Reconfigurable intelligent surface (RIS) has emerged as a promising solution to overcome the challenges of high path loss and easy signal blockage in millimeter-wave (mmWave) and terahertz (THz) communication systems. With the increase of RIS aperture and system bandwidth, the near-field beam split effect emerges, which causes beams at different frequencies to focus on distinct physical locations, leading to a significant gain loss of beamforming. To address this problem, we leverage the property of Fresnel zone that the beam split disappears for RIS elements along a single Fresnel zone and propose beamforming design on the two dimensions of along and across the Fresnel zones. The phase shift of RIS elements along the same Fresnel zone are designed aligned, so that the signal reflected by these element can add up in-phase at the receiver regardless of the frequency. Then the expression of equivalent channel is simplified to the Fourier transform of reflective intensity across Fresnel zones modulated by the designed phase. Based on this relationship, we prove that the uniformly distributed in-band gain with aligned phase along the Fresnel zone leads to the upper bound of achievable rate. Finally, we design phase shifts of RIS to approach this upper bound by adopting the stationary phase method as well as the Gerchberg-Saxton (GS) algorithm. Simulation results validate the effectiveness of our proposed Fresnel zone-based method in mitigating the near-field beam split effect.

翻译：可重构智能表面（RIS）已成为克服毫米波（mmWave）和太赫兹（THz）通信系统中高路径损耗和信号易阻塞挑战的一种有前景的解决方案。随着RIS孔径和系统带宽的增加，近场波束分裂效应随之出现，导致不同频率的波束聚焦于不同的物理位置，从而引起显著的波束成形增益损失。为解决此问题，我们利用菲涅尔区的特性——即沿单个菲涅尔区的RIS单元波束分裂效应消失，并提出了沿菲涅尔区和跨菲涅尔区两个维度的波束成形设计。沿同一菲涅尔区的RIS单元相位偏移被设计为对齐，使得这些单元反射的信号在接收端能够同相叠加，而与频率无关。随后，等效信道的表达式被简化为跨菲涅尔区的反射强度经设计相位调制后的傅里叶变换。基于这一关系，我们证明了沿菲涅尔区相位对齐的均匀带内增益可实现速率的上界。最后，我们采用驻定相位法以及Gerchberg-Saxton（GS）算法设计RIS的相位偏移，以逼近该上界。仿真结果验证了我们提出的基于菲涅尔区的方法在缓解近场波束分裂效应方面的有效性。