The WiFi Channel as a Distributed Sensor

Most explanations of WiFi sensing stop at “CSI measures amplitude and phase.” This post goes one level deeper: what a single CSI snapshot actually contains, how multipath superposition works as a concrete model, and why collapsing that into RSSI throws away the information you need.

For the full physics treatment, see how it works . This is the worked-example version.

One packet, one matrix

When an ESP32 receives a WiFi frame, the PHY layer reports CSI as a complex vector:

CSI[k] = |CSI[k]| · e^(j·φ[k])     for k = 0, 1, ..., N-1

Each index k is one OFDM subcarrier — a narrow frequency slice of the channel. A typical 20 MHz WiFi channel has 64 subcarriers (52 data-bearing). You get 52 complex numbers per packet: 52 amplitude-phase pairs describing how the signal traveled at each frequency.

Stack packets over time and you have a 2D matrix:

         subcarrier 0   1   2  ...  51
time t0:    [CSI]    [CSI] [CSI] ... [CSI]
time t1:    [CSI]    [CSI] [CSI] ... [CSI]
...

This matrix is the fundamental sensing input. Every detection algorithm — variance thresholds, spectrograms, convolutional classifiers — operates on this structure or a transformation of it.

Multipath as superposition: a worked example

Suppose a WiFi link crosses a 5 m room. Three dominant paths reach the receiver:

PathDescriptionDelayRelative amplitude
0Direct (TX → RX)17 ns1.0
1Wall reflection25 ns0.6
2Floor reflection31 ns0.4

The channel at frequency \(f\) is:

\[ H(f) = 1.0 \cdot e^{-j2\pi f \cdot 17\text{ns}} + 0.6 \cdot e^{-j2\pi f \cdot 25\text{ns}} + 0.4 \cdot e^{-j2\pi f \cdot 31\text{ns}} \]

Each subcarrier \(k\) with frequency \(f_k\) gets a different complex value depending on how the three path phases align at that frequency. Constructive interference at some subcarriers, destructive at others — this is the frequency-selective fading pattern that CSI captures.

Now a person walks through the link. Their body adds a fourth path (or modifies path 1’s reflection off the wall behind them). The superposition changes. Some subcarriers rotate phase by π/4, others barely move. The pattern of which subcarriers changed — not just that something changed — carries information about where and how the body perturbed the field.

What RSSI throws away

RSSI integrates power across all subcarriers (and often across antennas and packets):

\[ \text{RSSI} \propto \sum_k |H(f_k)|^2 \]

Phase cancels in the sum. Frequency-selective structure is lost. Two completely different channel states — one with a person present, one without — can produce identical RSSI if the total power happens to match.

CSI preserves per-subcarrier amplitude and phase. A person breathing might rotate phase on subcarriers 12–18 by 0.1 radians while leaving subcarriers 30–40 unchanged. RSSI sees nothing. CSI sees a spatially structured perturbation — the signature of a scatterer at a specific geometry.

This is not a marginal improvement. It is the difference between sensing and not sensing.

Implications for system design

  1. Never reduce CSI to RSSI for sensing. If your pipeline only uses signal strength, you are leaving the mechanism on the table.
  2. Subcarrier selection matters. Not all subcarriers respond equally to a given motion. FreeDetector uses greedy selection of the most occupancy-responsive subcarriers. Feature extraction should use the full vector, learned attention, or selected indices — not a single arbitrary subcarrier.
  3. Time resolution is packet-rate. Each row in the CSI matrix arrives with one WiFi frame. At 100 packets/second, your Nyquist limit for motion is 50 Hz — fine for walking, marginal for heartbeat. CARM recommended ~800 samples/s for fine activity boundaries; ESP32 deployments typically run well below that.

The ill-posed recovery problem

Recovering body pose from CSI is fundamentally underdetermined. Person-in-WiFi (ICCV 2019) frames it explicitly: 9 antenna pairs × 30 subcarriers = ~270 scalar equations per frame to recover a high-dimensional skeleton. The system does not solve this geometrically — it learns segmentation masks and joint heatmaps from video labels. That is why pose estimation requires research-grade antenna arrays and labeled training pipelines, not a single ESP32 sniffing ambient traffic.

Where to go next