Hierarchical Beam Training for Extremely Large-Scale MIMO: From Far-Field to Near-Field

Extremely large-scale MIMO (XL-MIMO) is a promising technique for future 6G communications. The sharp increase of the number of antennas causes the 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 involves very high overhead. The improved fast near-field beam training scheme based on time-delay beamforming can significantly reduce the overhead, but it suffers from very high hardware cost and energy consumption caused by extra time-delay circuits. In this paper, we propose a near-field two dimension (2D) hierarchical beam training scheme to reduce the overhead without extra hardware circuits. Specifically, we first formulate the near-field codeword design problem for any required high or low resolutions with different angle and distance coverages. Next, we propose a Gerchberg-Saxton (GS)-based algorithm to obtain the unconstrained codeword by considering the ideal fully digital architecture. Based on the unconstrained codeword, an iterative optimization algorithm is then proposed to acquire the practical codeword by considering the more practical hybrid digital-analog architecture. Finally, with the help of the practical 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.