In this article, a multiuser (MU) satellite multiple-input–multiple-output (MIMO) downlink including a multibeam GEO satellite and multiple terrestrial users is considered. In order to meet the signal-to-interference-plus-noise ratio (SINR) requirements of different users while minimizing the satellite transmit power, the onboard precoding problem is investigated. Zero-forcing (ZF) and regularized ZF (RZF) precoding are first adopted and it is found that they can satisfy the SINR constraints by multiplying by a power allocation matrix. The required power allocation matrix is divided into two types: 1) equal power factor schemes and 2) unequal power factor schemes, and they are derived separately, where Karush–Kuhn–Tucker (KKT) conditions are used in RZF unequal power factor scheme and a heuristic algorithm is proposed to optimize the regularization factor in RZF schemes to further reduce the transmit power. Then, a semidefinite programming beamforming (SDPBF) is proposed to jointly optimize precoding and power allocation matrices. The closed-form expressions of the transmit power of the above five precoding schemes are derived and their performance is compared in the simulation part. The research results show that under the same conditions, the performance of RZF is better than that of ZF, the unequal power factor scheme is better than the equal power factor scheme, and SDPBF has the best performance. Besides, it is also found that in addition to changing the precoding method, activating more beams will further reduce the transmit power.

In this paper, the user selection problem is investigated in the multi-user satellite multiple-input multiple-output (MIMO) downlink, which includes a multi-beam geostationary earth orbit (GEO) satellite in space and multiple terrestrial users on the ground. Considering that the number of users is much larger than that of beams or feeds, user selection should be performed so that multiple users can be served successively in different time slots. In order to meet the quality of service (QoS) requirements of users and maximize the system sum rate, three user selection algorithms are proposed: greedy user selection (GUS) algorithm, add swap user selection (AS) algorithm, and random add swap user selection (RAS) algorithm. Among the three algorithms, only the “add” operation is adopted in the GUS algorithm, both the “add”, and “swap” operations are considered in the AS algorithm. On this basis, heuristic search and “random swap” operation are introduced and the RAS algorithm is obtained. The complexity of the above three algorithms is analyzed analytically and the RAS algorithm is found to have the highest complexity. Besides, the performance of the three algorithms is analyzed and compared through simulations, where the random user selection (RUS) algorithm is taken as a benchmark. Numerical results show that the system sum rate and energy efficiency are greatly improved by the proposed algorithms and the RAS algorithm has the best performance.