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

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

3 Admin r Assignment 1 questions r Assignment 1 office hours m Thursday AKW 307A

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 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 Recap: Impact of Channel on Decisions

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

8 Recap: Impacts of Channel static channel flat fading channel

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

MHz 124 channels (200 kHz) downlink MHz 124 channels (200 kHz) uplink frequency time GSM TDMA frame GSM time-slot (normal burst) ms 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 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 Simplest Code: Repetition After interleaving over L coherence time periods,

17 Performance

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 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 Space Diversity: Antenna Receive TransmitBoth

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 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 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 Sequential Frequency Diversity: FHSS (Frequency Hopping Spread Spectrum)

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 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 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 Bluetooth Architecture

28 Bluetooth Radio Link r Bluetooth shares the same freq. range as r Radio link is the most expensive part of a communication chip and hence chose simpler FHSS 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 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 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 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 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 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 : 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 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 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 DSSS Encoding user data d(t) chipping sequence c(t) resulting signal X = tbtb tctc t b : bit period t c : chip period

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

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): 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 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 42

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

45 DSSS/BPSK Decoding

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 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 ISI Effects

49 ISI Effects for Matched Filter Decoding

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]

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 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 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 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 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 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 s[0]s[1] s[2] s[3]s[4] 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 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 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!

Viterbi Algorithm: Summary r Invented in 1967 r Utilized in CDMA, GSM, , 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

Backup Slides

62 ISI Effects

63 Inquiry Hopping

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

65 Bluetooth Links

66 Bluetooth Packet Format Header

67 Multiple-Slot Packet