On the Relation Between Time-Domain
Equalizers and Per-Tone Equalizers for
DMT-Based Systems
Koen Vanbleu, Geert Ysebaert,...
On Equalization Alternatives and their
Relations for ADSL Modems
Koen Vanbleu, Geert Ysebaert, Gert Cuypers, Marc Moonen
K...
Overview
• ADSL Basics
 What? Multicarrier modulation
 Transmitter/Receiver
• ADSL Equalizer Design
 Problem Descriptio...
Introduction
• ADSL Basics
- Intro
- DMT Transmitter
- Why Equalization?
- DMT Receiver
• ADSL Equalizer
Design
- Problem ...
Multicarrier Modulation
• ADSL Basics
- Intro
- DMT Transmitter
- Why Equalization?
- DMT Receiver

•

Digital multicarrie...
Discrete Multitone: Transmitter

• ADSL Equalizer
Design
- Problem Description
- Current Equalizers
- Bit rate Maximizing
...
Why Equalization?
• ADSL Basics
- Intro
- DMT Transmitter
- Why Equalization?
- DMT Receiver

...

• ADSL Equalizer
Design...
Discrete Multitone: Receiver

• ADSL Equalizer
Design
- Problem Description
- Current Equalizers
noise
- Bit rate Maximizi...
DMT Equalization:
Problem Description
• ADSL Basics
- Intro
- DMT Transmitter
- Why Equalization?
- DMT Receiver

10

T ta...
Current ADSL Equalizers
• ADSL Basics
- Intro
- DMT Transmitter
- Why Equalization?
- DMT Receiver

Channel shorteners
e.g...
Bit rate Maximizing Equalizers:
Per-tone equalization
• ADSL Basics
- Intro
- DMT Transmitter
- Why Equalization?
- DMT Re...
Bit rate Maximizing Equalizers:
Per-tone equalization
• ADSL Basics
- Intro
- DMT Transmitter
- Why Equalization?
- DMT Re...
Bit rate Maximizing Equalizers:
Per-tone equalization
• ADSL Basics
- Intro
- DMT Transmitter
- Why Equalization?
- DMT Re...
• ADSL Basics
- Intro
- DMT Transmitter
- Why Equalization?
- DMT Receiver

Bit rate Maximizing (BM)
Equalizers:
Time-doma...
Bit rate Maximizing Equalizers:
Time-domain equalization
• ADSL Basics
- Intro
- DMT Transmitter
- Why Equalization?
- DMT...
Relation between ADSL equalizers
• ADSL Basics
- Intro
- DMT Transmitter
- Why Equalization?
- DMT Receiver
• ADSL Equaliz...
Relation between ADSL equalizers
• ADSL Basics
- Intro
- DMT Transmitter
- Why Equalization?
- DMT Receiver
• ADSL Equaliz...
Relation between ADSL equalizers
• ADSL Basics
- Intro
- DMT Transmitter
- Why Equalization?
- DMT Receiver
• ADSL Equaliz...
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Td and-fd-mmse-teq

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Td and-fd-mmse-teq

  1. 1. On the Relation Between Time-Domain Equalizers and Per-Tone Equalizers for DMT-Based Systems Koen Vanbleu, Geert Ysebaert, Gert Cuypers, Marc Moonen Katholieke Universiteit Leuven, ESAT / SCD-SISTA, Belgium IEEE Benelux Signal Processing Symposium Hilvarenbeek, the Netherlands April 16, 2004
  2. 2. On Equalization Alternatives and their Relations for ADSL Modems Koen Vanbleu, Geert Ysebaert, Gert Cuypers, Marc Moonen Katholieke Universiteit Leuven, ESAT / SCD-SISTA, Belgium IEEE Benelux Signal Processing Symposium Hilvarenbeek, the Netherlands April 16, 2004
  3. 3. Overview • ADSL Basics  What? Multicarrier modulation  Transmitter/Receiver • ADSL Equalizer Design  Problem Description  Current Equalizers (TD-MMSE)  Bit rate Maximizing Equalizers (FD-MMSE criterion) 3  Relations
  4. 4. Introduction • ADSL Basics - Intro - DMT Transmitter - Why Equalization? - DMT Receiver • ADSL Equalizer Design - Problem Description - Current Equalizers - Bit rate Maximizing Equalizers - Relations 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 Downstream Central Customer Upstream Down ADSL 6 Mbps 640 kbps 3.7 km 1.1 MHz ADSL2+ 5 Up Line length Frequency band 15 Mbps 1.5 Mpbs 1.8 km 2.2 MHz VDSL 52 Mbps 2.3 Mbps < 1 km 12 MHz
  5. 5. Multicarrier Modulation • ADSL Basics - Intro - DMT Transmitter - Why Equalization? - DMT Receiver • Digital multicarrier modulation scheme: Discrete Multitone (DMT) e.g. ADSL POTS • ADSL Equalizer Design - Problem Description - Current Equalizers - Bit rate Maximizing Equalizers - Relations UP 4 25 DOWN 138 1104 f (kHz) • • 6 Assign different frequency bins to up- and downstream directions Traditional telephony (POTS) still available over the same wire.
  6. 6. Discrete Multitone: Transmitter • ADSL Equalizer Design - Problem Description - Current Equalizers - Bit rate Maximizing Equalizers - Relations bits 10 Data symbols (QAM) Im 00 0 Re 11 ˆ xk , n 01 2 bits Cyclic Prefix ... • ADSL Basics - Intro - DMT Transmitter - Why Equalization? - DMT Receiver . . . N-point . . . IDFT CP P/S xl Im 7 4 bits ... Re N / 2 +1 Block transmission! N IDFT modulation (Inverse Discrete Fourier Transform)
  7. 7. Why Equalization? • ADSL Basics - Intro - DMT Transmitter - Why Equalization? - DMT Receiver ... • ADSL Equalizer Design - Problem Description - Current Equalizers - Bit rate Maximizing Equalizers - Relations CP ˆ xk , n N / 2 +1 . . . . . . N-point IDFT P/S ... N Transmitter 8 noise nl channel xl yl Why equalization? “Invert” channel distortion while not boosting noise
  8. 8. Discrete Multitone: Receiver • ADSL Equalizer Design - Problem Description - Current Equalizers noise - Bit rate Maximizing Equalizers - Relations CP nl Frequency Data symbols Domain Equalizer bits 1 tap / tone TEQ w yl h∗w h Time Domain Equalizer S/P . . . N-point DFT x 9 CP length + 1 . . . Im 00 Re 01 11 2 bits Im ~ dn T taps l 10 x x channel h xl ... • ADSL Basics - Intro - DMT Transmitter - Why Equalization? - DMT Receiver DFT demodulation Re 4 bits
  9. 9. DMT Equalization: Problem Description • ADSL Basics - Intro - DMT Transmitter - Why Equalization? - DMT Receiver 10 T taps y • ADSL Equalizer l Design - Problem Description - Current Equalizers To - Bit rate Maximizing Equalizers - Relations TEQ w CP 1 tap/tone S/P ~ ... N-point ... FEQ d ... FE n DFT Q Im 11 00 Re 01 2 bits ~ +e xk ,n ~k ,n maximize bit rate:  SNRn (w )   b = ∑ bits on tone n = ∑ log 2 1 +   Γn tones n tones n   ~ 2 E xk , n Residual ISI/ICI where SNRn ( w ) = ~ (w ) 2 E e k ,n Noise (RFI/XT/etc.) 10 { { } } is hard with time-domain equalizer w
  10. 10. Current ADSL Equalizers • ADSL Basics - Intro - DMT Transmitter - Why Equalization? - DMT Receiver Channel shorteners e.g. time-domain MMSE-TEQ design noise nl • ADSL Equalizer Design - Problem Description - Current Equalizers - Bit rate Maximizing Equalizers - Relations Channel h xl TIR b delay el - TIR = target impulse response of (CP-length+1) h∗w h L −1 min ∑ y w − x b s.t. constraint on w w, b 11 yl TEQ w l CP length + 1 l =0 T l T l 2 Constrained linear rate optimization! MMSE-TEQ No bit least-squares based
  11. 11. Bit rate Maximizing Equalizers: Per-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 ∆ Time Domain N Equalize r T taps yl TEQ w ∆ ∆ x ↓ N +ν x . . . ↓ N +ν . . . N-point DFT ~ FEQ d n ↓ N +ν y 12 x k, w ~ ~ = d F ((Y w )) ˆ Fn Y kw xk , n n n k  k    yk , ,,w yykkww . . . ~ ˆ xk , n
  12. 12. Bit rate Maximizing Equalizers: Per-tone equalization • ADSL Basics - Intro - DMT Transmitter - Why Equalization? - DMT Receiver T −1 • ADSL Equalizer Design - Problem Description - Current Equalizers - Bit rate Maximizing Equalizers  Per-tone equalization  BM-TEQ - Relations ∆ ∆ N ... ∆ ... ↓ N +ν ↓ N +ν ... ∆ yl 13 ∆ S/P N + ν ↓ ↓ N +ν ... PTEQ ... sliding ~ T ˆ xk , n N-point DFT T –tap linear combiner ... N-point DFT w for each tone n ↓ N +ν ~ ~ ~ = d F (Y w ) =( FFY )(wd ) ˆ xk , n ( n n Yk ) n k n n k      y k ,w wn
  13. 13. Bit rate Maximizing Equalizers: Per-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 2 K −1 min ∑ ( Fn Yk )w n − ~k ,n x ~ wn k =0 wd n • 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 14
  14. 14. • ADSL Basics - Intro - DMT Transmitter - Why Equalization? - DMT Receiver Bit rate Maximizing (BM) Equalizers: Time-domain equalization } 2  SNRn   where SNRn (w / w n ) = max ∑ log 2 1 +  2 Γn  tones n   E ~k , n ( w / w n ) e • ADSL Equalizer Design - Problem Description - Current Equalizers - Bit rate Maximizing Equalizers  Per-tone equalization  BM-TEQ - Relations { PTEQ: min wn 2 K −1 wd n min ∑ ~ w ,d n ∑ k = 0 tones n T taps yl 2 ~ (w ) = min ( F Y )w − ~ ∑ ek ,n n ∑ n k ~n xk ,n wn k =0 k =0 K −1 BM-TEQ: } K −1 ~ γ n d n ( Fn Yk )w − ~k ,n x with γ n 15 { E ~k ,n x CP TEQ S/P 2 ~ = f ( SNRn ) = g (ek ,n ) ~ FE d n Q x ... N-point ... ... DFT x
  15. 15. Bit rate Maximizing Equalizers: Time-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 K −1 min ∑ ~ w ,d n k = 0 tones n K −1 = min ∑ ~ w ,d n with ∑ ∑ k = 0 tones n ~ ~ (w, d ) γ n ek ,n n 2 ~ γ n d n ( Fn Yk )w − ~k ,n x 2 ~ ~ (d , w )) γ n = f ( SNRn ) = g (ek ,n n Iteratively-reweighted separable non-linear least squares-based frequency-domain MMSE-TEQ design 16
  16. 16. Relation between ADSL equalizers • 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 Block transmission/CP/Multicarrier FD-MMSE-TEQ: constrained linear LS or separable NL-LS Bit rate maximization BM-TEQ: iteratively reweighted separable NL-LS Only 1 tone 17 PTEQ: linear LS Remarkable correspondence between generalized eigenvalue problems
  17. 17. Relation between ADSL equalizers • ADSL Basics - Intro - DMT Transmitter - Why Equalization? - DMT Receiver • ADSL Equalizer Design - Problem Description - Current Equalizers - Bit rate Maximizing Equalizers - Relations 18 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
  18. 18. Relation between ADSL equalizers • 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 Block transmission/CP/Multicarrier FD-MMSE-TEQ: constrained linear LS or separable NL-LS Bit rate maximization BM-TEQ: iteratively reweighted separable NL-LS Only 1 tone 19 PTEQ: linear LS Remarkable correspondence between generalized eigenvalue problems
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