Stochastic 3-D Foliage Modeling at 80 GHz: Experimental Validation and Ray-Tracing Simulations

Abstract

A stochastic modeling methodology for 3-D foliage is presented, aimed at enhancing ray-tracing simulations. The model supports adjustable stochastic geometry, density, and shape to capture variability in foliage structures. The model is validated through experimental measurements of representative vegetation. The influence of foliage density and size on path loss and root mean square delay spread is analyzed to demonstrate the applicability of the model in the 80 GHz frequency band.

Figures (5)

• Figure 1: Photograph of the 80 GHz channel sounder. The RX is located behind the measured foliage. TX-RX separation is 30 m with the tree 15 m distant from the TX.
• Figure 2: A 3D visualization of the simulated scene with RX, TX and the foliage model. (a) Triangular element $\mathcal{F}_n$ represents $n$-th face and $D$ stands for diameter. This visualization assumes a density of $\rho=0.125\,\mathrm{m}^3$ and a shape perturbation parameter $\sigma=0.1$. (b) Increased density of $\rho=0.5\,\mathrm{m}^3$, $\sigma=0.1$. (c) The influence of an increased shape perturbation parameter to $\sigma=1$. Note that the internal triangle area $A=2$$\mathrm{m}^2$: Simulations show a low sensitivity to $A$, so the highest acceptable number was chosen to reduce the computation load. Smaller $A$ would result in higher number of internal triangles to fill $\Omega$.
• Figure 3: (a) Measured and ray-traced PDPs (b) RMS delay spread as a function of the tree volume. We generate fifty 3D tree realizations for each simulated tree crown volume $V_\mathrm{target}\in\{200,1000\}$$\mathrm {m}^3$. The depicted heatmap shows the occurrence of a certain RMS DS value. Other parameters are: triangle density $\rho=0.125$, triangle area $A=2$ m$^2$, perturbation strength $\sigma=0.1$ m and number of subdivisions $n_{\text{subdiv}}=2$.
• Figure 4: (a) RMS delay spread and (b) Received signal strength evaluation of fifty realizations of the tree model for each simulated leaf density $\rho$.
• Figure 5: CDF evaluation of the simulated and measured PDPs as shown in Fig. \ref{['fig_pdp']}. The CDFs of the individual CIRs $|h(t,\tau)|^2$ are depicted with varied leaf density $\rho \in \{0,1\}$.