Optimal CSD and Truncated SVD for Channel Estimation

1. Optimal CSD and Truncated SVD for Channel Estimation Authors: Date: 2008-09-08 Wahyul Syafei, KIT JAPAN

2. Abstract Adjusting the cyclic shift of long training field will minimize the condition number. Truncating the singular value decomposition of the estimated channel will minimize the noise effect. Combination of both technique will enhance the channel estimation quality Wahyul Syafei, KIT JAPAN

3. Optimal CSD and Truncated SVD for Channel Estimation • Singular-Value truncation: minimizing noise effect on estimated CIR. • Cyclic shift adjustment of Long preamble on the successive antenna: minimizing Condition-number between singular values of the estimated CIR. Wahyul Syafei, KIT JAPAN

4. MIMO-OFDM Tx system Time domain Cyclic shift Channel Coding Mux CP Long Preamble 1 d1 Mapper IFFT Mux CP Long Preamble 2 Mapper IFFT d2 … … Mux CP Long Preamble N dN Mapper IFFT Wahyul Syafei, KIT JAPAN

5. MIMO-OFDM Rx system Error detection Maximum Likelihood Decoder de Mux CP Channel estimation 1 d1 FFT de Mux CP Channel estimation 2 FFT d2 … … de Mux CP Channel estimation N dN FFT Wahyul Syafei, KIT JAPAN

6. Cyclic Shifting on LTF Tx Antenna # LTF 1 STF C0 C1 C2 cs SIG DATA STF cs C0 C1 C2 SIG DATA 2 N STF C2 cs C0 C1 SIG DATA Wahyul Syafei, KIT JAPAN

7. MISO case L1 h1 Long preamble 1 rlp Channel estimator L2 h2 Long preamble 2 Error of ML estimation will be minimized if: or with L are the long preamble symbols and already known by the receiver. Wahyul Syafei, KIT JAPAN

8. MISO case 32 32 145 Wahyul Syafei, KIT JAPAN

9. SV-Truncation To minimize the noise effect, SV-truncation ( ) is proposed. From the known LTF:  The new term of known LTF becomes: Estimated CIR is: Exp. the truncated SVD for q =2, 32 32 Wahyul Syafei, KIT JAPAN 145

10. V X+ Proposed L S V D (32 X 145) Inner product truncation U (16 X 1) (64 X 1) S/P Add zeros FFT rlp,j Add zeros FFT (64 X 1) (145 X 1) (32 X 1) (16 X 1) 64 SV-Truncation (32 X 32) (32 X 145) (32 X 145) (145 X 145) Wahyul Syafei, KIT JAPAN

11. Condition Number The ratio between the biggest singular value to the smallest one, written as: If the CN =1, then is the constant X identity matrix and zeros matrix, which is easier to be handled. Regarding the SVD truncation, there is a Partial Condition Number: Find the smallest value (PCN 1), by adjusting the cyclic shift, as shown in Simulation 1. Wahyul Syafei, KIT JAPAN

12. Simulation 1, find the optimal CS CS=80 CS=18 CS=64 No truncation Wahyul Syafei, KIT JAPAN

13. Find the optimal q  1. Consider the noise part. 2. Consider the channel error. where and… Wahyul Syafei, KIT JAPAN

14. Find the optimal q Example for q = 0, where 32-q 32 32-q 32 Considering the channel error and noise part, we have.  min as shown in Simulation 2. Wahyul Syafei, KIT JAPAN

15. Simulation 2, find the optimal q CS=18 samples; min J is found at q=4 CS=80 samples; min J is found at q=5 CS=64 samples; min J is found at q=5 Wahyul Syafei, KIT JAPAN

16. Simulation 3, Performance Wahyul Syafei, KIT JAPAN

17. Conclusion • The truncation of SVD of the estimated channel will minimize the noise effect. • The cyclic shift adjustment will minimize the partial condition number of SVD of the estimated channel. • The combination of both will increase the quality of channel estimation. Wahyul Syafei, KIT JAPAN

18. References • IEE802.11a • IEE802.11n draft Wahyul Syafei, KIT JAPAN