on a baseband system5.1.2 Effect of noise on DSB-SC AM
5.1.3 Effect of noise on SSB AM
5.1.4 Effect of noise on conventional
A5.2 Carrier-Phase Estimation with a phase-Locked Loop (PLL)
5.2.1 The phase-locked loop (PLL)
5.2.2 Effect of additive noise on phase estimation
A5.3 Effect of noise on angle modulation5..3.1 Threshold effect in angle modulation
5.3.2 Pre-emphasis and De-emphasis filtering
A5.4 Comparison of analog-modulation systems
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OutlineA5.5 Effects of transmission losses and noise in analog
communication systems
5.5.1 Characterization of thermal noise sources
5.5.2 Effective noise temperature and noise figure
5.5.3 Transmission losses
5.5.4 Repeaters for signal transmission
A5.6 Further reading
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5 Effect of Noise on Analog Communication Systems
)The effect of noise on various analog communication systemswill be analysis in this chapter.
)Angle-modulation systems and particularly FM, can providea high degree of noise immunity, and therefore are desirablein cases of severe noise and/or low signal power.
)The noise immunity is obtained at the price of sacrificingchannel bandwidth because he bandwidth requirements ofangle-modulation systems is considerably higher thanamplitude-modulation systems.
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-W W
LPT
Nu(t) r(t)
m(t)
5.1 Effect of Noise on linear-Modulation Systems
(1) Baseband system) (1) Baseband system
( ) 02
n
NS f =
0
00
2
w
nw
NP df N W
+
= =:RP received power
0 0
R R
b N
S P PThen
N P N W
= =
baseband
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m(t) DSB-SCDemodulation
Nu(t)
r(t)
DSB-SCmodulation
5.1 Effect of Noise on linear-Modulation Systems
(2) DSB-SC AM) (2) DSB-SC AM
( ) ( ) ( )cos 2c c cu t A m t f t = +
( ) ( ) ( )( ) ( )
( ) ( ) ( ) ( )
cos 2
cos 2 sin 2
c c c
c c s c
r t u t n tA m t f t
n t f t n t f t
= += +
+
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5.1 Effect of Noise on linear-Modulation Systems
(2) DSB-SC AM)Coherent demodulation
( ) ( )
( ) ( ) ( )
( ) ( ) ( )
( ) ( ) ( )
( ) ( ) ( ) ( ) ( )
( ) ( )
( ) ( )
cos 2
cos 2 cos 2
cos 2 cos 2
sin 2 cos 21 1
cos cos( ) sin2 2
1 cos 421
cos(4 ) si2
c
c c c c
c c c
s c c
c c c s
c c c
c c s
r t f t
A m t f t f t
n t f t f t
n t f t f t
A m t n t n t
A m t f t
n t f t n t
+
= + +
+ +
+
= + +
+ + +
+ + ( )n 4 cf t +
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5.1 Effect of Noise on linear-Modulation Systems
(2) DSB-SC AM)
) If PLL is employed
)Assume
)Message power :
( ) ( ) ( ) ( ) ( ) ( )1 1
cos cos sin2 2
c c c sy t A m t n t n t = + +
coherent or synchronon demodc =
( ) ( ) ( )1 1
0 2 2c c cy t A m t n t = = = +
( )
( )
22
0
2
2
4
04
4
c
cM
cM
AP E M t
AR
AP
=
=
=
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5.1 Effect of Noise on linear-Modulation Systems
(2) DSB-SC AM
)Noise power :
Note that :
0
1
4
cn nP P=
-fc
fc
BPF
nw
(t) n(t)
c sn n nP P P= =
( ) ( ) ( ) 2
0 , -2
0,
n W
c
S f S f H f
Nf f W
otherwise
=
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5.1 Effect of Noise on linear-Modulation Systems
(2) DSB-SC AM
)
( )
0
2
2
0
0 00
2 22
0, 0
41 224
2 2
cM
c M
n
c c MR
R
DSB b
AP
S P A P
N P WNWN
A A PP E M t
S P S
N N W N
= = =
= =
= =
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5.1 Effect of Noise on linear-Modulation Systems
(3) SSB-AM) (3) SSB-AM
with ideal-phase coherent demodulator
( ) ( ) ( ) ( ) ( )cos 2 sin 2ct c c cu t A m t f t A m t f t = ( ) ( ) ( )
( ) ( ) ( ) ( ) ( ) ( )cos 2 sin 2ct c c c s c
r t u t n t
A m t n t f t Am t n t f t
= +
= + +
( ) ( ) ( ) ( ) ( )1 1cos 22 2
c c cy t LPF r t f t A m t n t= = +
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5.1 Effect of Noise on linear-Modulation Systems
(3) SSB-AM
( )
0
2
0
00
-
1
4
1 1 4 4
22
c
c M
n n n
n n
P A P
P P P
NP S f df W WN
=
= =
= = =
0
20
0, 0
c M
SSB n
S P A P
N P WN
= =
2 2
2
0,
2 2c cR M c MM
SSB b
A Abut P P P A P
S S
N N
= + =
=
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5.1 Effect of Noise on linear-Modulation Systems
(4) Conventional AM) (4) Conventional AM
for synchronous demodulation (similar to DSB, except using
instead of m(t) )
by a dc block
( ) ( ) ( )
( ) ( ) ( ) ( ) ( ) ( )
1 cos 2
1 cos 2 sin 2
c n c
c n c c s c
u t A am t f t
r t A am t n t f t n t f t
= +
= + +
( )1 nam t+ ( ) ( ) ( )
1 11
2 2c n cy t A am t n t = + +
( ) ( ) ( )1 1
2 2c n cy t A am t n t= +
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5.1 Effect of Noise on linear-Modulation Systems
(4) Conventional AM
but
0
2 2 00 0
2 22 2
0 00
1 1 1 1, 4
4 4 4 2 21
41 22
n c
nn
c M n n
c Mc M
NP A a P P p W N W
A a P A a PS
N N WN W
= = = =
= =
22
12 nc
R M
A
P a P = + 2 22
20, 0
2 2
2 20
1
1 2
1 1
nn
n
n n
n n
c MM
A M M
M MR
bM M
b b
A a Pa PS
N a P N W
a P a PP Sa P N W a P N
S S
N N
+ = +
= = + +
=
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5.1 Effect of Noise on linear-Modulation Systems
(4) Conventional AM
In practical application : 0.8 0.9
0.1NM
a
P
0, 1
0, 0, 1,
0.075 ,
. . 11 ( 11 )
AM b
dB AM dB
S S
N N
S Si e dB a lost of dB
N N
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5.1 Effect of Noise on linear-Modulation Systems
(4) Conventional AM
Envelope detector
( ) ( ) ( ){ } ( ) ( ) ( )
( ) ( ) ( ) ( )2
2
1 cos 2 sin 2
1
c n c c s c
r c n c s
r t A am t n t f t n t f t
V t A am t n t n t
= + +
= + + +
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5.1 Effect of Noise on linear-Modulation Systems
(4) Conventional AMACase 1
After removing the dc component,
The same as y(t) for the synchronous demodulation, without the coefficient
( ) ( )( )
( ) ( )( ) ( ) ( )( )( ) ( ) ( )
1 ( ) 1,
1 ( ) 1, . . 1 ( )
1 ( )
c n
s c n c n
r c n c
P n t A am t
P n t A am t i e A am t n t
V t A am t n t
+
+ +
+ +
( ) ( ) ( )( )c n cy t A am t n t= +
0, 2 0, 1
under high SNR
AM AM
S S
N N
=
( ) ( )1 ( )c nA am t n t+
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5.1 Effect of Noise on linear-Modulation Systems
(4) Conventional AMACase 2 ( ) ( )1 ( )c nA am t n t+
( ) ( )( ) ( )( ) ( )
( )( ) ( ) ( ) ( ) ( )( )
( ) ( )
( )
( ) ( ) ( )( )
( )( )
( )( )( )
( )( )
( )( )( )
( )
2 2
22 2 2
2 2
2 2
2
1
1 2 1
2
1 1
1 1
1
1
r c n c s
c n c s c c n
c c
c s nc s
c cn n
n
c cn n
n
n c
V t A am t n t n t
A am t n t n t A n t am t
A n t
n t n t am tn t n t
A n tV t am t
V t
A n tV t am t
V t
V t A am
= + + +
= + + + + +
+ + +
+
+ +
+ +
= + + ( )( ) ( )cosn nt t
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5.1 Effect of Noise on linear-Modulation Systems
(4) Conventional AMNotes: i) Signal and noise components are no longer additive.
ii) Signal component is multiple by the noise and is no
longer distinguishable.iii) no meaningful SNR can be defined.
It is said that this system is operating below the threshold==> threshold effect
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5.1 Effect of Noise on linear-Modulation Systems
)
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5.1 Effect of Noise on linear-Modulation Systems
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5.1 Effect of Noise on linear-Modulation Systems
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5.2 Carrier-Phase Estimation with a phase-Locked Loop (PLL)
)Consider DSB-SC AM
assume , zero-mean (i.e. no dc component)
the average power at the output of a narrow band filter
tuned to the carrier frequency fc is zero.
( ) ( ) ( ) ( ) ( ) ( )cos 2c c cr t u t n t A m t f t n t = + = + +
( ) 0E m t =
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5.2 Carrier-Phase Estimation with a phase-Locked Loop (PLL)
Let
There is signal power at the frequency , which canbe used to drive a PLL.
( ) ( ) ( )
( ) ( ) ( )
22 2 2
2 22 2
cos 21 1
cos 4 22 2
c c c
c c c c
r t A m t f t noise terms
A m t A m t f t noise terms
= + +
= + + +
( ) ( )2 0 0mE m t R = >
2 cf
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5.2 Carrier-Phase Estimation with a phase-Locked Loop (PLL)
)
)The mean value of the output of Bandpass filter is a sinusoidwith frequency , phase , and amplitude
.
2 cf 2 c
( )( )2 2 2
2
cc
H fA E m t
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5.2.1 The phase-locked loop (PLL) )
)
) If input to the PLL is and output of the
VCO is , represents the estimate of ,then
( )cos 4 2cf t
( )sin 4 2cf t ( ) ( ) ( )
( )
cos 4 2 sin 4 2
1 sin2
2
c ce t f t f t
=
= + ( )1 sin 2 2 22
cf t
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5.2.1 The phase-locked loop (PLL) )
) Loop filter is a lowpass filter, dc is reserved as is removed.
) It has transfer function
) n(t) provide the control voltage for VCD (see section 5.3.3).
)The VCO is basically a sinusoidal signal generation with aninstantaneous phase given by
where is a gain constant in radians/ volt-sec.
4 cf
( ) ( )2
1 21
1
1
s
G s s
+
= +
( )4 2 4t
c c vf t f t k v d
= vk
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5.2.1 The phase-locked loop (PLL) )
)The carrier-phase estimate at the output of VCO is :
and its transfer function is .
)Double-frequency terms resulting from the multiplication ofthe input signal to the loop with the output of the VCD isremoved by the loop filter
PLL can be represented by the closed-loop system modelas follows.
( )2t
vk v d
=
vks
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5.2.1 The phase-locked loop (PLL) )
)
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5.2.1 The phase-locked loop (PLL) )
) In steady-state operation, when the loop is tracking the phaseof the received carrier, is small.
)With this approximation, PLL is represented the linear modelshown below.
( )1 sin22
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5.2.1 The phase-locked loop (PLL) )
closed-loop transfer function
where the factor of has been absorbed into the gainparameter k
( )( )
( )
/
1 /
kG s sH s
kG s s
=
+
( ) 21
11sG ss
+= +
( )2
212
1
11
s
H ss s
k k
+
= + + +
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5.2.1 The phase-locked loop (PLL) )
)The closed-loop system function of the linearized PLL issecond order when the loop filter has a signal pole and signalzero.
)The parameter determines the position of zero in H(s),whileK, and control the position of the closed-loopsystem poles.
2
21
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5.2.1 The phase-locked loop (PLL) )
)The denominator ofH(s) may be expressed in the standardform
where : loop-damping factor
: natural frequency of the loop
( )2
2 2 n nD s s w s w= + +
n
w
2
1
1, 2n n
kw w
k
= = +
( )( )2 2
22
2 /
2
n n n
n n
w w k s wH s
s w s w
+ =
+ +
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5.2.1 The phase-locked loop (PLL) )
)The magnitude response as a function of thenormalized frequency is illustrated, with the dampingfactor as a parameter and .
( )20log H jw
nw w
1 1
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5.2.1 The phase-locked loop (PLL) )
)
)The one-side noise equivalent bandwidth
)Trade-off between speed of response and noise in the phaseestimate
1 a critical damped loop response
1 a under-damped loop response
1 a over-damped loop response
=
<
>
( )( )
( )2 2 2
2 2 1 2
12
1/ / 1
4 8 /n
neq
nK
K wB
w
+ += =
+
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5.2.2 Effect of additive noise on phase estimation
) PLL is tracking a signal as
which is corrupted by additive narrowband noise
, are assumed to be statistically independentstationary Gaussian noise.
( ) ( )( )cos 2c cs t A f t t = +
( ) ( ) ( ) ( ) ( )cos 2 sin 2c c s cn t n t f t n t f t =
( )cn t ( )sn t
( ) ( ) ( )( ) ( ) ( )( )
( ) ( ) ( )( ) ( ) ( )( )( ) ( ) ( )( ) ( ) ( )( )
( ) ( ) ( ) ( ) ( )
cos 2 sin 2
cos sin- sin + cos
c c s c
c c s
s c s
j t
c s c s
n t x t f t t x t f t t
where x t n t t n t tx t n t t n t t
x t jx t n t jn t e
= + +
= +=
+ = +
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5.2.2 Effect of additive noise on phase estimation
)Problem 4.29 a phase shift does not change the first twomoments of nc(t) and ns(t).
i.e. xc(t) and xs(t) have exactly the same statisticalcharacteristics asnc(t) and ns(t).
( ) ( ) ( ) ( )( ){ }
( )( ) ( ) ( )( ) ( ) ( )( ){( ) ( ) ( ) ( ) ( )( )}
( )( ) ( ) ( ) ( )
2sin 2
sin sin 4
cos cos 4
sin cos
c
c c c c c
s s c
c c s
e t LPF s t n t f t t
LPF A x t A x t f t t t
x t x t f t t t
A x t x t
= + +
= + + + + +
+ + +
= +
( )( )
( )( )
( )( )
,
sin sin cosc s
c c c
e t x t x t
A A A
=
= +
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5.2.2 Effect of additive noise on phase estimation
)The equivalent model is shown as below
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5.2.2 Effect of additive noise on phase estimation
)When the power of the incoming signal is muchlarger than the noise power, .
)Then we may linearize the PLL shown as bellow.
2
2c
c
AP =
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5.2.2 Effect of additive noise on phase estimation
is additive at the input to the loop, the variance of thephase error , which is also the variance of the VCOoutput phase is
Bneq: one-sided noise equivalent bandwidth of the loop, given by
( )( )
( )( )
( )1 sin cosc s
c c
x t x tn t
A A =
( )1n t
2 0 2
neq
c
N B
A =
( )( )
( )2 2 2
2 2 1 2
12
1/ / 1
4 8 /n
neq
nK
K wB
w
+ += =
+
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5.2.2 Effect of additive noise on phase estimation
)Note that is the power of the input sinusoid, and issimply proportional to the total noise power with thebandwidth of the PLL divided by the input signal power,
hence
where is defined as the SNR
Thus, the variance of is inversely proportional to the SNR.
2
2cA
2
2
1
L
=
L
2
0
2
2
cA
L N
neqB
=
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5.2.2 Effect of additive noise on phase estimation
)Note : the variance of linearmodel is close to the exactvariance for 3
L
>
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5.2.2 Effect of additive noise on phase estimation
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5.2.2 Effect of additive noise on phase estimation
)By computing the autocorrelation and power spectral densityof these two noise component, one can show that bothcomponents have spectral power in frequency band centered
at 2 fc.
) Lets select Bneq
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5.2.2 Effect of additive noise on phase estimation
)This approximation allows us to obtain a simple expressionfor the variance of the phase error as
whereSL is called the squaring loss and is given as
sinceSL
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5.2.2 Effect of additive noise on phase estimation
)Costas loop
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5.2.2 Effect of additive noise on phase estimation
( ) ( ) ( ) ( )
( ) ( ) ( ) ( ) ( )
( ) ( ) ( )
( ) ( ) ( )
( ) ( )
cos 2
cos 2 cos 2
sin 2 cos 2
1 cos cos2 2
1 sin double frequency terms
2
c c
c c c c c
s c c
cc
s
r t A m t f t n t
y t A m t f t n t f t
n t f t f t
A m t n
n t
= +
= +
= +
+
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5.2.2 Effect of additive noise on phase estimation
( )( )
( )
( ) ( ) ( ) ( ) ( ) ( )( )
( ) ( ) ( ) ( ) ( )
( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )
2 2
sin 24
cos sin sin4
sin cos cos4
1 cos sin sin cos4
c s
c
cc s
cc s
c s c s
e t y yA m t
A m tn t n t
A m tn t n t
n t n t n t n t
=
=
=
+
+ +
+ +
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5.2.2 Effect of additive noise on phase estimation
)These terms (signal noise and noise noise) are similar tothe two noise terms at the input of the PLL for the squaringmethod.
) In fact, if the loop filter in the Costas loop is identical to thatused in the squaring loop, the two loops are equivalent.
)Under this condition the pdf of the phase error, and the
performance of the two loops are identical.) In conclusion, the squaring PLL and the Costas PLL are two
practical methods for deriving a carrier-phase estimation for
synchronous demodulation of a DSB-SC AM signal.
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5.3 Effect of noise on angle modulation
)RX for a general angle-modulated signal
( ) ( )( )
( )( )( )( )
cos 2
cos 2 2 , FM
cos 2 , PM
c c
t
c c f
c c p
u t A f t t
A f t k m d
A f t k m t
= +
+=
+
3 ff f i l d l i
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5.3 Effect of noise on angle modulation
) Assume: signal power is much higher than noise power
i.e.
)
( ) ( ) ( ) ( ) ( ) ( )( ):bandpass Gaussian noise
cos 2 sin 2c c s cn t
r t u t n t f t n t f t = +
( ) 1n cP V t A
( ) ( ) ( )( )( )
( )
( )
2 2 1cos 2 tan
cos 2
sc s c
c
n c n
phaseEnvelope
n tn t n t n t f t
n t
V t f t t
= + +
= +
53Eff t f i l d l ti
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5.3 Effect of noise on angle modulation
53Eff t f i l d l ti
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5.3 Effect of noise on angle modulation
Note that
( ) ( ) ( )( )
( )( ) ( ) ( )( )
( ) ( ) ( )( )
( ) ( )( )
( ) ( ) ( ) ( )( )
1
cos
sin
cos 2 tan cos
cos
cos 2 sin
c n n
n n
c
c n n
c n n
nc n
c
r t A V t t
V t t t
f t t A V t t t
A V t t
V tf t t t t
A
= +
+ + +
+
+ +
( )( )
( )
PM
2 FM
p
t
f
k m tt
k m d
=
53Eff t f i l d l ti
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5.3 Effect of noise on angle modulation
)The output of the demodulator is
where
(noise component)
( )
( ) ( )
( ) ( )
( ) ( ) ( ) ( )( )
( ) ( ) ( ) ( )( )
12
12
,
,
sin , PM
sin , FM
n
c
n
c
p n
df ndt
V t
p nA
V tdf ndt A
k m t Y t PM
y t k m t Y t FM
k m t t t
k m t t t
+
= +
+ =
+
( ) ( ) ( ) ( )( )1
sinn cV t
n nA
cY t t t A
53Effect of noise on angle mod lation
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5.3 Effect of noise on angle modulation
)Noise component
)The autocorrelation function
( ) ( ) ( ) ( )( )
( ) ( )( ) ( )( ) ( ) ( )( ) ( )( )( ) ( )( ) ( ) ( )( )
1
1
sin
sin cos cos sin
cos sin
n
c
c
c
V t
n nA
n n n nA
s cA
Y t t t
V t t t V t t t
n t t n t t
=
=
=
( ) ( ) ( ) ( )( ) ( )( )
( ) ( )( ) ( )( )
( ) ( )( ) ( )
2
2
1( cos cos
sin sin
1cos
s
c
c
n n n
c
n
n
c
E Y t Y t E R t tA
R t t
R E t tA
+ = +
+ +
= +
53Effect of noise on angle modulation
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5.3 Effect of noise on angle modulation
) Assumem(t) is a sample function of a zero-mean stationary
Gaussian processM(t) with autocorrelation
then
) is a zero-mean, stationary Gaussian process
( )MR
( )( )
( )
PM
2 FM
p
t
f
k M tt
k M d
=
( )t
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5.3 Effect of noise on angle modulation
)At any fixed time t, the random variable
is the difference between two jointly Gaussian randomvariables.
) is a Gaussian R.V. with zero mean and variance
( ) ( ) ( ),Z t t t = +
( ),Z t
( ) ( ) ( )
( ) ( )
2 2 2 2
2 0
Z E t E t R
R R
= + +
=
53Effect of noise on angle modulation
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5.3 Effect of noise on angle modulation
) Autocorrelation function
( ) ( ) ( )
( ) ( ) ( )( )
( )( ) ( )( )
( ) ( )
( )
( )( ) ( )( )
212
2
c
2
c
,2
c
2
c
0
2
c
1= cosA
1= R e
A
1= R eA
1= R e
A
1= R eA
n
c
c
c
z
c
c
Y n n
n
j t
n
jZ tn
n
R R
n
R E Y t Y t
R E t
R E e
R E e
R e
R e
+
= +
+
( )( ) ( )( )0
2
c
1=
A cR R
nR e
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5.3 Effect of noise on angle modulation
)Power spectral density
where and G(f) is its Fourier transform.
( ) ( )( )
( ) ( ) ( )( )
( )
( ) ( )
( )
( ) ( )
0
2
- 0
2
- 0
2
1
c
c
c
Y Y
R R
n
c
R
n
c
R
n
c
S f F R
F R eA
e F R gA
eS f G f
A
=
=
=
=
( ) ( )Rg e =
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5.3 Effect of noise on angle modulation
)The bandwidth of is half the bandwidth Bc of the angle-modulated signal, which for high modulation indices is muchlarger than W, the message bandwidth.
)Since the bandwidth of the angle-modulated signal is defined
as the frequencies that contain 98%-99% of the signal power,G(f) is very small in the neighborhood of and
( )g
2cBf =
( ) 0 2,0,
c
c
B
nN fS f
otherwise
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5.3 Effect of noise on angle modulation
)A typical example ofG(f), and the result of theirconvolution is shown below.
)cn
S f
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5.3 Effect of noise on angle modulation
)BecauseG(f) is very small in the neighborhood of ,
the resultingSY(f) has almost a flat spectrum for , thebandwidth of the message.
i.e. for | f |
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5.3 Effect of noise on angle modulation
)The power spectrum of the noise component at the output ofthe demodulator in the frequency interval | f |
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5.3 Effect of noise on angle modulation
)PM has a flat noise spectrum and FM has a parabolic noisespectrum.
)The effect of noise in FM for higher-frequency components is
much higher than the effect of noise on low-frequencycomponents.
)The noise power at the output of the lowpass filter is the noise
power in the frequency range [ -W, +W ].
( )0 0
00
22
320 0
2 2
2
, PM, PM
2, FM , FM
3
W
n nW
W
Wcc
W
Wc c
P S f df
WNN
df AA
N W Nf df
A A
+
+
+
=
= =
5.3Effect of noise on angle modulation
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5.3 Effect of noise on angle modulation
)Output signal power
)The SNR
0
2
,
2,
PM
FM
p M
sf M
k P
P k P
=
0
0
2 2
0
2 20
20
, PM2
3 , FM2
p c M
s
n f c M
k A P
N WPS
N P k A PW N W
= =
5.3Effect of noise on angle modulation
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5.3 Effect of noise on angle modulation
)Note that is the received signal power, denote by PR.
)
)The output SNR
2
2cA
( )
( )
max , PM
max. FM
p p
f
f
k m t
k m t
W
=
=
( )( )
( )( )
2
max0
20
max0
, PW
3 , FM
p
f
MR m t
MR m t
PP
N WS
PN PN W
=
5.3 Effect of noise on angle modulation
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g
) Let
)The output SNR of a baseband system with the same receivedpower
0
R
b
S P
N N W
=
( )( )
( )( )
2
max
2
0max
, PW
3 , FM
p
f
M m tb
M m tb
SP
NS
N SPN
=
5.3 Effect of noise on angle modulation
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g
)Note that in the above expression is the average-to-peak power ratio of the message signal (or, equivalently, thepower content of normalized message, ).
)Therefore,
( )( )2
max
MP
m t
MP
2
20
, PW
3 , FM
n
n
p M
b
f M
b
SP NS
N SP
N
=
5.3 Effect of noise on angle modulation
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g
) Carsons rule
) The ration of the channel bandwidth to the message
bandwidth
) We can express the output SNR in terms of the bandwidthexpansion factor
( )2 1cB W= +
( )2 1cB
W = = +
( )( )( )( )
2
2
21
max
210
max
, PW
3 , FM
M m tb
M m tb
SP
NS
N SP
N
=
5.3 Effect of noise on angle modulation
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g
) In both PM and FM, the output SNR is proportional to thesquare of the modulation index .
ATherefore, increasing increases the output SNR even with
low received power.AThis is in contrast to amplitude modulation where such an
increase in the received SNR is not possible.
)The increase in the received SNR is obtained by increasingthe bandwidth.
ATherefore, angle modulation provides a way to trade-offbandwidth for transmitted power.
)The relation between the output SNR and the bandwidthexpansion factor, , is a quadratic relation.
AThis is far from optimal
5.3 Effect of noise on angle modulation
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g
) In fact, if we increase such that the approximation
( ) does not hold, a phenomenon known as thethreshold effect will occur, and the signal will be lost in the
noise.
) In both PM and FM the output SNR is proportional to thesquare of the modulation index . Therefore, increasing
increases the output SNR even with low received power.
( )( ) 1n cp V t A
5.3 Effect of noise on angle modulation
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)A comparison of the above result with the SNR in amplitudemodulation shows that, in both case, increasing thetransmitter power will increase the output SNR, but the
mechanisms are totally different.) In AM, any increase in the received power directly increases
the signal power at the output of the receiver.
) In angle modulation the message is in the phase of themodulated signal and, consequently, increasing thetransmitter power does not increase the demodulated messagepower. In angle modulation what increases the output SNR is
a decrease in the received noise power.
5.3.1 Threshold Effect in Angle Modulation
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)The noise analysis of angle demodulation schemes is based onthe assumption that the SNR at the demodulator input is high.
)This assumption of high SNR is a simplifying assumption that
is usually made in analysis of nonlinear-modulation systems.
)Threshold effect
AThere exists a specific signal to noise ratio at the input of the
demodulator known as the threshold SNR, beyond which signalmutilation occurs.
AThe existence of the threshold effect places an upper limit on the trade-off between bandwidth and power in an FM system.
AThis limit is a practical limit in the value of the demodulationindex .
AThreshold in an FM system
f
( ) ( ),
20 1SN b th = +
5.3.1 Threshold Effect in Angle Modulation
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) In general, there are two factors that limit the value of thedemodulation index .
AThe limitation on channel bandwidth which effects through
Carsons rule.AThe limitation on the received power that limits the value of
to less than what is derived from Equation .
( ) ( ),
20 1SN b th = +
5.3.1 Threshold Effect in Angle Modulation
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( )( )2
12max
MP
m t=
( ) ( )
23
20
S S
N N b
=
( ) ( ),
20 1SN b th = +
( ) ( )2
0 60 1S
MN P = +
5.3.1 Threshold Effect in Angle Modulation
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)
5.3.1 Threshold Effect in Angle Modulation
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5.3.1 Threshold Extension in Frequency modulation
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) In order to reduce the threshold, in other words, in order todelay the threshold effect to appear at lower-received signalpower, it is sufficient to decrease the input-noise power at the
receiver.AThis can be done by increasing the effective system bandwidth
at the receiver.
)Two approaches to FM threshold extension are to employFMFB or PLL-FM at the receiver.
) In application where power is very limited and bandwidth isabundant, these systems can be employed to make it possible
to use the available bandwidth more efficiently.)Using FMFB, the threshold can be extended approximately
by 5 - 7 dB.
5.3.2 Pre-emphasis and De-emphasis Filtering
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)The objective in pre-emphasis and de-emphasis filtering is todesign a system which behaved like an ordinary frequencymodulator demodulator pair in the low frequency band of
the message signal and like a phase modulator demodulatorpair in the high-frequency band of the message signal.
)At the demodulator , we need a filter that at low frequencieshas a constant gain and at high frequencies behaves as anintegrator.
)The demodulator filter which emphasizes high frequencies iscalled the pre-emphasis filter and the demodulator filter
which is the inverse of the modulator filter is called the de-emphasis filter.
5.3.2 Pre-emphasis and De-emphasis Filtering
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5.3.2 Pre-emphasis and De-emphasis Filtering
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)The characteristics of the pre-emphasis and de-emphasisfilters depend largely on the power-spectral density of themessage process.
) In commercial FM broadcasting of music and voice, thefrequency response of the receiver (de-emphasis) filter is
where
is the 3-dB frequency of the filter
( )0
11
d ff
H fj
=+
61
0 2 75 102100f Hz
=
5.3.2 Pre-emphasis and De-emphasis Filtering
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)The noise component after the de-emphasis filter has a powerspectral density
)The noise power at the output of the demodulator
( ) ( ) ( )0
2
20
2
202 1
1
nPD n d
fc f
S f S f H f
N fA
=
=+
( )
2
20
202
310
2
0 0
12
tan
W
nP D nP DW
W
fW
c f
c
c
P S f df
N fdf
A
N f W W
f fA
+
+
=
=+
=
5.3.2 Pre-emphasis and De-emphasis Filtering
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)The ratio of the output SNRs
( )
( )
( )
( )( )
0
30
2
30 02
0 0
0
0 0
0
0
2
3
2 1
3
1
tan
1 3 tan
c
c
SnN PD
SnPDN
N W
A
N f W Wf fA
Wf
W Wf f
P
P
=
=
=
5.3.2 Pre-emphasis and De-emphasis Filtering
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)
5.3.2 Pre-emphasis and De-emphasis Filtering
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5.3.4 Comparison of Analog0Modulation System
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) Linear modulation system
ADSB-SC
AConventional AM
ASSB-SC
AVSB
)Nonlinear modulation system
AFMAPM
5.3.4 Comparison of Analog0Modulation System
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)The bandwidth efficiency of the system
ASSB-SC > SSB > VSB > DSB-SC > DSB
APM = FM
AThe most bandwidth-efficient analog communication system isthe SSB-SC system with a transmission bandwidth equal to thesignal bandwidth.
APM and particularly FM are least-favorable systems whenbandwidth is the major concern, and their use is only justifiedby their high level of noise immunity.
5.3.4 Comparison of Analog0Modulation System
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)The power efficiency of the system
AAngle-modulation scheme and particularly FM provide a highlevel of noise immunity and, therefore, power efficiency.
AConventional AM and VSB+C are least power-efficient system.
5.3.4 Comparison of Analog0Modulation System
h f i l i f
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)The case of implementation of system
AThe simplest receiver structure is the receiver for conventionalAM, and the structure of receiver for VSB+C system is only
slightly more complicated.A FM receivers are also easy to implement.
ADSB-SC and SSB-SC require synchronous demodulation andtheir receiver structure is much more complicated.
5.5 Effects of transmission losses and noise in analogcommunication systems
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( ) ( ) ( ) , 1.r t s t n t = +