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*To*: STDS-802-3-10GBT@LISTSERV.IEEE.ORG*Subject*: Re: [10GBT] Issues with solarsep_varlen7a.m*From*: Glenn Golden <gdg@zplane.com>*Date*: Thu, 8 Jul 2004 09:02:21 -0600*In-Reply-To*: Message from George Zimmerman <gzimmerman@SOLARFLARE.COM> of "Wed, 07 Jul 2004 13:30:03 PDT." <D59797D4377CDE44B0C4A5A8C7675BA770A9F4@solar008.SolarFlarecom.com>*Reply-To*: gdg@zplane.com*Sender*: stds-802-3-10gbt@IEEE.ORG

> > 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.

**References**:**Re: [10GBT] Issues with solarsep_varlen7a.m***From:*George Zimmerman <gzimmerman@SOLARFLARE.COM>

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