Channel Estimation

1. Channel Estimation 黃偉傑

2. Small Scale Fading -- 1 • Problem 1: multi-path induces delay spread.

3. Impulse Response Model of a Multipath Channel • A mobile radio channel may be modeled as a linear filter with a time varying impulse response, where the time variation is due to receiver motion in space. • The filtering nature of the channel is caused by the summation of amplitudes and delays of the multiple arriving waves at any instant of time.

4. Channel Impulse Response • Due to the different multipath waves which have propagation delays which vary over different spatial locations of the receiver, the impulse response of the linear time invariant channel should be a function of the position of the receiver.

5. Received Signal

6. Channel Estimation Techniques Based on PilotArrangement in OFDM Systems

7. Reference • Sinem Coleri, Mustafa Ergen, Anuj Puri, and Ahmad Bahai, “Channel Estimation Techniques Based on Pilot Arrangement in OFDM Systems,” IEEE Trans. On Broadcasting., Vol. 48, No. 3, pp. 223-229, Sep., 2002.

8. Outline • OFDM Overview • Pilot Arrangement • Channel Estimation @ Block-Type • Channel Estimation @ Comb-Type Pilot • Interpolation @ Comb-Type

9. Introduction • The channel estimation can be performed by either inserting pilot tones into all of the subcarriers of OFDM symbols with a specific period (block type) or inserting pilot tones into each OFDM symbol (comb type). • The block type estimation can be based on Least Square (LS) or Minimum Mean-Square (MMSE). • The comb type estimation can be based on LS or MMSE or Least Mean-Square (LMS) then interpolate the channel.

10. OFDM Overview • Divides high-speed serial information signal into multiple lower-speed sub-signals. • Transmits simultaneously at different frequencies in parallel. • Modulation ( BPSK,QPSK,16QAM, 64QAM). • Pilot subcarriers used to prevent frequency and phase shift errors.

11. Benefits of OFDM • Higher data rates • Overlap of subcarriers • Lower bandwidth than spread spectrum. • High spectral efficiency • Lower multi-path distortion • Usage of cyclic prefix

12. System Architecture

13. System Architecture Input to Time Domain 1 2 3 Guard Interval Channel 4 5 Guard Removal Output to Frequency Domain 6 Channel 7 Estimated Channel Output ICI AWGN Channel Estimation

14. Pilot Arrangement • Comb Type • Some sub-carriers are reserved for pilots for each symbol • Block Type • All sub-carriers reserved for pilots with a specific period

15. Channel Estimation @Block-Type • If ISI is eliminated by the guard interval, we can write where

16. Channel Estimation @Block-Type [1] • If the time domain channel vector h is Gaussian and uncorrelated with the channel noise W, the frequency domain MMSE estimate of h is given by: where

17. Channel Estimation @Block-Type [1] • The LS estimate is represented by : where

18. Channel Estimation @Block-Type • When the channel is slow fading, the channel estimation inside the block can be updated using the decision feedback equalizer at each sub-carrier. • For fast fading, the comb-type estimation performs much better. Decision Feedback Equalizer

19. Channel Estimation @Block-Type Block type

20. Channel Estimation @ Comb-Type • The Np pilot signals uniformly inserted in X(k) according to the following equation: where L= # of Carriers / Np and xp(m) is the mth pilot carrier value. • We define {Hp(k) k=0,1,…,Np} as the frequency response of the channel at pilot sub-carriers • Yp(k)and Xp(k) are output and input at the kth pilot sub-carrier respectively.

21. Channel Estimation @ Comb-Type • The estimate of the channel at pilot sub-carriers based on LS estimation is given by: • Yp(k)and Xp(k) are output and input at the kth pilot sub-carrier respectively. • Since LS estimate is susceptible to noise and ICI, MMSE is proposed while compromising complexity.

22. Channel Estimation @ Comb-Type d5 P7 d4 P-21 d17 P-7 d18 d23 DC d24 d29 d30 d42 P21 d43 d47 d0 -26 -21 -7 0 7 21 26

23. Interpolation @ Comb-Type • Linear Interpolation • Second Order Interpolation • Low pass Interpolation • Spline Cubic Interpolation • Time Domain Interpolation

24. Interpolation @ Comb-Type • Linear Interpolation

25. Interpolation @ Comb-Type • Second Order Interpolation

26. Interpolation @ Comb-Type • Low Pass Interpolation (interp in MATLAB) • Insert zeros into the original sequence • Low-pass FIR filter while passing original data unchanged • Interpolation such that mean-square error between ideal and interpolated values min.

27. Interpolation @ Comb-Type [2] • Spline Cubic Interpolation (spline in MATLAB)

28. Interpolation @ Comb-Type • Spline Cubic Interpolation-cont.

29. Interpolation @ Comb-Type [3] • Time Domain Interpolation • The time domain interpolation is a high-resolution interpolation based on zero-padding and DFT/IDFT. • We first convert it to time domain by IDFT: • The signal is interpolated by transforming the points into N points with the following method:

30. Interpolation @ Comb-Type • Time Domain Interpolation • The estimation of the channel at all frequencies is obtained by:

31. Conclusion • OFDM System • Block Type • Direct or Decision Feedback • Comb Type • LS or LMS estimation at pilot frequencies • Interpolation Techniques • Linear • Second Order • Low Pass • Spline • Time Domain • Modulation • BPSK,QPSK,16QAM,64QAM

32. References • [1] Steven M. Kay, “Fundamentals of Statistical Signal Processing Estimation Theory,” Prentice Hall, 1993. • [2] Erwin Kreyszig, “Advanced Engineering Mathematics,”John wiley & Sons, 1983. • [3] Yuping Zhao, Aiping Huang, “A novel channel estimation method for OFDM mobile communication systems based on pilot signals and transform-domain processing ,”IEEE VTC , Vol. 3, May 1997. • [4] Sinem Coleri, Mustafa Ergen, Anuj Puri, and Ahmad Bahai, “Channel Estimation Techniques Based on Pilot Arrangement in OFDM Systems,”IEEE transactions on Broadcasting, Vol. 48, No. 3, September 2002.