Master Thesis Presentation

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Master Thesis Presentation

• Capacity of Hybrid Open-loop and Closed-loop
  MIMO with Channel Uncertainty at Transmitter.
• Lu Wei, Communications Laborartory.
• Thesis advisor Prof. Olav Tirkkonen.
• 18th, March 2008.

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Outline

• Transmit diversity techniques.
• Our research problem.
• Formulations and Simplifications.
• Numerical results.
• Conclusion.

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Transmit diversity techniques Open-loop case

• Open-loop case space-time block code.
• 2 transmit and 1 receieve antennas Alamouti
  code
• Optimal linear open-loop transmit diversity
  scheme It provides full diversity, with linear
  matched filter detection and it reaches channel
  capacity.
• 
  

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Closed-loop case

• Requring channel state information at transmitter
  
• Optimal w is
• Being able to have complete channel state
  information gives us a 3dB gain in SNR over the
  Alamounti code

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Hybrid Open-loop and Closed-loop Methods

• Significant performance gap between open-loop and
  closed-loop schemes.
• Assuming the transmitter has partial but not
  perfect knowledge about the channel.
• Question how to improve a predetermined code so
  that the channel imperfection is taken into
  account ?
• reqiures 1. modeling the channel imperfection.
• 2. adopted an appropriate signal
  model.

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Channel Imperfection

• One model exists in the literature is
• Degree of correlation, normalized correlation
  coefficient
• pdf of the true channel, conditioned on the
  imperfect CSI, is complex Gaussian distributed
• conditional mean
• conditional covariance

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The Signal Model

• Consider a predetermined Alamouti code,
• diagonal beam weighting matrix
• the unitary beamforming matrix
• When
• When

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Our Research Problem

• What is the value of P matrix that will maximize
  the mutual information between Tx and Rx, when
  certain channel feedback is available?
• This same problem has been solved by George
  Jongren, et al. under the criterion of minimizing
  block error rate.
• Our work considers the information theoretic
  performance criterion of maximizing the mutual
  information and which permits an analytical
  solution.

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Formulations and Simplifications

• The capacity can be expressed as
• Average out the true but unknown channel to
  obtain
• Our objective is

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Formulations and Simplifications

• Under the i.i.d fading assumption
• With the change of variable
• the capacity expression is now,
• Making a change of variable again to obtain
• and the capacity over the corresponding
  distribution is

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Formulations and Simplifications

• Remind that our problem is to maximize the
  capacity with respect to P
• We could rely on numerical methods to find the
  optimal P value.
• An efficient approximation method can be utilized
  for the capacity integration as well.

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Capacity Approximation

• Two steps approaches for the appro.
• First, weighted sum of non-central chi-square
  variables approximated by a single central one
• Mean fits
• Variance fits

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Capacity Approximation

• Second, using a Lemma by Porteous
• Lemma,
• Combining the chi-square approximation in
  equation with the Porteous Lemma, the capacity
  can be calculated as

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Numerical Results
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Numerical Results
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Numerical Results
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Numerical Results
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Conclusion

• The proposed beamformer could benefit the from
  open-loop and closed-loop methods according to
  the channel feedback quality.
• We have achieved the optimal combing of
  open-loop and closed-loop in mutual information
  optimal sense.
• The analytical framework could possibly be
  extented to more than 2 Tx case.

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• Thank you!