1. Wireless PHY: Digital Demodulation and Wireless Channels Y. Richard Yang 09/13/2012

2. 2 Outline r Admin and recap r Digital demodulation r Wireless channels

3. 3 Admin r Assignment 1 posted

4. 4 r Demodulation r Low pass filter and FIR r Convolution Theorem r Digital modulation/demodulation r ASK, FSK, PSK r General representation Recap

5. Recap: g i () for BPSK 5 r 1: m g 1 (t) = cos(2πf c t) t in [0, T] r 0: m g 0 (t) = -cos(2πf c t) t in [0, T] r Note: g 1 (t) = -g 0 (t) cos(2πf c t)[0, T] 1 g 1 (t)g 0 (t)

6. Recap: Signaling Functions g i () for QPSK 6 r 11: m cos(2πf c t + π/4) t in [0, T] r 10: m cos(2πf c t + 3π/4) t in [0, T] r 00: m cos(2πf c t - 3π/4) t in [0, T] r 01: m cos(2πf c t - π/4) t in [0, T] Q I 11 01 10 00

7. Recap: QPSK Signaling Functions as Sum of cos(2πf c t), sin(2πf c t) 7 r 11: cos(π/4 + 2πf c t) t in [0, T] -> cos(π/4) cos(2πf c t) + -sin(π/4) sin(2πf c t) r 10: cos(3π/4 + 2πf c t) t in [0, T] -> cos(3π/4) cos(2πf c t) + -sin(3π/4) sin(2πf c t) r 00: cos(- 3π/4 + 2πf c t) t in [0, T] -> cos(3π/4) cos(2πf c t) + sin(3π/4) sin(2πf c t) r 01: cos(- π/4 + 2πf c t) t in [0, T] -> cos(π/4) cos(2πf c t) + sin(π/4) sin(2πf c t) sin( 2πf c t ) 11 00 10 cos( 2πf c t ) [cos(π/4), sin(π/4)] 01 [cos(3π/4), sin(3π/4)] [cos(3π/4), -sin(3π/4)] [-sin(π/4), cos(π/4)] We call sin(2πf c t) and cos(2πf c t) the bases.

8. Recap: Demodulation/Decoding 8 r Considered a simple on-off setting: sender uses a single signaling function g(), and can have two actions m send g() or m nothing (send 0) r How does receiver use the received sequence x(t) in [0, T] to detect if sends g() or nothing?

9. Recap: Design 9 r Streaming algorithm: use all data points in [0, T] m As each sample x i comes in, multiply it by a factor h T-i-1 and accumulate to a sum y m At time T, makes a decision based on the accumulated sum at time T: y[T] xTxT x2x2 x1x1 x0x0 h0h0 h1h1 h2h2 hThT ****

10. Determining the Best h 10 where w is noise, Design objective: maximize peak pulse signal- to-noise ratio

11. Determining the Best h 11 Assume Gaussian noise, one can derive Using Fourier Transform and Convolution Theorem:

12. Determining the Best h 12 Apply Schwartz inequality By considering

13. Determining the Best h 13

14. Determining Best h to Use 14 xTxT x2x2 x1x1 x0x0 gTgT g2g2 g1g1 g0g0 **** xTxT x2x2 x1x1 x0x0 h0h0 h1h1 h2h2 hThT ****

15. Matched Filter Decision is called Matched filter. Example 15 decision time

16. Summary of Progress 16 r After this “complex” math, the implementation/interpretation is actually the following quite simple alg: m precompute auto correlation: m compute the correlation between received x and signaling function g, denoted as m if is closer to output sends g m else output sends nothing

17. Applying Scheme to BPSK 17 r Consider g 1 alone, compute, check if close to : | - | r Consider g 0 alone, compute, check if close to : | - | r Pick closer m if | - | - | pick 1 m else pick 0 cos(2πf c t)[0, T] 1 g 1 (t)g 0 (t)

18. Applying Scheme to BPSK 18 r since g 0 = -g 1 m = - r rewrite as m if | - | - | pick 1 m else pick 0 cos(2πf c t)[0, T] 1 g 1 (t)g 0 (t)

19. Interpretation 19 r For any signal s, computes the coordinate (projection) of s when using g 1 as a base m cleaner if g1 is normalized (i.e., scale g1 by sqrt of ), but we do not worry about it yet g 1 =cos(2πf c t)[0, T] =-

20. Applying Scheme to QPSK: Attempt 1 20 r Consider g 00 alone, compute … r Consider g 01 alone, compute … r Consider g 10 alone, compute … r Consider g 11 alone, compute … r Issues m Complexity: need to compute M correlation, where M is number of signaling functions Think of 64-QAM m Objective the previous scheme is defined for a single signaling function, does it work for M?

21. Decoding for QPSK using bases 21 r 4 signaling functions g 00 (), g 01 (), g 10 (), g 11 () r For each signaling function, computes correlation with the bases (cos(), sin()), e.g., m g 00 : [a 00, b 00 ] m Q: Where did we see a similar computation format for computing a 00, b 00 ? r For received signal x, computes a x = and b x = (how many correlations do we do now?)

22. QPSK Demodulation/Decoding 22 sin( 2πf c t ) cos( 2πf c t ) [a 01,b 01 ] [a 10,b 10 ] [a 00,b 00 ] [a 11,b 11 ] [a x,b x ] Q: how to decode?

23. Look into Noise 23 r Assume sender sends g m (t) [0, T] r Receiver receives x(t) [0, T] r Consider one sample where w[i] is noise r Assume white noise, i.e., prob w[i] = z is

24. 24 Likelihood r What is the likelihood (prob.) of observing x[i]? m it is the prob. of noise being w[i] = x[i] – g[i] r What is the likelihood (prob.) of observing the whole sequence x? m the product of the probabilities

25. Likelihood Detection 25 r Suppose we know r Maximum likelihood detection picks the m with the highest P{x|g m }. r From the expression We pick m with the lowest ||x-g m || 2

26. Back to QPSK 26

27. QPSK Demodulation/Decoding 27 sin( 2πf c t ) cos( 2πf c t ) [a 01,b 01 ] [a 10,b 10 ] [a 00,b 00 ] [a 11,b 11 ] [a x,b x ] Q: what does maximum likelihood det pick?

28. General Matched Filter Detection: Implementation for Multiple Sig Func. 28 r Basic idea m consider each g m [0,T] as a point (with coordinates) in a space m compute the coordinate of the received signal x[0,T] m check the distance between g m [0,T] and the received signal x[0,T] m pick m* that gives the lowest distance value

29. Computing Coordinates 29 r Pick orthogonal bases {f 1 (t), f 2 (t), …, f N (t)} for {g 1 (t), g 2 (t), …, g M (t)} r Compute the coordinate of g m [0,T] as c m = [c m1, c m2, …, c mN ], where r Compute the coordinate of the received signal x[0,T] as x = [x 1, x 2, …, x N ] r Compute the distance between r and c m every cm and pick m* that gives the lowest distance value

30. Example: Matched Filter => Correlation Detector 30 received signal x

31. 31 BPSK vs QPSK BPSK QPSK f c : carrier freq. R b : freq. of data 10dB = 10; 20dB =100 111000 01 A t

32. BPSK vs QPSK r A major metric of modulation performance is spectral density (SD) r Q: what is the SD of BPSK vs that of QPSK? r Q: Why would any one use BPSK, given higher QAM? 32 Spectral Density = bit rate ------------------- width of spectrum used

33. Context r Previous demodulation considers only additive noise, and does not consider wireless channel’s effects m Wireless channels more than add some noise to a signaling function g(t) r We next study its effects 33

34. 34 Outline r Admin and recap r Digital demodulation r Wireless channels

35. Signal Propagation

36. 36 r Isotropic radiator: a single point m equal radiation in all directions (three dimensional) m only a theoretical reference antenna r Radiation pattern: measurement of radiation around an antenna zy x z yx ideal isotropic radiator Antennas: Isotropic Radiator Q: how does power level decrease as a function of d, the distance from the transmitter to the receiver?

37. 37 Free-Space Isotropic Signal Propagation r In free space, receiving power proportional to 1/d² (d = distance between transmitter and receiver) r Suppose transmitted signal is cos(2  ft), the received signal is m P r : received power m P t : transmitted power m G r, G t : receiver and transmitter antenna gain m (=c/f): wave length Sometime we write path loss in log scale: Lp = 10 log(Pt) – 10log(Pr)

38. 38 Log Scale for Large Span dB = 10 log(times) Slim/Gates ~100B Obama ~10M ~10K 1000 times 40 dB 10,000 times 30 dB 10,000 x 1,000 40 + 30 = 70 dB

39. 39 Path Loss in dB dB = 10 log(times) source 10 W d1 1 mW 1 uW 1000 times 40 dB 10,000 times 30 dB 10,000 x 1,000 40 + 30 = 70 dB power d2

40. 40 dBm (Absolute Measure of Power) dBm = 10 log (P/1mW) source 10 W d1 1 mW 1 uW 1000 times 40 dB 10,000 times 30 dB 10,000 x 1,000 40 + 30 = 70 dB power d2 40 dBm -30 dBm

41. 41 Number in Perspective (Typical #)

42. 42 Exercise: 915MHz WLAN (free space) r Transmit power (Pt) = 24.5 dBm r Receive sensitivity = -64.5 dBm r Receiving distance (Pr) = r Gt=Gr=1

43. 43 Two-ray Ground Reflection Model r Single line-of-sight is not typical. Two paths (direct and reflect) cancel each other and reduce signal strength m P r : received power m P t : transmitted power m G r, G t : receiver and transmitter antenna gain m h r, h t : receiver and transmitter height

44. 44 Exercise: 915MHz WLAN (Two-ray ground reflect) r Transmit power (Pt) = 24.5 dBm r Receive sensitivity = -64.5 dBm r Receiving distance (Pr) = r Gt=Gr=hr=ht=1

45. 45 Real Antennas r Real antennas are not isotropic radiators r Some simple antennas: quarter wave /4 on car roofs or half wave dipole /2  size of antenna proportional to wavelength for better transmission/receiving /4 /2 Q: Assume frequency 1 Ghz, = ?

46. 46 Figure for Thought: Real Measurements

47. 47 r Receiving power additionally influenced by m shadowing (e.g., through a wall or a door) m refraction depending on the density of a medium m reflection at large obstacles m scattering at small obstacles m diffraction at edges reflection scattering diffraction shadow fading refraction Signal Propagation: Complexity

48. 48 Signal Propagation: Complexity Details of signal propagation are very complicated We want to understand the key characteristics that are important to our understanding

49. 49 Outline r Admin and recap r Digital demodulation r Wireless channels m Intro m shadowing

50. 50 Shadowing r Signal strength loss after passing through obstacles r Same distance, but different levels of shadowing: It is a random, large-scale effect depending on the environment

51. Example Shadowing Effects 51 i.e. reduces to ¼ of signal 10 log(1/4) = -6.02

52. Example Shadowing Effects 52 i.e. reduces to ¼ of signal 10 log(1/4) = -6.02

53. 53 JTC Indoor Model for PCS: Path Loss A: an environment dependent fixed loss factor (dB) B: the distance dependent loss coefficient, d : separation distance between the base station and mobile terminal, in meters L f : a floor penetration loss factor (dB) n: the number of floors between base station and mobile terminal Shadowing path loss follows a log-normal distribution (i.e. L is normal distribution) with mean:

54. 54 JTC Model at 1.8 GHz

55. 55 Outline r Admin and recap r Digital demodulation r Wireless channels m Intro m Shadowing m Multipath

56. 56 r Signal can take many different paths between sender and receiver due to reflection, scattering, diffraction Multipath

57. 57 r Example: reflection from the ground or building Multipath Example: Outdoor ground

58. 58 Multipath Effect (A Simple Example) d1d1 d2d2 phase difference: Assume transmitter sends out signal cos(2  f c t)

59. Multipath Effect (A Simple Example) r Where do the two waves totally destruct? r Where do the two waves totally construct? 59

60. Sensitivity: Change Location r If receiver moves to the right by /4: d 1 ’ = d 1 + /4; d 2 ’ = d 2 - /4; -> 60 Implication: By moving a quarter of wavelength, destructive turns into constructive. Assume f = 1G, how far do we move?

61. Backup Slides 61

62. 62 Dipole: Radiation Pattern of a Dipole http://www.tpub.com/content/neets/14182/index.htm http://en.wikipedia.org/wiki/Dipole_antenna