1. The Adaptive Algorithm of Symbol Timing And Carrier Phase Estimation in OFDM Systems Jun Wu, Qun Zhou and K.K.M.Cheng Department of Electronic Engineering, The Chinese University of Hong Kong, N.T., Hong Kong
老師：高永安
學生：蔡育修

2. Outline Introduction OFDM Symbol Structure
Timing and Carrier Phase Estimator
Estimation and Correction of Residual Timing Offset
Results and Conclusion

3. Introduction OFDM is highly sensitive to synchronization error.
Two problems in the design of OFDM receiver：
a. symbols timing synchronization.
b. mismatch of the oscillators in the transmitter and receiver carrier phase offset.
OFDM synchronization：
a. use of pilot symbols lowers the data rate.
b. use cyclic prefix loss of power.
The advantage for this paper：needs only several pilot symbols and simply computation.

4. Residual timing offset
OFDM Symbol Structure
N： number of subcarriers.
X(k)：the complex–valued data symbols. (after mapping)
L：2m (m is positive integer)，L<N
X(1) = X(2)
X(N-1) = X(N-2) = X*(1)
X(N/L + 1) = X(1)
X(N - (N/L + 1)) = X*(1)
Timing & carrier phase
Residual timing offset

5. Timing and Carrier Phase Estimator
Assume timing offset d samples and carrier phase offset θ.
When N is large , each subchannel can be consider as flat fading channel Hk , k = 1,2,N-1,N-2 are approximately equal.

6. After FFT,

7. Timing estimator
If the amplitude of channel can be estimated. When d is small,

8. Im[Y(1)Y*(2)]>0, (i+1)-th OFDM
But in practice, the channel is unknown, and the noise will result in the error value of d.
Adaptive algorithm
Im[Y(1)Y*(2)]
Stable point
怪!!
Im[Y(1)Y*(2)]>0, (i+1)-th OFDM
symbol is toward d=0;
Otherwise, toward d=N.

9. βs can be set a large initial value accelerate the timing synchronization.
βs decreases each time until βs is equal to residual timing offset small.
萬一太早結束?

10. Phase offset, base on the similar thoery.
Adaptive algorithm
Im[Y(1)Y(N-1)]
Stable point

11. βc set a large initial value for rapid convergence, then decreases each time until a fixed value, which determinate the phase accuracy.

12. Estimation and Correction of Residual Timing Offset
The synchronization algorithm acquire to within several samples.
The residual offset may cause phase rotation of every sample, results in serious bit error rate.
Assume that actual delay is dact, the residual offset is
The samples of OFDM symbol will rotate
A咧?!

13. 16QAM
constellation
Estimate

14. The information of △di is included in the phase of r.
So we can make decision on the phase of r, then deduce the residual timing offset △di .
L = 16
noise mean power
Signal mean power

15. For L = 16, if △di ≦ 7, the dact can be obtained as table.
The accuracy of this method is concerned with ,
only when
We also calculate , and adopt the average phase of r and r1 to estimate the residual timing offset.
萬一平均後，相角不在table上?

16. Results and Conclusion
N = 256, L = 16, 16QAM, pilot symbols are
In each simulation, symbols are used.
The performance of the estimators：MSE.
First, consider the AWGN channel which consists of 13 independent fading taps.
Time-invariant flat fading per subcarrier & OFDM symbol.

17. Real part
Imaginary part

18. Ideal 16QAM system