ELEC 350Communications Theory and

Systems: I

Effects of Noise on Communication Systems

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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

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Reference SNR

• Carrier to noise ratio

• Baseband signal to noise ratio

• received power

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0b

RPS

N N W

2

02

cAC

N N

RP

DSB-SC Demodulation

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SSB Modulation

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Envelope Detection

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AM Signal to Noise Ratio (SNR)

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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

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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

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-12

0 = 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

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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.

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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

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cf

cf

Carrier Phase Estimation

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Phase-Locked Loop (PLL)

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PLL Model

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Linear Model of a PLL

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Linearized PLL Model with AWGN

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Effect of Additive Noise onPLL Performance

• Loop filter input

• Normalized noise term

• Variance of the VCO output phase

• Loop SNR

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( ) 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

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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

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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

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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

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Angle Modulation

• The modulated signal

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))(2cos()(

FMdmktfA

PMtmktfAt

fcc

pcc

))(22cos(

))(2cos(

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Angle Demodulator Output

• The output of the demodulator is

• where is defined as

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( ) ( ) 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

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( )nY t

1

( ) ( )cos ( ) ( )sin ( )n s c

c

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

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2

( )( ) c

n

n

Y

c

S fS f

A

( )nY

R

0 / 2( )

0 otherwisec

c

n

N f BS f

0

2/ 2

( )

0 otherwisen

c

cY

Nf B

AS f

Angle Modulation Noise PSD

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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

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FM Signal to Noise Ratio (SNR)

• Output signal power

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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)

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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

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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

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Threshold Effect in FM• At threshold

• Carson’s rule

• Assume

• then

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,

20( 1)f

b th

S

N

2( 1)c fB W

2

1

(max | ( ) |) 2n

MM

PP

m t

23

2f

o b

S S

N N

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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

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Threshold Reduction

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FMFB Demodulator

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FMFB Demodulator

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PLL Demodulator

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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

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Noise PSD for PM and FM

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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

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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

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

• Assume and

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2 1 for | |fCr f W R r

0

0

( ) 1 where 1/ 2p

fH f j f Cr

f

0

1( )

1dH f

fjf

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Pre-emphasis and De-emphasis Filters

• Pre-emphasis filter

– low-pass filter

• De-emphasis filter

– high-pass filter

• Noise PSD

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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

( ) 1p

fH f j

f

Noise PSD and SNR Gain

• The noise power at the demodulator output

• The ratio of output SNRs is

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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

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0f f nMP

2 233 37.5

N 2 N Nnf M f

b b bo

S S S SP

N

15.7 dBN bo

S S

N

Example (Cont.)

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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

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Dolby-B Noise Reduction

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Comparison of Analog Modulation

• Linear modulation

– DSB-SC

– SSB-SC

– VSB

– Conventional AM

• Nonlinear modulation

– PM

– FM

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Comparison Criteria

• Bandwidth efficiency

• Power efficiency

– SNR at demodulator output

• Simplicity of the transmitter and receiver implementation

– Receiver complexity is most important

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Bandwidth Efficiency

• SSB-SC is best

• VSB

• DSB-SC and Conventional AM

• FM is worst – using Carson’s rule:

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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

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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)

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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

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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

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Channel Model

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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 sides

P0 = Pt + Gt + Gr – L0 (dB)

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

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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

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Noisy Resistor Connected to a Load

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Amplified Noise

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Output SNR

The noise figure is defined as

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0 (1 / )

1

1 /

si

o neq e

i e

PS

N N B T T

S

N T T

0

1 eTFT

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

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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