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I hope this is the right place to ask a radar related question, otherwise I would be grateful for a pointer to the correct forum.

I want to compute the angular resolution of a radar system but so far I have found different formulas and I am not sure which one to choose. I am also wondering why there is a range dependency in some formulas while anothers I found just assumes the angular resolution to be proportional to the 3dB-Beamwidth, see last equation below.

Further it would be nice to know, where the following formulas are coming from and what their main underlying assumptions are.

I know this might be a lot to ask, but a brief explanation would be great since all of these formulas are some kind of "rules-of-thumb" as far as I understand.

One formula I found here:

To start with, let us assume that we can build an antenna as large as necessary to meet our azimuth resolution requirement. The rule of thumb governing antenna size is
dazimuth ≈ λR/L
where, dazimuth = resolvable distance in the azimuth direction, λ = wavelength of radar, R = range, L = length of the antenna.

Here is another formula, I found here

S_A >= 2Rsin(Θ/2)
Θ = antenna beamwidth (Theta)
SA = angular resolution as a distance between two targets
R = slant range aim - antenna [m]

Another document I only have as a hard copy computes the angular resolution as:

dazimuth ≈ kappa * BW
where, dazimuth = resolvable distance in the azimuth direction, kappa = is a real valued constant between 1 and 2, BW = is the 3dB-beamwidth.

Edit: I want to model the angular resolution of a uniform linear array with drone targets flying at approx. 100kmh at low altitude above ground.

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    \$\begingroup\$ The first formula isn't angular resolution but resolution in meters. It depends on distance because the further away something is the wider the beam gets when measured in meters. You can draw the triangle and convert the linear and angular resolutions back and forth using the tangent function. \$\endgroup\$
    – user1850479
    Jul 3, 2021 at 16:20
  • \$\begingroup\$ ok, I see. Is the second formula a similar equation for the azimuth resolution in meters aswell? Is there a difference between the resolution in cross-range and angular resolution, i.e. is the first one given in meters and the second given in radians/degrees? \$\endgroup\$
    – sehan2
    Jul 3, 2021 at 16:44
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    \$\begingroup\$ Yes, the second equation is also solving for meters rather than degrees of angle. Not sure i understand the question about the difference between meters and degrees. \$\endgroup\$
    – user1850479
    Jul 3, 2021 at 17:28
  • \$\begingroup\$ The scenario envisioned by the 2nd equation is a rotating radar whose beam passes over two different objects (as can be seen from the picture). This is not an imaging radar. More like the radar you see on a boat or, I guess, in an air traffic control center. I believe the first equation is for synthetic aperture imaging radar. It is trying to help you size the aperture. \$\endgroup\$
    – user57037
    Jul 3, 2021 at 17:35
  • \$\begingroup\$ Can you describe what you want to accomplish with the radar system? Edit the question to include this additional information. Don't reply in the comment section. Are you trying to track birds in flight? Cars on the road? Aircraft? Boats? Detect incoming projectiles? Automatic target recognition? Give us some idea of the type of radar system and the information you need to extract from it. \$\endgroup\$
    – user57037
    Jul 3, 2021 at 17:40

1 Answer 1

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All three formulas are basically the same. The general relationship for azimuth resolution is range X beamwidth. In your first formula the beamwidth is approximated by L/λ (the size of the antenna in wavelengths). In the second formula, for small beamwidths, sin(Θ/2) reduces to Θ/2. Then the formula reduces to RΘ which is the same as the first formula. The third formula only uses the beamwidth and not range so it only gives the angular resolution. For azimuth resolution you need to multiply by range. Then the formula becomes the same as the first two except for the arbitrary constant kappa which appears to be an empirical estimate to account for characteristics of a particular radar.

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  • \$\begingroup\$ Thank you for your answer. Now it makes much more sense. I have one followup question. What is the difference between angular resolution and azimuth resolution? I seem to find both terms used interchangeably on different sites on the internet and I am not completely sure if I understand them correctly. \$\endgroup\$
    – sehan2
    Jul 3, 2021 at 20:38
  • \$\begingroup\$ Angular resolution is measured in degrees or radians and is independent of range. Azimuth resolution is measured in yards or meters and is proportional to range. Basically azimuth resolution is angular resolution multiplied by range. \$\endgroup\$
    – Barry
    Jul 3, 2021 at 20:59
  • \$\begingroup\$ Great thank you, now I got it. \$\endgroup\$
    – sehan2
    Jul 4, 2021 at 6:03

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