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

2

OutlineIntroduction

MotivationSystem block

Viterbi decoding using channel state information (CSI)

One-tap frequency domain LMS weighting valueCSI aided Viterbi algorithmMean offsetTime-average methods

Simulation resultsWith CSI onlyWith CSI and mean offset

Conclusions & Future works

3

OutlineIntroduction






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.

f

Sampling points 1f

T

5

MotivationHowever, 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 ToneData Tone

Channel Spectrum

6

System blockHere, we use the weighting values of one-tap frequency domain LMS equalizers as different CSI.

Signal from radio receiver

Remove Cyclic Prefix

FFTFrequency Domain

EqualizerDe-mapping

De-interleaver

QuantizationViterbi

DecoderReceived Data bits

CSI from LMS weighting value

Some other CSI sources:

1. Known signal from standardization [1]

2. LMS error signal [2]

7

Viterbi decoding using CSICSI aided Viterbi decoder block diagram

Buffer BMC SAM

SPMTrace Back

Soft decision coded data

Decoded data bits

CSI from updated LMS weighting value

BMC: Branch Metric Calculation

SAM: State Accumulate Metric

SPM: Survival Path Matrix

8

OutlineIntroduction






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 bitk, l : k-th subcarrier and l-th OFDM symbol

XYZwed

'

2rs

H

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)

FFT P/SA/D S/P

EQ0

channel

Rx Data

EQk

EQ1

,k lY,n ly

11

LMS algorithmTo avoid big received power, the NLMS is replaced for LMS algorithm.The NLMS recursively updated tap weights

' *, 1 , , , ,k l k l k k l k lw w e Y

'*, ,

.kk l k lY Y

LMS Filter

Adaptive Weight Control Mechanism +

+

,k lY,k lw

*, , ,k l k l k lZ w Y

,k ld

,k le

where

The desired signal is assumed to be the same as transmitted signal

12

LMS weighting valueFrom [3], we derived the Wiener solution of one-tap frequency domain LMS equalizer is

thus, we could get the CSI as

,

, 2 2( ) .

k ljk

o k l

k N

H ew

H

, 2 2

( ) .ko k l

k N

Hw

H

Consider the noise and channel only

2

2

,

1CSI .k k

k l

Hw

13

Other CSI sourcesWe also compare the proposed method with other two CSI sources

CSI from long training symbols :

CSI from LMS error signal :

' ' * ' ' *21, 1, 2, 2,CSI .

2k k k k

k k

L L L LH

2

2

,

1CSI ,k k

k l

He

'

1L '

2L and are 1st and 2nd received long training symbols in 802.11a standard

14

Viterbi algorithmThe probability of the received bits could be model as

from central limit theory

( ) ( )1 2

1

( , ,..., | ) ( | ).L

m mL l l

l

p r r r p r s

s

2( )

1 2 21

2

21

1 ( )( , ,..., ) exp[ ]

22

1 ( )( ) exp[ ],

22

Lm l

Ll nn

LL l

l nn

r sp r r r

r s

s

2( )

1 2 21

1 ( )ln( ( , ,..., )) ln( ) .

22

Lm l

Ll nn

r sp r r r L

s

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

2,( )

21

( )( ) ,

2

Lk l km

k kl k

r sD

r ,s

2k

( ) 2,

1

( ) ( ) ,L

mk k k k l k

l

D CSI r s

r ,s

16

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

-2 -1.5 -1 -0.5 0 0.5 1 1.5 2-2

-1.5

-1

-0.5

0

0.5

1

1.5

2BPSK equalized signal constellation before mean offset

In-phase

Qua

drat

ure

10dB, 1000 symbols

transmitted signal

-2 -1.5 -1 -0.5 0 0.5 1 1.5 2-2

-1.5

-1

-0.5

0

0.5

1

1.5

2QPSK equalized signal constellation before mean offset

In-phase

Qua

drat

ure

10dB, 1000 symbols

transmitted signal

*, , ,[ ( ) ] 0.783.k l k k l k lE w H X N

17

Mean offsetThus, after considering the mean offset

rewrite this, we could derive the final math expression with CSI and mean offset

( ) 2,

1

( , ) ( ) .L

mk k k k l k k

l

D CSI A s

r s r

,( ) 2 2

1

( , ) ( ) .L

k lmk k k k k

l k

rD CSI A s

A

r s

18

Time-average methodsIf we want to calculate

there are two time-average methods applied here :

,[ ]k lE

, 1 , , ,0

1 1,

1 1 1

L

k l k l k l k ll

Lv v

L L L

, 1 , , 1(1 ) ,k l k l k l

: time-averaged value

: newly entered value

: forgetting factor ( 0 < < 1 )

v

19

Time-average methodsWhen 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.

,k lv

,k l

, 1 , , ,0

1 1,

1 1 1

L

k l k l k l k ll

Lv v

L L L

20

Time-average methodsWhen 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

, 1 , , 1(1 ) ,k l k l k l

,k lv

,k l

21

OutlineIntroduction






22

Simulation environmentsIEEE 802.11a standardTransmission data per packets = PSDU 256 BytesTransmission packets = 1000 packetsExponentially decaying Rayleight fadingwith sampling period and RMS time CFO = 3125 HzSFO = 800 Hz = 0.16-bit soft decision Viterbi decoding

50sT ns 50RMST ns

23

Inner receiver structureFFTInitial Equalizer

Update Coefficients of Equalizer

Phase Compensation

Frequency Domain

Equalizer

Phase Compensation

Estimate Phase Error

Outer Receiver

Decision

, , 0k lY l

,k lY

,k lw

,k ld,k lZ

We also adopted this structure from [4].

The advantage of this structure is the phase compensation.

24

Simulations ~ with CSI onlyBPSK, performance in BER and PER

2 4 6 8 10 12 14 1610

-6

10-5

10-4

10-3

10-2

10-1

100

Eb / No (dB)

Bit

Err

or R

ate

(BE

R)

BPSK, PSDU 256 Bytes, 1000 frames, step=0.1

no CSI + hard decision

no CSI + soft decisionweighting as CSI

2 4 6 8 10 12 14 1610

-3

10-2

10-1

100

Eb / No (dB)

Pac

ket

Err

or R

ate

(PE

R)




“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

2 4 6 8 10 12 14 1610

-6

10-5

10-4

10-3

10-2

10-1

100

Eb / No (dB)

Bit

Err

or R

ate

(BE

R)

QPSK, PSDU 256 Bytes, 1000 frames, step=0.1



2 4 6 8 10 12 14 1610

-3

10-2

10-1

100

Eb / No (dB)

Pac

ket

Err

or R

ate

(PE

R)




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


2 4 6 8 10 12 14 16 1810

-6

10-5

10-4

10-3

10-2

10-1

100

Eb / No (dB)

Bit

Err

or R

ate

(BE

R)


error

long trainweighting

2 4 6 8 10 12 14 16 1810

-3

10-2

10-1

100

Eb / No (dB)

Pac

ket

Err

or R

ate

(PE

R)


error

long trainweighting

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


2 4 6 8 10 12 14 1610

-6

10-5

10-4

10-3

10-2

10-1

100

Eb / No (dB)

Bit

Err

or R

ate

(BE

R)


error

long trainweighting

2 4 6 8 10 12 14 1610

-3

10-2

10-1

100

Eb / No (dB)

Pac

ket

Err

or R

ate

(PE

R)


error

long trainweighting

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

2 4 6 8 10 12 14 1610

-6

10-5

10-4

10-3

10-2

10-1

100

Eb / No (dB)

Bit

Err

or R

ate

(BE

R)

BPSK, PSDU 256 Bytes, 1000 frames, step = 0.1

error + offset

long train + offsetweighting + offset

2 4 6 8 10 12 14 1610

-3

10-2

10-1

100

Eb / No (dB)

Pac

ket

Err

or R

ate

(PE

R)

BPSK, PSDU 256 Bytes, 1000 frames, step = 0.1

error + 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

292 4 6 8 10 12 14 1610

-6

10-5

10-4

10-3

10-2

10-1

100

Eb / No (dB)

Bit

Err

or R

ate

(BE

R)

QPSK, PSDU 256 Bytes, 1000 frames, step = 0.1

error + offset

long train + offset

weighting + offset

2 4 6 8 10 12 14 1610

-3

10-2

10-1

100

Eb / No (dB)

Pac

ket

Err

or R

ate

(PE

R)

QPSK, PSDU 256 Bytes, 1000 frames, step = 0.1

error + offset


Simulations ~ with CSI and mean offsetQPSK, 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

2 4 6 8 10 12 14 1610

-6

10-5

10-4

10-3

10-2

10-1

100

Eb / No (dB)

Bit

Err

or R

ate

(BE

R)

Performance comparison in BPSK modulation

hard decision

soft decisionCSI added

CSI + offset

2 4 6 8 10 12 14 1610

-3

10-2

10-1

100

Eb / No (dB)

Pac

ket

Err

or R

ate

(PE

R)

Performance comparison in BPSK modulation

hard decision


CSI + offset

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 ~ comparisonQPSK, 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

2 4 6 8 10 12 14 1610

-6

10-5

10-4

10-3

10-2

10-1

100

Eb / No (dB)

Bit

Err

or R

ate

(BE

R)

Performance comparison in QPSK modulation

hard decision


CSI + offset

2 4 6 8 10 12 14 1610

-3

10-2

10-1

100

Eb / No (dB)

Pac

ket

Err

or R

ate

(PE

R)

Performance comparison in QPSK modulation

hard decision


CSI + offsest

32

OutlineIntroduction






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 802.11a standard.

35

References[1] Weon C. Lee, Hyung M. Park, Kyung J. Kang and Kuen B. Kim, 1998, “Pe

rformance 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.

36

Thank you~

Documents

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

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