# Welcome!
Let's start by presenting myself quickly!
Disclaimer
Ray Tracing's ABC
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.
# Tracing paths We now use TX/RX.
Order = 0
Order = 1
Order = 2
Order = 3
Order = 4
# In a previous work we presented a method for tracing paths.
FPT
MPT
See how MPT is applied in 3D.
# DRT
We are often interested on computing the received power as a function of the position.
Placing 'camera' on top X-Y view. This gives us a very nice overview of what for call the 'coverage map'.
Moving RX positiong to find the best position
Moving TX positiong to find the best position
Knowing the derivative would be useful...
Maybe one of the most recent and popular work on DRT applied to radio-propagation is Sionna.
Using auto-diff, they have created an easy to use radio-network optimization tool.
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.
Without those (possible infinitely) high-order paths or complex interaction types, we have "holes" in our domain, which is an issue for gradient-based optimization. What if we could have a fake transparancy that would fake a possible link between RX and TX?
Present work and contents
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.
Showing steps
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.
Future work
Finals words
That's all folks!