1. CSI Feedback for Closed-loop MIMO-OFDM Systems based on B-splines
Ren- Shian Chen , Ming-Xian Chang
Institute of Computer and Communication Engineering
National Cheng Kung University
2010/12/06
Ren-Shian Chen

2. Outline System and Channel Model Parameterization of CSI
The B-splines
Model the CRs Variation across Subchannels
Coefficient Analyse and Gaussian Quantization
The Analysis of Coefficient Variance
Gaussian Quantization
Numerical Results
Conclusion

3. Outline System and Channel Model Parameterization of CSI
The B-splines
Model the CRs Variation across Subchannels
Coefficient Analyse and Gaussian Quantization
The Analysis of Coefficient Variance
Gaussian Quantization
Numerical Results
Conclusion

4. System Model Forward channel: Feedback channel: Gaussian quantization
Parameterization
Based on B-spline
Forward channel:
Model B of IEEE TGn channel models: Rayleigh fading channel with taps and we assume fdTs=0.01
Cyclic prefix is longer than the channel taps.
Perfect CSI at the receiver.
Feedback channel:
A error free feedback link.

5. Channel Model
In this paper, our simulation channel model is formed by modified Jackes model.
We assume that the channel is constant during one block period.
We use IEEE TGn model B (9 taps) as our power delay profile.
We assume that for simplification here.

6. Outline System and Channel Model Parameterization of CSI
The B-splines
Model the CRs Variation across Subchannels
Coefficient Analyse and Gaussian Quantization
The Analysis of Coefficient Variance
Gaussian Quantization
Numerical Results
Conclusion 6

7. The B-splines
A B-spline of order n, denoted by , is an n-fold convolution of the B-spline of zero order
For n = 0, 1, 2 we have the following B-splines

8. Outline System and Channel Model Parameterization of CSI
The B-splines
Model the CRs Variation across Subchannels
Coefficient Analyse and Gaussian Quantization
The Analysis of Coefficient Variance
Gaussian Quantization
Numerical Results
Conclusion 8 8

9. Model the CRs Variation across Subchannels
In the modeling process, we transform estimated CRs of subchannels into B-spline coefficients at the receiver.
Let , where is the CR of the subchannels at some symbol time slot.
We partition into segments, with the segment
In this paper, we choose as the fitting curve, the receiver uses m to fit each

10. Model the CRs Variation across Subchannels

11. Model the CRs Variation across Subchannels
On each , we sample points, where the parameter is determined by
Let , where is the sampling point from , or

12. Model the CRs Variation across Subchannels
Define a matrix of size
Then the approximation of can be expressed as
By the least-squares-fitting principle :

13. Model the CRs Variation across Subchannels
After are determined, the receiver can feed back these to the transmitter with the quantization process.
The number of feedbak coefficients for each OFDM block is , which is usually much smaller than
For an MIMO-OFDM systems with transmit antennas and receive antennas, the number of feedback coefficients is

14. Outline System and Channel Model Parameterization of CSI
The B-splines
Model the CRs Variation across Subchannels
Coefficient Analyse and Gaussian Quantization
The Analysis of Coefficient Variance
Gaussian Quantization
Numerical Results
Conclusion 14 14

15. Coefficient Analyse and Gaussian Quantization
To implement efficient feedback, we need to quantize these coefficients.
The variations of coefficients have a great impact on the feedback load .
Through the constant matrix , each element of also has complex Gaussian distribution ( ) with zero mean and variance

16. Coefficient Analyse and Gaussian Quantization
By formula and with simulations, we can find out the coefficient’s variances.

17. Coefficient Analyse and Gaussian Quantization
We observe that the coefficients of B-splines have smaller variation than the coefficients of Polynomial.
Since the coefficients are complex Gaussian distribution, the Gaussian quantization (GQ) algorithm can be applied before the feedback.
The GQ algorithm is based on two primary condition, the nearest neighborhood condition (NCC) and the centroid condition (CC) .
Gaussian Quantization

18. Outline System and Channel Model Parameterization of CSI
The B-splines
Model the CRs Variation across Subchannels
Coefficient Analyse and Gaussian Quantization
The Analysis of Coefficient Variance
Gaussian Quantization
Numerical Results
Conclusion 18 18 18

19. Numerical Results

20. Numerical Results

21. Numerical Results

22. Numerical Results

23. Outline System and Channel Model Parameterization of CSI
The B-splines
Model the CRs Variation across Subchannels
Coefficient Analyse and Gaussian Quantization
The Analysis of Coefficient Variance
Gaussian Quantization
Numerical Results
Conclusion 23 23 23 23

24. Conclusion
We propose an efficient CRs feedback approach based on the B-spline model.
We compare the performance with Polynomial model.
The proposed algorithm has better performance when we use smaller number of fed-back bits.
The proposed algorithm can attain the upper bound of system capacity with low feedback load.

25. Ren-Shian Chen E-mail : q38981179@mail.ncku.edu.tw
Thanks for your attention !
Ren-Shian Chen

27. Polynomial Model
L=10 27