ee541_451_class3
TRANSCRIPT
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EE 551/451, Fall, 2007
Communication Systems
Zhu Han
Department of Electrical and Computer Engineering
Class 3
Sep. 4th, 2007
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Review of last classReview of last class
Random Process
Stationary, Ergodic
Mean, correlation, covariance, power spectrum density
Gaussian Process
Noise Central limit theorem
Narrowband Noise
In-phase and Quadrature phase N0/2 power each Gaussian
Envelope (Rayleigh distribution) and phase (uniform)
Ricean distribution
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Baseband and Carrier CommunicationBaseband and Carrier Communication
Baseband:
Describes signals and systems whose range of frequencies is measuredfrom 0 to a maximum bandwidth or highest signal frequency
Voice: Telephone 0-3.5KHz; CD 0-22.05KHz
http://www.youtube.com/watch?v=YjO_VXHxsRw&mode=related&search=
Video: Analog TV 4.5MHz, TV channel is 0-6MHz. Digital,depending on the size, movement, frames per second,
Example: wire, coaxial cable, optical fiber, PCM phone
Carrier Communication:
Carrier: a waveform (usually sinusoidal) that is modulated torepresent the information to be transmitted. This carrier wave is usuallyof much higherfrequency than the modulating (baseband) signal.
Modulation: is the process of varying a carrier signalin order to usethat signal to convey information.
http://en.wikipedia.org/wiki/Waveformhttp://en.wikipedia.org/wiki/Sinusoidalhttp://en.wikipedia.org/wiki/Modulationhttp://en.wikipedia.org/wiki/Transmission_%28telecommunications%29http://en.wikipedia.org/wiki/Frequencyhttp://en.wikipedia.org/wiki/Carrier_wavehttp://en.wikipedia.org/wiki/Informationhttp://en.wikipedia.org/wiki/Informationhttp://en.wikipedia.org/wiki/Carrier_wavehttp://en.wikipedia.org/wiki/Frequencyhttp://en.wikipedia.org/wiki/Transmission_%28telecommunications%29http://en.wikipedia.org/wiki/Modulationhttp://en.wikipedia.org/wiki/Sinusoidalhttp://en.wikipedia.org/wiki/Waveform -
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ModulationModulation
Modulation
A process that causes a shift in the range of frequencies of a signal.
Gain advantages
Antenna size: half of the antenna size. Thousands of miles forbaseband
Better usage of limited bandwidth: less side lopes Trade bandwidth for SNR: CDMA
Robust to inter-symbol-interference (multipath delay)
Robust to errors and distortions
Types Analog: AM (DSB, SSB, VSB), FM, Delta modulation
Digital: ASK, FSK, PSK, QAM,
Pulse modulation: PCM, PDM, Fiber, phone
Advanced: CDMA (3G), OFDM (WLAN, WMAN), .
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Double SidebandDouble Sideband
Modulation: time: m(t)cos(wct), freq: 0.5[M(w-wc)+M(w+wc)]
Figure 2.4: LSB, USB, DSB
DSB-SC: suppressed carrier, no carrier frequency
Wc >= bandwidth of the signal to avoid aliasing.
Demodulation: e(t)=m(t)(cos(wct))^2=0.5(m(t)+m(t)cos(2wct))
E(w)=0.5M(w)+0.25(M(w+2wc)+M(w-2wc))
Low pass filter to remove the higher frequency
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DSB-SCDSB-SC
Example
t
t
t
)t(m
)t(
)(M
0
)(
0 cc
Upper sideband (USB)Lower sideband (LSB)
)t(
)tcos( c
)}tcos(
cF{
0 c
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Frequency ConversionFrequency Conversion
Move the signals to other
frequency
Multiplying two sinusoids resultsin two frequencies which are thesum and difference of thefrequencies of the sinusoids
multiplied.
To change the carrier frequency cof a modulated signal to an
intermediate frequency I we use
an oscillator to generate a sinusoidof frequency MIX such that
)]t)cos(()t)[cos(()tcos()tcos(21 ++=
)]t)cos(()t)2)[cos((t(m
)]t)cos(()t))[cos((t(m)tcos()tm(t)cos(Then
.
IIc21
MIXcMIXc21
MIXc
MIXcI
++=
++=
=
)tcos( MIX
BPF@ I
)tcos()t(m)t(e I211 =
m(t) (t) e1(t)
tt t
EXAMPLE : Let m(t)
be as shown.
)tcos()t(m)t( C=
SPECTRA
0cc
I I
0
)(M
)(
)(E1
0
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Amplitude ModulationAmplitude Modulation
Why DSB-SC not working: do not know the carrier frequency in receiver.
The last impulse functions indicate that the carrier is not suppressed in thiscase. For some M() shown, the modulated signal spectrum is as shown.
With this type of AM the demodulation can be performed with/without alocal oscillator synchronized with the transmitter.
[ ] [ ])()()()()(
)cos()]([)(
21
cccc
cAM
AMM
ttmAt
++++=
+=
0cc
0
)(M
)(
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AM ExampleAM Example
m(t) has a minimum value of about -0.4. Adding a dc offset of A=1 results in
A+m(t) being always positive. Therefore the positive envelope of is justA+m(t). An envelope detector can be used to retrieve this.
m(t)A+m(t)
0.7
-0.4
0.t
t
t
1.
A=1
)tcos()]t(mA[)t( cAM +=
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AM Example (cont.)AM Example (cont.)
The choice of dc offset should be such that A+m(t) should always be
positive. Otherwise envelope detector cannot be used, but coherent still ok For example, the minimum value of m(t) = -0.4 . Therefore A > |min(m(t))|
for successful envelope detection. What if A< |m(t) |.
In the previous example let A=0.3.
m(t)
A+m(t)
0.7
-0.4
0.t t
0
)tcos()]t(mA[)t( cAM +=
t
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Modulation IndexModulation Index
Let mp be the absolute negative peak of m(t).
EXAMPLE : Single-tone modulation. Let m(t)=2sin(20t)
on).demodulatissynchronouusestillcanwe(However,
used.benotcandetectionenvelopeandted,overmodulaissignalthe)mA(or1When
10,mAforthatseeweThen
A
m:INDEXMODULATION
amplitude.carriertheisAmA
p
p
p
p
=
2.1ofoffsetdcFor2A1ii)4A0.5i).A
2
A
m
;2mp
p
======== t
m(t)
t t t
5.0=1= 2=
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Sideband and Carrier PowerSideband and Carrier Power
%33%100x12
11,For
%100x2
P
A.Bor,Bm
)tBcos(m(t)let,exampleFor
.PA
P
PP
P
powerTotal
poweruseful:Efficiency
power.usefultheispowersidebandThe
m(t).ofpowertheisPwherePPpowerSideband2
APpowerCarrier
power.sidebandtheandpowercarrierofsumtheispowersignalAMtotalTheitself.signalthecontainwhichsidebandsistermsecondtheandcarriertheistermfirstThe
)tcos()t(m)tcos(A)t(
max
2
2
2A
2B
m
AB
p
m
m2m
sc
s
mm21
s
2
c
ccMA
222
=+
==
+===
====
+=
+==
=
=
+=
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AM DecoderAM Decoder
Rectifier Detector: synchronous
Envelope Detector: asynchronous
AM signal RC
t
ttt
+
vc(t)
-
Non-coherent receiver has 3dB worst
performance than coherent. Cheaper for
Non-coherent receiver, Nextel.
Coherent detection: Receiver can recover the
frequency and phase of the transmitter by PLL.Error of timing causes the performance error floor
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QAMQAM
AM signal BANDWIDTH : AM signal bandwidth is twice the bandwidth
of the modulating signal. A 5kHz signal requires 10kHz bandwidth for AMtransmission. If the carrier frequency is 1000 kHz, the AM signal spectrumis in the frequency range of 995kHz to 1005 kHz.
QUADRARTURE AMPLITUDE MODULATION is a scheme that allowstwo signals to be transmitted over the same frequency range.
Equations
Coherent in frequency
and phase. Expensive
TV for analog
Most modems
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SSB FrequencySSB Frequency
)(M
0 B2B2
cc
SSB (Upper sideband)
0
0cc
)(SSB
baseband
DSB
SSB
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SSB MathSSB Math
)(M +
)(M
[ ]
( )
( )
)sgn()M()(M)}{sgn( H j
)t(jmm(t)t
1
)t(jmm(t))t(mthatshowcanweSimilarly,
m(t).oftransformHilbertthecalledis)t(m
dt
)(m1t
1)t(m)t(mewher
)t(jmm(t)t
1)t(jmm(t))t(m
t
j
tj
1)}{sgn(
)}{sgn()}(M{m(t))t(m)sgn()(M)(M2
)sgn(1)(M)(U)(M)(M
h2
1
2
1
h
h
h21
211
1121
21
21
==
=
=
=
=
+=
+=
=
=
+=+=
+==
+
++
1F
F
FF
How to generate mh(t) ?
H()
M() Mh()
0forj
0forj
)jsgn(-)M(
)(M)H(
)sgn()M(j)(M
H
H
=
=
=
= 1)H( =
)H(2
2Transfer function of a Hilbert transformer
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SSB HilbertSSB Hilbert
SSB signal can be expressed in terms of m(t) and its Hilbert transform
( )
{ }{ }
{ }
{ }
{ } )LSBforUSB,for(-)tsin()t(m)tcos(m(t))(general,In
;)tsin()t(m)tcos(m(t))(thatshowcanweSimilarly,
)tsin()t(m)tcos(m(t))(
)tsin()t(m)tcos(m(t)
)ee)(t(mj)ee)(t(m
}e))t(jm)t(m(e))t(jm)t(m({)(M)(M
e))t(jm)t(m({}e)t(m{)(M
}e))t(jm)t(m({}e)t(m{)(M
)(M)(M)(
chcSSB
chcLSBSSB
chcUSBSSB
chc
tjtjh2
1tjtj21
tjh2
1tjh2
1cc
tjh2
1tjc
tjh2
1tjc
ccUSBSSB
cccc
cc
cc
cc
+=
+=
=
=
++=++=++
==+
+==
++=
+
++
+
1-
1-
1-
1-
1-
1-
1-1-
1-1-
F
F
F
F
F
F
FF
FF
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SSB GeneratorSSB Generator
Selective Filtering using filters with sharp cutoff characteristics. Sharp
cutoff filters are difficult to design. The audio signal spectrum has no dccomponent, therefore , the spectrum of the modulated audio signal has a null
around the carrier frequency. This means a less than perfect filter can do a
reasonably good job of filtering the DSB to produce SSB signals.
Baseband signal must be bandpass
Filter design challenges
No low frequency components
cc 0
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Single Sideband (SSB)Single Sideband (SSB) Purpose : to reduce the bandwidth requirement of AM by one-half. This is
achieved by transmitting only the upper sideband or the lower sidebband ofthe DSB AM signal.
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SSB DemodulationSSB Demodulation
[ ] [ ]
).(gettousedbecanfilterlowpass
)2sin()())cos(1)(()cos()sin()()cos()()cos()(
21
21
tmA
ttjmttmtttjmttmtt chccchccSSB +==
[ ]
( )
( )
large.betohasAsincelowveryisschemethisofefficiencyThe
.(t)mA,m(t)Afor)(
1A
))(2)())((())())(((E(t)
))(tan),cos(A)Bsin()Acos({Re
?)cos()()sin()())cos())(()(ofenvelopetheisWhat
.signalsSSBsuchdemodulatetousedbecandetectorenvelope
)sin()()cos()()cos()(
h
)(2)()(
22222
1-22
2
2
2
2
21
21
21
>>>>+
+++=
+++=++=
=++=+
+=++=
++=
+
+
tmA
tAmtmtmAtmtmA
Bcall
ttEttmttmAt
An
ttmttmtAt
A
tm
A
tm
A
tm
hh
AB
cchcCSSB
chccCSSB
h
Synchronous, SSB-SC demodulation
SSB+C, envelop detection
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SSB vs. AMSSB vs. AM
Since the carrier is not transmitted, there is a reduction by 67%
of the transmitted power (-4.7dBm). --In AM @100%modulation: 2/3 of the power is comprised of the carrier; withthe remaining (1/3) power in both sidebands.
Because in SSB, only one sideband is transmitted, there is a
further reduction by 50% in transmitted power
Finally, because only one sideband is received, the receiver'sneeded bandwidth is reduced by one half--thus effectivelyreducing the required power by the transmitter another 50%
(-4.7dBm (+) -3dBm (+) -3dBm = -10.7dBm).
Relative expensive receiver
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Vestigial Sideband (VSB)Vestigial Sideband (VSB) VSB is a compromise between DSB and SSB. To produce SSB signal from
DSB signal ideal filters should be used to split the spectrum in the middle sothat the bandwidth of bandpass signal is reduced by one half. In VSB system
one sideband and a vestige of other sideband are transmitted together. The
resulting signal has a bandwidth > the bandwidth of the modulating
(baseband) signal but < the DSB signal bandwidth.
cc
SSB (Upper sideband)
0
0cc
)(SSB
VSB Spectrum
c
)(VSB
c
DSB
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VSB TransceiverVSB Transceiver
)t2cos( c
Hi()
m(t) )(VSB
)t2cos( c
LPF
Ho()
)(M )(VSB
Transmitter Receiver
e(t)
[ ]
[ ]
)(H)(H
1)(HOR
B2for1)(H)(H)(HhaveshouldweThus
this.removesfilterLowpass
)(H)]2(M)(H)2(M)(H[
)(H)(M)(H)(H)(H)(E)(M
termfreq.Hightermfreq.High
])2(M)(H)(M)(H)(M)(H)2(M)(H[
)]()([)(E)(H)](M)(M[)(
rad/secB2todbandlimiteis)(M
cicio
ocici
occicci
ocicio
ccicicicci
cVSBcVSB
iccVSB
++=
=++
++++++==
++++++=++=
++=
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Other Facts about VSBOther Facts about VSB
Envelope detection of VSB+C
TV:
DSB, SSB and VSB
DSB bandwidth too high
SSB: baseband has low
frequency component, receivercost
Relax the filter and baseband
requirement with modest increase
in bandwidth
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ComparisonComparison
AM
DSB
QAM 1 2
Common types & modulated signal1. AM: ( ) [1 ( )]cos(2 )
2. DSB: ( ) ( )cos(2 )
3. QAM: ( ) ( ) cos(2 ) ( )sin(2 )
4. SSB:
c c
c c
c c c c
s t A m t f t
s t A m t f t
s t A m t f t A m t f t
SSB
VSB
2
( ) ( ) cos(2 ) ( )sin(2 )
5. VSB: ( ) ( )cos(2 ) ( )sin(2 )
Complex domain representation:
( ) Re{ ( ) },
complex envelop:
c
c c c c
c c c c
j f t
s t A m t f t A m t f t
s t A m t f t A m t f t
s t g t e
%
( ) ?
Bandwidth: 2 ( : message bandwdith)m m m
g t
B B B B
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AM BroadcastingAM Broadcasting
History
Frequency
Long wave: 153-270kHz
Medium wave: 520-1,710kHz, AM radio
Short wave: 2,300-26,100kHz, long distance, SSB, VOA
Limitation
Susceptibility to atmospheric interference
Lower-fidelity sound, news and talk radio
Better at night, ionosphere.
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TelevisionTelevision
Digital Display (CRT)
Analog Display (TV)
Eliminate flicker effects
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Deflection Signal and SynchronizationDeflection Signal and Synchronization
525525 30=8.27M
Deflection signal and synchronization signal
http://www.ntsc-tv.com/images/tv/raster.gif -
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Solar Power and Human EyeSolar Power and Human Eye
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RGB, LIQRGB, LIQ
mL=0.3mr+0.59mg+0.11mb
mI=0.6mr+0.28mg-0.32mb
mQ=0.21mr-0.52mg+0.31mb
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BandwidthBandwidth
VSB and QAM
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TV standards in the worldTV standards in the world