基于稀疏随机阵列配置的CS-MIMO雷达感知矩阵构造
收稿日期: 2015-10-29
修回日期: 2016-01-15
网络出版日期: 2016-01-18
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
Received date: 2015-10-29
Revised date: 2016-01-15
Online 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
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。
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 . DOI: 10.7527/S1000-6893.2016.0020
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.
[1] ENDER J H G. A brief review of compressive sensing applied to radar[C]//Proceedings of the 14th International Radar Symposium, 2013:3-16.
[2] CANDES E J, WAKIN M B. An introduction to compressive sampling(a sensing/sampling paradigm that goes against the common knowledge in data acquisition)[J]. IEEE Signal Processing Magazine, 2008, 25(2):21-30.
[3] DONOHO D L. Compressed sensing[J]. IEEE Transactions on Information Theory, 2006, 52(4):1289-1306.
[4] YU Y, PETROPULU A P, POOR H V. CSSF MIMO RADAR:Compressive-sensing and step-frequency based MIMO radar[J]. IEEE Transactions on Aerospace and Electronic Systems, 2012, 48(2):1490-1504.
[5] 顾福飞, 张群, 管桦, 等. 基于压缩感知的MIMO-SAR运动误差补偿与成像[J]. 航空学报, 2014, 35(3):838-847. GU F F, ZHANG Q, GUAN H, et al. Motion error compensation and imaging for MIMO-SAR based on compressed sensing[J]. Acta Aeronautica et Astronautica Sinica, 2014, 35(3):838-847(in Chinese).
[6] ELAD M. Optimized projections for compressed sensing[J]. IEEE Transactions on Signal Processing, 2007, 55(12):5695-5702.
[7] CANDES E J. The restricted isometry property and its implications for compressed sensing[J]. Comptes Rendus Methematique, 2008, 346(9):589-592.
[8] PENG Z N, ZHANG G, ZHANG J D, et al. Optimized measurement matrix design using spatiotemporal chaos for CS-MIMO radar[J/OL]. Mathematical Problems in Engineering, 2014:1-8[2015-08-26]. http://dx.doi.org/10.1155/2014/916451.
[9] YU Y, PETROPULU A P, POOR H V. Measurement matrix design for compressive sensing-based MIMO radar[J]. IEEE Transactions on Signal Processing, 2011, 59(11):5338-5352.
[10] ZHANG J D, ZHU D Y, ZHANG G. Adaptive compressed sensing radar oriented toward cognitive detection in dynamic sparse target scene[J]. IEEE Transactions on Signal Processing, 2012, 60(4):1718-1729.
[11] LI G, ZHU Z H, YANG, D H, et al. On projection matrix optimization for compressive sensing systems[J]. IEEE Transactions on Signal Processing, 2013, 61(11), 2887-2898.
[12] YAN W J, WANG Q, SHEN Y. Shrinkage-based alternating projection algorithm for efficient measurement matrix construction in compressive sensing[J]. IEEE Transactions on Instrumentation and Measurement, 2014, 63(5):1073-1084.
[13] 张劲东, 张弓, 潘汇, 等. 基于滤波器结构的压缩感知雷达感知矩阵优化[J]. 航空学报, 2013, 34(4):864-872. ZHANG J D, ZHANG G, PAN H, et al. Optimized sensing matrix design of filter structure based compressed sensing radar[J]. Acta Aeronautica et Astronautica Sinica, 2013, 34(4):864-872(in Chinese).
[14] YANG M, ZHANG G. Parameter identifiability of monostatic MIMO chaotic radar using compressed sensing[J]. Progress in Electromagnetics Research B, 2012, 44:367-382.
[15] CARIN L, LIU D H,GUO B. Coherence, compressive sensing, and random sensor arrays[J]. IEEE Antennas and Propagation Magazine, 2011, 53(4):28-39.
[16] LIU Y, WU M Y, WU S J. Fast OMP algorithm for 2D angle estimation in MIMO radar[J]. Electronics Letters, 2010, 46(6):444-445.
[17] CANDES E J, PLAN Y. A probabilistic and RIPless theory of compressed sensing[J]. IEEE Transactions on Information Theory, 2011, 57(11):7235-7254.
[18] HUGEL M, RAUHUT H, STROHMER T. Remote sensing via l1 minimization[J]. Foundations of Computational Mathematics, 2014, 14(1):115-150.
[19] DONOHO D L, ELAD M, TEMLYAKOV V N. Stable recovery of sparse overcomplete representations in the presence of noise[J]. IEEE Transactions on InformationTheory, 2006, 52(1):6-18.
[20] LI J, STOICA P, XU L, et al. On parameter identifiability of MIMO radar[J]. IEEE Signal Processing Letters, 2007, 14(12):968-971.
/
| 〈 |
|
〉 |
CJA