Cooperative Communication: Diversity, Freedom and Energy

1
Cooperative Communication Diversity, Freedom
and Energy

• David Tse
• Wireless Foundations
• U.C. Berkeley
• MSRI Workshop
• April 11, 2006

Joint work with Salman Avestimehr.
2
Optimal Relaying

• Capacity of general relay channels open for
  almost 40 years.
• Ask instead how relaying can optimally exploit
  the key resources of a wireless fading channel
• diversity
• degrees of freedom
• energy
• This can be answered to a great extent by
  focusing on different SNR regimes.

3
High and Low SNR

• High SNR diversity and multiplexing tradeoff
• (Laneman et al, Azarian and El Gamal)
• Low SNR diversity and energy transfer.

4
Outline of Talk

• Quick discussion of high SNR diversity
  multiplexing results.
• Focus on low SNR.
• Derive a simple, non-coherent scheme which
  achieves the outage capacity of the relay channel.

5
Fading Relay Channel Model
R
g
h2
D
S
h1

• Rayleigh fading channels AWGN noise
• Slow fading gains random but remain constant.
• Half duplex constraint.
• No CSI at transmitters.

6
High SNR Diversity-Multiplexing Tradeoff
7
Partial Decode-Forward
R

• First Phase S broadcasts first part of message.
  R joins in whenever it can decode.
• Second Phase S transmits second part of message
  and R continues to relay first part.
• Destination decodes first part using signal from
  both relay and source, cancels, then decodes
  second part coming from source only.

duration ?
duration 1-?
D
S
8
DM Tradeoff of Partial DDF
Improves over DDF but does not reach MISO.
9
Partial DF with full CSI Achieves MISO
10
Low SNR Regime
11
Impact of Fading at Low SNR

• C? Outage capacity at outage probability ?.

Diversity is particularly important at low SNR
and small outage probability!
12
Cutset Bound
R
g
h2
D
S
h1

• For given channel gains, cutset bound yields
• Bound on outage capacity
• Name of the game at low SNR is energy transfer.

13
Decode-Forward

• Does not meet the cutset bound.
• Relay cannot forward the received energy once
  it cannot decode the message.

Exploits Diversity
MFMC upper bound
Decode-Forward
14
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 !
Relay amplifies too much noise.
Why?
15
Burstiness Comes to Rescue

• 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.
• - This scheme achieves the cutset bound in this
  regime (in contrast to Zahedi El Gamal 03 for
  AWGN).

16
Summary of results so far
MFMC upper bound
Decode-Forward
Amplify-Forward
Bursty Amplify-Forward
Outage Capacity
17
Channel Knowledge

• The result assumes perfect channel knowledge at
  the destination so that signals along the direct
  and indirect paths can be coherent combined.
• Turns out that this optimal performance can be
  achieved with bursty M-ary pulse position
  modulation and non-coherent detection.

18
Energy Detection

• Direct path
• Indirect path
• Energy detection sum of energies received along
  the two paths, scaled by the respective noise
  variances.
• Subtlety noise variance along indirect path
  depends on the S-R gain, which is unknown.
• At low SNR, number of positions M in PPM is
  large and we can estimate the noise variance.

19
Conclusion

• A simple non-coherent scheme achieves the low-SNR
  outage capacity of fading relay channels.
• Bursty transmission is used to avoid noise
  amplification and channel estimation.