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Low Earth orbit (LEO) satellite constellations rely on inter-satellite links(ISLs) to provide global connectivity. However, one significant challenge is toestablish and maintain inter-plane ISLs, which support communication betweendifferent orbital planes. This is due to the fast movement of theinfrastructure and to the limited computation and communication capabilities onthe satellites. In this paper, we make use of antenna arrays with either Butlermatrix beam switching networks or digital beam steering to establish theinter-plane ISLs in a LEO satellite constellation. Furthermore, we present agreedy matching algorithm to establish inter-plane ISLs with the objective ofmaximizing the sum of rates. This is achieved by sequentially selecting thepairs, switching or pointing the beams and, finally, setting the data rates.Our results show that, by selecting an update period of 30 seconds for thematching, reliable communication can be achieved throughout the constellation,where the impact of interference in the rates is less than 0.7 % when comparedto orthogonal links, even for relatively small antenna arrays. Furthermore,doubling the number of antenna elements increases the rates by around one orderof magnitude.

Inter-Plane Inter-Satellite Connectivity in LEO Constellations: Beam Switching vs. Beam Steering