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Capacity Gain from Transmitter and Receiver Cooperation

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Node cooperation increases capacity. ... Cooperation mode may be ... With equal power allocation and Rx phase CSI, cooperation offers no capacity gain. ... – PowerPoint PPT presentation

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Title: 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).

10
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
11
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.
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