# Can I/Q signals from two perpendicular antennas be simplified to any less than 4 signals?

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?

I/Q processing is a useful abstraction for processing radio signals, particularly when you're interested in phase information for things like separating the sidebands or demodulating FM/PM. As such, it is primarily a software abstraction; they don't normally exist as separate physical signals except perhaps inside an FPGA or other signal-processing chip. You'll have just one cable from each antenna to the signal processing board.

What do you hope to gain by trying to invent a different abstraction?

In general, you will want the "full" signal from each antenna, because you don't know which direction a signal will be coming from, and either antenna could be completely nulled out.

• What I hope to gain is a reduction in the number of ADC channels I need, and the subsequent processing. If I can simplify the signals before or immediately after the mixer with some simple analog electronics, it would be a big win in terms of the amount of data I need to move and process. – Phil Frost Jul 3 '13 at 12:30
• But aren't you using RF front-end chips that integrate all of that anyway? In order to get a meaningful answer to this question, I think you need to provide more details about the RF band(s) you're working in and the nature of the signals (e.g., modulation) that you're receiving. – Dave Tweed Jul 3 '13 at 13:20
• The RF front-end is a very simple IQ mixer that works over HF, going into a PC audio interface. (Actually the mixer works beyond VHF, but I have antialiasing filters only up to HF). I can't tell you what signals or modulation are of interest, because the whole point of an SDR is to delegate that responsibility to the software. My concern is just the hardware. – Phil Frost Jul 3 '13 at 13:28
• You can move from IQ to a single-signal scheme by doubling the sampling rate and switching to a non-zero center frequency, however this is the same amount of data, just collected from one faster converter via a different circuit than collected from two. Except where the limits of available/affordable converter technology are being pushed, it's usually a decision made based on what sort of circuit seems easier to build well. – Chris Stratton Oct 31 '13 at 15:06

You need all four signals.

I/Q processing is there to keep you from getting shafted by phase cancellation between your received signal and your local oscillator (LO) when you heterodyne to baseband.

Consider: Assume your LO and your received signal are on the same frequency, but have a phase offset. Mixing the two results in an output signal, with and attenuation from phase cancellation that is proportional to $(1 + \sin \omega)$, where $\omega$ is the phase offset angle in radians. If the two signals are 180 degrees out, they cancel completely.

I/Q processing uses two mixers and an LO that emits two signals, on the same frequency but 90 degrees out-of-phase. If the received signal is 180 degrees out from one LO signal, it will only be 90 degrees out from the other, and that side of the I/Q pair will still have output.

As a freebie, you get phase information. The degree of cancellation on the two signals tells you the exact phase angle of the incoming signal against your LO.

This is EXACTLY the same principle as your two loop antennas, rotated 90 degrees. If the signal you are interested in is on the null from one antenna, you still get signal from the other antenna, and now you know where the signal is coming from.

That's why you do full I/Q processing on both antenna signals, which means you need all four signals.

• It seems to me that the phase of a signal, and it's heading, are orthogonal. By having two I/Q pairs, I have the phase information twice. Put another way: with one antenna there are two degrees of freedom (phase & amplitude, or the Cartesian equivalent, I & Q). If I add a heading, that's just one more DOF, so why would I need two more signals? – Phil Frost Oct 31 '13 at 14:32
• Untrue. You need both I&Q to differentiate positive and negative frequencies (unless your system represents more bandwidth than your filters permit to be present), and you need this from each antenna to determine spatial information. Of course, if you don't care about the possibility of getting confused should you get similar signals at mirror image frequencies displaced from the center of your bandwidth, then you can contemplate throwing away some of the information, perhaps from one antenna only. – Chris Stratton Oct 31 '13 at 14:52
• Fundamentally, this answer is a bit misleading - I&Q aren't need to simply give "phase information" relative to the LO (that you can find out in the simple sense from either by itself) but to differentiate positive and negative frequencies of the same magnitude - those above the LO or those below it. A non-IQ system has to be built with filters such that only one of those possibilities can be meaningfully present, allowing a downstream analysis to safely assume that a frequency is positive or negative. – Chris Stratton Oct 31 '13 at 15:04

If both antennas simultaneously received a direct signal from the same source, the two IQ pairs (four numbers) would would include redundant information, since one could define three numbers, phi, r1, and r2 such that

i1 = cos(phi) * r1
q1 = sin(phi) * r1
i1 = cos(ph2) * r2
q1 = sin(ph2) * r2


In practice, however, there's no guarantee that signals will only arrive via a direct path. It's possible that an antenna may receive reflected signals as well. Imagine that the transmitter and receiver are placed so that a direct signal is blocked, but reflective surfaces exist on either side; a signal reflected off one side will arrive at the receiver from a direction perpendicular to that of a signal reflected off the other. Depending upon the exact distances, the signals reaching the antennas could have any possible phase relationship. While it might be advantageous to determine a couple of parameters phi1 and phi2 and then compute a master output signal as:

net = (I1*cos(phi1)+Q1*cos(phi1))*cos(phi2)+(I2*cos(phi1)+Q2*cos(phi1))*sin(phi2)


Determining what the parameters phi1 and phi2 should be is apt to be difficult unless one has all four IQ signals to work with.