sdroxide-brown

C-QUAM (AM stereo) decoding — design note

A proposal for decoding Motorola C-QUAM AM stereo on the medium-wave broadcast band, as a receive-only SWL feature of this fork. Written before any code; the aim is to fix the signal model, the integration points and the test plan, and to name the risks while they are still cheap to change.

Status: implemented. Mode::Cquam (receive-only) exists, with the decoder in crates/sdroxide-dsp/src/demod.rs and synthetic round-trip, pilot and carrier-inversion tests that pass. It is unverified against a real signal until the 918 kHz capture below is decoded, so the blend thresholds and the sign conventions are still first-cut.

Scope

• Receive only, first pass. C-QUAM transmit (an encoder, a 25 Hz pilot, phase modulation) is a later question and not needed for listening.
• Broadcast use: the medium-wave band (MW), where C-QUAM is actually on the air (US / Canada / Brazil, historically Japan). The mode stays selectable anywhere AM is, like every other mode.
• Fork feature, not an amateur-band one. Upstream may not want it in the AM receiver itself, so it should be its own mode, leaving AM and SAM untouched.

The signal, briefly

C-QUAM keeps an ordinary AM envelope (so a diode detector hears mono) and hides the stereo difference in the carrier phase:

s(t) = [1 + (L + R)] · cos(ω_c t + φ(t))
φ(t) ∝ (L − R) plus a 25 Hz pilot term

• An envelope detector — AM as we already have it — yields L + R. That is the “compatible” mono, and it is why the standard is called compatible.
• The difference L − R appears in quadrature after synchronous detection, together with a low-level 25 Hz pilot.
• The pilot exists for one reason: without a phase reference the decoder cannot tell L from R — a phase-inverted carrier would swap the channels. Locking the 25 Hz pilot fixes the sense, and its quality is the natural mono/stereo switch.

So a C-QUAM receiver is: carrier recovery, in-phase = L + R, quadrature = L − R + pilot, a 25 Hz pilot PLL for the sense, and a matrix.

Why this fits the codebase

Two of the three hard parts already exist, which is what makes this a small feature rather than a project:

• Carrier recovery: SamDemod already carries a second-order PLL and coherent detection; its in-phase arm is exactly the L + R we need, and its quadrature arm is available.
• The stereo plumbing is already generic: the Demodulator trait has stereo_diff (the (L − R)/2 channel), stereo_locked, stereo_blend and set_stereo_enabled, and RxChain already carries the side channel to the audio device (it is how WFM stereo and RDS work today).
• The pilot-locked stereo decoder has a working template: WfmDemod’s PilotPll locks a 19 kHz pilot, regenerates the suppressed subcarrier, recovers the side channel, blends to mono on poor lock, and drives the UI lamp. C-QUAM is the same shape at 25 Hz.

Integration points

• sdroxide-types — a new Mode::Cquam:
  • Appended at the end of the Mode enum, not beside Am/Sam: Command is carried as postcard on the wire and variants are numbered by position, so inserting one would renumber every mode a remote client sends.
  • Mode::ALL (currently [Mode; 39]), label() ("C-QUAM"), is_rx_only() (true), the filter default (like Am/Sam, ±5 kHz), and whatever channel/kind classification Am/Sam use.
  • Menu order is a UI concern (below), independent of the enum position.
• sdroxide-dsp — CquamDemod in demod.rs, dispatched from make_demod alongside Mode::Am/Mode::Sam.
• Engine — nothing beyond the existing mode routing; the RX chain already handles a stereo demod.
• UI — the mode appears in the AM group of the mode list; a STEREO indicator (the WFM one, driven by stereo_locked()) and, if wanted, the blend as a diagnostic. top_bar.rs already special-cases Mode::Wfm for its stereo/RDS chips.
• Docs — the user manual’s mode list and the README comparison table.

Decoder design

Blocks, in order:

1. Complex bandpass, as SamDemod does (PASSBAND_TAPS), ±~5 kHz about the carrier — narrow enough to reject the adjacent channel without clipping the L − R sidebands.
2. Carrier PLL — the existing SamDemod loop. Rotate by e^{−jθ}; the real part I is L + R, the imaginary Q is the difference plus pilot.
3. DC block on I — the carrier term, as SamDemod already does.
4. 25 Hz pilot recovery from Q — a narrow band-pass plus a PLL, mirroring PilotPll: track frequency and phase, report locked() and a blend() figure from lock quality (the way WFM derives its blend from pilot SNR).
5. L − R — multiply Q by the recovered pilot reference (giving the correct sense) and low-pass to the audio band. A degree of phase alignment matters: the pilot reference, not Q alone, is what guarantees L is L.
6. Matrix and blend — L = M + S, R = M − S, with M = (L + R)/2 (post-DC) and S = (L − R)/2. Blend S toward zero as pilot lock falls, so a weak or fading signal falls back to a clean mono rather than a wrong stereo.
7. Stereo output — via the trait’s stereo_diff; stereo_locked from the pilot PLL, exactly as WFM does.

Parameters to pick and document: audio low-pass corner (~5 kHz), pilot loop natural frequency (a few Hz) and damping, lock/blend thresholds and time constants, and the L − R low-pass.

Testing

The synthesised-signal route covers nearly everything without a recording:

• Round trip: a small C-QUAM encoder in the test module (the pattern modulator.rs already uses for AM/SSB) encodes a known L/R tone pair; the decoder must recover both, with the right channel sense and separation.
• Pilot loss / inversion: with the pilot removed the decoder must fall back to mono and not emit a swapped or half-level stereo; with an inverted pilot the sense must stay correct. This is the case a naive quadrature decoder gets wrong, so it gets a test of its own.
• Tuning and fading: an off-tune carrier, and a two-tone selective-fading simulation (a moving notch), to exercise the PLL and the blend.
• Golden WAV in crates/sdroxide-dsp/tests if a stable recording is worth keeping.
• Real validation: a capture of an actual C-QUAM station. See below.

Real-signal validation

A real signal is available: 918 kHz, receivable between 10:00 and 20:00 local. That is daytime, so it is a groundwave path and should be stable — the easier case, not the night-time fading one — which makes it a good fixture for tuning the decoder and the blend.

Capture it as raw IQ, not demodulated audio: the stereo lives in the carrier’s phase, and an AM or WFM audio recording throws exactly that away. sdroxide already records the format it can replay (--record-iq writes raw interleaved CF32; REC on the top strip does the same):

# Once the mode exists. Tune to 918 kHz, record 30-60 s, and replay it.
sdroxide --record-iq 918k.cf32            # or press REC
sdroxide --file 918k.cf32 --rate <captured> --freq 918000 --mode Cquam

Record at the front end’s own rate — a couple of hundred kHz about 918 kHz is plenty — and long enough to cover a stereo passage and a mono one, so the mono/stereo switch can be heard as well as tested. The file stays a local fixture: a broadcast recording is the station’s copyright, so it is not committed. The repository keeps the synthetic tests; the capture is what turns “unverified against real signals” into “verified” on the developer’s machine.

Open questions

• Off-air verification: available — 918 kHz, 10:00–20:00 local, daytime and therefore groundwave (see above). Capture it once the decoder exists; until then the synthetic tests carry the weight.
• Sense policy: how aggressively to refuse stereo when the pilot is marginal. A clean mono beats a wrong or warbling stereo; the blend curve decides this.
• Where the STEREO control lives: a lamp only (like WFM), or a lamp plus a manual mono/stereo override and blend readout.
• Transmit: out of scope now; note that modulator.rs makes it a bounded follow-up if a transmit-capable path is ever wanted.

Effort

A focused feature: a new demodulator (~200–300 lines) plus a pilot PLL (~100), a small amount of mode plumbing, a UI lamp, and the test module and its synthetic encoder (~150). One short branch. The main cost is the real-signal validation, not the code.

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