Lab 8.22 — Packet-level CSS synchronization and PER¶

Goal¶

Extend the signal-level CSS detector from Labs 8.20/8.21 into a deterministic packet receiver:

detect a repeated-upchirp preamble and estimate packet start;
verify a two-symbol sync word and two downchirps;
estimate coarse integer-bin and fine fractional-bin CFO;
correct CFO before payload decisions;
measure SER, PER, missed detections and false alarms;
expose sample-rate-offset sensitivity.

The waveform remains CSS/LoRa-like, not LoRa-compatible. It deliberately omits the LoRa header, whitening, coding, interleaving and CRC.

Packet structure¶

noise prefix | 8 upchirps | sync symbols 18,52 | 2 downchirps |
16 payload symbols | noise suffix

The packet-start metric dechirps each candidate preamble window, accumulates FFT-bin power over all repeated chirps and compares the strongest bin with the mean bin power. The sync word and downchirps reject a high timing metric that does not have the expected packet structure.

CFO estimation¶

The preamble FFT peak supplies the integer-bin CFO. Phase advance of that peak across consecutive repeated chirps supplies the fractional-bin CFO:

CFO = integer FFT-bin shift + phase_step / (2π)

The default experiment injects 1.25 bin spacings. Without correction every payload packet fails; after synchronization and correction the reference -6 dB point reaches zero PER for the deterministic seed.

Run¶

python blocks/block_08_modulation_and_synchronization/python/lab_8_22_css_packet_sync_per.py

Generated artifacts¶

docs/assets/lab822_css_timing_metric.png
docs/assets/lab822_css_per_vs_snr.png
docs/assets/lab822_css_sro_sensitivity.png
docs/assets/lab822_css_packet_metrics.json

Statistical scope¶

1000 packets at every SNR point;
16,000 compared payload symbols per SNR point;
1000 independent noise-only false-alarm trials;
200 packets per sample-rate-offset point.

The zero-error points are finite tests, not proof of an arbitrarily low PER. With 1000 clean packets, the usual zero-failure 95% upper bound is approximately 3/1000.

Acceptance criteria¶

the example packet start, sync word and downchirps are recovered;
normalized CFO error is below 0.05 bin;
corrected PER is lower than uncorrected PER at the reference point;
at least 1000 packets are evaluated per SNR point;
missed-detection and false-alarm statistics are present;
the SRO sweep shows both degradation and the benefit/limit of resampling correction.