2. ECEN5533 Modern Communications Theory Lecture #119 August 2014 Dr. George Scheets www.okstate.edu/elec-engr/scheets/ecen5533 n Review Chapter 1.1 - 1.4 Problems: 1.1a-c, 1.4, 1.5, 1.9

3. ECEN5533 Modern Communications Theory Lecture #221 August 2014 Dr. George Scheets n Review Chapter 1.5 - 1.8 Problems: 1.13 - 1.16, 1.20 n Quiz #1 u Local: Tuesday, 4 September, Lecture 6 u Off Campus DL: < 11 September

4. ECEN5533 Modern Communications Theory Lecture #326 August 2014 Dr. George Scheets n Review Appendix A Problems: Quiz #1, 2011-2013 n Quiz #1 u Local: Thursday, 4 September, Lecture 6 u Off Campus DL: < 11 September

5. ECEN5533 Modern Communications Theory Lecture #428 August 2014 n Read: 5.1 - 5.3 n Problems: 5.1 - 5.3 n Quiz #1 u Local: Thursday, 4 September, Lecture 6 u Off Campus DL: < 11 September www.okstate.edu/elec-engr/scheets/ecen5533/

6. ECEN5533 Modern Communications Theory Lecture #52 September 2014 Dr. George Scheets n Read 5.4 & 5.5 n Problems 5.7 & 5.12 n Quiz #1 u Local: Thursday, 4 September, Lecture 6 u Off Campus DL: < 11 September u Strictly Review (Chapter 1) Full Period, Open Book & Notes

7. Grading n In Class: 2 Quizzes, 2 Tests, 1 Final Exam Open Book & Open Notes WARNING! Study for them like they’re closed book! n Graded Homework: 2 Design Problems n Ungraded Homework: Assigned most every class Not collected Solutions Provided Payoff: Tests & Quizzes

8. Why work the ungraded Homework problems? n An Analogy: Commo Theory vs. Football n Reading the text = Reading a playbook n Working the problems = playing in a scrimmage n Looking at the problem solutions = watching a scrimmage n Quiz = Exhibition Game n Test = Big Game

9. To succeed in this class... n Show some self-discipline!! Important!! For every hour of class...... put in 1-2 hours of your own effort. n PROFESSOR'S LAMENT If you put in the time You should do fine. If you don't, You likely won't.

10. Course Emphasis n Digital Analog n Binary M-ary n Wide Band Narrow Band

11. French Optical Telegraph Source: January 1994 Scientific American nDnDnDnDigital M-Ary System uMuMuMuM = 8 x 8 x 4 = 256

12. French System Map Source: January 1994 Scientific American

13. Trend is to Digital n Phonograph → Compact Disk n Analog NTSC TV → Digital HDTV n Video Cassette Recorder → Digital Video Disk n AMPS Wireless Phone → 4G LTE n Terrestrial Commercial AM & FM Radio n Last mile Wired Phones

14. Review... n Fourier Transforms X(f) Table 2-4 & 2-5 n Power Spectrum Given X(f) n Power Spectrum Using Autocorrelation u Use Time Average Autocorrelation

15. Review of Autocorrelation n Autocorrelations deal with predictability over time. I.E. given an arbitrary point x(t1), how predictable is x(t1+tau)? time Volts t1 tau

16. Review of Autocorrelation n 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

17. 255 point discrete time White Noise waveform (Adjacent points are independent) time Volts 0 V dc = 0 v, Normalized Power = 1 watt If true continuous time White Noise, no predictability.

18. R xx (0) n The sequence x(n) x(1) x(2) x(3)... x(255) n multiply it by the unshifted sequence x(n+0) x(1) x(2) x(3)... x(255) n to get the squared sequence x(1) 2 x(2) 2 x(3) 2... x(255) 2 n Then take the time average [x(1) 2 +x(2) 2 +x(3) 2... +x(255) 2 ]/255

19. R xx (1) n The sequence x(n) x(1) x(2) x(3)... x(254) x(255) n multiply it by the shifted sequence x(n+1) x(2) x(3) x(4)... x(255) n to get the sequence x(1)x(2) x(2)x(3) x(3)x(4)... x(254)x(255) n Then take the time average [x(1)x(2) +x(2)x(3) +... +x(254)x(255)]/254

20. Review of Autocorrelation n If the average is positive... u Then x(t) and x(t+tau) tend to be alike Both positive or both negative n If the average is negative u Then x(t) and x(t+tau) tend to be opposites If one is positive the other tends to be negative n If the average is zero u There is no predictability

21. Autocorrelation Estimate of Discrete Time White Noise tau (samples) Rxx 0

22. 255 point Noise Waveform (Low Pass Filtered White Noise) Time Volts 23 points 0

23. Autocorrelation Estimate of Low Pass Filtered White Noise tau samples Rxx 0 23

24. Autocorrelation & Power Spectrum of C.T. White Noise Rx(τ)Rx(τ) tau seconds 0 A G x (f) Hertz0 A watts/Hz Rx(τ) & Gx(f) form a Fourier Transform pair. They provide the same info in 2 different formats.

25. Autocorrelation & Power Spectrum of White Noise R x (tau) tau seconds 0 A G x (f) Hertz0 A watts/Hz Average Power = ∞ D.C. Power = 0 A.C. Power = ∞

26. Autocorrelation & Power Spectrum of Band Limited C.T. White Noise R x (tau) tau seconds 0 A G x (f) Hertz0 A watts/Hz -W N Hz 2AW N 1/(2W N ) Average Power = 2AW N watts D.C. Power = 0 A.C. Power = 2AW N watts

27. Autocorrelations n Time Average Autocorrelation u Easier to use & understand than Statistical Autocorrelation E[X(t)X(t+τ)] u Fourier Transform yields G X (f) n Autocorrelation of a Random Binary Square Wave u Triangle riding on a constant term u Fourier Transform is sinc 2 & delta function n Linear Time Invariant Systems u If LTI, H(f) exists & G Y (f) = G X (f)|H(f)| 2

28. Cosine times a Noisy Serial Bit Stream X = Cos(2πΔf)

29. LTI If input is x(t) = Acos(ωt) output must be of form y(t) = Bcos(ωt+θ) Filter x(t) y(t)

30. RF Antenna Directivity n Maximum Power Intensity Average Power Intensity n WARNING! Antenna Directivity is NOT = Antenna Power Gain 10w in? Max of 10w radiated. n Treat Antenna Power Gain = 1 n Antenna Gain = Power Gain * Directivity n High Gain = Narrow Beam

31. Directional Antennas

32. RF Antenna Gain n Antenna Gain is what goes in RF Link Equations n In this class, unless specified otherwise, assume antennas are properly aimed. u Problems specify peak antenna gain n High Gain Antenna = Narrow Beam

33. Parabolic Directivity source: en.wikipedia.org/wiki/Parabolic_antenna

34. Effective Isotrophic Radiated Power n EIRP = P t G t n Path Loss L s = (4*π*d/λ) 2

35. Link Analysis n Final Form of Analog Free Space RF Link Equation P r = EIRP*G r /(L s *M*L o ) (watts) n Derived Digital Link Equation E b /N o = EIRP*G r /(R*k*T*L s *M*Lo) (dimensionless)

36. Public Enemy #1: Thermal Noise n Models for Thermal Noise: *White Noise & Bandlimited White Noise *Gaussian Distributed n Noise Bandwidth u Actual filter that lets A watts of noise thru? u Ideal filter that lets A watts of noise thru? u Peak value at |H(f = center freq.)| 2 same? F Noise Bandwidth = width of ideal filter (+ frequencies). n Noise out of an Antenna = k*T ant *W N

37. Examples of Amplified Noise n Radio Static (Thermal Noise) n Analog TV "snow" 2 seconds of White Noise

38. Review of PDF's & Histograms n 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

39. 255 point discrete time White Noise waveform (Adjacent points are independent) time Volts 0 V dc = 0 v, Normalized Power = 1 watt If true continuous time White Noise, No Predictability.

40. 15 Bin Histogram (255 points of Uniform Noise) Volts Bin Count

41. Volts Bin Count Time Volts 0

42. 15 Bin Histogram (2500 points of Uniform Noise) 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.

43. Discrete Time White Noise Waveforms (255 point Exponential Noise) Time Volts 0

44. 15 bin Histogram (255 points of Exponential Noise) Volts Bin Count

45. Discrete Time White Noise Waveforms (255 point Gaussian Noise) Thermal Noise is Gaussian Distributed. Time Volts 0

46. 15 bin Histogram (255 points of Gaussian Noise) Volts Bin Count

47. 15 bin Histogram (2500 points of Gaussian Noise) Volts Bin Count 0 400

48. Previous waveforms n Are all 0 mean, 1 watt, White Noise 0 0

49. Autocorrelation & Power Spectrum of White Noise R x (tau) tau seconds 0 A G x (f) Hertz0 A watts/Hz The previous White Noise waveforms all have same Autocorrelation & Power Spectrum.

50. Autocorrelation (& Power Spectrum) versus Probability Density Function n Autocorrelation: Time axis predictability n PDF: Voltage liklihood n Autocorrelation provides NO information about the PDF (& vice-versa)... n...EXCEPT the power will be the same... PDF second moment E[X 2 ] = R x (0) = area under Power Spectrum = A{x(t) 2 } n...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

51. Satellite vs Sun, Daytime, Northern Hemisphere 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.

52. 2013 Fall Sun Outage, Microspace's AMC-1 Source: www.ses.com/4551568/sun-outage-data x

53. Band Limited Continuous Time White Noise Waveforms (255 point Gaussian Noise) Time Volts 0 If AC power = 4 watts & BW = 1,000 GHz...

54. Probability Density Function of Band Limited Gausssian White Noise f x (x) Volts0.399/σ x =.399/2 = 0.1995 Time Volts 0

55. Autocorrelation & Power Spectrum of Bandlimited Gaussian White Noise R x (tau) tau seconds 0 G x (f) Hertz0 2(10 -12 ) watts/Hz -1000 GHz 4 500(10 -15 )

56. How does PDF, R x (τ), & G X (f) change if +3 volts added? (255 point Gaussian Noise) Time Volts 3 AC power = 4 watts 0

57. Power Spectrum of Band Limited White Noise G x (f) Hertz0-1000 GHz 9 G x (f) Hertz0 2(10 -12 ) watts/Hz -1000 GHz 2(10 -12 ) watts/Hz No DC 3 vdc → 9 watts DC Power

58. Autocorrelation of Band Limited White Noise R x (tau) tau seconds 0 13 9 R x (tau) tau seconds 0 4 500(10 -15 ) No DC 3 vdc → 9 watts DC Power

59. How does PDF change if x(t) has 3 v DC? f x (x) Volts0 σ 2 x = E[X 2 ] -E[X] 2 = 4 0 f x (x) Volts3 σ 2 x = E[X 2 ] -E[X] 2 =4

60. Band Limited Continuous Time White Noise Waveforms (255 point Gaussian Noise) Time Volts 3 AC power = 4 watts DC power = 9 watts Total Power = 13 watts 0

61. Model for an Active Device S in & N in GS in & G(N in + N ai ) G N amp = kT amp W n + + G > 1

62. Noise Figure n F = SNR in /SNR out u WARNING! Use with caution. If input noise changes, F will change. u WARNING! Use with caution. If input noise changes, F will change. n F = 1 + T amp /T in u T in = 290 o K (default)

63. Model for a Passive Device S in & N in GS in & G(N in + N ai ) G N amp = kT passive W n + + G < 1 T passive = (L-1)T physical

64. Temperatures... n Active Device (T amp ) u From Spec Sheet (may have F) n Passive Device (T cable or T passive ) u (L-1)*T physical

65. System Noise (Actual) Noise Striking Antenna = N o W Thermal = kT surroundings 1000*10 9 = k*290*1000*10 9 = 4.00 n watts Much of this noise doesn't exit system. Blocked by system filters. kT ant W N = ??? System Cable + Amp Noise exiting Antenna that will exit the System = kT ant 6*10 6 = 12.42*10 -15 watts Noise Antenna "Sees" = Noise exiting antenna = N o W Antenna ≈ kT ant 1000*10 9 = 2.07 n watts (T antenna = 150 Kelvin)

66. System Noise (Simplified Model) System Cable + Amp Noise Actually Exiting Antenna = Noise Antenna "Sees" ≠ Noise Exiting Antenna that will exit the System = kT ant W N = 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.

67. SNR Considering all the noise Noise Seen by Antenna = N o W Antenna = kT ant 1000*10 9 = 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

68. SNR Considering Noise Hitting Antenna That Can Reach the Output Noise seen by Antenna TCRO = N o W N = kT ant 6*10 6 = 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.

69. SNR of Actual System Improves 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

70. SNR of Model Worsens 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