Spherical Harmonic Expansion of Fisher�Bingham Distribution and 3-D Spatial Fading Correlation for Multiple-Antenna Systems
Date
2016
Authors
Alem, Yibeltal F.;Khalid, Zubair;Kennedy, Rodney
Journal Title
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Publisher
IEEE
Abstract
This paper considers the 3-D spatial fading correlation (SFC) resulting from an angle-of-arrival (AoA) distribution that can be modeled by a mixture of Fisher-Bingham distributions (FB-distributions) on the sphere. By deriving a closed-form expression for the spherical harmonic transform for the component FB-distributions, with arbitrary parameter values, we obtain a closed-form expression of the 3-D SFC for the mixture case. The 3-D SFC expression is general and can be used in arbitrary multiantenna array geometries and is demonstrated for the cases of a 2-D uniform circular array (UCA) and a 3-D regular dodecahedron array (RDA). In computational aspects, we use recursions to compute the spherical harmonic coefficients and give pragmatic guidelines on the truncation size in the series representations to yield machine precision accuracy results. The results are further corroborated through numerical experiments to demonstrate that the closed-form expressions yield the same results as significantly more computationally expensive numerical integration methods.
Description
Keywords
Fisher-Bingham distribution, spherical harmonic expansion, spatial correlation, MIMO, angle of arrival (AoA).
Citation
Florian Pfaff, Gerhard Kurz, Uwe D. Hanebeck, "Filtering on the unit sphere using spherical harmonics", Multisensor Fusion and Integration for Intelligent Systems (MFI) 2017 IEEE International Conference on, pp. 124-130, 2017., https://doi.org/10.1109/TVT.2015.2463731
Florian Pfaff, Gerhard Kurz, Uwe D. Hanebeck, "Filtering on the unit sphere using spherical harmonics", Multisensor Fusion and Integration for Intelligent Systems (MFI) 2017 IEEE International Conference on, pp. 124-130, 2017., https://doi.org/10.1109/TVT.2015.2463731
Florian Pfaff, Gerhard Kurz, Uwe D. Hanebeck, "Filtering on the unit sphere using spherical harmonics", Multisensor Fusion and Integration for Intelligent Systems (MFI) 2017 IEEE International Conference on, pp. 124-130, 2017., https://doi.org/10.1109/TVT.2015.2463731
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Source
IEEE Transactions on Vehicular Technology
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Journal article
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Open Access
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Author/s Accepted Manuscript (AAM) / Post-print