Unconstrained Synthesis of Covariance Matrix for MIMO Radar Transmit Beampattern
Unconstrained Synthesis of Covariance Matrix for MIMO Radar Transmit Beampattern
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DOI：
10.1109/tsp.2011.2153200
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发表时间：
2011-08
影响因子：
5.4
通讯作者：
Sajid Ahmed;J. Thompson;Y. Pétillot;B. Mulgrew
中科院分区：
文献类型：
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作者：
Sajid Ahmed;J. Thompson;Y. Pétillot;B. Mulgrew
多输入多输出（MIMO）雷达与相控阵雷达相比具有许多优点：提高了空间分辨率、更好的参数可识别性和更大的发射波束设计灵活性。发射波束图案的设计通常要求波形具有任意的自相关和互相关特性。波形的相关/协方差矩阵R必须是半正定的，因此期望波束图的合成通常是约束优化问题。为了简化约束优化问题，本文提出了两种算法来合成所需波束方向图的波形协方差矩阵。在第一个提出的算法的协方差矩阵R的平方根矩阵的元素被参数化使用的坐标的超球，隐含地满足的约束。这产生了一个迭代算法，其收敛速度可以通过提供良好的初始值显着增加。在第二种算法中，利用协方差矩阵R中的约束和冗余信息来找到封闭形式的解。第二种算法的缺点是，它可能会产生一个伪协方差矩阵（伪CM），不能保证是半正定的。然而，伪CM可以很容易地转换成协方差矩阵使用本征值分解和/或收缩方法。此外，伪CM也可以用于为第一算法提供良好的初始值，以实现更快的收敛。
Multiple-input multiple-output (MIMO) radars have many advantages over their phased-array counterparts: improved spatial resolution; better parametric identifiably and greater flexibility to design the transmit beampattern. The design of the transmit beampatterns generally requires the waveforms to have arbitrary auto- and cross-correlation properties. The correlation/covariance matrix, R, of the waveforms must be positive semidefinite, therefore synthesis of a desired beampattern is usually a constrained optimization problem. In this paper, to simplify the constrained optimization problem, two algorithms are proposed to synthesize the waveform covariance matrix for the desired beampattern. In the first proposed algorithm the elements of a square-root matrix of the covariance matrix R are parameterized using the coordinates of a hypersphere that implicitly fulfil the constraints. This yields an iterative algorithm, whose convergence speed can be increased significantly by providing good initial values. In the second algorithm the constraints and redundant information in the covariance matrix R are exploited to find a closed-form solution. The drawback of the second algorithm is that it may yield a pseudocovariance matrix (pseudo-CM) that is not guaranteed to be positive semidefinite. However, the pseudo-CM can be easily converted into a covariance matrix using eigenvalue decomposition and/or shrinkage methods. Moreover, a pseudo-CM can also be used to provide good initial values for the first algorithm to enable faster convergence.