通过穷举搜索和新的亚优RMRA的代数公式发现最优鲁棒最小冗余阵列
Discovering Optimal Robust Minimum Redundancy Arrays (RMRAs) through Exhaustive Search and Algebraic Formulation of a New Sub-Optimal RMRA
AI总结：
本文通过穷举搜索和代数公式发现最优鲁棒最小冗余阵列，扩展了已知配置范围并提出新的亚优阵列。
摘要：
现代稀疏阵列在经济性方面达到最大，它们在提供特定孔径所需传感器数量上保持相同，同时保持差共阵无孔。因此，这些阵列容易受到单个传感器故障的影响。相反，双倍冗余稀疏阵列（TFRSAs）和鲁棒最小冗余阵列（RMRAs）由于其共阵中的固有冗余性，能够抵御单个传感器故障。目前，已知的最优RMRA配置仅限于传感器数量N=6到N=10。为此，本文提出了两个目标：（i）开发一种系统算法，以发现N>10的最优RMRAs；（ii）获得一个新近/亚优RMRA家族，可以完全用闭式表达式（CFEs）指定。我们通过MATLAB实现的穷举搜索技术解决寻找RMRAs的组合优化问题。成功发现了N=11到14的最优RMRAs，并通过所提出的方法确定了N=15到20的近/亚优阵列。作为穷举搜索的副产品，还获得了一个庞大的有效近/亚优RMRAs目录。在第二阶段，通过应用模式挖掘和代数泛化到通过穷举搜索获得的阵列上，获得了新TFRSA的CFEs。所提出的家族具有传感器位置、可用孔径和可实现的自由度（DOFs）的CFEs。这些CFEs已通过MATLAB彻底验证，并发现适用于N≥8。因此，可以得出结论，这项工作的创新性是双重的：扩展已知最优RMRAs的目录，并制定一个遵循CFEs的亚优RMRA。
英文摘要：
Modern sparse arrays are maximally economic in that they retain just as many sensors required to provide a specific aperture while maintaining a hole-free difference coarray. As a result, these are susceptible to the failure of even a single sensor. Contrarily, two-fold redundant sparse arrays (TFRSAs) and robust minimum redundancy arrays (RMRAs) ensure robustness against single-sensor failures due to their inherent redundancy in their coarrays. At present, optimal RMRA configurations are known only for arrays with sensor counts N=6 to N=10. To this end, this paper proposes two objectives: (i) developing a systematic algorithm to discover optimal RMRAs for N>10, and (ii) obtaining a new family of near-/sub-optimal RMRA that can be completely specified using closed-form expressions (CFEs). We solve the combinatorial optimization problem of finding RMRAs using an exhaustive search technique implemented in MATLAB. Optimal RMRAs for N = 11 to 14 were successfully found and near/sub-optimal arrays for N = 15 to 20 were determined using the proposed technique. As a byproduct of the exhaustive search, a large catalogue of valid near- and sub-optimal RMRAs was also obtained. In the second stage, CFEs for a new TFRSA were obtained by applying pattern mining and algebraic generalizations to the arrays obtained through exhaustive search. The proposed family enjoys CFEs for sensor positions, available aperture, and achievable degrees of freedom (DOFs). The CFEs have been thoroughly validated using MATLAB and are found to be valid for $N\geq8$. Hence, it can be concluded that the novelty of this work is two-fold: extending the catalogue of known optimal RMRAs and formulating a sub-optimal RMRA that abides by CFEs.
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