StatOpt

StatOpt is a statistical eye modelling and link optimization tool for wireline communications, originally developed in MATLAB, now ported to Python 3. Uses statistical methods to model various wireline effects to estimate the performance of different link configurations, provides estimates for Bit Error bates, eye dimensions, as well as various plots relating to link performance.

By default, an equalized PAM-4 link has been created. This link is ready to simulate out of the box. Enjoy!

Features

• Reading in Touchstone (.s4p) files for channel data
• Simulating and characterizing the performance of different modulation schemes such as PAM-4, with different signalling (including 1+D and 1+0.5D)
• Introducing the impairment effects of cross-talk, jitter, noise, and distortion
• Plotting channel and equalizer behaviour curves
• Optimizing equalizers for a given system configuration using a genetic algorithm

Operation

Operation of the StatOpt tool is meant to be simple. The majority of user effort is in configuring the simulation to suit one's needs. The general flow for setting up and running a simulation is as follows.

1. Upload desired Touchstone (.s4p) files and/or .mat files to describe distortion or pulses.
   • Files for channels need to go into the /channels/ folder. (Both .s4p and .mat channel descriptions).
   • All others (predefined pulses, distortion, etc.) are to be kept in the base directory, alongside this readme file.
2. Configure simulation settings to match desired parameters. Check the example files for baseline configurations.
   • Refer to desired files for channels
   • Set desired output plots
   • Adjust the amount of taps in equalizers
   • Select the parameters to be adjusted in the adaption process, if enabled
3. Adjust the statopt.py script to read the simulation configuration function from the desired simulation file.
4. Run the statopt.py script.
   • If the simulation is expected to take a long time, the user will need to confirm that they want the simulation to proceed.
5. Wait for the simulation to complete.
6. Enjoy the results!

Tip: To increase the speed of the simulation, reduce the number of impulse response pre- and post-cursors. Do note that this will reduce the accuracy of the final results.

Example Outputs

The following output plots are generated using the configuration in generateUserSettingsExample0.py. Note: Distortion and ISI Trajectory plots are not plotted by default when executing the example as provided. Distortion is not actually enabled for it (by default) and ISI trajectories takes a very long time to render.

System Response characteristics

Inter-Symbol Interference

Using the pulse response with the different possible data strings to record the different possible inter-symbol interference trajectories for the system to take.

Influences on the System

Note: in example 0 distortion is not enabled by default, hence the simple distortion curves.

Final Probability Density and Bit Error Rate

Knob Definitions

There are many knobs that can have an effect on the simulation, here is a complete list with explanations:

General Settings

Setting Knob	Explanation
general.symbolRate	The system sampling rate [samples/second]
general.signalingMode	The modulation scheme ('standard': conventional baseband, '1+D' and '1+0.5D': partial signaling, 'clock': a clock signal) NOTE: Adaption is primarily tuned for standard signaling.
general.modulation	Number of modulation levels (2: NRZ, 4: PAM4)
general.samplesPerSymb	Time-domain resolution of the eye diagram
general.yAxisLength	Voltage-domain resolution of the eye diagram
general.numbSymb	Number of periods to display in the eye diagram
general.contLevels	Number of contour levels in the eye diagram
general.targetBER	Bit-error-rate level to perform eye measurements (Verical/horizontal eye opening, COM, also used as target for adaption)
general.plotting.channelResponse	Display channel response
general.plotting.CTLEResponse	Display CTLE response
general.plotting.pulseResponse	Display pulse response
general.plotting.jitterSource	Display jitter distribution
general.plotting.noiseSource	Display noise distribution
general.plotting.distortionSource	Display linear distortion
general.plotting.ISI	Display trace eye diagram (CAREFUL: THIS CAN TAKE A LONG TIME TO DISPLAY)
general.plotting.PDFInitial	Display impairment-free eye diagram
general.plotting.PDFCrossTalk	Display eye diagram after adding cross-talk
general.plotting.PDFDistorted	Display eye diagram after adding linear distortion
general.plotting.PDFJitter	Display eye diagram after adding jitter
general.plotting.PDFNoise	Display eye diagram after adding noise
general.plotting.PDFFinal	Display final eye diagram
general.plotting.BER	Display BER contour levels superimposed over BER plot
general.plotting.BER2	Display BER contour levels superimposed over eye diagram (final PDF)
general.plotting.results	Display eye measurement results

Adaption

Setting Knob	Explanation
adaption.adapt	Run adaption algorithm NOTE: Adaption is primarily tuned for standard signaling.
adaption.totalParents	Number best candidates to keep from previous generation
adaption.childrenPerParent	Number of new candidates to generate per parent
adaption.totalMutations	Number of randomly generated candidates
adaption.mode1Generations	Number of generations to run while applying coarse adjustment
adaption.mode2Generations	Number of generations to run while applying fine adjustment
adaption.knobs	Specify which knobs to optimize (must provide full path i.e.: 'transmitter.EQ.taps.pre1')

Transmitter Settings

Setting Knob	Explanation
transmitter.signalAmplitude	Transmitter supply voltage (peak differential) [V]
transmitter.includeSourceImpedance	Include 50ohm source impedance (halves transmit signal voltage). NOTE: this just scales the output, the simulation does not handle reflections.
transmitter.tRise	Signal rise time [s]
transmitter.TXBandwidth	Transmitter analog bandwidth [Hz]
transmitter.preCursorCount	Number of ISI pre-cursors to consider in eye diagram generation
transmitter.postCursorCount	Number of ISI post-cursors to consider in eye diagram generation
transmitter.EQ.addEqualization	Apply FIR equalization
transmitter.EQ.taps	Specify FIR equalization tap values
transmitter.jitter.addJitter	Apply transmitter jitter
transmitter.jitter.stdDeviation	Specify random jitter standard deviation [UI]
transmitter.jitter.amplitude	Specify deterministic jitter amplitude [UI]
transmitter.jitter.DCD	Specify duty-cycle distortion jitter [UI]
transmitter.noise.addNoise	Apply transmitter noise
transmitter.noise.stdDeviation	Specify random noise standard deviation [V]
transmitter.noise.amplitude	Specify deterministic noise amplitude [V]
transmitter.noise.frequency	Specify deterministic noise frequency [Hz]
transmitter.distortion.addDistortion	Add transmitter linear distortion
transmitter.distortion.fileName	File specifying 1-to-1 voltage mapping (structure containing "input" and "output" vectors of same length)

Channel Settings

Setting Knob	Explanation
channel.addChannel	Apply channel to link
channel.addCrossTalk	Apply crosstalk
channel.addNotch	Apply a notch to channel transfer function
channel.notchFreq	Specify notch frequency [Hz]
channel.notchAttenuation	Specify notch attenuation [dB]
channel.modelCircuitTF	Convolve link response with an additional pulse response to model a circuit who's response is known
channel.modelCircuitTFName	Specify additional pulse response file
channel.overrideResponse	Override transmitter and channel response with a custom pulse response (can still apply receiver equalization)
channel.overrideFileName	Specify custom pulse response file
channel.approximate	Approximate cross-talk as a noise source to speed up simulation
channel.makeAsynchronous	Assume aggressor channels are not synchronized with victim channel and thus impairment is applyed to all sampling phases equally
channel.fileNames	Specify channel files (includes THRU, NEXT and FEXT channels)
channel.noise.addNoise	Apply thermal noise
channel.noise.noiseDensity	Specify thermal noise density [V^2/Hz]

Receiver Settings

Setting Knob	Explanation
receiver.signalAmplitude	Specify receiver supply voltage [V] (Y-limits of receiver plots)
receiver.preAmp.addGain	Apply pre-amplification
receiver.preAmp.gain	Specify pre-amplification gain
receiver.CTLE.addEqualization	Apply continuous-time linear equalization
receiver.CTLE.zeroFreq	Specify CTLE transfer function zero frequency [Hz]
receiver.CTLE.zeroNumb	Specify number of zeros to apply to CTLE transfer function
receiver.CTLE.pole1Freq	Specify primary CTLE transfer function pole frequency [Hz]
receiver.CTLE.pole1Numb	Specify number of primary poles to apply to CTLE transfer function
receiver.CTLE.pole2Freq	Specify secondary CTLE transfer function pole frequency [Hz]
receiver.CTLE.pole2Numb	Specify number of secondary poles to apply to CTLE transfer function
receiver.FFE.addEqualization	Apply FFE equalization
receiver.FFE.taps	Specify FFE tap values
receiver.DFE.addEqualization	Apply DFE equalization
receiver.DFE.taps	Specify DFE tap values
receiver.jitter.addJitter	Apply receiver jitter
receiver.jitter.stdDeviation	Specify random jitter standard deviation [UI]
receiver.jitter.amplitude	Specify deterministic jitter amplitude [UI]
receiver.jitter.DCD	Specify duty-cycle distortion jitter [UI]
receiver.noise.addNoise	Apply receiver noise
receiver.noise.stdDeviation	Specify random noise standard deviation [V]
receiver.noise.amplitude	Specify deterministic noise amplitude [V]
receiver.noise.frequency	Specify deterministic noise frequency [Hz]
receiver.distortion.addDistortion	Add receiver linear distortion
receiver.distortion.fileName	File specifying 1-to-1 voltage mapping (structure containing "input" and "output" vectors of same length)

Dependancies

In addition to running Python 3.10 or newer, the following libraries are needed to run this code:

• NumPy
• SciPy
• matplotlib
• scikit-rf
• Python Control Library

These can all be automatically installed/verified to be the right versions using the following command in the project directory:

pip install -r requirements.txt

NOTE: This may run on earlier versions of the packages and Python, but it has only been extensively tested on Python 3.10 with the package versions specified as the minimums in requirements.txt.

Future Work

• Investigate the use of an alternative, more interactive graphics library for figures like pyqt or Altair
• Consider allowing the chaining of .s4p files to allow systems to be more flexible. For example allowing one to change the transmission line but keeping the same die-to-pad channel.
• Speed up simulation of RX CTLE step. Currently lsim is responsible for 90% of run time during adaption.
  • Attempt to parallelize its operation across all channels in a given link configuration
  • Consider replacing lsim with a convolution operation like what is done for pulse response generation. This is probably what goes on inside lsim but we could avoid repeatly calculating this repsonse by recording it the first time for a given CTLE. Then whenever the response is needed, read it from memory and convole which is much faster than recalculating the impulse reponse repeatedly.

Credit

Originally written in MATLAB by Jeremy Cosson-Martin and Jhoan Salinas for Ali Sheikholeslami's research group. Porting to Python was done by Savo Bajic as a project for Ali Sheikholeslami's wireline course, ECE1392, based on version 1.11 in MATLAB, although it has been updated since in parallel with the MATLAB version.

The Touchstone files used for examples were provided by Samtec and TE Connectivity as part of of their works towards 100 Gb/s lanes. More information is available in the Touchstone folder readme.