## 3 Results and Discussion  
### Scenario Overview  
The Equatorial Spread F (ESF) scenario simulated in [18] is chosen as the baseline simulation for multi-constellation GNSS comparisons. ESF is a type of ionospheric irregularity that often occurs in the post-sunset equatorial region of the ionosphere and it is typically seen as plasma bubbles or plumes within unstable plasma depletions. Studies show that ESF is generated by plasma instabilities; primarily the (generalized) Rayleigh-Taylor instability along with other secondary instabilities that impact the development of the plasma bubble/plume [22]. ESF can negatively affect communication signals and disturb satellite operation. In terms of the impacts on GNSS, it causes signal scintillation (i.e., rapid temporal fluctuations in amplitude and phase), signal delay due to TEC gradient, and eventually degradation in the navigation reliability and accuracy. Therefore, it is significant to study ESF to mitigate its potential impacts on satellite communication and operation systems. According to the phase screen scintillation theory discussed in [23], amplitude scintillation is mainly caused by plasma density irregularities with the scale size corresponding to the dimension of the first Fresnel zone of the RF signals. The Fresnel length is expressed as \(\sqrt{2\lambda\cdot h}\), where \(\lambda\) is the signal wavelength and \(h\) is the altitude of the ionospheric irregularities. The ionospheric irregularities (assuming \(h\) = 350 km) mostly contribute to the amplitude scintillation of GPS L1 band (19 cm) is approximately 400 m [24]. Phase screen theory indicates amplitude scintillation is positively correlated with the plasma density fluctuations, i.e., higher electron density deviation will induce larger S4. Past ESF observations results by [25] are consistent with these scintillation characteristics produced by equatorial plasma bubbles. Plasma bubbles can occur for hours after sunset. Smaller-scale ionospheric irregularities measured by radar appear to decay faster. The ionospheric impact on GNSS signals can be customized in the Spirent GNSS simulator by modeling TEC and amplitude scintillation. By default, TEC variation can be modeled vertically only, and the S4 can only by modeled in a region lower than 350 km defined by a horizontal grid with the minimum resolution of 10 by 15 degrees. A cuboid region with a few plasma bubbles was simulated in the VTFTFB by setting the one-dimensional vertical TEC profile and two-dimensional horizontal S4 grid. Using a \(Ne\) measurement from the PLUMEX I sounding rocket (SR) campaign [26], a vertical \(Ne\) profile including three obvious plasma bubbles is used to derive the vertical TEC profile. Horizontally, the S4 was set as 0.4 in the cuboid region ranges from 290 to 350 km vertically, 20:00 to 21:00 local time (LT) longitudinally, and 0\({}^{\circ}\) to 10\({}^{\circ}\) S latitudinally, which is above the Jicamarca Radio Observatory (JRO) in Peru. Modeling the S4 value as 0.4 is consistent with the S4 value simulated by [27] in a similar simplified plasma bubble scenario. When a formation of two small satellites with on-board GNSS receivers fly through this ESF region, TEC and S4 between the GNSS constellation(s) and the two spacecraft can be measured. This scenario is illustrated in Figure 3. If the dual spacecraft are flying in proximity at different altitudes, the vertical \(Ne\) in between can be estimated by dividing the vertical TEC difference from the vertical separation. Compared to some single satellite missions (e.g., LEO GNSS tomography, radio occultation) or ground based remote sensing techniques, this LEO formation flight concept is more advantageous to observing the global and microscale morphology (e.g., precise structure and location) of irregularities that potentially induce GNSS scintillations.