Professor Dr Arshad Abbas Khan
PhD UEC TOKYO JAPAN
Post-Doc Georgia Tech
UNITED STATES OF AMERICA
Research Chair SCHOOL OF ELECTRICAL ENGINEERING OSU
UNITED STATES
5. Read 5.4 & 5.5
Problems 5.7 & 5.12
Quiz #1
Local: Thursday, 28 September, Lecture 6
Off Campus DL: < 11 October
Strictly Review (Chapter 1)
Full Period, Open Book & Notes
6. In Class: 2 Quizzes, 2 Tests, 1 Final Exam
Open Book & Open Notes
WARNING!
Study for them like they’re closed book!
Graded Homework: 2 Design Problems
Ungraded Homework:
Assigned most every class
Not collected
Solutions Provided
Payoff: Tests & Quizzes
7. 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
8. Show some self-discipline!! Important!!
For every hour of class...
... put in 1-2 hours of your own effort.
PROFESSOR'S GUIDE
If you put in the time
You 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
12. 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
13. Fourier Transforms X(f)
Table 2-4 & 2-5
Power Spectrum
Given X(f)
Power Spectrum
Using Autocorrelation
Use Time Average Autocorrelation
14. Autocorrelations deal with predictability over
time. I.E. given an arbitrary point x(t1), how
predictable is x(t1+tau)?
time
Volts
t1
tau
15. Autocorrelations deal with predictability over
time. I.E. given an arbitrary waveform x(t), how
alike is a shifted version x(t+τ)?
Volts
τ
16. time
Volts
0
Vdc = 0 v, Normalized Power = 1 watt
If true continuous time White Noise,
no predictability.
17. • 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 sequence
x(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
18. • 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 sequence
x(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
19. • 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 opposites
If one is positive the other tends to be negative
• If the average is zero
– There is no predictability
26. 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
28. If input is x(t) = Acos(ωt)
output must be of form
y(t) = Bcos(ωt+θ)
Filter
x(t) y(t)
29. Maximum Power Intensity
Average Power Intensity
WARNING!
Antenna Directivity is NOT =
Antenna Power Gain
10w in? Max of 10w radiated.
Treat Antenna Power Gain = 1
Antenna Gain = Power Gain * Directivity
High Gain = Narrow Beam
30.
31. 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
34. Final Form of Analog Free Space
RF Link Equation
Pr = EIRP*Gr/(Ls*M*Lo) (watts)
Derived Digital Link Equation
Eb/No = EIRP*Gr/(R*k*T*Ls*M*Lo)
(dimensionless)
35. • 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
36. Radio Static (Thermal Noise)
Analog TV "snow"
2 seconds
of White Noise
37. 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
38. time
Volts
0
Vdc = 0 v, Normalized Power = 1 watt
If true continuous time White Noise,
No Predictability.
41. Volts
Bin
Count
0
0
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.
49. 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]2
δ(f) = A{x(t)}2
63. Active Device (Tamp)
From Spec Sheet (may have F)
Passive Device (Tcableor Tpassive)
(L-1)*Tphysical
64. 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 = ???
System
Cable + 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)
65. System
Cable + Amp
Noise Actually Exiting Antenna
= Noise Antenna "Sees"
≠ Noise Exiting Antenna
that will exit the System
= kTantWN
= 12.42*10-15
watts
Antenna
Power
Gain = 1
Signal Power in =
Signal Power out
This is the
model we use.
We don't worry about
noise that won't make the output.
66. Noise Seen by Antenna
= NoWAntenna
= kTant1000*109
= 2.07 n watts
Signal Power Picked Up by Antenna
= 10-11
watts
System
Cable + Amp
SNR at "input" of antenna = 10-11
/(4*10-9
) = 0.0025
SNR at output of antenna = 10-11
/(2.07*10-9
) = 0.004831
SNR at System Output = 43.63
67. Noise seen by Antenna TCRO
= NoWN
= kTant6*106
= 12.42 femto watts
Signal Power Picked Up by Antenna
= 10-11
watts
System
Cable + Amp
SNR at output of antenna = 805.2
SNR at System Output = 43.63
This is the
noise we're
worried about.
68. Filtering...
Removes noise power outside signal BW
Lets the signal power through
System
Cable + Amp
SNR at Antenna Input = 0.0025
SNR at Antenna Output = 0.004831
SNR at System Output = 43.67
69. Only considers input noise that is in
the signal BW & can reach the output.
Cable & electronics dump in more
noise.
System
Cable + Amp
SNR at antenna output = 805.2
SNR at System Output = 43.67
