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Re: [10GBT] Issues with solarsep_varlen7a.m



Glenn,

I've only published the MMSE Pulse analysis source code for the 1000BASE-T
receiver. Of course, there was a front-end analog receive filter (a
Butterworth LPF with an 80MHz 3dB point) included in the analysis.

Regards,
Sailesh Rao.

>From: Glenn Golden <gdg@zplane.com>
>Reply-To: gdg@zplane.com
>To: STDS-802-3-10GBT@listserv.ieee.org
>Subject: Re: [10GBT] Issues with solarsep_varlen7a.m
>Date: Thu, 8 Jul 2004 13:22:59 -0600
>
>George,
>
>I think you may have misinterpreted my comments.  I was agreeing with
>Sailesh.
>
>A T/2 FFF is an appropriate comparison if -- as in our case -- the
>available measurements only go out to Fs or less.  You seem to be
>putting words in his mouth by saying
>
> > the folded SNR result is NOT, as Sailesh asserts, limited to T/2
> > spaced FFE systems
>
>because he didn't assert that.  He only said it was valid for that case,
>which it is.
>
> > The folded SNR calculation as done in the matlab code is valid for a T/2
> > fractionally-spaced Decision Feedback Equalizer.
>
>As he points out, no FS front end (regardless of sampling fraction) has
>been proposed, and TTBOMK -- though I am not familiar with all the
>presentations since Day 1 -- I haven't seen any proposals so far about
>tuning analog front end phase so as obtain favorable compromise folding.
>
>Given that, using the folded SNR (as per the present solarsep code) is an
>optimistic way to model it.   A more realistic way is to just fold what
>you get out of the front end filter, in whatever way you have chosen to
>model that.  This seems to me to have been Sailesh's point.  The solarsep
>code has, in effect, chosen to model the front end as the optimum matched
>filter.  Others may disagree with that choice.  If the code were to use
>(folded signal/folded noise) instead of folded-SNR, then it would get the
>right answer in either case.
>
> > 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.
>
>I haven't seen Sailesh's code, so I can't comment, but I suspect that he is
>well aware that the front end filtering should be included in the transfer
>function prior to folding. If it's really not in the code that way, then
>of course that's a mistake.  Or perhaps he's assuming a front end with
>relatively sharp rolloff, in which case it's not necessary to explicitly
>model it, I don't know.  Maybe he can comment on this.
>
>
> > If we were to assume a front-end filter function, why not assume
> > an optimal design to get best performance?
>
>Why not do the folding computation in a way which allows the user to make
>whatever assumption he wants regarding the front end? If you want to assume
>MF and get the best performance, fine, put that in there and you'll get the
>right answer.  If I or someone else wants to assume a compromise front end,
>and (e.g.) see what effects large ripples near Fs/2 have on the folding,
>then we can put that front end model in and get the right answer for that
>case too.  But with the code as it is, using folded SNR, you won't get the
>right answer.
>
>
> > As you also point out, the argument that Sailesh is making is a small
>one.
>
>I did not make such an unequivocal statement. I said that _if_ the
>assumption
>is smooth channel rolloff, or fairly sharp front end rolloff, then the
>difference will be small.  But I also said that if there are ripples near
>Fs/2 [I mistakenly wrote 1/(2Fs)] and the front end rolloff is gradual,
>then
>the difference may not be small.  It all depends on the size of the ripples
>and the way the phases add.  However, someone interested in exploring this
>effect would not be able to do so with the solarsep code as it is. They
>would be able to do so if the code performed folding in the suggested way.
>
> > 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
>
>For a smoothly rolled off channel, this is not surprising, since the folded
>and unfolded spectra are nearly identical, regardless of front end
>assumptions.
>
>How about trying a channel with big ripples near Fs/2, and a
>less-than-optimal
>front end phase, comparing that against no-folding?  In that case, if the
>folding were more realistically modelled, the differential from no-folding
>could be larger, and in _either direction_, depending on the details of the
>ripples and front end.  It may or may not be significant.  But with the
>solarsep code as-is, it is not even possible to model this case to find
>out.
>Furthermore, if you did attempt to model it with solarsep, you would only
>ever see an _improvement_ over the no-folding case, never a degradation.
>That seems potentially dangerous, if e.g. there do turn out to be cases of
>interest in which the real-world differential is non-negligible and in the
>wrong direction.
>
>The point is that if the solarsep code just performed folding in the
>suggested way, then experiments involving both optimum and sub-optimum
>front-ends could be performed.
>
>Glenn Golden
>Principal Engineer
>Teranetics, Inc.
>ggolden@teranetics.com
>
>
>
>
>
>
>George Zimmerman writes:
> > 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
> > perspective.
> > -george
> >
> > -----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
> > To: STDS-802-3-10GBT@listserv.ieee.org
> > 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
> > (channel*MF)
> > 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
> > indicated.
> >
> > 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
> > making.
> > The sum-of-SNRs folding is an upper bound.  Thus, the solarsep code
> > yields
> > optimistic results, unless the assumed system model includes a
> > fractionally
> > spaced or MF front end.
> >
> > For our channel, as long as the rolloff is smooth, the 'optimism' will
> > not
> > be very large, because even if translates are completely out of phase,
> > the
> > in-band translate magnitudes dominate.  Similarly if the front-end rolls
> > off reasonably above 1/(2Fs).  But if there are large ripples near
> > 1/(2Fs)
> > and shallow front-end rolloff, then significant dips in the folded
> > spectrum
> > can be introduced which could result in non-negligible MSE differential
> > between the solarsep method and a more realistic (synchronous, no MF)
> > evaluation.
> >
> > Glenn Golden
> > Principal Engineer
> > Teranetics, Inc.

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