In a multi-beam satellite communication system, traffic requests are typically asymmetric across beams and highly heterogeneous among terminals. In practical operations, it is important to achieve a good match between the offered and requested traffic, i.e., to improve the performance of Offered Capacity to requested Traffic Ratio (OCTR). Due to satellites' payload constraints and limited flexibilities, it is a challenging task for resource optimization. In this paper, we tackle this issue by formulating a max-min resource allocation problem, taking fairness into account such that the lowest OCTR can be maximized. To exploit the potential synergies, we introduce Non-Orthogonal Multiple Access (NOMA) to enable aggressive frequency reuse and mitigate intra-beam interference. Although NOMA has proven its capabilities in improving throughput and fairness in 5G terrestrial networks, for multi-beam satellite systems it is unclear if NOMA can help to enhance the OCTR performance, and hence is worth quantifying how much gain it can bring. To solve the problem, we design a suboptimal algorithm to firstly decompose the original problem into multiple convex subproblems by fixing power allocation for each beam, and secondly adjust beam power to improve the minimum OCTR in iterations. Numerical results show the convergence of the proposed algorithm and the superiority of the proposed NOMA scheme in max-min OCTR.

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