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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

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bitrate maximizing equalizers for adsl modems

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
Overview
  • ADSL Basics
    • What?
    • Transmitter/Receiver
  • ADSL Equalizer Design
    • Problem Description
    • Current Equalizers
    • Bitrate Maximizing Equalizers
  • Conclusions
introduction
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
introduction1
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
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
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
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

discrete multi tone receiver

ADSL Basics

  • - Intro
  • - DMT Transmitter
  • - Why Equalization?
  • - DMT Receiver
  • ADSL Equalizer Design
  • - Problem Description
  • - Current Equalizers
  • - Bitrate Maximizing
  • Equalizers
  • Conclusions
Discrete Multi Tone: Receiver

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
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
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
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

slide12

Current ADSL Equalizers (3)

  • 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
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
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
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
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
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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