<b>TOPOLOGY AND GROUND COVERAGE OPTIMIZATION FOR NON-TERRESTRIAL NETWORKS</b>

<p dir="ltr">The burgeoning interest in satellite topology configuration, driven by the increasing demand for edge computing and the decreasing cost of communication satellite components, highlights a critical need for computationally efficient methods to determine optimal network configurations. Current approaches often struggle to achieve the high computational speed required for dynamic optimization, particularly when dealing with complex, non-linear constraints and objective functions. This research addresses these gaps by developing high-performance, efficient coverage analysis for large-scale satellite constellations and robust methodologies for establishing effective inter-satellite link (ISL) configurations.</p><p dir="ltr">For ground coverage optimization, we employed a Mixed-Integer Linear Programming (MILP) framework using a real-world demand distribution. A key innovation involved developing a novel linear approximation to convex functions, which allowed us to leverage high-speed linear solvers. This approach significantly improved computational efficiency compared to traditional iterative convex optimization methods. Our results demonstrate substantial improvements, including an approximately 90% increase in fairness of ground coverage, a 30% increase in overall demand satisfaction, and a 15% increase in coverage for low-demand areas.</p><p dir="ltr">For satellite topology optimization, we developed an end-to-end differentiable and annealed constraint structure. This method utilized computational graphs and gradient descent to efficiently determine optimal ISL configurations. The findings for this section were equally significant: multi-hop latency was reduced by 30-50%. These results confirm our ability to effectively optimize with respect to convex functions in high-dimensional scenarios, enabling the optimization of multiple constellations with accurate hardware parameters.</p><p dir="ltr">Furthermore, the successful application of gradient-based methods for high-speed topology optimization of large constellations represents a significant advancement in the field.</p>