Colocated MIMO radar waveform design for transmit beampattern formation
Colocated MIMO radar waveform design for transmit beampattern formation
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DOI：
10.1109/taes.2014.140249
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发表时间：
2015-05
影响因子：
4.4
通讯作者：
Haisheng Xu;Rick S. Blum;Jian Wang;Jian Yuan
中科院分区：
文献类型：
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作者：
Haisheng Xu;Rick S. Blum;Jian Wang;Jian Yuan
本文研究了共址MIMO雷达波形设计方法，通过最小化集成旁瓣电平，获得比竞争方法更低旁瓣电平的波束方向图。首先，一个二次规划问题，制定了波束方向图设计的最小综合旁瓣电平的标准。推导出一个定理，提供了一个封闭形式的分析最优解，似乎是一个扩展的瑞利商最小化的可能奇异矩阵的二次型。这种奇异性发生在感兴趣的问题，但在这些奇异矩阵的情况下，最佳解决方案的证明不能在文献中找到。接下来，添加一个额外的约束，以获得所需的3 dB波束宽度的波束方向图，从而在一个非凸的二次约束的二次规划，这是NP-难。一个半定规划和高斯随机半定松弛被用来确定可行的解决方案任意接近的解决方案，以原问题。理论和数值分析说明了改变设计中采用的发射机数量和正交波形的影响。数值比较进行评估所提出的设计方法。
In this paper, colocated MIMO radar waveform design is considered by minimizing the integrated side-lobe level to obtain beam patterns with lower side-lobe levels than competing methods. First, a quadratic programming problem is formulated to design beam patterns by using the criteria for a minimal integrated side-lobe level. A theorem is derived that provides a closed-form analytical optimal solution that appears to be an extension of the Rayleigh quotient minimization for a possibly singular matrix in quadratic form. Such singularities are shown to occur in the problem of interest, but proofs for the optimum solution in these singular matrix cases could not be found in the literature. Next, an additional constraint is added to obtain beam patterns with desired 3 dB beamwidths, resulting in a nonconvex quadratically constrained quadratic program which is NP-hard. A semidefinite program and a Gaussian randomized semidefinite relaxation are used to determine feasible solutions arbitrarily close to the solution to the original problem. Theoretical and numerical analyses illustrate the impacts of changing the number of transmitters and orthogonal waveforms employed in the designs. Numerical comparisons are conducted to evaluate the proposed design approaches.