The root-MUSIC algorithm for direction finding with interpolated arrays
Signal Processing
Regular Article: Computing Fourier Transforms and Convolutions on the 2-Sphere
Advances in Applied Mathematics
An efficient algorithm for two-dimensional frequency estimation
Multidimensional Systems and Signal Processing
Matrix computations (3rd ed.)
A fast spherical harmonics transform algorithm
Mathematics of Computation
Multidimensional rank reduction estimator for parametric MIMO channel models
EURASIP Journal on Applied Signal Processing
Low complexity azimuth and elevation estimation for arbitrary array configurations
ICASSP '09 Proceedings of the 2009 IEEE International Conference on Acoustics, Speech and Signal Processing
Detection and tracking of MIMO propagation path parameters using state-space approach
IEEE Transactions on Signal Processing
Spherical harmonic transforms using quadratures and least squares
ICCS'06 Proceedings of the 6th international conference on Computational Science - Volume Part III
Array interpolation and bias reduction
IEEE Transactions on Signal Processing - Part I
IEEE Transactions on Signal Processing
Beamspace Transform for UCA: Error Analysis and Bias Reduction
IEEE Transactions on Signal Processing
DoA Estimation Via Manifold Separation for Arbitrary Array Structures
IEEE Transactions on Signal Processing
UCA Root-MUSIC With Sparse Uniform Circular Arrays
IEEE Transactions on Signal Processing - Part II
The Spherical-Shell Microphone Array
IEEE Transactions on Audio, Speech, and Language Processing
Unifying spherical harmonic and 2-D Fourier decompositions of the array manifold
Asilomar'09 Proceedings of the 43rd Asilomar conference on Signals, systems and computers
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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 liink 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 spedra 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(QlogQ) 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.