Vestigial Sideband Modulation

Vestigial Sideband Modulation
KEEE343 Communication Theory
Lecture #11, April 7, 2011
Prof. Young-Chai Ko
koyc@korea.ac.kr

Summary
·•Vestigial sideband modulation
·•Baseband representation of modulated wave
·•Baseband representation of pass-band filter
·•Frequency division multiplexing
·•Introduction to Angle Modulation

Generation of LSB SSB Using Wideband Low-Pass Filter
DSB Spectrum
H L (f)
f c
SSB Spectrum
f c
f c
f c
H L (f)
sgn(f f c )
sgn(f + f c )

Generation of USB SSB Using High-Pass (or Passband)
Filter
DSB Spectrum
H HP (f)
f c
SSB Spectrum
f c
f c
f c
H HP (f) = sgn(f + f c ) + sgn(f + f c )
sgn(f + f c )
sgn(f f c )

SSB Modulated Wave
• Lower Sideband SSB
s LSB (t) = 1 2 m(t) cos(2 f ct)+ 1 2 ˆm(t)sin(2 f ct)
• Upper sideband SSB
s USB (t) = 1 2 m(t) cos(2 f ct)
1
2 ˆm(t)sin(2 f ct)

Applications of SSB and Difficulties in Implementing SSB
• Two difficulties of SSB modulations
• Designing and implementing the sharp Low-pass (or High-pass/pass-band)
filter is not easy for circuit designer.
• Hence, the message signal which does not contain the significant energy in
the DC area is often modulated by the SSB such as the speech signal.
Spectrum of Speech Signal (Example)
0 [Hz]
• However, the SSB cannot be applicable for the message signal which
contains the significant energy around zero frequency such as video
signal, computer data, and etc.

Vestigial Sideband (VSB) Modulation
• VSB Modulation
• Modulation to overcome the two difficulties of the SSB modulations.
• Allow a small amount, or vestige, of the unwanted sideband to appear at
the output of an SSB modulator
• The design of the sideband filter is simplified since the need for sharp
cutoff at the carrier frequency is eliminated.
• In addition, a VSB system has improved low-frequency response and
can even have dc response.

Idea of VSB Modulator
• Pass-band (or High-pass) filter for USB-SSB modulation
|H U (f)|
f c
f c
• The filter below is much easier to design and implement
1 ✏ 1 1
✏
f c f 1
f c
f c + f 1

• Consider the two-tone message signal given as
m(t) =A cos(2 f 1 t)+B cos(2 f 2 t)
• Message signal multiplied by the carrier wave, that is, DSB signal
e DSB (t) = (A cos(2 f 1 t)+B cos(2 f 2 t)) · cos(2 f c t)
= 1 2 A cos(2 (f c + f 1 )t)+ 1 2 A cos(2 (f c f 1 )t)
+ 1 2 B sin(2 (f c + f 1 )t)+ 1 2 B sin(2 (f c f 1 )t)

• Spectrum of DSB signal
1
2 B 1
1
2 A 1
2 A 2 B
• Frequency response of the VSB filter
f c f 2 f c f 1 f
f c + f 1 f c + f 2
c
1 ✏ 1 ✏
f c
• Output response
s(t) = 1 2 A cos(2⇥(f c f 1 )t)
+ 1 2 A(1 ) cos(2⇥(f c + f 1 )t)
+ 1 2 B cos(2⇥(f c + f 2 )t)
f c f 1
f c + f 1
f c + f 2
1
1
1
2 A 2 [A(1 )] 2 B
f c f 1 f c + f 1
f c f 2
f c + f 2

Demodulation of VSB Signal (Coherent method)
• Downconvert (by Multiplying 4 cos(2 f c t) ) and low pass filtering
• Downconvert
d(t) = s(t) · 4 cos(2⇥f c t)
= 1 2 A cos(2⇥(f c f 1 )t) · 4 cos(2⇥f c t)
+ 1 2 A(1 ) cos(2⇥(f c + f 1 )t) · 4 cos(2⇥f c t)
+ 1 2 B cos(2⇥(f c + f 2 )t) · 4 cos(2⇥f c t)
cos(2 (f c + f 1 )t) · cos(2 f c t)= 1 apple
cos(2 (2f c + f 1 )t) + cos(2 f 1 t)
2
Low-Pass Filtering
1
2 cos(2 f 1t)

• Signal after Low-pass filtering
⇥(t) = A cos(2⇤f 1 t)+A(1 ) cos(2⇤f 1 t)+B cos(2⇤f 2 t)
= A cos(2⇤f 1 t)+B cos(2⇤f 2 t)

Television Signals
[Ref: Haykin & Moher, Textbook]

Baseband Representation of Modulated Waves
• DSB modulated wave signal
s DSB (t) =Am(t) cos(2 f c t)
• SSB modulated wave signal
s SSB (t) = 1 2 Am(t) cos(2 f ct) ± 1 2 A ˆm(t)sin(2 f ct)
• In general, we can write the “linear modulated wave” as
s(t) =s I (t) cos(2 f c t) s Q (t)sin(2 f c t)
Carrier wave with frequencyf c
quadrature-phase version of the carrier
c(t) = cos(2 f c t) ĉ(t) =sin(2 f c t)
Orthogonal each other

• We can rewrite the modulated wave as
s(t) =s I (t)c(t)
s Q (t)ĉ(t)
in-phase component of s(t)
quadrature(-phase) component of s(t)
• Introduce the complex envelop of the modulated wave s(t)
˜s(t) =s I (t)+js Q (t)
• Define the complex carrier wave
˜c(t) =c I (t)
jc Q (t)

• Consider the following
˜s(t) · exp(j2 f c t) =
apple
s I (t)+js Q (t) ·
apple
cos(2 f c t)+j sin(2 f c t)
• Real term
apple
⇥ ˜s(t) · exp(j2 f c t) = s I (t) · cos(2 f c t) s Q (t) · sin(2 f c t)
• Imaginary term
apple
˜s(t) · exp(j2 f c t) = s I (t)sin(2 f c t)+s Q (t) cos(2 f c t)
˜s(t)
X
apple
· s(t)
exp(j2 f c t)

• Now consider
˜s(t) =s I (t)+js Q (t) =a(t)e j (t)
where
a(t) =
q
s 2 I (t)+js2 Q (t),
(t) = tan 1 s Q(t)
s I (t)
• Then we can represent the modulated wave as
apple
s(t) = <
apple
= <
˜s(t)e j2⇥f ct
a(t)e j[2⇥f ct+ (t)]
= a(t) cos[2⇥f c t + (t)]
apple
= < a(t)e j (t) e j2⇥f ct

• Three different representation of modulated wave using its equivalent
baseband signal
s(t) = s I (t) cos(2⇥f c t) s Q (t)sin(2⇥f c t)
apple
= < ˜s(t)e j2 f ct
= a(t) cos[2⇥f c t + (t)]

Superheterodyne Receiver
[Ref: Haykin & Moher, Textbook]

Communication Chipset Architecture
LNA
Receiver
÷ 2
PLL
ABB Section
90
0
antenna
switch
90
0
÷ 2
PLL
ABB
Digital
Baseband
IC
Power
Amplifier
Switchplexer
Transmitter
module
PA Ctrl
26MHz Osc.
LDO’s

Frequency-Division Multiplexing
• To transmit a number of communication signals over the same channel, the
signals must be kept apart so that they do not interfere with each other, and
thus they can be separated at the receiving end.
• FDM (Frequency division multiplexing)
• TDM (Time division multiplexing)
• SDM (Space division multiplexing)
• CDM (Code division multiplexing)

Block Diagram of FDM

Angle Modulation
• Basic Definition of Angle Modulation
s(t) =A c cos[ i (t)] = A c cos[2⇥f c t + ⇤ c ]
• Phase modulation (PM) if
i(t) =2⇥f c t + k p m(t)
• Frequency modulation (FM) if
Z t
i(t) =2⇥f c t +2⇥k f m(⇤) d⇤
0