Say I have two magnetic loop antennas oriented perpendicularly, such that one antenna has a null facing east/west, while the other has the null facing north/south. Each of these antennas is connected to a receiver with an I/Q mixer, and then I feed these I/Q signals to a software defined radio for demodulation and processing.
The goal here is to implement a goniometer (see fig.2) (another description with Adcock antennas) in software, for direction finding or spatial filtering. By combining the antenna signals in some ratio, it's as if I have a single magnetic loop antenna which I can virtually rotate to any angle. But if I can do this in software, I can have many such spatial filters at one time, or make spatial waterfall displays, or other such cool stuff. Think of it as Ambisonics for RF.
This requires four signals: I and Q for each antenna, times two antennas = four signals.
Here's the question: is it practical, through some electric or mathematical manipulation, to simplify this to three or fewer signals I'd need to process? It seems to me that an incoming wave will have some frequency and amplitude, information already contained in just one I/Q pair. My second antenna adds additional information by capturing the rotation of the plane of the received wave front around the up-down axis. Does this require an additional two signals?