For near-field communications, it is a hardware-efficient means to form an extremely large-scale array (XL-array) by concatenating multiple modular arrays (also referred to as subarrays). In this letter, we aim to investigate the effect of time synchronization errors among transmissions of different subarrays on the beam-focusing performance. To this end, we first characterize the beam pattern function when the transmit beamforming is designed based on maximum ratio transmission (MRT) under the premise of perfect time synchronization. As this function is highly difficult for analysis, we then consider a typical case with two subarrays. Interestingly, we show that for this case, the beam-focusing effect still persists even in the presence of time synchronization errors, while the focused location is deviated from the user location with an angle offset upper-bounded by 1/M, where M denotes the number of antennas in each subarray. Subsequently, for the general case with multiple subarrays, despite analytical intractability, we numerically show that time synchronization errors give rise to an imbricated (instead of focused) beam pattern. This may significantly degrade multi-user communication performance in practice due to the reduced desired signal power and increased inter-user interference.

翻译：针对近场通信，通过级联多个模块化阵列（也称子阵列）来构建超大规模阵列（XL-array）是一种硬件高效的实现方式。本文旨在研究不同子阵列传输间的时间同步误差对波束聚焦性能的影响。为此，我们首先在完美时间同步前提下，基于最大比传输（MRT）设计发射波束赋形，推导出波束图案函数。由于该函数分析难度极高，我们进而考虑两个子阵列的典型情况。有趣的是，研究表明在此情形下即使存在时间同步误差，波束聚焦效应依然存在，但聚焦位置偏离用户位置，且角度偏移上界为1/M（M为每个子阵列的天线数）。随后，针对多子阵列的普遍情形，尽管解析分析存在困难，我们通过数值仿真证明：时间同步误差会导致波束图案呈现叠瓦状（而非聚焦状）。这一现象可能因期望信号功率降低和用户间干扰增强而在实践中显著恶化多用户通信性能。