Part 2 of Weak-Signal Engineering, a 14-part deep dive into decoding the marginal regime — where a receiver locks but under-decodes, and four levers roughly doubled GopherTrunk’s yield. Part 1 defined that regime and introduced the thread capture: a ~10 dB TETRA control channel that locks and decodes ~12% of its BSCH. Before we touch a single equalizer tap, this part fixes the measurement problem — because two of the most natural quality metrics in DSP have already, on this project, pointed confidently in the wrong direction. If the verdict number is wrong, every lever after it optimizes the wrong thing.
TL;DR: EVM is a trap in front of a blind equalizer, and wideband carrier SNR is a trap in front of a phase-noise problem. A numerically-unstable CMA variant once drove differential EVM from 34% to 8% — textbook “constellation opened” — while CRC-valid frames stayed at zero: blind CMA minimises modulus error, not correctness, and it has spurious constant-modulus minima that look gorgeous and carry nothing. In #764, the capture that decoded worse had the higher wideband FFT carrier SNR — carrier-clean but modulation-degraded is the signature of reciprocal mixing. The numbers to trust, in order: CRC-valid frames per opportunity (the verdict), then demod-side in-channel SNR (advisory), then everything else (scenery). Rule of the series: never conclude an equalizer helps from EVM; decode to CRC.
Key takeaways
- Every metric is an answer to a specific question — and usually not yours. EVM answers “how far are symbols from the ideal grid?”; a decoder asks “were the bits right?”. Those correlate on well-behaved channels and diverge exactly when you’re doing something interesting.
- A blind equalizer can optimize the metric instead of the signal. CMA’s
cost is constant modulus; an output that is perfectly constant-modulus and
perfectly wrong scores perfectly. The 34%→8%-with-CRC-0 incident is pinned in
the
SnapshotLMSdoc comment so nobody re-learns it. - Where you measure matters as much as what. #764’s wideband FFT said the 10 MS/s capture was cleaner; the in-channel demod said it was 10 dB worse. Both were right — about different bandwidths.
- Yield needs a denominator. “778 CRC-valid bursts” means nothing without
the opportunity count; GopherTrunk’s harnesses always report
okandfailtogether, and the ratio is the number.
Cheat sheet
| Concern | What it does | Where it lives |
|---|---|---|
| EVM, measured properly | reference-grid error vs ideal constellation | Signal Lab VSA — signal-lab-07, /reference/error-vector-magnitude/ |
| The EVM-trap record | doc-comment history: EVM 34%→8%, CRC 0 | internal/dsp/equalizer/snapshot_lms.go (package doc) |
| What CMA optimizes | error proxy \|y\|² − R², not bit correctness |
internal/dsp/equalizer/cma.go (Process) |
| The verdict harness | CRC-clean BSCH counts, one variable isolated | internal/scanner/ccdecoder/pipelines_tetra_equalizer_test.go (decodeCCBSCHYield) |
| Voice-path verdict | CRC-valid TCH/S per burst opportunity | internal/radio/tetra/tch.go (DecodeTCHSSoft → crcOK) |
| The carrier-SNR trap | wideband-clean, in-channel-degraded (#764) | internal/scanner/ccdecoder/ddc_highrate_test.go |
In this post
- What EVM actually measures — and the assumptions riding along.
- Beauty with zero truth — the equalizer that polished a corpse.
- The carrier-SNR trap — #764’s cleaner-but-worse capture.
- The numbers you can trust — a short, ordered list.
- Instrumenting for yield — what the harnesses report and why.
What EVM actually measures
Error vector magnitude is the RMS distance between your received symbols and the nearest ideal constellation points, normalised to the constellation’s scale. It is a fine instrument — Signal Lab’s VSA computes it, and on a cooperative signal it tracks decode quality closely enough that lab equipment vendors quote sensitivity in EVM.
But look at what the definition smuggles in. EVM assumes the “nearest ideal point” is the transmitted point — that your symbols are merely perturbed, not relabeled. It assumes the reference grid itself is right: correct phase, correct scale, correct decision boundaries. On a marginal channel, after an adaptive stage that is allowed to rotate, scale, and reshape the signal, every one of those assumptions is up for negotiation. A symbol that lands crisply on the wrong ideal point contributes almost nothing to EVM and everything to the bit error rate. EVM measures tidiness. Decoders consume identity.
On a differential modulation like
π/4-DQPSK there’s a further
subtlety: you can compute EVM on the differentials (the s·conj(prev)
products) rather than the raw symbols, which conveniently cancels any constant
rotation. GopherTrunk’s equalizer experiments did exactly that — and it still
lied, which is the story that gives this post its title.
Beauty with zero truth
The incident is preserved, deliberately, in the doc comment of the trained equalizer — because it is the reason the trained equalizer exists:
// internal/dsp/equalizer/snapshot_lms.go (shape) — package history
// CMA's cost J = E[(|y|²−R²)²] is satisfied by any equalizer output that has
// the right modulus, so it has spurious minima and can converge to a
// constant-modulus but WRONG solution — the failure the package history
// records (a numerically-unstable CMA once drove differential EVM 34%→8%
// while CRC stayed 0). Training to a known reference removes that ambiguity…
Unpack what happened. A blind CMA variant — since replaced — was inserted ahead of the TETRA differential decoder and evaluated the obvious way: measure differential EVM before and after. Before: 34%, a smeared mess. After: 8%, which for π/4-DQPSK is a genuinely clean-looking constellation. Anyone grading on appearance ships that change. But the CRC-valid frame count on the same capture was zero. Not reduced — zero. The equalizer had found an output that satisfied its cost function beautifully: constant modulus, tight clusters, and a time-varying relationship to the transmitted symbols that destroyed every single dibit on its way through the differential decode.
The mechanism has two halves, and the series treats each in its own part.
First, CMA’s cost J = E[(|y|² − R²)²] genuinely does not mention
correctness — any constant-modulus output is a candidate minimum, including
spurious ones (Part 4). Second, an adapting filter in front of a
differential decoder injects a time-varying phase that no differential can
cancel (Part 5). Either half alone can make EVM improve while yield dies. The
one-line lesson entered the project’s permanent vocabulary: never conclude an
equalizer helps from EVM; decode to CRC.
The carrier-SNR trap
EVM is not the only metric with a blind spot. #764 — the investigation the Ten Megasamples postmortem narrates in full — turned on a pair of captures of the same site: one at 2.5 MS/s that locked cleanly (demod SNR ≈19.7 dB, EVM 7.4%), one at 10 MS/s that never locked (≈9.5 dB, EVM 22.5%). The natural first move was a wideband FFT of both files to compare signal quality — and the FFT said the 10 MS/s capture had the higher carrier SNR. Cleaner file, by that measurement. Worse decode, by 10 dB.
Both measurements were correct. A wideband FFT bin integrates the carrier’s power against the noise floor around it; it is nearly blind to energy that stays close to the carrier. Oscillator phase noise — in that case, reciprocal mixing at the Airspy’s native 10 MS/s clock — smears energy from the carrier onto its own modulation sidebands. Carrier-clean but modulation-degraded is that mechanism’s exact signature, and only an in-channel, demod-side measurement sees it, because only the demodulator asks the question at the bandwidth where the damage lives. The proof that the deficit was baked into the samples (an independent 4:1 decimation replayed through the proven 2.5 MS/s path reproduced the same ≈9.5 dB) is Part 12’s subject; the metric lesson stands alone: a measurement made in the wrong bandwidth answers a different question, confidently.
The numbers you can trust
The series’ working hierarchy, from verdict to scenery:
| Rank | Metric | Role | Caveat |
|---|---|---|---|
| 1 | CRC-valid frames / opportunities | the verdict | needs an honest denominator |
| 2 | Payload bit-error rate vs known truth | verdict, synthetic only | only where truth is known (tests) |
| 3 | In-channel demod SNR | advisory — places you on Part 1’s cliff | not a verdict; measure post-channel-filter |
| 4 | EVM | advisory — useful on unprocessed signals | never after a blind adaptive stage |
| 5 | Wideband carrier SNR, dBFS | scenery — capture hygiene | blind to phase noise, says nothing about decode |
Two design notes on rank 1. First, the opportunity count has to be honest:
counting CRC passes per detected burst lets a change that suppresses burst
detection look like a yield improvement. GopherTrunk’s harnesses count
ok and fail from the same detector so the denominator can’t be gamed by
the thing under test. Second, CRC yield inherits the CRC’s own false-positive
floor — a 16-bit check passes garbage at ~1/65536 — which is negligible at
healthy yields but worth remembering when a sweep reports single-digit counts:
Part 8 and the DMO colour-recovery story both lean on dominance over that
chance floor, not mere non-zero counts.
Instrumenting for yield
The principle only bites if the code makes yield cheap to read. Three places it shows up, all of which later parts use as scoreboards:
// internal/radio/tetra/tch.go (shape) — the per-burst verdict
func DecodeTCHSSoft(type5LLR []float32) (frameA, frameB []byte, crcOK bool, errs float32, ok bool)
Every TCH/S decode returns crcOK alongside the speech frames — the composer
and the replay harnesses tally it per opportunity, which is how “soft-decision
410 → 778 bursts” was ever a statement anyone could make. The CC-side
equivalent is decodeCCBSCHYield from Part 1, which returns (ok, fail)
with exactly one boolean of configuration difference between the two arms.
And the periodic tetra: decode status line carries the same counters into
production logs (bsch_fail, sb_bursts, and friends), so an operator’s
debug log is a yield instrument — the ~210-transitions-per-hour session was
diagnosed from those lines alone, before any capture was replayed.
How that principle shaped the Go code
- Verdict functions return their own denominator. Decoders return
crcOK/okper call rather than logging aggregate percentages, so any caller — test, composer, status line — can build an honest ratio over exactly the population it cares about. - A/B harnesses isolate one boolean.
decodeCCBSCHYieldmirrors the production pipeline except for the single parameter under test, so a yield delta is attributable to one change, not to drifted wiring. - The trap is documented where you’d re-fall into it. The EVM incident
lives in the
SnapshotLMSdoc comment — the exact place someone evaluating a new equalizer will be reading when they’re tempted to grade it by EVM.
Where this goes next
With the measurement rules fixed, we can finally look at the enemy itself.
Part 3
is about inter-symbol interference and the linear channel model y = h∗x + n:
what multipath and band-edge group delay actually do to a constellation, which
impairments are invertible and which are not — and the one domain fact
(a linear channel is only a convolution over raw symbols, never over
differentials) that quietly dictates the architecture of every equalizer in
the rest of the series.
FAQ
Is EVM ever the right metric? Yes — on signals that haven’t passed through an adaptive stage that could game it. For grading a capture’s raw modulation quality, comparing antennas, or watching a transmitter drift, Signal Lab’s VSA EVM is exactly the tool. The rule is scoped: EVM must not be the verdict on a decode-chain change, because decode-chain changes can optimize it directly.
Why does CRC yield beat bit-error rate as the field verdict? Because on-air you don’t know the transmitted bits, so you can’t count bit errors — the CRC is the only ground truth the air gives you. In synthetic tests, where truth is known, GopherTrunk does use payload bit-error (Part 7’s 13% → 0% result is exactly that); the two verdicts are used where each is available.
Couldn’t a change also game the CRC metric? Only by actually decoding correctly — which is the point of using it. The two gameable edges are the denominator (fixed by counting opportunities from the same detector) and the CRC’s chance floor (~1/65536 for a 16-bit check), which matters only for near-zero counts and is why marginal sweeps demand dominance, not presence.
What’s “demod SNR” versus the FFT SNR my waterfall shows? The waterfall number is carrier power over the noise floor in FFT-bin bandwidth — a wideband, pre-demod view. Demod SNR is estimated inside the decode chain, in the channel bandwidth, after filtering — it sees everything the decoder sees, including phase noise folded onto the modulation. #764 is the canonical case where they disagree by design.
Do I need special builds to read yield on my own system?
No. The TETRA decode-status debug line carries the burst and failure counters,
and every capture-replay harness prints its ok/fail tallies. If you can
reproduce a symptom in a capture, you already have a yield instrument —
which is why the auto-recorders exist.
Series navigation
Part 2 of 14 · ← Part 1: The Marginal Regime · Next → Part 3: ISI & the Linear Channel — What an Equalizer Can & Can’t Fix