# Performance Evaluation of Random Access Methods for IoT-over-Satellite
## 3 Method
### System Model
#### 3.1.3 Satellite Constellation Model  
In this framework we consider practical constellations in order to obtain insights into realistic network performance. The constellation models adopted in this work are in the form of Walker-Delta and Walker-Star constellations which are illustrated in Figure 6. These two constellations are widely used in the satellite communication industry, for example in recent deployments by SpaceX's StartLink and by OneWeb. Walker constellations can be described with the parameter vector \(\{h,i,N_{s},P,F\}\)[44], where \(h\) is the constellation altitude, \(i\) is the orbital planes' inclination, \(N_{s}\) is the total number of satellites in the constellation, \(P\) is the number of orbital planes, and \(F\) is the phasing parameter representing the shift between satellite relative locations in subsequent orbital planes. The orbital planes are equally spaced around Earth's rotational axis and each plane consists of \(N_{s}/P\) satellites that are equally spaced along the circular orbit. Below we explain the difference between Walker-Delta and Walker-Star:  
* **Walker-Delta Constellation:** The Walker-Delta constellation is widely adopted by many satellite projects, such as Starlink and Kupier [11; 13]. Walker-Delta constellations reduce the variation in the inter-distances between satellites providing a denser distribution of satellites around the equator and mid-latitude locations [45], illustrated  
Figure 4: Illustration of the satellite footprint, whereby the blue patch represents the footprint when limited by the satellite antenna beamwidth, \(\psi\), and the green patch represents the maximum satellite footprint limited by the Earth’s occlusion, i.e., horizon-limited, \(\psi_{o}\). Figure 5: An example of the average satellite availability for variable ground device latitudes with \(N_{s}=480\) and \(h=550\) km. The satellite antenna beamwidth is set to \(80^{\circ}\) whereas the remaining constellation parameters considered are summarized in Table 1.  
in Figure 5. In addition, Walker-Delta configuration enables the utilization of inter-satellite links (ISLs) facilitating communication between the different satellites in the constellation. In Walker-Delta the orbital planes are equally spaced and rotated around the earth rotational axis, with a right ascension of the ascending node angle (RAAN) \(\Omega\in\{0,\frac{2\pi}{P},2\frac{2\pi}{P},\dots,(P-1)\frac{2\pi}{P}\}\). * **Walker-Star Constellation:** The Walker-Star constellation is also widely adopted by current commercial satellite providers, such as Iridium and OneWeb [12; 46]. Walker-Star constellations typically have their inclination angle, \(i\), close to \(90^{\circ}\). This configuration enables true global availability where even the poles are provided coverage unlike Walker-Delta constellations. However, this comes at the cost of an unnecessarily high density of satellites at the poles along with slightly reduced density at the equator. Figure 5 shows a comparison between the availability of Walker-Delta and Walker-Star constellations, the altitude and number of satellites are intentionally reduced to show the variation in availability time. Such low availability is acceptable in delay-tolerant IoT applications, however broadband networks are designed with either larger higher altitudes and/or larger number of satellites in order to provide 100% coverage time. Another difference to the Walker-delta is that the orbital planes RAAN in Walker-Star are spread across the range 0 to \(\pi\) instead of 0 to \(2\pi\), i.e., \(\Omega\in\{0,\frac{\pi}{P},2\frac{\pi}{P},\dots,(P-1)\frac{\pi}{P}\}\). Mercator projection of both Walker-Star and Walker-Delta constellations are shown in Figure 7, where the blue patches represent the footprint of the satellites in the constellation.