  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.
