In this paper, we study efficient beam coverage design for multi-antenna systems in both far-field and near-field cases. To reduce the computational complexity of existing sampling-based optimization methods, we propose a new low-complexity yet efficient beam coverage design. To this end, we first formulate a general beam coverage optimization problem to maximize the worst-case beamforming gain over a target region. For the far-field case, we show that the beam coverage design can be viewed as a spatial-frequency filtering problem, where angular coverage can be achieved by weight-shaping in the antenna domain via an inverse FT, yielding an infinite-length weighting sequence. Under the constraint of a finite number of antennas, a surrogate scheme is proposed by directly truncating this sequence, which inevitably introduces a roll-off effect at the angular boundaries, yielding degraded worst-case beamforming gain. To address this issue, we characterize the finite-antenna-induced roll-off effect, based on which a roll-off-aware design with a protective zoom is developed to ensure a flat beamforming-gain profile within the target angular region. Next, we extend the proposed method to the near-field case. Specifically, by applying a first-order Taylor approximation to the near-field channel steering vector (CSV), the two-dimensional (2D) beam coverage design (in both angle and inverse-range) can be transformed into a 2D inverse FT, leading to a low-complexity beamforming design. Furthermore, an inherent near-field range defocusing effect is observed, indicating that sufficiently wide angular coverage results in range-insensitive beam steering. Finally, numerical results demonstrate that the proposed FT-based approach achieves a comparable worst-case beamforming performance with that of conventional sampling-based optimization methods while significantly reducing the computational complexity.

翻译：本文研究了多天线系统在远场和近场场景下的高效波束覆盖设计。为降低现有基于采样的优化方法的计算复杂度，我们提出了一种新的低复杂度且高效的波束覆盖设计方案。为此，我们首先构建了一个通用的波束覆盖优化问题，旨在最大化目标区域内的最坏情况波束赋形增益。对于远场情况，我们证明波束覆盖设计可视为一个空域-频率滤波问题，其中角度覆盖可通过在天线域利用逆傅里叶变换进行权重整形来实现，从而产生一个无限长的加权序列。在有限天线数量的约束下，我们提出了一种直接截断该序列的替代方案，但这不可避免地会在角度边界引入滚降效应，导致最坏情况波束赋形增益下降。为解决此问题，我们刻画了有限天线数引起的滚降效应，并在此基础上开发了一种具有保护性放大的滚降感知设计，以确保目标角度区域内平坦的波束赋形增益分布。接着，我们将所提方法扩展至近场情况。具体而言，通过对近场信道导向矢量进行一阶泰勒近似，二维（角度与逆距离）波束覆盖设计可转化为一个二维逆傅里叶变换，从而实现低复杂度的波束赋形设计。此外，我们观察到一种固有的近场距离散焦效应，表明足够宽的角度覆盖会导致波束指向对距离不敏感。最后，数值结果表明，所提出的基于傅里叶变换的方法在实现与传统的基于采样的优化方法相当的最坏情况波束赋形性能的同时，显著降低了计算复杂度。