Capacity and Power Allocation for Transmitter and Receiver Cooperation in Fading Channels

1
Capacity and Power Allocation for Transmitter and
Receiver Cooperation in Fading Channels

• Chris T. K. Ng
• Andrea J. Goldsmith
• Wireless Systems LabStanford University

2
Cooperation in Wireless Networks

• Cooperation in wireless networks can increase
  capacity.

• Wireless nodes can cooperate in different ways.
• E.g., transmitter vs. receiver cooperation.
• Depends on network geometry, CSI and power
  allocation assumptions.
• Benefits of cooperation in fading channels.
• Relay is close to either the transmitter or the
  receiver.
• Transmitters only have CDI.
• Equal power allocation, or optimal power
  allocation.

3
System Model

• Rayleigh flat-fading with additive white Gaussian
  noise.
• Expected channel power gain between Tx and Rx
  cluster is normalized to unity, but within
  cluster it is denoted by g.
• Average network power constraint P.

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CSI and Power Allocation

• We assume a fast fading environment.
• Rx has CSI, Tx has only CDI.
• Transmission rate characterized by ergodic
  capacity.
• We consider two models of power allocation.
• i) Tx and relay have equal average power
  constraints (P /2).
• ii) Optimal power allocation. Tx has power aP
  relay has power (1-a)P.
• Transmitters cannot adapt to instantaneous
  channel realizations.

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Cooperation Strategies

• Capacity of the relay channel is an open problem.
• The cut-set bound provides a capacity upper
  bound.
• Achievable schemes
• Cover and El Gamal79 Decode-and-forward (DF)
  and Compress-and-forward (CF).
• Kramer, Gastpar and Gupta05 DF is close to
  optimal when relay is close to Tx. CF performs
  well when relay is close to Rx.
• Cooperation strategies
• DF for transmitter cooperation.
• CF for receiver cooperation.
• No cooperation capacity of a single-user channel.

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Transmitter Cooperation

• Capacity bounds evaluation.
• Without CSIT, Host-Madsen et al.05, Kramer et
  al.05 showed that it is optimal for the Tx and
  relay to send uncorrelated signals.
• Tx cut-set bound
• DF rate

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Receiver Cooperation

• Rx cut-set bound
• CF rate
• Wyner-Ziv compression cannot be applied directly
  since joint distribution of received signals is
  not iid.
• Sub-optimal scheme compress signal ignoring side
  information.

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Cooperative Capacity Gain Equal Power Allocation
Tx and Rx cut-set bounds
Tx DF rate
Rx CF rate
No cooperation
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Cooperative Capacity Gain Optimal Power
Allocation
Rx cut-set bound
Tx cut-set bound
Rx CF rate
Tx DF rate
No cooperation
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Effects of Fading Optimal Power Allocation
Rx coop
Tx coop
No cooperation
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Effects of Fading Equal Power Allocation
No fading
Tx DF rate
No cooperation
Fading
Tx DF rate
No cooperation
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Limits on Cooperation

• Tx cooperation
• No CSIT MISO has same capacity as SISO under
  same total power constraint.
• Rx cooperation
• Equal power constraint SIMO has same capacity as
  SISO.
• CSIT and power allocation necessary for
  cooperative capacity gain.

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Conclusion Power Allocation

• Capacity gain from transmitter and receiver
  cooperation.
• Under Rayleigh fading channels.
• Different power allocation assumptions.
• Equal power allocation.
• DF Tx cooperation is capacity-achieving.
• Optimal power allocation.
• CF Rx cooperation outperforms Tx cooperation.
• Best cooperation strategy depends on the power
  allocation assumption.

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Conclusion Effects of Fading

• Cooperative capacity gain under fading channels
  vs. static channels.
• Cooperation provides resilience to fading.
• Under fading capacity becomes more sensitive to
  power allocation.
• Cooperating nodes need to be closer together for
  DF to be capacity achieving.
• Limits on cooperation.
• Large clusters of cooperating nodes.
• CSIT necessary for transmitter cooperation.
• Power allocation necessary for receiver
  cooperation.