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I wanted to clarify that,

  1. If an ULA has certain crab angle with the velocity direction, then it can be used to estimate both elevation and azimuth angles of the target, is that right?
  2. If that's correct, what is a practical value of crab angle which is used and how much range of azimuth and elevation angle can it cover?

My doubt stems from the fact that is used in a paper, where they have considered an ULA and then while calculating the normalized spatial frequency (nsf), have used azimuth and elevation angle. If ULA can estimate only 1 direction, why did they take into consideration both angles while calculating the nsf.The excerpt is added below with the part highlighted.

I have added a link to the paper End-to-End Moving Target Indication for Airborne Radar Using Deep Learning

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No, a ULA can only measure angle in the dimension it has degrees of freedom in (a 1D array can only measure angle in 1 dimension). If it's a vertical array, it can measure elevation angle only, and if it's a horizontal array, it measures azimuth angle only.

If a 1D array is oriented somewhere in between horizontal and vertical, it can still only measure angle in 1D relative to its orientation (i.e., "azimuth" relative to the array axis). You need a 2D array to measure angle in 2 dimensions.

Edit

In answer to ananya's comment, it is true that when computing the signal phase difference between 2 channels, both azimuth and elevation angles are taken into account. This is because what the array really measures is a projection of the received signal along the array axis. Therefore the phase difference between 2 adjacent channels can be expressed as $ d \cdot \cos(\phi) \cdot 2\pi/\lambda = d \cdot \cos(\theta) \cdot \cos(\psi) \cdot 2\pi/\lambda $ (where $\psi$ is the elevation/depression angle).

So in reality the angle that a 1D array can measure is the angle $\phi$ (which can be expressed in terms of $\theta$ and $\psi$). In terms of phase, it can't tell the difference between two signals arriving at angle $\phi$ relative to the array axis. Stated another way, all signals arriving from directions specified by the surface of a cone with the array axis as its axis and opening angle $\phi$ will appear identical to the array in terms of phase.

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    $\begingroup$ My doubt stems from the fact that is used in a paper, where they have considered an ULA and then while calculating the normalized spatial frequency (nsf), have used azimuth and elevation angle. If ULA can estimate only 1 direction, why did they take into consideration both angles while calculating the nsf. I have added the excerpt in my question $\endgroup$ Commented Feb 5 at 13:50
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    $\begingroup$ @ananya You are conflating what a steering vector fundamentally is with doing actual angle of arrival estimation. You can do some kind of angle estimation with the former, but steering vectors are not usually introduced for this purpose. They are instead first typical introduced to show how to steer a beam, and then we can talk about what kind of angle estimation may be necessary. $\endgroup$ Commented Feb 5 at 16:46
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    $\begingroup$ @ananya I see what you're talking about, and I have updated my answer. See if that helps. $\endgroup$ Commented Feb 23 at 2:09
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In general, no, a ULA cannot unambiguously resolve azimuth and elevation. A single linear aperture only gives you the projection of the signal's direction on to the ULA's axis. Thus, it can only resolve one angular dimension.

If you can provide a link to the paper, I may be able to give you better insights, but as far as I'm aware, the only way to get azimuth and elevation with a ULA is to move the ULA in such a way that it synthesizes an aperture in the second dimension perpendicular to the ULA. But, with this in mind, you would need multiple snapshots to form the geometry, not just a single snapshot. There's a variety of ways in which this could be done, but if there's a way to do it in a single snapshot, I would need to see the paper to give you insights.

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  • $\begingroup$ I have added a link to the paper in my original post $\endgroup$ Commented Feb 5 at 16:05
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    $\begingroup$ @ananya this paper is presenting everything in 3D geometry because it's good to have proper notational conventions in place when you extend from 2D to 3D. However, this paper is just working in angle-Doppler, not angle-angle-Doppler. The purpose of including the crab angle is that it can spread the clutter ridge in angle-Doppler space, or tilt it in some way. The normalized spatial frequency is correct in terms of az and el angles. It's important to recognize that the phase shift across the ULA will only be proportional to one of those angles. $\endgroup$ Commented Feb 5 at 17:13

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