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Outage-Optimal Relaying In the Low SNR Regime

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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  1. Outage-Optimal RelayingIn the Low SNR Regime Salman Avestimehr and David Tse University of California, Berkeley

  2. 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)

  3. S2 R D S1 S D Relay Symmetrical Cooperative communication • Single-antenna mobiles share their antennas • - Virtual Multiple-Antenna system • Two scenarios:

  4. Outline • Explaining the Relay Scenario • Motivations • Upper bound on the outage capacity • Different protocols: Decode-Forward Amplify-Forward Bursty Amplify-Forward • Further Directions

  5. 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

  6. 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

  7. 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

  8. 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:

  9. 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

  10. 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

  11. 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

  12. 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?

  13. Summary of results MFMC upper bound Decode-Forward Amplify-Forward Bursty Amplify-Forward Outage Capacity

  14. 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

  15. 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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