近场和远场中低复杂度波束覆盖设计：一种傅里叶变换方法
Low-complexity Design for Beam Coverage in Near-field and Far-field: A Fourier Transform Approach
AI总结：
本文提出了一种基于傅里叶变换的低复杂度波束覆盖设计方法，适用于近场和远场多天线系统，通过空间-频率滤波和泰勒近似实现高效波束成形，降低计算复杂度并保持性能。
摘要：
本文研究了多天线系统在远场和近场情况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。为此，我们首先提出了一个通用的波束覆盖优化问题，以最大化目标区域内的最坏情况波束成形增益。在远场情况下，我们表明波束覆盖设计可以视为一个空间-频率滤波问题，其中通过在天线域中使用反傅里叶变换进行加权整形，可以实现角覆盖，从而得到无限长的加权序列。在有限天线数量的约束下，通过直接截断该序列提出了一种替代方案，这不可避免地在角边界处引入滚降效应，导致最坏情况波束成形增益下降。为了解决这个问题，我们基于有限天线引起的滚降效应进行了特征化，从而开发出一种具有保护放大器的滚降感知设计，以确保在目标角区域内的波束成形增益剖面平坦。接下来，我们将所提出的方法扩展到近场情况。具体来说，通过将近场信道指向向量（CSV）进行一阶泰勒近似，可以将二维（2D）波束覆盖设计（在角度和反向距离方面）转换为二维反傅里叶变换，从而得到低复杂度的波束成形设计。此外，观察到一种固有的近场距离模糊效应，表明足够宽的角覆盖会导致距离不敏感的波束指向。最后，数值结果表明，所提出的基于傅里叶变换的方法在最坏情况波束成形性能上与传统基于采样的优化方法相当，同时显著降低了计算复杂度。
英文摘要：
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.
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