1. Multichannel TEQ Design Based on the Maximum Composite SSNR
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Multichannel TEQ Design Based on the Maximum Composite SSNR
*M. Milosevic, **L. Pessoa, and
*B. L. Evans
36th Asilomar IEEE Conf. On Signals, Systems and Computers
Nov 3-6, Pacific Grove, CA
11/23/2018

2. 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 n+1 samples causes ISI
Time-domain equalizer (TEQ) used to shorten the channel
11/23/2018
MPE’02 Asilomar

3. 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]
11/23/2018
MPE’02 Asilomar

4. Problem: Multichannel TEQ Designx1 h1 w y1 x2 h2 w y2 xK hK w yK
input
channels
TEQ
output
11/23/2018
MPE’02 Asilomar

5. Motivation
Design multichannel TEQs for classes of loops present in carrier service area
Simplify G Fast Retrain with multichannel TEQ that is applied every time modem recovers from disturbance and the line is slightly different
11/23/2018
MPE’02 Asilomar

6. 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
Yellow – leads to Hkwall
Gray – leads to Hkwin
sample number
Channel hk (blue line)
11/23/2018
MPE’02 Asilomar

7. 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
11/23/2018
MPE’02 Asilomar

8. Multichannel TEQ Design Algorithm
Find the optimal TEQs wkopt for every channel: 1 through K
Select w= wkopt for which CSSNR p(w) is maximized for all k in the set
Find the maximum of p(w) closest to the initial point using Levin/Almogy iteration
11/23/2018
MPE’02 Asilomar

9. Simulation Results Channels jointly shortened: CSA loops 1-8
Example: CSA loop 1 and CSA loop 5
11/23/2018
MPE’02 Asilomar

10. 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
11/23/2018
MPE’02 Asilomar

11. 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)
11/23/2018
MPE’02 Asilomar