on the mimo channel capacity predicted by kronecker and müller models
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On the MIMO Channel Capacity Predicted by Kronecker and Müller Models. Müge KARAMAN ÇOLAKOĞLU Prof. Dr. Mehmet ŞAFAK COST 289 4th Workshop, Gothenburg, Sweden April 11-12, 200 7. Outline. MIMO Channel Models Kronecker model Müller model Results Conclusion. Kronecker Model-1. - PowerPoint PPT PresentationTRANSCRIPT
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On the MIMO Channel Capacity Predicted by
Kronecker and Müller Models
Müge KARAMAN ÇOLAKOĞLU
Prof. Dr. Mehmet ŞAFAK
COST 289 4th Workshop, Gothenburg, SwedenApril 11-12, 2007
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Outline
MIMO Channel Models Kronecker model Müller model
Results Conclusion
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Kronecker Model-1
Assumptions: Flat fading channel Only doubly-scattered rays are considered
LOS multipath component ignored Single scattered signals ignored
Source of fading Local scatterers Number of scatterers Typically >10 Fading correlations are separated Tx have no CSI, Rx have CSI
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Kronecker Model-2
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Kronecker Model-3
Sensitivity against the model parameters(wavelength=0.15 m)
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Müller Model-1
Assumptions: Frequency-selective fading channel Scatterers can be distinguished in time and
space (Different locations and delays) Only singly-scattered rays are considered
No LOS, no multiple scattering Tx and Rx at the foci of concentric (equi-
delay) ellipses Asymptotic in the number of scatterers,
and of the transmit- and receive antennas
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Müller Model-2
Delay and space coordinates for the Müller model
Propagation coefficient between th Tx and th Rx antenna
v
l
lvl
Sj
llv eAh1
)(,,,
,,,,
1
1L
k k
y H x
Received signal at time :k
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Müller Model-3 Singular values of the random channel matrix H show
fewer fluctuations, become deterministic as its size goes infinity
Approximates finite size matrices Singular value distributions can be calculated analytically Only the surviving physical parameters show significant
influence on the singular value distribution and characterise the MIMO channel
In the asymptotic limit, singular values of H for flat fading and frequency-selective fading channels are the same
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Müller Model-4 Surviving physical parameters that dominate
the value of the channel capacity:
R
T
N
NSystem load:
Total richness:RN
S
Attenuation distribution (assumed):
, 1A (for all ),
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Results-1
Parameters used for the Kronecker model
(m)
dt
(m)
dr
(m)
Rt0
(m)
Rr0
(m)
Dt
(m)
Dr
(m)
R(m)
0.15 0.15 0.15 50 50 50 50 50000
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Results-2 Effects of the
number of Tx and Rx antennas for
4R
T
N
N
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Results-3 Effect of the
number of scatterers for
3
1
R
T
N
N 3RN
S
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Results-4 Effect of the
number of Tx antennas
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Results-5 Effect of the
number of Rx antennas
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Results-6 Effect of
the number of scatterers
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Conclusion-1
Kronecker model: Valid for flat-fading channels May be more appropriate for urban
channels May lead to pessimistic capacity
predictions in suburban areas Some measurement results show that
model fails under certain circumstances
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Conclusion-2
Müller model: Valid for frequency-selective fading channels May describe suburban channels more accurately Simple and characterizes the channel by
the number of Tx antennas the number of Rx antennas the chanel richness (usually ignored in other models)
Capacity predictions by the Müller model may be higher compared with the Kronecker model
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Thank You...
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Channel Capacity-1
Finding average capacity-Method 1: Replace mean value of by deterministic
correlation matrix Find eigenvalues and the capacity
Issue: How to model the correlation matrix ? (correlation between antenna elements, angular spread of signals, scattering richness)
HHH
H
TN N
CR
HHI
detlog2
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Channel Capacity-2
Finding average capacity-Method 2: Elements of are zero mean Gaussian
random variables is central Wishart matrix.
Joint pdf of the ordered eigenvalues of a complex Wishart matrix is known.
Determine the capacity by using joint pdf of the ordered eigenvalues.
Issue: Hard to determine the marginal pdf’s analytically.
HHHH
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Kronecker Model-3
Isolates the fading
correlations
Simplify the simulation and the analysis
Underestimates the channel capacity (high corelation )
Should be used at low correlation chanels
Assumes double scattering from local scatterers
More suited for urban channels
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Kronecker Model-4
Sensitivity against the model parameters(wavelength=0.15 m)
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Müller Model-4
It is assumed that Eigenvalue distribution of the space-time channel
matrix does not changes if the delay times of particular paths vary.
No need to distinguish between the distributions of path attenuations conditioned on different delays.
A uniform power delay profile is assumed. The paths that have same delay are assumed attenuated
at the same rate.
, 1,A for all and