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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。
Perceptual matrix in compressed sensing (CS) theory plays a key role in the acquisition of observational data and signal reconstruction. At present, most researches introduce the Gaussian random matrix as the measurement matrix to realize the compression observation. Such measurement matrix has high requirements on the hardware and the project is difficult to realize. A novel perceptual matrix construction method based on sparse random array configuration is proposed in CS-MIMO radar. When MIMO radar array elements are configured as sparse random arrays satisfying some probability distribution, The Kronecker product that receives steering vectors can act as a compression measure. The relationship between normalized cross-correlation coefficient, Gram matrix and array pattern of perceptual matrix is analyzed theoretically. It is also proved that the perceptual matrix constructed when the position of random elements satisfies the uniform distribution satisfies the compression perception Reconstruction conditions. In this sparse random array configuration, it can avoid the extra introduction of random measurement matrix and reduce the number of array elements required, thus greatly reducing the complexity of the CS-MIMO radar system. Simulation results show that this method has a lower normalized correlation coefficient of perceptual matrix, which can reduce the number of elements and achieve better reconstruction performance than full array CS-MIMO radar. The amount of computation is greatly reduced.