指導教授:高永安 學 生:蘇家弘

1. Joint Weighted Least-Squares Estimation of CFO and Timing Offset for OFDM Systems Over Multipath Fading Channels 指導教授:高永安 學 生:蘇家弘

2. P. Y. Tsai, H. Y. Kang, T. D. Chiueh, ” Joint Weighted Least-Squares Estimation of Carrier-Frequency Offset and Timing Offset for OFDM Systems Over Multipath Fading Channels,” IEEE Trans. VTC, vol. 54, NO. 1, Jan. 2005.

3. OFDM block diagram

4. OFDM signal with synchronization errors • N-th time domain sample of the i-th transmitted symbol can be expressed as • Ng : Cyclic Prefix • Ts : sample interval • Ak,i : k-th complex data of the i-th symbol

5. Multipath fading channel with a channel impulse response • Received signal is presented as • Δf : CFO • δTs : SFO

6. The received complex frequency domain data on the k-th subcarrier of the i-th symbol Zk,i as Normalized CFO ε= Δf *T

7. Zk,i is further decomposed into three components, signal term Sk,i ; interference term Ik,i ; noise term Vk,i • Magnitude attenuation function

8. Signal term • ICI term Small ε and δ

9. When both CFO and SFO are present • Consequently, Sk,i/Hk will be shifted in phase by

10. Weighted Least Squares(WLS) • Assume J pilots are inserted among N subcarriers denoted by xj ,j=0,1…,J-1. Pilot data are differentially encoded with PN-sequence Cxj,i ={+1,-1} and Axj,i=Axj,i-1Cxj,I • The averaged phase difference between two consecutive OFDM symbols at the receiver arg(.) is the phase of its argument and summation

11. Since δ* ε can be ignored

12. Vector form is • where y=Xb+e y=[y0y1… yJ-1]T e=[e0e1… eJ-1]T

13. Assume the channel is stationary during these symbols; the WLS estimate of b is given • The estimated CFO and SFO can be obtained by

14. If we assume that the error vector e is zero mean, the WLS estimation is • The covaricance matrix of the estimation error becomes