Transmitter and Dispersion Eye Closure Quaternary (TDECQ) is a recently introduced figure of merit for PAM-4 transmitters designed for several classes of 200GHz/400GHz fiber links with maximal reaches ranging from 100m to 10km. The details of the standardized measurement may be found in IEEE 802.3 2018 [1]. It involves passing the light emitted from the transmitter through a one-meter length of highly dispersive fiber, representing the worst-case dispersion the signal would undergo in normal operation. The light is then converted into an electrical signal and passed through a fourth-order Bessel filter before being collected on storage oscilloscope. A calculation is then performed on the signal to determine the maximum amount of noise that could be added to the signal while still conforming to a maximal bit-error rate prescribed in the standard. This amount of noise is compared to the amount that could be supported by an undistorted signal, and the ratio in dB is calculated as the value of TDECQ.

In this example we demonstrate, the use of a compound element in INTERCONNECT that allows the user to perform this measurement.

### Block Diagram

Above is the test circuit we use for the measurement. A Short Stress Pattern Random – Quaternary (SSPRQ) signal with 4 level gray coding is fed to a PAM4 modulator, then the received signal is passed to the TDECQ block. The TDECQ block consists a 1 meter highly dispersive fiber, a PIN photodetector and a 4th order Bessel filter. The SSPRQ pattern is also fed to the TDECQ block as the reference.

### Symbol Error Rate Estimation

The TDECQ calculation is done in the TDECQ block in the analysis script. The calculation has the following phases:

*Phase 1: initialize equalizer*

- Generate reference signal from transmitter (TX) signal power and reference symbol pattern
- Pick the best least-squares fit from a sample within the unit interval (UI)
- Output: initial equalizer tap weights, thresholds

*Phase 2: optimize equalizer*

- Minimize the symbol error rate (SER) as a function of tap weights
- Iterate until the maximum noise \(\sigma_G\) is found such that SER = 4.8e-4

*Phase 3: calculate TDECQ*

$$

T D E C Q=10 \log 10\left(\frac{O M A}{6} \times \frac{1}{Q_{t} \sqrt{\sigma_{G}^{2}+\sigma_{S}^{2}}}\right)

$$

where OMA is the outer optical modulation amplitude of the signal, \(Q_t\) is 3.414 consistent with the Bit Error Rate (BER) and target SER for Gray coded PAM4, \(\sigma_S\) is the detector noise and \(\sigma_G\) is the allowed noise that can be add to the signal at level.

### Simulation Steps

*Step 1:* We perform a TDECQ measurement on an ideal PAM-4 transmitter and observe that when the fiber dispersion and Bessel filter are turned off, we obtain a TDECQ value very near zero as expected.

*Step 2:* We connect the TDECQ element to an idealized PAM-4 transmitter and we run a sweep where the signal transition as a fraction of the unit interval are made larger and larger, and a TDECQ measurement is made in each case. The results are then plotted.

*Step 3:* With connection still in place, we return the transition time to zero and we now increase the amount of additive noise added to the output of the ideal AM modulator. Once again, using a sweep the TDECQ value is measured and plotted against the amount of noise added.

### Run and Result

*Ideal TDECQ calculation*

- Open INTERCONNECT and install the provided CML “tdecq.cml”.
- Open the file “tdecq_ideal_signal_file.icp”.
- Run the simulation
- Type “runanalysis” in the script prompt. The calculation will take a couple of minutes.

Note in the results of the TDECQ element that the TDECQ result is approximately 0.03, very near to the expected value of zero.

*Non-ideal TDECQ calculation*

- Open the file “tdecq_non_ideal_signal_file.icp”. Note that with the CML installed once, it will be saved into INTERCONNECT and you can drag and drop the TDECQ element from the Design Kits folder and use it afterwards.
- Open and run the script file “tdecq_non_ideal_signal_sweep.lsf”. This file will sweep through the rise/fall period of the the NRZ signal, and also the standard noise added to the system to measure the trend of the TDECQ.
- Finally, the sweep results will be plotted by the script. notice that as the transitions and noise are made larger, the TDECQ value increases, as can be seen in the following figures.

### References

[1] IEEE 802.3-2018 – IEEE Standard for Ethernet