WiFi case study
Measured indoor signal strength follows the exponentiated Ornstein–Uhlenbeck model, and fast reversion decides which search policies lead.
The data
The Feng, Nguyen and Luo (2024) dataset covers a 92 by 15 metre floor on a 0.6 metre grid. It has 642 reference points, 120 samples each, and 13 access points.
The model holds
After detrending by a path-loss model, the residual signal strength along traces is close to Gaussian. Its spatial correlation is exponential with a length of about 11 grid units, 6.6 to 7.1 metres, plus a short-scale component carrying roughly half the variance.
Two independent implementations, with different detrending, agree. This matches the classical shadowing model of Gudmundson (1991).
Replaying the policies
The model was fitted on 25 training traces, and 125 search episodes were replayed on 25 held-out traces. The payoff is the exponentiated signal, the objective the policies optimize.
| policy | mean payoff | gain over the incumbent |
|---|---|---|
| incumbent | 2.596 | |
| two-shot rule | 3.184 | +22.6% |
| three-shot rule | 3.442 | +32.5% |
| knowledge gradient | 4.224 | +62.7% |
| equispaced probes | 4.409 | +69.8% |
Why far probes lead here
The correlation length of about 11 grid units is short against traces of 15 to 92, so far probes are nearly fresh draws. For small correlation $\rho$ the exact formulas give a revisiting window
$$\big(b_-,\ e^{2\Theta}\big) \;\to\; \big(0.586\sqrt\rho,\ 1 + 2\rho\big),$$and an interior premium of order $\rho(1 - b^2)$. The interior option's edge is of order $\rho$, while the variance of a fresh draw is of order one.
Fast reversion therefore makes measuring far away and taking the best optimal to leading order. Equispaced probing and the knowledge gradient lead because the regime says they should.
Refinements
- Report gains conditional on the incumbent's standardized value and position, where the phase diagram predicts the three-shot rule beats far probing.
- Add a per-trace random intercept for the elevated mean of detected traces.
- Model the trace boundary, since fleeing to infinity maps to the far end of a short trace.
Code: casestudy/wifi/.