Part 4 of Signal Lab, a 10-part series on GopherTrunk’s offline signal-analysis workbench. The dashboard gave you EVM and SNR as numbers; now we give them a picture.
TL;DR: The constellation, eye diagram, and symbol scope are three views of the same thing — how cleanly the demod is separating symbols. A clean C4FM signal shows four tight rails; a clean CQPSK signal shows four tight clusters in the I/Q plane. As SNR drops, rails blur and clusters spread — the eye closes. An open eye means comfortable symbol decisions; a closed eye means the demod is guessing.
Key takeaways
- Constellation = where symbols land in the I/Q plane; tight points mean low EVM.
- Eye diagram = symbol transitions overlaid; a wide-open eye means a big decision margin.
- C4FM shows four rails; CQPSK shows four clusters — different modulations, same “tight is healthy” rule.
- These plots explain the numbers. A high EVM looks like a fuzzy constellation and a closing eye.
- The symbol scope ties it to time — which symbols, in what order, drifted.
Cheat sheet
| Surface / plot | What it shows |
|---|---|
| Constellation | Symbol positions in the I/Q plane (rails or clusters) |
| Eye diagram | Overlaid symbol transitions; eye opening = decision margin |
| Symbol scope | Recovered symbols over time |
gophertrunk siglab serve |
Renders all three in the browser console |
| /constellation.html | Docs: constellation reference |
| /eye-diagram.html | Docs: eye-diagram reference |
In this post
- What a constellation is and how to read it.
- Clean vs noisy C4FM — the four rails.
- CQPSK constellations — clusters, not rails.
- The eye diagram — opening and closing, and why it matters.
- The symbol scope — the time-domain companion.
What a constellation is
A constellation diagram plots each recovered symbol as a point in the I/Q plane — in-phase on one axis, quadrature on the other. Its shape is a fingerprint of the modulation, and its tightness is a direct readout of quality. Ideal symbols land exactly on their target points; real symbols scatter around them, and the spread of that scatter is precisely what EVM measures. So the constellation is the picture behind the EVM number from Part 2: low EVM is a tidy constellation, high EVM is a smear.
The plot is theme-aware and lives in the browser console’s visualization panel, alongside the docs’ own constellation reference. You don’t read absolute coordinates off it — you read shape and spread.
Clean vs noisy C4FM: the four rails
C4FM — the 4-level continuous-phase FM that carries P25 Phase 1, and the family GopherTrunk’s channel rate is built around — encodes two bits per symbol as one of four frequency deviations. On a constellation it shows up as four vertical rails: four distinct symbol levels. A healthy C4FM capture draws four tight, well-separated rails. A weak one blurs them until adjacent rails touch and the demod can no longer tell a level from its neighbor.
Reese’s shortcut: count the gaps. Four clear gaps between rails means a comfortable decoder. When the gaps vanish, so does the lock margin — and you’ll see it in the histogram (Part 2) and the decode-error rate at the same time.
CQPSK: clusters, not rails
Not every P25 signal is C4FM. The CQPSK / LSM path (linear-simulcast-friendly modulation, used by some P25 Phase 1 systems and the natural companion to simulcast infrastructure) is a phase modulation: symbols land as four clusters arranged in the I/Q plane rather than four vertical rails. The health rule is identical — tight, well-separated clusters are good; clusters that bloom into each other are bad — but the shape tells you which demod path is in play. If you expected rails and see clusters (or vice versa), you’re looking at the wrong modulation for the system, which is itself a useful diagnosis. Part 7’s VSA metrics quantify exactly how far each cluster sits from ideal.
The eye diagram: opening and closing
The eye diagram overlays many symbol transitions on top of each other, aligned to the symbol clock. The result looks like one or more “eyes.” The height of an open eye is the vertical decision margin — how much room the slicer has to place a symbol correctly — and the width is timing margin, how much clock jitter it can tolerate before sampling at the wrong instant.
As SNR falls, noise thickens every trace and the opening shrinks — the eye closes. A fully closed eye means transitions cover the decision point and the demod can no longer reliably tell one symbol from the next; that’s the visual partner of a rising decode-error rate and a lost lock. Reading the eye is a fast gut check: can I still see daylight in the middle? If yes, the capture has margin; if no, it’s marginal no matter what the lock line optimistically says for an instant.
The symbol scope: quality over time
The constellation and eye pool all symbols together; the symbol scope puts them back in order, plotting recovered symbols over time. That time axis matters when quality isn’t constant — a capture that’s clean for four seconds and then craters when a neighboring transmitter keys up will show a tidy constellation on average but an obvious degradation in the scope right at that moment. Pair the scope with the console’s live event stream (Part 3) and you can line up a burst of symbol errors with the exact stage or grant where it happened.
Together these three plots — constellation, eye, symbol scope — turn the abstract EVM/SNR pair into something you can see go wrong. Ada’s habit, once Reese drilled it in: read the numbers first for the verdict, then open the constellation to confirm the story and the eye to judge how much margin is left.
The same plots across protocols
C4FM and CQPSK are the P25 Phase 1 cases, but the constellation is a fingerprint for every protocol the engine decodes, and learning to read the shape is a fast way to sanity-check what you’re actually looking at:
- DMR and NXDN are 4-level FSK families like C4FM — expect four rails. DMR’s TDMA structure means the constellation is built from alternating time slots, so a healthy DMR capture still shows four clean rails even though the bursts interleave two logical channels.
- P25 Phase 2 uses H-CPM (a continuous-phase modulation), so its picture is denser than the four crisp rails of Phase 1 — a reminder that “which protocol” changes what “clean” looks like.
- TETRA is π/4-DQPSK, a phase modulation whose ideal constellation is eight points on two rotated QPSK rings; a healthy TETRA capture shows those points tight and the ring well-formed.
The practical lesson is that the number and arrangement of clusters or rails should match the modulation you expect. If you told the engine “P25 Phase 1 C4FM” and the constellation shows phase-plane clusters instead of vertical rails, either the system is actually running the CQPSK/LSM variant or you’ve mislabeled the capture — and the plot caught it before the metrics did. When a signal won’t decode and you’re not sure what it is at all, that’s the cue to hand it to blind identification (Part 8), which reads exactly this kind of structure to name a candidate.
A reading workflow
Reese’s routine for any new capture is a fixed order, because each plot answers a different question and answering them out of order wastes time:
- Histogram and dashboard first — is the rate right (the 2% rule) and did it lock? No point plotting a capture that’s decoding at the wrong sample rate.
- Constellation — does the shape match the expected modulation, and how tight is the spread? This is your EVM sanity check.
- Eye — is there daylight in the middle? This is your margin check: a tight constellation with a barely-open eye is closer to the edge than it looks.
- Symbol scope — if quality is uneven, when did it degrade? Line the dip up against the live event stream to find the cause.
Four plots, four questions, in the order that fails fast. Ada now runs it by reflex; it’s the single habit that turned her “why won’t this lock” flailing into a diagnosis in under a minute.
Where this goes next
You can now see modulation quality, not just read it. Part 5 zooms out from individual symbols to the spectrum — the PSD, the spectrogram/waterfall, and the spectral-occupancy metrics (occupied bandwidth, channel power, ACPR, flatness) that describe a signal’s shape in frequency rather than its symbols in the I/Q plane. The docs’ constellation and eye-diagram pages go deeper on each plot.
FAQ
Why four rails for C4FM but four clusters for CQPSK? They’re different modulations. C4FM is a 4-level frequency modulation, so its symbols separate along one axis (four rails). CQPSK is a phase modulation, so its four symbols separate as points around the I/Q plane (four clusters). Same symbol count, different geometry.
What exactly does a “closing eye” mean? The vertical opening in the eye is the demod’s decision margin. As noise grows, traces thicken and the opening shrinks; a closed eye means noise now covers the decision point and the demod can’t reliably separate symbols — expect errors and lost lock.
How does this relate to EVM? Directly. EVM measures how far symbols scatter from their ideal points, which is exactly the spread you see in the constellation. Low EVM is a tight constellation and an open eye; high EVM is a smear and a closing eye.
Where do I view these plots?
In the browser console (gophertrunk siglab serve, Part 3), which renders the
constellation, eye diagram, and symbol scope from the analyzed capture.
Series navigation
Part 4 of 10 · ←Part 3 · Next → Part 5: PSD, Spectrogram & Occupancy