Interference Mitigation in Multibeam Satellite Networks as an Optimal Sublattice Problem

Resource distribution in radio networks aims at maximizing spectrum utilization while minimizing interference. In this paper, we consider the problem of uniform radio resource distribution on a periodic grid. We formulate the problem as finding the sublattice configuration that maximises the distance between adjacent resources, crucial for reducing interference and improving throughput performance. Leveraging concepts from lattice theory and discrete geometry, we present an enumerative, parallelizable algorithm to explore all possible sublattices and efficiently identify the optimal configurations. Additionally, we investigate the existence and properties of scaled-rotated sublattices, exploring how different lattice geometries impact optimal solutions. Numerical results demonstrate the effectiveness of the proposed algorithm and highlight insights into optimal sublattice design for various lattice structures. Furthermore, the results are applied to the identification of the beam layout in a fixed multibeam geostationary satellite. Numerical results show that the spectral efficiency of the optimised sublattice is higher than all other sublattices. This work thus advances the field of radio resource distribution and offers practical implications for improving satellite network performance.