Potential inaccuracies in corner reflector simulation

[Luke-Jacobs]

Hello, my name is Luke and I am a PhD student researching remote sensing. I have been using Sionna to simulate radar, and I have been running some experiments trying to calibrate Sionna's raytracing output to my radar's output. This involves scaling the energy of Sionna paths by a calibration factor so that for the same object, the CIR of Sionna and my radar are closely matching. It is common to use an object of known RCS- like a trihedral corner reflector- to perform this calibration, so I have designed a corner reflector object in Blender and have simulated it in Sionna. However, I have noticed that Sionna seems to drastically underestimate the energy reflected by the corner reflector.

I have attached code that simulates the CIR of a large trihedral reflector (each side 5 cm length) and a small metal plate (5 cm side length).

Corner reflector at 122cm distance with 6.5 GHz radar:

Metal plate at 122cm distance with 6.5 GHz radar:

According to RCS equations of these objects, the trihedral should reflect more energy than the metal plate, but in simulation, much less energy is reflected (seen by a smaller corner reflector peak in the CIR plot):

Energy of plate peak: -46.40 dB (8.33 ns)
Energy of corner peak: -88.78 dB (8.67 ns)

This has made me wonder if this particular geometry is not well simulated by raytracing and/or the accuracy of path energy decreases as the number of reflections increases. I would be great to know if this is true (and if there are other known geometries that Sionna struggles to simulate) or if I have setup my simulation code incorrectly.

Here is a picture of a sample of rays scattering from the corner reflector (in my full simulation I used 2M rays) for visualization:

(I set the scattering coefficient of the PEC material to 1.0 and the scattering pattern to directive with an alpha parameter of 20 because I was not getting any specular reflection paths from the corner reflector.)

Any help would be appreciated! I have attached my code and 3d models. Thank you Sionna developers for creating this tool and its excellent documentation.

files_for_reproducible_code.zip

[jhoydis]

Hi @Luke-Jacobs,

Without having looked at your code, I suspect that what is happening is the following:

1. You can only get a specular reflection if you can construct a propagation path for which the incoming angle with respect to the surface normal equals the outgoing angle with respect to surface normal. In the way that the cube is oriented, you will likely not get any such path. The same holds for the metal plate, whose normal seems however pointing more towards the transmitter and receiver.

2. For diffusely reflected paths, this constraint does not hold. However, the strength of each path depends on the chosen scattering pattern. As your pattern is very directive, only paths that are close to a specular reflection will convey useful energy. That explains why you get more energy from the metal plate than from the cube.

A first sanity check would be to test what happens if you pick the Lambertian pattern (which radiates energy uniformly in all directions). In this case, only the cross section should matter and the cube consequently reflect more energy.

You could also play around with the orientation of the cube which should have a very strong impact on the received energy if you use a directional scattering pattern.

[Luke-Jacobs]

Hi Jakob,

Thanks for the reply. It is hard to see from the screenshot I took, but the reflector is actually a corner reflector like below and not a cube:

I wasn't expecting to get a purely-specular path from the corner reflector, since it never reflects rays exactly back towards the radar. It reflects them back at the same angle, but at a position offset from the initial incidence point:

I was expecting to get some energy reflected back to the radar by scattering, however, since the lobe in the directive pattern has some width to it and therefore does not need to satisfy the exact-angle constraint as you said.

I think the problem might be caused by how Sionna computes the fields of 3rd-order reflection paths. Is there a kind of weighting that happens at the field computation stage that weighs lower-order paths with higher weight than higher-order paths? I am expecting that most of the energy reflected by the corner will be in 3rd-order paths, since these paths are the ones that retroreflect. This is a diagram of it with and without the scattering lobes added:

Ideally, Sionna would model the first two reflections as specular and the last as scattering to return the path to the receiver.

I changed the scattering pattern to Lambertian, but it gave an even lower return than with the Directive pattern, probably because it attenuates 3rd-order paths more than the Directive pattern.

Hopefully there is a solution to this since there are many trihedral corner reflectors in indoor environments (like corners of rooms). Let me know if this makes sense and if you have any thoughts.

[mlouielu]

I think the problem comes from the scattering coefficient, essentially corner reflector has two reflections, making the energy dispersed after diffuse scattering.

I've tested it with a isotropic scattering pattern, where:

• Energy is spread equally over hemisphere (2π steradians)
• Probability of any specific direction = 1/(2π)
• Each reflection gets scaled by 1/prob = 2π

So if we calculate the energy spreads out in a diffuse scattering case (.scattering_coefficient=1):

Corner Reflector (Double Reflection):

Initial field: E₀
After Face1: E₁ = E₀ × Jones₁ × 2π
After Face2: E₂ = E₁ × Jones₂ × 2π = E₀ × Jones₁ × Jones₂ × (2π)²

Plate (Single Reflection):

After Plate: E₁ = E₀ × Jones₁ × 2π

That means, the amplitude scaling creates a 31.9 dB penalty compared to single (20×log₁₀((2π)²) = 31.9 dB)

I've reconstruct your code/case with isotropic scattering pattern (see appendix) and get a similar result to analytical value when .scattering_coefficient=1:

• Corner Reflector: range-Doppler peak: -14.43 dB
• Plate: range-Doppler peak: 18.10 dB
• Difference: 32.53 dB (similar to what we said above)

But, if we reduce .scattering_coefficient to 0.1 ($R=\sqrt{1-S^2} = \sqrt(1-(0.1^2)) = 0.995$ (39)), it gives us 99% of energy to specular reflection, and 1% to diffuse scattering, which suits more to the corner reflector case, thus we get:

• Corner Reflector: range-Doppler peak: 11.92 dB
• Plate: range-Doppler peak: 11.98 dB

S=0.1, α=0	S=1, α=0
Have specular reflections in it (purple)	No specular reflection

Moreover, if we rotate the corner reflector and plate, it then shows the corner reflector property!

α (rad)	Corner Reflector (dB)	Plate (dB)
0.0	11.92	11.98
0.1	6.5 dB	-26.22
0.2	-22.34	-38.85
0.3	-23.09	-39.39
0.4	-18.83	-24.82
0.5	-24.67	-40.31

Also, in the reference [Degli-Esposti07], they concluded that:

Besides, the optimum scattering coefficient values are of 0.05, 0.2, and 0.4 in the three considered topologies, respectively. Being the latter topology quite representative of simple, brick-wall suburban buildings, we can infer that is a realistic value for field prediction in suburban areas, in agreement with previous work [11]-[13].

So I think, pick a smaller S to start and then compare/calibrate with your HW measurement should works for you.

---

Appendix

@sionna.rt.radio_material.scattering_pattern_registry.register(name="iso")
class IsotropicPattern(ScatteringPattern):
    r"""
    Perfect isotropic scattering pattern that distributes energy uniformly
    in all directions, completely independent of incident direction.

    This pattern treats every surface as a perfect diffuser that scatters
    energy equally in all directions over the hemisphere.
    """

    def __init__(self):
        """
        Initialize the isotropic scattering pattern.
        No parameters needed - energy is always distributed uniformly.
        """
        # Normalization factor for hemisphere: 1/(2π) for energy conservation
        self.normalization = 1.0 / (2.0 * np.pi)

    def __call__(self, ki_local: mi.Vector3f, ko_local: mi.Vector3f) -> mi.Float:
        r"""
        Compute the scattering pattern value.

        :param ki_local: Direction of incident wave (IGNORED - not used)
        :param ko_local: Direction of scattered wave (IGNORED - not used)
        :return: Constant scattering pattern value (uniform in all directions)
        """
        # Return constant value regardless of any directions
        # This creates uniform scattering in all directions
        return mi.Float(self.normalization)