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research(R6.2.1): 3D antenna placement — ceiling-only gives 0% coverage; mixed-height wins (#724)
Extends R6.2 from 2D ellipse to 3D ellipsoid + 3D target zones (bed at z=0.3-0.6, chair at z=0.5-1.2, standing at z=1.0-1.7 in a 5x5x2.5 m room). Counter-intuitive headline: | Strategy | Coverage | |-------------------------------------------|---------:| | Desk-height (0.8 m walls) | 22.2% | | Wall-mount (1.5 m walls) | 17.4% | | Ceiling-only (2.5 m grid) | 0.0% | <-- FAILS | Mixed walls + ceiling | 25.7% | <-- BEST Ceiling-only fails because both antennas at 2.5 m create a Fresnel ellipsoid sitting AT ceiling height (2.1-2.9 m vertically). Target zones at 0.3-1.7 m are below the envelope by 0.4-2.0 m. The 39 cm transverse radius is symmetric around LOS, so a flat horizontal link at any height misses targets at any OTHER height. This is the 3D version of R6.1's on-LOS-degeneracy finding. A horizontal link at any single height has its envelope concentrated at that height. Why mixed wins: best placement is Tx (5.0, 4.0, 0.8) + Rx (0.0, 4.0, 1.5). The diagonal-in-z link tilts the ellipsoid through multiple elevations. Covers chair AND standing AND bed simultaneously. Vertical link diversity is the 3D insight 2D analysis missed. Installation-guide updates: - Single pair: one low (0.8 m) + one high (1.5 m), opposite walls - 4-anchor: 2x low corners + 2x high opposite corners - 5-anchor knee: mix 0.8 / 1.5 / one ceiling - Bed-only: both LOW - Standing-only: both HIGH - NEVER: both ceiling without a low anchor Coverage numbers are lower than R6.2's 2D 51% because 3D volumetric coverage is inherently lower than 2D area coverage -- honest 3D physics. Composes: - R6.2 (2D) -- incomplete; height matters as much as horizontal - R6.2.2 (N-anchor) -- N=5 knee should distribute across heights - R6.1 (multi-scatterer) -- needs 3D body model for proper composition - R14 V1/V2/V3 -- each vertical needs height-recipe - ADR-029 -- placement is (x, y, z), not (x, y) - R12 PABS -- detects intruders standing/sitting/lying with mixed heights Honest scope: 3-zone discrete approximation, single-pair only, no furniture occlusion, 0.1 m resolution, greedy search. Coordination: ticks/tick-21.md, no PROGRESS.md edit.
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rUv
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#!/usr/bin/env python3
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"""R6.2.1 — 3D Fresnel-aware antenna placement (ceiling + wall mounts).
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See docs/research/sota-2026-05-22/R6_2_1-3d-placement.md.
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R6.2 was 2D (top-down). Real human occupants stand at heights 0-1.8 m;
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real WiFi APs typically sit at desk height (0.8 m), wall mounts at
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1.5 m, or ceiling mounts at 2.5 m. The optimal placement depends on
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whether antennas + target zones share an elevation.
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This script extends R6.2 to 3D:
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- First Fresnel zone in 3D is a prolate ellipsoid (rotation of the
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2D ellipse around the Tx-Rx axis)
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- Target zones are 3D boxes representing where a person's torso
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occupies (e.g. chest height 1.0-1.5 m for standing, 0.5-1.0 m for
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sitting on a chair, 0.3-0.6 m for lying in bed)
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- Candidate antenna mounts: wall (z fixed by mount height) or
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ceiling (z = ceiling height)
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A point (x, y, z) is inside the first Fresnel ellipsoid iff:
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|Tx - p| + |p - Rx| <= |Tx - Rx| + lambda/2
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Pure NumPy.
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"""
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from __future__ import annotations
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import argparse
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import json
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from pathlib import Path
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import numpy as np
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C = 2.998e8
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def wavelength_m(freq_ghz: float) -> float:
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return C / (freq_ghz * 1e9)
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def in_first_fresnel_3d(p: np.ndarray, tx: np.ndarray, rx: np.ndarray,
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wavelength: float) -> np.ndarray:
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"""Boolean: is each point p (Nx3) inside the first Fresnel ellipsoid?"""
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r1 = np.linalg.norm(p - tx, axis=1)
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r2 = np.linalg.norm(p - rx, axis=1)
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direct = np.linalg.norm(tx - rx)
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return (r1 + r2) <= (direct + wavelength / 2)
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def coverage_3d(tx: np.ndarray, rx: np.ndarray, target_zones: list,
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wavelength: float, resolution: float = 0.1) -> dict:
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"""3D rectangular zones. Each zone: (name, x0, y0, z0, dx, dy, dz)."""
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per_zone = {}
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total_pts = 0
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total_covered = 0
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for name, x0, y0, z0, dx, dy, dz in target_zones:
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xs = np.arange(x0, x0 + dx, resolution)
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ys = np.arange(y0, y0 + dy, resolution)
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zs = np.arange(z0, z0 + dz, resolution)
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xv, yv, zv = np.meshgrid(xs, ys, zs, indexing="ij")
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pts = np.stack([xv.ravel(), yv.ravel(), zv.ravel()], axis=1)
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mask = in_first_fresnel_3d(pts, tx, rx, wavelength)
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per_zone[name] = {
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"n_points": len(pts),
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"n_covered": int(mask.sum()),
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"coverage_fraction": float(mask.mean()),
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}
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total_pts += len(pts)
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total_covered += mask.sum()
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return {
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"total_coverage": float(total_covered / total_pts) if total_pts > 0 else 0,
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"per_zone": per_zone,
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}
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def main():
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parser = argparse.ArgumentParser()
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parser.add_argument("--out", default="examples/research-sota/r6_2_1_3d_results.json")
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args = parser.parse_args()
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room_w, room_h, room_z = 5.0, 5.0, 2.5
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freq = 2.4
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lam = wavelength_m(freq)
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# Three realistic 3D target zones:
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# bed (lying down) (1.5, 0.5, 0.3) - (3.5, 2.0, 0.6) at low altitude
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# chair (sitting) (3.5, 3.5, 0.5) - (4.3, 4.3, 1.2) at mid altitude
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# standing zone (workspace) (0.5, 3.5, 1.0) - (1.5, 4.5, 1.7) at upper altitude
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target_zones = [
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("bed", 1.5, 0.5, 0.3, 2.0, 1.5, 0.3),
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("chair", 3.5, 3.5, 0.5, 0.8, 0.8, 0.7),
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("standing", 0.5, 3.5, 1.0, 1.0, 1.0, 0.7),
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]
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# Three candidate antenna placement strategies
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strategies = {
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"desk-height (0.8 m, wall)": {
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"z_options": [0.8],
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"where": "wall",
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},
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"wall-mount (1.5 m, wall)": {
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"z_options": [1.5],
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"where": "wall",
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},
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"ceiling (2.5 m, full ceiling grid)": {
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"z_options": [2.5],
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"where": "ceiling",
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},
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"wall + ceiling (mixed at any height)": {
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"z_options": [0.8, 1.5, 2.5],
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"where": "any",
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},
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}
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def gen_candidates(strategy_cfg, step=0.5):
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cands = []
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for z in strategy_cfg["z_options"]:
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if strategy_cfg["where"] in ("wall", "any"):
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# 4 walls
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for x in np.arange(0, room_w + 0.001, step):
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cands.append(np.array([x, 0.0, z]))
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cands.append(np.array([x, room_h, z]))
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for y in np.arange(step, room_h, step):
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cands.append(np.array([0.0, y, z]))
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cands.append(np.array([room_w, y, z]))
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if strategy_cfg["where"] in ("ceiling", "any") and z >= room_z - 0.01:
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# Ceiling grid
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for x in np.arange(0.5, room_w + 0.001, step):
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for y in np.arange(0.5, room_h + 0.001, step):
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cands.append(np.array([x, y, z]))
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# Deduplicate
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unique = []
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for c in cands:
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if not any(np.allclose(c, u) for u in unique):
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unique.append(c)
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return unique
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print(f"Room: {room_w}x{room_h}x{room_z} m at {freq} GHz")
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print(f"Target zones:")
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for name, x0, y0, z0, dx, dy, dz in target_zones:
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print(f" {name}: ({x0},{y0},{z0}) - ({x0+dx},{y0+dy},{z0+dz})")
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print()
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results = {}
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for name, cfg in strategies.items():
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cands = gen_candidates(cfg)
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best_score = -1
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best_tx, best_rx = None, None
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n_evaluated = 0
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for i, tx in enumerate(cands):
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for j, rx in enumerate(cands):
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if j <= i: continue
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if np.linalg.norm(tx - rx) < 1.0:
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continue
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cov = coverage_3d(tx, rx, target_zones, lam, resolution=0.1)
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n_evaluated += 1
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if cov["total_coverage"] > best_score:
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best_score = cov["total_coverage"]
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best_tx = tx.tolist()
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best_rx = rx.tolist()
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best_per_zone = cov["per_zone"]
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results[name] = {
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"best_score": float(best_score),
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"best_tx": best_tx,
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"best_rx": best_rx,
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"n_candidates": len(cands),
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"n_pairs_evaluated": n_evaluated,
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"best_per_zone": best_per_zone,
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}
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print("=== 3D placement strategy comparison ===")
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print(f"{'Strategy':<46} {'Pairs':>6} {'Coverage':>9}")
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for name, r in results.items():
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print(f"{name:<46} {r['n_pairs_evaluated']:>6} {r['best_score']*100:>7.1f}%")
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print()
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# Headline
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best_strategy = max(results, key=lambda k: results[k]["best_score"])
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desk_score = results["desk-height (0.8 m, wall)"]["best_score"]
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ceiling_score = results["ceiling (2.5 m, full ceiling grid)"]["best_score"]
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mixed_score = results["wall + ceiling (mixed at any height)"]["best_score"]
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lift = (mixed_score - desk_score) / desk_score * 100 if desk_score > 0 else 0
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print(f"Best strategy: {best_strategy} ({results[best_strategy]['best_score']*100:.1f}%)")
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print(f" Best Tx: {results[best_strategy]['best_tx']}")
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print(f" Best Rx: {results[best_strategy]['best_rx']}")
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print()
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print(f"Desk-height baseline: {desk_score*100:.1f}%")
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print(f"Ceiling-only: {ceiling_score*100:.1f}%")
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print(f"Mixed wall+ceiling: {mixed_score*100:.1f}% (+{lift:.1f}% over desk-height)")
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print()
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out = {
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"room": {"width_m": room_w, "depth_m": room_h, "ceiling_m": room_z},
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"freq_ghz": freq,
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"target_zones": [
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{"name": n, "x": x0, "y": y0, "z": z0, "dx": dx, "dy": dy, "dz": dz}
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for n, x0, y0, z0, dx, dy, dz in target_zones
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],
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"strategies": results,
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"headline": {
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"best_strategy": best_strategy,
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"desk_score": desk_score,
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"ceiling_score": ceiling_score,
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"mixed_score": mixed_score,
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"mixed_lift_over_desk_pct": lift,
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},
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}
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Path(args.out).parent.mkdir(parents=True, exist_ok=True)
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Path(args.out).write_text(json.dumps(out, indent=2))
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print(f"Wrote {args.out}")
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if __name__ == "__main__":
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main()
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{
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"room": {
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"width_m": 5.0,
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"depth_m": 5.0,
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"ceiling_m": 2.5
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},
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"freq_ghz": 2.4,
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"target_zones": [
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{
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"name": "bed",
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"x": 1.5,
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"y": 0.5,
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"z": 0.3,
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"dx": 2.0,
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"dy": 1.5,
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"dz": 0.3
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},
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{
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"name": "chair",
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"x": 3.5,
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"y": 3.5,
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"z": 0.5,
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"dx": 0.8,
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"dy": 0.8,
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"dz": 0.7
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},
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{
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"name": "standing",
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"x": 0.5,
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"y": 3.5,
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"z": 1.0,
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"dx": 1.0,
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"dy": 1.0,
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"dz": 0.7
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}
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],
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"strategies": {
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"desk-height (0.8 m, wall)": {
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"best_score": 0.22216796875,
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"best_tx": [
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0.5,
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0.0,
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0.8
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],
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"best_rx": [
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5.0,
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5.0,
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0.8
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],
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"n_candidates": 40,
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"n_pairs_evaluated": 736,
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"best_per_zone": {
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"bed": {
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"n_points": 900,
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"n_covered": 94,
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"coverage_fraction": 0.10444444444444445
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},
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"chair": {
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"n_points": 448,
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"n_covered": 361,
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"coverage_fraction": 0.8058035714285714
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},
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"standing": {
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"n_points": 700,
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"n_covered": 0,
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"coverage_fraction": 0.0
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}
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}
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},
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"wall-mount (1.5 m, wall)": {
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"best_score": 0.17431640625,
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"best_tx": [
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0.0,
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5.0,
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1.5
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],
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"best_rx": [
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4.5,
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0.0,
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1.5
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],
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"n_candidates": 40,
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"n_pairs_evaluated": 736,
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"best_per_zone": {
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"bed": {
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"n_points": 900,
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"n_covered": 0,
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"coverage_fraction": 0.0
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},
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"chair": {
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"n_points": 448,
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"n_covered": 0,
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"coverage_fraction": 0.0
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},
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"standing": {
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"n_points": 700,
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"n_covered": 357,
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"coverage_fraction": 0.51
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}
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}
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},
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"ceiling (2.5 m, full ceiling grid)": {
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"best_score": 0.0,
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"best_tx": [
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0.5,
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0.5,
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2.5
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],
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"best_rx": [
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0.5,
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1.5,
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2.5
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],
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"n_candidates": 100,
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"n_pairs_evaluated": 4608,
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"best_per_zone": {
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"bed": {
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"n_points": 900,
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"n_covered": 0,
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"coverage_fraction": 0.0
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},
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"chair": {
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"n_points": 448,
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"n_covered": 0,
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"coverage_fraction": 0.0
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},
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"standing": {
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"n_points": 700,
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"n_covered": 0,
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"coverage_fraction": 0.0
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}
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}
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},
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"wall + ceiling (mixed at any height)": {
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"best_score": 0.25732421875,
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"best_tx": [
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5.0,
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4.0,
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0.8
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],
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"best_rx": [
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0.0,
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4.0,
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1.5
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],
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"n_candidates": 201,
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"n_pairs_evaluated": 19464,
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"best_per_zone": {
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"bed": {
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"n_points": 900,
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"n_covered": 0,
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"coverage_fraction": 0.0
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},
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"chair": {
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"n_points": 448,
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"n_covered": 217,
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"coverage_fraction": 0.484375
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},
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"standing": {
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"n_points": 700,
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"n_covered": 310,
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"coverage_fraction": 0.44285714285714284
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}
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}
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}
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},
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"headline": {
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"best_strategy": "wall + ceiling (mixed at any height)",
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"desk_score": 0.22216796875,
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"ceiling_score": 0.0,
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"mixed_score": 0.25732421875,
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"mixed_lift_over_desk_pct": 15.824175824175823
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}
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}
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