36th Asilomar IEEE Conf. On Signals, Systems and ComputersNov 3-6, Pacific Grove, CA

04/19/23 1

*The University of Texas at Austin

**Motorola, Inc.

Multichannel TEQ Design Based on the Maximum

Composite SSNR

*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) - samples long inserted between symbols to prevent inter-symbol interference (ISI)

• Channel longer than 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

wh1 y1x1

whK yKxK

wh2 y2x2

channels TEQinput 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 • Hk

win – rows of Hk starting from (the transmission delay)

• Hkwall – remainder of Hk

• Ak = (Hkwin)T Hk

win

• 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

Yellow – leads to Hkwall

Gray – leads to Hkwin

sample number

Channel hk (blue line)

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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:

wBw

wAw

k

kT

T

SSNR Modified

K

k k

kkβp1

T

T

)()(wBw

wAww

)(max wwp

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

kkkkkkkkk for λλfor λ satisfies optoptoptoptopt wBwAw

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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 Melsa’s 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)