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

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Recap: Demodulation of Digital Modulation Setting Sender uses M signaling functions g1(t), g2(t), …, gM(t), each has a duration of symbol time T Each value of a symbol has a corresponding signaling function The received x maybe corrupted by additive noise Maximum likelihood demodulation picks the m with the highest P{x|gm} For Gaussian noise,

Recap: Matched Filter Demodulation/Decoding Project (by matching filter/correlation) each signaling function to bases Project received signal x to bases Compute Euclidean distance sin(2πfct) cos(2πfct) [a01,b01] [a10,b10] [a00,b00] [a11,b11] [ax,bx]

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

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

Multipath Effect (A Simple Example) Assume transmitter sends out signal cos(2 fc t) d1 d2 phase difference:

Multipath Effect (A Simple Example) Suppose at d1-d2 the two waves totally destruct, i.e., if receiver moves to the right by /4: d1’ = d1 + /4; d2’ = d2 - /4; constructive Discussion: how far is /4? What are implications?

Multipath Effect (A Simple Example): Change Frequency Suppose at f the two waves totally destruct, i.e. If we look at a different frequency f’: the two waves construct (d1-d2)/c is called delay spread. Discussion: how far is ½ c/(d1-d2)?

Multipath Delay Spread RMS: root-mean-square

Multipath Effect (moving receiver) example d d1 d2 Suppose d1=r0+vt d2=2d-r0-vt d1d2

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

Waveform v = 65 miles/h, fc = 1 GHz: fc v/c = 109 * 30 / 3x108 = 100 Hz 10 ms deep fade Q: how far does the car move between two deep fade?

Multipath with Mobility

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

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

JTC Model: Delay Spread Residential Buildings

Dispersed Signal -> ISI Dispersed signal can cause interference between “neighbor” symbols, Inter Symbol Interference (ISI) Assume 300 meters delay spread, the arrival time difference is 300/3x108 = 1 us if symbol rate > 1 Ms/sec, we will have ISI In practice, fractional ISI can already substantially increase loss rate signal at sender LOS pulse multipath pulses signal at receiver LOS: Line Of Sight

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

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

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 use fade margin—increase power or reduce distance today bit/packet error rate at deep fade diversity equalization; spread-spectrum; OFDM; directional antenna ISI

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

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

Baseline: Previous Additive Gaussian Noise

Baseline: Additive Gaussian Noise

Baseline: Additive Gaussian Noise Conditional probability density of y(T), given sender sends 1: Similarly, conditional probability density of y(T), given sender sends 0:

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

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

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

Comparison flat fading channel static channel

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

Main Storyline Today Communication over a flat fading channel has poor performance due to significant probability that channel is in a deep fade Reliability is increased by providing more resolvable signal paths that fade independently Name of the game is how to exploit the added diversity in an efficient manner

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

Outline Recap Wireless channels Physical layer design design for flat fading how bad is flat fading? diversity to handle flat fading time

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

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

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

Performance

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

Outline Recap Wireless channels Physical layer design design for flat fading how bad is flat fading? diversity to handle flat fading time space

Space Diversity: Antenna Receive Transmit Both

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

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

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

Frequency Diversity: FHSS (Frequency Hopping Spread Spectrum) Two versions slow hopping: several user bits per frequency fast hopping: several frequencies per user bit tb user data 1 1 1 t f f1 f2 f3 td slow hopping (3 bits/hop) t td f f1 f2 f3 fast hopping (3 hops/bit) t tb: bit period td: dwell time

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

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

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

DSSS Wider spectrum to reduce frequency selective fading and interference Provides frequency diversity un-spread signal spread signal Bb Bs : num. of bits in the chip * Bb dP/df f sender dP/df f

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

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

DSSS Encoding tb: bit period tc: chip period tb user data d(t) 1 -1 X chipping sequence c(t) -1 1 1 -1 1 -1 1 -1 1 1 -1 1 -1 1 = resulting signal -1 1 1 -1 1 -1 1 1 -1 -1 1 -1 1 -1 tb: bit period tc: chip period

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

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

DSSS Decoding (BPSK): Another View compute correlation for each bit time bit time 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; c: chipping seq. s: modulating sinoid

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

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

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

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

DSSS/BPSK Decoding

Why Does DSSS Work: A Spectrum Perspective sender dP/df dP/df f ii) user signal broadband interference narrowband interference i) f receiver dP/df dP/df dP/df iii) iv) v) f f f 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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