Reconfigurable intelligent surface (RIS)-aided terahertz (THz) communications have been regarded as a promising candidate for future 6G networks because of its ultra-wide bandwidth and ultra-low power consumption. However, there exists the beam split problem, especially when the base station (BS) or RIS owns the large-scale antennas, which may lead to serious array gain loss. Therefore, in this paper, we investigate the beam split and beamforming design problems in the THz RIS communications. Specifically, we first analyze the beam split effect caused by different RIS sizes, shapes and deployments. On this basis, we apply the fully connected time delayer phase shifter hybrid beamforming architecture at the BS and deploy distributed RISs to cooperatively mitigate the beam split effect. We aim to maximize the achievable sum rate by jointly optimizing the hybrid analog/digital beamforming, time delays at the BS and reflection coefficients at the RISs. To solve the formulated problem, we first design the analog beamforming and time delays based on different RISs physical directions, and then it is transformed into an optimization problem by jointly optimizing the digital beamforming and reflection coefficients. Next, we propose an alternatively iterative optimization algorithm to deal with it. Specifically, for given the reflection coefficients, we propose an iterative algorithm based on the minimum mean square error technique to obtain the digital beamforming. After, we apply LDR and MCQT methods to transform the original problem to a QCQP, which can be solved by ADMM technique to obtain the reflection coefficients. Finally, the digital beamforming and reflection coefficients are obtained via repeating the above processes until convergence. Simulation results verify that the proposed scheme can effectively alleviate the beam split effect and improve the system capacity.

翻译：可重构智能表面辅助的太赫兹通信因其超宽带宽和超低功耗，被视为未来6G网络的重要候选技术。然而，当基站或可重构智能表面配备大规模天线时，会出现波束分裂问题，可能导致严重的阵列增益损失。因此，本文针对太赫兹可重构智能表面通信中的波束分裂与波束形成设计问题展开研究。具体而言，我们首先分析了不同尺寸、形状和部署方式的可重构智能表面所引发的波束分裂效应。在此基础上，在基站端采用全连接时间延迟器-移相器混合波束形成架构，并部署分布式可重构智能表面以协同减轻波束分裂效应。我们旨在通过联合优化基站的混合模数波束形成与时间延迟以及可重构智能表面的反射系数，最大化可实现的和速率。为解决上述优化问题，我们首先根据不同可重构智能表面的物理方向设计模拟波束形成与时间延迟，随后将问题转化为联合优化数字波束形成与反射系数的优化模型。接着，提出了一种交替迭代优化算法进行求解：在固定反射系数的条件下，基于最小均方误差技术提出迭代算法获取数字波束形成；随后利用低秩分解和单调凸二次变换方法将原问题转化为可接受乘子法求解的二次约束二次规划问题以获得反射系数；最终通过重复上述过程直至收敛得到数字波束形成与反射系数。仿真结果表明，所提方案能有效缓解波束分裂效应并提升系统容量。