*3.3. 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 × 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 × 5 element phased array antenna. The advantage of the higher orbit altitude is wider field of view of the

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 × 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 × 5 patch antenna, demonstrating the advantage of a higher altitude orbit.

**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◦, 60◦, and 90◦ inclination, 20 Parallel Measurements Maximum per sampling, and an RCG Threshold of 15.

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.

## **4. Examples**

#### *4.1. 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◦, 60◦, and 90◦. Since there is a plane inclined at 90◦, 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◦ and the ZTC at other latitudes below 80◦ 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◦S and 30◦N, the mid-latitude zone is defined by the two sets of boundaries, 30–60◦ north and south, and the polar zone is defined by the two sets of boundaries, 60–90◦ north and south. As illustrated in Table 1, the mid-latitude and polar ZTC measurements for the 30◦-60◦-90◦ 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◦ 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]. **Table 1.** Constellation Optimization through the Proposed Iterative Method. The constellations all feature 3 evenly distributed orbit planes of 8 evenly spaced satellites per plane at an altitude of 800 km. The coverage metrics described above were evaluated with the 3 × 5 element phased array antenna and a RCG minimum threshold of 15. By making these discrete adjustments in the inclinations of individual planes, we can keep the GSC near 100% while incrementally improving the GTC.


There are two possible approaches for correcting the ZTC drop near 60◦. First, a designer can either raise the inclination of first plane, which was initially placed at 30◦, or lower the inclination of the third plane, which was initially placed at 90◦. 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◦. 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.

Starting from the baseline of a 3-Plane 30◦-60◦-90◦ constellation, the progression of this logic and the corresponding changes in GSC, ZSC, GTC, and ZTC are illustrated by the results provided in Table 1. After a few iterations, we find a significant improvement from the original baseline in the 3-Plane 50◦-75◦-80◦ constellation. In each step of the process, GSC always remains close to a complete 100%, but most progressions showed growth in the GTC of each prototype constellation. By incrementally raising the first plane inclination, we can slowly increase the GTC. However, once we reach a point where the first two inclinations are starting to get closer, we find that raising the second plane would create a more significant increase in this metric. This is evident by the GTC change between the 45◦-60◦-90◦ and the 45◦-65◦-90◦ constellations. Additionally, the increase in the inclination of the first plane from 45◦ to 50◦ allows for one more small rise in GTC without moving the first plane too close to the second plane while allowing for significant equator coverage. Finally, we can take advantage of the 10◦ reach from the set inclination to lower the third plane down from 90◦ to 80◦ while both improving ZTC at inclinations lower than 80◦ and maintaining the ZTC between 80◦ and 90◦.

When comparing this 50◦-75◦-80◦ constellation to others with no separation in plane inclinations, such as the 30◦-30◦-30◦ or 90◦-90◦-90◦, the differences in GTC and ZTC are prominent. Since the 30◦-30◦-30◦ constellation's max inclination is equatorial, its midlatitude ZTC, polar ZTC, and GTC are all much smaller than other constellations considered, making it less than ideal for a globally effective design. On the other hand, the 90◦-90◦-90◦ constellation has a relatively large GTC, but its equatorial ZTC is much smaller than other designs considered. Although the 50◦-75◦-80◦ constellation does not have the largest ZTC of these three constellations in any of the regions, its zonal and global metrics are still relatively good. Considering the goal of this design study is to maximize ZTC at all

latitudes, the 50◦-75◦-80◦ constellation is a good design candidate, for its zonal metrics are large at all latitudes and are further characterized by a large GTC.
