# Angle of arrival

Angle of Arrival measurement, or AoA, is a method for determining the direction of propagation of a radio-frequency wave incident on an antenna array. AoA determines the direction by measuring the Time Difference of Arrival (TDOA) at individual elements of the array -- from these delays the AoA can be calculated.

Generally this TDOA measurement is made by measuring the difference in received phase at each element in the antenna array. This can be thought of as beamforming in reverse. In beamforming, the signal from each element is delayed by some weight to "steer" the gain of the antenna array. In AoA, the delay of arrival at each element is measured directly and converted to an AoA measurement.

Consider, for example, a two element array spaced apart by one-half the wavelength of an incoming RF wave. If a wave is incident upon the array at boresight, it will arrive at each antenna simultaneously. This will yield 0° phase-difference measured between the two antenna elements, equivalent to a 0° AoA. If a wave is incident upon the array at broadside, then a 180° phase difference will be measured between the elements, corresponding to a 90° AoA.

A current application of AoA is in the geodesic location or geo-location of cell phones. The aim is either to comply with regulations that require cell systems to report the location of a cell phone placing an emergency (i.e., 911) call or, other, to provide a special service to telle the bearer of the cell phone, where he is. Multiple base stations would calculate the AoA of the cell phone's signal, and this information would be combined to determine the phone's location on the earth.

AoA is generally used to discover the location of pirate radio stations or of any military radio transmitter.

In submarine acoustics, AoA is the method to localize objects with active or passive ranging.

In optics, AoA is considered from the perspective of interferometry.