Outage optimal relaying in the low snr regime
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Outage-Optimal Relaying In the Low SNR Regime. Salman Avestimehr and David Tse University of California, Berkeley. Diversity. Unreliability of fading channels - Diversity gain. Transmit Diversity - Creates more diversity Diversity gain=2.

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Outage-Optimal Relaying In the Low SNR Regime

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Outage optimal relaying in the low snr regime

Outage-Optimal RelayingIn the Low SNR Regime

Salman Avestimehr

and

David Tse

University of California, Berkeley


Diversity

Diversity

  • Unreliability of fading channels

  • - Diversity gain

  • Transmit Diversity

  • - Creates more diversity

  • Diversity gain=2

  • Transmit diversity: may not be practical

  • - most handsets (size)

  • - wireless sensor network (size, power)


Cooperative communication

S2

R

D

S1

S

D

Relay

Symmetrical

Cooperative communication

  • Single-antenna mobiles share their antennas

  • - Virtual Multiple-Antenna system

  • Two scenarios:


Outline

Outline

  • Explaining the Relay Scenario

  • Motivations

  • Upper bound on the outage capacity

  • Different protocols:

    Decode-Forward

    Amplify-Forward

    Bursty Amplify-Forward

  • Further Directions


The relay scenario

The Relay Scenario

R

g

h2

D

S

h1

  • Rayleigh fading channels + AWGN noise

  • Slow fading

  • Half-Duplex constraint

  • Channel State Information available at the receiver only

  • Average power constraint (P) on both S and R


The relay scenario cont

The Relay Scenario (cont.)

  • The problem is hard: Look at different regimes

  • Two Regimes of interest: high SNR, low SNR

  • High SNR (Laneman et. al. & Azarian et. al.):

    Diversity-Multiplexing tradeoff

  • Low SNR

    - CDMA

    - Sensor Networks


Why low snr

Why Low SNR

S

D

h

  • The capacity loss from fading is more significant at low SNR

The impact of diversity (e=0.01)

The impact of fading

  • The impact of diversity on capacity is more significant at low SNR


Outage capacity

Outage Capacity

S

D

h

  • nats/s (fixed h)

  • Outage event at rate R:

  • For outage probability, e:

  • Outage Capacity:

  • For MISO channel:

  • For example at =0.01:


Upper bound on the performance

Upper Bound on the Performance?

R

R

  • Min-cut max-flow bound:

  • The corresponding bound on the outage capacity,

P

g

g

h2

h2

bP

D

D

S

S

h1

h1

(1-b)P


Different protocols

Different Protocols

  • Decode-Forward:

  • First Time-slot: Source transmits the vector of encoded data.

  • Second time-slot: If relay was able to decode data, it will re-encode it and transmit it.

  • Not optimal, why?

    cut set:

:Exploits Diversity

MFMC upper bound

Decode-Forward


Amplify forward

Amplify-Forward

  • First Time-slot: Source transmits the vector of encoded data, x.

  • Second time-slot: Relay retransmits the received vector by amplifying.

No Diversity !

Why?

MFMC upper bound

Decode-Forward

Amplify-Forward


A better protocol

A Better Protocol ?

  • Bursty Amplify-Forward:

    - To have less noisy observation at the Relay, source transmits rarely (a fraction of the time) but with high power:

    be large

    - In order to be power efficient, we should pick a such that the effective rate is small:

    be small

    - Can we pick such a ?

    Yes, because at low outage probability is small.

    - The achievable rate of this scheme:

    - Why optimal?


Summary of results

Summary of results

MFMC upper bound

Decode-Forward

Amplify-Forward

Bursty Amplify-Forward

Outage Capacity


Further directions

Further directions

  • Full CSI (both Rx and Tx know the channel):

  • Allocate some power for beam forming

  • Can also be achieved by BAF + beam forming

R

P

g

h2

bP

D

S

h1

(1-b)P


The gain from full csi

The gain from Full CSI

  • With full CSI:

    the gain is small.

  • The reason is that in the previous optimization, only small amount of power will be allocated for beam-forming (6%).

  • In MISO the gain is 3dB, as all the power is used for beam-forming.


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