Advisor: Yung-An Kao Student: Chi-An Young

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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

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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

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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

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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 .

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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

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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

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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

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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

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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

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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

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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

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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

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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.

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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

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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

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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)

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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

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Future work

Apply the equalizer structure to time-variant channel

The optimal solution of CSI

Hardware implementation

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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!