6D Movable Metasurface (6DMM) in Downlink NOMA Transmissions

This letter proposes a novel six-dimensional movable metasurface (6DMM)-assisted downlink non-orthogonal multiple access (NOMA) system, in which a conventional base station (BS) equipped with fixed antennas serves multiple users with the assistance of a reconfigurable intelligent surface (RIS) with six-dimensional spatial configurability. In contrast to traditional RIS with static surface, the proposed 6DMM architecture allows each element to dynamically adjust its position and orient the whole metasurface in yaw-pitch-roll axes, enabling both in spatial and electromagnetic controls. We formulate a sum-rate maximization problem that jointly optimizes the BS NOMA-based beamforming, phase-shifts, element positions, and rotation angles of metasurface under constraints of NOMA power levels, unit-modulus of phase-shifts, power budget, inter-element separation and boundaries of element position/orientation. Due to non-convexity and high-dimensionality, we employ a probabilistic cross-entropy optimization (CEO) scheme to iteratively refine the solution distribution based on maximizing likelihood and elite solution sampling. Simulation results show that the proposed CEO-based 6DMM-NOMA architecture achieves substantial rate performance gains compared to 6DMM sub-structures, conventional static RIS, and other multiple access mechanisms. It also highlights the effectiveness of CEO providing probabilistic optimization for solving high-dimensional scalable metasurface.