1 CFO Estimation with ICI Cancellation for OFDM Systems 吳宗威

2 Outline Motivations Background knowledge Conventional CFO estimation strategies Modified CFO estimation strategies Simulation results Conclusions

3 Outline Motivations Background knowledge Conventional CFO estimation strategies Modified CFO estimation strategies Simulation results Conclusions

4 Motivations  Every OFDM model has a specific form in the carrier frequency offset system.  When we estimate the frequency offset by pilot,the ICI still exists. It is intuitive to decrease the ICI first, then estimate it.

5 Outline Motivations Background knowledge Conventional CFO estimation strategies Modified CFO estimation strategies Simulation results Conclusions

6 OFDM System Model  C is pilot sequence  h is time domain channel impulse response  w is additive white Gaussian noise.  N data information {S(k)} which have been modulated with N modulation values {X(k)} on every sub-carrier x ( t ) Channel h ( t) S ( k) r (t ) S/P P/S X (k ) x ( n) Adding Pilots C(n) & IFFT Adding Cyclic Prefix & P/S DAC Signal Mapper z (t ) FFT Remove Cyclic Prefix & S/P ADC Signal Demapper AWGN w ( t)  The OFDM system model:

7 OFDM System Model  The nth sample of an OFDM block generated by IFFT : N: number of subcarriers Ng: length of cyclic prefix

8 UWB Channel Model  Four environments in this UWB channel model:  CM1 model is based on LOS (0-4m) channel measurements in [2] Time Signal strength : cluster decay factor : path decay factor : cluster arrival rate : the arrival rate of path within each cluster

9 Outline Motivations Background knowledge Conventional CFO estimation strategies Modified CFO estimation strategies Simulation results Conclusions

10 Sensitivity for Carrier Frequency Offset  The OFDM system model with CFO: x ( t ) Channel h ( t) S ( k ) S/P X ( k ) x(n) Adding Pilots C(n)& IFFT Adding Cyclic Prefix & P/S DAC Signal Mapper z (t ) r (t ) P/S FFT Remove Cyclic Prefix & S/P ADC Signal Demapper AWGN w ( t)  is the ratio of the actual frquency offset to the sub-carrier spacing

11 Sensitivity for Carrier Frequency Offset  The n-th received sample of the m-th symbol is given by FFT

12  Amplitude reduction:  Phase shift: Sensitivity for Carrier Frequency Offset .. ..

13 Pilot tone - aided CFO Estimation  PTA with weighting (PTAW) CFO estimation: f  Let P denote the set of indexes of the Np pilot carriers I Q R1R1 R2R2 Pilot1 (n 1 ) Pilot2 (n 2 ) Pilot3 (n 3 ) t RmRm R m+D

14 Outline Motivations Background knowledge Conventional CFO estimation strategies Modified CFO estimation strategies Simulation results Conclusions

15 Matrix form of R(k)      

16 

17    

18 A math property  A(k), k=0…N-1 is the DFT of a(n), n=0,…,N-1  

19 The Problem Can we find a matrix B, such that 

20 B is in fact a matrix that does Gaussian Reduction to 

21 The term is the key point.Because if the ratio between each term is irrelevant to, then we can definitely finish the matrix B.

22 The numerator of is actually. And the denominator because So, we can regard as Thus, the ratio between each term is irrelevant to.

23 However, is zero when k=0. So we need a estimate for the denominator of  Choose the PTAW estimate for the denominator of  B is the matrix does Gaussian reduction to the cyclic matrix composed of

24 The Procedure Step1: Estimate the frequency offset by PTAW Step2: Substitute the estimate into the denominator of Step3: multiply the matrix B with the incoming symbol and the previous symbol Step4: Apply the PTAW again, then we have a more accurate estimate.

25 Outline Motivations Background knowledge Conventional CFO estimation strategies Modified CFO estimation strategies Simulation results Conclusions

26 Different Modulation BPSK

27 QPSK

28 8PSK

29 16PSK

30

31 Recursive

32 Random initial condition Random initial condition =0.5 Delta_f=0.1

33 Outline Motivations Background knowledge Conventional CFO estimation strategies Modified CFO estimation strategies Simulation results Conclusions

34 Conclusions  Advantages:  The key advantages of our proposed algorithms is to provide more accurate frequency synchronization.  Estimate the frequency offset without knowing the channel response first.  Complexity: N*Np multiplier.

35 Thank you ~

36 Reference [1] J. R. Foerster, Ed., “Channel Modeling Sub-committee Report Final,” IEEE P SG3a contribution. [2] H. Chen and G.J. Pottie, "A Comparison of Frequency Offset Tracking Algorithms for OFDM", GLOBECOM '03, vol.2, pp , Dec [3] K. Shi, E. Serpedin, and P. Ciblat, “Decision-directed fine synchronization for coded OFDM systems,” in Proc. IEEE International Conf. on Acoustics, Speech, and Signal Processing. (ICASSP’04), vol. 4, pp , May 2004.