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Re: [10GBT] Issues with solarsep_varlen7a.m

Regarding your first comment, the optimum DFE analysis does not assume
any special phase relationship for the noise transfer function, (it
assumes a Gaussian source, which can be colored) so your statement about
the alien crosstalk environment's random phase variations doesn't apply.
It does rely on the phase profile of the line.

Regarding Hiroshi's analysis, while he does not show the 2.5 bit case,
he clearly does show the preference for lower baud rates, in agreement
with Gottfried's analysis.  I'm glad you have no issues with Gottfried's
analysis.  I disagree with your implication that the results are so
sensitive to the background noise.  They are clearly dominated by the
ANEXT levels, unless the transmit PSD is severely lowered, in which case
the background noise becomes a much larger issue.

We come back to the key point - what do YOU think the DFE SNRs are?  Are
you optimizing receiver filters or are you just assuming them.  Please
state what you believe the magnitude of the difference is.


-----Original Message-----
From: stds-802-3-10gbt@IEEE.ORG [mailto:stds-802-3-10gbt@IEEE.ORG] On
Behalf Of sailesh rao
Sent: Thursday, July 08, 2004 12:23 PM
Subject: 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
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
aware that his results were pessimistic for the 100m Cat-6 2.5bit PAM
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
>as any baud spaced FFE.  As you point out, the folded SNR result is
>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
>front end filtering prior to baud sampling, and, therefore is
>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
>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
>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
>I will also point out that the optimality of the lower baud rates is
>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
> > >
> > > 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 --
>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
>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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