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 Pilot Arrangement 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 , Sep., 2002.

8. Outline OFDM Overview Pilot Arrangement
Channel Block-Type
Channel Comb-Type Pilot
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 1 Input to Time Domain 2 Guard Interval 3 Channel4
Guard Removal 5
Output to Frequency Domain 6
Output
Channel
ICI
AWGN 7
Channel Estimation
Estimated Channel

14. Pilot Arrangement Comb Type Block 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
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
[1]

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

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

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-Typed0 d4
P-21 d5
d17
P-7
d18
d23 DC
d24
d29 P7
d30
d42
P21
d43
d47
-26
-21 -7 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
Spline Cubic Interpolation (spline in MATLAB)
[2]

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

29. Interpolation @ Comb-Type
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:
[3]

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

31. Conclusion OFDM System Block Type Comb Type Modulation
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.