Self-Correcting Beam Training Scheme for Metasurface Enabled XL-MIMO with Hardware Limitations

Reconfigurable intelligent surfaces (RISs) are considered as an efficient solution for the implementation of extremely large-scale MIMO (XL-MIMO). To mitigate the complexity of channel information acquisition, beam training is identified as an effective solution by selecting the optimal beam from a predefined codebook. However, practical hardware limitations of RIS result in the overlap of codeword coverage, i.e., non-orthogonal beams, which degrades the accuracy of optimal beam selection. In this paper, we propose a self-correcting hierarchical beam training scheme, where beam training is designed as a sequential process based on a tailored long short-term memory network. Received powers of sequentially selected multi-layer codewords are integrated to construct quasi-orthogonality for optimizing the beam selection. Beam training is thus reformulated as a sequential codeword classification problem. A codeword priority adjustment procedure is then designed to prevent the beam selection from looping among layers according to the visit frequency to each codeword of the current selection path. Simulation results show that our proposed method outperforms existing beam training approaches in terms of beam selection accuracy and sum rate in the presence of hardware limitations.