Performance Analysis of MIMO Systems with IRM

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Performance Analysis of MIMO Systems with IRM

• By
• Junwu Zhang
• Xuefeng Zhao
• Bin Xue

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Multiple-Input Multiple-Output(MIMO)?

• The use of multiple antennas at both ends of a
  wireless link promise significant improvements in
  terms of spectral efficiency.
• Do all transmitter antennas use orthogonal waves?
  No.
• Does each receiver antenna receive signals from
  all the transmitters? Yes.
• How to detect signals from different
  transmitters?
• Different transmission paths have different
  fading (or independent fading).

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Example of a MIMO System (1-user)
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Performance Analysis

• n transmit antennas
• m receiving antennas
• Cti is transmitted by transmitter i at time t
• Rayleigh or Rician fading, quasistatic flat
  fading for l time slots, ai,j is the fading
  coefficient from i to j, complex Gaussian
  variable with mean E(ai,j ) variance 0.5 per
  dimension
• Constellation-independent

• The signal received at antenna j at time t is a
  noisy superposition of the n transmitted signals

Noise is zero-mean complex Gaussian random
variable with variance N0/2
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Performance Analysis
For code words c and e in l time slots, assume c
? e.

• Assume the receiver has complete channel
  information,

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Performance Analysis
For code words c and e in l time slots, assume c
? e.

• The distance between these two code words,

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Performance Analysis
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Performance Analysis
Notice that

• Thus matrix A is Hermitian.
• From linear algebra
• Unitary Matrix VVI
• For a Hermitian matrix A, there exists unitary
  matrix V and diagonal matrix D such that VAVD.
  The rows of V,v1, v2, vn are a complete
  orthonormal basis of Cn given by eigenvectors of
  A. The diagonal elements of D are eigenvalues of
  A.
• If ABB, eigenvalues of A are nonnegative.

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Performance Analysis
Let
bi,j are independent complex Gaussian random
variables with variance 0.5 and mean E(bi,j). Let
Ki,j E(bi,j)2, bi,j are independent Rician
distributions with pdf
I0(.) Bessel function of the first kind.
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Performance Analysis
Since bi,j are Rician distributions, solve for
the average over Rician distribution of bi,j
For Rayleigh fading, E(ai,j) 0 and thus Ki,j
Ebi,j2 0
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Performance Analysis
For Rayleigh fading, Eai,j 0 and thus Ki,j
Ebi,j2 0
Design Criteria for Rayleigh SpaceTime Codes
The Rank Criterion In order to achieve the
maximum diversity mn, the matrix B(c,e) has to be
full rank for any codewords c and e. If B(c,e)
has minimum rank r over the set of distinct pairs
of codewords, then a diversity of rm is
achieved. The Determinant Criterion Suppose
that a diversity benefit of rm is our target. The
minimum of the absolute value of the sum of the
determinants of all of all principal rr
cofactors of A(c,e) taken over all pairs of
distinct codewords c and e corresponds to the
coding advantage, where r is the rank of B(c,e).
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Performance Analysis
For Rician fading with large SNR,
Design Criteria for Rician SpaceTime Codes
The Rank Criterion Same as for Rayleigh
fading. The Determinant Criterion Suppose that
a diversity benefit of rm is our target. The
minimum of the following
over distinct codewords c and e has to be
maximized.
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IRM Interference-Resistant-Modulation

• Performance
• Co-channel interference
• Vs.
• diversity gain and coding gain
• Can we improve the performance without
  introducing coding or bandwidth expansion?
• Yes.
• IRM Interference-Resistant-Modulation

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Basic Idea

• Choose the rotation matrix R such that
• Increase the rank of B(c,e) over distinct code
  words
• Increase the determinant of B(c,e) over distinct
  code words
• One possible distance-preserving transformation
  is to multiply this matrix by an orthogonal
  matrix R. the optimal matrix R maximizes the
  fading resistance of the transformed
  constellation.

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Example of Rotation(L2,3)
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Rotation Matrix for High Dimension
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Transmitter structure for a multiuser system with
IRM
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Simulation Result (1)Distance Matrix
Determinant Vs. Rotation Degree

• Best Rotation angle for n2, m1,L2
• ?126.6 degree ?263.4 degree

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Simulation Result (2)(Bit Error Ratio Vs. SNR)

• Use single user BER as baseline
• When SNR increases, the BER of 2 users IRM with
  optimum rotation angle approaches the baseline

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Simulation Result (3)(Optimum IRM Vs.
non-optimum IRM)

• Use single user BER as baseline
• Optimum IRM performs better than non-optimum IRM

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References

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References

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•  

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Thank You. Questions?