Capacity of Fading Channels With Channel Side Information

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Capacity of Fading Channels With Channel Side
Information
Goldsmith, A.J.   Varaiya, P.P.   California
Inst. of Technol., Pasadena, CA IEEE
Transactions on Information TheoryPublication
Date Nov 1997On page(s) 1986-1992Volume 43,
  Issue 6 
203
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Outline

• System Model
• Optimal Channel Capacity
• Channel known to Tx Rx
• Channel known to Rx Only
• Sub-optimal Channel Capacity
• Channel Inversion
• Truncated Channel Inversion
• Numerical Results
• Conclusion

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System Model

• Assumptions
• gi Stationary Ergodic
• No Estimation Error
• No Feedback delay

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Outline

• System Model
• Optimal Channel Capacity
• Channel known to Tx Rx
• Channel known to Rx Only
• Sub-optimal Channel Capacity
• Channel Inversion
• Truncated Channel Inversion
• Numerical Results
• Conclusion

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Channel Known at Tx Rx
J. Wolfowitz, Coding Theorems of Information
Theory, 2nd ed. New York Springer-Verlag, 1964.
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Channel Known at Tx Rx
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Channel Known at Tx Rx

• Transmit Power is allowed to adapt
• Coding Theorem There exists a coding scheme with
  average power S that achieves any rate R lt C(S)
  with arbitrarily small probability of error.

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Channel Known at Tx Rx
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Channel Known at Tx Rx
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Channel Known only at Rx

• McEliece has shown that
• provided that channel variation satisfy a
  compatibility constraint.
• The Constraint
• Channel is i.i.d. (independently identically
  distributed)
• Input distribution is same regardless of channel
  state

R. J. McEliece and W. E. Stark, Channels with
block interference, IEEE Trans. Inform. Theory,
vol. IT-30, pp. 4453, Jan. 1984.
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Channel Known only at Rx

• Therefore, fading AWGN channel satisfy the
  constraint only if fading is i.i.d and constant
  Transmit Power S.

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Outline

• System Model
• Optimal Channel Capacity
• Channel known to Tx Rx
• Channel known to Rx Only
• Sub-optimal Channel Capacity
• Channel Inversion
• Truncated Channel Inversion
• Numerical Results
• Conclusion

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Sub-optimal (Channel Inversion)
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Sub-optimal (Truncated Channel Inversion)
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Outline

• System Model
• Optimal Channel Capacity
• Channel known to Tx Rx
• Channel known to Rx Only
• Sub-optimal Channel Capacity
• Channel Inversion
• Truncated Channel Inversion
• Numerical Results
• Conclusion

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Capacity in log-normal Fading
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Capacity in Rayleigh Fading
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Capacity in Nakagami Fading
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Conclusion

• Capacity of Fading AWGN channel with average
  power constraint is calculated.
• When Channel is known to both Tx and Rx Optimal
  adaptation is water filling for power and
  variable rate multiplexed coding.
• In correlated fading, adaptive schemes yields
  higher capacity and lower complexity.
• However iid fading, this gain is not appreciable.
• Channel inversion has lowest coding and decodeing
  complexity, but suffers large capacity loss under
  severe fading
• The capacity of all schemes converges to AWGN as
  fading severity if reduced.