集群天线阵列：从确定性到随机建模

Swarm antenna arrays: From deterministic to stochastic modeling

摘要

集群天线阵列由部署于无人平台的分布式天线单元构成，为无线感知与通信提供了前所未有的灵活性与环境适应性。然而，分布式架构及无人平台位置的随机扰动削弱了多天线单元的协同增益，对实现相干信号合成构成了严峻挑战。集群天线的空间拓扑结构、平台的位置扰动以及天线规模对信号聚合性能的影响机理尚不明确。该文从确定性与随机性双重视角出发，探究集群天线阵列实现波束赋形的可行性。首先，针对多线性形式的集群天线阵列结构，构建了理论分析框架，推导了该类天线拓扑在波束合成过程中产生栅瓣的充要条件。对于双线性天线阵列，在不引入栅瓣的前提下，可放宽经典的半波长间距约束。该结论突破了传统均匀线性阵列设计中关于栅瓣抑制必须满足半波长间距的固有准则。随后，系统研究了天线位置扰动对波束赋形性能的影响。结果表明，天线的位置扰动将导致主瓣增益下降，主瓣增益的衰减无法通过单纯增加天线规模予以有效补偿；相反，增大天线规模的主要作用在于抑制旁瓣电平的波动方差，提升波束方向图的稳定性。最后，基于欧几里得随机矩阵的谱分析方法，研究了大规模无序天线阵列中涌现的确定性行为。当天线位置服从某种完全随机的空间分布时，其对应的欧几里得随机矩阵经验谱分布在天线数量趋于无穷时，几乎必然收敛于一个确定性极限。该结果揭示了无序天线阵列结构中蕴含的内在规律性，为后续大规模无序天线阵的建模与性能分析提供了必要的数学工具。

Abstract

Swarm antenna arrays, composed of spatially distributed antennas mounted on unmanned agents, offer substantial flexibility for wireless sensing and communication. However, their reconfigurable architecture, susceptibility to collisions, and inherently stochastic nature present significant challenges to achieving collaborative gain. This paper investigates the feasibility of achieving coherent beamforming in such systems from both deterministic and stochastic perspectives. First, a rigorous theoretical framework is developed to characterize the necessary and sufficient conditions for the emergence of grating lobes in multiple linear configurations and further show that for dual linear arrays, the classical half-wavelength spacing constraint can be safely relaxed without introducing spatial aliasing. Second, a theoretical analysis, supported by empirical validation, is presented and demonstrated that coherent gain can be approximately preserved under realistic positional perturbations. The proposed results reveal that spatial perturbations introduce measurable degradation in the main lobe, an effect that cannot be mitigated merely by increasing the number of antennas. Instead, the primary benefit of scaling lies in reducing the variance of perturbation-induced fluctuations. Finally, the emergent deterministic behavior of large-scale disordered arrays is examined by analyzing the spectral properties of the associated Euclidean random matrices. These results provide new theoretical foundations and practical design guidelines for enabling coherent functionality in swarm antenna arrays.

关键词

集群天线阵列 / 阵列方向图 / 波束赋形 / 相位补偿 / 扰动 / 欧几里得随机矩阵

Key words

swarm antenna arrays / array pattern / beamforming / phase compensation / perturbation / Euclidean random matrix

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基金资助

国家自然科学基金(12141107)

武汉市重点研发计划(2024050702030100)