4 research outputs found
Sparse Array Design via Fractal Geometries
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.Comment: 16 pages, 9 figures, 1 Tabl
Robustness of Coarrays of Sparse Arrays to Sensor Failures
Sparse arrays can identify O(N^2) uncorrelated sources using N physical sensors. This property is because the difference coarray, defined as the differences between sensor locations, has uniform linear array (ULA) segments of length O(N^2) . It is empirically known that, for sparse arrays like minimum redundancy arrays, nested arrays, and coprime arrays, this O(N^2) segment is susceptible to sensor failure, which is an important issue in practical systems. This paper presents the (k-)essentialness property, which characterizes the combinations of the failing sensors that shrink the difference coarray. Based on this, the notion of fragility is proposed to quantify the reliability of sparse arrays with faulty sensors, along with comprehensive studies of their properties. It is demonstrated through examples that there do exist sparse arrays that are as robust as ULA and at the same time, they enjoy O(N^2) consecutive elements in the difference coarray
Robustness of Coarrays of Sparse Arrays to Sensor Failures
Sparse arrays can identify O(N^2) uncorrelated sources using N physical sensors. This property is because the difference coarray, defined as the differences between sensor locations, has uniform linear array (ULA) segments of length O(N^2) . It is empirically known that, for sparse arrays like minimum redundancy arrays, nested arrays, and coprime arrays, this O(N^2) segment is susceptible to sensor failure, which is an important issue in practical systems. This paper presents the (k-)essentialness property, which characterizes the combinations of the failing sensors that shrink the difference coarray. Based on this, the notion of fragility is proposed to quantify the reliability of sparse arrays with faulty sensors, along with comprehensive studies of their properties. It is demonstrated through examples that there do exist sparse arrays that are as robust as ULA and at the same time, they enjoy O(N^2) consecutive elements in the difference coarray