# Welcome!
# Audio propagation analogy I like to introduce my subject with a small analogy.
Let the speaker emit audio waves towards the audience.
Let us focus on one of the listeners.
In free space, sound arrives in a direct path.
But what if we have a wall?
Like in a tunnel, the sound waves will reflect on this wall, and reach the listener a second time, with a different delay and volume.
Of course, we can have many walls.
Or obstacles that obstruct some paths.
What if the target changes?
Of course, the same logic can be applied to radio networks.
What we did, if actually called Ray Tracing (RT)
Table of contents
RT and EM Fundamentals
We are interested in broadcasting waves from a BS
In a simplified model, the BS emits waves isotropically.
Using Huygen's principle, we can decompose a wave front into a series of new wave sources.
Each source now broadcasts waves, each with a fraction of the original energy
RT considers each ray path individually.
In a constant speed space, ray paths are linear.
Maybe, we reach some obstacle.
If we decide to apply reflection.
We can do that for very complex scenes and many paths.
Example of tracing paths in 3D Urban scene.
In Radio-propa., we have two quantities: E and B. Both are vectors (3D) and complex. But, only 2 components are needed!! Hence 2x2 dyadic matrices. The most used quantify if E, from which we usually determine the received power (plane wave, lossless medium).
By superposition, E (and B) can be computed by summing the contribution from each path.
Where C accounts for: - D the dyadic coefficients for polarization; - alpha the path attenuation; - and the path delay.
The basic RT pipeline is as follows.
Next pipeline step.
Next pipeline step.
Next pipeline step.
Next pipeline step.
RT example in a city (Munich).
Then we perform RT.
From paths, we can compute the coverage map.
Or reuse paths to compute the CIR.
RT's implementation presents many challenges, mainly the exponential number of paths we can test.
Order = 0
Order = 1
Order = 2
Order = 3
Order = 4
Another challenge is the total path coverage versus the order and types of interaction considered.
If we add diffraction.
Or if we add scattering.
Listing RT applications, with graphics being the most active community in DRT.
Listing other channel modeling methods. RT provides a good trade-off between accuracy, speed, and interpretability of the model. We currently mainly use RL, a variant of RT, which we will describe later.
Let us motivate this thesis subject.
Recall the example from before (RL). When launching rays, most of them will never reach the UE.
Let's go back to our first example.
Only one ray reaches UE.
But what if UE was slightly off?
You could create a larger 'inclusion' sphere.
Or launch more rays.
Not very efficient!
How to exactly find paths?
Let's introduce the Image Method.
Checking LOS.
Computing the first image.
Computing the second image.
Computing the second coordinate.
Computing the first coordinate.
RL - RT comparison
What if we want to simulate something else than reflection on planar surfaces?
Treating each interaction individually.
Adding angles
See how MPT is applied in 3D.
RL - RT comparison
Differentiable Ray Tracing part!
How to compute derivatives?
Our problem is only piecewise diff. and continuous.
Constraints about our approximation.
Examples.
Let's animate alpha.
Thanks to that, and other things, we can create a fully DRT!
We can create an optimization problem.
Let's see how it converge. Actually, tests have shown: 1.5 to 2 increase in success rate, where 92% to 98% of already successful runs still converge with our method.
Now, we will take a look at the status of work.
Let us review the initial goals.
Updated Gantt diagram.
Let us review the work achieved so far.
Let us review the work achieved so far.
Past and future collaborations.
Let's conclude this.
Questions time!
ML structure.
Diffraction.
RT runtime.
Keller cone.
Edge diffraction.