Geometry-Coded Multi-Source Acoustic Direction Finding with a Pseudohyperboloidal Receiver
Year: 2026
Type: preprint
Abstract: Localizing several simultaneous sound sources becomes difficult when their directions are close, because the measured acoustic fields become strongly correlated before the inverse problem is solved. Conventional systems address this mainly through larger apertures, more sensors, calibration, and digital signal processing. Here we investigate a different approach: using the passive boundary itself to transform the incident field before measurement. We use the term Geometric Wave Engineering (GWE) for this geometry-first strategy. GWE does not require a new acoustic equation or an exotic material. Instead, it asks whether a deliberately designed boundary can act as a passive analogue preprocessor that converts source direction into a more distinguishable complex pressure pattern. The test geometry is a second-order pseudohyperboloid (PHB-2), generated from a radially displaced hyperbolic meridian. For a restricted inherited meridional ray family, this geometry possesses an exact focal-contraction law. The law is used only as an analytical design anchor and to identify a candidate sensing manifold; finite-frequency acoustic behaviour is then tested independently. The central hypothesis is that PHB geometry can reorganize the acoustic forward operator so that nearby source directions become more separated in complex amplitude-phase state space. This is evaluated using planar scalar-wave calculations, full 3-D scalar-pressure FDTD, and a frequency-domain meridional finite-element model with azimuthal reconstruction. Exact PHB is compared with close volume-matched perturbations, a smooth volume-matched control, broader deformations, and a conventional circular array. The calculations show that directional information can increase even when pressure amplitude does not. In the strongest cross-discretization two-source benchmark with known source count and on-dictionary directions, exact PHB correctly recovers 201 of 220 source pairs (91.36%), compared with 78 of 220 (35.45%) for the smooth matched control. For the closest predefined pair, separated by 0.483821° on the unit sphere, recovery is 77.5% versus 10.0%. The results support a bounded but testable conclusion: within the examined family, a PHB-based passive boundary can reorganize the acoustic state space and substantially improve the separability of close simultaneous sources. The study does not establish universal optimality of exact PHB. Unknown source count, arbitrary off-grid directions, realistic losses, reverberation, and experimental hardware remain open validation problems.
Author: Vladimir Khaustov
Language: English
Subfield: Signal Processing
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7215716505
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