Hierarchical Codebook Design Using Scale-Changeable Reconfigurable Holographic Surfaces in Near-Far Field Communications

Reconfigurable holographic surfaces (RHSs) have been proposed as a cost-effective and power-efficient solution for extremely large-scale arrays, where the amplitude of electromagnetic waves radiated at each element is controlled to achieve high directive gain. However, the complexity of acquiring real-time channel state information (CSI) required for beamforming is prohibitively high, especially when the near-field expansion brought by the large-scale RHS is considered. In this paper, we propose a codebook-based beam training scheme for a large-scale RHS-enabled communication system to bypass CSI estimation. Unlike traditional phase-controlled arrays, the amplitude-controlled property of the RHS implies that each RHS element can be selectively activated. This motivates an array reconfiguration method where a scale-changeable RHS array is constructed to generate gain-flat beams with different coverage in the angle-range domain. A hierarchical RHS codebook is then proposed where the coverage of the codewords in each layer is progressively refined. To address the substantial beam search overhead in the near-far field, a two-stage beam training scheme is performed in the proposed codebook, thereby reducing the overhead to a logarithmic level of the element number. The simulation results show that the proposed scheme performs better than phased arrays given the same input power in terms of sum rate, and it also approaches the upper bound achieved by the exhaustive search at a significantly reduced overhead.