532 research outputs found
Sparse Array DFT Beamformers for Wideband Sources
Sparse arrays are popular for performance optimization while keeping the
hardware and computational costs down. In this paper, we consider sparse arrays
design method for wideband source operating in a wideband jamming environment.
Maximizing the signal-to-interference plus noise ratio (MaxSINR) is adopted as
an optimization objective for wideband beamforming. Sparse array design problem
is formulated in the DFT domain to process the source as parallel narrowband
sources. The problem is formulated as quadratically constraint quadratic
program (QCQP) alongside the weighted mixed -norm squared
penalization of the beamformer weight vector. The semidefinite relaxation (SDR)
of QCQP promotes sparse solutions by iteratively re-weighting beamformer based
on previous iteration. It is shown that the DFT approach reduces the
computational cost considerably as compared to the delay line approach, while
efficiently utilizing the degrees of freedom to harness the maximum output SINR
offered by the given array aperture
Devil's staircase phase diagram of the fractional quantum Hall effect in the thin-torus limit
After more than three decades the fractional quantum Hall effect still poses
challenges to contemporary physics. Recent experiments point toward a fractal
scenario for the Hall resistivity as a function of the magnetic field. Here, we
consider the so-called thin-torus limit of the Hamiltonian describing
interacting electrons in a strong magnetic field, restricted to the lowest
Landau level, and we show that it can be mapped onto a one-dimensional lattice
gas with repulsive interactions, with the magnetic field playing the role of a
chemical potential. The statistical mechanics of such models leads to interpret
the sequence of Hall plateaux as a fractal phase diagram, whose landscape shows
a qualitative agreement with experiments.Comment: 5 pages main text, 11 pages supplementary, 2 figure
Novel Algorithms for Analyzing the Robustness of Difference Coarrays to Sensor Failures
Sparse arrays have drawn attention because they can identify O(N²) uncorrelated source directions using N physical sensors, whereasuniform linear arrays (ULA) find at most N−1 sources. The main reason is that the difference coarray, defined as the set of differences between sensor locations, has size of O(N²) for some sparse arrays. However, the performance of sparse arrays may degrade significantly under sensor failures. In the literature, the k-essentialness property characterizes the patterns of k sensor failures that change the difference coarray. Based on this concept, the k-essential family, the k-fragility, and the k-essential Sperner family provide insights into the robustness of arrays. This paper proposes novel algorithms for computing these attributes. The first algorithm computes the k-essential Sperner family without enumerating all possible k-essential subarrays. With this information, the second algorithm finds the k-essential family first and the k-fragility next. These algorithms are applicable to any 1-D array. However, for robust array design, fast computation for the k-fragility is preferred. For this reason, a simple expression associated with the k-essential Sperner family is proposed to be a tighter lower bound for the k-fragility than the previous result. Numerical examples validate the proposed algorithms and the presented lower bound
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
Thinned coprime arrays for DOA estimation
Sparse arrays can generate a larger aperture than traditional uniform linear arrays (ULA) and offer enhanced degrees-of-freedom (DOFs) which can be exploited in both beamforming and direction-of-arrival (DOA) estimation. One class of sparse arrays is the coprime array, composed of two uniform linear subarrays which yield an effective difference co-array with higher number of DOFs. In this work, we present a new coprime array structure termed thinned coprime array (TCA), which exploits the redundancy in the structure of the existing coprime array and achieves the same virtual aperture and DOFs as the conventional coprime array with much fewer number of sensors. An analysis of the DOFs provided by the new structure in comparison with other sparse arrays is provided and simulation results for DOA estimation using the compressive sensing based method are provided
Design of Nonredundant Sparse Planar Arrays With Reduced Mutual Coupling
Most existing sparse planar arrays cannot fully realize their potential in terms of the degrees-of-freedom (DOFs) due to redundancies in their co-array generation. Meanwhile, the small interelement spacing in conventional planar arrays may cause serious mutual coupling effects. In this article, a series of designs for nonredundant sparse planar arrays in different application scenarios are proposed. They can obtain the maximum possible DOFs under the constraints of area and the number of array elements. We first present the rule for nonredundancy design for planar arrays, which is the basic criterion for the following optimization problems. According to generalized disjunctive programming, we establish systematic solutions for array designs by two mixed-integer linear programming optimization approaches. Then, three classes of nonredundant planar arrays are designed to achieve minimum area, predetermined area, and reduced mutual coupling, respectively. In particular, the nonredundant planar arrays with reduced mutual coupling can be designed to both avoid small interelement spacing and obtain the minimum area, which makes them more robust to mutual coupling conditions. Simulation results are provided to demonstrate the superiority of the proposed planar array configurations for direction-of-arrival estimation
Super Nested Arrays: Sparse arrays with Less Mutual Coupling than Nested Arrays
In array processing, mutual coupling between sensors has an adverse effect on the estimation of parameters (e.g., DOA). Sparse arrays, such as nested arrays, coprime arrays, and minimum redundancy arrays (MRAs), have reduced mutual coupling compared to uniform linear arrays (ULAs). With N denoting the number of sensors, these sparse arrays offer O(N^2) freedoms for source estimation because
their difference coarrays have O(N^2)-long ULA segments. These arrays have different shortcomings: coprime arrays have holes in the coarray, MRAs have no closed-form expressions, and nested arrays have relatively large mutual coupling. This paper introduces a new array called the super nested array, which has all the good properties
of the nested array, and at the same time reduces mutual coupling significantly. For fixed N, the super nested array has the same physical aperture, and the same hole-free coarray as does the nested array. But the number of sensor pairs with separation λ/2 is significantly
reduced. Many theoretical properties are proved and simulations are included to demonstrate the superior performance of these arrays
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