  This paper proposes an energy-efficient RIS-enabled NOMA communication for
LEO satellite networks. The proposed framework simultaneously optimizes the
transmit power of ground terminals at LEO satellite and passive beamforming at
RIS while ensuring the quality of services. Due to the nature of the considered
system and optimization variables, the problem of energy efficiency
maximization is formulated as non-convex. In practice, it is very challenging
to obtain the optimal solution for such problems. Therefore, we adopt
alternating optimization methods to handle the joint optimization in two steps.
In step 1, for any given phase shift vector, we calculate efficient power for
ground terminals at satellite using Lagrangian dual method. Then, in step 2,
given the transmit power, we design passive beamforming for RIS by solving the
semi-definite programming. To validate the proposed solution, numerical results
are also provided to demonstrate the benefits of the proposed optimization
framework.
