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And the magnitude of the difference is? I believe you will find it is small enough not to change the results.
Because the simulation was made to be power-spectrum independent, the comment you made about the frequency base and TX power is correct; however, however, the effect is small because the system is evaluated and limited by impairments proportional to the power spectrum. If background noise were increased, this difference would matter, more. Also if you eliminated Alien NEXT, this effect matters more.
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.
On the SNRs used for 2, 3, & 4 bits, these numbers are close approximations, and the difference is small (< .25 dB), but the uncoded margin numbers from these equations haven’t generally been used. When comparing multiple baud rates, however, the margin y aren’t the scaling factors used for the margin vs. baud rate graphs. The graphs are based on the information bits per symbol and these are the ones that were used in the presentations showing the difference in baud rates.
For coded systems I use the directly computed DFE SNRs and then compare them to the SNR required by the coded system.
Sailesh – if you wish to provide refined code, be my guest.
I would like to bring up some issues with the solarsep_varlen7a.m matlab code that is found on
I believe that these issues alter the conclusions that one could derive from this code.
1. Frequency Base:
The frequency base for the DFE margin calculations is being inferred from the first column in the Insertion Loss files found in this directory. As a result, the frequency base ranges from 0 to 650MHz in all cases. However, the average power P is being distributed evenly over (line 391)
bwmhz=1250MHz for the 2-bit PAM system,
bwmhz=1000MHz for the 2.5-bit PAM system,
bwmhz=833MHz for the 3-bit PAM system
This means that 48% of the input power is unused in the 2-bit system, 35% is unused in the 2.5-bit system and only 22% is unused in the 3-bit system. This tips the scale in favor of the 3-bit PAM system.
2. Folded SNR calculation:
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.
As done in the matlab code, this calculation also tips the scale in favor of the 3-bit PAM system since signal power is assumed to be zero for f>650MHz due to (1) above.
3. SNR Requirement for 1E-12 BER
The SNR requirement for 2.5bit PAM is 3.01dB worse than the SNR requirement for 2-bit PAM.
The SNR requirement for 3bit PAM is 6.23dB worse than the SNR requirement for 2-bit PAM.
The code is using 2.95dB and 5.94dB respectively in lines 446, 456 and 466, which also tips the scale in favor of the 3-bit PAM system.