# A Clutter Loss Model for Satellite Communication Systems
## 7 Model Validation  
The commercial ray tracer SIRADEL(r) [19] is used to validate the proposed model. The chosen urban environment for validation is a square area with a lateral dimension of 1.2 km in the city of Hong Kong, which is deemed appropriate due to the high building density and the scarcity of vegetation. The statistics of buildings are obtained as detailed in Section 3 from the available SIRADEL(r) data by deploying 500 survey points. CDF curves of the clutter loss are obtained through ray tracing by deploying 15 antennas across the map, within the same region, as the survey points (see Figure 15), to serve as transmitting base stations, while a box of receivers is placed all around the map to collect outgoing rays (see Figure 16). Transmitting antennas are assumed to be omnidirectional, with a transmission power (total radiated power, TRP) of 60 dBm and a height of 18 m from the ground. The wave polarization is vertical. The box of receivers consists of a grid for each side, with receivers spaced 5 m along \(x\), \(y\) and \(z\). In this context, a \"point receiver\" is considered (without a physical dimensions), which collects the information of all rays reaching it: amplitude, delay, departing direction, arrival direction, etc. The box is designed to enclose all buildings, so the last grid point should be at a height \(h_{rx}>h_{b}\), where \(h_{b}\) is the maximum height of the buildings. Figure 14: Clutter loss cumulative distributions: comparison between the proposed model and the ITU-R P.2402 model, for elevation angles of 15, 40 and 70 degrees in Melbourne (base station height fixed at 18 m). The rationale for using only 15 antennas and a 5 m distance between the receivers in SIRADEL(r) is related to computational complexity: indeed, ray-tracing simulations are computationally intensive to run and, in addition, generate large amounts of data. Such parameters allow for achieving a very good trade-off between statistical relevance and computational complexity, both regarding simulations and data post-processing. Once the output data are available from the ray-tracing simulation, the clutter loss experienced by each ray is evaluated as follows:  
1. For the \(i\)-th receiver, we collect: 1. The power received from the \(j\)-th ray \(P_{r}^{i,j}\); 2. The time delay of the \(j\)-th ray \(\tau^{i,j}\). 2. The length of the \(j\)-th ray path is computed as \(\ d^{i,j}=\tau^{i,j}\cdot c\), where \(c\) is the speed of light. 3. The clutter loss experienced by the \(j\)-th ray at the \(i\)-th receiver is calculated in dB as \[L_{cl}^{i,j}=P_{t}[dBm]-P_{r}^{i,j}[dBm]-20\cdot\log_{10}\left(\frac{4\pi d^{ i,j}}{\lambda}\right)\] (29) where the last term is the free space path loss. Figure 16: Layout of receivers in the ray-tracing simulation. Notice that only some of the receivers are indicated in red. Figure 15: Survey points (red dots) and BSs (blue triangles) simulated with the ray tracer. For each positive elevation angle \(\psi\) (i.e., the possible elevation of a satellite), the clutter loss CDF curve is built by collecting all \(L_{el}^{ij}\) values associated with each receiver \(i\) and for the rays leaving the receiver with elevation angle \(\psi_{s}=\pm\psi\). The elevation angle step is \(1^{\circ}\). Notice that rays may leave the base station with a positive or negative angle (with respect to the horizon), but after multiple reflections, they travel towards the sky with a positive \(\psi\) angle. Thus, the CDFs derived from ray-tracing simulations represent the average clutter loss experienced by rays departing from the base station in positive and negative directions. For this reason, the clutter loss CDFs obtained from SIRADEL\(\copyright\) are compared in Figure 17, for a few selected elevation angles and for TM polarization, with the \(\pm\psi\) averaged clutter loss curves of the proposed model. The CDF curves obtained by the ray tracer and proposed model show quite good agreement.