Ch5 Analog

7/29/2019 Ch5 Analog

1/104

NCCUWireless Comm. Lab.

Chapter 5Effect of Noise on Analog Communication

Systems


2/104

2CCU

Wireless Access Tech. Lab.

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


3/104

3CCU


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


4/104

4CCU


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.


5/104

5CCU


-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


6/104

6CCU


m(t) DSB-SCDemodulation

Nu(t)

r(t)

DSB-SCmodulation


(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

= += +

+


7/104

7CCU



(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 +


8/104

8CCU



(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

=

=

=


9/104

9CCU



(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

=


10/104

10CCU



(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

= = =

= =

= =


11/104

11CCU



(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= = +


12/104

12CCU



(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

= + =

=


13/104

13CCU



(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= +


14/104

14CCU



(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

+ = +

= = + +

=


15/104

15CCU



(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


16/104

16CCU



(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

= + +

= + + +


17/104

17CCU



(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+


18/104

18CCU



(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


19/104

19CCU



(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


20/104

20CCU



)


21/104

21CCU




22/104

22CCU




23/104

23CCU


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 =


24/104

24CCU



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


25/104

25CCU



)

)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


26/104

26CCU


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


27/104

27CCU



) 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


28/104

28CCU



)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


29/104

29CCU



)


30/104

30CCU



) 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


31/104

31CCU



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

+

= + + +


32/104

32CCU



)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


33/104

33CCU



)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

+ =

+ +


34/104

34CCU



)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


35/104

35CCU



)

)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

+ += =

+


36/104

36CCU



) 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

= + +

= +=

+ = +


37/104

37CCU



)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

=

= +


38/104

38CCU



)The equivalent model is shown as below


39/104

39CCU



)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 =


40/104

40CCU



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

+ += =

+


41/104

41CCU



)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

=


42/104

42CCU



)Note : the variance of linearmodel is close to the exactvariance for 3

L

>


43/104

43CCU




44/104

44CCU



)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


45/104

45CCU



)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


46/104

46CCU



)Costas loop


47/104

47CCU



( ) ( ) ( ) ( )

( ) ( ) ( ) ( ) ( )

( ) ( ) ( )

( ) ( ) ( )

( ) ( )

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

= +

= +

= +

+


48/104


49/104

49CCU



( )( )

( )

( ) ( ) ( ) ( ) ( ) ( )( )

( ) ( ) ( ) ( ) ( )

( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )

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

=

=

=

+

+ +

+ +


50/104

50CCU



)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.


51/104

51CCU


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


52/104

52CCU



) 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


53/104

53CCU





54/104

54CCU



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

=



55/104

55CCU



)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


56/104

56CCU



)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


57/104

57CCU



) 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



58/104

58CCU



)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

= + +

=



59/104

59CCU



) 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



60/104

60CCU



)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 =



61/104

61CCU



)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


62/104

62CCU



)A typical example ofG(f), and the result of theirconvolution is shown below.

)cn

S f



63/104

63CCU



)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 |


64/104

64CCU



)The power spectrum of the noise component at the output ofthe demodulator in the frequency interval | f |


65/104

65CCU



)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


66/104

66CCU



)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


67/104

67CCU



)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

=



68/104

68CCU


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

=



69/104

69CCU


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

=



70/104

70CCU


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

=



71/104

71CCU


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



72/104

72CCU


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



73/104

73CCU


)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


74/104

74CCU


)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 = +



75/104

75CCU


) 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 = +



76/104

76CCU


( )( )2

12max

MP

m t=

( ) ( )

23

20

S S

N N b

=

( ) ( ),

20 1SN b th = +

( ) ( )2

0 60 1S

MN P = +



77/104

77CCU


)



78/104

78CCU


5.3.1 Threshold Extension in Frequency modulation


79/104

79CCU


) 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


80/104

80CCU


)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.



81/104

81CCU




82/104

82CCU


)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

=



83/104

83CCU


)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

+

+

=

=+

=



84/104

84CCU


)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

=

=

=



85/104

85CCU


)



86/104

86CCU


5.3.4 Comparison of Analog0Modulation System


87/104

87CCU


) Linear modulation system

ADSB-SC

AConventional AM

ASSB-SC

AVSB

)Nonlinear modulation system

AFMAPM



88/104

88CCU


)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.



89/104

89 CCUWireless Access Tech. Lab.

)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.


h f i l i f


90/104


)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


91/104


( ) ( ) ( ) , 1.r t s t n t = +

Ch5 Analog

Documents

Transcript of Ch5 Analog