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The development of low-orbit (LEO) satellites has attracted wide attention from industry and academia. Due to the scarcity of spectrum resources, LEO satellites in spectrum use respect have to share spectrum with other systems in space. In order to alleviate the shortage of space spectrum resources, spectrum sharing has been widely paid attention. Focusing on the sharing of spectrum between low-orbit (LEO) satellites and legacy geostationary orbit (GEO) satellites, a cognitive collaboration optimization method for sharing spectrum among LEO satellite groups and GEO satellite is proposed. At the expense of assisting in relaying information from GEO satellite, LEO satellite groups are granted the right to use the authorized spectrum of GEO satellite. With the minimum transmit rate of GEO satellite guaranteed and the transmit power threshold of each LEO satellite as the constraints, the optimization problem by optimizing forward matrix and precoding vector at each LEO satellite is established to maximize the minimum transmission rate in LEO satellite group. Considering established non-convex optimization problem, precoding vector and forward matrix optimization solving algorithm is proposed by jointly adopting bisection method, primal-contrapositive transform and primal-dual method. The proposed scheme is validated through numerical simulation. This paper provides a potential spectrum sharing method among GEO and LEO satellites to support theoretical basis and experimental data for parameter design, such as the number of LEO satellites participating in the cooperation. The cooperation performance and cooperative node selection in space time-dependent networks will be discussed in future research.
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