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

Costa, Mário; Richter, Andreas; Koivunen, Visa

doi:10.1109/tsp.2010.2050315

Cited by 80 publications

(55 citation statements)

References 31 publications

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“…In [15], we have also shown that the equivalence matrix provides a bijective mapping between the sampling matrices as ΓΞ = Φ and Γ = ΦΞ † . Here, the concept of equivalence matrix is extended to vector-fields.…”

Section: Equivalence Of the Decompositionsmentioning

confidence: 90%

“…This section provides a unification of such representations. In particular, we extend the concept of equivalence matrix [15] to vector-fields and show that the three decompostions of the array steering vector are equivalent. The equivalence matrix is shown to provide a bijective relation among the three sampling matrices.…”

Section: Equivalence Of the Decompositionsmentioning

confidence: 99%

“…It is important to mention that (3) is a decomposition of the periodic array manifold since the 2-D Fourier basis are orthogonal on the torus (T ) but not on the 2-sphere (S 2 ). This becomes crucial when Φ s is computed from calibration measurement data [15].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Steering vector modeling for polarimetric arrays of arbitrary geometry

Costa

Richter

Koivunen

2010

2010 IEEE Sensor Array and Multichannel Signal Processing Workshop

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In this paper, the algebraic modeling of the steering vector for dual-polarized real-world arrays with unknown configuration is addressed. The formalism provided by the wavefield modeling theory is extended to vector-fields such as completely polarized electromagnetic waves. In particular, compact expressions for decomposing the array steering vector in different orthonormal basis functions are proposed. Such decompositions are shown to be equivalent under mild conditions that typically hold in practice. Recent results on algebraic modeling of sensor arrays are generalized to vector-fields and unified. These results allow for high-resolution direction-of-arrival and polarization estimation when array calibration measurement data is available only. We show that reduced computational complexity may be achieved by making use of the Fast Fourier Transform. Such computational savings may be obtained without compromising the performance of the estimation algorithms and irrespective of the antenna array configuration. The results in this paper contribute to array design as well by providing closed-form expressions for the array steering vector, which are useful in optimizing different array performance criteria. Simulations on direction-of-arrival and polarization estimation using a real-world polarimetric array are carried out, validating our analytical results.

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Section: Equivalence Of the Decompositionsmentioning

confidence: 90%

Section: Equivalence Of the Decompositionsmentioning

confidence: 99%

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Steering vector modeling for polarimetric arrays of arbitrary geometry

Costa

Richter

Koivunen

2010

2010 IEEE Sensor Array and Multichannel Signal Processing Workshop

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“…Reference [4] developed two eigenstructure-based algorithms for 2-D estimation with UCAs. However, these methods introduce errors in the form of bias and excess variance, and hence, the obtained estimates may be far from optimal [5]. Furthermore, these methods involve eigenvalue decomposition; thus, the computational load is significant.…”

Section: Introductionmentioning

confidence: 99%

Accurate 2-D AOA Estimation and Ambiguity Resolution for a Single Source under Fixed Uniform Circular Arrays

Zuo

Pan

2017

International Journal of Antennas and Propagation

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This paper presents an analytic algorithm for accurate two-dimensional (2-D) angle of arrival (AOA) estimation of a single source under fixed uniform circular arrays (UCAs). Algebraic and explicit formulations for 2-D AOA estimation are first developed in the Fourier domain. It is shown that three is the minimum number of antennas for 2-D AOA estimation based on phase measurement. Then a signal model for phase extraction is established with equivalent phase noises through observations of signal samples corrupted by additive Gaussian white noise. Under fixed UCAs, 2-D AOA estimation of a single source would suffer from phase ambiguity, and hence, ambiguity resolution is also addressed in the Fourier domain by integer search. Numerical examples are provided to verify the effectiveness and appealing performance of the proposed 2-D AOA estimation algorithm.

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“…The EADF is usually utilized to model a geometry-based channel due to its accuracy and low complexity (e.g. [20][21][22]). …”

Section: Introductionmentioning

confidence: 99%

An Efficient Response Distribution Function for 3D MIMO Channel Modeling from a Scatterer View

Sheng¹,

Wang

et al. 2016

IJFGCN

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A Radio Environment Map (REM) maps its geolocation information to the propagation characteristics as complementary information for an adaptive communication of cognitive radio (CR). In this paper we propose a novel theoretical three dimension (3D) Multiple Input Multiple Output (MIMO) channel model. The proposed model parameterizes the geolocation information of interacting obstacles referred as scatterers. An efficient response distribution function (ERDF) is developed to interpolate the array response for an arbitrary scatterer location. It is shown that the mutual information of the proposed model is consistent with a conventional geometry-based model with the lower simulation time. It allows us to generate channels with all possible scatterer distribution on the surface of a building effectively.

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

Cited by 80 publications

References 31 publications

Steering vector modeling for polarimetric arrays of arbitrary geometry

Steering vector modeling for polarimetric arrays of arbitrary geometry

Accurate 2-D AOA Estimation and Ambiguity Resolution for a Single Source under Fixed Uniform Circular Arrays

An Efficient Response Distribution Function for 3D MIMO Channel Modeling from a Scatterer View

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