# Spatial and Temporal Sampling Properties of a Large GNSS-R Satellite Constellation
## 3 GNSS-R Coverage Simulations
### Effect of Measurement RCG on Constellation Coverage  
A third critical design feature of a constellation is the antenna gain of its measurements. The impact of antenna gain on science measurement quality is characterized by the Range Corrected Gain (RCG). A higher RCG represents higher signal-to-noise ratio data and higher quality estimates of geophysical quantities derived from them, such as ocean surface wind speed [17]. Two ways are considered to control the RCG values, changing the design of the receiving antenna assumed on each of the satellites and raising the RCG threshold required for data usage.  
The antenna used by a GNSS-R sensor is typically designed to accommodate a particular orbit altitude. A higher altitude will increase the propagation distance and decrease the received signal strength. This decrease can be mitigated by increasing the antenna gain. Alternatively, a decrease in altitude will restrict the field of view of an antenna pattern projected onto the Earth surface. This restriction can be mitigated by widening the antenna pattern. Fortuitously, a wider antenna pattern tends to have a lower antenna gain, so these two considerations can be accommodated jointly by the same adjustment in antenna design as a function of orbit altitude. Two orbit altitudes and corresponding antenna designs are considered here. The first assumes a similar configuration as is used by the CYGNSS constellation--namely a 500 km altitude and a 2 \(\times\) 3 element phased array antenna. Although CYGNSS operates at an altitude of 525 km, the results at 500 km provides nearly identical performance. The second option is an 800 km orbit and a 3 \(\times\) 5 element phased array antenna. The advantage of the higher orbit altitude is wider field of view of the  
Figure 7: 24 h Temporal Coverage measurements at different latitudes for 24-satellite constellations at 800 km, 16 parallel measurements per sampling, and operating with an RCG Threshold of 15. As the initial 30\({}^{\circ}\) inclination plane of 24 satellites is divided in smaller planes with raised inclinations allows the constellation’s Zonal and Global Temporal Coverage to be shaped and increased.  
antenna, which allows for more available specular point reflections to be sampled. This is demonstrated in the curves of Figure 8. When we compare the RCG values of samples collected from the CYGNSS configuration and the 3 \(\times\) 5 antenna at 800 km altitude, we can see that the CYGNSS antenna will retrieve significantly fewer parallel measurements for the same RCG threshold as the 3 \(\times\) 5 patch antenna, demonstrating the advantage of a higher altitude orbit.  
It is important to consider where the minimum RCG threshold is set. A threshold of 15 has been found to be sufficient for providing high-quality science data to most applications. The implications of this threshold on the number of usable samples are illustrated in Figure 9. The figure considers the fraction of all samples retained given different lower-bound RCG thresholds. The reference baseline is usage of all samples (i.e., no threshold). The results show that all three constellations will have 50% of collected data fall below threshold when it is set to RCG > 15.  
Figure 8: Parallel Measurement Comparison between antenna patterns at their corresponding altitudes over 24 h using a 3-Plane constellation with each plane at 30\({}^{\circ}\), 60\({}^{\circ}\), and 90\({}^{\circ}\) inclination, 20 Parallel Measurements Maximum per sampling, and an RCG Threshold of 15.