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Re: [10GBT] Issues with solarsep_varlen7a.m


Since we are dealing with an alien crosstalk dominated noise environment
with its random phase variations, I didn't consider the possibility of an
analog matched filter prior to the sampler.

Hiroshi (takatori_1_0504.pdf) did not consider 2.5bit PAM as one of the
uncoded alternatives.

I have no issues with Gottfried's analysis (ungerboeck_1_0504.pdf) and I'm
aware that his results were pessimistic for the 100m Cat-6 2.5bit PAM case
because of the large background noise (-135dBm/Hz) used in the analysis.
However, I'm not expecting such large background noise in a practical
10GBASE-T receiver.

Sailesh Rao.

>From: George Zimmerman <gzimmerman@SOLARFLARE.COM>
>Reply-To: "IEEE P802.3an" <STDS-802-3-10GBT@LISTSERV.IEEE.ORG>
>Subject: Re: [10GBT] Issues with solarsep_varlen7a.m
>Date: Thu, 8 Jul 2004 09:24:49 -0700
>Glen -
>Thanks for a good description of the key difference.  The optimal DFE
>result includes optimization of filtering prior to baud sampling as well
>as any baud spaced FFE.  As you point out, the folded SNR result is NOT,
>as Sailesh asserts, limited to T/2 spaced FFE systems (that is just one
>way of implementing the optimality for the first fold).  It is well
>known in practice that the SNR on limiting cases can be optimized by
>tuning the front end filter.
>On the other hand, the MMSE analysis that Sailesh is assuming assumes NO
>front end filtering prior to baud sampling, and, therefore is inherently
>pessimistic.  Such a design would suffer from aliased noise.  Any real
>system would have a filtering prior to baud sampling.  If we were to
>assume a front-end filter function, why not assume an optimal design to
>get best performance?  This leads us right back to the optimum folded
>SNR relation of the DFE found in the code.
>As you also point out, the argument that Sailesh is making is a small
>one.  If I eliminate the folding entirely, the absolute DFE SNR results
>change between approximately 0.1 and 0.2 dB, and the relative values (2
>vs. 2.5 vs. 3 bits/baud/pair PAM) change by 0.1 dB.
>Sailesh -
>I hope this answers your folded SNR question.  On your question on the
>March presentation, I'm not sure which parameters you have in question,
>but if you give me a call, I'll be happy to look up whatever information
>you're missing.  The SNR comparison is generated as margin relative to
>capacity, which is scaled relative to 6.02 dB/bit/baud/pair.  This can
>be found in lines 470-494 of the code, not the section you were
>commenting on.  The channel model used is stated in the presentation.
>Previous emails with Samir on the reflector have clarified the
>command-line parameters that correspond to our now-agreed Models 1 2 &
>3. (careful - I recall the first part of the exchange had a sign error).
>A result similar to those from March can be found on Slide 5 of
>mclellan_1_0504, except this one is now for our agreed channel model #1.
>I will also point out that the optimality of the lower baud rates is for
>both the longer channels, and that it has been independently presented
>in takatori_1_0504 and Ungerboeck_1_0504, and, at the latter analysis
>(Ungerboeck) comes at the problem from a completely different
>-----Original Message-----
>From: stds-802-3-10gbt@IEEE.ORG [mailto:stds-802-3-10gbt@IEEE.ORG] On
>Behalf Of Glenn Golden
>Sent: Thursday, July 08, 2004 8:02 AM
>Subject: Re: [10GBT] Issues with solarsep_varlen7a.m
> >
> > Sailesh Rao <saileshrao@OPTONLINE.NET> writes:
> > >
> > > The folded SNR calculations in lines 443, 453 and 463 are not right.
> > >
> > > If f1 and f2 are mirror frequencies about fs/2, the formula being
> > > used
> >
> > > is
> > >
> > > S/N = ABS(S1/N1) + ABS(S2/N2) ;
> > >
> > > However, the actual SNR at the folded frequency would be
> > >
> > > S/N = ABS(S1+S2)/ABS(N1+N2)
> > >
> > > where S1, S2, N1, and N2 are complex phasors. Therefore, in the
> > > context of folding, the actual PSD of the signal becomes relevant,
> > > whereas the original Salz formula for the optimum DFE SNR is
> > independent of the PSD.
> >
> >
> > George Zimmerman <gzimmerman@SOLARFLARE.COM> writes:
> > >
> > > On the folded SNR calculation, however, you are incorrect.  The
> > > optimum DFE is based on a folded SNR which is the sum of the SNRs,
> > > not
> >
> > > the sum of the signal over the sum of the noise.  You can check
> > > either
> >
> > > Salz, or for a more direct representation, please check Pottie &
> > > Eyuboglu, JSAC, August 1991, equation 6.
> > >
> >
>The Salz DFE analysis assumes a prefilter prior to the baud sampler.
>Following optimization (in AWGN) the prefilter turns out to be
>equivalent to the cascade of a channel matched filter followed by
>a one-sided synchronous tapped delay line.  The matched filter's phase
>(conjugate to channel) ensures that the net transfer function
>lies on the positive real axis prior to the baud sampler.  Thus, all
>folding translates (f0+k/T, k = -inf ... inf) add unidirectionally,
>eliminating the effects of channel phase.  It is only because of this
>phase alignment that the optimized integrand involves the sum-of-SNRs,
>and not sum-of-signal/sum-of-noise.  (The same holds for a DFE with
>fractionally spaced FFF.)
>But for a synchronous DFE in the absence of a matched filter -- probably
>the system of interest to most of us -- no special phase alignment of
>the translates can be assumed, and the relevant folding expression (for
>flat AWSS noise with variance N0) is
>     abs(SUM H(f0+k/T)) ** 2 / N0 ,
>          k
>H(f) being the net transfer function from the Tx to the Rx baud sampler
>input.  Except for a missing "**2", this is essentially as Sailesh
>The bottom line is that without a MF or fractionally spaced FFF, the
>value of the summation depends on the channel and front-end phases at
>the translate frequencies, which is the point I believe Sailesh was
>The sum-of-SNRs folding is an upper bound.  Thus, the solarsep code
>optimistic results, unless the assumed system model includes a
>spaced or MF front end.
>For our channel, as long as the rolloff is smooth, the 'optimism' will
>be very large, because even if translates are completely out of phase,
>in-band translate magnitudes dominate.  Similarly if the front-end rolls
>off reasonably above 1/(2Fs).  But if there are large ripples near
>and shallow front-end rolloff, then significant dips in the folded
>can be introduced which could result in non-negligible MSE differential
>between the solarsep method and a more realistic (synchronous, no MF)
>Glenn Golden
>Principal Engineer
>Teranetics, Inc.

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