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Communication Systems

Lecture 7

Dong In Kim

School of Info/Comm Engineering

Sungkyunkwan University

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Outline

� Expression of SSB signals

� Waveform of SSB signals

� Modulators for SSB:

� Frequency discrimination

� Phase discrimination

� Coherent Detection of SSB

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Expression of SSB Signals

� The USB signal is:

� Proof:

� It is easier to prove in frequency domain.

� Shifting M(f) to get SSB:

f

M(f)

fUSB(f) fc-fc

( ) ( )[ ]tftmtftmA

tscc

c

usbππ 2sin)(ˆ2cos)(

2)( −=

( )tftmAtSccdsbπ2cos)()( =

[ ])()(2

)(ccffMffM

AfS c

++−=

� Recall the definitions of pre-envelopes or analytic signals Mp(f) and Mn(f):

� The DSB signal is:

� Its FT is:

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Expression of the SSB� � The USB signal can be written in terms of Mp(f) and Mn(f) as:

� Taking IFT,

� Next, we write mp(t) and mn(t) in terms of m(t) and :)(ˆ tm

)()sgn()()( fMffMfMp

+=

)()sgn()()( fMffMfMn

−=

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Expression of the SSB

� Similarly, LSB signal can be written as:f

M(f)

f

LSB(f) fc-fc

( ) ( )( )tftmtftmA

tscc

c

lsbππ 2sin)(ˆ2cos)(

2)( +=

� Proof: Shifting:

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Expression of the SSB

� As a summary, a unified expression of both USB and

LSB is given by

( ) ( )( )tftmtftmA

tscc

c

ssbππ 2sin)(ˆ2cos)(

2)( m=

� The minus sign gives USB.

� The plus sign gives LSB.

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Outline

� Expression of SSB signals

� Waveform of SSB signals

� Modulators for SSB:

� Frequency discrimination

� Phase discrimination

� Coherent Detection of SSB

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Waveform of SSB Signals

� Recall: DSB and AM only affects the amplitude of the carrier.

� However, SSB changes both amplitude and phase of the carrier!

� Proof:

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Example

( ) ( ) ( )tftftftm000

6cos9.04cos4.02cos)( πππ +−=

Find the SSB waveform for

Solution:

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SSB in the Time Domain

( )m t

( )m̂ t

USB

LSB)(tR

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Outline

� Expression of SSB signals

� Waveform of SSB signals

� Modulators for SSB:

� Method 1: frequency domain approach:

�Frequency discrimination

� Method 2: time domain approach:

� Phase discrimination

� Coherent Detection of SSB

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Generation of SSB by

Frequency Discrimination

� Problems:

DSB

� Method 1: Generate DSB first, then filter out unnecessary sideband:

� Filter for USB: Filter for LSB:

f

M(f)

f

f

f

or

f f

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Phase Discrimination

Modulation for SSB

� Method 2: Implement the time-domain expression:

( ) ( )( )tftmtftmA

tscc

c

ssbππ 2sin)(ˆ2cos)(

2)( m=

Only need near-ideal filter

around f=0:

Easier than ideal filter

around fc (variable)

Need to implement Hilbert transform

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Outline

� Expression of SSB signals

� Waveform of SSB signals

� Modulators for SSB:

� Frequency discrimination

� Phase discrimination

� Coherent Detection of SSB

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Coherent Detection of SSB

� SSB is similar to QAM that we studied before:

� � The coherent detection is still applicable to SSB:

� multiply with carrier, then LPF

� Assume demodulation carrier has a phase error:

)2cos(' φπ +tfAcc

)2sin()()2cos()()( 21

tftmAtftmAtsccccππ +=

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Coherent Detection of SSB

)2cos(' φπ +tfAcc

� After LPF:

== )( :0 If tyD

φ

� So phase error will cause some decoding distortions.

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Envelope Detection of SSB

Carrier reinsertion

is local carrier

From pilot tone or oscillator

ˆ( ) cos [ ( )cos( ) ( )sin( )]2

ˆ( ) cos ( )sin( )2 2

cc c c

c cc c

Ae t K t m t t m t t

A AK m t t m t t

If K large enough, e(t) ( ) cos .2

cc

AK m t t

This method is not efficient

which is a standard AM signal can use an envelope detector

DEnvelope y (t) ( ).2

cAK m t

cos cK t

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Summary of SSB� Advantage:

� More bandwidth-efficient than DSB

� Disadvantages:

� Cannot be used in signals with DC (Need near-ideal filters to avoid distortion)

� Solution: Vestigial sideband modulation (VSB)

� Send one sideband plus a small part of the other sideband

� Achieved by a filter after the DSB signal

� The filter can be designed so that the message can still be recovered by the

coherent DSB demodulator.

� Used in TV modulation.

X(f)

M(f) S(f)

cf

cf-

cf

cf-

cf

cf-

H(f)

S(f)

X(f)

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Vestigial Sideband (VSB)

VSB sends a small portion of the other

sideband around fc

Bandwidth is slightly more than SSB

The implementation is much simpler than SSB

Can be used in signals with DC, e.g., TV

x tm t DSB

Modulator

VSBx t

vH f

VSB filter (BP)

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cont …

VSB modulation

x tm t DSB

Modulator

VSBx t

vH f

cfcf

X f

cfcf

vH f

cfcf

VSBX f

How to design VSB filter so that we can recover m(t)?

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( ) [ ( ) ( )] ( )VSB c c vX f M f f M f f H f

VSB filter

DSB

VSB output

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VSB Demodulation

Coherent demodulation:

Multiply by carrier

vsbx t d t

2cos ctw

Dy t

( ) ( ) ( )VSB c VSB cD f X f f X f f

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( ) [ ( ) ( )] ( )VSB c c vX f M f f M f f H f

1 1[ ( 2 ) ( )] ( ) [ ( ) ( 2 )] ( )

2 2c c c cM f f M f H f f M f M f f H f f

1 1( ) [ ( )] ( ) [ ] ( )

2 2D c cY f M f H f f M f H f f

( )[ ( ) ( )]

2c c

M fH f f H f f

After low pass filter

So if [ ( ) ( )] constant, m(t) can be recovered.c cH f f H f f

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Condition on VSB Filter

H(f) is anti-symmetric around fc

[ ( ) ( )] constantc cH f f H f f

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VSB Demodulation 2

Carrier reinsertion and envelope detector can

still be used for VSB

1 1 1( ) cos 0.4cos2 0.9cos3m t t t t

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VSB Demodulation 2

Message

VSB output

After carrier reinsertion

cos ( )c rK t x tThe message can be recovered

from the envelope

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Summary of Linear Modulation

Scheme Modulator

Complexity

Demodulator

Complexity

Power

Efficiency

Bandwidth

DSB-SC Simple Complex

(coherent) 1 2W

AM Simple Simple

(envelope detector)

<= 1/3

(single tone) 2W

SSB Complex Coherent: complex

Envelope: simple

1: w/o carrier

Low: with carrier W

VSB Simpler than SSB Coherent: complex

Envelope: simple

1: w/o carrier

Low: with carrier W + WVSB

WVSB: width of the vestigial sideband.

WVSB

W