Reconfigurable intelligent surfaces (RISs) represent a pioneering technology to realize smart electromagnetic environments by reshaping the wireless channel. \textcolor[rgb]{0,0,0}{Jointly designing the transceiver and RIS relies on the channel state information (CSI), whose feedback has not been investigated in multi-RIS-assisted frequency division duplexing systems.} In this study, the limited feedback of the RIS-assisted wireless channel is examined by capitalizing on the ability of the RIS in channel customization. \textcolor[rgb]{0,0,0}{By configuring the phase shifters of the surfaces using statistical CSI, we customize a sparse channel in rich-scattering environments, which significantly reduces the feedback overhead in designing the transceiver and RISs. Since the channel is customized in terms of singular value decomposition (SVD) with full-rank, the optimal SVD transceiver can be approached without a matrix decomposition and feeding back the complete channel parameters. The theoretical spectral efficiency (SE) loss of the proposed transceiver and RIS design is derived by considering the limited CSI quantization. To minimize the SE loss, a bit partitioning algorithm that splits the limited number of bits to quantize the CSI is developed.} Extensive numerical results show that the channel customization-based transceiver with reduced CSI can achieve satisfactory performance compared with the optimal transceiver with full CSI. Given the limited number of feedback bits, the bit partitioning algorithm can minimize the SE loss by adaptively allocating bits to quantize the channel parameters.

翻译：可重构智能表面（RIS）是一种通过重塑无线信道实现智能电磁环境的开创性技术。收发机与RIS的联合设计依赖于信道状态信息（CSI），但在多RIS辅助的频分双工系统中，CSI的反馈问题尚未得到充分研究。本研究利用RIS在信道定制中的能力，探讨了RIS辅助无线信道的有限反馈问题。通过利用统计CSI配置表面的移相器，我们在富散射环境中定制了稀疏信道，从而显著降低了收发机与RIS设计中的反馈开销。由于该信道在全秩条件下基于奇异值分解（SVD）进行定制，因此无需矩阵分解或反馈完整信道参数即可逼近最优SVD收发机。针对有限CSI量化，推导了所提出的收发机与RIS设计方案的理论频谱效率（SE）损失。为最小化SE损失，提出了一种比特分配算法，将有限数量的量化比特分配给CSI参数。大量数值结果表明，与具有完整CSI的最优收发机相比，基于信道定制的低CSI收发机能够实现令人满意的性能。在反馈比特数量受限的情况下，该比特分配算法通过自适应分配量化比特以压缩信道参数，从而最小化SE损失。