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ECEN5533 Modern Communications TheoryLecture #1 19 August 2014Dr. George Scheetswww.okstate.edu/elec-engr/scheets/ecen5533
ECEN5533 Modern Communications TheoryLecture #1 19 August 2014Dr. George Scheetswww.okstate.edu/elec-engr/scheets/ecen5533
Review Chapter 1.1 - 1.4Review Chapter 1.1 - 1.4Problems: 1.1a-c, 1.4, 1.5, 1.9Problems: 1.1a-c, 1.4, 1.5, 1.9
ECEN5533 Modern Communications TheoryLecture #2 21 August 2014Dr. George Scheets
ECEN5533 Modern Communications TheoryLecture #2 21 August 2014Dr. George Scheets
Review Chapter 1.5 - 1.8Review Chapter 1.5 - 1.8Problems: 1.13 - 1.16, 1.20Problems: 1.13 - 1.16, 1.20
Quiz #1Quiz #1 Local: Tuesday, 4 September, Lecture 6Local: Tuesday, 4 September, Lecture 6 Off Campus DL: Off Campus DL: << 11 September 11 September
ECEN5533 Modern Communications TheoryLecture #3 26 August 2014Dr. George Scheets
ECEN5533 Modern Communications TheoryLecture #3 26 August 2014Dr. George Scheets
Review Appendix AReview Appendix AProblems: Quiz #1, 2011-2013Problems: Quiz #1, 2011-2013
Quiz #1Quiz #1 Local: Thursday, 4 September, Lecture 6Local: Thursday, 4 September, Lecture 6 Off Campus DL: Off Campus DL: << 11 September 11 September
ECEN5533 Modern Communications TheoryLecture #4 28 August 2014
ECEN5533 Modern Communications TheoryLecture #4 28 August 2014
Read: 5.1 - 5.3Read: 5.1 - 5.3 Problems: 5.1 - 5.3Problems: 5.1 - 5.3 Quiz #1Quiz #1
Local: Thursday, 4 September, Lecture 6Local: Thursday, 4 September, Lecture 6 Off Campus DL: Off Campus DL: << 11 September 11 September
www.okstate.edu/elec-engr/scheets/ecen5533/www.okstate.edu/elec-engr/scheets/ecen5533/
ECEN5533 Modern Communications TheoryLecture #5 2 September 2014Dr. George Scheets
ECEN5533 Modern Communications TheoryLecture #5 2 September 2014Dr. George Scheets Read 5.4 & 5.5Read 5.4 & 5.5 Problems 5.7 & 5.12Problems 5.7 & 5.12 Quiz #1Quiz #1
Local: Local: Thursday, 4 SeptemberThursday, 4 September, Lecture 6, Lecture 6 Off Campus DL: Off Campus DL: << 11 September 11 September Strictly Review (Chapter 1)Strictly Review (Chapter 1)
Full Period, Open Book & NotesFull Period, Open Book & Notes
GradingGrading In Class: 2 Quizzes, 2 Tests, 1 Final ExamIn Class: 2 Quizzes, 2 Tests, 1 Final Exam
Open Book & Open NotesOpen Book & Open NotesWARNING! WARNING! Study for them like they’re closed book!Study for them like they’re closed book!
Graded Homework: 2 Design ProblemsGraded Homework: 2 Design Problems Ungraded Homework: Ungraded Homework:
Assigned most every classAssigned most every classNot collectedNot collectedSolutions ProvidedSolutions ProvidedPayoff: Tests & QuizzesPayoff: Tests & Quizzes
Why work the ungraded Homework problems?Why work the ungraded Homework problems? An Analogy: Commo Theory vs. FootballAn Analogy: Commo Theory vs. Football Reading the text = Reading a playbookReading the text = Reading a playbook WorkingWorking the problems = the problems =
playing in a scrimmage playing in a scrimmage Looking at the problem solutions = Looking at the problem solutions =
watching a scrimmage watching a scrimmage Quiz = Exhibition GameQuiz = Exhibition Game Test = Big GameTest = Big Game
To succeed in this class...To succeed in this class...
Show some self-discipline!! Important!!Show some self-discipline!! Important!!For every hour of class...For every hour of class...
... put in 1-2 hours of your own effort.... put in 1-2 hours of your own effort.
PROFESSOR'S LAMENTPROFESSOR'S LAMENTIf you put in the timeIf you put in the timeYou should do fine.You should do fine.If you don't,If you don't,You likely won't.You likely won't.
Course EmphasisCourse Emphasis
DigitalDigital AnalogAnalog
Binary Binary M-aryM-ary
Wide BandWide Band Narrow BandNarrow Band
French Optical Telegraph
French Optical Telegraph
Source:January 1994Scientific American
Digital M-Ary SystemDigital M-Ary System M = 8 x 8 x 4 = 256M = 8 x 8 x 4 = 256
Trend is to DigitalTrend is to Digital
Phonograph → Compact DiskPhonograph → Compact Disk Analog NTSC TV → Digital HDTVAnalog NTSC TV → Digital HDTV Video Cassette Recorder Video Cassette Recorder
→ Digital Video Disk→ Digital Video Disk AMPS Wireless Phone → 4G LTEAMPS Wireless Phone → 4G LTE Terrestrial Commercial AM & FM RadioTerrestrial Commercial AM & FM Radio Last mile Wired PhonesLast mile Wired Phones
Review...Review...
Fourier Transforms X(f)Fourier Transforms X(f)Table 2-4 & 2-5Table 2-4 & 2-5
Power SpectrumPower SpectrumGiven X(f) Given X(f)
Power SpectrumPower SpectrumUsing AutocorrelationUsing Autocorrelation Use Time Average AutocorrelationUse Time Average Autocorrelation
Review of AutocorrelationReview of Autocorrelation
Autocorrelations deal with predictability over time. I.E. Autocorrelations deal with predictability over time. I.E. given an arbitrary point given an arbitrary point x(t1)x(t1), how predictable is , how predictable is x(t1+tau)x(t1+tau)??
time
Volts
t1
tau
Review of AutocorrelationReview of Autocorrelation
Autocorrelations deal with predictability over time. I.E. Autocorrelations deal with predictability over time. I.E. given an arbitrary waveform given an arbitrary waveform x(t)x(t), how alike is a shifted , how alike is a shifted version version x(t+x(t+ττ))??
Voltsτ
255 point discrete time White Noise waveform
(Adjacent points are independent)
255 point discrete time White Noise waveform
(Adjacent points are independent)
time
Volts
0
Vdc = 0 v, Normalized Power = 1 watt
If true continuous time White Noise, no predictability.
Rxx(0)Rxx(0)
The sequence x(n)The sequence x(n)x(1) x(2) x(3) ... x(255)x(1) x(2) x(3) ... x(255)
multiply it by the unshifted sequence x(n+0)multiply it by the unshifted sequence x(n+0)x(1) x(2) x(3) ... x(255)x(1) x(2) x(3) ... x(255)
to get the squared sequenceto get the squared sequencex(1)x(1)22 x(2) x(2)22 x(3) x(3)22 ... x(255) ... x(255)22
Then take the time averageThen take the time average[x(1)[x(1)22 +x(2) +x(2)22 +x(3) +x(3)22 ... +x(255) ... +x(255)22]/255]/255
Rxx(1)Rxx(1)
The sequence x(n)The sequence x(n)x(1) x(2) x(3) ... x(254) x(255)x(1) x(2) x(3) ... x(254) x(255)
multiply it by the shifted sequence x(n+1)multiply it by the shifted sequence x(n+1)x(2) x(3) x(4) ... x(255)x(2) x(3) x(4) ... x(255)
to get the sequenceto get the sequencex(1)x(2) x(2)x(3) x(3)x(4) ... x(254)x(255)x(1)x(2) x(2)x(3) x(3)x(4) ... x(254)x(255)
Then take the time averageThen take the time average[x(1)x(2) +x(2)x(3) +... +x(254)x(255)]/254[x(1)x(2) +x(2)x(3) +... +x(254)x(255)]/254
Review of AutocorrelationReview of Autocorrelation
If the average is positive...If the average is positive... Then x(t) and x(t+tau) tend to be alikeThen x(t) and x(t+tau) tend to be alike
Both positive or both negativeBoth positive or both negative If the average is negativeIf the average is negative
Then x(t) and x(t+tau) tend to be oppositesThen x(t) and x(t+tau) tend to be oppositesIf one is positive the other tends to be negativeIf one is positive the other tends to be negative
If the average is zeroIf the average is zero There is no predictabilityThere is no predictability
Autocorrelation Estimate of Discrete Time White NoiseAutocorrelation Estimate of Discrete Time White Noise
tau (samples)
Rxx
0
255 point Noise Waveform(Low Pass Filtered White Noise)255 point Noise Waveform(Low Pass Filtered White Noise)
Time
Volts
23 points
0
Autocorrelation Estimate of Low Pass Filtered White NoiseAutocorrelation Estimate of Low Pass Filtered White Noise
tau samples
Rxx
0
23
Autocorrelation & Power Spectrum of C.T. White Noise
Autocorrelation & Power Spectrum of C.T. White Noise
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.
Autocorrelation & Power Spectrum of White NoiseAutocorrelation & Power Spectrum of White Noise
Rx(tau)
tau seconds0
A
Gx(f)
Hertz0
A watts/Hz
Average Power = ∞D.C. Power = 0A.C. Power = ∞
Autocorrelation & Power Spectrum of Band Limited C.T. White Noise
Autocorrelation & Power Spectrum of Band Limited C.T. White Noise
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
AutocorrelationsAutocorrelations Time Average AutocorrelationTime Average Autocorrelation
Easier to use & understand than Easier to use & understand than Statistical Autocorrelation E[X(t)X(t+Statistical Autocorrelation E[X(t)X(t+ττ)])]
Fourier Transform yields GFourier Transform yields GXX(f)(f)
Autocorrelation of a Random Binary Square WaveAutocorrelation of a Random Binary Square Wave Triangle riding on a constant termTriangle riding on a constant term Fourier Transform is sincFourier Transform is sinc22 & delta function & delta function
Linear Time Invariant SystemsLinear Time Invariant Systems If LTI, H(f) exists & GIf LTI, H(f) exists & GYY(f) = G(f) = GXX(f)|H(f)|(f)|H(f)|22
RF Antenna DirectivityRF Antenna Directivity Maximum Power IntensityMaximum Power Intensity
Average Power Intensity Average Power Intensity WARNING!WARNING!
Antenna DirectivityAntenna Directivity is NOT = is NOT = Antenna Power GainAntenna Power Gain
10w in? Max of 10w radiated.10w in? Max of 10w radiated. Treat Antenna Power Gain = 1Treat Antenna Power Gain = 1 Antenna Gain = Power Gain * Directivity Antenna Gain = Power Gain * Directivity
High Gain = Narrow BeamHigh Gain = Narrow Beam
RF Antenna Gain RF Antenna Gain
Antenna Gain is what goes in RF Link Antenna Gain is what goes in RF Link EquationsEquations
In this class, unless specified otherwise, In this class, unless specified otherwise, assume antennas are properly aimed.assume antennas are properly aimed. Problems specify peak antenna gainProblems specify peak antenna gain
High Gain Antenna = Narrow BeamHigh Gain Antenna = Narrow Beam
Parabolic DirectivityParabolic Directivity s
ourc
e: e
n.w
ikip
edia
.org
/wik
i/P
arab
olic
_an
ten
na
Effective Isotrophic Radiated Power
Effective Isotrophic Radiated Power
EIRP = PEIRP = PttGGtt
Path Loss LPath Loss Ls s = (4*= (4*ππ*d/*d/λλ))22
Link AnalysisLink Analysis
Final Form of Analog Free Space Final Form of Analog Free Space RF Link EquationRF Link EquationPPrr = EIRP*G = EIRP*Grr/(L/(Lss*M*L*M*Loo) ) (watts)(watts)
Derived Digital Link EquationDerived Digital Link EquationEEbb//NNoo = EIRP*G = EIRP*Grr/(R*k*T*L/(R*k*T*Lss*M*Lo)*M*Lo)
(dimensionless)(dimensionless)
Public Enemy #1: Thermal NoisePublic Enemy #1: Thermal Noise Models for Thermal Noise: Models for Thermal Noise:
*White Noise & Bandlimited White Noise*White Noise & Bandlimited White Noise*Gaussian Distributed*Gaussian Distributed
Noise BandwidthNoise Bandwidth Actual filter that lets A watts of noise thru?Actual filter that lets A watts of noise thru? Ideal filter that lets A watts of noise thru?Ideal filter that lets A watts of noise thru? Peak value at |H(f = center freq.)|Peak value at |H(f = center freq.)|22 same? same?
Noise Bandwidth = width of ideal filter (+ frequencies).Noise Bandwidth = width of ideal filter (+ frequencies).
Noise out of an Antenna = k*TNoise out of an Antenna = k*Tantant*W*WNN
Examples of Amplified NoiseExamples of Amplified Noise Radio Static (Thermal Noise)Radio Static (Thermal Noise) Analog TV "snow"Analog TV "snow"2 seconds
of White Noise
Review of PDF's & HistogramsReview of PDF's & Histograms Probability Density Functions (PDF's), of which a Probability Density Functions (PDF's), of which a
Histograms is an estimate of shape, frequently (but not Histograms is an estimate of shape, frequently (but not always!) deal with the voltage likelihoods always!) deal with the voltage likelihoods
Time
Volts
255 point discrete time White Noise waveform
(Adjacent points are independent)
255 point discrete time White Noise waveform
(Adjacent points are independent)
time
Volts
0
Vdc = 0 v, Normalized Power = 1 watt
If true continuous time White Noise, No Predictability.
15 Bin Histogram(255 points of Uniform Noise)15 Bin Histogram(255 points of Uniform Noise)
Volts
BinCount
15 Bin Histogram(2500 points of Uniform Noise)15 Bin Histogram(2500 points of Uniform Noise)
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.
Discrete TimeWhite Noise Waveforms(255 point Exponential Noise)
Discrete TimeWhite Noise Waveforms(255 point Exponential Noise)
Time
Volts
0
15 bin Histogram(255 points of Exponential Noise)15 bin Histogram(255 points of Exponential Noise)
Volts
BinCount
Discrete TimeWhite Noise Waveforms
(255 point Gaussian Noise)Thermal Noise is Gaussian Distributed.
Discrete TimeWhite Noise Waveforms
(255 point Gaussian Noise)Thermal Noise is Gaussian Distributed.
Time
Volts
0
15 bin Histogram(255 points of Gaussian Noise)15 bin Histogram(255 points of Gaussian Noise)
Volts
BinCount
15 bin Histogram(2500 points of Gaussian Noise)15 bin Histogram(2500 points of Gaussian Noise)
Volts
BinCount
0
400
Previous waveformsPrevious waveforms
Are all 0 mean, 1 watt, White Noise Are all 0 mean, 1 watt, White Noise
0
0
Autocorrelation & Power Spectrum of White NoiseAutocorrelation & Power Spectrum of White Noise
Rx(tau)
tau seconds0
A
Gx(f)
Hertz0
A watts/Hz
The previous WhiteNoise waveforms all
have same Autocorrelation& Power Spectrum.
Autocorrelation (& Power Spectrum)
versus Probability Density Function
Autocorrelation (& Power Spectrum)
versus Probability Density Function Autocorrelation: Time axis predictabilityAutocorrelation: Time axis predictability
PDF: Voltage liklihoodPDF: Voltage liklihood Autocorrelation provides Autocorrelation provides NONO information about the information about the
PDF (& vice-versa)...PDF (& vice-versa)... ......EXCEPTEXCEPT the power will be the same...the power will be the same...
PDF second moment E[XPDF second moment E[X22] = R] = Rxx(0) = area(0) = area
under Power Spectrum = A{x(t) under Power Spectrum = A{x(t)22}} ......ANDAND the D.C. value will be related. the D.C. value will be related.
PDF first moment squared E[X] PDF first moment squared E[X]22 = constant = constant term in autocorrelation = E[X] term in autocorrelation = E[X]22δδ(f) = A{x(t)}(f) = A{x(t)}22
Satellite vs Sun, Daytime, Northern HemisphereSatellite vs Sun, Daytime, Northern Hemisphere
x
WinterSun is belowsatelliteorbital plane.
x
Fall Sun → sameplane assatellite.
x
Spring Sun→ sameplane asSatellite.
x
SummerSun is abovesatelliteorbital plane.
2013 Fall Sun Outage, Microspace's AMC-12013 Fall Sun Outage, Microspace's AMC-1
Source: www.ses.com/4551568/sun-outage-data
x
Band Limited Continuous TimeWhite Noise Waveforms
(255 point Gaussian Noise)
Band Limited Continuous TimeWhite Noise Waveforms
(255 point Gaussian Noise)
Time
Volts
0
If AC power = 4 watts & BW = 1,000 GHz...
Probability Density Function of Band Limited Gausssian White Noise
Probability Density Function of Band Limited Gausssian White Noise
fx(x)
Volts0
.399/σx = .399/2 = 0.1995Time
Volts
0
Autocorrelation & Power Spectrum of Bandlimited Gaussian White Noise
Autocorrelation & Power Spectrum of Bandlimited Gaussian White Noise
Rx(tau)
tau seconds0
Gx(f)
Hertz0
2(10-12) watts/Hz
-1000 GHz
4
500(10-15)
How does PDF, Rx(τ), & GX(f)change if +3 volts added?
(255 point Gaussian Noise)
How does PDF, Rx(τ), & GX(f)change if +3 volts added?
(255 point Gaussian Noise)
Time
Volts
3
AC power = 4 watts
0
Power Spectrum of Band Limited White Noise
Power Spectrum of Band Limited White Noise
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
Autocorrelation of Band Limited White Noise
Autocorrelation of Band Limited White Noise
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
How does PDF change if x(t) has 3 v DC?How does PDF change if x(t) has 3 v DC?
fx(x)
Volts0
σ2x = E[X2] -E[X]2 = 4
0
fx(x)
Volts3
σ2x = E[X2] -E[X]2 = 4
Band Limited Continuous TimeWhite Noise Waveforms
(255 point Gaussian Noise)
Band Limited Continuous TimeWhite Noise Waveforms
(255 point Gaussian Noise)
Time
Volts
3
AC power = 4 wattsDC power = 9 wattsTotal Power = 13 watts
0
Model for an Active DeviceModel for an Active Device
Sin
&Nin
GSin
&G(Nin + Nai)
G
Namp = kTampWn
+
+
G > 1
Noise FigureNoise Figure
F = SNRF = SNRinin/SNR/SNRoutout
WARNING! Use with caution.WARNING! Use with caution.If input noise changes, F will change. If input noise changes, F will change.
F = 1 + TF = 1 + Tampamp/T/Tinin
TTin in = 290= 290oo K (default) K (default)
Model for a Passive DeviceModel for a Passive Device
Sin
&Nin
GSin
&G(Nin + Nai)
G
Namp = kTpassiveWn
+
+
G < 1
Tpassive = (L-1)Tphysical
Temperatures...Temperatures...
Active Device (TActive Device (Tampamp) ) From Spec Sheet (may have F)From Spec Sheet (may have F)
Passive Device (TPassive Device (Tcable cable or Tor T passive passive))
(L-1)*T(L-1)*Tphysicalphysical
System Noise (Actual)System Noise (Actual)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)
System Noise (Simplified Model)System Noise (Simplified Model)
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.
SNR Considering all the noiseSNR Considering all the noiseNoise 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
SNR Considering Noise Hitting Antenna That Can Reach the Output
SNR Considering Noise Hitting Antenna That Can Reach the Output
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.
SNR of Actual System ImprovesSNR of Actual System ImprovesFiltering...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
SNR of Model WorsensSNR of Model WorsensOnly 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