In extremely large-scale multiple input multiple output (XL-MIMO) systems for future sixth-generation (6G) communications, codebook-based beam training stands out as a promising technology to acquire channel state information (CSI). Despite their effectiveness, when the pilot overhead is limited, existing beam training methods suffer from significant achievable rate degradation for remote users with low signal-to-noise ratio (SNR). To tackle this challenge, leverging the error-correcting capability of channel codes, we introduce channel coding theory into hierarchical beam training to extend the coverage area. Specifically, we establish the duality between hierarchical beam training and channel coding, and the proposed coded beam training scheme serves as a general framework. Then, we present two specific implementations exemplified by coded beam training methods based on Hamming codes and convolutional codes, during which the beam encoding and decoding processes are refined respectively to better accommodate to the beam training problem. Simulation results have demonstrated that, the proposed coded beam training method can enable reliable beam training performance for remote users with low SNR, while keeping training overhead low.

翻译：在面向未来第六代（6G）通信的超大规模多输入多输出（XL-MIMO）系统中，基于码本的波束训练成为获取信道状态信息（CSI）的一项有前景技术。尽管现有波束训练方法有效，但在导频开销有限的情况下，对于低信噪比（SNR）的远距离用户，其可达速率性能会显著下降。为应对这一挑战，本文利用信道编码的纠错能力，将信道编码理论引入分层波束训练以扩展覆盖范围。具体而言，我们建立了分层波束训练与信道编码之间的对偶关系，提出的编码波束训练方案可作为通用框架。随后，我们以基于汉明码和卷积码的编码波束训练方法为例，给出了两种具体实现方式，在此过程中分别优化了波束编码与解码流程，以更好地适配波束训练问题。仿真结果表明，所提出的编码波束训练方法能够为低信噪比下的远距离用户实现可靠的波束训练性能，同时保持较低的训练开销。