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

In this paper, we investigate the reconfigurable intelligent surface (RIS)-aided terahertz (THz) communication system with the sparse radio frequency chains antenna structure at the base station (BS). To overcome the beam split of the BS, different from the conventional single-layer true-time-delay (TTD) scheme, we propose a double-layer TTD scheme that can effectively reduce the number of large-range delay devices, which involve additional insertion loss and amplification circuitry. Next, we analyze the system performance under the proposed double-layer TTD scheme. To relieve the beam split of the RIS, we consider multiple distributed RISs to replace an ultra-large size RIS. Based on this, we formulate an achievable rate maximization problem for the distributed RISs-aided THz communications via jointly optimizing the hybrid analog/digital beamforming, time delays of the double-layer TTD network and reflection coefficients of RISs. Considering the practical hardware limitation, the finite-resolution phase shift, time delay and reflection phase are constrained. To solve the formulated problem, we first design an analog beamforming scheme including optimizing phase shift and time delay based on the RISs' locations. Then, an alternatively optimization algorithm is proposed to obtain the digital beamforming and reflection coefficients based on the minimum mean square error and coordinate update techniques. Finally, simulation results show the effectiveness of the proposed scheme.