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 E-mail : q38981179@mail.ncku.edu.tw

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

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

System Model Forward channel: Feedback channel: Gaussian quantization Parameterization Based on B-spline Forward channel: Model B of IEEE 802.11 TGn channel models: Rayleigh fading channel with 9 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.

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 802.11 TGn model B (9 taps) as our power delay profile. We assume that for simplification here.

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

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

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

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 .

Model the CRs Variation across Subchannels

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

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 :

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 .

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

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

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

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

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

Numerical Results

Numerical Results

Numerical Results

Numerical Results

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

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.

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

Polynomial Model L=10 27