# Spatial and Temporal Sampling Properties of a Large GNSS-R Satellite Constellation
## 4 Examples  
### Application of Design Methodology  
By qualifying these three design spaces, they can now be applied towards optimizing a constellation design. One potential optimization task could be to maximize ZTC at all latitudes while maintaining ZSC as close to 100% at those same latitudes. For this scenario, it can be assumed that 24 satellites are available for use similarly to the examples discussed previously in this report. By doing so, this constellation will have more than enough satellites to guarantee a near 100% ZSC over the course of a 24 h test while allowing for greater manipulability of its ZTC. With 24 satellites provided, a constellation designer would then need to decide how to spatially organize these elements. As described above in Section 3.2, the most practical pattern organization would be to divide the 24 satellites into 3 evenly distributed planes of 8 satellites. The result of doing so while holding other variables constant is further illustrated in Figure 6.  
Once the satellites are placed into orbit planes, it is up to the constellation designer to set each plane's orbit inclination. To maintain near 100% GSC while having an evenly distributed ZTC, it would make sense to start with a configuration with planes inclined at 30\({}^{\circ}\), 60\({}^{\circ}\), and 90\({}^{\circ}\). Since there is a plane inclined at 90\({}^{\circ}\), not only is a GSC near 100% as described in Section 3.1, but also a ZTC distribution as illustrated in Figure 5 will be achieved. However, when observing this ZTC distribution over latitude, it can be noted that both the ZTC drops significantly near 60\({}^{\circ}\) and the ZTC at other latitudes below 80\({}^{\circ}\) are significantly below the maximum coverage value of 4. This behavior can be observed by analyzing the coverage metrics across larger zones, defined as equatorial, mid-latitude, and polar. More specifically, the equatorial zone is bounded by the latitudes 30\({}^{\circ}\)S and 30\({}^{\circ}\)N, the mid-latitude zone is defined by the two sets of boundaries, 30-60\({}^{\circ}\) north and south, and the polar zone is defined by the two sets of boundaries, 60-90\({}^{\circ}\) north and south. As illustrated in Table 1, the mid-latitude and polar ZTC measurements for the 30\({}^{\circ}\)-60\({}^{\circ}\)-90\({}^{\circ}\) constellation are significantly lower than the equatorial ZTC. When considering this information along with the ZTC plot in Figure 5, the mid-latitude and polar ZTC drops can be attributed to the smaller quantity of satellites in polar orbits and the placement of the mid-latitude plane at 60\({}^{\circ}\) inclination. In order to overcome the lack of uniformity and raise the overall ZTC, it is necessary to adjust each plane's inclination. An alternative approach is to design fitness functions that score constellations based on these coupled global performance metrics [19]. Figure 9: RCG Thresholding Comparison for 3-Plane constellations at 800 km, 16 parallel measurements per sampling, and with 8 satellites per plane. For all listed constellations, the fraction of measurements below threshold converges around RCG Value of 15. There are two possible approaches for correcting the ZTC drop near 60\({}^{\circ}\). First, a designer can either raise the inclination of first plane, which was initially placed at 30\({}^{\circ}\), or lower the inclination of the third plane, which was initially placed at 90\({}^{\circ}\). By adjusting these inclinations, additional coverage can be shifted towards the latitude where ZTC is lacking. However, shifting too much may cause new significant drops to form. Second, a designer can raise or lower the inclination of the second plane, which was initially placed at 60\({}^{\circ}\). Although this approach may not eliminate the ZTC drop, it will reposition it to a latitude where it may become more simple to perform the first method.