| 1. |
- Bernland, Anders, et al.
(author)
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Estimation of Spherical Wave Coefficients from 3D Positioner Channel Measurements
- 2012
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Reports (other academic/artistic)abstract
- Electromagnetic vector spherical waves have been used recently to model antenna channel interaction and the available degrees of freedom in MIMO systems. However, there are no previous accounts of a method to estimate spherical wave coefficients from channel measurements. One approach, using a 3D positioner, is presented in this letter, both in theory and practice. Measurement results are presented and discussed. One conclusion is that using randomly positioned measurements within a volume is less sensitive to noise than using only measurements on the surface.
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| 2. |
- Bernland, Anders, et al.
(author)
-
Physical limitations on the scattering of electromagnetic vector spherical waves
- 2010
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Reports (other academic/artistic)abstract
- Understanding the interaction between electromagnetic waves and matter is vital in applications ranging from classical optics to antenna theory. This paper derives physical limitations on the scattering of electromagnetic vector spherical waves. The assumptions made are that the heterogeneous scatterer is passive, and has constitutive relations which are on convolution form in the time domain and anisotropic in the static limit. The resulting bounds limit the reflection coefficient of the modes over a frequency interval, and can thus be interpreted as limitations on the absorption of power from a single mode. They can be used within a wide range of applications, and are particularly useful for electrically small scatterers. The derivation follows a general approach to derive sum rules and physical limitations on passive systems on convolution form. The time domain versions of the vector spherical waves are used to describe the passivity of the scatterer, and a set of integral identities for Herglotz functions are applied to derive sum rules from which the physical limitations follow.
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| 3. |
- Bernland, Anders, et al.
(author)
-
Sum rules and constraints on passive systems
- 2010
-
Reports (other academic/artistic)abstract
- A passive system is one that cannot produce energy, a property that naturally poses constraints on the system. A system on convolution form is fully described by its transfer function, and the class of Herglotz functions, holomorphic functions mapping the open upper half plane to the closed upper half plane, is closely related to the transfer functions of passive systems. Following a well-known representation theorem, Herglotz functions can be represented by means of positive measures on the real line. This fact is exploited in this paper in order to rigorously prove a set of integral identities for Herglotz functions that relate weighted integrals of the function to its asymptotic expansions at the origin and infinity. The integral identities are the core of a general approach introduced here to derive sum rules and physical limitations on various passive physical systems. Although similar approaches have previously been applied to a wide range of specific applications, this paper is the first to deliver a general procedure together with the necessary proofs. This procedure is described thoroughly, and exemplified with examples from electromagnetic theory.
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| 4. |
- Nordebo, Sven, et al.
(author)
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On the relation between optimal wideband matching and scattering of spherical waves
- 2010
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Reports (other academic/artistic)abstract
- Using an exact circuit analogy for the scattering of vector spherical waves, it is shown how the problem of determining the optimal scattering bounds for a homogeneous sphere in its high-contrast limit is identical to the closely related, and yet very different problem of finding the broadband tuning limits of the spherical waves. Using integral relations similar to Fano's broadband matching bounds, the optimal scattering limitations are determined by the static response as well as the high-frequency asymptotics of the reflection coefficient. The scattering view of the matching problem yields explicitly the necessary low-frequency asymptotics of the reflection coefficient that is used with Fano's broadband matching bounds for spherical waves, something that appears to be non-trivial to derive from the classical network point of view.
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| 5. |
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