Extremely large-scale MIMO (XL-MIMO) is a promising technique for future 6G communications. The sharp increase in the number of antennas causes electromagnetic propagation to change from far-field to near-field. Due to the near-field effect, the exhaustive near-field beam training at all angles and distances requires very high overhead. The improved fast near-field beam training scheme based on time-delay structure can reduce the overhead, but it suffers from very high hardware costs and energy consumption caused by time-delay circuits. In this paper, we propose a near-field two dimension (2D) hierarchical beam training scheme to reduce the overhead without the need for extra hardware circuits. Specifically, we first formulate the multi-resolution near-field codewords design problem covering different angle and distance coverages. Next, inspired by phase retrieval problems in digital holography imaging technology, we propose a Gerchberg-Saxton (GS)-based algorithm to acquire the theoretical codeword by considering the ideal fully digital architecture. Based on the theoretical codeword, an alternating optimization algorithm is then proposed to acquire the practical codeword by considering the hybrid digital-analog architecture. Finally, with the help of multi-resolution codebooks, we propose a near-field 2D hierarchical beam training scheme to significantly reduce the training overhead, which is verified by extensive simulation results.

翻译：超大规模MIMO（XL-MIMO）是未来6G通信的一项有前景技术。天线数量的急剧增加导致电磁传播从远场转变为近场。由于近场效应，在所有角度和距离上进行穷举式近场波束训练会带来极高的开销。基于时延结构的改进型快速近场波束训练方案虽能降低开销，但需依赖时延电路，导致硬件成本与能耗过高。本文提出一种近场二维分层波束训练方案，可在无需额外硬件电路的情况下降低开销。具体而言：首先，我们构建了覆盖不同角度和距离范围的多分辨率近场码字设计问题；其次，受数字全息成像技术中相位恢复问题的启发，针对理想全数字架构，提出基于Gerchberg-Saxton（GS）的算法来获取理论码字；在此基础上，针对模数混合架构，提出交替优化算法获取实际码字；最后，借助多分辨率码本，提出近场二维分层波束训练方案，显著降低训练开销，并通过大量仿真结果验证其有效性。