Multichannel TEQ Design Based on the Maximum Composite SSNR

1. This presentation will probably involve audience discussion, which will create action items. Use PowerPoint to keep track of these action items during your presentation • In Slide Show, click on the right mouse button • Select “Meeting Minder” • Select the “Action Items” tab • Type in action items as they come up • Click OK to dismiss this box • This will automatically create an Action Item slide at the end of your presentation with your points entered. Multichannel TEQ Design Based on the Maximum Composite SSNR *M. Milosevic, **L. Pessoa, and *B. L. Evans 11/17/2014

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+1samples causes ISI • Time-domain equalizer (TEQ) used to shorten the channel 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] MPE’02 Asilomar

4. Problem: Multichannel TEQ Design x1 y1 h1 w x2 y2 h2 w xK yK hK w input channels TEQ output MPE’02 Asilomar

5. 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 MPE’02 Asilomar

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

9. Simulation Results • Channels jointly shortened: CSA loops 1-8 • Example: CSA loop 1 and CSA loop 5 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) 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) MPE’02 Asilomar