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

1. Review Chapter 1.1 - 1.4Review Chapter 1.1 - 1.4
Problems: 1.1a-c, 1.4, 1.5, 1.9Problems: 1.1a-c, 1.4, 1.5, 1.9

2.  Review Chapter 1.5 - 1.8
Problems: 1.13 - 1.16, 1.20
 Quiz #1

3. Quiz #1

4.  Read: 5.1 - 5.3
 Problems: 5.1 - 5.3
 Quiz #1

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

9.  Digital Analog
 Binary M-ary
 Wide Band Narrow Band

10.  Digital M-Ary System
 M = 8 x 8 x 4 = 256
Source:
January 1994
Scientific American

11. Source:
January 1994
Scientific American

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

20. tau (samples)
Rxx
0

21. Time
Volts
23 points
0

22. tau samples
Rxx
0
23

23. Rx(τ)
tau seconds0
A
Gx(f)
Hertz0
A watts/Hz
Rx(τ) & Gx(f) form a
Fourier Transform pair.
They provide the same info
in 2 different formats.

24. Rx(tau)
tau seconds0
A
Gx(f)
Hertz0
A watts/Hz
Average Power = ∞
D.C. Power = 0
A.C. Power = ∞

25. Rx(tau)
tau seconds0
A
Gx(f)
Hertz0
A watts/Hz
-WN Hz
2AWN
1/(2WN)
Average Power = 2AWN watts
D.C. Power = 0
A.C. Power = 2AWN watts

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

27. X
=
Cos(2πΔf)

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

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

32. source:en.wikipedia.org/wiki/Parabolic_antenna

33.  EIRP = PtGt
 Path Loss Ls= (4*π*d/λ)2

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.

39. Volts
Bin
Count

40. Volts
Bin
Count
Time
Volts
0

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.

42. Time
Volts
0

43. Volts
Bin
Count

44. Time
Volts
0

45. Volts
Bin
Count

46. Volts
Bin
Count
0
400

47.  Are all 0 mean, 1 watt, White Noise
0
0

48. Rx(tau)
tau seconds0
A
Gx(f)
Hertz0
A watts/Hz
The previous White
Noise waveforms all
have same Autocorrelation
& Power Spectrum.

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

50. x
Winter
Sun is
below
satellite
orbital
plane.
x
Fall Sun
→ same
plane as
satellite.
x
Spring Sun
→ same
plane as
Satellite.
x
Summer
Sun is
above
satellite
orbital
plane.

51. Source: www.ses.com/4551568/sun-outage-data
x

52. Time
Volts
0
If AC power = 4 watts &
BW = 1,000 GHz...

53. fx(x)
Volts0
.399/σx = .399/2 = 0.1995
Time
Volts
0

54. Rx(tau)
tau seconds0
Gx(f)
Hertz0
2(10-12
) watts/Hz
-1000 GHz
4
500(10-15
)

55. Time
Volts
3
AC power = 4 watts
0

56. 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

57. 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

58. fx(x)
Volts0
σ2
x = E[X2
] -E[X]2
= 4
0
fx(x)
Volts3
σ2
x = E[X2
] -E[X]2
= 4

59. Time
Volts
3
AC power = 4 watts
DC power = 9 watts
Total Power = 13 watts
0

60. Sin
&
Nin
GSin
&
G(Nin + Nai)
G
Namp = kTampWn
+
+
G > 1

61.  F = SNRin/SNRout
 WARNING! Use with caution.
If input noise changes, F will change.
 F = 1 + Tamp/Tin
 Tin= 290o
K (default)

62. Sin
&
Nin
GSin
&
G(Nin + Nai)
G
Namp = kTpassiveWn
+
+
G < 1
Tpassive = (L-1)Tphysical

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