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

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 AKW 307A m Others to be announced later today

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

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 ]

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

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

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?

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 Multipath Delay Spread RMS: root-mean-square

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

Derivation 12 See for cos(u)-cos(v)

Derivation 13 See for cos(u)-cos(v)

Derivation 14 See for cos(u)-cos(v)

Derivation 15 See for cos(u)-cos(v)

Derivation 16 See for cos(u)-cos(v)

Derivation 17 See for cos(u)-cos(v)

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 Multipath with Mobility

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

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 JTC Model: Delay Spread Residential Buildings

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

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

29 Background

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

31 Baseline: Additive Gaussian Noise

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

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

34 Baseline: Error Probability Error probability decays exponentially with signal-noise-ratio (SNR). See A.2.1:

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

36 Comparison static channel flat fading channel

37 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

38 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

39 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

40 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

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

42 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 !

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

44 Performance

45 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

46 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

47 Space Diversity: Antenna Receive TransmitBoth

48 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

49 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

50 r Discrete changes of carrier frequency m sequence of frequency changes determined via pseudo random number sequence m used in , 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)

51 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

52 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

53 Direct Sequence Spread Spectrum (DSSS) r One symbol is spread to multiple chips m the number of chips is called the expansion factor m examples : 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 symbols/s –how many chips per symbol?

54 Direct Sequence Spread Spectrum (DSSS) r The increased rate provides frequency diversity (explores frequency in parallel)

55 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 dP/df f sender dP/df f

56 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

DSSS Encoding Data: [1 -1 ] 57 chip:

58 DSSS Encoding user data d(t) chipping sequence c(t) resulting signal X = tbtb tctc t b : bit period t c : chip period

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

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

DSSS Decoding (BPSK): Another View 61 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

62 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?

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 63

64 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)

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

66 DSSS/BPSK Decoding

67 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

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