# A Clutter Loss Model for Satellite Communication Systems
## 3 The Urban Environment  
The proposed clutter loss model has a mixed physical and statistical nature. On the one hand, it considers the main impairments affecting a wave propagating in an urban environment, i.e., reflections, refraction and diffraction (scattering due to the surface roughness is not considered, as it is of limited impact at frequencies up to 10 GHz). The rays emitted isotropically by the base station interact with the buildings under the plane wave assumption. On the other hand, the proposed methodology is far from being a complete ray-tracing approach, which requires a deterministic description of the urban environment: for each ray, the building distances and heights are randomly extracted from the associated statistics, which characterize a specific city.  
In fact, the building height and distance statistics are gathered according to Report ITU-R P.2402 [11], which also includes the results obtained for two sample cities, namely, Melbourne (Australia) and London (United Kingdom).  
Without describing all the details included in [11], the cumulative distribution functions (CDFs) are calculated for a number of survey points representative of the expected base station locations within the area (e.g., along the street central lines, the curb lines, the edges of pavements/sidewalks) on building facades (although the statistics do not change if the base station is on the building roof). As shown in Figure 1, from each of these points, for all horizontal radials at 10-degree intervals, the roof height at which the radial intersects the building facade (without considering any parts of the roof higher than this point) is recorded, as well as the horizontal distances to the first and second buildings. The second building may be part of the first: the key point in identifying it is that the ray travels over un-built-on ground before reaching it. The distance from the survey point to either the first or the second building is limited to 1000 m: if no building is met on the radial by such a distance, the first and second building distances are set to 500 m, and the building heights are set to 0 m. In this way, following the other criteria defined in [11], it is possible to build statistics of the building height and distance from the survey points, which can be achieved by resorting to any survey method: direct surveying, 3D models derived either from LIDAR or stereo photography, large-scale digital maps with building heights.  
Figures 2 and 3 depict the CDFs of the building distance and height, respectively, for London and Melbourne, derived from twelve survey points scattered across the considered area of each city [11]. It is evident that the statistics present marked discrepancies, due to the different planimetric and altimetric structures of the two cities. London is a typical business area with narrow streets and relatively close buildings, while Melbourne is laid out in a rectangular grid with wide main roads, but many narrow passages within the city blocks.  
Figure 1: Scheme used to calculate the urban statistics. \(D_{b1}\) represents, for each ray, the horizontal distance between the base station and the facade of the first building along the ray path; \(D_{b12}\) is the horizontal distance between the facade of the first building and that of the second building along the ray path. \(D_{b1}\) and \(D_{b12}\) are calculated for each ray leaving the base station (with a radial step of 10 degrees), which is placed in a number of survey points in the city close to a building facade and at a height of 5–6 m above the ground. The roof height, \(H_{b1}\), at which the radial intersects the building facade is also recorded.  
Figure 3: CDFs of the building height (Hb1) for London and Melbourne, extracted from [11].  
Figure 2: CDFs of the building distance (Db1 and Db12) for London and Melbourne, extracted from [11].