Packet-Rate Floor for Motion Sensing

Motivation

Week 3 derived a hard bound: a packet stream sampling the channel at rate PRR can represent Doppler shifts only up to f_max = PRR/2, and the maximum Doppler for motion along the dominant reflection path is f_D = 2v/λ, giving a speed ceiling v_max = λ·PRR/4. At 5.32 GHz this puts walking (~1.4 m/s) exactly at PRR = 100 Hz, and a 20 Hz passive trickle at 0.28 m/s — below which a walking person aliases away before any model runs.

This is asserted from sampling theory and confirmed only in a synthetic workbook. It has not been measured on physically-modelled CSI, where multipath, scattering geometry, and the bistatic Doppler factor (cos α + cos β, not a clean 2) complicate the clean bound. The lab needs to know the empirical packet-rate floor for its own crowd-sensing target, because the deployable (passive) stance inherits whatever rate the environment produces. If the real breakpoint sits well above 100 Hz, passive capture is unviable for motion and the thesis must say so; if it sits at or below the closed-form bound, the bound is a usable design rule.

No vault campaign has swept PRR as an independent variable. sharma2024_c8a2 ↗ motivates the low-rate passive regime; guarino2026_e72c ↗ flags capture-parameter under-reporting as a reproducibility failure. This experiment fills the gap and produces a citable design rule.

Setup

Simulator

• Channel-simulator family (IP-094): sionna-csi-runner with the IP-110 Doppler-CFR upgrade, driven by a coupled walk scenario (JuPedSim → emitter trajectory → ray-traced CSI), as in the c-multifloor / c-ip110-showcase lineage.
• Generate one high-rate master run per scene at the highest feasible CSI frame rate (the "ground-truth" sampling), then decimate to each target PRR. Decimating a single physically-consistent run isolates PRR as the only varied factor (no re-simulation noise between rates).

Independent variable

• PRR sweep: {1000, 500, 200, 100, 50, 20} Hz (decimation of the master run).

Controlled / fixed

• Scene geometry, wall materials, TX/RX placement, agent walk paths, carrier frequency (run at both 2.4 and 5.32 GHz so the λ dependence of the ceiling is itself tested).
• Agent speed band: include a slow (~0.7 m/s), normal (~1.4 m/s), and brisk (~2.0 m/s) walk so the breakpoint can be located per speed.

Procedure

1. Master run(s): launch the coupled walk→CSI campaign at max CSI rate for each (carrier, speed) cell. Persist the full-rate CSI HDF5.
2. Decimate each master run to the six target PRRs (drop frames uniformly; keep timestamps).
3. Per (PRR, carrier, speed):
   • Compute the Doppler spectrum (STFT over packets) and read off the maximum recoverable Doppler and the aliasing onset.
   • Compute a downstream motion-detection metric — AUC / F1 of "is a person walking through this link right now?" against the simulator's motion ground truth — using a fixed, simple detector (variance-of-Doppler-energy threshold) so the metric reflects the data, not model capacity.
4. Locate the breakpoint: the PRR at which the detection metric crosses a fixed degradation threshold (e.g. AUC < 0.7), per speed and carrier.
5. Compare the measured breakpoint PRR against the closed-form PRR_min = 4v/λ.

Expected Outputs

• dataset/exp007/csi_master/ — full-rate ray-traced CSI per (carrier, speed)
• dataset/exp007/metric_vs_prr.csv — detection metric per (PRR, carrier, speed)
• dataset/exp007/doppler/ — Doppler spectra at each PRR (showing aliasing onset)
• Figure: detection metric vs PRR, with the closed-form v_max = λ·PRR/4 ceiling overlaid (the empirical-vs-theoretical comparison)
• A one-line design rule: "for walking-speed sensing at f_c, capture at ≥ X Hz."

Analysis Plan

Primary

1. Breakpoint vs theory: does the measured PRR floor track 4v/λ? Report the ratio (empirical / theoretical) per cell; a ratio near 1 validates the design rule, a ratio >1 quantifies the real-world penalty from the bistatic geometry factor.
2. λ dependence: the 2.4 GHz floor should be ~2.2× lower in PRR than 5.32 GHz for the same speed (longer λ → higher v_max per Hz). Confirm the slope.
3. Aliasing signature: show that below the floor, walking Doppler energy folds into the low-frequency band (the artefact W3 §5 predicts).

Guardrails (per the campaign-rigor audit)

• This is a simulator-internal validation — state that explicitly; it tests the sampling claim, which is geometry-agnostic, not a sensing-accuracy claim about the real world.
• Use a fixed, dumb detector so the result is about the data's information content, not a tuned model (avoids the self-confirming trap).
• The real-hardware follow-on (FeitCSI on AX210 at configurable injection rate) is the external check; flag it as required before any thesis claim.

Success Criteria

• PRR swept over ≥5 rates on physically-consistent decimated runs, at ≥2 carriers and ≥3 speeds
• Measured detection-vs-PRR breakpoint located for each cell
• Empirical breakpoint compared against 4v/λ with a reported ratio and tolerance
• Aliasing-below-floor demonstrated in the Doppler spectra
• A citable capture-rate design rule produced for the lab's carrier(s)

Related Work in Vault

• sharma2024_c8a2 ↗ — the low-rate passive regime this floor constrains
• guarino2026_e72c ↗ — capture-parameter reporting as a reproducibility issue
• zheng2019_5389 ↗ — Widar3.0's high active rate; the BVP/DFS features assume it
• meneghello2023_0a93 ↗ — a high-rate active collection at the wide-band end

Dependencies

• IP-110 Doppler-CFR sionna-csi-runner (coupled walk→CSI chain), runnable locally (--where local rebuilds the engine)
• A coupled walk scenario with motion ground truth (reuse the c-multifloor / c-ip110-showcase scene staging)
• (Follow-on) FeitCSI + Intel AX210 for the real-hardware check

Notes

This is the cleanest "design rule" experiment seeded by WS501 — it converts a sampling-theory bound into a measured, carrier-specific capture-rate floor the lab can quote when defending its collection setup. It also stress-tests the W3 lecture's central claim on real ray-traced data, closing the loop between the course and the platform. Pairs with EXP-008 Active Injection vs Passive Sniffing, which asks whether mean rate is even the right axis once arrivals are bursty.