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Sparse Array Design via Fractal Geometries
IEEE Transactions on Signal Processing ( IF 5.4 ) Pub Date : 2020-01-01 , DOI: 10.1109/tsp.2020.3016772
Regev Cohen , Yonina C. Eldar

Sparse sensor arrays have attracted considerable attention in various fields such as radar, array processing, ultrasound imaging and communications. In the context of correlation-based processing, such arrays enable to resolve more uncorrelated sources than physical sensors. This property of sparse arrays stems from the size of their difference coarrays, defined as the differences of element locations. Thus, the design of sparse arrays with large difference coarrays is of great interest. In addition, other array properties such as symmetry, robustness and array economy are important in different applications. Numerous studies have proposed diverse sparse geometries, focusing on certain properties while lacking others. Incorporating multiple properties into the design task leads to combinatorial problems which are generally NP-hard. For small arrays these optimization problems can be solved by brute force, however, in large scale they become intractable. In this paper, we propose a scalable systematic way to design large sparse arrays considering multiple properties. To that end, we introduce a fractal array design in which a generator array is recursively expanded according to its difference coarray. Our main result states that for an appropriate choice of the generator such fractal arrays exhibit large difference coarrays. Furthermore, we show that the fractal arrays inherit their properties from their generators. Thus, a small generator can be optimized according to desired requirements and then expanded to create a fractal array which meets the same criteria. This approach paves the way to efficient design of large arrays of hundreds or thousands of elements with specific properties.

中文翻译:

通过分形几何进行稀疏阵列设计

稀疏传感器阵列在雷达、阵列处理、超声成像和通信等各个领域引起了广泛关注。在基于相关的处理环境中,与物理传感器相比,此类阵列能够解析更多不相关的源。稀疏数组的这个特性源于它们的差异coarrays的大小,定义为元素位置的差异。因此,具有大差异协阵列的稀疏阵列的设计非常有趣。此外,对称性、稳健性和阵列经济性等其他阵列特性在不同应用中也很重要。许多研究提出了不同的稀疏几何形状,专注于某些属性而缺乏其他属性。将多个属性合并到设计任务中会导致组合问题,这些问题通常是 NP-hard。对于小型阵列,这些优化问题可以通过蛮力解决,但是,在大规模时它们变得棘手。在本文中,我们提出了一种可扩展的系统方法来设计考虑多个属性的大型稀疏阵列。为此,我们引入了一种分形阵列设计,其中生成器阵列根据其差异 coarray 递归扩展。我们的主要结果表明,对于合适的发电机,这种分形阵列具有大差异综合。此外,我们展示了分形数组从它们的生成器继承了它们的属性。因此,可以根据所需要求优化小型发生器,然后扩展以创建满足相同标准的分形阵列。
更新日期:2020-01-01
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