Extremely Large-scale Array (ELAA) promises to deliver ultra-high data rates with increased antenna elements. However, increasing antenna elements leads to a wider realm of near-field, which challenges the traditional design of codebooks. In this paper, we propose novel near-field codebook schemes based on the fitting formula of codewords' quantization performance. First, we analyze the quantization performance properties of uniform linear array (ULA) and uniform planar array (UPA) codewords. Our findings reveal an intriguing property: the correlation formula for ULA codewords can be represented by the elliptic formula, while the correlation formula for UPA codewords can be approximated using the ellipsoid formula. Building on this insight, we propose a ULA uniform codebook that maximizes the minimum correlation based on the derived formula. Moreover, we introduce a ULA dislocation codebook to further reduce quantization overhead. Continuing our exploration, we propose UPA uniform and dislocation codebook schemes. Our investigation demonstrates that oversampling in the angular domain offers distinct advantages, achieving heightened accuracy while minimizing overhead in quantifying near-field channels. Numerical results demonstrate the appealing advantages of the proposed codebook over existing methods in decreasing quantization overhead and increasing quantization accuracy.

翻译：极大规模阵列（ELAA）有望通过增加天线单元实现超高速率数据传输。然而，天线单元数量的增加导致近场区域显著扩大，这对传统码本设计提出了挑战。本文基于码字量化性能的拟合公式，提出了新颖的近场码本方案。首先，我们分析了均匀线阵（ULA）和均匀面阵（UPA）码字的量化性能特性。研究发现一个有趣的性质：ULA码字的相关函数可用椭圆公式描述，而UPA码字的相关函数可近似采用椭球公式。基于这一发现，我们提出了基于推导公式最大化最小相关性的ULA均匀码本。此外，为降低量化开销，我们进一步提出了ULA错位码本。在此基础上，我们继续探索并提出了UPA均匀与错位码本方案。研究表明，角度域过采样具有显著优势：在降低近场信道量化开销的同时实现更高精度。数值结果表明，相较于现有方法，所提码本在减少量化开销与提升量化精度方面具有显著优势。