高自由度低互耦的广义二阶嵌套MIMO雷达DOA估计

doi:10.12305/j.issn.1001-506X.2021.10.15

摘要/Abstract

摘要：

针对传统二阶嵌套阵自由度低、互耦率高的问题, 提出高自由度、低互耦的广义二阶嵌套多输入多输出(multiple input multiple output, MIMO)雷达阵列, 用于波达方向(direction of Arrival, DOA)估计。首先, 在传统二阶嵌套阵的收发两端分别引入互质扩展因子, 抑制阵元互耦的同时提升阵列的自由度; 其次, 推导了“和差联合阵列”结构下, 包括互质扩展因子、连续虚拟阵元数和总虚拟阵元数在内的自由度闭式解; 最后, 针对不同互质扩展因子造成的离散孔洞问题, 基于原子范数最小化理论, 在不连续点出填补虚拟阵元, 并建立恢复填补虚拟阵元等价接收信号的凸优化模型, 结合多重信号分类算法进行DOA估计。仿真实验验证了阵列结构的合理性和算法的有效性。

关键词: DOA估计, 嵌套阵, 自由度, 互耦率, 和差联合阵列, 原子范数最小化

Abstract:

In view of low degree of freedom and high mutual coupling of traditional two-level nested array, this paper proposes a generalized two-level nested multiple input multiple output (MIMO) configuration with high degree of freedom and low mutual coupling, which is used for direction of arrival (DOA) estimation. Firstly, the traditional two-level nested array of the transmitting array and receiving array are introduced into the coprime extension factors to reduce mutual coupling and increase degree of freedom. Secondly, the close-form expressions of degree of freedom including the coprime expansion factors, the number of continuous virtual elements and the total number of virtual elements under the structures of "sum-difference co-array" are derived. Finally, for the discrete holes caused by the different coprime expansion factors, the virtual elements is filled at the discontinuous points and establishes the convex optimization model of reconstructing the equivalent received signal of the filling virtual array elements, and combining with multiple signal classification algorithm for DOA estimation. Simulation results demonstrate the rationality of the array structure and effectiveness of the algorithm.

Key words: direction of arrival (DOA) estimation, nested array, degree of freedom, mutual coupling, sum-difference co-array, atomic norm minimization

中图分类号:

TN953

张宇乐, 胡国平, 周豪, 岳世杰, 赵飞龙. 高自由度低互耦的广义二阶嵌套MIMO雷达DOA估计[J]. 系统工程与电子技术, 2021, 43(10): 2819-2827.

Yule ZHANG, Guoping HU, Hao ZHOU, Shijie YUE, Feilong ZHAO. DOA estimation of generalized two-level nested MIMO radar with high degree of freedom and low mutual coupling[J]. Systems Engineering and Electronics, 2021, 43(10): 2819-2827.

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T	最优M₁, M₂, N₁, N₂	自由度2l+1
T=4k	M₁=M₂=N₁=N₂=T/4	(T⁴+8T³-64T+64)/64
T=4k+1	M₁=N₁=N₂=(T-1)/4, M₂=(T+3)/4	(T⁴+8T³+2T²-64T-11)/64
T=4k+2	M₁=N₁=(T-2)/4, M₂=N₂=(T+2)/4	(T⁴+8T³+8T²-32T+16)/64
T=4k+3	M₁=M₂=N₂=(T+1)/4, N₁=(T-3)/4	(T⁴+8T³+2T²-48T+21)/64

阵列结构	互质扩展因子α, β	Ω_t	Ω_r
传统二阶嵌套阵	α=1, β=1	0.531 2	0.531 2
广义二阶嵌套阵1	α=1, β=17	0.531 2	0
广义二阶嵌套阵2	α=2, β=17	0.388 4	0
广义二阶嵌套阵3	α=4, β=17	0.174 1	0

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