1. Whitening-Rotation Based MIMO Channel Estimation
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CWC Research Review - ‘03
Whitening-Rotation Based MIMO Channel Estimation
Aditya Jagannatham
UCSD

2. TX Rx A MIMO Communication System: r- receive t - transmit Receiver
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A MIMO Communication System: Rx
Transmitter
Receiver
= Antenna TX
t - transmit
r- receive
Each channel is characterized by a Complex fading Coefficient
hij represents the channel between the ith receiver and jth transmitter
Arranging these as a matrix we get a ‘Flat Fading’ Channel Matrix ‘H’

3. Estimating H is the problem of Channel Estimation
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System Model:
MIMO System H
where
System
Model
Estimating H is the problem of Channel Estimation

4. H Problem Statement Blind Outputs Data MIMO System Training
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Problem Statement
Blind Outputs
Data
MIMO System H
Training
Training Output
Statistical
Information

5. Issues in Channel Estimation
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Issues in Channel Estimation
As the number of channels increases, employing entirely training data to learn
the channel would result in poorer spectral efficiency.
-Calls for efficient use of blind and training information
As the diversity of the MIMO system increases, the operating SNR decreases.
- Calls for more robust estimation strategies
* Constellation Size = 4

6. ESTIMATION STRATEGIES Training Based Estimation
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ESTIMATION STRATEGIES Training Based Estimation
MIMO System H
Training
Blind Outputs
Data
Training Output
Constraint
Solution
+ denotes pseudo-inverse

7. H Blind Estimation MIMO System Entirely Data !!
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Blind Estimation
MIMO System H
Entirely Data !!
Estimate channel from DATA
No Training Necessary
Uses information in source statistics

8. Training Blind Training Vs Blind Estimation Increasing Simplicity
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Training Vs Blind Estimation
Training
Blind
Increasing Efficiency
Increasing Simplicity

9. SemiBlind Estimation – ‘Whitening-Rotation’
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SemiBlind Estimation – ‘Whitening-Rotation’
Goals :
Use as few training symbols as possible
Use total information – Training + Blind
Total Information
Key Idea :
H is decomposed as the product of
A ‘Whitening’ Matrix W and a ‘Rotation’ Matrix Q

10. W can be estimated Blind from output Data
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Procedure
Estimating W :
W can be estimated Blind from output Data
Output Correlation =
Estimate Output Correlation
Estimate W such that,
Q is the non-minimum phase part and cannot be estimated using Second Order Statistics
How do we estimate Q ??

11. Estimating – ‘Q’ the rotation matrix
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Estimating – ‘Q’ the rotation matrix
Solution : Estimate Q from the training sequence !
Advantages
Unitary matrix Q parameterized by a significantly lesser number of parameters than M.
r x r unitary - r2 parameters
r x r complex - 2r2 parameters
As the number of receive antennas increases, size of H increases while that of Q remains constant
- size of M is r x t
- size of Q is t x t

12. Parameter Sizes of Matrices
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Parameter Sizes of Matrices
# of Parameters
“Accuracy can be improved by estimating only Q from training data while estimating H blind without employing training information”
- CR Bound for Channel Estimation error is proportional to the number of parameters.

13. ‘ROSE’ – Rotation Optimization SemiBlind
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‘ROSE’ – Rotation Optimization SemiBlind
Minimize the ‘True-Likelihood’ :
subject to :
Goal :
Procedure
Step 1: Minimize the ‘Modified-Likelihood’ :
Step 2: Employ this estimate of Q to minimize the True likelihood
Step 3:Using the estimate of Q compute jointly optimal estimates of W,Q

14. 2/25/2019
Simulations
Fading coefficients (entries of H) are circular Gaussian random variables (Rayleigh Fading)
Input data is 16 QPSK.
Different H sizes ( 4 X 4, 8 X 4 et al.) have been considered
Input SNR  dB ( )
Error is.
Estimation error Vs different pilot lengths is plotted for a fixed total length (N)

15. H is 8 X 4, SNR = 13 dB, N (Total # Samples) = 400
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Simulation Results
H is 8 X 4, SNR = 13 dB, N (Total # Samples) = 400
ROSE performs better for very low Pilot lengths ( 20 symbols approximately)

16. ROSE performs better for all pilot lengths
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Simulation Results
Total Optimization
ROSE performs better for all pilot lengths

17. Conclusions A Semi-Blind algorithm has been proposed
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Conclusions
A Semi-Blind algorithm has been proposed
Motivation for the formulation has been presented.
Its performance has been studied through simulations.

18. ROSE now performs better up to PILOT length 60 symbols.
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Low Power Scenario
H is 8 X 4, Additional - 6db Fade on Channel
ROSE now performs better up to PILOT length 60 symbols.
Performance (as compared to Training) improves as SNR decreases