Bounds for sparse planar and volume arrays

Meurisse, Yann; Delmas, Jean

doi:10.1109/18.904563

Cited by 20 publications

(21 citation statements)

References 8 publications

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“…Indeed, the constant is computed by the normalization condition (integration over the whole domain of definition should be equal to 1) (6) Note that, by using the mean value theorem for integrals, we have (7) where is the surface of the host and is the exclusion surface for the center of #2 due to element #1. Equation (7) means that the previous integral is of order . For example, if the prior probability is uniform, we have (8) In this case, the integral of (7) is exactly equal to and the normalization factor reads as follows: (9) • derivation Following the same path, we can derive (10) In the previous expression is the excluded area for the placement of element due to the placement of element .…”

Section: Array Construction and Statistical Analysismentioning

confidence: 98%

See 1 more Smart Citation

A Stochastic Study of Large Arrays Related to the Number of Electrically Large Aperture Radiators

Kaifas

Babas

Miaris

et al. 2014

IEEE Trans. Antennas Propagat.

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A study of the maximally sparse large planar arrays with electrically large elements is presented. The conditional probabilities of the element placements and their resulting auxiliary radiation integrals are derived. Through them the average and the directivity pattern formulas are also derived. Employing these formulas, we present a convex method that provides a solution to the maximally sparse problem when main lobe constraints are imposed on the directivity pattern. In particular, by taking the possible types of elements into account, we manage to obtain the lower bound of the directivity that an array should exhibit. This lower bound is analytically derived in the form of a Pareto (sub-) set that classifies the possible arrays into feasible and nonfeasible ones. This Pareto set can also enable tradeoff studies to be conducted without the need to consider the full range of every parameter. From the procedure, several acceptable combinations of elements are obtained. Simulation results, which confirm the methodology, are presented.Index Terms-Aperiodic arrays, maximally sparse arrays.

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Section: Array Construction and Statistical Analysismentioning

confidence: 98%

“…Stochastic methods have been used in [6] and references therein. Array configurations known as linear minimumredundancy (MR) arrays or linear minimum-hole (MH) arrays (also called optimum nonredundant arrays) have also been proposed, [7]. Note that the above studies focus mainly on point sources arranged at most in a linear path.…”

Section: Introductionmentioning

confidence: 99%

A Stochastic Study of Large Arrays Related to the Number of Electrically Large Aperture Radiators

Kaifas

Babas

Miaris

et al. 2014

IEEE Trans. Antennas Propagat.

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show abstract

“…On the one hand, the ULA with a constant inter-sensors spacing d and for which S 3 = S 5 = 0. On the other hand, the minimum hole and redundancy linear array (MHRLA) with inter-spacings d, 3d, 2d [12] and for which S 3 = 0. Thanks to a larger aperture, the MHRLA exhibits a lower far-field CRB, for instance, CRB MHRLA FF (θ)/CRB ULA FF (θ) ≈ 0.22.…”

Section: Now Wrtmentioning

confidence: 99%

Nonuniform linear antenna arrays for enhanced near field source localization

Gazzah¹,

Delmas²

2014

2014 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

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Arrays of sensors freely located along an axis are considered in this paper that are used to localize a near-field emitting source. Using Taylor expansion and a suitable coordinate system, simple, yet rich to interpret, Cramer-Rao bounds relative to the direction and range parameters are derived. Our analysis allows in particular to unveil a family of non-uniform linear arrays with better near field estimation capabilities, compared to the well-established uniform linear arrays.

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“…Let denote the solution of (7), where the subscript refers to "restricted planar." It has been shown that [29] (8)…”

Section: Sparse Planar Arraysmentioning

confidence: 99%

Sparse Array Design for Azimuthal Direction-of-Arrival Estimation

Rubsamen

2011

IEEE Trans. Signal Process.

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We propose a novel approach to the design of array geometries for azimuthal direction-of-arrival (DOA) estimation. The proposed array design is related to that of minimum redundancy arrays, but the array sensors are not required to lie on a uniform grid. Based on the proposed array geometry design, we develop a subspace-based DOA estimation technique, which allows to estimate the DOAs of more sources than sensors, using only second-order statistics of the received data. This DOA estimation technique is related to the covariance augmentation technique, but in contrast to the latter technique, it provides nonambiguous DOA estimates for the full 360 azimuth field-of-view.Index Terms-Direction-of-arrival estimation, sparse planar arrays.

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Bounds for sparse planar and volume arrays

Cited by 20 publications

References 8 publications

A Stochastic Study of Large Arrays Related to the Number of Electrically Large Aperture Radiators

A Stochastic Study of Large Arrays Related to the Number of Electrically Large Aperture Radiators

Nonuniform linear antenna arrays for enhanced near field source localization

Sparse Array Design for Azimuthal Direction-of-Arrival Estimation

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