Satellite Clusters Flying in Formation: Orbital Configuration-Dependent Performance Analyses

This paper considers a downlink satellite communication system where a satellite cluster, i.e., a satellite swarm consisting of one leader and multiple follower satellites, serves a ground terminal. The satellites in the cluster form either a linear or circular formation moving in a group and cooperatively send their signals by maximum ratio transmission precoding. We first conduct a coordinate transformation to effectively capture the relative positions of satellites in the cluster. Next, we derive an exact expression for the orbital configuration-dependent outage probability under the Nakagami fading by using the distribution of the sum of independent Gamma random variables. In addition, we obtain a simpler approximated expression for the outage probability with the help of second-order moment-matching. We also analyze asymptotic behavior in the high signal-to-noise ratio regime and the diversity order of the outage performance. Finally, we verify the analytical results through Monte Carlo simulations. Our analytical results provide the performance of satellite cluster-based communication systems based on specific orbital configurations, which can be used to design reliable satellite clusters in terms of cluster size, formation, and orbits.

Performance Analysis of Satellite Communication System Under the Shadowed-Rician Fading: A Stochastic Geometry Approach

In this paper, we consider a downlink satellite communication system where multiple satellites are uniformly distributed over a sphere at a certain altitude. We analytically derive three things: 1) the satellite-visible probability for a given location, which is defined as the probability that a terminal sees at least one satellite above the minimum elevation angle, i.e., a pre-defined elevation angle above which the terminal can be served by a satellite, 2) the distribution of distance between the terminal and serving satellite when the terminal is associated with the nearest satellite, and 3) the exact expressions for the outage probability and throughput of the system. With the derived expressions, the system throughput maximization problem is formulated under the satellite-visibility and outage constraints. To solve the problem, we reformulate the problem with bounded feasible sets and obtain the optimal solution by using an exhaustive search. Using the Poisson limit theorem, we derive approximated expressions for the satellite-visible probability, outage probability, and system throughput, which reduce computational complexity of performance evaluation and search time for the optimal solution of the throughput maximization problem. Simulation results perfectly match the derived exact expressions for the outage probability and system throughput. It is also shown that the analytical results of the approximated expressions are fairly close to those of the exact expressions.