Extremely large-scale arrays (XL-arrays) have emerged as a promising technology for enabling near-field communications in future wireless systems. However, the huge number of antennas pose demanding challenges on the hardware cost and energy consumption, especially when the antennas employ high-resolution phase shifters (PSs). To address this issue, in this paper, we consider discrete PSs at the XL-array which are practically more energy efficient, and investigate the impact of PS resolution on the near-field beam-focusing effect. To this end, we propose a new Fourier series expansion method to efficiently tackle the difficulty in characterising the beam pattern properties under phase quantization. Interestingly, we analytically show, for the first time, that 1) discrete PSs introduce additional grating lobes; 2) the main lobe still exhibits the beam-focusing effect with its beam power increasing with PS resolution; and 3) there are two types of grating lobes, featured by the beam-focusing and beam-steering effects, respectively. Finally, numerical results demonstrate that the grating lobes generally degrade the communication performance. However, a low-resolution of 3-bit PSs can achieve similar beam pattern and rate performance with the continuous PS counterpart, while it attains much higher energy efficiency.

翻译：极大规模阵列（XL-arrays）已成为未来无线系统中实现近场通信的关键技术。然而，天线数量的急剧增加对硬件成本和能耗提出了严峻挑战，尤其是在采用高分辨率移相器（PSs）时。为解决这一问题，本文研究采用实际能效更高的离散移相器的XL-阵列，并探究移相器分辨率对近场波束聚焦效应的影响。为此，我们提出一种新的傅里叶级数展开方法，以有效解决相位量化下波束方向图特性表征的难题。有趣的是，我们首次通过理论分析证明：1）离散移相器会引入额外的栅瓣；2）主瓣仍呈现波束聚焦效应，其波束功率随移相器分辨率提升而增强；3）存在两类栅瓣，分别具有波束聚焦效应和波束赋形效应。最后，数值结果表明栅瓣通常会降低通信性能。然而，采用3比特低分辨率移相器即可实现与连续移相器相近的波束方向图和速率性能，同时能获得显著更高的能效。