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

2 Reference Y. Mostofi, D.C. Cox, “ICI mitigation for pilot-aided OFDM mobile systems,” IEEE trans. on wireless communications, vol.4, Mar 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 “Iterative solutions of nonlinear equations in several variables,” academic press 1970

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

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

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

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 Piecewise linear approximation Minimize

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 Piecewise linear approximation Hence

11 Piecewise linear approximation Frequency domain relationship:

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

13 Method 1: using CP Inserting into Q matrix

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 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 Method 2: utilizing adjacent symbols From the figure above

17 Method 2: utilizing adjacent symbols

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 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 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 Solve the matrix inverse problem(2)

22 Solve the matrix inverse problem(2) Then

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 Solve the matrix inverse problem(3)