lectures on digital communication by prof.dr.a.abbas
TRANSCRIPT
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Review Chapter 1.1 - 1.4Review Chapter 1.1 - 1.4Problems: 1.1a-c, 1.4, 1.5, Problems: 1.1a-c, 1.4, 1.5, 1.91.9
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Review Chapter 1.5 - 1.8Problems: 1.13 - 1.16, 1.20
Quiz #1
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Quiz #1
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Read: 5.1 - 5.3 Problems: 5.1 - 5.3 Quiz #1
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Read 5.4 & 5.5 Problems 5.7 & 5.12 Quiz #1
Local: Thursday, 28 September, Lecture 6
Off Campus DL: < 11 OctoberStrictly Review (Chapter 1)
Full Period, Open Book & Notes
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In Class: 2 Quizzes, 2 Tests, 1 Final ExamOpen Book & Open NotesWARNING! Study for them like they’re closed book!
Graded Homework: 2 Design Problems Ungraded Homework:
Assigned most every classNot collectedSolutions ProvidedPayoff: Tests & Quizzes
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An Analogy: Commo Theory vs. Football Reading the text = Reading a playbook Working the problems =
playing in a scrimmage Looking at the problem solutions =
watching a scrimmage
Quiz = Exhibition Game Test = Big Game
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Show some self-discipline!! Important!!For every hour of class...
... put in 1-2 hours of your own effort.
PROFESSOR'S GUIDEIf you put in the timeYou should do fine.You have only three days in your life one is today do it today second is yesterday that has gone forget about it third is tomorrow but many of you do not have tomorrow so do every thing today Imam Ali
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Digital Analog
Binary M-ary
Wide Band Narrow Band
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Digital M-Ary System M = 8 x 8 x 4 = 256
Source:January 1994Scientific American
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Source: January 1994Scientific American
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Phonograph → Compact Disk Analog NTSC TV → Digital HDTV Video Cassette Recorder
→ Digital Video Disk AMPS Wireless Phone → 4G LTE Terrestrial Commercial AM
& FM Radio Last mile Wired Phones
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Fourier Transforms X(f)Table 2-4 & 2-5
Power SpectrumGiven X(f)
Power SpectrumUsing Autocorrelation Use Time Average Autocorrelation
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Autocorrelations deal with predictability over time. I.E. given an arbitrary point x(t1), how predictable is x(t1+tau)?
time
Volts
t1
tau
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Autocorrelations deal with predictability over time. I.E. given an arbitrary waveform x(t), how alike is a shifted version x(t+τ)?
Voltsτ
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time
Volts
0
Vdc = 0 v, Normalized Power = 1 watt
If true continuous time White Noise, no predictability.
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• The sequence x(n)x(1) x(2) x(3) ... x(255)
• multiply it by the unshifted sequence x(n+0)x(1) x(2) x(3) ... x(255)
• to get the squared sequencex(1)2 x(2)2 x(3)2 ... x(255)2
• Then take the time average[x(1)2 +x(2)2 +x(3)2 ... +x(255)2]/255
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• The sequence x(n)x(1) x(2) x(3) ... x(254) x(255)
• multiply it by the shifted sequence x(n+1)x(2) x(3) x(4) ... x(255)
• to get the sequencex(1)x(2) x(2)x(3) x(3)x(4) ... x(254)x(255)
• Then take the time average[x(1)x(2) +x(2)x(3) +... +x(254)x(255)]/254
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• If the average is positive...– Then x(t) and x(t+tau) tend to be alike
Both positive or both negative• If the average is negative
– Then x(t) and x(t+tau) tend to be oppositesIf one is positive the other tends to be negative
• If the average is zero– There is no predictability
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tau (samples)
Rxx
0
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Time
Volts
23 points
0
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tau samples
Rxx
0
23
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Rx(τ)
tau seconds0
A
Gx(f)
Hertz0
A watts/Hz
Rx(τ) & Gx(f) form a Fourier Transform pair.
They provide the same infoin 2 different formats.
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Rx(tau)
tau seconds0
A
Gx(f)
Hertz0
A watts/Hz
Average Power = ∞D.C. Power = 0A.C. Power = ∞
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Rx(tau)
tau seconds0
A
Gx(f)
Hertz0
A watts/Hz
-WN Hz
2AWN
1/(2WN)Average Power = 2AWN wattsD.C. Power = 0A.C. Power = 2AWN watts
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Time Average Autocorrelation Easier to use & understand than
Statistical Autocorrelation E[X(t)X(t+τ)] Fourier Transform yields GX(f)
Autocorrelation of a Random Binary Square Wave Triangle riding on a constant term Fourier Transform is sinc2 & delta function
Linear Time Invariant Systems If LTI, H(f) exists & GY(f) = GX(f)|H(f)|2
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X
=
Cos(2πΔf)
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If input is x(t) = Acos(ωt)output must be of form
y(t) = Bcos(ωt+θ)
Filterx(t) y(t)
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Maximum Power Intensity Average Power Intensity
WARNING!Antenna Directivity is NOT =
Antenna Power Gain10w in? Max of 10w radiated.
Treat Antenna Power Gain = 1 Antenna Gain = Power Gain * Directivity
High Gain = Narrow Beam
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Antenna Gain is what goes in RF Link Equations
In this class, unless specified otherwise, assume antennas are properly aimed. Problems specify peak antenna gain
High Gain Antenna = Narrow Beam
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sou
rce:
en
.wik
iped
ia.o
rg/w
iki/
Par
abol
ic_a
nte
nn
a
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EIRP = PtGt
Path Loss Ls = (4*π*d/λ)2
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Final Form of Analog Free Space RF Link EquationPr = EIRP*Gr/(Ls*M*Lo) (watts)
Derived Digital Link EquationEb/No = EIRP*Gr/(R*k*T*Ls*M*Lo)
(dimensionless)
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• Models for Thermal Noise: *White Noise & Band limited White Noise*Gaussian Distributed
• Noise Bandwidth– Actual filter that lets A watts of noise thru?– Ideal filter that lets A watts of noise thru?– Peak value at |H(f = center freq.)|2 same?• Noise Bandwidth = width of ideal filter (+ frequencies).
• Noise out of an Antenna = k*Tant*WN
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Radio Static (Thermal Noise) Analog TV "snow"
2 secondsof White Noise
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Probability Density Functions (PDF's), of which a Histograms is an estimate of shape, frequently (but not always!) deal with the voltage likelihoods
Time
Volts
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time
Volts
0
Vdc = 0 v, Normalized Power = 1 watt
If true continuous time White Noise, No Predictability.
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Volts
BinCount
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Vol
ts
Bin
Cou
nt
Time
Volts
0
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Volts
BinCount
00
200
When bin count range is from zero to max value, a histogram of a uniform PDF source will tend to look flatter as the number of sample points increases.
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Time
Volts
0
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Volts
BinCount
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Time
Volts
0
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Volts
BinCount
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Volts
BinCount
0
400
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Are all 0 mean, 1 watt, White Noise
0
0
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Rx(tau)
tau seconds0
A
Gx(f)
Hertz0
A watts/Hz
The previous WhiteNoise waveforms all
have same Autocorrelation& Power Spectrum.
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Autocorrelation: Time axis predictability PDF: Voltage liklihood Autocorrelation provides NO information about
the PDF (& vice-versa)... ...EXCEPT the power will be the same...
PDF second moment E[X2] = Rx(0) = area under Power Spectrum = A{x(t)2}
...AND the D.C. value will be related. PDF first moment squared E[X]2 = constant term in autocorrelation = E[X]2δ(f) = A{x(t)}2
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x
WinterSun is belowsatelliteorbital plane.
x
Fall Sun → sameplane assatellite.
x
Spring Sun→ sameplane asSatellite.
x
SummerSun is abovesatelliteorbital plane.
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Source: www.ses.com/4551568/sun-outage-data
x
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Time
Volts
0
If AC power = 4 watts & BW = 1,000 GHz...
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fx(x)
Volts0
.399/σx = .399/2 = 0.1995Time
Volts
0
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Rx(tau)
tau seconds0
Gx(f)
Hertz0
2(10-12) watts/Hz
-1000 GHz
4
500(10-15)
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Time
Volts
3
AC power = 4 watts
0
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Gx(f)
Hertz0-1000 GHz
9
Gx(f)
Hertz0
2(10-12) watts/Hz
-1000 GHz
2(10-12) watts/Hz
No DC
3 vdc → 9 watts DC Power
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Rx(tau)
tau seconds0
13
9
Rx(tau)
tau seconds0
4
500(10-15)
500(10-15)
No DC
3 vdc → 9 watts DC Power
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fx(x)
Volts0
σ2x = E[X2] -E[X]2 = 4
0
fx(x)
Volts3
σ2x = E[X2] -E[X]2 = 4
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Time
Volts
3
AC power = 4 wattsDC power = 9 wattsTotal Power = 13 watts
0
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Sin
&Nin
GSin
&G(Nin + Nai)
G
Namp = kTampWn
+
+
G > 1
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F = SNRin/SNRout WARNING! Use with caution.
If input noise changes, F will change.
F = 1 + Tamp/Tin Tin = 290o K (default)
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Sin
&Nin
GSin
&G(Nin + Nai)
G
Namp = kTpassiveWn
+
+
G < 1
Tpassive = (L-1)Tphysical
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Active Device (Tamp) From Spec Sheet (may have F)
Passive Device (Tcable or T passive)
(L-1)*Tphysical
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Noise Striking Antenna = NoWThermal
= kTsurroundings1000*109 = k*290*1000*109
= 4.00 n watts
Much of this noise doesn't exit system.Blocked by system filters. kTantWN = ???
SystemCable + Amp
Noise exiting Antenna that will exit the System =kTant6*106 = 12.42*10-15 watts
Noise Antenna "Sees" = Noise exiting antenna = NoWAntenna
≈ kTant1000*109 = 2.07 n watts
(Tantenna = 150 Kelvin)
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SystemCable + Amp
Noise Actually Exiting Antenna = Noise Antenna "Sees" ≠ Noise Exiting Antenna that will exit the System = kTantWN = 12.42*10-15 watts
AntennaPower
Gain = 1Signal Power in =Signal Power out
This is the model we use.
We don't worry aboutnoise that won't make the output.
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Noise Seen by Antenna = NoWAntenna
= kTant1000*109 = 2.07 n wattsSignal Power Picked Up by Antenna = 10-11 watts
SystemCable + Amp
SNR at "input" of antenna = 10-11/(4*10-9) = 0.0025SNR at output of antenna = 10-11/(2.07*10-9) = 0.004831SNR at System Output = 43.63
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Noise seen by Antenna TCRO = NoWN
= kTant6*106 = 12.42 femto wattsSignal Power Picked Up by Antenna = 10-11 watts
SystemCable + Amp
SNR at output of antenna = 805.2
SNR at System Output = 43.63
This is the noise we're
worried about.
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Filtering...Removes noise power outside signal BWLets the signal power through
SystemCable + Amp
SNR at Antenna Input = 0.0025SNR at Antenna Output = 0.004831SNR at System Output = 43.67
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Only considers input noise that is in the signal BW & can reach the output.Cable & electronics dump in more
noise.
SystemCable + Amp
SNR at antenna output = 805.2 SNR at System Output = 43.67
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