Bitrate Maximizing Equalizers for Bitrate Maximizing Equalizers for ADSL Modems ADSL Modems

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Bitrate Maximizing Equalizers for Bitrate Maximizing Equalizers for

ADSL Modems ADSL Modems

Koen Vanbleu

Promotor: Marc Moonen

Collaborators: Geert Ysebaert, Gert Cuypers KULeuven, ESAT SCD-SISTA, Belgium KULeuven, ESAT SCD-SISTA, Belgium

February 6, 2003

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Overview Overview

• ADSL Basics

What?

Transmitter/Receiver

• ADSL Equalizer Design

Problem Description

Current Equalizers

Bitrate Maximizing Equalizers

• Conclusions

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Introduction Introduction

• Communication at high rates towards customer

telephone wire, cable, fiber, wireless

• Communication over telephone wire

Evolution: ever increasing bitrates

E.g. Time to download 10 Mbyte file

Modem Time

56 Kbps

Voice band modem 24 minutes 128 Kbps ISDN 10 minutes 6 Mbps ADSL 13 seconds 52 Mbps VDSL 1.5 seconds

• ADSL Basics - Intro

- DMT Transmitter - Why Equalization?

- DMT Receiver

• ADSL Equalizer Design

- Problem Description - Current Equalizers - Bitrate Maximizing Equalizers

• Conclusions

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Introduction Introduction

• Broadband communication over telephone line

ADSL (Asymmetric Digital Subscriber Line)

VDSL (Very high bit rate Digital Subscriber Line)

Bitrate is function of the line length

Upstream

Downstream

Customer Central

300 m 6.4 Mbps

52 Mbps VDSL

3 km 640 Kbps

6 Mbps ADSL

Line length Up

Down Frequency band

1.1 MHz 8.8 MHz

- DMT Receiver

• Conclusions

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

Modulation and Duplexing Modulation and Duplexing

• Assign different frequency bins to up- and downstream directions

Frequency Division Duplexing (FDD)

Overlap: Echo Cancellation (EC)

f (kHz)

POTS UP DOWN POTS UP

&DOWN DOWN

4 25 138 1104 4 25 138 1104 ^{f (kHz)}

e.g. ADSL

• Multicarrier modulation scheme: Discrete Multitone (DMT)

- DMT Receiver

• Conclusions

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Discrete Multi Tone: Transmitter Discrete Multi Tone: Transmitter

00

11 10

01 Re Im

2 bits

Re Im

4 bits

bits Data symbols (QAM)

...

P/S CP

x

k

Cyclic Prefix

0

IFFT N-point ..

.

.. .

...

IFFT modulation

(Inverse Fast Fourier Transform) 1 N

2 /  N

- DMT Receiver

• Conclusions

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Why Equalization?

channel

yk

nk

noise ...

P/S CP

x

k

IFFT N-point ..

.

.. .

...

N 1

2 /  N

X

n

Transmitter

Why equalization?

“Invert” channel distortion while not

boosting noise

- DMT Receiver

• Conclusions

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Discrete Multi Tone: Receiver Discrete Multi Tone: Receiver

00

11 10

01 Re Im

2 bits

Re Im

4 bits bits

Data symbols

...

S/P CP

.. .

FFT N-point

FFT demodulation ..

. FEQ

Unbiased Frequency

Domain Equalizer 1 tap / tone

.. channel h .

nk

noise

yk

x

k ^{TEQ w}

T

taps Time Domain Equalizer

- DMT Receiver

• Conclusions

k

h h

k^k

 w

^k

CP length + 1

k

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DMT Equalization:

Problem Description Problem Description

S/P CP

... FFT FEQ

TEQ w

y

k

T

taps

...

1 tap/tone

N-point

To maximize bitrate:





n

n b

tones

tone on

bits

00

11 10

01 Re{X}

Im{X}

2 bits

- DMT Receiver

• Conclusions

n n

n

X E

Z  

FEQ D_n

 _



 





 



n n

n

D

SNR

tones

2

) ,

1 (

log w

is hard with time-domain equalizer w

where

 



²



2

, ) ) (

, (

n n

n

E E D

X D E

SNR w  w

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Current ADSL Equalizers (1) Current ADSL Equalizers (1)

- DMT Receiver

• Conclusions

• Channel shorteners, e.g. MMSE-based TEQ [Al-Dhahir, Cioffi]

Channel h

nk

noise

x

k

y

_k ^{TEQ w}

delay TIR b

e

k

  ^w ^b

b

w,

s.t. constraint on or min E e

_k ²

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

MMSE criterion  ADSL bitrate maximization

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Current ADSL Equalizers (2) Current ADSL Equalizers (2)

- DMT Receiver

• Conclusions

• Approximate Bitrate Maximizing TEQs [Al-Dhahir], [Evans]

S/P CP

... FFT FEQ D_n TEQ w

y

k

T

taps

...

1 tap/tone

N-point

Z

_n

 X

_n

 E

_n

 _



 





 



n n

SNR

n

b

tones

2

1

Maximize

log

based on SNR at FFT output

 



²



1 2

) ( )

, (

) , ) (

( w h w

h w w

n n

n

E I N

X D

SNR E

 



residual ISI/ICI noise

Approximations!

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Current ADSL Equalizers (3) Current ADSL Equalizers (3)

• Approximate Bitrate Maximizing TEQs (continued)

 



²



1 2

) ( )

, (

) , ) (

( w h w

h w w

n n

n

E I N

X D

SNR E

 



residual ISI/ICI noise Examples of approximations :

•

• not only depending on walled shortened impulse response

• : do not forget DFT leakage!

n n

n

H W

D

^1

 I

n

N

n

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Bitrate Maximizing Equalizers (1) Bitrate Maximizing Equalizers (1)

- DMT Receiver

• Conclusions

S/P CP

... FFT FEQ D_n TEQ w

y

k

T

taps

...

N-point ...

Z

_n

 X

_n

 E

_n

 _



 





 



n n

n

D

b SNR

tones

2

) ,

1 (

log w

where

 



²



2

, ) ) (

, (

n n

n

E E D

X D E

SNR w  w

Maximize

AND

 



^*



2

)

(

_n

n

E Y X

X D E

 w

)

n

(w Y

n n

n

D Z X D Y X

E ( w , )    ( w ) 

then

= residual ISI/ICI+noise sources (XT, RFI, …)

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Bitrate Maximizing Equalizers (2) Bitrate Maximizing Equalizers (2)

Exact bitrate maximizing (BM-)TEQ cost function









 





^N^G



n n

T

n T

b

1

log

2

w B

w

w A

w

• Nonlinear cost function in w only with A_n and B_n

• tone dependent matrices

• function of signal statistics

- DMT Receiver

• Conclusions

• Recursive Gauss-Newton updating algorithm:

• attains good local optimum

• adaptivity (to track channel/noise changes)

• however: high complexity

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Bitrate Maximizing Equalizers (3) Bitrate Maximizing Equalizers (3)

- DMT Receiver

• Conclusions

Bitrate maximizing equalizers:

• Bitrate maximizing (single) TEQ: N_G= all used tones  nonlinear cost function

• “Per group” equalization: BM-TEQ w per group S_G of N_G tones  nonlinear cost function

• “Per tone” equalization: N_G= 1 tone

 (advantageous) linear MMSE problem [Vanacker, Leus, Moonen]









 





^N^G



n n

T

n T

b

1

log

2

w B

w

w A

w

HIGHER BITRATE

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Bitrate Maximizing Equalizers (4) Bitrate Maximizing Equalizers (4)

- DMT Receiver

• Conclusions

Simulations

Bitrate Maximizing-TEQ Per-Tone Equalizer

MMSE-based TEQs

Approx. Bitrate Max. TEQs

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Conclusions Conclusions

- DMT Receiver

• Conclusions

• ADSL Equalizer Design

• Truly Bitrate Maximizing Per-Group Equalizer

• Time-Domain Equalizer (1 group of tones)

• Per-Tone Equalizer (groups of 1 tone)

• Recursive Gauss-Newton algorithm

• Good local optimum

• Complex

Bitrate Maximizing Equalizers for Bitrate Maximizing Equalizers for ADSL Modems ADSL Modems