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On the Relation Between Time-Domain On the Relation Between Time-Domain Equalizers and Per-Tone Equalizers Equalizers and Per-Tone Equalizers for DMT-Based Systems for DMT-Based Systems Koen Vanbleu, Geert Ysebaert, Gert Cuypers, Marc Moonen Katholieke Universiteit Katholieke Universiteit Leuven, ESAT Leuven, ESAT / / SCD-SISTA, Belgium SCD-SISTA, Belgium April 16, 2004 IEEE Benelux Signal Processing Symposium Hilvarenbeek, the Netherlands
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Page 1: Td and-fd-mmse-teq

On the Relation Between Time-On the Relation Between Time-Domain Equalizers and Per-Tone Domain Equalizers and Per-Tone

Equalizers for DMT-Based SystemsEqualizers for DMT-Based Systems

Koen Vanbleu, Geert Ysebaert, Gert Cuypers, Marc Moonen

Katholieke Universiteit Katholieke Universiteit Leuven, ESATLeuven, ESAT//SCD-SISTA, BelgiumSCD-SISTA, Belgium

April 16, 2004

IEEE Benelux Signal Processing SymposiumHilvarenbeek, the Netherlands

Page 2: Td and-fd-mmse-teq

Koen Vanbleu, Geert Ysebaert, Gert Cuypers, Marc Moonen

Katholieke Universiteit Katholieke Universiteit Leuven, ESATLeuven, ESAT//SCD-SISTA, BelgiumSCD-SISTA, Belgium

April 16, 2004

IEEE Benelux Signal Processing SymposiumHilvarenbeek, the Netherlands

On On Equalization Alternatives and Equalization Alternatives and their Relations for ADSL Modemstheir Relations for ADSL Modems

Page 3: Td and-fd-mmse-teq

3

OverviewOverview

• ADSL Basics

What? Multicarrier modulation

Transmitter/Receiver

• ADSL Equalizer Design

Problem Description

Current Equalizers (TD-MMSE)

Bit rate Maximizing Equalizers (FD-MMSE criterion)

Relations

Page 4: Td and-fd-mmse-teq

5

IntroductionIntroduction

Broadband communication over telephone line ADSL (Asymmetric Digital Subscriber Line) ADSL2 / ADSL2+ (Second-Generation ADSL) VDSL (Very high bit rate Digital Subscriber Line) Bit rate is function of the line length

Upstream

Downstream

CustomerCentral

• ADSL Basics - Intro - DMT Transmitter - Why

Equalization? - DMT Receiver

• ADSL Equalizer Design

- Problem Description

- Current Equalizers

- Bit rate Maximizing

Equalizers - Relations

Down Up Line length

Frequency band

ADSL 6 Mbps 640 kbps 3.7 km 1.1 MHz

ADSL2+

15 Mbps 1.5 Mpbs 1.8 km 2.2 MHz

VDSL 52 Mbps 2.3 Mbps < 1 km 12 MHz

Page 5: Td and-fd-mmse-teq

6

• Traditional telephony (POTS) still available over the same wire.

Multicarrier ModulationMulticarrier Modulation

• Assign different frequency bins to up- and downstream directions

f (kHz)

POTS UP DOWN

4 25 138 1104

e.g. ADSL

• Digital multicarrier modulation scheme: Discrete Multitone (DMT)

• ADSL Basics - Intro - DMT Transmitter - Why

Equalization? - DMT Receiver

• ADSL Equalizer Design

- Problem Description

- Current Equalizers

- Bit rate Maximizing

Equalizers - Relations

Page 6: Td and-fd-mmse-teq

7

Discrete Multitone: TransmitterDiscrete Multitone: Transmitter

...

P/S

CP

lx

Cyclic Prefix

• ADSL Basics - Intro - DMT Transmitter - Why

Equalization? - DMT Receiver

• ADSL Equalizer Design

- Problem Description

- Current Equalizers

- Bit rate Maximizing

Equalizers - Relations

00

11

10

01

Re

Im

2 bits

Re

Im

4 bits

bits Data symbols (QAM)

0

IDFT

N-point

.

.

.

.

.

.

...

IDFT modulation (Inverse Discrete Fourier Transform)

N12/ N

nkx ,ˆ

Blocktransmission!

Page 7: Td and-fd-mmse-teq

8

Why Equalization?Why Equalization?

channel

ly

lnnoise

...

P/S

CP

lxIDFT

N-point

.

.

.

.

.

.

...

N

12/ N

Transmitter

Why equalization?“Invert” channel

distortion while not boosting noise

• ADSL Basics - Intro - DMT Transmitter - Why

Equalization? - DMT Receiver

• ADSL Equalizer Design

- Problem Description

- Current Equalizers

- Bit rate Maximizing

Equalizers - Relations

nkx ,ˆ

Page 8: Td and-fd-mmse-teq

9l

h

Discrete Multitone: ReceiverDiscrete Multitone: Receiver

00

11

10

01Re

Im

2 bits

Re

Im

4 bits

bits

Data symbols

channel h

lnnoise

lylx

• ADSL Basics - Intro - DMT Transmitter - Why

Equalization? - DMT Receiver

• ADSL Equalizer Design

- Problem Description

- Current Equalizers

- Bit rate Maximizing

Equalizers - Relations

wh

lCP length + 1

...S/P

CP

.

.

.DFT

N-point

DFT demodulation

.

.

.

Frequency Domain

Equalizer

1 tap / tonex

x

x

nd~

TEQ w

tapsT

Time Domain

Equalizer

Page 9: Td and-fd-mmse-teq

10

DMT Equalization: DMT Equalization: Problem DescriptionProblem Description

S/P

CP

... DFT

FEQ

TEQ w

ly

T taps

...

...

1 tap/tone

N-point

To maximize bit rate:

n

nbtones

toneonbits

00

11

10

01

Re

Im

2 bits

• ADSL Basics - Intro - DMT Transmitter - Why

Equalization? - DMT Receiver

• ADSL Equalizer Design

- Problem Description

- Current Equalizers

- Bit rate Maximizing

Equalizers - Relations

nknk ex ,,~~

FEQ

n n

nSNR

tones2

)(1log

w

is hard with time-domain equalizer w

nd~

where

2,

2

,

)(~

~

)(w

w

nk

nkn

eE

xESNR Residual ISI/ICI

Noise (RFI/XT/etc.)

Page 10: Td and-fd-mmse-teq

11

Current ADSL EqualizersCurrent ADSL Equalizers• ADSL Basics - Intro - DMT Transmitter - Why

Equalization? - DMT Receiver

• ADSL Equalizer Design

- Problem Description

- Current Equalizers

- Bit rate Maximizing

Equalizers - Relations

Channel shortenerse.g. time-domain MMSE-TEQ design

l

h

Channel h

lnnoise

lxly

No bit rate optimization!

wh

CP length + 1

l

TEQ w

Constrained linear least-squares based MMSE-TEQ

wbxwybw,

on constraint s.t.min1

0

2

L

l

Tl

Tl

TIR = target impulse response of (CP-length+1)

delay TIR b

le

-

Page 11: Td and-fd-mmse-teq

12

wy

wY

,

)(

k

k

Bit rate Maximizing Equalizers:Bit rate Maximizing Equalizers:Per-tone equalizationPer-tone equalization• ADSL Basics

- Intro - DMT Transmitter - Why

Equalization? - DMT Receiver

• ADSL Equalizer Design

- Problem Description

- Current Equalizers

- Bit rate Maximizing

Equalizers Per-tone equalization BM-TEQ

- Relations

DFTN-point

TEQ w

tapsT

Time Domain Equalize

r

wy

wY

,

)(~~̂

,

k

knnnk Fdx

.

.

.

x

x

x

nd~

FEQ

nkx ,~̂

ly

.

.

.

wy

,k

N

N

N

N

.

.

.

wy

wY

,

)(

k

knF

Page 12: Td and-fd-mmse-teq

13

Bit rate Maximizing Equalizers:Bit rate Maximizing Equalizers:Per-tone equalizationPer-tone equalization

ly

S/P

N

N

N

...N

N

N

...1T

...

...

...

DFT

N-point

T

DFTN-pointsliding

wy

wY

,

)(~~̂

,

k

knnnk Fdx

PTEQ ...

• ADSL Basics - Intro - DMT Transmitter - Why

Equalization? - DMT Receiver

• ADSL Equalizer Design

- Problem Description

- Current Equalizers

- Bit rate Maximizing

Equalizers Per-tone equalization BM-TEQ

- Relations

)( knF Y n

nkn dFw

wY )~

()(

n

T –tap linear combiner

w for each tone

nkx ,~̂

Page 13: Td and-fd-mmse-teq

14

Bit rate Maximizing Equalizers:Bit rate Maximizing Equalizers:Per-tone equalizationPer-tone equalization

21

0,

~

~)(min

K

knk

d

nkn xF

n

n

ww

wY

• Least-squares criterion per tone: “design TEQ per tone”

• Optimizes the SNR per tone Performs always better than a TEQ

• Efficient computation: exploit sliding DFT structure

similar complexity as TEQ

• ADSL Basics - Intro - DMT Transmitter - Why

Equalization? - DMT Receiver

• ADSL Equalizer Design

- Problem Description

- Current Equalizers

- Bit rate Maximizing

Equalizers Per-tone equalization BM-TEQ

- Relations

Page 14: Td and-fd-mmse-teq

15

Bit rate Maximizing (BM) Bit rate Maximizing (BM) Equalizers:Equalizers:

Time-domain equalizationTime-domain equalization• ADSL Basics - Intro - DMT Transmitter - Why

Equalization? - DMT Receiver

• ADSL Equalizer Design

- Problem Description

- Current Equalizers

- Bit rate Maximizing

Equalizers Per-tone equalization BM-TEQ

- Relations

21

0,

~

21

0,

~)(min)(~min

K

knk

d

nkn

K

knnk xFe

n

nn

www

wYwPTEQ:

n n

nSNR

tones2 1logmax where

2,

2

,

)/(~

~

)/(

nnk

nknn

eE

xESNR

wwww

BM-TEQ:

21

0 tones,~

,

~)(~

min

K

k nnkknnn

dxFd

n

wYw

with )~()( ,nknn egSNRf

TEQly S/P

CP

... DFT

FEQ

T taps

...

...

N-pointnd

~

x

x

Page 15: Td and-fd-mmse-teq

16

Bit rate Maximizing Equalizers:Bit rate Maximizing Equalizers:Time-domain equalizationTime-domain equalization• ADSL Basics

- Intro - DMT Transmitter - Why

Equalization? - DMT Receiver

• ADSL Equalizer Design

- Problem Description

- Current Equalizers

- Bit rate Maximizing

Equalizers Per-tone equalization BM-TEQ

- Relations

21

0 tones,~

,

21

0 tones,~

,

~)(~

min

)~

,(~min

K

k nnkknnn

d

K

k nnnkn

d

xFd

de

n

n

wY

w

w

w

with )),~

(~()( , wnnknn degSNRf

Iteratively-reweighted separable non-linear least squares-based

frequency-domain MMSE-TEQ design

Page 16: Td and-fd-mmse-teq

17

Relation between ADSL Relation between ADSL equalizersequalizers• ADSL Basics

- Intro - DMT Transmitter - Why

Equalization? - DMT Receiver

• ADSL Equalizer Design

- Problem Description

- Current Equalizers

- Bit rate Maximizing

Equalizers - Relations

(Channel shortening) TD-MMSE-TEQ: constrained linear LS

FD-MMSE-TEQ: constrained linear LS or separable NL-LS

Block transmission/CP/Multicarrier

Bit rate maximization

BM-TEQ: iteratively reweighted separable NL-LS

PTEQ: linear LS

Only 1 toneRemarkable

correspondence between generalized eigenvalue

problems

Page 17: Td and-fd-mmse-teq

18

Relation between ADSL Relation between ADSL equalizersequalizers• ADSL Basics

- Intro - DMT Transmitter - Why

Equalization? - DMT Receiver

• ADSL Equalizer Design

- Problem Description

- Current Equalizers

- Bit rate Maximizing

Equalizers - Relations

TD-MMSE-TEQReal FD-MMSE-TEQ 1Complex FD-MMSE-TEQ 1Real FD-MMSE-TEQ 2Complex FD-MMSE-TEQ 2Real BM-TEQ Complex BM-TEQ Real PTEQComplex PTEQ

Page 18: Td and-fd-mmse-teq

19

Relation between ADSL Relation between ADSL equalizersequalizers• ADSL Basics

- Intro - DMT Transmitter - Why

Equalization? - DMT Receiver

• ADSL Equalizer Design

- Problem Description

- Current Equalizers

- Bit rate Maximizing

Equalizers - Relations

(Channel shortening) TD-MMSE-TEQ: constrained linear LS

FD-MMSE-TEQ: constrained linear LS or separable NL-LS

Block transmission/CP/Multicarrier

Bit rate maximization

BM-TEQ: iteratively reweighted separable NL-LS

PTEQ: linear LS

Only 1 toneRemarkable

correspondence between generalized eigenvalue

problems