Measuring TDECQ on a PAM4 Transmitter

Scope

This article describes the TDECQ measurement for PAM4 optical transmitters as standardized in IEEE 802.3, at the 53.125 GBd (100G per lane) and 106.25 GBd (200G per lane) signaling rates used by DR, FR, and LR module classes. It covers the reference receiver chain and its constants, the capture and setup requirements on a sampling oscilloscope, the computation itself, the companion metrics recorded alongside, and the ways the measurement goes wrong on a real bench. The electrical-lane analogues (TDECQ's electrical cousins in the CEI specifications) follow the same logic and are out of scope, as is receiver testing.

What is actually being measured

TDECQ answers one question: how much more optical power does this transmitter need than an ideal one, at a fixed, standardized receiver, to reach the FEC-threshold error ratio? The glossary entry gives the definition; the operational content is the fixed chain. The captured waveform is filtered by a fourth-order Bessel-Thomson response with 3 dB bandwidth at half the symbol rate (26.5625 GHz at 53.125 GBd, 53.125 GHz at 106.25 GBd), equalized by a 5-tap, symbol-spaced feed-forward equalizer optimized to minimize the reported value, and sampled in two histogram windows placed 0.05 UI either side of the sampling instant. Gaussian noise is added mathematically until the symbol error ratio computed from those histograms reaches $4.8 \times 10^{-4}$, and

$$\mathrm{TDECQ} = 10 \log_{10}\!\left( \frac{\mathrm{OMA}_\text{outer} / (6 \, Q_t)}{\sigma_G} \right), \qquad Q_t = 3.414,$$

where $\sigma_G$ is the tolerable added noise, reduced by the equalizer's own noise enhancement. The SER target is the RS(544,514) pre-FEC bit error ratio of $2.4 \times 10^{-4}$ doubled, since Gray-coded PAM4 converts one symbol error into one bit error out of two bits.

Two features of the definition drive bench practice. The measurement is referenced to OMA rather than average power, so extinction ratio moves TDECQ not at all when OMA is held fixed; and the equalizer inside the measurement means TDECQ prices the noise enhancement $C_\text{eq} = \lVert c \rVert_2$ of whatever equalization the waveform demands, so bandwidth shortfalls cost more than the visual eye closure suggests.

Equipment and setup

The instrument is a sampling (equivalent-time) oscilloscope with a calibrated optical plug-in. At 106.25 GBd the optical bandwidth requirement is roughly 60 GHz to keep the instrument from becoming part of the device under test; the scope then applies the Bessel-Thomson response in software relative to its calibrated hardware response. Configure, in order:

1. Pattern. Drive the transmitter with SSPRQ (short stress pattern random, quaternary), the standardized pattern for TDECQ; it exercises the worst-case run lengths and transitions that a short PRBS misses. Pattern lock must be achieved so the scope can average per-symbol.
2. Clock. Provide either an explicit clock to the scope or use its clock recovery with the loop bandwidth the specification requires; TDECQ is defined with a specific jitter transfer, and a wrong loop bandwidth silently filters jitter into or out of the result.
3. Power into the plug-in. Set launch power well above the scope noise floor but below plug-in overload; the computation subtracts a calibrated instrument noise term, and the subtraction fails at the extremes.
4. Averaging and record length. Enough waveforms that the histograms are populated; conformance test software enforces minimums.

Procedure

1. Capture the pattern-locked waveform through the software Bessel-Thomson reference filter.
2. Measure $\mathrm{OMA}_\text{outer}$ from the defined flat regions of the pattern (means of the settled outer levels), and record the extinction ratio alongside.
3. Let the analysis optimize the 5-tap FFE and the sampling phase to minimize TDECQ; record the tap weights if the software exposes them, since taps far from $(0, 0, 1, 0, 0)$ are the signature of a bandwidth-limited part.
4. Read TDECQ, and record RLM (level mismatch) with it; RLM captures the level-spacing nonlinearity that the linear FFE cannot repair, which is why the standards bound it separately (0.95 is the usual class of floor).
5. Repeat across the operating corners that matter (temperature, wavelength lane, warm-up state); TDECQ of a marginal part drifts with all three.

A conformant DR/FR-class transmitter typically lands with a few tenths of a dB to a dB of margin under a ceiling near 3.4 dB; the exact limit is per-PMD in the clause tables.

What moves the number

The PAM4 Eye & TDECQ Explorer implements the reference chain on a synthesized waveform, and its certified values illustrate the sensitivities. From a clean baseline of 0.67 dB (the residual is the reference filter itself plus the off-center histogram windows), cutting transmitter bandwidth from 0.80 to 0.45 of the baud rate raises TDECQ to 1.47 dB while the equalizer's noise gain climbs from 1.1 to 2.5 dB; at 0.35 of the baud the numbers are 2.27 dB and 3.9 dB. Adding 2.5% RMS noise to the clean baseline instead produces 1.63 dB with the equalizer nearly idle: a similar TDECQ through entirely different physics, distinguishable on the bench by the tap weights and the histogram shapes. Skewing the levels to RLM 0.52 costs about 0.45 dB of TDECQ and no equalizer effort at all, and dropping extinction ratio from 6 to 4 dB at fixed OMA moves TDECQ by exactly nothing while raising the average power the laser must supply by 1.43 dB.

The diagnostic split this enables is the practical value of the measurement: a failing TDECQ with hard-working taps points at bandwidth (driver, modulator, or the package between them); a failing TDECQ with idle taps and smeared histograms points at noise (bias networks, RIN, or the instrument); a healthy TDECQ with failing RLM points at the level map (drive swing, bias point, or DSP pre-distortion).

Bench failure modes

The recurring corruptions, roughly in order of frequency: launch power too low, which lets instrument noise dominate the histograms and inflates TDECQ unpredictably; loss of pattern lock or marginal clock recovery, which smears the histograms with what looks like jitter; a dirty or damaged fiber end-face ahead of the plug-in, which adds both loss and multipath interference; wrong reference filter bandwidth for the baud rate; and histogram windows populated by too few samples, which makes the reported value wander run to run. A TDECQ that changes by more than a few hundredths of a dB between consecutive runs on a warm part is a setup problem until proven otherwise.

There is also a definitional boundary worth respecting: TDECQ models added noise as white and Gaussian and the receiver as the reference chain, no more. Impairments that violate the model, multipath interference prominent among them, are only partially captured, and a transmitter can conform while stressing a real receiver in ways the metric undercounts. The standards handle this with separate line items (for example overload and MPI limits) rather than by stretching TDECQ.

The Datacenter Link Budget Explorer shows where the transmitter's TDECQ allowance sits inside the end-to-end power budget, and the receiver sensitivity entry covers the floor the budget must clear.

References: IEEE Std 802.3bs-2017, clause 121.8.5 (TDECQ, SSPRQ, reference receiver); IEEE Std 802.3cd-2018 (100G per lane); IEEE 802.3dj project documents (200G per lane); Keysight, "How to Test 1.6T Optical Transmitter Conformance" (application note, 2026).