pathsolver, cir and cfr calculation

[novuss2]

Hello Sionna team,

I have some question about how the calculation of the pathsolver works.

Your Documentation (Primer on Electromagnetics / Frequency & Impulse Response) suggests to me that first sionna calculates the CFR and second the CIR with an IFT of the CFR. In the source Code it looks like it is the other way round. Also I can't understand the equation of (23) and the one equation before (not 22). How do I get a scalar when I'm multiplying three matrices and furthermore what is the transfer matrix T? It is written that scattering and free space path loss is represented by the transfer matrix but I can't imagine how. What are the dimensions representing? I'm just lost here^^.

The intention behind my question is to understand how Sionna RT could simulate a multicarrier modulation.
As far as I understood Sionna calculates with raytracing all the delays and amplitudes. The CIR function uses the results and the given frequency and calculates the phasors to generate a cir. The CFR function calculates for a given spectrum the fourier coefficients and generates the cfr. But it does not recalculate path loss, scattering and the antenna patterns which are theoretically frequency dependent. So the CFR gets an error dependent on the bandwidth amplified by the distance of the rays. Is this insignificant?

I'm happy with any answers or hints where I'm wrong,
greetings Victor

[jhoydis]

Hi @novuss2,

1. Concerning (23), note that $\mathbf{C}_\text{T}$ and $\mathbf{C}_\text{R}$ are vectors defining the RX and TX antenna patterns, respectively. Please refer to their definition in (14) and the lines after. This explains how you get a scalar.

2. You can represent the free-space propagation by an identity matrix multiplied by $e^{-jk_0r}/r$, as explained just after (22). For all other scattering processes (specular reflection, refraction, diffuse scattering (also called diffuse reflection), diffraction), you will find the definitions of the transfer matrix in the corresponding sections of the EM Primer. We do not explicitly provide a value for $\mathbf{T}$ for all cases but rather a relationship between the incoming and outgoing fields from which one can easily extract the transfer matrix.

3. Ray tracing computes the channel gains $a_i$ and corresponding delays $\tau_i$ for multiple propagation paths from a transmitter to a receiver in parallel at a given carrier frequency $f$. The key assumption is that $a_i$ and $\tau_i$ are constant for the bandwidth of interest (which is a reasonable assumption in most cases). That means that we can compute $H(f)$ for any frequency $f'$ in the vicinity of $f$ as described in (26). This is what we call the CFR. For extremely large bandwidth, you might make an error, but this is insignificant. If you wanted to avoid it, you would need to compute $a_i(f')$ and $\tau_i(f')$ for all frequencies of interest.

4. The computation of the CIR makes the same assumption because $a_i$ and $\tau_i$ are assumed constant with respect to the frequency in the integral in (27). And could compute more precise channel taps (the discrete low pass-filtered CIR) by computing the IDFT of the CFR which is computed with the refined method described in 3). However, I do not think that this really needed for most practical purposes.

Hope that helps.

[novuss2]

Thank you very much