Multiple Input Multiple Output systems MIMO

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Multiple Input- Multiple Output systems (MIMO)

• 9th semester Adaptive Antennas
• October 2nd, 2003
• Persefoni (Persa) Kyritsi

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Outline

• SISO to MISO/ SIMO to MIMO
• Interpretations of capacity
• Parallel channels
• Directional analysis
• Detection algorithms
• From narrowband to broadband
• High capacity and how to get it
• Practical considerations
• Conclusions

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Single Input- Single Output systems (SISO)
x(t) transmitted signal y(t) received
signal g(t) channel transfer function n(t)
noise (AWGN, ?2)
g
y(t)
x(t)

• y(t) g x(t) n(t)

Signal to noise ratio Capacity
C log2(1?)
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Single Input- Multiple Output (SIMO) Multiple
Input- Single Output (MISO)

• Principle of diversity systems (transmitter/
  receiver)
• Higher average signal to noise ratio
• Robustness
• - Process of diminishing return
• Benefit reduces in the presence of correlation
• Maximal ratio combining gt
• Equal gain combining gt
• Selection combining

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Idea behind diversity systems

• Use more than one copy of the same signal
• If one copy is in a fade, it is unlikely that all
  the others will be too.
• C1xNgtC1x1
• C1xN more robust than C1x1

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Multiple Input- Multiple Output systems (MIMO)
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Power definitions for MIMO

• Average gain
• Average signal to noise ratio
• Normalized channel transfer matrix

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Expressions for the Shannon capacity
K rank of H, ui eigenvalues of H
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Interpretation I The parallel channels approach

• Singular value decomposition of H H SUVH
• S, V unitary matrices (VHVI, SSH I)
• U diag(uk), uk singular values of H
• V/ S input/output eigenvectors of H
• Any input along vi will be multiplied by ui and
  will appear as an output along si

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The math
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Vector analysis of the signals

• 1. The input vector x gets projected onto the
  vis
• 2. Each projection gets multiplied by a different
  gain ui.
• 3. Each appears along a different si.
• Note power conservation

u1
ltx,v1gt
ltx,v1gt u1 s1
u2
ltx,v2gt
ltx,v2gt u2 s2
uK
ltx,vKgt uK sK
ltx,vKgt
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Capacity sum of capacities

• The channel has been decomposed into K parallel
  subchannels
• Total capacity sum of the subchannel capacities
• All transmitters send the same power
• ExEk

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Interpretation II The directional approach

• Singular value decomposition of H H SUVH
• Eigenvectors correspond to spatial directions
  (beamforming)

(vi)1
1 M
x
(vi)M
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Example of directional interpretation
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Detection algorithms

• Maximum likelihood linear detector
• y H x n ? xest Hy
• H (HH H)-1 HH Pseudo inverse of H
• Problem find nearest neighbor among QM points
• (Q constellation size, M number of
  transmitters)
• VERY high complexity!!!

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Solution BLAST algorithm

• BLAST Bell Labs lAyered Space Time
• Idea NON-LINEAR DETECTOR
• Step 1 H (HH H)-1 HH
• Step 2 Find the strongest signal
• (Strongest the one with the highest post
  detection SNR)
• Step 3 Detect it (Nearest neighbor among Q)
• Step 4 Subtract it
• Step 5 if not all yet detected, go to step 2

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Discussion on the BLAST algorithm

• Its a non-linear detector!!!
• Two flavors
• V-BLAST (easier)
• D-BLAST (introduces space-time coding)
• Achieves 50-60 of Shannon capacity
• Error propagation possible
• Very complicated for wideband case

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From narrowband to wideband

• Wideband delay spread gtgt symbol time
• - Intersymbol interference
• Frequency diversity
• SISO channel impulse response
• SISO capacity

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Matrix formulation of wideband case
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Equivalent treatment in the frequency domain

• Wideband channel Many narrowband channels
• H(t) ? H(f)

Noise level
f
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Objective High capacity

• Capacity depends on
• Eigenvalues
• Signal to noise ratio
• Power roll-off depends on the environment
• Rank depends on the scattering
• Distribution of eigenvalues depends on the
  correlation

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For high capacity
Limits Power constraints System size Correlation

• Ideally
• As high gain as possible
• As many eigenvectors as possible
• As orthogonal as possible

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Example Uncorrelated correlated channels
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Practical considerations

• Coding
• Detection complexity
• Channel estimation
• Interference

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Coding limitations

• Capacity Maximum achievable data rate that can
  be achieved over the channel with arbitrarily low
  probability of error
• SISO case
• Constellation limitations
• Turbo- coding can get you close to Shannon!!!
• MIMO case
• Constellation limitations as well
• Higher complexity
• Space-time codes very few!!!!

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Channel estimation

• The channel is not perfectly estimated because
• it is changing (environment, user movement)
• there is noise DURING the estimation
• An error in the channel transfer characteristics
  can hurt you
• in the decoding
• in the water-filling
• Trade-off Throughput vs. Estimation accuracy
• What if interference (as noise) is not white????

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Interference

• Generalization of other/ same cell interference
  for SISO case
• Example cellular deployment of MIMO systems
• Interference level depends on
• frequency/ code re-use scheme
• cell size
• uplink/ downlink perspective
• deployment geometry
• propagation conditions
• antenna types

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Extensions

• Optimal power allocation
• Optimal rate allocation
• Space-time codes
• Distributed antenna systems
• Many, many, many more!

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Summary and conclusions

• MIMO systems are a promising technique for high
  data rates
• Their efficiency depends on the channel between
  the transmitters and the receivers (power and
  correlation)
• Practical issues need to be resolved
• Open research questions need to be answered