AI 中文总结
研究线源近场采样问题，基于空间自由度开发几何感知采样框架，通过视长公式推导DoF密度表达式，采用自适应非均匀采样策略及引入反应模式密度，所提策略接近最优性能且优于单一基于传播模式DoF密度的采样。
AI 中文摘要
近场采样旨在用最少数量的测量点来表示发射和接收区域之间的电磁场，同时保留主要空间模式。本文基于空间自由度（DoF）开发了一种几何感知采样框架。利用视长公式为简单线源几何结构的传播模式DoF密度推导闭式表达式，给出总DoF及其局部分布。从累积DoF密度的等增量获得单DoF采样点，产生自适应非均匀采样策略直至奇异值谱的拐点。为改善拐点之外其余模式的表示，引入反应模式密度来指导额外边缘样本的放置。制定了基于算子的采样误差泛函，证明其下限为由连续信道算子被忽略的奇异值。数值结果表明，所提出的采样策略接近奇异值分解获得的最优性能，且显著优于仅基于传播模式DoF密度的采样。
英文摘要
Near-field sampling seeks to represent electromagnetic fields between transmitting and receiving regions using a minimal number of measurement points while preserving the dominant spatial modes. This paper develops a geometry-aware sampling framework based on spatial degrees of freedom (DoF). A view-length formulation is used to derive closed-form expressions for the propagating-mode DoF density for simple line-source geometries, providing both the total DoF and its local distribution. One-DoF sampling points are obtained from equal increments of the cumulative DoF density, yielding an adaptive nonuniform sampling strategy up to the knee of the singular-value spectrum. To improve the representation of the remaining modes beyond the knee, a reactive-mode density is introduced to guide the placement of additional edge samples. An operator-based sampling error functional is formulated and shown to be lower-bounded by the neglected singular values of the continuous channel operator. Numerical results demonstrate that the proposed sampling strategy closely approaches the optimal performance obtained from singular-value decomposition and significantly outperforms sampling based solely on the propagating-mode DoF density.
