ELEC 350 Communications Theory and Systems: Iagullive/noise.pdf · 2007. 11. 30. · ELEC 350 Fall...

ELEC 350Communications Theory and

Systems: I

Effects of Noise on Communication Systems

ELEC 350 Fall 2007 1

Noise in Analog Systems

• Most analog continuous-wave systems are bandpass -> suffer from bandpass noise

• Design the BP filter just wide enough to pass u(t) without distortion

– Minimize the noise power input to the demodulator

• Figure of Merit – SNR at demodulator output

• Reference – baseband SNR


Reference SNR

• Carrier to noise ratio

• Baseband signal to noise ratio

• received power


0b

RPS

N N W

2

02

cAC

N N

RP

DSB-SC Demodulation

6ELEC 350 Fall 2007

SSB Modulation

7ELEC 350 Fall 2007

Envelope Detection

8ELEC 350 Fall 2007

AM Signal to Noise Ratio (SNR)

9ELEC 350 Fall 2007

2

0 0

2

0 0

2 22 2 2

2

0 0

2 2

2 2

0

2

/ 2 1

2 1

1 1

o

o

nn n

o n

n n

n n

o c m

oDSB bn

o c m

oSSB n

c mc m mo

oAM n m

m m

b bm m

R

R

R

PP A PS S

N P N W N W N

PP A PS

N P N W N W

A a PA a P a PPS

N P N W a P N W

Pa P a P S S

a P N W a P N N

Comparison• Coherent detection of SSB performs the same as

coherent detection of DSB-SC, but half the BW

• SSB and DSB-SC have no SNR degradation compared to the baseband SNR

• The only effect is to translate the message signal to a bandpass channel

• The noise performance of Conventional AM is inferior due to the power in the carrier

• No tradeoff between noise performance and bandwidth

ELEC 350 Fall 2007 10

Example 5.1.1

• m(t) has bandwidth 10 KHz, power 16W and amplitude 6

• Channel attenuation 80 dB

• AWGN with PSD

• Required SNR at least 50 dB

• Determine the required transmitter power and channel bandwidth with

1. DSB AM

2. SSB AM

3. Conventional AM with modulation index a = 0.8

ELEC 350 Fall 2007 11

-120 = N /2 = 10 W/HzXS f

Meeting with term 3B students - class of 2009

Time: November 20, 2007 (Tuesday) 6:00 PM – 7:30 PM

Place: University Club, Fireside Lounge

Selection of Specializations & Electives in CE, EE, and BSENG Programs

12ELEC 350 Fall 2007

Carrier Acquisition

• Signals with a suppressed carrier (SC) such as DSB-SC AM require synchronous detection.– require a local carrier to be generated at the receiver.

• However, this carrier cannot be generated by itself locally because it must be phase synchronous with the transmitted signal.

• Therefore the local carrier must somehow be acquired from the incoming modulated signal.

• A Phase Locked Loop (PLL) can be used for this purpose.

ELEC 350 Fall 2007 13

DSB-SC Carrier-Phase Estimation

• If an incoming sinusoid is noisy a PLL can be used to clean it up. This occurs because the PLL LPF is narrow-band and the VCO gives the average frequency.

• The coherent reference for product detection of DSB-SC cannot be obtained using an ordinary phase-locked loop because there are no spectral components at

• The Squaring Loop and the Costas Loop exploit the fact that the DSB-SC signal is symmetric about the carrier frequency

ELEC 350 Fall 2007 14

cf

cf

Carrier Phase Estimation


Phase-Locked Loop (PLL)


PLL Model


Linear Model of a PLL


ELEC 350 Fall 2007 19

Linearized PLL Model with AWGN


Effect of Additive Noise onPLL Performance

• Loop filter input

• Normalized noise term

• Variance of the VCO output phase

• Loop SNR

ELEC 350 Fall 2007 21

( ) sin ( )sin ( )cosc c se t A x t x t

1

( )sin ( )cos( ) c s

c c

x t x tn t

A A

02

ˆ 2

neq

c

N B

A

2

2

ˆ 0

1 cL

neq

A

N B

ELEC 350 Fall 2007 22

ELEC 350 Fall 2007 23

Squaring Loss

• The squaring loop output is

• Both noise terms contain spectral power in the frequency band centered at

• Variance of the VCO output phase

• is the squaring loss

ELEC 350 Fall 2007 24

2 2( ) ( ) 2 ( ) ( ) ( )y t u t u t n t n t

22 ( ) ( ) ( )u t n t n t

2 cf

2

ˆ

1

L LS

LS 1

/ 21

Lbp neq

L

SB B

ELEC 350 Fall 2007 25

Assignment 5 Due Nov. 30, 2007

• P&S 5.3

• P&S 5.4

• P&S 5.5

• P&S 5.8

• P&S 5.10

• P&S 5.11

ELEC 350 Fall 2007 26

ELEC 350 Fall 2007 27

Angle Modulation

• The modulated signal

ELEC 350 Fall 2007 28

))(2cos()(

FMdmktfA

PMtmktfAt

fcc

pcc

))(22cos(

))(2cos(

ELEC 350 Fall 2007 29

ELEC 350 Fall 2007 30

Angle Demodulator Output

• The output of the demodulator is

• where is defined as

ELEC 350 Fall 2007 31

( ) ( ) PM

( ) 1( ) ( ) FM

2

p n

f n

k m t Y t

y t dk m t Y t

dt

( )nY t

( )( ) sin( ( ) ( ))nn n

c

V tY t t t

A

Noise Component• The noise component can be written as

• are the in-phase and quadraturecomponents of the bandpass noise

• are independent, lowpass, Gaussian noise processes

ELEC 350 Fall 2007 32

( )nY t

1

( ) ( )cos ( ) ( )sin ( )n s cc

Y t n t t n t tA

( ) ( )s cn t and n t

( ) ( )s cn t and n t

2 2

2

2 2

2 2

1( ) ( )cos ( )sin

1 1( ) cos sin ( )

n s c

c c

Y n n

c

n n

c c

R R RA

R RA A

Noise PSD

Taking the Fourier transform of gives

where

so

ELEC 350 Fall 2007 33

2

( )( ) c

n

n

Y

c

S fS f

A

( )nY

R

0 / 2( )

0 otherwisecc

n

N f BS f

0

2/ 2

( )

0 otherwisen

c

cY

Nf B

AS f

Angle Modulation Noise PSD


0

0

0

2

20

2

0

2

3

0

2

PM

( )

FM

2PM

2FM

3

c

n

c

c

n

c

N

AS f

Nf

A

WN

AP

W N

A

Noise PSD for PM and FM


FM Signal to Noise Ratio (SNR)

• Output signal power

ELEC 350 Fall 2007 36

0

0

2

2

PMmax m(t)

3 FMmax m(t)

p MR

f MR

o

PP

N WS

NP

PN W

0

2

2

PM

FM

p M

s

f M

k PP

k P

FM Signal to Noise Ratio (SNR)


2

2

2

2

PMN

3 FMN

12 PM

max m(t)

123 FM

max m(t)

n

n

p M

b

f M

b

M

M

b

b

o

o

SP

S

N SP

SP

N

S

N

SP

N

Observations• The output SNR is proportional to the square of the

modulation index• Angle modulation allows a tradeoff between SNR and

bandwidth• The relationship between the output SNR and the

bandwidth expansion factor is quadratic• Increasing too much results in the threshold effect

where the signal is lost in noise• Compared with AM, increasing the transmitted power

increases the output SNR – but the mechanisms differ• In FM, noise affects higher frequencies more than

lower frequencies

ELEC 350 Fall 2007 38

Threshold Effect• The noise analysis of angle modulation

assumes that the SNR at the demodulator input is high

• In this case, the noise can be approximated as additive

• At low SNRs, the signal and noise at the demodulator output are mixed and the signal cannot be distinguished from the noise

• The SNR below which signal mutilation occurs is called the threshold SNR

ELEC 350 Fall 2007 39

Threshold Effect in FM• At threshold

• Carson’s rule

• Assume

• then

ELEC 350 Fall 2007 40

,

20( 1)fb th

S

N

2( 1)c fB W

2

1

(max | ( ) |) 2nM

M

PP

m t

23

2f

o b

S S

N N

ELEC 350 Fall 2007 41

Threshold Reduction

• Threshold reduction in FM receivers may be achieved by

– Negative feedback (commonly referred to as an FMFB demodulator), or

– A phase-locked loop demodulator

• FMFB can improve the threshold by 4-8 dB

• PLL improvements of 4-8 dB have also been reported

ELEC 350 Fall 2007 42

Threshold Reduction


FMFB Demodulator


ELEC 350 Fall 2007 46

PLL Demodulator


Noise in Angle Modulation

• The noise PSD at the demodulator output is

– flat for PM

– parabolic for FM

• FM performs better for low frequencies

• PM performs better for high frequencies

• Solution: Design a system that uses FM for low frequencies and PM for high frequencies

ELEC 350 Fall 2007 48

Noise PSD for PM and FM


Pre-emphasis and De-emphasis

• The phase of the transmitted signal is

• At high frequencies use PM

– At the transmitter, a differentiator followed by an FM modulator

– At the receiver, an FM demodulator followed by an integrator

ELEC 350 Fall 2007 50

FM)(2

PM)()( t

f

p

dmk

tmkt

Pre-emphasis and De-emphasis Filters

• In order to produce an undistorted version of the original message at the receiver output, we must have

ELEC 350 Fall 2007 51

( ) ( ) 1 for W Wp dH f H f f

• Assume and

ELEC 350 Fall 2007 52

2 1 for | |fCr f W R r

0

0

( ) 1 where 1/ 2pf

H f j f Crf

0

1( )

1dH f f

jf

ELEC 350 Fall 2007 53

Pre-emphasis and De-emphasis Filters

• Pre-emphasis filter

– low-pass filter

• De-emphasis filter

– high-pass filter

• Noise PSD

ELEC 350 Fall 2007 54

0

1 1( )

( )1

d

p

H ffH f

jf

2 20

22

2

0

1( ) ( ) | ( ) |

1PD on n d

c

NS f S f H f f

fA

f

0

( ) 1pf

H f jf

Noise PSD and SNR Gain

• The noise power at the demodulator output

• The ratio of output SNRs is

ELEC 350 Fall 2007 55

3

0

0 0

3 arctan

oPD

D

no

n

o

S W

PN f

S P W W

N f f

3

0 0

2

0 0

2( ) arctan

PD PD

W

n nW

c

N f W WP S f df

A f f

Example – Broadcast FM

• W = 15KHz = 2100 Hz = 5 = ½

• Find the improvement in output SNR with pre-emphasis and de-emphasis

ELEC 350 Fall 2007 56

0f f nMP

2 233 37.5N 2 N Nn

f M f

b b bo

S S S SP

N

15.7 dBN bo

S S

N

Example (Cont.)


3

0

0 0

3 arctan

1 364.4321.27

3 5.711

PDo o

o o

W

fS S

N NW W

f f

S S

N N

13.28 dB

= 13.28+15.74 + dB

PDo o

b

S S

N N

S

N

CFUV-FM Radio


Dolby-B Noise Reduction

ELEC 350 Fall 2007 59

Comparison of Analog Modulation

• Linear modulation

– DSB-SC

– SSB-SC

– VSB

– Conventional AM

• Nonlinear modulation

– PM

– FM

ELEC 350 Fall 2007 60

Comparison Criteria

• Bandwidth efficiency

• Power efficiency

– SNR at demodulator output

• Simplicity of the transmitter and receiver implementation

– Receiver complexity is most important

ELEC 350 Fall 2007 61

Bandwidth Efficiency

• SSB-SC is best

• VSB

• DSB-SC and Conventional AM

• FM is worst – using Carson’s rule:

ELEC 350 Fall 2007 62

cB W

cW B 2W

cB 2W

c2 B 6Wf

c5 B 12Wf

Power Efficiency

• Output SNR for a given received signal power

• Angle modulation and in particular FM provides the highest SNR gain

• Conventional AM and VSB+carrier are worst

ELEC 350 Fall 2007 63

Implementation Complexity

• Conventional AM and VSB+C demodulators have extremely simple receiver structures

– envelope detector

• FM also has a simple structure

– discriminator + AM demodulator

• To obtain better FM performance use a PLL

• SSB-SC and DSB-SC require coherent detectors (Squaring Loop or a Costas Loop)

ELEC 350 Fall 2007 64

Final Comments

• SSB modulation provides optimum noise performance and bandwidth efficiency with amplitude modulation

• Conventional AM provides the simplest receiver structure making it the most common wireless communication technique

• FM improves the noise performance at the expense of increased transmission bandwidth

ELEC 350 Fall 2007 65

Noise in Communication Systems

• Two major factors that limit performance

– signal attenuation

– noise

• The first has already been considered in detail in the discussion of link budgets

ELEC 350 Fall 2007 66

Channel Model

ELEC 350 Fall 2007 67

Link Received Power

• P0 = PtGtGr/L0– Pt is the transmit power in watts

– Gt is the transmit antenna gain

– Gr is the receive antenna gain

– L0 is the path loss between points A and B

• Taking log10 of both sidesP0 = Pt + Gt + Gr – L0 (dB)

• The attenuation is = Gt + Gr – L0 (dB)


Receiver Sensitivity

• Pn = K(S/N)WF

– K = Watts/Hz

– S/N is the required output signal-to-noise ratio

– W is the bandwidth

– F is the noise figure

• Pn = S/N + W + F - 204 (dB)

• The link will work as long as

M = P0 - Pn > 0 dB

69

20.410

ELEC 350 Fall 2007

Noisy Resistor Connected to a Load


Amplified Noise


Output SNR

The noise figure is defined as

ELEC 350 Fall 2007 72

0 (1 / )

1

1 /

si

o neq e

i e

PS

N N B T T

S

N T T

0

1 eT

FT

0

1 si

o i neq

PS S

N F N FN B

Link Budget• The required signal power is Pn = Psi

• Therefore

or

in dB

ELEC 350 Fall 2007 73

0

1 n

o i neq

PS S

N F N FN B

0n neq

o

SP FN B

N

0n neq

o

SP F N B

N

ELEC 350 Communications Theory and Systems: Iagullive/noise.pdf · 2007. 11. 30. · ELEC 350 Fall...

Documents

Transcript of ELEC 350 Communications Theory and Systems: Iagullive/noise.pdf · 2007. 11. 30. · ELEC 350 Fall...