1. 研 究 生：吳濟廷 指導教授：高永安 口試日期：2005.07.04 長庚大學電機所 無線通訊實驗室
以一階頻域LMS等化器係數為通道資訊於OFDM系統解碼器 Using the Weighting Value of One-Tap Frequency Domain LMS Equalizer as Channel State Information for Viterbi Decoder of OFDM systems
研 究 生：吳濟廷
指導教授：高永安
口試日期：
長庚大學電機所 無線通訊實驗室

2. Outline
Introduction
Motivation
System block
Viterbi decoding using channel state information (CSI)
One-tap frequency domain LMS weighting value
CSI aided Viterbi algorithm
Mean offset
Time-average methods
Simulation results
With CSI only
With CSI and mean offset
Conclusions & Future works

3. Outline
Introduction
Motivation
System block
Viterbi decoding using channel state information (CSI)
One-tap frequency domain LMS weighting value
CSI aided Viterbi algorithm
Mean offset
Time-average methods
Simulation results
With CSI only
With CSI and mean offset
Conclusions & Future works

4. Introduction
The basic idea of OFDM is to divide the available spectrum into several sub-channels.
In conventional Viterbi algorithm, each path is seem to experience the same fading level.

5. Motivation
However, in presence of channel fading, each subcarrier is experiencing different channel statuses.
Thus, the different reliabilities for each subcarrier are given, named channel state information (CSI).
Transmit Spectrum
Receive Spectrum
Channel Training Tone
Data Tone
Channel Spectrum

6. System block
Here, we use the weighting values of one-tap frequency domain LMS equalizers as different CSI.
Some other CSI sources:
Known signal from standardization [1]
LMS error signal [2]

7. Viterbi decoding using CSI
CSI aided Viterbi decoder block diagram
BMC: Branch Metric Calculation
SAM: State Accumulate Metric
SPM: Survival Path Matrix

8. Outline
Introduction
Motivation
System block
Viterbi decoding using channel state information (CSI)
One-tap frequency domain LMS weighting value
CSI aided Viterbi algorithm
Mean offset
Time-average methods
Simulation results
With CSI only
With CSI and mean offset
Conclusions & Future works

9. Parameter definition : transmitted signal in frequency domain
: received signal in frequency domain
: equalized signal
: LMS weighting value
: LMS error signal
: LMS desired signal
: LMS step size
: frequency domain channel response
: noise variance
: total phase rotation
: received bit
: transmitted bit
k, l : k-th subcarrier and l-th OFDM symbol

10. One-tap frequency domain LMS equalizer
There’s a one-tap frequency domain LMS equalizer on each subcarrier after FFT.
It could compensate…
In common communication system: Magnitude and phase distortion
In OFDM system:
Carrier frequency offset (CFO)
Sampling frequency offset (SFO)

11. LMS algorithm
To avoid big received power, the NLMS is replaced for LMS algorithm.
The NLMS recursively updated tap weights
where
The desired signal is assumed to be the same as transmitted signal

12. LMS weighting value
From [3], we derived the Wiener solution of one-tap frequency domain LMS equalizer is
thus, we could get the CSI as
Consider the noise and channel only

13. Other CSI sources
We also compare the proposed method with other two CSI sources
CSI from long training symbols :
CSI from LMS error signal :
and are 1st and 2nd received long training symbols in a standard

14. Viterbi algorithm
The probability of the received bits could be model as
from central limit theory

15. CSI aided Viterbi algorithm
after simplification
because is unpredictable in OFDM systems( CFO, SFO and step size…etc.), we used the CSI to reflect the variance term

16. Mean offset
Due to the undesired effects, the mean of equalized signal shifts respectively, we named this situation “ mean offset ”.

17. Mean offset Thus, after considering the mean offset
rewrite this, we could derive the final math expression with CSI and mean offset

18. Time-average methods If we want to calculate
there are two time-average methods applied here :
: time-averaged value
: newly entered value
: forgetting factor ( 0 < < 1 )

19. Time-average methods
When calculate the NLMS input power and mean offset, the time-average method we used is
represents the time-averaged input power and time- averaged mean offset respectively.
represents the l-th input power and l-th equalized signal respectively.

20. Time-average methods 
When calculate the channel state information, the time-average method we used is
is time-averaged channel state information
is newly entered channel state information
is called forgetting factor, 0< <1 

21. Outline
Introduction
Motivation
System block
Viterbi decoding using channel state information (CSI)
One-tap frequency domain LMS weighting value
CSI aided Viterbi algorithm
Mean offset
Time-average methods
Simulation results
With CSI only
With CSI and mean offset
Conclusions & Future works

22. Simulation environments
IEEE a standard
Transmission data per packets = PSDU 256 Bytes
Transmission packets = 1000 packets
Exponentially decaying Rayleight fading
with sampling period and RMS time
CFO = 3125 Hz
SFO = 800 Hz
= 0.1
6-bit soft decision Viterbi decoding

23. Inner receiver structure
We also adopted this structure from [4].
The advantage of this structure is the phase compensation.

24. Simulations ~ with CSI only
BPSK, performance in BER and PER
“no CSI + hard decision”= conventional OFDM system with hard decision
“no CSI + soft decision”= conventional OFDM system with 6-bit soft decision
“weighting as CSI”= the proposed method with 6-bit soft decision

25. Simulations ~ with CSI only
QPSK, performance in BER and PER
“no CSI + hard decision”= conventional OFDM system with hard decision
“no CSI + soft decision”= conventional OFDM system with 6-bit soft decision
“weighting as CSI”= the proposed method with 6-bit soft decision

26. Simulations ~ with CSI only
BPSK, performance in BER and PER
“error”= using LMS error signal as channel state information
“longtrain”= using long training symbol as channel state information
“weighting”= using LMS weighting value as channel state information

27. Simulations ~ with CSI only
QPSK, performance in BER and PER
“error”= using LMS error signal as channel state information
“longtrain”= using long training symbol as channel state information
“weighting”= using LMS weighting value as channel state information

28. Simulations ~ with CSI and mean offset
BPSK, performance in BER and PER
“error + offset”= using LMS error signal as CSI plus mean offset mechanism
“longtrain + offset”= using long training symbol as CSI plus mean offset mechanism
“weighting + offset”= using LMS weighting value as CSI plus mean offset mechanism

29. Simulations ~ with CSI and mean offset
QPSK, performance in BER and PER
“error + offset”= using LMS error signal as CSI plus mean offset mechanism
“longtrain + offset”= using long training symbol as CSI plus mean offset mechanism
“weighting + offset”= using LMS weighting value as CSI plus mean offset mechanism

30. Simulations ~ comparison
BPSK, performance in BER and PER
“hard decision”= conventional OFDM system with hard decision
“soft decision”= conventional OFDM system with soft decision
“CSI added”= CSI from LMS weighting value without mean offset mechanism
“CSI + offset”= CSI from LMS weighting value with mean offset mechanism

31. Simulations ~ comparison
QPSK, performance in BER and PER
“hard decision”= conventional OFDM system with hard decision
“soft decision”= conventional OFDM system with soft decision
“CSI added”= CSI from LMS weighting value without mean offset mechanism
“CSI + offset”= CSI from LMS weighting value with mean offset mechanism

32. Outline
Introduction
Motivation
System block
Viterbi decoding using channel state information (CSI)
One-tap frequency domain LMS weighting value
CSI aided Viterbi algorithm
Mean offset
Time-average methods
Simulation results
With CSI only
With CSI and mean offset
Conclusions & Future works

33. Conclusions
We could observe that, comparing to conventional OFDM system, the proposed method gains the performance by giving different reliabilities.
Compare with other methods, the proposed method has the best performance due to updating coefficients and robustness to decision error.
Mean offset mechanism is considered to obtain the better performance

34. Future works
In 16QAM and 64 QAM modulation, due to the different magnitudes, the mean offset mechanism is hard to applied.
The updated LMS weights make the hardware complex and plenty of computations.
Other code rates are applied to conform with IEEE a standard.

35. References
[1] Weon C. Lee, Hyung M. Park, Kyung J. Kang and Kuen B. Kim, 1998, “Performance analysis of Viterbi decoder using channel state information in COFDM system,” IEEE Transactions on Broadcasting, Vol. 44, no.4.
[2] Yong Wang, JianHua Ge, Bo Ai, Pei Liu and ShiYong Yang, 2004, “A soft decoding scheme for wireless COFDM with application to DVB-T,” IEEE Transactions on Consumer Electronics, Vol.50, No.1, pp
[3]黃凡維, 2004, “一階最小均方差頻域等化器應用於正交分頻多工系統之特性分析,” 長庚大學電機工程研究所碩士論文.
[4] Y. A. Kao, C. H. Su, S. K. Lee, C. L. Hsiao and P. L. Chio, 2005, “A robust design of inner receiver structure for OFDM systems,” Digest of technical papers, ICCE, pp

36. Thank you~