# Physics of Human-WiFi Interaction ## Human Tissue as a Dielectric at 2.4 GHz Human tissue is electrically characterised by complex permittivity: `ε* = ε' − jε''`. At 2450 MHz: | Tissue | Relative Permittivity (ε') | Conductivity (σ, S/m) | Penetration Depth | |---|---|---|---| | Muscle | 52–54 | 1.8–2.4 | ~1.5–2 cm | | Skin (wet) | 42 | 1.6 | ~2–3 cm | | Skin (dry) | 37–38 | 1.5 | ~2–3 cm | | Fat | 5 | 0.1 | ~9–12 cm | | Blood | 58–60 | 2.5 | ~1.2 cm | | Whole body (avg) | ~38.5 | ~2.4 | — | Sources: Gabriel et al. 4-Cole-Cole model; IFAC-CNR Dielectric Properties Database; IT'IS Foundation. At 2.4 GHz, the free-space wavelength is λ = c/f = 3×10⁸ / 2.4×10⁹ ≈ **12.5 cm**. Inside human tissue, the effective wavelength is shortened by √ε' ≈ 7×, to ~1.7 cm inside muscle. The body is therefore electrically large — many wavelengths in extent — making it an effective scatterer. --- ## Why 2.4 GHz Interacts Strongly with the Body ### 1. Polar Water Absorption Liquid water's orientational polarisation relaxation frequency falls in the low-GHz range. At 2.4 GHz, water molecules cannot fully follow the rapidly oscillating field, producing dielectric loss (energy absorbed as heat). The human body is approximately 60–70% water by mass (higher in muscle, lower in fat), making it a strong absorber. ### 2. High Ionic Conductivity Bodily fluids (blood, interstitial fluid, cytoplasm) contain dissolved ions. At 2.4 GHz, σ ≈ 2.4 S/m for average tissue — roughly a million times higher than distilled water. This drives significant conduction current and Ohmic loss. ### 3. Body as a Large Obstacle Empirical measurements show that human body shadowing causes additional link attenuation of **3–12 dB** depending on orientation and environment. A frontal cross-section presents a cylinder of ~30–50 cm diameter; a side view is ~20–25 cm. Both are multiple wavelengths wide, limiting diffraction around the body — most incident energy is absorbed. ### 4. Penetration Depth (Skin Depth) `δ = 1/α` where `α = (2πf/c) · Im(√ε*)`. For muscle at 2.4 GHz: δ ≈ 1.5–2 cm. Signal amplitude falls to 1/e of its surface value within ~2 cm of entering tissue — the body is essentially **opaque** to 2.4 GHz. --- ## Effect on Multipath Indoor WiFi propagation involves many multipath components: direct LOS, reflections off walls/ceiling/floor/furniture, diffracted paths. The received signal is the superposition of all these. When a human body enters the environment: - **New scatter paths are created**: The body surface reflects incident energy in all directions, creating new multipath components that add to (or subtract from) existing ones. - **Existing paths are perturbed**: Paths passing close to or through the body are attenuated and phase-shifted. - **LOS is shadowed**: If the body is between TX and RX, the direct path is attenuated by 3–12 dB. - **Dynamic multipath**: As the body moves, the lengths of all affected paths change, producing time-varying CSI amplitude and phase variations. Sensitivity is highest when path length changes are on the order of λ/2 ≈ 6.25 cm, which produces ~π radians of phase shift and transitions between constructive and destructive interference. --- ## Fresnel Zone Theory ### Definition The n-th Fresnel zone is the set of all points P such that: ``` |TX→P| + |P→RX| = |TX→RX| + n·λ/2 ``` This defines an ellipsoid with TX and RX at its foci. ### First Fresnel Zone Radius The maximum radius of the first Fresnel zone at a point distance d₁ from TX and d₂ from RX: ``` r₁ = √(λ · d₁ · d₂ / (d₁ + d₂)) ``` At the midpoint of the link (d₁ = d₂ = D/2): ``` r₁_max = (1/2) · √(λ · D) ``` For 2.4 GHz (λ = 0.125 m) at various link distances: | Link distance D | r₁_max | |---|---| | 2 m | 0.25 m | | 5 m | 0.40 m | | 10 m | 0.56 m | | 20 m | 0.79 m | A human body (diameter ~0.4–0.5 m) occupies a significant fraction of the first Fresnel zone on all typical indoor links of 2–10 m. ### The Odd/Even Zone Effect Fresnel zones alternate between constructive and destructive contributions: - **Odd zones** (1st, 3rd, 5th…): contributions arrive roughly in-phase with LOS — constructive. - **Even zones** (2nd, 4th, 6th…): contributions arrive roughly anti-phase — destructive. As a person moves through successive Fresnel zone boundaries (each λ/2 of path length change = one zone crossing), CSI amplitude varies sinusoidally. Key signatures: - **Person inside FFZ**: Strong amplitude perturbation, sinusoidal variation with movement - **Person on FFZ boundary**: Maximum rate of change in CSI - **Person outside FFZ**: Weaker perturbation via diffraction ### Fresnel Zone Localization In a multi-link system, each TX-RX pair defines a set of Fresnel zone ellipsoids. If a person's presence shifts the CSI in a way indicating they are within the n-th Fresnel zone of a given link, this constrains the person to an ellipsoidal shell. With multiple links, the constraints intersect: - 1 link: an ellipsoidal shell (no position constraint, only distance sum constraint) - 2 links: intersection of 2 ellipsoids → typically 2–4 candidate points (ambiguity) - 3+ links: sufficient for a unique solution in most geometries Phase measurement precision determines which Fresnel zone the person is in. A phase resolution of 0.1 rad translates to path length precision of ≈ λ/(4π) × 0.1 ≈ 1 mm — but hardware phase noise is much larger in practice (~0.5–2 rad per sample), requiring averaging. --- ## Implication for Spaxel The human body as a "saltwater bag" is an accurate physical model: - High water content (~70%) → strong 2.4 GHz absorption - High ionic conductivity → opaque to WiFi at skin depth ~2 cm - Electrically large body (multiple wavelengths) → significant scatter and shadow - First Fresnel zone radii match human body dimensions at 2–10 m indoor links This means WiFi CSI can reliably detect the presence of a human-sized conductive mass. What it cannot do is resolve internal structure — limbs, posture, fine geometry. The detectable unit is the blob, not the body.