Sparse Doppler Sensing Based on Nested Arrays

Cohen, Regev; Eldar, Yonina C.

doi:10.1109/tuffc.2018.2872870

Cited by 19 publications

(9 citation statements)

References 54 publications

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“…Symmetric arrays are favorable in various applications such as DOA estimation [16] and ultrasound imaging [4], [5], [39]. Symmetry improves DOA estimation as it reduces the computational burden and aids in calibration [12]- [16], [40].…”

Section: A Symmetrymentioning

confidence: 99%

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Sparse Array Design via Fractal Geometries

Cohen¹,

Eldar²

2020

Preprint

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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. Hence, the design of thinned arrays with large difference coarrays is of great interest. In addition to the difference coarray, other array properties such as symmetry, robustness and array economy are important in different applications. Such design tasks lead 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 introduce a fractal array design in which a generator array is recursively expanded according to its difference coarray. Our main result is 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 provides a simple and efficient way for designing large scale sparse arrays with specific properties.

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Section: A Symmetrymentioning

confidence: 99%

“…S ENSOR array design plays a key role in various fields such as radar [1], radio [2], communications [3] and ultrasound imaging [4]- [6]. In particular, two major applications of array processing [7]- [9] are direction-of-arrival (DOA) estimation and beamforming used for detecting sources impinging on an array.…”

Section: Introductionmentioning

confidence: 99%

Sparse Array Design via Fractal Geometries

Cohen¹,

Eldar²

2020

Preprint

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“…Toeplitz covariance estimation arises in a range of applications, including direction of arrival (DOA) estimation [1][2][3], spectrum-sensing for cognitive radio [4,5], medical and radar imaging [6][7][8], [9][10][11] and Gaussian process regression (kriging) and kernel machine learning [12,13]. We focus on estimation methods with low sample complexity, can be measured in two ways [14]:…”

Section: Introductionmentioning

confidence: 99%

Low-Rank Toeplitz Matrix Estimation Via Random Ultra-Sparse Rulers

Lawrence

Musco

et al. 2020

ICASSP 2020 - 2020 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

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We study how to estimate a nearly low-rank Toeplitz covariance matrix T from compressed measurements. Recent work of Qiao and Pal addresses this problem by combining sparse rulers (sparse linear arrays) with frequency finding (sparse Fourier transform) algorithms applied to the Vandermonde decomposition of T . Analytical bounds on the sample complexity are shown, under the assumption of sufficiently large gaps between the frequencies in this decomposition.In this work, we introduce random ultra-sparse rulers and propose an improved approach based on these objects. Our random rulers effectively apply a random permutation to the frequencies in T 's Vandermonde decomposition, letting us avoid frequency gap assumptions and leading to improved sample complexity bounds. In the special case when T is circulant, we theoretically analyze the performance of our method when combined with sparse Fourier transform algorithms based on random hashing. We also show experimentally that our ultra-sparse rulers give significantly more robust and sample efficient estimation then baseline methods.

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“…Using the virtual array model of coprime array, the DOA estimation performance can be effectively improved. In [19], and [20], the structure of nested arrays is given, and the nested arrays are extended to multi-level cascade. On the basis of coprime array and nested array, an improved sparse array is presented in [21] and [22], these array adopt the form of multi-level cascade, which can effectively improve the array DOF.…”

Section: Introductionmentioning

confidence: 99%

“…4,6,13,14,17,19, 39, 40, 43, 45}. The sparse array MSC-DiSA can effectively expand the array aperture and improve the array DOF.…”

mentioning

confidence: 99%

An Underdetermined Source Number Estimation Method for Non-Circular Targets Based on Sparse Array

Zhang

Wang

et al. 2019

IEEE Access

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Source number estimation is one of the key technologies of wireless location, and it is also the basis of parameter estimation and location solution. In order to improve the accuracy of existing non-circular source number estimation and realize underdetermined source number estimation, this paper presents a noncircular source number estimation method based on sparse array. This method firstly uses the non-circular characteristics of received sources to expand the array aperture, then combines the structural characteristics of sparse array to construct a virtual array model, and extracts the response parts of continuous virtual array elements for spatial smoothing processing. Finally, the minimum description length (MDL) method is used to realize the effective estimation of non-circular source number. The complexity analysis and simulation experiments are given, and the results of Monte Carlo experiments show that compared with the traditional source number estimation method, this method can not only improve the accuracy of the source number estimation but also realize the effective estimation of the source number in undetermined conditions.

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Sparse Doppler Sensing Based on Nested Arrays

Cited by 19 publications

References 54 publications

Sparse Array Design via Fractal Geometries

Sparse Array Design via Fractal Geometries

Low-Rank Toeplitz Matrix Estimation Via Random Ultra-Sparse Rulers

An Underdetermined Source Number Estimation Method for Non-Circular Targets Based on Sparse Array

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