Antenna Array radius and DOA resolution

Hello. This may seem a dumb question, but I have worked a little with the other DOA estimation equipment (although it may have used a pseudo-doppler instead of a phase-coherent method as KrakenSDR does), and it did not require readjusting the antenna radius depending on the frequency. So is it possible (at least in theory), programmatically, to make Kraken DOA estimation resolution more precise on lower or the opposite, higher than 0.5 spacing multipliers to resolve ambiguities somehow? For instance, if my antenna radius is 1m (~128MHz), but I set the desired frequency to 446 MHz (~29 cm radius), I know that the antenna radius is actually 100/29 times bigger than it should be, and with that knowledge, I can adjust my DOA estimation, or at least provide +1 possible estimation with, let’s say, less certainty. I.e. I can assume that the wave has changed the phase 100/29 times (less, to be particular since the number of antennas is not even and there are no opposite ones) while traveling between the antennas and calculate DOA accordingly.
I hope you understand what I mean. The idea is not to re-adjust the static antenna array that is set on top of the 10m mast every time I want to change the frequency. Thank you

For pseudo-doppler you also need to adjust the radius in exactly the same manner. For both there will always be the hard limit of 0.5*lambda on the upper frequency for avoiding ambiguities. Then the limit on the lower frequency will be the resolution limit.

There is always a range of frequencies that a single radius will work decently for though. I suggest using the Excel calculator and calculating a radius that works for the frequencies you are interested in.

@krakenrf_carl , this question brings up something I have been meaning to ask, does the Kraken software / hardware measure the phase of arrival at each individual element and do calculations from that? Or are element sets combined in software as a phased array to form beams, and those beams cycled in virtual space? I realize those two questions are very similar.

Is there a theory of operations someplace that describes basic Kraken functions?

Thanks,

T!

I found this video about the different RDF methods to provide a helpful, high-level overview. An Introduction to Direction Finding - YouTube
Correlative interferometry starts at How correlative interferometry works if you want to skip the basics and other DF techniques.

The software receives 5 raw sets of IQ data from the Kraken, and makes phase comparisons between them in software, with CH0 being a reference. So it’s all done in software.

Does the software consider some inaccuracies in cables, dipoles, boom ends having ±5 mm distance to each other etc? I mean, maybe when the frequency is set, the software somehow makes a calibration (for instance the first antenna sends a signal, and the rest 4 antennas receive it, and software checks that the phase in antenna 1 should have been X knowing the antenna radius, but it was X+2 degrees, so during this session it will subtract 2 degrees on each DOA measurement from antenna 1)

Everything after the KrakenSDR is not included in the calibration, which is why the lengths and construction of the cables and antennas should be identical.

Including the antennas and cables in the calibration would be difficult as we’d need to pass noise through the antennas into the Kraken. Obviously it’s not legal in most places to broadcast wideband noise into the air though.

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Is legal issue of broadcasting noise the only problem, or there are some other issues in this idea of calibration?

Also you’d have to manually accurately position the noise source at at least one angle of the array. Possibly more to improve calibration.

So you’d be performing a new manual calibration on each frequency retune and startup.

EDIT: Actually it might be possible to isolate the antenna and cables calibration from the Krakensdr calibration with this method. But it would change when the array size changes, or is moved etc.

I’ve thought of the 1st antenna as a source and the rest 4 as receivers, then 2nd antenna as an emission source and the rest as receivers, etc.

Can it be done programmatically (in theory) via Kraken software? This kind of calibration/adjustment. Or KrakenSDR hardware can not emit anything?

The KrakenSDR hardware for regulatory reasons is physically incapable of transmitting anything, so that calibration method won’t be possible with the KrakenSDR as is. You would need to design some sort of external calibration circuit if you wanted to do that.

I have used, and designed pseudo-doppler systems. As long as the antenna distance is <.5 lambda, it will work. Unlike the correlative interferometry, the doppler is just looking at the simulated doppler phase, and different radius doesn’t affect that - it does affect the magnitude of the phase shift, which affects the accuracy, depending on the SNR.

Also, small errors in antenna placement may produce less AOA errors than with CI [I haven’t done the math on that]

This, I think, it has an advantage over correlative interferometry in not requiring a different data table for each antenna spacing, and probably in being less sensitive to small errors in antenna spacing.

The reason I am thinking about this is operational issues with antenna placement, plus it would be nice to switch frequencies radically (i.e. between ~121.5 and ~406.0xx) while using an array spacing that is optimal for the higher frequency while still providing useful, if less precise, DF"ing on the lower frequency.

Has anyone written pseudo-doppler code for Kraken/Kerberos?

Not aware of anyone having done this. I suppose it is possible, just by switching between each antenna in software.

But for CI, the array will also work if the antenna distance is <.5 lambda. The resolution just gets progressively worse the smaller the distance is. I believe the degradation in performance would be similar if not the same as with doppler.

Thanks. Yes, it would be possible.

Here is my understanding: with doppler, resolution isn’t really the way to look at it, since it doesn’t resolve multiple signals the way CI can. It is simply bearing accuracy of a single signal.

The accuracy is dependent on how well you can measure the phase of the pseudo-doppler modulation of the received signal. That ultimately depends on the SNR in the audio. Closer antenna spacing reduces the amplitude of the doppler signal, which in a PM receiver would be a sampled sine wave and in narrow band FM is more complex. Low pass filtering, or coherent integration of the modulation frequency, leaves you with a signal whose phase angle can be measured by zero crossing time. I did this years ago using a little 8 bit MCU and it was excellent.

So with high SNR in the audio, you can have antennas relatively close together and get good accuracy.

You can increase SNR by “spinning” the antennas faster, thereby raising the amplitude of the audio phase shift signal. Averaging bearings, after throwing out ones with a low accuracy, can help.

Obviously, multipath or multiple signals are a problem, and the CI is better at resolving those, I believe. And, parasitic effects may limit how close you can put antennas.

Note that you can change the antenna spacing without needing recalibration. Inaccuracies in the antenna placement are, I think, better tolerated than with CI, but I’m not certain.

Anyway, a doppler option might be useful.