Scalable SpaceTime Trellis Codes SSTTC

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Scalable Space-Time Trellis Codes (SSTTC)

• Bahador Amiri Madhan Jaganathan
• Fall 2006

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Outline

• Drawbacks for STBC and STTC
• Scaleable Space Time Code Design
• Distance Spectrum Computation
• Simulation Results
• Performance Comparison with other methods

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Motivation

• Complexity of STTC for higher number of transmit
  antennas or larger constellation size (grows up
  exponentially).
• STBC needs different design when the number of
  transmit antennas varies between 2 and 4.
• STBC does not provide good coding gain.
• At low SNR, full diversity for OSTBC can not be
  achieved because of asymptotic design criteria.
• Question
• Is it possible to design Space-time codes that
  are scalable for any number of transmit antenna
  and provide maximum coding gain and low
  complexity?

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SSTTC Design (I)
Mapping of QPSK constellation

• 8-state QPSK-STTC of Vucetic

Mapping of two QPSK signals into 16-PSK
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SSTTC Design (II)

• Block Diagram of the transmitter

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Probability of Error
Structure of regular codes is such that
A(d) of code words having distance d
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Computation of Distance Spectrum

• Uses Control Theory/Masons Rule to compute A(d)
  and distances
• For irregular codes this simplification does not
  work
• The distance between each possible codeword pair
  needs to be computed.

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Computation of Distance Spectrum

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Error Distances at a single trellis step
D
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Distance Spectrum

• Matrix D gives distances of codewords for a
  single trellis step
• Distance between codewords is sum of codeword
  distances over all trellis steps
• Matrix is multiplied for each trellis step
• Distance(c2,c1) DDD DL
• DL has polynomials in X
• D(1,1) 0.15X3 0.39X5 0.09X5.1

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Distance Spectrum
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Merge Diverge Matrices
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Probability of Error for Rayleigh Fading
Distance Merge(Z) Path(Y) Diverge(X)
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Probability of Error for Rayleigh Fading
Distance Merge(Z) Path(Y) Diverge(X)
D(1,1) 0.15X2Y1.5Z3 0.39X2.1Y3.5Z1.3 X5
Matrices are reconstituted from the polynomial
and their Eigen values computed
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Distance Spectrum

• Minimizing worst error case pair wise error
  probability will not guarantee best performance
  for low SNR.
• Initial STTC design criteria was optimum for
  asymptotic SNR.
• Distance spectrum provides better tool for
  performance analysis at low SNR.
• Truncated union bound is a function of distance
  spectrum of the code.
• Numerical results illustrate that distance
  spectrum analysis provides accurate
  characterization of relative performance of
  space-time codes.
• Distance spectrum analysis is computationally
  efficient tool.
• State reduction techniques can be used for
  quasi-regular trellis codes to reduce computation
  of distance spectrum calculation.

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Distance Spectrum

• Distance Spectrum of SSTTC with different mappings

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Distance Spectrum

• Distance Spectrum for best possible mapping for
  proposed algorithm

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Performance Comparison (I)

• Frame error rate performance comparison between
  16PSK of proposed algorithm (PA) and 16-QAM of
  Tarokhs STTC

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Performance Comparison (II)

• Frame error rate comparison between 16PSK-8state
  STBC-MTCM and proposed SSTTC method for 2X2,3,4
  and 5 MIMO system

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Performance Comparison (III)

• Decoding Complexity comparison between proposed
  algorithm and 16PSK STBC-TCM

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Advantages and Disadvantages

• Advantages
• Scalability For any number of transmit antenna
  and any constellation size.
• Simple decoding Technique The complexity of
  decoder increases linearly with number of
  transmit antennas and constellation size.
• Performance for practical SNR High coding gain
  with reasonable diversity gain provides good
  performance for low and moderate SNR
• Disadvantage
• Diversity gain is not full then for high SNR
  performance is not as good as other techniques
  with full diversity. By increasing the number of
  received antenna importance we get much better
  performance than other methods.

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Future Plan

• Find the upper bound for frame error rate from
  distance spectrum.
• Compare upper bound of frame error rate for this
  method with other techniques.
• Find the exact diversity order of SSTTC.
• Capacity calculation for SSTTC.

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• Questions?