NDLI: Unified Array Manifold Decomposition Based on Spherical Harmonics and 2-D Fourier Basis

Content Provider	IEEE Xplore Digital Library
Author	Costa, M. Richter, A. Koivunen, V.
Copyright Year	1991
Abstract	In this paper, we derive a unified framework for orthonormal decomposition of the array manifold on scalar fields. Such fields are encountered in cases where polarization is not considered, e.g., single polarized radio waves and acoustic pressure. The results generalize and unify different decompositions of the array manifold, found in recent literature, to arrays of arbitrary geometry including conformal arrays. The concept of equivalence matrix is introduced, establishing a link between the spherical harmonics and 2-D Fourier basis functions. Under some mild assumptions that typically hold in practice, a one-to-one relationship between spherical harmonic spectra and 2-D Fourier spectra may be established. Additionally, it is shown that the rows of the equivalence matrix and the 2-D Fourier spectra of the array manifold span the same subspace. With such results the spherical harmonic and 2-D Fourier decompositions of the array manifold vector, i.e., Wavefield Modeling and 2-D Effective Aperture Distribution Function (EADF) are shown to be equivalent. Results on the modeling capabilities of both orthonormal decompositions are obtained. Moreover, the equivalence matrix is shown to facilitate noise attenuation. A fast spherical harmonic transform with complexity O(Q logQ) can be obtained by exploiting the equivalence matrix, where Q represents the total number of points on the sphere. Finally, the equivalence matrix allows to gain more insight into the relation between rotating a function on the sphere and on the torus. These contributions facilitate high-resolution array processing both in elevation and azimuth irrespective of the array structure or imperfections.
Sponsorship	IEEE Signal Processing Society
Starting Page	4634
Ending Page	4645
Page Count	12
File Size	837904
File Format	PDF
ISSN	1053587X
Volume Number	58
Issue Number	9
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2010-09-01
Publisher Place	U.S.A.
Access Restriction	One Nation One Subscription (ONOS)
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Sensor arrays Matrix decomposition Signal processing algorithms Transmission line matrix methods Array signal processing Apertures Distribution functions Calibration Polarization Parameter estimation equivalence matrix DoA estimation array calibration measurements wavefield modeling effective aperture distribution function (EADF) spherical harmonics fast spherical harmonic transform
Content Type	Text
Resource Type	Article
Subject	Signal Processing Electrical and Electronic Engineering

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