基于稀疏随机阵列配置的CS-MIMO雷达感知矩阵构造

doi:10.7527/S1000-6893.2016.0020

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基于稀疏随机阵列配置的CS-MIMO雷达感知矩阵构造

彭珍妮^1,2, 贲德², 张弓², 徐笛²

1. 南京航空航天大学中小型无人机先进技术工信部重点实验室, 南京 210016;
2. 南京航空航天大学雷达成像与微波光子技术教育部重点实验室, 南京 210016

收稿日期:2015-10-29 修回日期:2016-01-15 出版日期:2016-03-15 发布日期:2016-01-18
通讯作者: 彭珍妮,Tel.:025-84892892,E-mail:pengzhenni@nuaa.edu.cn E-mail:pengzhenni@nuaa.edu.cn
作者简介:彭珍妮,女,硕士,助理研究员。主要研究方向:雷达信号处理、新体制雷达。Tel:025-84892892,E-mail:pengzhenni@nuaa.edu.cn;贲德,男,教授,博士生导师,中国工程院院士。主要研究方向:雷达系统。Tel:025-84892451,E-mail:bende01@sohu.com
基金资助:
国家自然科学基金(61501233,61071163,61271327,61471191);江苏高等学校优势学科建设工程资助项目

Sensing matrix construction for CS-MIMO radar based on sparse random array

PENG Zhenni^1,2, BEN De², ZHANG Gong², XU Di²

1. Key Laboratory of Unmanned Aerial Vehicle Technology, Ministry of Industry and Information Technology, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China;
2. Key Laboratory of Radar Imaging and Microwave Photonics, Ministry of Education, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China

Received:2015-10-29 Revised:2016-01-15 Online:2016-03-15 Published:2016-01-18
Supported by:
National Natural Science Foundation of China(61501233, 61071163, 61271327, 61471191);A Project Funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions

摘要/Abstract

摘要：

压缩感知(CS)理论中的感知矩阵在观测数据获取和信号重建过程中起关键性作用。目前,大部分研究通过引入高斯随机矩阵作为测量矩阵实现压缩观测,这类测量矩阵对硬件要求很高,工程实现困难。提出了一种基于稀疏随机阵列配置的压缩感知-多输入多输出(CS-MIMO)雷达中的感知矩阵构造方法,当MIMO雷达阵元配置为满足某种概率分布的稀疏随机阵列时,发射与接收导引矢量的Kronecker积能够起到压缩测量的作用。从理论上分析了所构造的感知矩阵的归一化互相关系数、Gram矩阵以及阵列方向图之间的内在联系,并证明了当随机阵元位置满足均匀分布时所构造的感知矩阵满足压缩感知重构条件。在这种稀疏随机阵列配置方式下,既可以避免额外引入随机测量矩阵,又能减少所需的阵元个数,从而大大降低CS-MIMO雷达系统复杂度。仿真实验表明,该方法具有较低的感知矩阵归一化互相关系数,与满阵CS-MIMO雷达相比能够在减少阵元个数的同时获得良好的重构性能,且使重构所需运算量大大降低。

关键词: 压缩感知, 多输入多输出雷达, 感知矩阵构造, 随机阵列配置, 重构条件

Abstract:

The sensing matrix of the compressive sensing(CS) theory plays an important role in data acquisition and signal recovery. Most of the previous research takes the Gaussian random matrix as the measurement matrix. However, it is hard to be implemented in physical electric circuit. A novel sensing matrix construction framework for CS-MIMO(multiple-input multiple-output) radar is proposed in this paper based on the sparse random array configuration. The elements of the linear array are placed at random with a fixed large aperture and when the positions of the random elements follow one certain probability distribution, the kronecker product of the transmitting and the receiving array steer vectors can serve as the sensing matrix. The relations between the cross correlations of the sensing matrix, the Gram matrix and the array pattern are investigated in detail. In particular, it is proved that the sensing matrix could satisfy the CS nonuniform recovery property when the random array is following the uniform distribution. Based on the sparse random array configuration, the CS-MIMO radar can not only avoid the additional random measurement matrix but also reduce the required elements. So the complexity of the CS-MIMO radar system is greatly reduced. The simulation experimental results show that the proposed method has lower cross correlations of the sensing matrix. Compared with the CS-MIMO radar with filled array, the proposed method is capable of better recovery performance with less elements, and the computation load for recovery is greatly reduced.

Key words: compressive sensing, multiple-input multiple-output radar, sensing matrix construction, random array configuration, recovery property

中图分类号:

彭珍妮, 贲德, 张弓, 徐笛. 基于稀疏随机阵列配置的CS-MIMO雷达感知矩阵构造[J]. 航空学报, 2016, 37(3): 1015-1024.

PENG Zhenni, BEN De, ZHANG Gong, XU Di. Sensing matrix construction for CS-MIMO radar based on sparse random array[J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2016, 37(3): 1015-1024.

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E-mail：hkxb@buaa.edu.cn

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主管单位：中国科学技术协会主办单位：中国航空学会北京航空航天大学

基于稀疏随机阵列配置的CS-MIMO雷达感知矩阵构造

Sensing matrix construction for CS-MIMO radar based on sparse random array

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