1. ICI mitigation in OFDM systems 2005/11/2 王治傑

2. 2 Reference Y. Mostofi, D.C. Cox, “ICI mitigation for pilot-aided OFDM mobile systems,” IEEE trans. on wireless communications, vol.4, Mar 2005. W.G. Jeon, K.H. Chang and Y.S. Cho.”an equalization technique for OFDM systems in time-varying multipath channels,” IEEE trans. on communications, vol.47 Jan. 1999 “Iterative solutions of nonlinear equations in several variables,” academic press 1970

3. 3 System model Assume the normalized length of the channel is always less than or equal to G in this paper

4. 4 System model A constant channel is assumed over the time interval. for represents the kth channel tap in the guard and data interval respectively The channel output can be expressed as follow:

5. 5 System model where Furthermore is the average of the mth tap over 0<t<N*T s

6. 6 Simple pilot extraction A rough estimation for. Here we insert L equally spaced pilot at l i

7. 7 Piecewise linear approximation For normalized Doppler of up to 20%, linear approximation is a good estimate of channel time- variations and the effect on correlation characteristics is negligible

8. 8 Piecewise linear approximation Minimize

9. 9 Piecewise linear approximation Assume, it can be easily seen that F is minimized at s=N/2-1 or s=N/2. Therefore we approximate with the estimate of We have. Then can be expressed as follows:

10. 10 Piecewise linear approximation Hence

11. 11 Piecewise linear approximation Frequency domain relationship:

12. 12 Method 1: using CP The output CP vector can be written as Define

13. 13 Method 1: using CP Inserting into Q matrix

14. 14 Method 1: using CP Recommended procedure  Set the initial estimate of H slope to zero  Estimate H mid from pilots  Solve for X  Solve for ζ  Use to estimate H slope

15. 15 Method 2: utilizing adjacent symbols A constant slope is assumed over the time duration of T+(N/2)*T s for the former and T for the latter The former can handle lower Doppler values without processing delay while the latter would have a better performance

16. 16 Method 2: utilizing adjacent symbols From the figure above

17. 17 Method 2: utilizing adjacent symbols

18. 18 Solve the matrix inverse problem The bottleneck is to solve which contains N simultaneous equations Also, it requires NxN matrix inversion and has complexity O(N 3 )

19. 19 Solve the matrix inverse problem(1) The general solution are not adequate  Gauss-Jordan elimination Although it can raise accuracy by pivoting  Cholesky’s method Use iterative method  Jacobi iteration  Gauss-Seidel Sufficient condition: diagonally dominant

20. 20 Solve the matrix inverse problem(2) Remove those less dominant ICI terms. Then transform the matrix H’ to a block- diagonal matrix H’’, e.g., Y=HX

21. 21 Solve the matrix inverse problem(2)

22. 22 Solve the matrix inverse problem(2) Then

23. 23 Solve the matrix inverse problem(2) Finally, the size of the matrix inverse is lowered to (q+1) by (q+1) This method is only available when the multipath fading channel is slowly time varying.

24. 24 Solve the matrix inverse problem(3)