Reduced Order Models for Fast Antenna Characterization

In this paper, the problem of computing the number of degrees of freedom (NDF) of the field radiated by a strip current along all the possible lines orthogonal to the source is addressed. As well known, the NDF is equal to the number of singular values of the radiation operator that are before a critical index at which they abrupt decay. Unfortunately, in the considered case, the solution of the associate eigenvalue problem is not known in closed-form, and this prevents us from directly evaluating the singular values of the radiation operator. To overcome this drawback, a weighted adjoint operator is exploited. The latter allows obtaining an eigenvalue problem whose solution is known in closed-form but, at the same time, it modifies the behavior of the singular values. However, since the change affects only the dynamics of the singular values but not the critical index at which they abrupt decay, the NDF of the radiated field can be analytically estimated by resorting to the weighted adjoint operator.INDEX TERMS dimension of data, eigenvalue problem, inverse source problem, integral equation, radiation operator, singular values, NDF.

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“…At this stage, the kernel has still a complicate structure. However, by approximating the amplitude factors as follows (15) and by choosing…”

Section: Study Of T T † W In the Case |Xo| > Amentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

NDF of the Near-Zone Field on a Line Perpendicular to the Source

Pierri

Moretta

2021

IEEE Access

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“…In this appendix, it is shown how to derive the approximation of the amplitude terms z(ζ o ) fa(ζo,ζ) φ a (ζo,ζ) and z(ζ o ) f−a (ζo,ζ) φ −a (ζo,ζ) made in (14) and (15).…”

Section: Appendix C the Transformation Its Inverse And The Derivative Of The Inverse For The Casementioning

confidence: 99%

“…Both the metrics depend on the geometric parameters of the configuration and both are linked to the singular values decomposition (SVD) of the radiation operator, which is a key mathematical tool widely used in electromagnetics [15]- [20]. The link between the singular values decomposition and the metrics mentioned above appears immediately clear considering that the point spread function can be expressed in terms of the singular system of the radiation operator while the number of degrees of freedom is given by the number of relevant singular values of such an operator [21] [22].…”

Section: Introductionmentioning

confidence: 99%

NDF of the near-zone field on a line perpendicular to the source

Pierri¹,

Moretta²

2021

Preprint

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<div>In this paper, the problem of computing the number of degrees of freedom (NDF) of the field radiated by a strip current along all the possible lines orthogonal to the source is addressed.</div><div>As well known, the NDF is equal to the number of singular values of the radiation operator that are before a critical index at which they abrupt decay. Unfortunately, in the considered case, the solution of the associate eigenvalue problem is not known in closed-form, and this prevents us from directly evaluating the singular values of the radiation operator. To overcome this drawback, a weighted adjoint operator is exploited. The latter allows obtaining an eigenvalue problem whose solution is known in closed-form but, at the same time, it modifies the singular values behavior. However, since the change affects only the dynamics of the singular values but not the critical index at which they abrupt decay, the NDF of the radiated field can be analytically estimated by resorting to the weighted adjoint operator. <br></div>

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“…Both the metrics depend on the geometric parameters of the configuration and both are linked to the singular values decomposition (SVD) of the radiation operator, which is a key mathematical tool widely used in electromagnetics [13] - [17]. The link between the singular values decomposition and the metrics mentioned above appears immediately clear if we consider that the point spread function can be expressed in terms of the singular system of the radiation operator while Manuscript received November 19, 2020. the number of degrees of freedom is given by the number of relevant singular values of such an operator [18] [19].…”

Section: Introductionmentioning

confidence: 99%

NDF of the near-zone field on a line perpendicular to the source

Pierri¹,

Moretta²

2021

Preprint

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<div><div>In the manuscript, we address the problem of evaluating the</div><div>number of degrees of freedom (NDF) of the field radiated by a strip source along all the directions orthogonal to it. </div><div>The NDF represents at the same time the number of independent functions required to represent the data with a given degree of accuracy, and the dimension of the unknowns subspace that can be stably reconstructed. For such reason, the knowledge of the NDF gives insight on the forward and on the inverse problems and it represents one of the metrics to evaluate the achievable performance in the inversion.</div></div><div>The main difficulty arises since in near-zone the eigenvalue</div><div>problem that must be solved for the computation of the NDF,</div><div>involves a non-convolution and non-bandlimited kernel. In the paper, we show how to overcome this drawback and how to obtain a closed-form expression of the NDF which highlights the role played by the configuration parameters.</div>

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Reduced Order Models for Fast Antenna Characterization

Cited by 14 publications

References 13 publications

NDF of the Near-Zone Field on a Line Perpendicular to the Source

NDF of the Near-Zone Field on a Line Perpendicular to the Source

NDF of the near-zone field on a line perpendicular to the source

NDF of the near-zone field on a line perpendicular to the source

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