A single antenna can hear a signal but not tell WHERE it came from. Put two a known gap apart and the wave hits one a hair before the other — that phase difference IS the bearing to the source. It’s how radio direction-finders hunt a transmitter and how a phone reads an ultra-wideband tag’s direction. Slide the source around and watch the phase tilt.
Angle-of-arrival from a two-element array: a plane wave from bearing θ reaches antennas spaced d apart with a path difference d·sinθ, hence a phase difference Δφ = 2πd·sinθ/λ. Measure Δφ and invert: θ = arcsin(Δφ·λ/2πd). One array gives a bearing (a line of position); cross two bearings and you have a fix. Spacing d ≤ λ/2 avoids ambiguity. A fail-loud self-check throws unless the recovered bearing matches the true one. ◆ real array signal processing, node-verified.
A clean two-element phase-interferometer (the exact Δφ↔θ relation); real direction-finding uses many elements (beamforming/MUSIC) for accuracy and to break the front/back ambiguity of a pair — the phase-difference-is-bearing mechanism is exact.