基于压缩感知的阵列天线稀疏优化与子阵划分方法研究

The technical complexity and cost of array antenna especially for huge array can be greatly reduced by using the sparse synthesis and subarray partition techniques, and the research in this field has attracted growing attention. In recent years, as significant progress in the application of compressed sensing (CS) in synthesis of array antenna has been made, the development of sparse synthesis and subarray partition has also been driven forward as well. However, big challenges are still there, e.g. the correlation as well as the computation cost are very high resulted from fixed grids. In this study, we try to solve this problem by using the parameter learning method based on the generalized compressed sensing model so as to break through the limitation of fixed grids and improving the optimization performance along with the computation efficiency. And on this basis, we design and manufacture prototypes of sparse array antenna. In view of the problem of planar subarray partition minimization, we use the total variance minimization method after establishing the compressed sensing model to realize the optimal subarray partition for achieving the predefined pattern with as less subarray as possible. At the same time, we also explore the application of subarray partition of a planar array to forming a mono-pulse antenna by synthesizing the sum and difference patterns based on the joint sparse recovery theory. This work is expected to inaugurate a new hot topic and promote the technical development of antenna array synthesis as well as the related research progress in China.

利用稀疏优化和子阵划分技术可以极大地降低阵列天线（尤其是大规模阵列天线）的实现难度和工程造价，其研究在阵列天线领域备受重视。近年来，压缩感知理论和方法在阵列天线中的应用研究不断深入，有力推动了稀疏优化和子阵划分技术的发展。然而，该研究工作仍面临着很大挑战，例如稀疏阵压缩感知综合方法受限于固定网格划分带来的高相关性、大计算量等问题，项目拟基于参数学习方法，建立稀疏阵优化的广义压缩感知模型，突破固定网格限制，提高算法的优化性能和计算效率，设计并实现稀疏阵样件。针对平面阵最小化子阵数的子阵划分问题，项目拟从全变分稀疏变换入手，建立子阵划分的压缩感知模型，实现满足目标方向图要求的最优子阵划分，并基于联合稀疏恢复理论，研究其在单脉冲天线和差方向图形成中的应用。项目的研究有望开拓新的研究热点，推动阵列天线综合技术的发展，提升我国在该领域的研究水平。

利用稀疏优化和子阵划分技术可以极大地降低阵列天线（尤其是大规模阵列天线）的实现难度和工程造价，其研究在阵列天线领域备受重视。近年来，压缩感知理论和方法在阵列天线中的应用研究不断深入，有力推动了稀疏优化和子阵划分技术的发展。然而，该工作仍面临着很大挑战，例如稀疏阵压缩感知综合方法受限于固定网格划分带来的高相关性、大计算量等问题，基于压缩感知的子阵划分技术还处于初步探索阶段。针对现阶段阵列天线稀疏优化与子阵划分中存在的问题，课题开展了以下研究：.1）研究了稀疏阵优化模型的物理约束，理论分析并仿真验证了当前优化模型受限于固定网格划分，提出了用动态网格代替固定网格，建立了稀疏阵优化的广义压缩感知模型；.2）针对最小化阵元数的稀疏阵优化问题，提出了基于无栅格压缩感知的稀疏阵综合算法。该算法通过引入动态网格，赋予阵元位置自学习能力，对直线阵和平面阵的笔形波束/赋形波束综合均有效。仿真实验验证了所提算法的有效性，与现有稀疏优化算法相比，所提算法稀疏效果更好。.3）将所提算法从直线阵、平面阵推广到同心圆环阵中，提出了基于无栅格压缩感知的稀疏同心圆环阵综合算法。仿真实验表明，相比于传统的压缩感知方法，所提方法可以获得更低的副瓣电平。.4）基于所提的无栅格压缩感知稀疏阵综合算法，以矩形贴片为天线单元，采用共面共馈方式进行馈电，研制了Ku频段微带稀疏阵天线，实测结果满足设计要求；开展了稀疏阵的相关特性研究，理论分析与仿真实验表明，稀疏阵的稀疏率随阵列口径的增大而增大，随可扫描角度的增大而变小。.5）研究了最小化子阵数的子阵划分方法，将最小化子阵数的子阵划分问题转化为稀疏重建问题，从而利用凸优化算法对这种多变量优化问题进行高效求解，提出了基于压缩感知的子阵划分方法，并分别应用到星载干涉高度计平面阵天线和单脉冲雷达天线和差波束的设计中。