Adaptive Codebook Design and Beam Training for RIS-Aided Communication Systems With Hardware Constraints

Reconfigurable intelligent surface (RIS) has emerged as a promising solution to enable ultra-massive multiple-input multiple-output (MIMO) for 6G wireless communications. To direct the transmitted beam towards users with low pilot overhead, multi-resolution codebook-based beam training has been proposed for RIS-aided communication systems, which employs codewords with varying beamwidths to progressively narrow the search range and identify the optimal beam direction. However, the hardware constraints of the RIS such as the limited control capability, mutual coupling and manufacturing tolerances have not been fully considered, which may result in non-ideal beam patterns and misleading beam search directions, thereby degrading the overall beam training performance. To address this issue, in this paper, we revisit the multi-resolution codebook design and beam training scheme by taking the RIS hardware constraints into account. First, we propose a wide-beam generation method via multi-beam superposition, where the RIS reflection coefficients are optimized to achieve high beam gain with suppressed undesired fluctuations. Then, to mitigate the impact of the residual fluctuations in beam patterns, a posterior-based beam training scheme is proposed to adaptively correct erroneous beam search directions, thereby improving the beam training accuracy. To experimentally evaluate the proposed scheme, we implement a prototype RIS with $32\times 32$ reflective elements and deploy a 26 GHz millimeter-wave RIS-aided wireless communication testbed. Numerical and experimental results indicate that our approach achieves low training overhead and a data rate close to the exhaustive search method.