Topology vs area for CSI occupancy — what drives fingerprint discriminability and sniffer count?

Executive summary

If you want to count people in a building from Wi-Fi, you place a handful of radios and read how the signal between them bends as bodies move. A natural, appealing hypothesis is that a building's floor plan shape — how its rooms connect, which hallways everything funnels through — decides how many sensors you need: a twisty, many-roomed floor should need more sensors than a simple open one of the same size. We tried to prove that room-graph topology beats raw floor area as the predictor.

The headline, stated honestly: in simulation, it did not. When we measured each Tx–Rx link's discriminability (how much a moving body swings that link's signal) against the number of walls its path crosses, the relationship was essentially flat (Spearman ρ = +0.14), and it stayed flat even after removing floor-to-floor differences. Plain floor area was the stronger predictor (ρ = −0.54), and area also best predicted the minimum number of sensors (ρ = −0.74). So the simulated evidence favours the boring baseline — bigger floors need more sensors, roughly regardless of their topology. As a bonus, the co-registered BLE channel was 2.49× more discriminable per link than CSI.

But the honesty does not stop there. This refutation rests on a corpus where topology barely varied — only 4 of 40 links were true line-of-sight; almost every Tx–Rx pair crossed exactly one wall. A fair test needs a floor set deliberately balanced for line-of-sight vs non-line-of-sight links. That "fair fight" campaign (c-csi-topology-los-balanced) was designed to fix exactly this — and it never ran: all three of its sessions are 0-run feasibility probes, blocked because the simulator has no way to place balanced links, the spatial database was down, and the floor corpus was too small. So the current state is: the strong topology claim is refuted in silico on an admittedly unfair corpus, the hypothesis is demoted plausible → speculative, and the deciding fair test is still owed. All of this is simulation on a uniform-material ray-tracer — a real Wi-Fi/BLE capture (IP-106) is the standing gate.

The problem, in plain words

Imagine two apartments of the same square footage. One is a single open loft; the other is chopped into eight little rooms off a central hallway. Drop the same Wi-Fi sensors in both. Intuitively the chopped-up one should be "richer" — signals bounce off more walls, every location has a more distinctive fingerprint, so you can tell locations apart with fewer sensors. That intuition has real support: a study in actual multi-zone homes found that a central, high-traffic room contaminates its neighbours' fingerprints, while a tucked-away peripheral room is far easier to read (jung2025). And crowd-counting-through-walls work shows room shape, not just size, biases the count (depatla2018 ↗). So "topology should matter" is not a wild guess.

The question that actually pays the bills is how many sensors a building needs. If topology drives it, you'd survey each floor's graph and place sensors adaptively; if plain area drives it, you just scale sensors with square footage and stop worrying about the floor plan. That is a real deployment decision, and the two answers cost very different amounts of engineering. This card tries to settle it — first in simulation, cheaply, before anyone climbs a ladder.

What we are trying to prove

• Hypothesis (falsifiable): a floor's room-adjacency topology — operationalised here as wall-count-on-path per link, with betweenness/diameter/degree as the broader family — predicts CSI/BLE fingerprint discriminability and the minimum sniffer count better than floor area does. If wall-count does not out-predict area, and the line-of-sight vs non-line-of-sight contrast is flat, the strong form fails.
• What a null means: a flat topology↔discriminability relation means the simple area + access-point-count baseline is enough — you size a sensor deployment from floor area, not from a graph survey. That is a valuable negative: it removes a speculative, expensive arm from the system-design story.
• The trap we walked into (and must not repeat): a null can come from no evidence or from no variance. If the corpus almost never produces line-of-sight links, a flat result proves nothing about topology — it proves the corpus was unfair. That is exactly why the balanced-placement campaign exists, and exactly why its non-execution matters.

How the experiment works (plain method)

1. The runs that exist (c-csi-topology-sniffer-count): exp-csi-static ray-traces 6 ResPlan apartment floors × 2 seeds = 12 runs. Each run drops a single body at 80 random positions and records, for every Tx–Rx link, how the amplitude swings — plus a co-registered BLE-RSSI fingerprint solved from the same channel, for free.
2. Discriminability, per link = the standard deviation (in dB) of a link's mean amplitude across the 80 body positions — how much a single moving person swings that link. A link that barely moves cannot tell locations apart.
3. Topology, per link = wall-count-on-path: how many wall segments the straight Tx→Rx line crosses, computed by 2-D segment intersection from each run's own scene file (no external database needed). Floor area (bounding box) is the competing predictor.
4. The horse race (the powered re-reduction, session 01KVZRDA…): switch the unit of analysis from the floor (only 6 — hopelessly underpowered, and area is tangled with graph diameter) to the link (40). Correlate wall-count vs area against discriminability; run the line-of-sight-vs-non-line-of-sight defeater; and greedily find the smallest link subset (k*) that keeps most of the location separation, then ask whether k* tracks topology or area.
5. The fair fight that was owed (c-csi-topology-los-balanced): rebuild the corpus so every floor has ≥10 line-of-sight and ≥10 non-line-of-sight links by construction, then re-run the horse race on a design where topology finally has room to move.

What we've found so far (honest, across both campaigns)

Campaign 1 — c-csi-topology-sniffer-count (REAL: 12 runs, powered link-as-unit re-reduction, all 4 criteria resolved):

Verdict: the wall-count-on-path operationalisation of layout-topology-fingerprint-discriminability is refuted in silico; floor area is the operative predictor. Hypothesis demoted plausible → speculative (the real-home literature analogy is what keeps it off refuted). One figure (fig_csi_topology_linkunit.png) was rendered; note the session carried no criticism.md.

The load-bearing caveat, in the campaign's own words: "most Tx–Rx pairs cross exactly one wall," so the *area-dominance and the within-floor null carry the verdict more than the wall-count axis on its own. It tests one operationalisation, not the full graph-metric set (a weak floor-level mean_degree ρ = +0.37 survives, unpowered).

Campaign 2 — c-csi-topology-los-balanced (PHANTOM: 0 runs across all three sessions):

This is the "fair fight" designed to fix Campaign 1's imbalance — and it has never executed a single run. Its latest session (01KWZE3BVCERY4G514G3PDM5ZT, 2026-07-07) is a feasibility probe that sealed with all three success criteria unresolved and re-confirmed three blockers: (1) the sionna-csi-runner exposes no stratified-los placement key — "≥10 LOS + ≥10 NLOS links per floor by construction" is simply not expressible today; (2) PostGIS was down on the runner, so scene staging via gis export-floor was impossible; (3) only ~10 ResPlan floors are staged against a ≥20-floor target. Per the brief's own instruction, "this campaign must not be re-dispatched" until all three are cleared. No hypothesis was retired by it, and no numbers were produced — it is honestly a 0-compute write-up, and this card treats it as such.

Net position: the strong topology claim is refuted on an unfair corpus; the fair corpus does not yet exist; area is the safe deployment predictor for now.

How to read the figure

• fig_csi_topology_linkunit.png (the only real figure, from the powered re-reduction) — per-link discriminability D (y, the dB spread a moving body induces) plotted against wall-count-on-path and, separately, against floor area. The story is in the slopes: the wall-count panel is essentially flat (ρ = +0.14 — a cloud with no rise), while the area panel slopes down (ρ = −0.54). A companion panel shows the BLE vs CSI per-link discriminability, where BLE sits ~2.5× higher. Read the rank trend, not individual points, and read it with the caveat firmly in mind: the line-of-sight side of the wall-count axis has only 4 links, so the "flat" is as much absence of spread as absence of effect. There is no figure for c-csi-topology-los-balanced because it produced no runs.

Review panel

Each voice is a prepared expert with a one-line stance and the literature it argues from. Verdicts are about this experiment and its current evidence, not the idea in the abstract.

Key references

• jung2025 — real multi-zone homes where topology (betweenness contamination) demonstrably matters; the tension against the sim null.
• depatla2018 ↗ — room shape, not just area, biases through-wall counting.
• afghantoloee2021 ↗ — optimal indoor sensor count is topology-dependent; the OR baseline for k*.
• wang2025 ↗ — CSI-specific placement guidance for crowd counting.
• zhen2022 ↗ — layout reshapes BLE coverage; adaptive placement gains.
• demrozi2021 ↗ — BLE occupancy, the second (2.49×-more-discriminable) modality's real-world basis.
• rampa2022 ↗ — the multipath/multi-body mechanism a uniform-material ray-tracer under-represents.
• zou2018 ↗ — device-free CSI counting baseline.
• zhang2026, guarino2026 ↗ — the reproducibility bar the SWE voice invokes.
• wang2026, huang2025 — the sim-to-real generalizability gap and a public real-CSI anchor for the red-team's cross-check.
• rusca2024 ↗ — the privacy-proportionate design posture the ethics voice argues from.