# Methodology for Simulating 5G and GNSS High-Accuracy Positioning
## 2 Scenario Definition
### GNSS Satellite Visibility  
The nominal conditions of satellite navigation systems are defined by an open sky scenario, because they are designed to operate only with line-of-sight (LoS) signals. Thus, the GNSS performance is severely degraded with a reduced satellite visibility and dense multipath, such as in urban and indoor environments. Indeed, the urban canyon is a typical example of harsh GNSS environment. As it is shown in Figure 2a, the buildings at both street sides block part of the sky, hence the number of visible GNSS satellites is reduced. Assuming a negligible diffraction contribution at the building edges, the height of the surrounding buildings determines the minimum elevation of a visible satellite, also known as the elevation mask \(\theta_{\mathrm{m}}\). Several models can be found in the literature to define the elevation mask for straight street scenarios, such as those summarized in Table 1. The simplest GNSS visibility model is based on a constant elevation mask for a certain range of satellite azimuth values \(\varphi_{\mathrm{m}}\). As shown in Figure 2b, the elevation mask of the urban canyon scenario is set to \(60^{\circ}\) for a range of azimuths corresponding to the blocking buildings and to \(5^{\circ}\) for the rests of azimuths, according to the ETSI specification in [13]. However, this model is not accurate in terms of a representative building, because a constant elevation mask is not accurate in terms of a representative building, because a constant elevation mask is not accurate in terms of a representative building. Figure 1: Average distance to the three closest BSs of a representative LTE network deployment. Figure 2: Definition of the urban canyon parameters and the sky plot of its elevation mask, according to ETSI TS 103.246-3 [13] and the proposed model. elevation mask results in a building height that increases along the straight street (instead of being constant as expected). This can be circumvented with a generalized elevation mask model as in [20], where representative streets are modeled based on the street width, the building height and the receiver location within the street. Our approach is to simplify this generalized model for a receiver located in the middle of a symmetrical street, where only the aspect ratio of the street needs to be defined. As in [21], the elevation mask is then defined as function of the satellite azimuth \(\varphi_{\mathrm{m}}\) as  
\[\theta_{\mathrm{m}}\left(\varphi_{\mathrm{m}}\right)=\left|\mathrm{atan} \left(\frac{h}{d}\cdot\cos\left(\varphi_{\mathrm{m}}\right)\right)\right|, \tag{1}\]  
where \(d\) is the minimum distance between the receiver and the blocking building, and \(h\) is the height of the building. Indeed, the specific values of the distance to the building and its height do not strictly need to be defined, but their ratio can be obtained for a maximum elevation mask \(\theta_{\mathrm{max}}\) at \(\varphi_{\mathrm{m}}=0\), as \(h/d=\mathrm{atan}(\theta_{\mathrm{max}})\). In this sense, the proposed model can be compared with the standard model in [13] for a symmetrical infinite road and \(\theta_{\mathrm{max}}=60^{\circ}\), as shown in Figure 2b. For the sake of simplicity, the elevation mask of the receiver antenna and a finite road length are not considered in this work, but these parameters can be easily adopted as boundaries of the proposed model. The impact of the standard and the proposed models can now be compared as function of the maximum elevation mask. Let us consider the elevation and azimuth of the GPS satellite orbits over one day in the north hemisphere. For instance, the GPS orbits are obtained from the public database of the ground reference station of Delft University of Technology with latitude \(51^{\circ}59^{\circ}09.7\"\) N and longitude \(4^{\circ}23^{\prime}14.9\"\) E on the 16 March 2016 at 00:00:01 UTC. Then, the GPS satellite visibility is computed by filtering the visible satellites for a certain elevation mask.