Hi Norm,
Nice presentation! I agree with your observation that SER calculated based on your documentation is the right way!
I suspect there may be a problem with your Matlab code for I recollect getting like curvy waveforms for the Left and Right Cumulative Histograms and then fixed it, I need to go through my notes to recollect what I did.
In the upcoing Monday meeting, I will share my Maltab script in calculating TDECQ with the incorporation of the Table 180-16 constrains then we can debug the root cause for the that noisy/ curvy Cumulative Histograms in documenting the root cause.
To help validate the proposed analytical SER calculation proposed by you, compare it against the measured symbol error rate obtained directly from the equalized waveform. The measured SER can be computed by slicing the equalized samples to the nearest PAM4
level and comparing the resulting decisions with the transmitted symbols.
levels = [0.333 0.667 1.000 1.333];
decisions = arrayfun( ...
@(v)slicer_pam4(v,levels), ...
yEq);
SERmeas = mean(decisions ~= txValid);
function decision = slicer_pam4(x, levels)
[~,idx] = min(abs(levels - x));
decision = levels(idx);
end
Below are a few observations for the Left and Right Cumulative Histograms.
Observation #1
- One can observe that the curve decreases toward 0 at the threshold location then increase again, forming a "V" shape.
- Essentially, computes probability mass between a bin and the threshold.
Observation #2
- My PAM4 levels are approximately 0.333, 0.667, 1.000 and 1.333.
- The thresholds sit near 0.56, 0.83 and 1.10.
- Consequently:
P(y< Pth1)= approx. 25%
P(y< Pth2)= approx. 50%
P(y< Pth3)= approx. 75%
This confirms where exactly the maxima are showing.
Regards,
Hansel D'Silva
Standards Development Engineer- Amphenol
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