有限空间下广义周期互质阵列群相对最优结构选型与增强优化研究

Although the traditional uniform array has superior performance, limited by the volume, manufacturing and maintenance costs and data storage capacity constraints, it is difficult to be applied in reality. The generalized periodic coprime array is found to be able to use fewer array elements to obtain higher resolution. The array positions can be analytically expressed as well, which is convenient for optimization. Although it has lots of advantages, the existing research were conducted under the assumption of free space, which lacks of the space constraint consideration. The generalized periodic coprime structures in the limited space form an array structure group, which produces lots of selectivities. The optimization is limited to the degree-of-freedom or mutual coupling enhancement singly as well. To solve the above problems, this program tends to conduct the research from the following three aspects. First, based on the finite physical space, the influence of structural parameters on the array performance is studied. By means of partitioning and comparing the physical aperture boundary, we can obtain the set of structures satisfying the space constraints and determine the relative optimal structure. Second, combining the characteristics of generalized periodic coprime array, we try to adopt the idea of constructing and decomposing symmetrical structures to establish the optimization criteria and provide the joint optimization scheme. Third, calculate the key parameters, design and build experimental platform to verify the research results. This program takes space constraints into consideration at the first time and provides feasible selection and optimization strategies among all the possible geometries. It will provide theoretical guidance for the practical application of generalized periodic coprime structures.

受体积、制造维护成本、数据存储处理能力限制，大规模传统均匀阵虽然性能优越，但很难实现和应用。广义周期互质阵被发现能使用较少阵元，获得高分辨阵列性能，且阵元位置可解析表示，具有重要的实际应用价值。目前，对广义周期互质结构的选择与优化，多从单一结构入手，忽视了互质结构的群属性，缺乏布阵空间限制考虑，且优化目标单一。本课题拟从有限物理空间约束出发，深入研究结构分布参数和阵列性能的相互关系，有选择地划分比较互质群的物理孔径边界，获得满足空间限制的结构集合的快速选择方案，确定相对最优阵型。在此基础上，结合广义周期互质阵特点，采用对称结构构建与分解思想，建立结构优化准则，给出自由度与耦合性能联合提升的结构优化方案。测算关键参数，搭建实验平台，验证研究结果。本课题将传感器布放空间限制纳入考虑范围，将提供复杂多样互质阵列群背景下，具体可行的选型与优化策略，为广义周期互质结构的实际应用提供理论指导。

稀疏阵可以在保证空间探测能力不降低的同时，大幅减少传感器数量并增大传感器布放间隔，有效降低系统成本和电磁耦合影响。稀疏阵结构优化设计是提高相控阵自由度和探测精度的重要技术手段。现有优化结构未考虑布放空间的物理尺寸限制，在实际应用中具有极大限制。本项目以广义周期互质阵列群为研究对象，围绕有限空间条件限制下的结构性能分析、结构参数选择、最优结构设计、性能联合增强，取得了以下研究成果：（1）广义周期互质阵结构参数对结构性能的影响机理研究；（2）相对最优结构的快速选型方法；（3）基于密集子阵分解的嵌套阵优化设计准则与最优结构设计；（4）基于冗余元素去除的互质阵优化设计准则与最优结构设计；（5）稀疏阵测向实验平台搭建与测试分析。总的来说，基于协方差矩阵恢复的稀疏阵高分辨测向理论和优化方法，从理论上完成了有限空间限定条件下的结构群确定和最优选型技术研究，从设计层面给出了多种优化结构准则和方案，并建立了测向实验系统，实现了从理论到实验验证的闭环研究。项目组取得的一系列研究成果为我国稀疏阵列探测与定位的实用化进程奠定了理论基础。项目按照研究计划进行，研究成果包括国内外重要学术期刊论文12篇（SCI期刊论文9篇，EI期刊论文1篇，国际学术会议论文2篇）、授权发明专利3项、申请发明专利2项、培养博士研究生5人、硕士研究生2人。

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