R6.2.1 — 3D antenna placement: ceiling-only mounting is the WORST option

Status: 3D Fresnel ellipsoid + height-strategy benchmark · 2026-05-22

Counter-intuitive headline

Strategy	Coverage of 3 zones
Desk-height (0.8 m, walls)	22.2%
Wall-mount (1.5 m, walls)	17.4%
Ceiling-only (2.5 m, full ceiling grid)	0.0%
Mixed (any height, walls + ceiling)	25.7% ← best

Ceiling-only mounting completely fails — the Fresnel envelope sits at ceiling height (2.1-2.9 m) and never reaches floor-level targets (bed 0.3-0.6 m, chair 0.5-1.2 m, standing 1.0-1.7 m).

The physics

In 3D the first Fresnel zone is a prolate ellipsoid with foci at Tx and Rx. The transverse radius at the midpoint is sqrt(d·λ)/2. For a 5 m link at 2.4 GHz: 39 cm transverse. This is a symmetric envelope around the LOS line.

A ceiling-mounted link (Tx at 2.5 m, Rx at 2.5 m, horizontal LOS) has its Fresnel envelope vertically centred at 2.5 m, extending from 2.1 m to 2.9 m. Targets at 0.3-1.7 m are below the envelope by 0.4-2.0 m. Completely missed.

This is the 3D extension of the on-LOS-degeneracy finding from R6.1 — except now the issue is on-CEILING degeneracy. A flat horizontal link at any height blocks sensing in the perpendicular dimension.

Why mixed wins

The optimal mixed placement picks Tx at (5.0, 4.0, 0.8) — desk height — and Rx at (0.0, 4.0, 1.5) — wall-mount height. The link is diagonal in z as well as x. The Fresnel ellipsoid is tilted to thread multiple elevations: covers chair (z=0.5-1.2) AND standing zone (z=1.0-1.7) AND a portion of bed (z=0.3-0.6).

Vertical link diversity is the key 3D insight that 2D analysis missed.

Recommendations

Use case	3D placement recipe
Single Tx-Rx pair	One low (desk height ~0.8m), one high (wall ~1.5m), opposite walls
4-anchor multistatic (R6.2.2)	2× low corners + 2× high opposite corners
5-anchor (R6.2.2 knee)	Mix of 0.8 m / 1.5 m / one ceiling at 2.5 m for top-down coverage
Bed-only (sleep monitoring)	Both antennas low (0.5-0.8 m) and opposite sides of bed
Standing-only (gym, kitchen)	Both antennas high (1.5 m)
NEVER	Both antennas ceiling-mounted with no low-anchor

What this says about the installation guide

Current RuView installer instructions are 2D: "place seeds on opposite walls". The 3D scrutiny says:

1. Heights matter as much as horizontal positions. Mixed-height placement gives +15.8% coverage over desk-height-only.
2. Ceiling-mount fails alone. If using ceiling as part of a multi-anchor configuration, MUST also have at least one low-height anchor to bring the envelope down to floor-level targets.
3. Bedside sensing wants low anchors. A bed at 0.3-0.6 m can only be covered by low-height links. High-mounted antennas miss the bed entirely.

These should be added to the installer-guide as height recipes, alongside R6.2's horizontal-placement recipes.

Composes with prior threads

• R6.2 (2D placement) — 2D analysis hides height issues entirely; R6.2 alone gives wrong installer guidance.
• R6.2.2 (N-anchor multistatic) — N=5 anchors should be distributed across heights, not all at one elevation.
• R6.1 (multi-scatterer) — the multi-scatterer body model is 2D top-down; a 3D body model (head at z=1.7, chest at z=1.3, legs at z=0.5) would tighten the per-body-part contribution estimates per height.
• R14 (empathic appliances) — V1 lighting (bedroom: detect sleeper) needs low anchors. V3 (cognitive load at desk) needs mid-height. The placement strategy depends on the empathic-appliance use case.
• ADR-029 (multistatic) — anchor-count + placement-height are both required configuration parameters.

Honest scope

• Coverage numbers (22%, 17%, 26%) are lower than R6.2's 2D 51% because targets are 3D volumes now, not 2D areas. Volumetric coverage is inherently lower; a 3D point must be inside the ellipsoid in all three axes.
• 3 zones at distinct heights. Real rooms have continuous human occupancy distributions (people stand, sit, lie); the 3-zone setup is a discrete approximation.
• Single-pair only. Multi-anchor 3D (R6.2.2.1) would saturate much earlier than the 2D version because each anchor's ellipsoid is sparser in 3D.
• No furniture occlusion in 3D either.
• 0.1 m resolution. Finer resolution would refine the numbers slightly.
• Greedy single-pair search. Global optimum may be slightly higher; brute-force is feasible at this candidate count.

What this DOES enable

1. Updates the installation-guide recipe from "place on opposite walls" to "place at mixed heights on opposite walls".
2. Quantifies why ceiling-only WiFi sensing doesn't work — common mistake in DIY deployments.
3. Provides height-strategy recommendations per use case (sleep / sitting / standing).
4. A 3D placement search that can be added to wifi-densepose plan-antennas as a --3d flag.

What this DOES NOT enable

• Continuous occupancy distribution modelling (would need pose-trajectory data, R6.2.3).
• Multi-pair 3D optimisation (R6.2.2.1 — composition with R6.2.2 in 3D).
• Furniture / wall occlusion modelling (would need a 3D ray-tracing extension).
• Per-empathic-appliance optimised placement (would need V1/V2/V3 task-specific zones).

Next ticks (R6.2 family)

• R6.2.2.1: 3D multi-anchor union coverage — does the 5-anchor knee hold in 3D?
• R6.2.3: chest-centric target zones (R6.1 says chest is 27.6% of signal — placement should target chest specifically).
• R6.2 productisation: add --3d flag to the CLI tool.

Connection back

• R6 Fresnel forward model — direct 3D extension.
• R6.1 multi-scatterer — needs a 3D body model to compose properly with R6.2.1.
• R6.2 — 2D was incomplete; height matters as much as horizontal position.
• R6.2.2 — N-anchor knee likely shifts in 3D; needs follow-up benchmark.
• R14 V1/V2/V3 — each vertical needs its own height-recipe.
• ADR-029 — anchor placement specification needs (x, y, z) per anchor, not (x, y).
• R12 PABS — PABS sensitivity to structural changes inherits R6.2.1's coverage; mixed-height placements detect intruders standing AND sitting AND lying.