Linear Array (ULA) and DOA

#1

Hello. I am trying to set antennas into Linear Array (ULA) in order to improve accuracy, but I can not quite comprehend how to read the DOA angles correctly. I have created this beautiful image, which shows the linear antenna and 4 measurement cases:

  1. Test1 - the radio is 45 degrees relative to the array line
  2. Test2 - 90 degrees
  3. Test3 - 135 degrees
  4. Test4 - 180 degrees (the radio is on the line with the array)

diagram-ula
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What would be the possible DOA in each case? Is it:

  1. 315 or 225 degrees?
  2. 360 or 180 degrees?
  3. 45 or 135 degrees?
  4. 90 degrees? Or 90 or 270 degrees?

I’ve done a similar test, but got ambiguous results:

photo_2023-02-15_18-13-39
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photo_2023-02-15_18-13-42
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I have noticed that the signal is mirroring over the line 90*-270*, i.e. the Kraken is not sure where it is - at the front or behind the array (which is fine). But is line 90-270 the line of the array? I.e. is 90* DOA mean that the radio at the left from the antenna array, 180* - at the front (or behind), and 270* - at the right?

Thank you

#2

It’s really up to you if you want to redefine the angles, but I think it’s best defined as -90 to 90 (aka in full 360 deg, 270 to 0 to 90).

So in the compass display 0 deg should be orthogonal to the array.

The mirroring line is 270 - 90.

A signal direction orthogonal to the array would produce two results, 0deg and 180 deg.

A signal showing 45 deg would also show 135 deg.

#3

Thank you for confirming my theory :slight_smile: Today, I’ve done some extra tests that confirm it as well:

Test 1

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Test2

photo_2023-02-20_21-26-45
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Test3

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Test4

photo_2023-02-20_21-26-56
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I believe the probability of output being 45* vs 135* is the same, right? Also, are there any corner cases with the DOA output that may need knowing? Thank you

#4

Yes the two solutions are equally valid. If you have some prior knowledge about the signal direction, you might be able to rule one out.

Alternatively, if are driving around you’ll find that the true angle will converge, whilst the false angle will diverge. So in time you will get the solution.

But ULA on a car could be slower to converge compared to UCA. Since there is only a limited range of usable angles. You’ll see that for signals coming from the +90 / -90 ends of the array (like in Test 4) you’ll get very poor results, so only mostly orthogonal signals will work well.

This is because the array looks very tiny from the sides so you loose aperture. With the worst case being that the array looks like a single element from the +90 / - 90 degree angles.

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