Re: [10GBT] Issues with solarsep_varlen7a.m
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.