## 2 System Modeling
### Individual-Satellite-Oriented Multi-Directional FoV  
A previous study [12] incorporates the elevation angle of the sun (\(\theta_{s}\)) to model solar power impacting satellites. Specifically, when \(\theta_{s}\) is between \(0^{\circ}\) and \(90^{\circ}\), the sunlight affects the optical link based on incident angle, accordingly, while it is set at zero for all the other angles. Because the effect of the solar irradiance depends on the alignment among the sun, transmitter, and receiver, it is critical to evaluate the overall irradiance on individual satellites according to the relative position of each. From a practical perspective, the focus should shift to determine which receiver is affected by sunlight rather than evaluating the satellite body as a whole. This is particularly relevant for O-ISL configurations, where satellites typically host multiple transceiver terminals [13; 14; 15]. For single-transceiver systems, the elevation angle of the sun (\(\theta_{s}\)) is a critical factor. However, in systems employing multiple transceivers, the narrow-beam nature of optical communications necessitates evaluating whether solar light enters the FoV of each receiver. A multi-directional FoV model enables the simultaneous assessment of the FoVs of individual receivers in various directions. Figure 3 illustrates a satellite equipped with four optical modules, showing the feasibility of diverse optical link configurations. Depending on the position of the sun, each receiver is affected by different levels of solar interference. In unexposed areas, no module is affected by solar irradiance. In contrast, exposed areas, such as those in Figure 3a, reveal situations where certain modules are affected by solar interference. Meanwhile, other modules can maintain communication despite solar irradiance, as demonstrated in Figure 3b,c. These observations emphasize the importance of individually analyzing solar irradiance constraints for each receiver. The solar power decision range is confined to a maximum of \(90^{\circ}\), which means that the half FoV of the receiver is limited to \(45^{\circ}\). This range can significantly reduce the performance of O-ISLs. A wider FoV, although enabling broader coverage, increases the signal interference, reduces the received signals' strength (RSS), and causes additional costs because of the need for extra modules. Previous research [16] has identified the threshold angle for the optical link connectivity affected by solar interference, termed as the outage angle, as \(3^{\circ}\). This angle is determined by the vectors between the satellite-to-sun and satellite-to-adjacent satellite links. The outage angles could differ, especially for complex O-ISL configurations, where orientational parameters come into play. In addition to these analyses, Table 1 is provided to compare the overall investigation coverages of the simulation in our work with those in previous studies. As illustrated in Figure 4, the practical outage angle depends on the relative rotation of the satellite. In situation (a), the FoV from satellite A to satellite B, represented by the green dotted area, overlaps with that from satellite A to the sun, deteriorating the communication performance. However, in situation (b), although the relative positions are precisely the same, the slight rotation of satellite A makes the communication link unaffected by the solar light. This demonstrates the need for a dynamic outage angle that adapts to real-time orbital positions and satellite orientations. The dynamic nature of satellites orbiting Earth, with three-dimensional calculations, is required to implement a simulator capable for identifying solar interference and optimizing the overall path configuration. Moreover, the axial tilt and seasonal changes of the Earth should be considered. As shown in Figure 5, the axis of Earth's rotation changes depending on the season, affecting the sun's irradiation angles to the satellites as well.