Wireless Networks (PHY): Design for Diversity

Wireless Networks (PHY): Design for Diversity

Y. Richard Yang

9/18/2012

2

Admin

Assignment 1 questions am_usrp_710.dat was sampled at 256K Rational Resampler not Rational Resampler

Base

Assignment 1 office hours Wed 11-12 @ AKW 307A Others to be announced later today

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,

3

Recap: Matched Filter Demodulation/Decoding

Project (by matching filter/correlation) each signaling function to bases

Project received signal x to bases

Compute Euclidean distance, and pick closest

4

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

5

d

cdtftfEd

)]/(2cos[),(

Recap: Reasons

Shadowing 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

6

7

Multipath Effect (A Simple Example)

d1d2

1

11 ][2cos

d

tfcd

ft2cos

2121 22)(2 21dd

c

ddfff c

dcd

2

22 ][2cos

d

tfcd

phase difference:

Assume transmitter sends out signal cos(2 fc t)

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;

8

integer2121

dd

c

ddf

2121 22

dd

c

ddf

constructive

Discussion: how far is /4? What are implications?

Multipath Effect (A Simple Example): Change Frequency

9

Suppose at f the two waves totally destruct, i.e.

Smallest change to f for total construct:

(d1-d2)/c is called delay spread.

2121 22

dd

c

ddf

integer2121

dd

c

ddf

10

Multipath Delay SpreadRMS: root-mean-square

11

Multipath Effect(moving receiver)

d1d2

1

11 ][2cos

d

tfcd

ft2cos

example

2

22 ][2cos

d

tfcd

Suppose d1=r0+vt

d2=2d-r0-vtd1d2

d

Derivation

12

])[sin(])[2sin(2

])[2sin(])[2sin(2

])[2sin(])[2sin(2

])[2sin(])[2sin(2

)sin()sin(2

])[2cos(])[2cos(

0

0

0

0000

020020

00

2

2)2(

22

2

][2][2

2

][2][2

2

cvrd

cvf

cd

cdvtr

cd

cdvtr

cd

cvtrdvtr

cvtrdvtr

tftftftf

cvtrd

cvtr

ttf

ftf

ftf

ftf

tftf

cvtrd

cvtr

cvtrd

cvtr

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

Derivation

13

])[sin(])[2sin(2

])[2sin(])[2sin(2

])[2sin(])[2sin(2

])[2sin(])[2sin(2

)sin()sin(2

])[2cos(])[2cos(

0

0

0

0000

020020

00

2

2)2(

22

2

][2][2

2

][2][2

2

cvrd

cvf

cd

cdvtr

cd

cdvtr

cd

cvtrdvtr

cvtrdvtr

tftftftf

cvtrd

cvtr

ttf

ftf

ftf

ftf

tftf

cvtrd

cvtr

cvtrd

cvtr

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

Derivation

14

])[sin(])[2sin(2

])[2sin(])[2sin(2

])[2sin(])[2sin(2

])[2sin(])[2sin(2

)sin()sin(2

])[2cos(])[2cos(

0

0

0

0000

020020

00

2

2)2(

22

2

][2][2

2

][2][2

2

cvrd

cvf

cd

cdvtr

cd

cdvtr

cd

cvtrdvtr

cvtrdvtr

tftftftf

cvtrd

cvtr

ttf

ftf

ftf

ftf

tftf

cvtrd

cvtr

cvtrd

cvtr

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

Derivation

15

])[sin(])[2sin(2

])[2sin(])[2sin(2

])[2sin(])[2sin(2

])[2sin(])[2sin(2

)sin()sin(2

])[2cos(])[2cos(

0

0

0

0000

020020

00

2

2)2(

22

2

][2][2

2

][2][2

2

cvrd

cvf

cd

cdvtr

cd

cdvtr

cd

cvtrdvtr

cvtrdvtr

tftftftf

cvtrd

cvtr

ttf

ftf

ftf

ftf

tftf

cvtrd

cvtr

cvtrd

cvtr

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

Derivation

16

])[sin(])[2sin(2

])[2sin(])[2sin(2

])[2sin(])[2sin(2

])[2sin(])[2sin(2

)sin()sin(2

])[2cos(])[2cos(

0

0

0

0000

020020

00

2

2)2(

22

2

][2][2

2

][2][2

2

cvrd

cvf

cd

cdvtr

cd

cdvtr

cd

cvtrdvtr

cvtrdvtr

tftftftf

cvtrd

cvtr

ttf

ftf

ftf

ftf

tftf

cvtrd

cvtr

cvtrd

cvtr

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

Derivation

17

])[sin(])[2sin(2

])[2sin(])[2sin(2

])[2sin(])[2sin(2

])[2sin(])[2sin(2

)sin()sin(2

])[2cos(])[2cos(

0

0

0

0000

020020

00

2

2)2(

22

2

][2][2

2

][2][2

2

cvrd

cvf

cd

cdvtr

cd

cdvtr

cd

cvtrdvtr

cvtrdvtr

tftftftf

cvtrd

cvtr

ttf

ftf

ftf

ftf

tftf

cvtrd

cvtr

cvtrd

cvtr

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

18

Waveform

v = 65 miles/h, fc = 1 GHz: fc v/c =

10 ms

deep fade

])[sin(])[2sin(2 02cvrd

cvf

cd ttf

109 * 30 / 3x108 = 100 Hz

Q: how far does the car move between two deep fade?

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Multipath with Mobility

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Outline

Admin and recap Wireless channels

Intro Shadowing Multipath

• space, frequency, time deep fade• delay spread

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signal at sender

Multipath Can Disperse Signal

signal at receiver

LOS pulsemultipathpulses

LOS: Line Of Sight

Time dispersion: signal is dispersed over time

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JTC Model: Delay Spread

Residential Buildings

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signal at sender

Dispersed Signal -> ISI

signal at receiver

LOS pulsemultipathpulses

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 300/3x108 = 1 us if symbol rate > 1 Ms/sec, we will have ISI

In practice, fractional ISI can already substantially increase loss rate

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Channel characteristics change over location, time, and frequency

small-scale fading

Large-scalefading

time

power

Summary of Progress: Wireless Channels

path loss

log (distance)

Received Signal Power (dB)

frequency

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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)

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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

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Outline

Recap Wireless channels Physical layer design

design for flat fading• how bad is flat fading?

28

Background

For standard Gaussian white noise N(0, 1), Prob. density function: 2

2

21)(

w

ewf

2/2/121

22

)()1( xxx exQe

29

Background

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Baseline: Additive Gaussian Noise

N(0, N0/2) =

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Baseline: Additive Gaussian Noise

Baseline: Additive Gaussian Noise

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

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

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Baseline: Additive Gaussian Noise

Demodulation error probability:

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assume equal 0 or 1

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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

2/2/121

22

)()1( xxx exQe

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

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