36th Asilomar IEEE Conf. On Signals, Systems and Computers

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Multichannel TEQ Design Based on the Maximum
Composite SSNR

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• M. Milosevic, L. Pessoa, and
• B. L. Evans

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Introduction

• Discrete Multi-Tone (DMT) is multicarrier
  modulation used in xDSL
• Guard period (cyclic prefix) n- samples long
  inserted between symbols to prevent inter-symbol
  interference (ISI)
• Channel longer than n1 samples causes ISI
• Time-domain equalizer (TEQ) used to shorten the
  channel

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Published Work

• Many TEQ designs exist for the single-channel
  case
• Few attempt multichannel TEQ design
• Joint Maximum Shortening SNR method Melsa,
  Younce Rohrs, 1996
• FIR Channel-Shortening Equalizers for MIMO ISI
  Channels Al-Dhahir, 2001
• Multichannel TEQ design by loop classification
  Farhang-Boroujeny and Ding, 2001
• Eigenfilter Design Tkacenko Vaidyanthan 2002

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Problem Multichannel TEQ Design
x1
w
h1
y1
y2
x2
w
h2
xK
w
hK
yK
channels
TEQ
input
output
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Motivation

• Design multichannel TEQs for classes of loops
  present in carrier service area
• Simplify G.992.2 Fast Retrain with multichannel
  TEQ that is applied every time modem recovers
  from disturbance and the line is slightly
  different

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Definitions

• Hk convolution channel i matrix
• Hkwin n rows of Hk starting from D (the
  transmission delay)
• Hkwall remainder of Hk
• Ak (Hkwin)T Hkwin
• Bk (Hk)T Hk
• w TEQ FIR of M taps
• w T Ak w energy of windowed part of shortened
  channel
• w T Bk w energy of the of shortened channel

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Modified and Composite SSNR

• Define
• As TEQ shortens channel Modified SSNR goes to 1
  instead of Inf like SSNR
• Define Composite SSNR as
• Problem

Desired channel energy
ISI-causing channel energy
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Multichannel TEQ Design Algorithm

1. Find the optimal TEQs wkopt for every channel 1
   through K
2. Select w wkopt for which CSSNR p(w) is
   maximized for all k in the set
3. Find the maximum of p(w) closest to the initial
   point using Levin/Almogy iteration

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Simulation Results

• Channels jointly shortened CSA loops 1-8
• Example CSA loop 1 and CSA loop 5

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Simulation Results

• Compared to Melsas Joint MSSNR with equal
  weighting for all channels
• Higher p(w) indicates better removal of channel
  energy outside of desired window (100 max)

Method p(w) Bit Rate/Ch
MCSSNR 99.71 9.26 Mbps
Joint MSSNR 99.18 9.07 Mbps
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Conclusions

• Multichannel TEQs can be useful and perform well
• MCSSNR reports higher data rate than Joint MSSNR
• MCSSNR is expensive (multiple generalized
  eigenvector problems during algorithm)