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In this paper, we investigate the reconfigurable intelligent surface(RIS)-aided terahertz (THz) communication system with the sparse radiofrequency chains antenna structure at the base station (BS). To overcome thebeam split of the BS, different from the conventional single-layertrue-time-delay (TTD) scheme, we propose a double-layer TTD scheme that caneffectively reduce the number of large-range delay devices, which involveadditional insertion loss and amplification circuitry. Next, we analyze thesystem performance under the proposed double-layer TTD scheme. To relieve thebeam split of the RIS, we consider multiple distributed RISs to replace anultra-large size RIS. Based on this, we formulate an achievable ratemaximization problem for the distributed RISs-aided THz communications viajointly optimizing the hybrid analog/digital beamforming, time delays of thedouble-layer TTD network and reflection coefficients of RISs. Considering thepractical hardware limitation, the finite-resolution phase shift, time delayand reflection phase are constrained. To solve the formulated problem, we firstdesign an analog beamforming scheme including optimizing phase shift and timedelay based on the RISs' locations. Then, an alternatively optimizationalgorithm is proposed to obtain the digital beamforming and reflectioncoefficients based on the minimum mean square error and coordinate updatetechniques. Finally, simulation results show the effectiveness of the proposedscheme.

Beamforming Design for the Distributed RISs-aided THz Communications with Double-Layer True Time Delays