1. Wireless Networks (PHY): Design for Diversity Y. Richard Yang 9/18/2012

2. 2 Admin r Assignment 1 questions m am_usrp_710.dat was sampled at 256K m Rational Resampler not Rational Resampler Base r Assignment 1 office hours m Wed 11-12 @ AKW 307A m Others to be announced later today

3. Recap: Demodulation of Digital Modulation r Setting m Sender uses M signaling functions g 1 (t), g 2 (t), …, g M (t), each has a duration of symbol time T m Each value of a symbol has a corresponding signaling function m The received x maybe corrupted by additive noise r Maximum likelihood demodulation m picks the m with the highest P{x|g m } r For Gaussian noise, 3

4. Recap: Matched Filter Demodulation/Decoding r Project (by matching filter/correlatio n) each signaling function to bases r Project received signal x to bases r Compute Euclidean distance, and pick closest 4 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 ]

5. Recap: Wireless Channels r Non-additive effect of distance d on received signaling function m free space r Fluctuations at the same distance 5

6. Recap: Reasons r Shadowing m Same distance, but different levels of shadowing by large objects m It is a random, large-scale effect depending on the environment r Multipath m Signal of same symbol taking multiple paths may interfere constructively and destructively at the receiver also called small-scale fading 6

7. 7 Multipath Effect (A Simple Example) d1d1 d2d2 phase difference: Assume transmitter sends out signal cos(2  f c t)

8. Multipath Effect (A Simple Example) r Suppose at d 1 -d 2 the two waves totally destruct, i.e., if receiver moves to the right by /4: d 1 ’ = d 1 + /4; d 2 ’ = d 2 - /4; 8 constructive Discussion: how far is /4? What are implications?

9. Multipath Effect (A Simple Example): Change Frequency 9 r Suppose at f the two waves totally destruct, i.e. r Smallest change to f for total construct:  (d1-d2)/c is called delay spread.

10. 10 Multipath Delay Spread RMS: root-mean-square

11. 11 Multipath Effect (moving receiver) d1d1 d2d2 example Suppose d 1 =r 0 +vt d 2 =2d-r 0 -vt d1  d2 d

12. Derivation 12 See http://www.sosmath.com/trig/Trig5/trig5/trig5.html for cos(u)-cos(v)http://www.sosmath.com/trig/Trig5/trig5/trig5.html

13. Derivation 13 See http://www.sosmath.com/trig/Trig5/trig5/trig5.html for cos(u)-cos(v)http://www.sosmath.com/trig/Trig5/trig5/trig5.html

14. Derivation 14 See http://www.sosmath.com/trig/Trig5/trig5/trig5.html for cos(u)-cos(v)http://www.sosmath.com/trig/Trig5/trig5/trig5.html

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. Derivation 16 See http://www.sosmath.com/trig/Trig5/trig5/trig5.html for cos(u)-cos(v)http://www.sosmath.com/trig/Trig5/trig5/trig5.html

17. Derivation 17 See http://www.sosmath.com/trig/Trig5/trig5/trig5.html for cos(u)-cos(v)http://www.sosmath.com/trig/Trig5/trig5/trig5.html

18. 18 Waveform v = 65 miles/h, f c = 1 GHz:f c v/c = 10 ms deep fade 10 9 * 30 / 3x10 8 = 100 Hz Q: how far does the car move between two deep fade?

19. 19 Multipath with Mobility

20. 20 Outline r Admin and recap r Wireless channels m Intro m Shadowing m Multipath space, frequency, time deep fade delay spread

21. 21 signal at sender Multipath Can Disperse Signal signal at receiver LOS pulse multipath pulses LOS: Line Of Sight Time dispersion: signal is dispersed over time

22. 22 JTC Model: Delay Spread Residential Buildings

23. 23 signal at sender Dispersed Signal -> 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 us  if symbol rate > 1 Ms/sec, we will have ISI In practice, fractional ISI can already substantially increase loss rate

24. 24 r Channel characteristics change over location, time, and frequency small-scale fading Large-scale fading time power Summary of Progress: Wireless Channels path loss log (distance) Received Signal Power (dB) frequency signal at receiver LOS pulse multipath pulses

25. 25 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)

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 Wireless channels r Physical layer design m design for flat fading how bad is flat fading?

28. 28 Background For standard Gaussian white noise N(0, 1), Prob. density function:

29. 29 Background

30. 30 Baseline: Additive Gaussian Noise N(0, N 0 /2) =

31. 31 Baseline: Additive Gaussian Noise

32. r Conditional probability density of y(T), given sender sends 1: r Conditional probability density of y(T), given sender sends 0: 32

33. Baseline: Additive Gaussian Noise r Demodulation error probability: 33 assume equal 0 or 1

34. 34 Baseline: Error Probability Error probability decays exponentially with signal-noise-ratio (SNR). See A.2.1: http://www.eecs.berkeley.edu/~dtse/Chapters_PDF/Fundamentals_Wireless_Communication_AppendixA.pdf

35. 35 Flat Fading Channel BPSK: For fixed h, Averaged out over h, at high SNR. Assume h is Gaussian random:

36. 36 Comparison static channel flat fading channel

37. Backup Slides