In this paper, we propose random beam-based non-orthogonal multiple access (NOMA) for massive multiple-input multiple-output (MIMO) low earth orbit (LEO) satellite communication systems that operate with frequency-division duplexing (FDD). Our system model consists of a massive-antenna satellite and multiple single-antenna users within its coverage area. The satellite selectively serves a subset of users based on a target signal-to-interference-plus-noise power ratio (SINR). In the random beam-based NOMA, the satellite utilizes random beams, where each beam can support multiple users using NOMA. To facilitate user selection and power allocation, each user provides several scalar values obtained from statistical channel state information (CSI) as feedback to the satellite. This allows us to reduce the computational complexity of beamforming design and minimize the feedback overhead for channel acquisition. We propose two random beam-based NOMA schemes with varying complexities and feedback overheads. We optimize these schemes by solving joint user selection and power allocation problems. The numerical results demonstrate that our proposed schemes outperform conventional random beamforming, specifically orthogonal multiple access (OMA) at each beam, by supporting a greater number of users.
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