Near-field Beam-focusing Pattern under Discrete Phase Shifters

Abstract: 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 deployed pose demanding challenges on the hardware cost and power consumption, especially when the antennas employ high-resolution phase shifters (PSs). To address this issue, in this paper, we consider low-resolution 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 characterizing 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 property 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 properties, respectively. In addition, we provide intuitive understanding for the appearance of grating lobes under discrete PSs from an array-of-subarrays perspective. Finally, numerical results demonstrate that the grating lobes generally degrade communication rate 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.