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嶄新的一階頻域 RLS 等化器 結合通道資訊輔助 Viterbi 解碼器應用於 OFDM 系統中 A Novel one-tap frequency domain RLS equalizer combined with Viterbi decoder using channel state information in OFDM systems. Advisor: Yung-An Kao Student: Chi-An Young. Outline. Introduction Motivation OFDM system - PowerPoint PPT Presentation
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1
嶄新的一階頻域 RLS 等化器結合通道資訊輔助 Viterbi 解碼器應用於 OFDM 系統中
A Novel one-tap frequency domain RLS equalizer combined with
Viterbi decoder using channel state information in OFDM systems
Advisor: Yung-An Kao
Student: Chi-An Young
2
Outline
Introduction Motivation OFDM system
Novel one-tap frequency domain RLS equalizer Conventional LMS and RLS algorithm Novel equalizer structure
Viterbi decoding with channel state information Simulation results Conclusion & Future work
3
Motivation
To design a receiver in OFDM systems with following consideration: Channel effects & frequency offset
complexity
performance
4
Introduction
The advantage of OFDM’s parallel transmission scheme: makes the bandwidth more effective
f
Sampling points 1f
T
5
Introduction
strongly against multi-path channel frequency selective channel multiple flat fading sub-ch
annels
the sub-channel equalization in frequency domain is simple
Transmit Spectrum
Receive Spectrum
Channel Training ToneData Tone
Channel Spectrum
6
-1.5 -1 -0.5 0 0.5 1 1.5-1.5
-1
-0.5
0
0.5
1
1.5
Carrier frequency offset (CFO) CFO is due to the
oscillator mismatch from up converter and down converter
f
fn+1+δ ffn-1+δ f fn+δ f
Frequency offsetδ f presetLead to ICI
f
fn+1+δ ffn-1+δ f fn+δ f
Frequency offsetδ f presetLead to ICI
QPSK, IEEE802.11a spec. QPSK, IEEE802.11a spec. no noiseno noiseCFO=0.01x312.5kHz43 OFDM symbols
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Sampling frequency offset (SFO) SFO is caused by
the oscillator mismatch between A/D & D/A converter
t
t
Sample rate: Rx>Tx
Sample rate: Rx<Tx
Rxsample
Txsample
t
t
Sample rate: Rx>Tx
Sample rate: Rx<Tx
Rxsample
Txsample
QPSK, IEEE802.11a spec. QPSK, IEEE802.11a spec. no noiseno noiseSFO=800Hz43 OFDM symbols
-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
8
OFDM receiver block
Guard interval removal
S/P FFT P/SRX signal
1-tapFEQ
Symbol De-mapping
De-interleaver
ViterbiDecoder
CSI
Decodeddata
… … …
Guard interval removal
S/P FFT P/SRX signal
1-tapFEQ
Symbol De-mapping
De-interleaver
ViterbiDecoder
CSI
Decodeddata
… … …
signal affect by channel residual frequency offset, noise, etc..
A modified version of RLS algorithm is used
In the proposed FEQ structure, the scale of the signal constellation must be adjusted
CSI is obtain from 1-tap FEQ
an inner receiver structure from[*]
[*] 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.
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Parameter definition X : transmitted signal in frequency domain Y : received signal in frequency domain Z : equalized signal Z’ : equalized signal (proposed equalizer) H : channel response w : weight coefficient of equalizer e : error signal d : desired signal : LMS step size : RLS forgetting factor : correlation matrix k, l : k-th subcarrier and l-th OFDM symbol n : n-th de-interleaver output
'
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Inner receiver structure
FFTInitial 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
The advantage of this structure is the phase compensation.
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One-tap frequency domain LMS equalizer filtering equation:
weight adaptation
LMS Filter
Adaptive Weight Control Mechanism +
+
,k lY,k lw
*, , ,k l k l k lZ w Y
,k ld
,k le
'*, ,
.kk l k lY Y
*, , ,k l k l k lZ w Y
' *, 1 , , , ,k l k l k k l k lw w e Y
12
One-tap frequency domain LMS equalizer filtering equation:
weight adaptation:
*, , ,k l k l k lZ w Y
LMS Filter
Adaptive Weight Control Mechanism +
+
,k lY,k lw
*, , ,k l k l k lZ w Y
,k ld
,k le
RLS filter
LMS Filter
Adaptive Weight Control Mechanism +
+
,k lY,k lw
*, , ,k l k l k lZ w Y
,k ld
,k le
RLS filter
, , ,1
*
,k l k k l k l k lY Y 1 *
, , 1 , , ,k l k l k l k l k lw w e Y
[**] 張晉銓 , 2005, “ 一階遞迴最小平方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 .
13
Division is used in NLMS and RLS algorithm NLMS:
RLS:
'*, ,
.kk l k lY Y
1 *
, , 1 , , ,k l k l k l k l k lw w e Y
14
Novel one-tap frequency domain RLS equalizer(1/6) filtering equation:
definition of θk,l
update of θk,l
*, , ,k l k l k lZ w Y
*
, , ,k l k l k lY d
*
, , 1 , ,k l k k l k l k lY d
' *
, , ,k l k l k lZ Y
15
Novel one-tap frequency domain RLS equalizer(2/6) Definition of wk,l:
Rewrite RLS filtering equation:
1, , ,k l k l k lw
phase
magnitude: 1
, 1 , 1k l k l
1 *
, , 1 , 1 ,( )k l k l k l k lZ Y
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Novel one-tap frequency domain RLS equalizer(3/6) From the magnitude part of distorted signal is not
fully compensated (QPSK modulation is assumed, CNR=15dB):
-1.5 -1 -0.5 0 0.5 1 1.5
-1.5
-1
-0.5
0
0.5
1
1.5
Quadra
ture
In-Phase
Scatter plot
-1.5 -1 -0.5 0 0.5 1 1.5
-1.5
-1
-0.5
0
0.5
1
1.5
Quadra
ture
In-Phase
Scatter plot
1-tap FEQ input 1-tap FEQ output
' *
, , , ,k l k l k lZ Y
17
Novel 1-tap frequency domain RLS equalizer(4/6)
-1 1 3-3-1
-3
1
3
*, , ,k l k l k lZ w Y
: signal equalized by conventional RLS FEQ
3-3
-3
-1 1
-1
1
3
constellation size multiply by Φk,l times
Φk,l
Φk,l -Φk,l
Φk,l
Φk,l
Φk,l Φk,l
-Φk,l
Re Re
ImIm ' *
, , , ,
*
, ,
k l k l k l k l
k l k l
Z w Y
Y
: signal equalized by proposed RLS FEQ
18
Novel 1-tap frequency domain RLS equalizer(5/6) The update equation for Φk,l :
, , 1
*
, , ,k l k k k l kl lY Y
19
Novel 1-tap frequency domain RLS equalizer(6/6) division operation is not required
calculation of error signal is not used
must adjust the scale of constellation at symbol de-mapping device
Proposed1-tapFEQ
P/SSymbol
De-mapping
…
,k l
…
,k lY '
,k lZ
20
Viterbi Decoding with CSI(1/6)
Basic concept of Viterbi decoding:
to select the path on code trellis with the minimum
Euclidean distance
Viterbi decoding in OFDM system: in presence of channel fading, each subcarrier is
experiencing different channel condition
if we view each subcarrier with the same reliability, except for that the situation will not be reflected
decoding error probability may increase
21
Viterbi Decoding with CSI(2/6)
We use channel state information (CSI) to reflect different sub-channel fading
Concept: Adding CSI when calculating the Euclidean distan
ce
improve reliability on calculating the Euclidean distance
22
Viterbi decoding using CSI(3/6)
CSI aided Viterbi decoder block diagram[***]
BMC: Branch Metric Calculation
SAM: State Accumulate Metric
SPM: Survival Path Matrix
Buffer BMC SAM
SPMTrace Back
Soft decision
coded data
Decoded data bits
CSI
Buffer BMC SAM
SPMTrace Back
Soft decision
coded data
Decoded data bits
CSI
[***]W. C. Lee, H. M. Park, K. J. Kang and K. B. Kim, “Performance analysis of Viterbi decoder using channel state information in COFDM system,” IEEE Transactions on Broadcasting, Vol. 44, no.4, pp.488-496, Dec. 1998.
23
Viterbi decoding using CSI(4/6)
The calculation of the Euclidean distance:
When SNR is high enough:
2[ ]n nE H
2ˆn n
n
D Z S ˆ
nS :possible transmitted signal
24
Viterbi decoding using CSI(5/6)
Adding CSI to D :2
2 ˆC n n n
n
D Z S
the signal constellation that has been adjusted
22 1 * ˆn n n n n
n
Y S 2
* ˆn n n n
n
Y S
equalized signal:'
nZ
2
n
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Viterbi decoding using CSI(6/6)
Considering: system complexity system performance
We use to reflect channel condition2
n
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Simulation environments & parameters IEEE 802.11a standard
Transmission packets = 1000 packets
Transmission data per packets = PSDU 256 Bytes
Exponentially decaying Rayleigh fading
with sampling period and RMS time
CFO = 3125 Hz
SFO = 800 Hz
= 0.85
6-bit soft decision Viterbi decoding
50sT ns 50RMST ns
k
27
Simulation result
5 10 15 20 25 30 35 4010
-2
10-1
100
CNR
PE
R
6Mbps
9Mbps12Mbps
18Mbps
24Mbps
36Mbps48Mbps
54Mbps
PER performance for IEEE 802.11a (no CSI aided)
5 10 15 20 25 30 35 4010
-2
10-1
100
CNR
PE
R
6Mbps
9Mbps12Mbps
18Mbps
24Mbps
36Mbps48Mbps
54Mbps
PER performance for IEEE 802.11a (CSI aided)
28
conclusion
Division in the proposed algorithm is no longer used
By applying this FEQ structure, we can improve the system performance by CSI aided Viterbi decoder
29
Future work
Apply the equalizer structure to time-variant channel
The optimal solution of CSI
Hardware implementation
30
Reference
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.
W. C. Lee, H. M. Park, K. J. Kang and K. B. Kim, “Performance analysis of Viterbi decoder using channel state information in COFDM system,” IEEE Transactions on Broadcasting, Vol. 44, no.4, pp.488-496, Dec. 1998.
張晉銓 , 2005, “ 一階遞迴最小平方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 .
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Thanks for your attention!