[feat](trx-rds): improve RDS robustness with 9 DSP techniques
Tech 1: replace one-pole baseband LPF with FIR RRC matched filter (alpha=0.75, 4-chip span) — largest single measured improvement per empirical comparison (gr-rds RRC vs plain FIR: 32/38 vs 18/38 stations). Tech 2: 19 kHz pilot x3 -> 57 kHz coherent carrier reference via the triple-angle formula; fed from the WFM pilot Costas PLL when pilot_lock_level > 0.5, clearing to NCO fallback otherwise. Tech 3/7/8: OSD(2) soft-decision block decoder replaces hard CRC check. Per-bit soft magnitudes accumulated in Candidate::block_soft[26]. decode_block_soft() searches Hamming distance 0/1/2 (352 trials total) and returns the minimum Euclidean-cost valid codeword; ~2-3 dB gain. Tech 4: 8th-order 57 kHz BPF (4 cascaded biquads at Q=5) in wfm.rs replaces the previous single Q=10 biquad; ~6x steeper ACI stopband. Tech 5: Costas loop with tanh soft phase detector drives the RDS carrier NCO when no pilot reference is available (P+I, B_L ~20 Hz). Tech 6: Block A PI field LLR accumulation — signed per-bit LLR summed over 3 independent Block A observations before committing the PI value, correcting weak-signal false locks without delaying strong-signal lock. Tech 9: 8-tap complex CMA blind equalizer applied to IQ samples before FM discrimination; constant-modulus error (|y|^2 - R^2) drives tap adaptation without a training sequence, suppressing adjacent-channel interference at the source. Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com> Signed-off-by: Stan Grams <sjg@haxx.space>
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# RDS Reception Improvements — WIP
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Research into improving RDS demodulation robustness for two scenarios:
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adjacent channel interference (ACI) and weak signal (low SNR).
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## Signal Pipeline
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```
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Antenna → IF filter → FM discriminator → 57 kHz BPF → Costas PLL →
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Symbol timing → Manchester decode → Biphase decode →
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Block sync → (26,16) FEC → Group assembly
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```
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## Prioritized Implementation Plan
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| # | Technique | Scenario | Complexity | Expected Gain |
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|---|---|---|---|---|
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| 1 | RRC matched filter | ACI | Low | Largest measured (32 vs 18/38 stations in empirical test) |
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| 2 | 19 kHz pilot ×3 → 57 kHz carrier reference | Weak signal | Medium | 3–6 dB carrier phase noise reduction |
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| 3 | Erasure declaration + erasure decoding | Weak signal | Low | 1–3 dB |
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| 4 | 8th-order 57 kHz IIR bandpass filter | ACI | Low | Pre-filters ACI energy before Costas loop |
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| 5 | Costas `tanh` soft phase detector | Weak signal | Trivial | ~1 dB |
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| 6 | LLR accumulation across repeated groups | Weak signal | Low | √N SNR per repetition |
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| 7 | Chase-II soft-decision block decoder | Both | Medium | 1–2 dB |
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| 8 | OSD(2) block decoder | Both | Medium | 2–3 dB over hard-decision |
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| 9 | IF CMA blind equalizer (pre-demodulation) | ACI | High | 7–10 dB ACI protection ratio improvement |
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---
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## Technique Notes
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### 1. RRC Matched Filter
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RDS uses known BPSK pulse shaping per IEC 62106. The receiver should apply a Root Raised
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Cosine (RRC) matched filter rather than a generic FIR lowpass. The 2024 GNU Radio demodulator
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comparison showed RRC-based decoders (Bloessl's gr-rds) decoded 32/38 real stations vs. 18/38
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for plain FIR lowpass filter decoders — the single largest measured improvement.
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- Roll-off factor: 1.0 per standard; experiment with 0.35–0.8 for sharper stopband
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- Operate at 2375 Hz chip rate (Manchester doubles the symbol rate from 1187.5 baud)
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### 2. 19 kHz Pilot ×3 Carrier Reference
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Instead of running a Costas loop autonomously on the noisy 57 kHz subcarrier, multiply the
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clean 19 kHz stereo pilot tone by 3 to produce a phase-coherent 57 kHz reference. The pilot
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sits at much higher SNR than the RDS subcarrier. `redsea`'s own issue tracker identifies this
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as the dominant weak-signal failure mode; patent CN113132039A addresses the same problem.
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Without pilot lock, fall back to a Costas loop with a `tanh` soft phase detector (see #5).
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### 3. Erasure Decoding
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When `|LLR|` for a bit is below a confidence threshold, declare it an **erasure** (known-position
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error) rather than a hard ±1 decision. The (26,16) RDS block code corrects:
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- 5 random bit errors (hard decision)
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- **10 erasures** — 2× improvement at no added decoder complexity
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Requires propagating LLRs from the symbol detector to the syndrome decoder instead of hard
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bits. The Group 0B PI cross-check (PI appears in both Block A and Block C) gives free
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erasure resolution on the most critical field.
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### 4. 8th-Order 57 kHz IIR Bandpass Filter
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Hardware RDS chips (e.g. SAA6579) place an 8th-order bandpass filter at 57 kHz before the
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carrier recovery stage. In software, an equivalent high-order IIR or long FIR centered at
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57 kHz with ±4 kHz passband and steep roll-off attenuates adjacent-channel energy that bleeds
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into the MPX spectrum after FM discrimination. Insert this stage immediately after FM
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demodulation and before the Costas loop.
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### 5. Costas `tanh` Soft Phase Detector
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Replace the hard-slicer phase error `Re(z) * Im(z)` in the Costas loop with
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`tanh(Re(z)/σ) * Im(z)`. This is the ML-derived phase error estimator and approaches the
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Cramér-Rao bound at low SNR. Trivial code change, useful whenever the pilot reference (#2)
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is unavailable.
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### 6. LLR Accumulation Across Repeated Groups
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RDS transmits the same data repeatedly (PI: every group every ~87.6 ms; PS name: ≥5 groups/sec).
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Accumulate per-bit LLRs across N repetitions of the same field before decoding:
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```
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LLR_acc[i] += LLR_n[i] // for known-repeated bit positions
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```
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SNR improves as √N (3 dB per 4× accumulations). With ~11 PI observations per second, 1 second
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of accumulation is feasible before display latency becomes noticeable.
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### 7. Chase-II Soft-Decision Block Decoder
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The Chase-II algorithm generates `2^(2t)` hard-decision decoder trials by flipping the
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`2t` least-reliable bit positions (identified by smallest `|LLR|`), then picks the trial with
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minimum Euclidean metric. For the RDS (26,16) code with t=2: only 4 trials. The 26-bit block
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size makes this extremely fast.
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Expected gain: ~1–2 dB over hard-decision decoding.
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### 8. OSD(2) Block Decoder
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Ordered Statistics Decoding at order 2 approaches ML performance for short linear block codes.
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Procedure for the (26,16) code:
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1. Sort all 26 bit positions by `|LLR|` descending (most to least reliable).
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2. Gaussian-eliminate the 10×26 parity-check matrix to bring the most reliable positions into
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systematic form.
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3. Enumerate order-2 test patterns (all pairs from the least-reliable positions).
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4. Select the minimum Euclidean-metric codeword.
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The matrix is only 10×26 — Gaussian elimination is trivial. Expected gain: ~2–3 dB over
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hard-decision decoding, ~0.5–1.5 dB over Chase-II.
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Reference: Fossorier & Lin, "Soft decision decoding of linear block codes based on ordered
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statistics," IEEE Trans. Inf. Theory, 1995.
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### 9. IF CMA Blind Equalizer
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FM signals are constant-envelope, so the Constant Modulus Algorithm can equalize the IF signal
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without training data, driven by the cost `||s(t)|² - 1|`. A 2004 JSSC paper reports
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**7–10 dB improvement in adjacent channel protection ratio** using a 6th-order blind equalizer
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applied to the digitized IF signal before FM demodulation. This is the most powerful ACI
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technique but requires operating at IF sample rates and handling the full pre-demodulation
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signal. Implement last.
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---
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## Key References
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- [site2241.net 2024 demodulator comparison](https://www.site2241.net/january2024.htm) — empirical RRC vs. FIR data
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- [PySDR RDS end-to-end example](https://pysdr.org/content/rds.html) — complete Costas + M&M + block sync pipeline
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- [gr-rds / Bloessl](https://github.com/alexmrqt/fm-rds) — best-performing open source implementation
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- [redsea CHANGES.md](https://github.com/windytan/redsea/blob/master/CHANGES.md) — real-world weak signal bug history
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- [Fossorier & Lin OSD](https://www.semanticscholar.org/paper/Soft-decision-decoding-of-linear-block-codes-based-Fossorier-Lin/2fde1414cd33dacfb96b7b0d5bbbe74b803704da) — foundational soft decoding for cyclic codes
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- [IEEE: Digital RDS demodulation in FM subcarrier systems (2004)](https://ieeexplore.ieee.org/abstract/document/1412732)
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- [ResearchGate: DSP-based digital IF AM/FM car radio receiver (JSSC 2004)](https://www.researchgate.net/publication/4050364_A_DSP-based_digital_if_AMFM_car-radio_receiver) — CMA equalizer, 7–10 dB ACI improvement
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- [Information-Reduced Carrier Synchronization of BPSK/QPSK](https://www.researchgate.net/publication/254651395_Information-Reduced_Carrier_Synchronization_of_BPSK_and_QPSK_Using_Soft_Decision_Feedback)
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- IEC 62106 (RDS standard), IEC 62634 (receiver measurements)
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