Questions about the coefficients in the MC of coverage_map

[liyuxuan5603]

I am very interested in the Monte Carlo process you've implemented, but I find myself puzzled by the coefficients, particularly after reviewing the code and struggling to find a clear correspondence. I have two questions:
First, can the values calculated in coverage_map be effectively approximated as the power at the cell centers?
Second, could you explain how the coefficients in the code align with the formulas?
Thank you for your help.

[faycalaa]

Hi @liyuxuan5603,

1. Assuming that the number of samples used to compute the coverage map is sufficiently large and that the cell size is small enough, then the path loss measured by a receiver at the center of the coverage map cells should match the ones of the coverage map. Note that some of the unit tests of Sionna precisely check this..
2. The scaling in the code you have highlighted combines the scaling from Eq. (53) you mentioned and the scaling from the computation of channel impulse responses.

[liyuxuan5603]

@faycalaa I'm still confused with the term $r(\omega_n)^2$, could you point out the corresponding implementation in the code? Thank you for your kind help.

[faycalaa]

The term $r(\omega_n)^2$ cancels out when considering free space propagation ($E_r(\omega_n) \propto \frac{1}{r(\omega_n)}$, where $E_r$ is the received electric field). This is implemented by applying neither the free space propagation loss nor the scaling by $r(\omega_n)^2$ in Eq. (53) you mentioned.

[liyuxuan5603]

I've totally understood the equation. Thank you for your patient answer.