1. Wireless Networks (PHY): Design for Diversity Y. Richard Yang 9/20/2012

2. 2 Outline r Admin and recap r Design for diversity r Design to handle ISI

3. 3 Admin r Assignment 1 questions r Assignment 1 office hours m Thursday 3-4 @ AKW 307A

4. 4 r Channel characteristics change over location, time, and frequency small-scale fading Large-scale fading time power Recap: Wireless Channels path loss log (distance) Received Signal Power (dB) frequency signal at receiver LOS pulse multipath pulses

5. 5 Outline r Recap r Wireless channels r Physical layer design m design for flat fading how bad is flat fading? diversity to handle flat fading

6. 6 Recap: Impact of Channel on Decisions

7. 7 Recap: Impact of Channel Averaged out over h, at high SNR. Assume h is Gaussian random:

8. 8 Recap: Impacts of Channel static channel flat fading channel

9. 9 Outline r Recap r Wireless channels r Physical layer design m design for flat fading how bad is flat fading? diversity to handle flat fading

10. 10 Main Storyline Today r Communication over a flat fading channel has poor performance due to significant probability that channel is in a deep fade r Reliability is increased by providing more resolvable signal paths that fade independently r Name of the game is how to find and efficiently exploit the paths

11. 11 Where to Find Diversity? r Time: when signal is bad at time t, it may not be bad at t+  t r Space: when one position is in deep fade, another position may be not r Frequency: when one frequency is in deep fade (or has large interference), another frequency may be in good shape

12. 12 Outline r Recap r Wireless channels r Physical layer design m design for flat fading how bad is flat fading? diversity to handle flat fading –time

13. 13 Time Diversity r Time diversity can be obtained by interleaving and coding over symbols across different coherent time periods interleave coherence time

14. 14 12 3 4 5 6 78 935-960 MHz 124 channels (200 kHz) downlink 890-915 MHz 124 channels (200 kHz) uplink frequency time GSM TDMA frame GSM time-slot (normal burst) 4.615 ms 546.5 µs 577 µs tailuser dataTrainingS guard space Suser datatail guard space 3 bits57 bits26 bits 57 bits1 13 Example: GSM Time Structure S: indicates data or control

15. 15 Example: GSM Bit Assignments r Amount of time diversity limited by delay constraint and how fast channel varies r In GSM, delay constraint is 40 ms (voice) r To get better diversity, needs faster moving vehicles !

16. 16 Simplest Code: Repetition After interleaving over L coherence time periods,

17. 17 Performance

18. 18 Beyond Repetition Coding r Repetition coding gets full diversity, but sends only one symbol every L symbol times r We can use other codes, e.g. Reed-Solomon code

19. 19 Outline r Recap r Wireless channels r Physical layer design m design for flat fading how bad is flat fading? diversity to handle flat fading –time –space

20. 20 Space Diversity: Antenna Receive TransmitBoth

21. 21 User Diversity: Cooperative Diversity r Different users can form a distributed antenna array to help each other in increasing diversity r Interesting characteristics: m users have to exchange information and this consumes bandwidth m broadcast nature of the wireless medium can be exploited m we will revisit the issue later in the course

22. 22 Outline r Recap r Wireless channels r Physical layer design m design for flat fading how bad is flat fading? diversity to handle flat fading –time –space –frequency

23. 23 r Discrete changes of carrier frequency m sequence of frequency changes determined via pseudo random number sequence m used in 802.11, GSM, etc r Co-inventor: Hedy Lamarr m patent# 2,292,387 issued on August 11, 1942 m intended to make radio-guided torpedoes harder for enemies to detect or jam m used a piano roll to change between 88 frequencies Sequential Frequency Diversity: FHSS (Frequency Hopping Spread Spectrum) http://en.wikipedia.org/wiki/Hedy_Lamarr

24. 24 r Two versions m slow hopping: several user bits per frequency m fast hopping: several frequencies per user bit Sequential Frequency Diversity: FHSS (Frequency Hopping Spread Spectrum) user data slow hopping (3 bits/hop) fast hopping (3 hops/bit) 01 tbtb 011t f f1f1 f2f2 f3f3 t tdtd f f1f1 f2f2 f3f3 t tdtd t b : bit periodt d : dwell time

25. 25 r Frequency selective fading and interference limited to short period r Simple implementation r what is a major issue in design? r Uses only small portion of spectrum at any time m explores frequency sequentially m used in simple devices such Bluetooth FHSS: Advantages

26. 26 Bluetooth Design Objective r Design objective: a cable replacement technology m 1 Mb/s m range 10+ meters m single chip radio + baseband (means digital part) low power low price point (target price $5 or lower)

27. 27 Bluetooth Architecture

28. 28 Bluetooth Radio Link r Bluetooth shares the same freq. range as 802.11 r Radio link is the most expensive part of a communication chip and hence chose simpler FHSS 2.402 GHz + k MHz, k=0, …, 78 1,600 hops per second m A type of FSK modulation 1 Mb/s symbol rate m transmit power: 1mW

29. 29 Bluetooth Physical Layer r Nodes form piconet: one master and upto 7 slaves m Each radio can function as a master or a slave r The slaves follow the pseudorandom jumping sequence of the master A piconet

30. 30 Piconet Formation r Master hopes at a universal frequency hopping sequence (32 frequencies) m announce the master and sends Inquiry msg r Joining slave: m jump at a much lower speed m after receiving an Inquiry message, wait for a random time, then send a request to the master r The master sends a paging message to the slave to join it

31. 31 Outline r Recap r Wireless channels r Physical layer design m design for flat fading how bad is flat fading? diversity to handle flat fading –time –space –frequency »sequential »parallel

32. 32 Direct Sequence Spread Spectrum (DSSS) r Basic idea: increase signaling function alternating rate to expand frequency spectrum (explores frequency in parallel) f c : carrier freq. R b : freq. of data 10dB = 10; 20dB =100

33. 33 Direct Sequence Spread Spectrum (DSSS) r Approach: One symbol is spread to multiple chips m the number of chips is called the expansion factor m examples 802.11: 11 Mcps; 1 Msps –how may chips per symbol? IS-95 CDMA: 1.25 Mcps; 4,800 sps –how may chips per symbol? WCDMA: 3.84 Mcps; suppose 7,500 sps –how many chips per symbol?

34. 34 dP/df f f sender Effects of Spreading un-spread signal spread signal BbBb BbBb BsBs BsBs BsBs : num. of bits in the chip * B b

35. 35 DSSS Encoding/Decoding: An Operating View X user data chipping sequence modulator radio carrier spread spectrum signal transmit signal transmitter demodulator received signal radio carrier X chipping sequence receiver low pass products decision data sampled sums correlator

36. 36 DSSS Encoding user data d(t) chipping sequence c(t) resulting signal 1 11 1 1 1 111 X = tbtb tctc t b : bit period t c : chip period 11 1 11 1 1

37. DSSS Encoding Data: [1 -1 ] 37 chip: 11 1 11 1 1 1 1

38. DSSS Decoding Data: [1 -1] 38 1 1 1 chip: 11 1 11 1 11 1 Trans chips 11 1 Chip seq: inner product: 6 decision:1 1 1 1 11 1 decoded chips -6

39. DSSS Decoding with noise Data: [1 -1] 39 1 1 1 chip: 11 1 11 1 11 1 Trans chips 11 1 Chip seq: inner product: 4 decision:1 1 1 1 11 decoded chips -2

40. DSSS Decoding (BPSK): Matched Filter 40 s: modulating sinoid compute correlation for each bit time c: chipping seq. y: received signal take N samples of a bit time sum = 0; for i =0; { sum += y[i] * c[i] * s[i] } if sum >= 0 return 1; else return -1; bit time

41. 41 Outline r Recap r Wireless channels r Physical layer design m design for flat fading how bad is flat fading? diversity to handle flat fading –time –space –frequency »DSSS: why it works?

42. Assume no DSSS r Consider narrowband interference r Consider BPSK with carrier frequency fc r A “worst-case” scenario m data to be sent x(t) = 1 m channel fades completely at fc (or a jam signal at fc) m then no data can be recovered 42

43. 43 Why Does DSSS Work: A Decoding Perspective r Assume BPSK modulation using carrier frequency f : m A: amplitude of signal m f : carrier frequency m x(t): data [+1, -1] m c(t): chipping [+1, -1] y(t) = A x(t)c(t) cos(2  ft)

44. 44 Add Noise/Jamming/Channel Loss r Assume noise at carrier frequency f: r Received signal: y(t) + w(t)

45. 45 DSSS/BPSK Decoding

46. 46 dP/df f i) dP/df f ii) sender user signal broadband interference narrowband interference dP/df f iii) dP/df f iv) receiver f v) dP/df Why Does DSSS Work: A Spectrum Perspective i) → ii): multiply data x(t) by chipping sequence c(t) spreads the spectrum ii) → iii): received signal: x(t) c(t) + w(t), where w(t) is noise iii) → iv): (x(t) c(t) + w(t)) c(t) = x(t) + w(t) c(t) iv) → v) : low pass filtering

47. 47 Roadmap: Challenges and Techniques of Wireless PHY Design Performance affected Mitigation techniques Shadow fading (large-scale fading) Fast fading (small-scale, flat fading) Delay spread (small-scale fading) received signal strength bit/packet error rate at deep fade ISI use fade margin— increase power or reduce distance diversity equalization; spread- spectrum; OFDM; directional antenna

48. 48 ISI Effects

49. 49 ISI Effects for Matched Filter Decoding 123412341234

50. 50 ISI Problem Formulation r The problem: given received y[m], m = 1, …, L+2, where L is frame size and assume 3 delay taps (it is easy to generalize to D taps): y[1] = x[1] h0 + w[1] y[2] = x[2]h0 + x[1] h1 + w[2] y[3] = x[3]h0 + x[2]h1 + x[3] h2 + w[3] y[4] = x[4]h0 + x[3]h1 + x[2] h2 + w[4] y[5] = x[5]h0 + x[4]h1 + x[3] h2 + w[5] … y[L] = x[L]h0 + x[L-1]h1 + x[L-2]h2 + w[L] y[L+1] = x[L]h1 + x[L-1]h2 + w[L+1] y[L+2] = x[L]h2 + w[L+2] determine x[1], x[2], … x[L] http://en.wikipedia.org/wiki/Andrew_Viterbi

51. 51 ISI Equalization: Given y, what is x? y y[1] = x[1] h0 + w[1] y[2] = x[2]h0 + x[1] h1 + w[2] y[3] = x[3]h0 + x[2]h1 + x[3] h2 + w[3] y[4] = x[4]h0 + x[3]h1 + x[2] h2 + w[4] y[5] = x[5]h0 + x[4]h1 + x[3] h2 + w[5] … y[L] = x[L]h0 + x[L-1]h1 + x[L-2]h2 + w[L] y[L+1] = x[L]h1 + x[L-1]h2 + w[L+1] y[L+2] = x[L]h2 + w[L+2] x

52. 52 Solution Technique r Maximum likelihood detection: m if the transmitted sequence is x[1], …, x[L], then there is a likelihood we observe y[1], y[2], …, y[L+2] m we choose the x sequence such that the likelihood of observing y is the largest y[1] = x[1] h0 + w[1] y[2] = x[2]h0 + x[1] h1 + w[2] y[3] = x[3]h0 + x[2]h1 + x[3] h2 + w[3] y[4] = x[4]h0 + x[3]h1 + x[2] h2 + w[4] y[5] = x[5]h0 + x[4]h1 + x[3] h2 + w[5] … y[L] = x[L]h0 + x[L-1]h1 + x[L-2]h2 + w[L] y[L+1] = x[L]h1 + x[L-1]h2 + w[L+1] y[L+2] = x[L]h2 + w[L+2]

53. 53 Likelihood r For given sequence x[1], x[2], …, x[L] r Assume white noise, i.e, prob. w = z is r What is the likelihood (prob.) of observing y[1]? m it is the prob. of noise being w[1] = y[1] – x[1] h0

54. 54 Likelihood r The likelihood of observing y[2] m it is the prob. of noise being w[2] = y[2] – x[2]h0 – x[1]h1, which is r The overall likelihood of observing the whole y sequence (y[1], …, y[L+2]) is the product of the preceding probabilities

55. 55 One Technique: Enumeration foreach sequence (x[1], …, x[L]) compute the likelihood of observing the y sequence pick the x sequence with the highest likelihood Question: what is the computational complexity?

56. 56 Viterbi Algorithm r Objective: avoid the enumeration of the x sequences r Key observation: the memory (state) of the wireless channel is only 3 (or generally D for D taps) r Let s[0], s[1], … be the states of the channel as symbols are transmitted m s[0]: initial state---empty m s[1]: x[1] is transmitted, two possibilities: 0, or 1 m s[2]: x[2] is transmitted, four possibilities: 00, 01, 10, 11 m s[3]: x[3] is transmitted, eight possibilities: 000, 001, …, 111 m s[4]: x[4] is transmitted, eight possibilities: 000, 001, …, 111 r We can construct a state transition diagram r If we know the x sequence we can construct s, and vice versa

57. 57 s[0]s[1] s[2] s[3]s[4] 0 1 00 01 10 11 000 010 100 110 001 011 101 111 000 010 100 110 001 011 101 111 x[1]=0 x[1]=1 x[2]=0 x[2]=1 x[2]=0 x[2]=1 x[3]=0 x[3]=1 x[3]=0 x[3]=1 x[3]=0 x[3]=1 x[3]=0 x[3]=1 observe y[1]observe y[2]observe y[3] observe y[4] prob. of observing y[4]: w[4] = y[4]-x[4]h0-x[3]h1-x[2]h2 prob. of observing y[1]: w[1] = y[1]-x[1]h0 prob. of observing y[2]: w[2] = y[2]-x[1]h0-x[2]h1

58. 58 Viterbi Algorithm r Each path on the state-transition diagram corresponds to a x sequence m each edge has a probability m the product of the probabilities on the edges of a path corresponds to the likelihood that we observe y if x is the sequence sent r Then the problem becomes identifying the path with the largest product of probabilities

59. 59 Viterbi Algorithm: Largest Product to Shortest Path  If we take -log of the probability of each edge, the problem becomes identifying the shortest path problem!

60. Viterbi Algorithm: Summary r Invented in 1967 r Utilized in CDMA, GSM, 802.11, Dial-up modem, and deep space communications r Also commonly used in m speech recognition, m computational linguistics, and m bioinformatics 60 Original paper: Andrew J. Viterbi. Error bounds for convolutional codes and an asymptotically optimum decoding algorithm, April 1967 http://ieeexplore.ieee.org/search/wrapper.jsp?arnumber=1054010

61. Backup Slides

62. 62 ISI Effects

63. 63 Inquiry Hopping

64. 64 The Bluetooth Link Establishment Protocol FS: Frequency Synchronization DAC: Device Access Code IAC: Inquiry Access Code

65. 65 Bluetooth Links

66. 66 Bluetooth Packet Format Header

67. 67 Multiple-Slot Packet