Three validation stages are applied before any combined estimate is accepted. The pipeline is designed to reject weak, inconsistent, or physically implausible measurements rather than combine bands optimistically.
Harmonic-Alias-Assisted Acoustic Ranging on Commodity Smartphone Hardware
AliasProbe studies whether harmonic alias energy produced by stock smartphone audio hardware can be validated and coherently combined with the fundamental band to sharpen acoustic range response without hardware modification.
When a smartphone emits a 16–20 kHz chirp, speaker nonlinearity can generate harmonic energy above the nominal audio band. A portion of that energy folds through the 48 kHz sampling process into an 8–16 kHz alias band. If that band is shown to share the same propagation delay as the fundamental, the two can be combined to increase usable bandwidth and reduce matched-filter mainlobe width.
Three validation stages are applied before any combined estimate is accepted. The pipeline is designed to reject weak, inconsistent, or physically implausible measurements rather than combine bands optimistically.
The alias band is evaluated for detectability above the guard-interval noise floor. Split-half reproducibility is then checked by comparing independently averaged odd- and even-chirp subsets.
A generalized likelihood ratio test determines whether the fundamental and alias bands are consistent with a shared time of flight. If the estimated delays diverge, the measurement is rejected.
The surviving bands are combined using β-weighted generalized cross-correlation over the full 8–20 kHz aperture. Performance is then checked independently on held-out odd and even splits.
Held-out validation is central to the method. Odd and even chirp cycles are processed independently under the same acoustic setup; if sharpening does not reproduce across both partitions, the measurement is rejected.
Early experiments showed that a textbook analytic down-chirp was not an adequate reference for the alias-band matched filter. Correlation remained near zero despite visible energy in the aliased region.
The issue was that the observed alias is not a continuous-time idealization. It is the result of discrete-time squaring, hardware filtering, and ADC folding, all of which affect phase structure.
| Template | Peak ρ | Result |
|---|---|---|
| Ideal analytic down-chirp (continuous-time) | < 0.01 | × |
| Time-reversed fundamental chirp | < 0.01 | × |
| Windowed analytic ± phase offset grid search | 0.012 | × |
| Discrete x²[n] → bandpass filter | > 0.8 | ✓ |
The working reference is constructed directly from the transmitted samples:
where x[n] is the transmitted chirp sampled at 48 kHz. This construction matches the actual alias-generation mechanism and yields a reference aligned with the measured aliased signal.
All measurements were collected on one iPhone 15 Pro using the stock 48 kHz audio path and no external sensing hardware. Twelve hardware runs were attempted, and four passed all validation stages.
| Runs attempted | 12 |
| Runs accepted (all 3 gates passed) | 4 (33%) |
| Confirmed held-out range | 2.08×–2.46× |
| Conservative reference (Run 1) | 2.08× |
| Theoretical ceiling | 3× |
| Acquisition time | ~15 s |
| Processing time | <2 s on-device |
| Total per measurement | ~17 s |
Run 1 is the conservative reference case because its fundamental mainlobe width was already close to the 4 kHz theoretical baseline. In that run, the width decreased from 8.4 samples to 4.0 samples, corresponding to held-out sharpening of 2.08× and 2.10× across the two splits.
Run 8 reached 2.46× and 2.38×, but its fundamental baseline was broader than the nominal theoretical minimum. That makes it a stronger empirical result, but a weaker anchor for conservative interpretation.
Eight of twelve runs were rejected by the validation pipeline. The rejected cases fell into a small number of recurring categories:
Accepted runs consistently required strong drive, clean geometry, and substantial suppression of direct-path interference.
The alias band originates from speaker nonlinearity. When a 16–20 kHz chirp is driven through the speaker, second-harmonic energy can be generated in the 32–40 kHz range. The underlying identity:
At a 48 kHz sampling rate, frequencies above the 24 kHz Nyquist limit fold back into the recorded band. As a result, energy in 32–40 kHz appears after sampling as an aliased 8–16 kHz down-chirp.
Because this aliased band is derived from the same transmitted signal, it can carry the same propagation-delay information as the fundamental. The central question of AliasProbe is not whether the band exists in principle, but whether it can be validated well enough to support defensible coherent combination.
For matched-filter ranging, mainlobe width scales inversely with bandwidth. The fundamental-only system spans 4 kHz, while the combined aperture spans 12 kHz:
In practice, the achieved gain is lower because alias-band SNR, multipath, template mismatch, and phase instability limit how closely the hardware approaches the ideal case.
This is an early hardware study with a small accepted sample count. The present results support range-response sharpening claims, but not yet broad generalization.