This paper investigates the use of a reconfigurable intelligent surface (RIS) to aid point-to-point multi-data-stream multiple-input multiple-output (MIMO) wireless communications. With practical finite alphabet input, the reflecting elements at the RIS and the precoder at the transmitter are alternatively optimized to minimize the symbol error rate (MSER). In the reflecting optimization with a fixed precoder, two reflecting design methods are developed, referred as eMSER-Reflecting and vMSER-Reflecting. In the optimization of the precoding matrix with a fixed reflecting pattern, the matrix optimization is transformed to be a vector optimization problem and two methods are proposed to solve it, which are referred as MSER-Precoding and MMED-Precoding. The superiority of the proposed designs is investigated by simulations. Simulation results demonstrate that the proposed reflecting and precoding designs can offer a lower SER than existing designs with the assumption of complex Gaussian input.Moreover, we compare RIS with a full-duplex Amplify-and-Forward (AF) relay system in terms of SER to show the advantage of RIS.

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Aerial relays have been regarded as an alternative and promising solution to extend and improve satellite-terrestrial communications, as the probability of line-of-sight transmissions increases compared with adopting terrestrial relays. In this paper, a cooperative satellite-aerial-terrestrial system including a satellite transmitter (S), a group of terrestrial receivers (D), and an aerial relay (R) is considered. Specifically, considering the randomness of S and D and employing stochastic geometry, the coverage probability of R-D links in non-interference and interference scenarios is studied, and the outage performance of S-R link is investigated by deriving an approximated expression for the outage probability. Moreover, an optimization problem in terms of the transmit power and the transmission time over S-R and R-D links is formulated and solved to obtain the optimal end-to-end energy efficiency for the considered system. Finally, some numerical results are provided to validate our proposed analysis models, as well as to study the optimal energy efficiency performance of the considered system.