Upload
annabella-pearson
View
228
Download
7
Embed Size (px)
Citation preview
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
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
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
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
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
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
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)
BPSK, PSDU 256 Bytes, 1000 frames, step=0.1
no CSI + hard decision
no CSI + soft decisionweighting as CSI
“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
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)
QPSK, PSDU 256 Bytes, 1000 frames, step=0.1
no CSI + hard decision
no CSI + soft decisionweighting as CSI
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
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)
BPSK, PSDU 256 Bytes, 1000 frames, step=0.1
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)
BPSK, PSDU 256 Bytes, 1000 frames, step=0.1
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
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
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)
QPSK, PSDU 256 Bytes, 1000 frames, step=0.1
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
long train + offsetweighting + 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
long train + offsetweighting + 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
soft decisionCSI added
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
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 QPSK modulation
hard decision
soft decisionCSI added
CSI + offsest
32
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
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~