06jiwoong Nikhilmbs

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Jiwoong Lee, Nikhil Shetty

University of California, Berkeley

Cooperative diversity

in a Linear Multihop Vehicular Network

Fundamentals of Wireless Communications

May 10 2006


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General Network ModelGeneral Network Model

Linear Multihop Vehicular NetworkLinear Multihop Vehicular Network

Model Assumptions

Each Station = Relay & Recipient

Relay forwards (optionally after detection) Recipient detects and uses

Two Roles of a Relay

Extend the Range of the network Provide Cooperative Diversity to neighbors

dv

dh

S1,a

S1,b

S1,c

S2,a

S2,b

S2,c

Sn,a

Sn,b

Sn,c

S0


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Simplified Diagram

Channel Modeling: Linear Multihop ChannelChannel Modeling: Linear Multihop Channel

S1 S2 SnS0x0

h1

x1

h2


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Forwarding ProtocolsForwarding Protocols

Forwarding Protocol

Whether to forward : PHY

When to forward : MAC+PHY

What to forward : PHY

Forwarding Protocol What to forward

Analog Forwarding Forwarding with no Detecting

Amplify-and-Forward

Sufficient statistic Forward*

Digital Forwarding

Necessitate Detection and Decoding

MRC Decode-and-Forward

Blind Decode-and-Forward

Compress-and-Forward


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Motivation Questions:Motivation Questions:

Setup

In a Linear Multihop Vehicular Network

With periodic broadcast traffic

Part I

Q1. What protocol is suitable

in terms of pairwise error performance

for linear multihop communications ?

Part II

Q2. Delay?

Q3. Deployment planning criterionof Basestations ?


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Part IPart I

5 Lessons in this part


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Protocol 1: AmplifyProtocol 1: Amplify--andand--ForwardForward

Lesson 1 Coherent detection is impossible

Leads to possible severe under-utilization of DOF

Protocol Definition


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AF::Statistics AnalysisAF::Statistics AnalysisProduct Channel/Cumulative NoiseProduct Channel/Cumulative Noise

Define Product Channel

Expectation

Variance

Incomplete Gamma function

Define Cumulative Noise

Expectation

Variance


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AF::Expected received SNR atAF::Expected received SNR at SSnn

Expected received SNR

10 20 30 40 50n

0.2

0.4

0.6

0.8

1

received SNR

s

2=2

s2=1

s2=0.

Lesson 2

Non-coherent detection in AF

Performance becomes worse

Lesson 3 Signal energy 0, Noise energy remains


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Protocol 2: Sufficient Statistic ForwardingProtocol 2: Sufficient Statistic Forwarding

Coherent Detection + Analog Forwarding ?

Carry the phase information

Devise a new analog protocol:

Sufficient Statistic Forwarding

Protocol Definition


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SF::Statistics AnalysisSF::Statistics AnalysisProduct Noise/Cumulative NoiseProduct Noise/Cumulative Noise

Define Product Channel

Expectation

2nd Moment

Variance

Define Cumulative Noise

Expectation

Variance


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SF::Asymptotic StatisticsSF::Asymptotic Statistics

Lesson 4

For , typical error performance is bad For , cant determine typical error

performance Approach fails

Var[w] and E[h2] both increase at the same rate

?


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SF::Deep Fade Event AnalysisSF::Deep Fade Event Analysis

Pairwise error probaiblity

Deep Fade event

Deep Fade event probability

SF::P(Deep Fade)SF::P(Deep Fade) at 1at 1stst

HopHop

PDF

CDF

S1 S2 S3S0


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PDF

CDF

SF::P(Deep Fade)SF::P(Deep Fade) at 2at 2ndnd HopHop

S1 S2 S3S0

K: Modified Bessel Function of 2ndKind


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SF::P(Deep Fade)SF::P(Deep Fade) at 3at 3rdrd HopHop

S1 S2 S3S0

PDF

CDF G: Meijer G-function


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SF::P(Deep Fade)SF::P(Deep Fade) at 4at 4thth HopHop

S1 S2 S3S0

PDF

No appropriate Math expression

CDF

No appropriate Math expression

Stop here and See the result


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SF::Deep Fade EventSF::Deep Fade Event

Deep Fade Probability in SFn=3

n=1

n=2

Also P(Deep fade) for DF

Lesson 5

SF provides the coherent-detection

SF suffers from Deep-Fade with highprobability

.......... & Summary of Part I& Summary of Part I

Summary

No hope in Analog Forwarding

Always use Digital Forwarding


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Part IIPart II


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Need for delay analysisNeed for delay analysis

Traffic data, radio station, TV broadcast.

Require conditions on traffic pattern.

Require low jitter due to jitter bufferconstraints.

Requires delay analysis to bound performance.


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Delay AnalysisDelay Analysis

System Model

Assumptions:

Reasonable penetration of technology.

Quasi-static analysis.

Perfect scheduling of nodes.

Within a pair, nodes can hear each other well.


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Comparing two schemesComparing two schemes

Blind decode-and-forward (BDF)

Do not consider previous transmissions.

If packet received correctly forward ahead

else drop and neglect. Maximal Ratio Combining decode-and-forward

(MRC)

Collect energy over multiple transmissions ofthe same packet.

Maximal Ratio Combining of data.


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Use of outage probabilitiesUse of outage probabilities

Information sent in short packets.

Cannot code over a long time.

Channel is constant over packet transmissiontime.

Hence, outage probabilities are used.

Probability that the detection is corrupted at thenth transmission = outage probability for thedetection scheme over n transmissions.


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Outage ProbabilitiesOutage Probabilities

For MRC-DF,

High SNR Approximation

For BDF,


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Outage ProbabilitiesOutage Probabilities


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Delay AnalysisDelay Analysis

Every non-colliding transmission is an attempt.

If a_i is the number of attempts required at theith hop then total number of attempts

Total delay = Total attempts * TransmissionDelay (Assuming ideal MAC)


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Analysis of number of attemptsAnalysis of number of attempts

Attempt is successful if at least one node inadjacent group receives correctly.

Probability that both nodes fail to receive is

square of the outage probabilities.

Thus we end up with the cumulative

distribution.


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Characteristic of aCharacteristic of a


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ResultsResults forfor Blind decodeBlind decode

For Blind decode, since each transmission has anindependent and identical fade, pok= po1

k


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High SNR results for MRCHigh SNR results for MRC


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Delay plot (exact)Delay plot (exact)

Delays are higher for BDF at low SNR highoutage probabilities.


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Plots for Standard Deviation (exact)Plots for Standard Deviation (exact)

Jitters are widely different at low SNR highoutage probabilities.


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ConclusionsConclusions for Part 2for Part 2

High SNR Blind decode is as good as MRC.

Low SNR huge difference in the jittersexperienced.

Use of MRC - A robust system.

A Design for the worst case.

Deployment of base stations determined bythe jitter that you can absorb.

Any MAC can be analyzed on top if we can

characterize the number of successful attemptsper unit time.


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SummarySummary of the Talkof the Talk

Amplify and Forward not good.

Sufficient statistic forwarding better but stillnot good enough.

Digital Forwarding better than AnalogForwarding in multihop scenario.

Within Digital Forwarding, BDF as good as MRC-

DF at high SNR.

MRC-DF is suggested for a robust system.

In short, paper provides a guide to engineeringdesign for transport of real-time traffic onhighway networks.

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