This paper studies an extremely large-scale reconfigurable intelligent surface (XL-RIS) empowered covert communication system in the near-field region. Alice covertly transmits messages to Bob with the assistance of the XL-RIS, while evading detection by Willie. To enhance the covert communication performance, we maximize the achievable covert rate by jointly optimizing the hybrid analog and digital beamformers at Alice, as well as the reflection coefficient matrix at the XL-RIS. An alternating optimization algorithm is proposed to solve the joint beamforming design problem. For the hybrid beamformer design, a semi-closed-form solution for fully digital beamformer is first obtained by a weighted minimum mean-square error based algorithm, then the baseband digital and analog beamformers at Alice are designed by approximating the fully digital beamformer via manifold optimization. For the XL-RIS's reflection coefficient matrix design, a low-complexity alternating direction method of multipliers based algorithm is proposed to address the challenge of large-scale variables and unit-modulus constraints. Numerical results unveil that i) the near-field communications can achieve a higher covert rate than the far-field covert communications in general, and still realize covert transmission even if Willie is located at the same direction as Bob and closer to the XL-RIS; ii) the proposed algorithm can enhance the covert rate significantly compared to the benchmark schemes; iii) the proposed algorithm leads to a beam diffraction pattern that can bypass Willie and achieve high-rate covert transmission to Bob.
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