# Design of CubeSat-Based Multi-Regional Positioning Navigation and Timing System in Low Earth Orbit
## 3 Results
### Mission Analysis  
#### 3.3.1 Constellation Design  
As mentioned in the Mission Statement, the system shall provide persistent PNT services over the area of Germany. That means that a satellite constellation shall be designed in a way that at least four S/Cs are always covering the service area. It is essential that the S/Cs are placed into circular orbits with the same altitude to ensure that the distance between the S/C and ground users and GCSs is the same for all S/Cs throughout the mission. Additionally, the constellation's configuration should always remain constant. Thus, Walker constellations are evaluated. Since the area of service is not located in a polar area, Walker Delta geometries are the ones under inspection, with single-shell constellations being the ones considered. Moreover, the design of the constellation must conform with other parameters, like the Payload link budget, the TTC link budget, the expected radiation dose, the power budget, deorbit plan, etc. Certain criteria deemed critical are analyzed in depth as there is no assurance they will be met. In contrast, criteria for which the preliminary analysis indicates a sufficient margin surplus, making it highly likely they will be met, are not considered further at this stage. STK simulations of the constellation configuration were performed between the altitudes of 550 km and 750 km. A minimum elevation angle of 5\({}^{\circ}\) is assumed, meaning that, for lower elevation angles, no contacts are considered. This is chosen to mitigate the effects of the signal traveling through a longer atmospheric path, such as increased attenuation, multipath interference, and fading. Additionally, low elevation angles are more prone to encountering obstacles like buildings, trees, or terrain features, which can block or degrade the signal. The philosophy behind the coverage is that the S/C shall have their Payload antennas mounted on the nadir side and track the area of service as they pass near it. That way, the area covered by each S/C is constrained by the FOV (Field of View) of the Payload antenna. The Payload antenna is chosen to be GOMspace ANT2150-DUP. The Payload antenna's FOV is limited to a cone with a half-angle of 30\({}^{\circ}\), ensuring that the antenna achieves a gain of 5.5 dB at the cone's edge [9]. Whether or not a constellation configuration meets the coverage requirements is concluded via a 4-Asset Coverage Figure of Merit object in STK that assesses if the area of Germany is always covered by a minimum of four satellites for the duration of one year. In order to design a Walker Delta constellation, the parameters that need to be defined are the altitude, the inclination, the total number of satellites, the number of orbital planes, and the relative spacing between satellites in adjacent planes. Among those, the critical parameters are the altitude and the total number of satellites, and the main aim is to minimize them, while the variable describing the relative spacing between satellites in adjacent planes is always set to 1. The constellation design is performed in an iterative approach that implements the trial-and-error method and is described in Figure 4.  
The first step for such an analysis shall be to do a preliminary tradeoff analysis between altitude, which directly translates to Payload and TTC Link Budgets and TID (Total Ionizing Dose). For the first steps of the analysis, the inclination is selected to be 56\({}^{\circ}\) to match the one of Galileo because Galileo is a system optimized for coverage over Europe; and, even though this is a comparison between a LEO and a MEO system, at this point, it is considered an acceptable educated guess. This process led to finding an optimal inclination value of 61\({}^{\circ}\) and subsequently to Table 2, which includes information on the total number of satellites, the number of orbital planes, the minimum received power of PNT signals for a user at ground level, the TID of the S/C, and the average GDOP (Geometric Dilution of Precision) that were considered in the final tradeoff.