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：2005.07.04 長庚大學電機所無線通訊實驗室

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

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.

Receive Spectrum Transmit Spectrum Channel Spectrum Channel Training Tone Data Tone 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).

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

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

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

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)

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

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

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 802.11a standard

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

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

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

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

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

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.

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 

Simulation environments • IEEE 802.11a 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

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

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

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

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

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

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

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

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

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

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

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 802.11a standard.

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.84-88. [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.377-378.

Thank you~

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