Differential Geometry in Array Processing

Manikas, A.

doi:10.1142/p309

Cited by 44 publications

(61 citation statements)

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“…At any point of a curve embedded in , it is possible to attach a continuous, differentiable and orthonormal, in the "wide" sense, 1 system of coordinate vectors , [3], [7]. These coordinate vectors are indispensable in the differential geometric treatment of curves as it is easier to describe local properties (e.g., curvature, torsion) in terms of a local reference system than a global one, like an orthonormal Euclidean coordinate system attached at the origin.…”

Section: ) Array Manifold Curvesmentioning

confidence: 99%

“…It can be proven that if the curvatures of the array manifold remain constant, then the shape of will be a hyperhelix. This property of manifold curves is of high importance, since hyperhelical curves are easy to study and analyze due to their specific geometric structure [3].…”

Section: ) Array Manifold Curvesmentioning

confidence: 99%

“…The most important geometric properties of space surfaces embedded in multidimensional complex spaces are the following [3], [8]:…”

Section: ) Array Manifold Curvesmentioning

confidence: 99%

“…This real number, the Gaussian curvature, provides an indication of the local shape of the surface at the neighborhood of that point. In [3], the aforementioned theorem has been extended to manifold surfaces embedded in a complex -dimensional space, where the definition of the Gaussian curvature utilizes the intrinsic geometry of the manifold surface.…”

Section: ) Array Manifold Curvesmentioning

confidence: 99%

“…More importantly these new manifolds can be expressed, as we shall see shortly, as functions of the array manifold of (2) and for this reason will be referred to, henceforth, as extended array manifolds. For the remaining of this paper the symbols and will be used to denote an extended array manifold vector and the associated extended array manifold defined as (3) where, again, is a vector containing all the unknown, variable parameters and is the parameter space for .…”

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confidence: 99%

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Extended Array Manifolds: Functions of Array Manifolds

Efstathopoulos

Manikas

2011

IEEE Trans. Signal Process.

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Abstract-The response of an array processing system has been widely modelled using the concept of the array manifold. The conventional array manifold is a function of the geometry of the array, the carrier frequency and the directions of arrival (DOAs) of the sources only. However, the emergence of more sophisticated array systems, for instance antenna array communication systems, dictates the extension of this array manifold into various new types of manifolds that incorporate additional system and channel parameters, such as the code-division multiple access (CDMA) (spreading and scrambling) codes, the lack of synchronization, Doppler effects, polarization parameters, subcarriers, etc. This paper is concerned with the definition and geometric investigation of a generic model for these new manifolds that can be expressed as functions of the conventional array manifolds and, hence, are defined herein as extended array manifolds. Thus, initially, the concept of the extended array manifold is introduced and is shown to accommodate both existing and newly defined extensions of the widely employed in the literature conventional (or spatial) array manifold. Next, the geometric properties and parameters of the extended array manifold are studied and linked with the properties of the associated spatial array manifold in an attempt to facilitate the geometric study of the former by taking advantage of the well understood study of the latter.Index Terms-Array manifold, array processing, differential geometry, extended array manifold. NOTATION aScalar.Column vector.Matrix.element column vector of zeros.Conjugate, transpose, Hermitian.Hadamard product, Kronecker product.Round down to integer.Euclidean norm of the column vector .Element-wise exponentiation.

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Section: ) Array Manifold Curvesmentioning

confidence: 99%

Section: ) Array Manifold Curvesmentioning

confidence: 99%

“…The most important geometric properties of space surfaces embedded in multidimensional complex spaces are the following [3], [8]:…”

Section: ) Array Manifold Curvesmentioning

confidence: 99%

Section: ) Array Manifold Curvesmentioning

confidence: 99%

mentioning

confidence: 99%

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Extended Array Manifolds: Functions of Array Manifolds

Efstathopoulos

Manikas

2011

IEEE Trans. Signal Process.

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Sparse Arrays: Fundamentals

Vaidyanathan,

Kulkarni

2023

Sparse Arrays for Radar, Sonar, and Communications

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A new array concept using spatially distributed subarrays for unambiguous GNSS interference mitigation in automotive applications

et al. 2020

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Radio frequency interference (RFI) poses a severe problem for conventional GNSS receivers. Even low powered RFI can block the reception of satellite signals and prevent a position determination. Antenna array systems have been proven suitable to counteract RFI by incorporating spatial processing techniques. The large size of uniform rectangular arrays (URA) with half‐wave antenna spacing impedes an installation in cars intended for the consumer mass market, where a hidden installation is a strict requirement by industry and customers. This paper introduces a new approach, where a conventional URA is split into distributed linear subarrays with the aim to reduce their footprint but to maintain the possibility of spatial processing. The achievable gain in robustness against RFI is evaluated. Drawbacks in terms of manifold ambiguities and their consequences for spatial processing techniques are also discussed. Furthermore, the accuracy of positioning results derived from a field test is put into context with a single antenna receiver.

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Differential Geometry in Array Processing

Cited by 44 publications

References 0 publications

Extended Array Manifolds: Functions of Array Manifolds

Extended Array Manifolds: Functions of Array Manifolds

Sparse Arrays: Fundamentals

A new array concept using spatially distributed subarrays for unambiguous GNSS interference mitigation in automotive applications

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