BPSK's SNR estimate reads low on frames the FEC had to correct — decision-directed on the losing arm's decisions

[dc0sk]

The suspected defect

BPSK's estimate_snr_db (plugins/bpsk/src/demodulate.rs) rebuilds the transmitted symbols from
the differential decisions of the cancelled stream by integrating flips, then fits a per-window
least-squares gain (additive_snr_db_windowed, 16-symbol windows).

An isolated wrong decision inverts the reconstruction from that point on. Later windows absorb that
through their own fitted gain, so the damage is confined to the window containing the error — where
the fitted gain shrinks toward zero and most of the window is booked as noise. The common case is a
paired error (one bad symbol flips two differential bits), which re-inverts after one symbol and
costs one symbol, not a window.

So the reading depends on how many isolated decisions the cancelled arm got wrong, not only on the
channel. A 16-symbol window is two bytes, so a frame whose RS block needed > 16 byte corrections has
at least 9 of its ~128 windows holding an error. If each reads as noise, the estimate is capped near
10·log10(119/9) ≈ 11 dB Es/N0 whatever the true SNR. That is a prediction the measurement below is
consistent with, not a demonstration.

Why this surfaced now

Not new — every frame RS had to correct already carries it. #1428's union makes it more frequent:
when the uncancelled arm produces a frame, the estimate still comes from the cancelled arm's
decisions, which on that attempt were bad enough to fail RS.

Measured through ota_decode_burst on moderate_f1 @ 8 dB, 200 B, paired against a
variant-0-only build on the same channel realisation: on the 8 seeds both builds decode, the union's
reading is lower on all 8 — median −2.97 dB, range −0.70 to −6.88. One frame only the union decodes
read −19.3 dB.

Two limits on that evidence. The spans were not controlled: where the union won at an earlier onset,
the slice and the decisions both differ between builds, so the 8 pairs confound them. And the
−19.3 dB reading is 11 dB below the lowest value the documented misalignment sweep reached at its one
operating point (−8.39 dB at a true 5.82, engine.rs ~3180), so misalignment alone is an unlikely
account of it, not an excluded one.

Blast radius

• The rate ladder — measured: none. A decoded frame is never answered with a demotion
  (crates/openpulse-core/tests/success_based_climb.rs::a_decoded_frame_is_never_answered_with_a_demotion,
  fed −20 dB). By code read, the evidence climb (crates/openpulse-core/src/ota_rate.rs,
  proven_by_success) does not read the SNR; a low reading can only forgo the faster SNR climb for
  that frame.
• QSY scan and ADIF — by code read: none. The hard arm records no SNR (pending_snr is Some
  only on the soft branch), so last_rx_snr_db() never sees it.
• Operators: yes. It is carried in EngineEvent::OtaRateDecision.snr_db, which the daemon
  forwards wholesale to control clients. An operator can be shown −19 dB for a frame that decoded.

Proposed direction — a design decision, so for review before code

After a successful decode the transmitted symbols are known exactly (re-encode the corrected wire).
Estimating SNR against those — data-aided rather than decision-directed — would remove the mechanism
rather than the symptom, if the mechanism above is the right one.

Discriminating measurement first (a bpsk unit test, since symbol_stream is private): on one
decoded frame, compute the estimate on the SAME span with (i) the shipped decisions and (ii) the
oracle symbols. The mechanism above predicts (i) ≪ (ii) ≈ the reading a variant-0 decode gives.
Holding the span fixed is what removes the onset confound above. Do not instead point the
estimator at the uncancelled stream: it keeps the +β·a_{k+1} residual, capping a clean channel's
Es/N0 near 9.5 dB — a bias of the same size.

Refs #1428, #1363.

[dc0sk]

Closing: the mechanism named here is not what produced this issue's evidence

This issue called its mechanism suspected and consistent-with, not demonstrated, and named the span
confound itself. The discriminating test it proposed has now been run, and the limit it stated
turned out to be the answer.

Decisions on a fixed span. Same received span, two decision sequences: the shipped ones (the
cancelled arm's differential decisions, integrated exactly as estimate_snr_db does) and the true
transmitted symbols. The mechanism is real on AWGN: the gap grows with decision errors (−0.52 dB at
−2 dB, −1.56 dB at −4 dB) and follows windows holding a sign discontinuity (r = −0.78), not paired
errors (r = −0.12). On moderate_f1 it is at most −0.57 dB even for the worst frames (up to 99
decision errors and 27 damaged windows) — far from the −2.97 dB median reported here. That bound was
taken at the symbol boundary (lead 0); decisions at an early lock are worse and unmeasured.

What produced the −2.97 dB median is where the decoded span starts. In this issue's fixture the
union's span starts at 4000 and the variant-0-only build's at 4032 on every one of the 8 paired seeds.
Re-measuring on the same channel realisation with a fresh engine, changing only the span start,
reproduces 7 of the 8 paired differences to within 0.02 dB. The eighth (seed 22) is the variant-0
build's reading taken at a phase-2 AFC correction (settles=33). The underlying cause is a pre-existing
defect in BPSK's timing search, which locks 8 samples early whenever a lead makes that reachable and
caps the SNR estimate near 3.5 dB — filed as #1438, with the measurements.

Two corrections to the text above.

• The −19.3 dB frame (seed 94) is not explained by its span: on a fresh engine the same span reads
  +0.27 dB. The AFC state committed by the onset scan is the prime suspect; see BPSK's timing search locks 8 samples early whenever a lead makes that reachable — the SNR estimate is capped near 3.5 dB and BPSK's fast climb can never fire on the OTA path #1438.
• The proposed data-aided estimator would not help: it would still measure at the early lock, and the
  early lock is what caps the reading.

The apparatus is in PR #1439: plugins/bpsk/src/demodulate.rs,
module snr_decision_discriminator.

Superseded by #1438.