On the Relation Between Time-Domain On the Relation Between Time-Domain Equalizers and Per-Tone Equalizers for Equalizers and Per-Tone Equalizers for DMT-Based Systems DMT-Based Systems

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

DMT-Based Systems 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 Symposium Hilvarenbeek, the Netherlands

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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 Symposium Hilvarenbeek, the Netherlands

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

Relations for ADSL Modems

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Overview Overview

• ADSL Basics

 What? Multicarrier modulation

 Transmitter/Receiver

• ADSL Equalizer Design

 Problem Description

 Current Equalizers (TD-MMSE)

 Bit rate Maximizing Equalizers (FD-MMSE criterion)

 Relations

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Introduction Introduction

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

Customer Central

• 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

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6

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

Multicarrier Modulation Multicarrier 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)

- DMT Receiver

- Relations

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Discrete Multitone: Transmitter Discrete Multitone: Transmitter

...

P/S CP

x

l

Cyclic Prefix

- DMT Receiver

- 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) 1 N

2 /  N

n

x ˆ

k_,

Block

transmission!

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8

Why Equalization?

channel

yl

nl

noise ...

P/S CP

xl

IDFT N-point ..

.

.. .

...

N 1

2 /  N

Transmitter

Why equalization?

“Invert” channel distortion while not

boosting noise

- DMT Receiver

- Relations

n

x ˆ

k_,

(8)

9

l

h

Discrete Multitone: Receiver Discrete Multitone: Receiver

00

11 10

01 Re Im

2 bits

Re Im

4 bits bits

Data symbols

channel h

nl

noise

yl

x

l

- DMT Receiver

- Relations

w h 

l

CP length + 1

...

S/P CP

.. .

DFT N-point

DFT demodulation .. . Frequency

Domain Equalizer 1 tap / tone

x x

x

d~n

TEQ w

T

taps Time Domain Equalizer

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DMT Equalization:

Problem Description Problem Description

S/P CP

... DFT FEQ

TEQ w

y

l

T

taps

...

1 tap/tone

N-point

To maximize bit rate:





n

n b

tones

tone on

bits

00

11 10

01 Re Im

2 bits

- DMT Receiver

- Relations

n k n

k

e

x

_,

~

_,

~ 

FEQ

 _



 





 



n n

SNR

n tones

2

) 1 (

log w

is hard with time-domain equalizer w

d~n

where

 



^, ²



2 ,

)

~ (

~ )

(

w w

n k

n

E e

x

SNR  E

Residual ISI/ICI

Noise (RFI/XT/etc.)

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11

Current ADSL Equalizers Current ADSL Equalizers

- DMT Receiver

- Relations

Channel shorteners

e.g. time-domain MMSE-TEQ design

l

h

Channel h

nl

noise

x

l y_l

No bit rate optimization!

w h 

CP length + 1

l

TEQ w

Constrained linear least-squares based MMSE-TEQ

w b

x w

b

y

w,

s.t. constraint on min

¹

0



^ 2

 L



l

T l T

l

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

delay TIR b

e

l

-

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  

y w

w Y

,

) (

k

Bit rate Maximizing Equalizers:

Per-tone equalization Per-tone equalization

- DMT Receiver

 Per-tone equalization

 BM-TEQ - Relations

DFT N-point

TEQ w

T

taps Time Domain Equalizer







y w

w Y

,

)

~ ( ˆ~

,

k

k n

n n

k

d F

x 

. .. x

x

d~n

FEQ

n

x ˆ~

k_,

y

l

.. .

yk,w N







 N





 N





 N

. . .







y w

w Y

,

) (

k

F

n

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Bit rate Maximizing Equalizers:

Per-tone equalization Per-tone equalization

y

l

S/P







 N





 N





 N N ...







 N





 N 1 ...

 T

...

DFT

N-point

T DFT

N-point sliding



   

y w

w Y

,

)

~ ( ˆ~

,

k

k n

n n

k

d F

x

PTEQ ...

- DMT Receiver

) ( F Y

_n _k







n

n k

n

d

F

w

Y ~ ) (

) (

n

T –tap linear combiner

w for each tone

n

x ˆ~

k_,

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Bit rate Maximizing Equalizers:

Per-tone equalization Per-tone equalization



2 1

0

,

~

) ~ (

min 

^

 K



k

n k d

n k

n

x

F

n

n w

w

Y w

• 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

- DMT Receiver

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Bit rate Maximizing (BM) Equalizers:

Time-domain equalization Time-domain equalization

- DMT Receiver



2 1

0

,

~ 1 2

0

,

( ) min ( ) ~

min  ~ 

^











^K

k

n k d

n k

n K

k

n n

k

F x

e

n n

n w

w

w Y w

PTEQ:

 _



 





 

n n

SNR

n tones

2

1 log

max

where

 



^, ²



2 ,

) /

~ (

~ )

/ (

n n k

n k n

n E e

x SNR E

w w w

w 

BM-TEQ:

1 2

0 tones

, ,~

) ~

~ ( min  

^

 K



k n

n k k

n n

d n

d F x

n

w

 Y

with



_n

 f ( SNR

_n

)  g ( ~ e

_k_,n

)

TEQ

yl ^S/P

CP

... DFT

T

taps FEQ

...

N-point ...

d~n

x x

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Bit rate Maximizing Equalizers:

Time-domain equalization Time-domain equalization

- DMT Receiver

1 2

0 tones

, ,~

1 2

0 tones

~ , ,

) ~

~ ( min

~ ) ,

~ ( min

 













^K

k n

n k k

n n

d n

K

k n

n n

k d n

x F

d

d e

n n

w Y

w

w w



with

~ , ))

~ ( ( )

(

_n _k_,_n _n

w

n

 f SNR  g e d



Iteratively-reweighted

separable non-linear least squares-based frequency-domain MMSE-TEQ design

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Relation between ADSL equalizers Relation between ADSL equalizers

- DMT Receiver

- 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 tone

Remarkable correspondence between generalized eigenvalue problems

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Relation between ADSL equalizers Relation between ADSL equalizers

- DMT Receiver

- Relations

TD-MMSE-TEQ

Real FD-MMSE-TEQ 1 Complex FD-MMSE-TEQ 1 Real FD-MMSE-TEQ 2 Complex FD-MMSE-TEQ 2 Real BM-TEQ

Complex BM-TEQ Real PTEQ

Complex PTEQ

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Relation between ADSL equalizers Relation between ADSL equalizers

- DMT Receiver

- 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 tone

Remarkable correspondence between generalized eigenvalue problems

On the Relation Between Time-Domain On the Relation Between Time-Domain Equalizers and Per-Tone Equalizers for Equalizers and Per-Tone Equalizers for DMT-Based Systems DMT-Based Systems