How to get high resolution results from sparse and coarsely sampled data

Cuyt, Annie; Lee, Wen-shin

doi:10.1016/j.acha.2018.10.001

Cited by 21 publications

(44 citation statements)

References 28 publications

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“…Hence, the aliasing problem is solved. Note that we already know which sets (15) and (17) correspond to each other due to the shared Vandermonde system, in contrary to the theory of co-prime arrays, where a search step is required to match the results of both ULAs. When noise is present, both sets do not intersect exactly.…”

Section: A Sub-sampled Exponential Analysismentioning

confidence: 99%

“…When the spatial Nyquist bound is no longer satisfied, aliasing is introduced, which means that it is no longer possible to uniquely retrieve the ψ i from the Ψ i , defined in Section III by (6), since it is no longer guaranteed that |I(ψ i d)| < π. This aliasing problem is solved by using the output generated by a second ULA [17], as explained below.…”

Section: A Sub-sampled Exponential Analysismentioning

confidence: 99%

“…Since we choose σ and ρ co-prime, the intersection of the sets (15) and (17) only contains the desired Ψ i [17]. This is illustrated in Fig.…”

Section: A Sub-sampled Exponential Analysismentioning

confidence: 99%

“…In this paper we present a DOA estimation method that exploits some recent progress in exponential analysis and completely removes the dense Nyquist spacing requirement in ULAs [17]. Removing the Nyquist requirement allows for larger spacing between individual antenna elements, leading naturally to improved angular resolution as well as generally reduced mutual coupling.…”

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confidence: 99%

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Regular Sparse Array Direction of Arrival Estimation in One Dimension

Knaepkens

Cuyt

Lee

et al. 2020

IEEE Trans. Antennas Propagat.

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Traditionally regularly spaced antenna arrays follow the spatial Nyquist criterion to guarantee an unambiguous analysis. We present a novel technique that makes use of two sparse non-Nyquist regularly spaced antenna arrays, where one of the arrays is just a shifted version of the other. The method offers several advantages over the use of traditional dense Nyquistspaced arrays, while maintaining a comparable algorithmic complexity for the analysis. Among the advantages we mention: an improved resolution for the same number of receivers and reduced mutual coupling effects between the receivers, both due to the increased separation between the antennas. Because of a shared structured linear system of equations between the two arrays, as a consequence of the shift between the two, the analysis of both is automatically paired, thereby avoiding a computationally expensive matching step as is required in the use of so-called co-prime arrays. In addition, an easy validation step allows to automatically detect the precise number of incoming signals, which is usually considered a difficult issue. At the same time, the validation step improves the accuracy of the retrieved results and eliminates unreliable results in the case of noisy data. The performance of the proposed method is illustrated with respect to the influence of noise as well to the effect of mutual coupling. Index Terms-Array Antennas, Direction of Arrival Estimation, Sparse Arrays. I. INTRODUCTION D IRECTION of arrival (DOA) estimation, using array antenna systems, is a topic of increasing interest in a variety of applications including radar, remote sensing, radio frequency interference mitigation, and smart wireless networks [1]-[3]. One of the most well-known limitations in regularly spaced antenna array systems is, arguably, the requirement that the elements should have spacing closer than a half-wavelength (the spatial Nyquist criterion) in order to avoid aliasing resulting in ambiguous arrival angle estimates. Unique results can be obtained for larger spacings if a limited range of near-broadside receiving angles are considered, or if the antenna element patterns exhibit zeros in the end-fire directions, but in general this still limits the allowable spacing to distances close to the Nyquist limit.

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Section: A Sub-sampled Exponential Analysismentioning

confidence: 99%

Section: A Sub-sampled Exponential Analysismentioning

confidence: 99%

“…Since we choose σ and ρ co-prime, the intersection of the sets (15) and (17) only contains the desired Ψ i [17]. This is illustrated in Fig.…”

Section: A Sub-sampled Exponential Analysismentioning

confidence: 99%

mentioning

confidence: 99%

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Regular Sparse Array Direction of Arrival Estimation in One Dimension

Knaepkens

Cuyt

Lee

et al. 2020

IEEE Trans. Antennas Propagat.

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“…We will show that there is much more freedom to choose a set of different sampling functionals F k , where each sampling functional leads to a linear equation providing one condition for the vector of coefficients of the Prony polynomial. Our approach also covers previous ideas to identify the frequency parameters T j of the exponential sum in (1.1) using equispaced sampling sequences with different sampling sizes simultaneously, see [5].…”

Section: Introductionmentioning

confidence: 99%

The Generalized Operator Based Prony Method

Stampfer

Plonka

2020

Constr Approx

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The generalized Prony method introduced in [13] is a reconstruction technique for a large variety of sparse signal models that can be represented as sparse expansions into eigenfunctions of a linear operator A. However, this procedure requires the evaluation of higher powers of the linear operator A that are often expensive to provide.In this paper we propose two important extensions of the generalized Prony method that simplify the acquisition of the needed samples essentially and at the same time can improve the numerical stability of the method. The first extension regards the change of operators from A to ϕ(A), where ϕ is an analytic function, while A and ϕ(A) possess the same set of eigenfunctions. The goal is now to choose ϕ such that the powers of ϕ(A) are much simpler to evaluate than the powers of A. The second extension concerns the choice of the sampling functionals. We show, how new sets of different sampling functionals F k can be applied with the goal to reduce the needed number of powers of the operator A (resp. ϕ(A)) in the sampling scheme and to simplify the acquisition process for the recovery method.

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Multiscale matrix pencils for separable reconstruction problems

Cuyt

Lee

2023

Numer Algor

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The nonlinear inverse problem of exponential data fitting is separable since the fitting function is a linear combination of parameterized exponential functions, thus allowing to solve for the linear coefficients separately from the nonlinear parameters. The matrix pencil method, which reformulates the problem statement into a generalized eigenvalue problem for the nonlinear parameters and a structured linear system for the linear parameters, is generally considered as the more stable method to solve the problem computationally. In Section 2 the matrix pencil associated with the classical complex exponential fitting or sparse interpolation problem is summarized and the concepts of dilation and translation are introduced to obtain matrix pencils at different scales. Exponential analysis was earlier generalized to the use of several polynomial basis functions and some operator eigenfunctions. However, in most generalizations a computational scheme in terms of an eigenvalue problem is lacking. In the subsequent Sections 3–6 the matrix pencil formulation, including the dilation and translation paradigm, is generalized to more functions. Each of these periodic, polynomial or special function classes needs a tailored approach, where optimal use is made of the properties of the parameterized elementary or special function used in the sparse interpolation problem under consideration. With each generalization a structured linear matrix pencil is associated, immediately leading to a computational scheme for the nonlinear and linear parameters, respectively from a generalized eigenvalue problem and one or more structured linear systems. Finally, in Section 7 we illustrate the new methods.

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How to get high resolution results from sparse and coarsely sampled data

Cited by 21 publications

References 28 publications

Regular Sparse Array Direction of Arrival Estimation in One Dimension

Regular Sparse Array Direction of Arrival Estimation in One Dimension

The Generalized Operator Based Prony Method

Multiscale matrix pencils for separable reconstruction problems

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