I just coined the term "field antenna". It is by analogy to the lightfield camera or the soundfield microphone. Essentially, it is an antenna that captures not only the strength of an RF field, but also the direction of it.
Of course, these antennas already exist in forms, such as phased arrays used for radar, or four-square antennas popular on the lower bands. However, I have a somewhat different use case in mind: I want it to work at HF, for receive only, and I don't want to implement the phasing with a fixed network (or maybe a few switched networks) as in the four-square antenna. Instead, I want to perform the phasing in software.
One possible application: listening to radio in stereo, with the sound heard corresponding to the direction from which the signal was received, a "wetware rotator" of sorts.
Now, the usual way to doing this processing is to decompose the signal into circular harmonics. These are like spherical harmonics, but in two dimensions (circles) instead of 3 (spheres). For the sake of simplicity I'm stopping at the first harmonic (first-order), so I will have, perhaps after some processing, three signals:
- an omnidirectional signal (0-th order)
- a figure-of-eight pattern aimed East-West
- a similar figure-of-eight, but aimed North-South
Described mathematically, I'm looking for the responses in azimuth defined by:
$$ \frac{1}{\sqrt{2\pi}}, \frac{\cos \theta}{\sqrt{\pi}}, \frac{\sin \theta}{\sqrt{\pi}} $$
or described graphically:
Now here's the question: how might one realize such an antenna? Remember the antennas need not actually have these responses: they might have other responses from which these responses can be calculated.