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### Bitrate Maximizing Equalizers for ADSL Modems

Koen Vanbleu

Promotor: Marc Moonen

Collaborators: Geert Ysebaert, Gert Cuypers

KULeuven, ESAT SCD-SISTA, Belgium

February 6, 2003

Overview

- ADSL Basics
- What?
- Transmitter/Receiver
- ADSL Equalizer Design
- Problem Description
- Current Equalizers
- Bitrate Maximizing Equalizers
- Conclusions

Introduction

- ADSL Basics
- - Intro
- - DMT Transmitter
- - Why Equalization?
- - DMT Receiver
- ADSL Equalizer Design
- - Problem Description
- - Current Equalizers
- - Bitrate Maximizing
- Equalizers
- Conclusions

- 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

Introduction

Down

Up

Line length

ADSL

6 Mbps

640 Kbps

3 km

VDSL

52 Mbps

6.4 Mbps

300 m

Downstream

Central

Customer

Upstream

- ADSL Basics
- - Intro
- - DMT Transmitter
- - Why Equalization?
- - DMT Receiver
- ADSL Equalizer Design
- - Problem Description
- - Current Equalizers
- - Bitrate Maximizing
- Equalizers
- Conclusions

- 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

Modulation and Duplexing

- Multicarrier modulation scheme: Discrete Multitone (DMT)

e.g. ADSL

UP

&DOWN

POTS

UP

DOWN

POTS

DOWN

4

25

138

1104

f (kHz)

4

25

138

1104

f (kHz)

- ADSL Basics
- - Intro
- - DMT Transmitter
- - Why Equalization?
- - DMT Receiver
- ADSL Equalizer Design
- - Problem Description
- - Current Equalizers
- - Bitrate Maximizing
- Equalizers
- Conclusions

- Assign different frequency bins to up- and downstream directions
- Frequency Division Duplexing (FDD)
- Overlap: Echo Cancellation (EC)

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

Discrete Multi Tone: Transmitter

bits

Data symbols (QAM)

Cyclic Prefix

CP

Im

0

10

00

...

...

Re

11

01

2 bits

N-point

P/S

Im

IFFT

Re

...

...

4 bits

IFFT modulation

(Inverse Fast Fourier Transform)

- ADSL Basics
- - Intro
- - DMT Transmitter
- - Why Equalization?
- - DMT Receiver
- ADSL Equalizer Design
- - Problem Description
- - Current Equalizers
- - Bitrate Maximizing
- Equalizers
- Conclusions

Why Equalization?

CP

noise

...

...

channel

N-point

P/S

IFFT

...

...

Transmitter

- ADSL Basics
- - Intro
- - DMT Transmitter
- - Why Equalization?
- - DMT Receiver
- ADSL Equalizer Design
- - Problem Description
- - Current Equalizers
- - Bitrate Maximizing
- Equalizers
- Conclusions

Why equalization?

“Invert” channel distortion while not boosting noise

- - Intro
- - DMT Transmitter
- - Why Equalization?
- - DMT Receiver
- ADSL Equalizer Design
- - Problem Description
- - Current Equalizers
- - Bitrate Maximizing
- Equalizers
- Conclusions

Unbiased Frequency Domain Equalizer

1 tap / tone

Data symbols

Im

bits

10

00

CP

...

noise

Re

11

01

...

2 bits

...

...

Im

FEQ

channel h

TEQ w

N-point

S/P

FFT

Re

Time Domain Equalizer

taps

4 bits

FFT demodulation

CP length + 1

DMT Equalization: Problem Description

TEQ w

CP

where

is hard with time-domain equalizer w

- ADSL Basics
- - Intro
- - DMT Transmitter
- - Why Equalization?
- - DMT Receiver
- ADSL Equalizer Design
- - Problem Description
- - Current Equalizers
- - Bitrate Maximizing
- Equalizers
- Conclusions

Im{X}

10

00

Re{X}

T taps

1 tap/tone

N-point

11

01

...

...

...

S/P

FEQ Dn

FEQ

FFT

2 bits

To maximize bitrate:

Current ADSL Equalizers (1)

noise

Channel h

TEQ w

delay

TIR b

- ADSL Basics
- - Intro
- - DMT Transmitter
- - Why Equalization?
- - DMT Receiver
- ADSL Equalizer Design
- - Problem Description
- - Current Equalizers
- - Bitrate Maximizing
- Equalizers
- Conclusions

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

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

MMSE criterion ADSL bitrate maximization

Current ADSL Equalizers (2)

T taps

1 tap/tone

TEQ w

N-point

...

...

...

S/P

FEQ Dn

FFT

CP

Approximations!

based on SNR at FFT output

residual ISI/ICI

noise

- ADSL Basics
- - Intro
- - DMT Transmitter
- - Why Equalization?
- - DMT Receiver
- ADSL Equalizer Design
- - Problem Description
- - Current Equalizers
- - Bitrate Maximizing
- Equalizers
- Conclusions

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

Maximize

- not only depending on walled shortened impulse response
- : do not forget DFT leakage!

- Approximate Bitrate Maximizing TEQs (continued)

residual ISI/ICI

noise

Examples of approximations :

Bitrate Maximizing Equalizers (1)

TEQ w

CP

AND

then

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

- ADSL Basics
- - Intro
- - DMT Transmitter
- - Why Equalization?
- - DMT Receiver
- ADSL Equalizer Design
- - Problem Description
- - Current Equalizers
- - Bitrate Maximizing
- Equalizers
- Conclusions

T taps

N-point

...

...

...

S/P

FEQ Dn

FFT

Maximize

where

Bitrate Maximizing Equalizers (2)

- ADSL Basics
- - Intro
- - DMT Transmitter
- - Why Equalization?
- - DMT Receiver
- ADSL Equalizer Design
- - Problem Description
- - Current Equalizers
- - Bitrate Maximizing
- Equalizers
- Conclusions

Exact bitrate maximizing (BM-)TEQ cost function

- Nonlinear cost function in wonly with Anand Bn
- tone dependent matrices
- function of signal statistics

- Recursive Gauss-Newton updating algorithm:
- attains good local optimum
- adaptivity (to track channel/noise changes)
- however: high complexity

Bitrate Maximizing Equalizers (3)

- ADSL Basics
- - Intro
- - DMT Transmitter
- - Why Equalization?
- - DMT Receiver
- ADSL Equalizer Design
- - Problem Description
- - Current Equalizers
- - Bitrate Maximizing
- Equalizers
- Conclusions

- Bitrate maximizing equalizers:
- Bitrate maximizing (single) TEQ: NG = all used tones nonlinear cost function
- “Per group” equalization: BM-TEQ w per group SG of NG tones nonlinear cost function
- “Per tone” equalization: NG= 1 tone
- (advantageous) linear MMSE problem [Vanacker, Leus, Moonen]

HIGHER

BITRATE

Bitrate Maximizing Equalizers (4)

- ADSL Basics
- - Intro
- - DMT Transmitter
- - Why Equalization?
- - DMT Receiver
- ADSL Equalizer Design
- - Problem Description
- - Current Equalizers
- - Bitrate Maximizing
- Equalizers
- Conclusions

Simulations

Per-Tone Equalizer

Bitrate Maximizing-TEQ

MMSE-based TEQs

Approx. Bitrate Max. TEQs

Conclusions

- ADSL Basics
- - Intro
- - DMT Transmitter
- - Why Equalization?
- - DMT Receiver
- ADSL Equalizer Design
- - Problem Description
- - Current Equalizers
- - Bitrate Maximizing
- Equalizers
- 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

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