Robust Beamforming Design for Near-Field DMA-NOMA mmWave Communications With Imperfect Position Information

For millimeter-wave (mmWave) non-orthogonal multiple access (NOMA) communication systems, we propose an innovative near-field (NF) transmission framework based on dynamic metasurface antenna (DMA) technology. In this framework, a base station (BS) utilizes the DMA hybrid beamforming technology combined with the NOMA principle to maximize communication efficiency between near-field users (NUs) and far-field users (FUs). In conventional communication systems, obtaining channel state information (CSI) requires substantial pilot signals, significantly reducing system communication efficiency. We propose a beamforming design scheme based on position information to address with this challenge. This scheme does not depend on pilot signals but indirectly obtains CSI by analyzing the geometric relationship between user position information and channel models. However, in practical applications, the accuracy of position information is challenging to guarantee and may contain errors. We propose a robust beamforming design strategy based on the worst-case scenario to tackle this issue. Facing with the multi-variable coupled non-convex problems, we employ a dual-loop iterative joint optimization algorithm to update beamforming using block coordinate descent (BCD) and derive the optimal power allocation (PA) expression. We analyze its convergence and complexity to verify the proposed algorithm's performance and robustness thoroughly. We validate the theoretical derivation of the CSI error bound through simulation experiments. Numerical results show that our proposed scheme performs better than traditional beamforming schemes. Additionally, the transmission framework exhibits strong robustness to NU and FU position errors, laying a solid foundation for the practical application of mmWave NOMA communication systems.