AI 中文总结
该研究提出基于变分法的框架，克服现有MIMO阵列波束成形方法的点源近似误差、空间维度限制与几何推广难题，经MATLAB天线工具箱验证可提升近场精度。
AI 中文摘要
我们提出了一种新颖的基于变分法（CoV）的框架，用于表征任意多输入多输出（MIMO）阵列几何结构的连续电磁流形并在其上进行波束成形。该框架基于最先进技术（SotA）的离散矩量公式构建，同时克服了其三个基本局限性：（i）近场辐射算子产生的点源近似误差；（ii）波束成形空间被限制为硬件端口数量决定的N维子空间；（iii）难以推广到任意阵列几何结构。为此，我们将每个网格单元建模为二维平面贴片，通过高斯-勒让德（GL）求积法计算其空间平均格林函数，以可忽略的额外成本获得更精确的近场表示；同时引入L²(S_T)中的连续馈电函数w(p)，作为N端口网络的无限维极限，将优化提升到维度K>>N的硬件解耦电流子空间。作为应用示例，我们采用该基于CoV的框架推导了两种场景下的闭式最优波束成形器：无约束场强最大化，以及功率密度（PD）和区域约束下的近场方向图合成，确立了它们与离散广义匹配滤波器的精确类比。全波MATLAB Antenna Toolbox验证表明，对于线性和平面几何结构，该框架在相当的计算成本下，相比SotA基线实现了一致的近场精度提升。
英文摘要
We present a novel calculus of variations (CoV)-based framework for the characterizing of, and beamforming over, continuous electromagnetic manifolds of arbitrary multiple-input multiple-output (MIMO) array geometries. Building upon the discrete moment-matrix formulation of the state-of-the-art (SotA), the proposed framework simultaneously overcomes three of its fundamental limitations: (i) the point-source approximation error incurred by the near-field radiation operator; (ii) the confinement of the beamforming space to the N-dimensional subspace dictated by the hardware port count; and (iii) the generalization to arbitrary array geometries. To this end, each mesh element is modeled as a two-dimensional planar patch whose spatially averaged Green's function is evaluated via Gauss-Legendre (GL) quadrature, yielding a strictly more accurate near-field representation at negligible additional cost, while a continuous feeding function w(p) in L^2(S_T), introduced as the infinite-dimensional limit of the N-port network, lifts the optimization onto a hardware-decoupled current subspace of dimension K >> N. As an application example, we employ the proposed CoV-based framework to derive closed-form optimal beamformers for both unconstrained field-strength maximization, and a near-field pattern synthesis under a power density (PD) and region constraints, establishing their exact analogy to the discrete and generalized matched filters. Full-wave MATLAB Antenna Toolbox validation confirms consistent near-field accuracy gains over the SotA baseline for both linear and planar geometries at comparable computational cost.
CommentsSubmitted to an IEEE journal
