Extremely large-scale Array (ELAA) promises to deliver ultra-high data rates with more antenna elements. Meanwhile, the increase of antenna elements leads to a wider realm of near-field, which challenges the traditional design of codebooks. In this paper, we propose novel codebook design schemes which provide better quantized correlation with limited overhead. First, we analyze the correlation between codewords and channel vectors uniform linear array (ULA) and uniform planar array (UPA). The correlation formula for the ULA channel can be expressed as an elliptic function, and the correlation formula for the UPA channel can be represented as an ellipsoid formula. Based on the analysis, we design a uniform sampling codebook to maximize the minimum quantized correlation and a dislocation ULA codebook to reduce the number of quantized bits further. Besides, we give a better sampling interval for the codebook of the UPA channel. Numerical results demonstrate the appealing advantages of the proposed codebook over existing methods in quantization bit number and quantization accuracy.

翻译：超大规模阵列（ELAA）有望通过更多天线单元实现超高数据传输速率。然而，天线单元数量的增加导致近场区域显著扩展，这对传统码本设计提出了挑战。本文提出新型码本设计方案，以有限开销实现更优的量化相关性。首先，我们分析了均匀线性阵列（ULA）和均匀平面阵列（UPA）中码字与信道向量之间的相关性。ULA信道的相关性公式可表示为椭圆函数，而UPA信道的相关性公式则可用椭球函数表征。基于该分析，我们设计了一种均匀采样码本以最大化最小量化相关性，并提出了一种错位ULA码本以进一步减少量化比特数。此外，我们还给出了UPA信道码本的优化采样间隔。数值结果表明，相较于现有方法，所提出的码本在量化比特数和量化精度方面具有显著优势。