Capacity Gain from Transmitter and Receiver Cooperation

1
Capacity Gain from Transmitter and Receiver
Cooperation

• Chris T. K. Ng and Andrea J. Goldsmith
• Wireless Systems Lab
• Stanford University

2
Introduction

• Node cooperation increases capacity.
• But not clear if transmitter cooperation or
  receiver cooperation offers greater benefits.
• Consider a wireless point-to-point link. Suppose
  a relay can be deployed either
• Near the transmitter, or near the receiver.
• Which provides higher capacity improvement?
• Compare Tx and Rx co-op rates.
• Cooperation strategy depends on CSI and power
  allocation assumptions.

3
System Model

• Discrete-time AWGN relay channel.
• 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.

4
Transmitter cooperation rates

• Cut-set bound
• Achievable rate
• Decode-and-forward achieves the best known rate
  when Tx and relay are close

5
CSI and Power Models

• We consider two models of CSI
• Each node has full CSI (allows carrier
  synchronization between Tx and Relay).
• Receiver phase CSI only (no synchronization).
• Also two models of power allocation
• Optimal power allocation Tx has power constraint
  aP, and relay (1-a)P 0a1 needs to be
  optimized.
• Equal power allocation (a ½).
• Combination results in 4 separate cases.

6
Receiver cooperation rates

• Cut-set bound
• Achievable rate
• Compress-and-forward achieves the best known rate
  when Rx and relay are close
• The parameters a, p are optimized for the given
  model assumptions.

7
Cooperation Strategies

• Relative performance of Tx and Rx co-op.
• Suppose the cooperating nodes are close (g gt 2).
• Can derive the ordering of Tx and Rx co-op
  performance under different models.
• Non-cooperative scheme
• Capacity Cn is that of a single wireless link
  under the same average network power constraint.

8
Capacity gain comparison

• The rates are in descending order for g gt 2.

9
Numerical example

• Comparison of Tx and Rx co-op performance.
• Unit bandwidth, unit noise power, average network
  power constraint P 20.
• Cooperating nodes are separated by a distance d
  channel power gain g 1/d 2.
• Region of interest is when the cooperating nodes
  are close together
• When d lt 1/v2 (or g gt 2).

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Case 1 Optimal power allocation with full CSI
Tx Rx cut-set bounds

• Cut-set bounds are equal.
• Tx co-op rate is close to the bounds.
• Transmitter cooperation is preferable.

Tx co-op
Rx co-op
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Case 2 Equal power allocation with full CSI

• Tx co-op rate is higher than the cut-set bound of
  Rx co-op.
• Transmitter cooperation is superior.

Tx co-op
Rx cut-set bound
12
Case 3 Optimal power allocation with receiver
phase CSI

• Rx co-op rate is higher than the cut-set bound of
  Tx co-op.
• Receiver cooperation is superior.

Rx co-op
Tx cut-set bound
13
Case 4 Equal power allocation with receiver
phase CSI

• Non-cooperative capacity meets the cut-set bounds
  of Tx and Rx co-op.
• Cooperation offers no capacity gain.

Non-coop capacity
Tx Rx cut-set bounds
14
Effects of CSI and power allocation

• Cooperation mode may be dictated by the
  application.
• E.g., Tx co-op is natural for sensor networks
  collecting data for a single base station.
• Suppose the Tx/Rx cooperation mode is given
• How do CSI and power allocation affect
  performance?
• Can we capture (most of) the cooperative capacity
  gain with partial CSI without power allocation?

15
Transmitter Cooperation

• Optimal power allocation yields a marginal
  capacity gain.
• But full CSI is essential.

Opt power, full CSI
Equal power
CSIR
16
Receiver Cooperation

• Compress-and-forward does not require remote
  phase information.
• But optimal power allocation is essential.

Opt power
Equal power
17
Conclusion Cooperation strategy

• Capacity gain is only realized with the right
  cooperation strategy
• With full CSI, Tx co-op is superior.
• With optimal power allocation and receiver phase
  CSI, Rx co-op is superior.
• With equal power allocation and Rx phase CSI,
  cooperation offers no capacity gain.

18
Conclusion Effects of CSI and power allocation

• Effects of CSI and power allocation on
  cooperative gain
• Tx co-op
• Power allocation not essential (homogenous
  nodes),
• Full CSI (synchronous-carrier) is necessary.
• Rx co-op
• Only receiver CSI (asynchronous-carrier) is
  utilized
• Optimal power allocation (variable transmit
  power) is required.