1. Wireless Physical Layer Design: Diversity Y. Richard Yang 01/14/2011

2. Admin. r Homework 1 is linked on the schedule page 2

3. 3 Outline r Recap r Physical layer design

4. Why Can’t Distance Predict Channel Well? 4

5. Reason I: Shadowing r Same distance, but different levels of shadowing by large objects r It is a random, large-scale effect depending on the environment 5

6. 6 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:

7. 7 JTC Model at 1.8 GHz

8. Reason II: Multipath r Signal of same symbol taking multiple paths may interfere constructively and destructively at the receiver m small change in distance, large change in signal strength m also called small-scale fading r Signal of different symbols may interfere at the receiver 8

9. 9 r Channel characteristics change over location, frequency Multipath Effect (fixed receiver location) d1d1 d2d2 example phase difference:

10. Multipath (fixed receiver location) r Suppose at d 1 -d 2 the two waves totally destruct. (what does it mean?) r Q: can we find places where the two waves construct? 10

11. Option 1: Change Location r If receiver moves to the right by /4: d 1 ’ = d 1 + /4; d 2 ’ = d 2 - /4; -> 11 By moving a quarter of wavelength, destructive turns into constructive.

12. Option 2: Change Frequency 12 r Change frequency: r The change depends on delay spread

13. 13 Multipath Delay Spread RMS: root-mean-square

14. 14 r Channel characteristics change over time (location) Multipath Effect (moving receiver) d1d1 d2d2 example Suppose d 1 =r 0 +vt d 2 =2d-r 0 -vt d1  d2 d

15. Derivation 15 See http://www.sosmath.com/trig/Trig5/trig5/trig5.html for cos(u)-cos(v)http://www.sosmath.com/trig/Trig5/trig5/trig5.html

16. 16 Waveform v = 65 miles/h, f c = 1 GHz:f c v/c = 10 ms deep fade Q: How far does a car drive in ½ of a cycle? 10 9 * 30 / 3x10 8 = 100 Hz

17. 17 Multipath with Mobility

18. 18 Effect of Small-Scale Fading no small-scale fading small-scale fading

19. 19 signal at sender Multipath Can Spread Delay signal at receiver LOS pulse multipath pulses LOS: Line Of Sight Time dispersion: signal is dispersed over time

20. 20 signal at sender Multipath Can Spread Delay signal at receiver LOS pulse multipath pulses LOS: Line Of Sight Time dispersion: signal is dispersed over time

21. 21 signal at sender Multipath Can Cause ISI signal at receiver LOS pulse multipath pulses LOS: Line Of Sight Dispersed signal can cause interference between “neighbor” symbols, Inter Symbol Interference (ISI) Assume 300 meters delay spread, the arrival time difference is 300/3x10 8 = 1 ms  if symbol rate > 1 Ms/sec, we will have serious ISI In practice, fractional ISI can already substantially increase loss rate

22. 22 JTC Model: Delay Spread Residential Buildings

23. 23 The “Ugly” Wireless Channel path loss log (distance) Received Signal Power (dB) time location signal at receiver LOS pulse multipath pulses

24. 24 Representation of Wireless Channels r Received signal at time m is y[m], h l [m] is the strength of the l-th tap, w[m] is the background noise: r When inter-symbol interference is small: (also called flat fading channel)

25. 25 Outline r Recap r Physical layer design

26. 26 Preview: Challenges and Techniques of Wireless 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 today

27. 27 Outline r Recap r Physical layer design for flat fading m how bad is flat fading?

28. 28 Baseline: Stationary Channel y: the received signal x: the transmitted signal with amplitude a w: white noise N(0, N 0 /2), i.e., Q: error prob.?

29. 29 Baseline: Stationary Channel Error probability decays exponentially with signal-noise-ratio (SNR). y: the received signal x: the transmitted signal with amplitude a w: white noise N(0, N 0 /2) See A.2.1: http://www.eecs.berkeley.edu/~dtse/Chapters_PDF/Fundamentals_Wireless_Communication_AppendixA.pdf

30. 30 Flat Fading Channel BPSK: For fixed h, Averaged out over h, at high SNR. Assume h is Gaussian random:

31. 31 Comparison static channel flat fading channel

32. 32 Outline r Recap r Physical layer design for flat fading m how bad is flat fading? m diversity to handle flat fading

33. 33 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 exploit the added diversity in an efficient manner

34. 34 Diversity r Time: when signal is bad at time t, it may not be bad at t+  t r Space: when one position (with d1 and d2) is in deep fade, another position (with d’1 and d’2) may be not r Frequency: when one frequency is in deep fade (or has large interference), another frequency may be in good shape

35. 35 Outline r Recap r Physical layer design for flat fading m how bad is flat fading? m diversity to handle flat fading time

36. 36 Time Diversity r Time diversity can be obtained by interleaving and coding over symbols across different coherent time periods interleave coherence time

37. 37 Example: GSM 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 !

38. 38 Simplest Code: Repetition After interleaving over L coherence time periods,

39. 39 Performance

40. 40 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

41. 41 Outline r Recap r Physical layer design for flat fading m how bad is flat fading? m diversity to handle flat fading time space

42. 42 Space Diversity: Antenna Receive TransmitBoth

43. 43 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

44. 44 Outline r Recap r Physical layer design for flat fading m how bad is flat fading? m diversity to handle flat fading time space frequency

45. 45 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 Frequency Diversity: FHSS (Frequency Hopping Spread Spectrum) http://en.wikipedia.org/wiki/Hedy_Lamarr

46. 46 r Two versions m slow hopping: several user bits per frequency m fast hopping: several frequencies per user bit 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

47. 47 r Frequency selective fading and interference limited to short period r Simple implementation r Uses only small portion of spectrum at any time m explores frequency sequentially FHSS: Advantages

48. 48 Direct Sequence Spread Spectrum (DSSS) r In DSSS m one symbol is spread to multiple chips m the increased rate provides frequency diversity (explores frequency in parallel) m the number of chips is called expansion factor m examples IS-95 CDMA: 1.25 Mcps; 4,800 Sps 802.11: 11 Mcps; 1 Mbps

49. 49 Direct Sequence Spread Spectrum (DSSS) 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

50. 50 DSSS System Blocks 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

51. 51 Example: DSSS Using BPSK r Assume BPSK modulation using carrier frequency f : y(t) = A x(t)c(t) cos(2  ft) A: amplitude of signal f : carrier frequency x(t): data [+1, -1] c(t): chipping [+1, -1] r At receiver, incoming signal multiplied by c(t) m since, c(t) c(t) = 1, y(t)c(t) = A x(t) cos(2  f c t)

52. 52 DSSS r Wider spectrum to reduce frequency selective fading and interference r Provides frequency diversity un-spread signal spread signal BbBb BbBb BsBs BsBs BsBs : num. of bits in the chip * B b

53. Backup Slides

54. 54 Effects of Spreading on Interference r Assume jamming at carrier frequency f: r Then received signal y(t) + j(t) + w(t) Spreads strength of jamming signal by 1/expansion factor

55. 55 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 Effects of Spreading and Interference Intuition (high-level idea only): - multiply data x(t) by chipping sequence c(t) spreads the spectrum // this is i) to ii) - received signal: x(t) c(t) + w(t), where w(t) is noise // this is ii) to iii) - (x(t) c(t) + w(t)) c(t) = x(t) + w(t) c(t) // this is step (iv) - low pass filtering // this is iv) to v)

56. 56 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 Recap: Effects of Spreading and Interference

57. 57 Autocorrelation of Chipping Sequence r Choose chipping sequence with good autocorrelation r E.g., Barker code () used in 802.11