Integral Inequalities

Gradshteyn, I. S.; Ryzhik, I.M.

doi:10.1016/b978-0-12-294760-5.50023-4

Cited by 330 publications

(588 citation statements)

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“…In order to evaluate the integrals defining r v/h ss /uu , we use the results below [3.937, p488, [28]] (12) noting that [28] gives closed form expressions for both F s (.) and F c (.).…”

Section: A Spatial Correlation Of the 2d Componentmentioning

confidence: 99%

Polarized MIMO channels in 3-D: models, measurements and mutual information

Shafi¹,

Zhang

Moustakas³

et al. 2006

IEEE J. Select. Areas Commun.

241

146

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4G systems are expected to support data rates of the order of 100 Mbps in the outdoor environment and 1 Gbps in the indoor/stationary environment. In order to support such large payloads, the radio physical layer must employ receiver algorithms that provide a significant increase in spectrum efficiency (and hence capacity) over current wireless systems. Recently an explosion of MIMO studies have appeared with many journals presenting special issues on this subject. This has occured dur to the potential of MIMO to provide a linear increase in capacity with antenna numbers. Environmental conciderations and tower loads will often restrict the placing of large antenna spans on base stations. Similarly, customer device form factors also place a limit on the antenna numbers that can be placed with a mutual spacing of 0.5 wavelength. The use of cross-polarized antennas is widely used in modern cellular installtions as it reduces spacing needs and tower loads on base stations. Hence, this approach is also receiving considerable attention in MIMO systems. In order to study and compare various receiver architectures that are based on MIMO techniques, one needs to have an accurate knowledge of the MIMO channel. However, very few studies have appeared that characterize the cross-polarized MIMO channel. Recently, the third generation partnership standards bodies (3GPP/3GPP2) have defined a cross-polarized channel model for MIMO systems but this model neglects the elevation spectrum. In this paper we provide a deeper understanding of the channel model for cross-polarized systems for different environments and propose a composite channel impulse model for the cross-polarized channel that takes into account both azimuth and elevation spectrum. We use the resulting channel impulse response to derive closed form expressions for the spatial correlation. We also present models to describe the dependence of cross-polarization discrimination (XPD) on distance, azimuth and elevation and delay spread. In addition, we study the impact of array width, SNR and antenna slant angle on the mutual information (MI) of the system. In particular we present an analytical model for large system mean mutual information values and consider the impact of elevation spectrum on MI. Finally, the impace of multipath delays on XPD and MI is also explored. IEEE Journal on Selected Areas in CommunicationsThis work may not be copied or reproduced in whole or in part for any commercial purpose. Permission to copy in whole or in part without payment of fee is granted for nonprofit educational and research purposes provided that all such whole or partial copies include the following: a notice that such copying is by permission of Mitsubishi Electric Research Laboratories, Inc.; an acknowledgment of the authors and individual contributions to the work; and all applicable portions of the copyright notice. Copying, reproduction, or republishing for any other purpose shall require a license with payment of fee to Mitsubishi Electric Research Laboratories, ...

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“…In order to evaluate the integrals defining r v/h ss /uu , we use the results below [3.937, p488, [28]] (12) noting that [28] gives closed form expressions for both F s (.) and F c (.).…”

Section: A Spatial Correlation Of the 2d Componentmentioning

confidence: 99%

Polarized MIMO channels in 3-D: models, measurements and mutual information

Shafi¹,

Zhang

Moustakas³

et al. 2006

IEEE J. Select. Areas Commun.

241

146

View full text Add to dashboard Cite

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“…By changing the variable of integration from 4* to 1/c2 -1/X, the integral can be expressed in the form of a tabulated integral [4] and the result can be expressed in terms of the Bmag parameter:…”

Section: Theorymentioning

confidence: 99%

Beam distribution function after filamentation

Raubenheimer

Decker

Seeman

Proceedings Particle Accelerator Conference

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In this paper, we calculate the beam distribution function after filamentation (phase-mixing) of a focusing mismatch. This distribution is relevant when interpreting beam measurements and sources of emittance dilution in linear colliders. It is also important when considering methods of diluting the phase space density, which may be required for the machine protection system in future linear colliders, and it is important when studying effects of trapped ions which filament in the electron beam potential. Finally, the resulting distribution is compared with measured beam distributions from the SLAC linac.

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“…Here, we may use the addition theorem for Gegenbauer polynomials [28] to replace the second summation with…”

Section: Scalar Perturbationmentioning

confidence: 99%

Perturbation of FRW Spacetime in Np Formalism

Sharma

Khanal

2014

Int. J. Mod. Phys. D

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Jacobi polynomials appear to play a very important role in describing all the spin field (s = 0, 1/2, 1, 2) perturbation of the FRW spacetime. The formulation becomes very transparent when done in NP formalism. All the variables are separable, and the spatial eigenfuctions turn out to be Jacobian polynomials in different forms. In particular, the angular ones are expressible as spin weighted spherical harmonics which are just the spherical harmonics formed with Jacobi polynomials. The radial eigenfuctions are also Jacobi polynomials but with unconventional parameters. Various properties of these polynomials are used to describe the scalar, vector and tensor modes of the perturbation. The Green's function of the scalar perturbations and also its Lienard Wiecherte type potentials are derived, and are shown to reduce to the familiar ones in the limit to flat FRW case. Some of the components of the perturbed metric tensor h µν have also been calculated.

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Integral Inequalities

Cited by 330 publications

References 0 publications

Polarized MIMO channels in 3-D: models, measurements and mutual information

Polarized MIMO channels in 3-D: models, measurements and mutual information

Beam distribution function after filamentation

Perturbation of FRW Spacetime in Np Formalism

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