Ternary redundant sparse linear array design with high robustness

高鲁棒性的三元冗余稀疏线阵设计

School of Information Engineering and Automation, Kunming University of Science and Technology, Kunming 650504, China

Received: 4 May 2022

Abstract

Sparse linear array is prone to element failure affected by environmental and other factors in practical application, resulting in the decline of degrees of freedom and the attenuation or even failure of direction of arrival (DOA) estimation performance. To address this problem, a ternary redundant sparse array composed of three uniform linear arrays with different spacings at specific distances is designed, and the analytical expression of its degrees of freedom is derived. The configuration rules of the array are concise, and the difference coarrays of the array are hole-free. Mathematically proves that all virtual array elements can be covered with a weight of not less than 3 except the 4 farthest. The array has lower sensors importance and less generalized k-fragility. The array design takes into account the maximum degrees of freedom, redundancy and sparsity. In case of sensors failure, compared with the other sparse linear arrays, the array has more stable difference coarrays and higher uniform degrees of freedom. Compared with multiple-fold redundancy arrays, the array has lower mutual coupling. Simulation results show that the ternary redundant array has superior robustness and higher DOA estimation accuracy under sensors failure.

摘要

针对稀疏线阵在实际应用中受环境等因素影响发生阵元故障, 进而导致自由度下降和波达方向估计(direction of arrival, DOA)性能衰减甚至失效的问题, 设计一种由三段不同间距的均匀线阵以特定距离组成的三元冗余稀疏阵, 并推导出该阵列自由度的解析表达式。三元冗余阵配置规则简明, 差分共阵连续无孔, 数学证明可以不小于3的权重覆盖除最远端4个外所有虚拟阵元, 具有较低的阵元重要性和较小的广义k脆弱性。三元冗余阵设计兼顾最大自由度、冗余度和稀疏性, 阵元故障时, 与其他稀疏线阵相比, 有更稳定的差分共阵和更高的连续自由度; 与多重冗余阵相比, 有更低的阵列互耦。仿真实验显示出三元冗余阵在阵元故障下的优越鲁棒性和更高的DOA估计精度。