213 research outputs found
Analytic solutions to a Marcum Q-function-based integral and application in energy detection of unknown signals over multipath fading channels
This work presents analytic solutions for a useful integral in wireless
communications, which involves the Marcum function in combination with an
exponential function and arbitrary power terms. The derived expressions have a
rather simple algebraic representation which renders them convenient both
analytically and computationally. Furthermore, they can be useful in wireless
communications and particularly in the context of cognitive radio
communications and radar systems, where this integral is often encountered. To
this end, we derive novel expressions for the probability of detection in
energy detection based spectrum sensing over fading channels.
These expressions are given in closed-form and are subsequently employed in
analyzing the effects of generalised multipath fading conditions in cognitive
radio systems. As expected, it is shown that the detector is highly dependent
upon the severity of fading conditions as even slight variation of the fading
parameters affect the corresponding performance significantly.Comment: Latest/Preprint Versio
Effective Polymer Dynamics of D-Dimensional Black Hole Interiors
We consider two different effective polymerization schemes applied to
D-dimensional, spherically symmetric black hole interiors. It is shown that
polymerization of the generalized area variable alone leads to a complete,
regular, single-horizon spacetime in which the classical singularity is
replaced by a bounce. The bounce radius is independent of rescalings of the
homogeneous internal coordinate, but does depend on the arbitrary fiducial cell
size. The model is therefore necessarily incomplete. It nonetheless has many
interesting features: After the bounce, the interior region asymptotes to an
infinitely expanding Kantowski-Sachs spacetime. If the solution is analytically
continued across the horizon, the black hole exterior exhibits asymptotically
vanishing quantum-corrections due to the polymerization. In all spacetime
dimensions except four, the fall-off is too slow to guarantee invariance under
Poincare transformations in the exterior asymptotic region. Hence the
four-dimensional solution stands out as the only example which satisfies the
criteria for asymptotic flatness. In this case it is possible to calculate the
quantum-corrected temperature and entropy. We also show that polymerization of
both phase space variables, the area and the conformal mode of the metric,
generically leads to a multiple horizon solution which is reminiscent of
polymerized mini-superspace models of spherically symmetric black holes in Loop
Quantum Gravity.Comment: 14 pages, 4 figures. Added discussion about the dependency on
auxiliary structures. Matches with the published versio
The general dielectric tensor for bi-kappa magnetized plasmas
In this paper we derive the dielectric tensor for a plasma containing
particles described by an anisotropic superthermal (bi-kappa) velocity
distribution function. The tensor components are written in terms of the
two-variables kappa plasma special functions, recently defined by Gaelzer and
Ziebell [Phys. Plasmas 23, 022110 (2016)]. We also obtain various new
mathematical properties for these functions, which are useful for the
analytical treatment, numerical implementation and evaluation of the functions
and, consequently, of the dielectric tensor. The formalism developed here and
in the previous paper provides a mathematical framework for the study of
electromagnetic waves propagating at arbitrary angles and polarizations in a
superthermal plasma.Comment: Accepted for publication in Physics of Plasma
The Ramanujan master theorem and its implications for special functions
We study a number of possible extensions of the Ramanujan master theorem,
which is formulated here by using methods of Umbral nature. We discuss the
implications of the procedure for the theory of special functions, like the
derivation of formulae concerning the integrals of products of families of
Bessel functions and the successive derivatives of Bessel type functions. We
stress also that the procedure we propose allows a unified treatment of many
problems appearing in applications, which can formally be reduced to the
evaluation of exponential- or Gaussian-like integrals.Comment: 12 page
Analytic Expressions and Bounds for Special Functions and Applications in Communication Theory
This paper is devoted to the derivation of novel analytic expressions and bounds for a family of special functions that are useful in wireless communication theory. These functions are the well-known Nuttall Q-function, incomplete Toronto function, Rice Ie-function, and incomplete Lipschitz-Hankel integrals. Capitalizing on the offered results, useful identities are additionally derived between the above functions and Humbert, Ί1, function as well as for specific cases of the KampeÌ de FeÌriet function. These functions can be considered as useful mathematical tools that can be employed in applications relating to the analytic performance evaluation of modern wireless communication systems, such as cognitive radio, cooperative, and free-space optical communications as well as radar, diversity, and multiantenna systems. As an example, new closed-form expressions are derived for the outage probability over nonlinear generalized fading channels, namely, α-η-ÎŒ, α-λ-ÎŒ, and α-Îș-ÎŒ as well as for specific cases of the η-ÎŒ and λ-ÎŒ fading channels. Furthermore, simple expressions are presented for the channel capacity for the truncated channel inversion with fixed rate and corresponding optimum cutoff signal-to-noise ratio for single-antenna and multiantenna communication systems over Rician fading channels. The accuracy and validity of the derived expressions is justified through extensive comparisons with respective numerical results
Obliquely propagating electromagnetic waves in magnetized kappa plasmas
Velocity distribution functions (VDFs) that exhibit a power-law dependence on
the high-energy tail have been the subject of intense research by the plasma
physics community. Such functions, known as kappa or superthermal
distributions, have been found to provide a better fitting to the VDFs measured
by spacecraft in the solar wind. One of the problems that is being addressed on
this new light is the temperature anisotropy of solar wind protons and
electrons. In the literature, the general treatment for waves excited by
(bi-)Maxwellian plasmas is well-established. However, for kappa distributions,
the wave characteristics have been studied mostly for the limiting cases of
purely parallel or perpendicular propagation, relative to the ambient magnetic
field. Contributions to the general case of obliquely-propagating
electromagnetic waves have been scarcely reported so far. The absence of a
general treatment prevents a complete analysis of the wave-particle interaction
in kappa plasmas, since some instabilities can operate simultaneously both in
the parallel and oblique directions. In a recent work, Gaelzer and Ziebell [J.
Geophys. Res. 119, 9334 (2014)] obtained expressions for the dielectric tensor
and dispersion relations for the low-frequency, quasi-perpendicular dispersive
Alfv\'en waves resulting from a kappa VDF. In the present work, the formalism
introduced by Ref. 1 is generalized for the general case of electrostatic
and/or electromagnetic waves propagating in a kappa plasma in any frequency
range and for arbitrary angles. An isotropic distribution is considered, but
the methods used here can be easily applied to more general anisotropic
distributions, such as the bi-kappa or product-bi-kappa.Comment: Accepted for publication in Physics of Plasmas; added references for
section
Security Improvement for Energy Harvesting based Overlay Cognitive Networks with Jamming-Assisted Full-Duplex Destinations
This work investigates the secrecy capability of energy harvesting based overlay cognitive networks (EHOCNs). To this end, we assume that a message by a licensed transmitter is relayed by an unlicensed sender. Critically, the unlicensed sender uses energy harvested from licensed signals, enhancing the overall energy efficiency and maintaining the integrity of licensed communications. To secure messages broadcast by the unlicensed sender against the wire-tapper, full-duplex destinations - unlicensed recipient and licensed receiver - jam the eavesdropper at the same time they receive signals from the unlicensed sender. To this effect, we derive closed-form formulas for the secrecy outage probability, which then quantify the security performance of both unlicensed and licensed communications for EHOCNs with jamming-assisted full-duplex destinations, namely EHOCNwFD. In addition, optimum operating parameters are established, which can serve as essential design guidelines of such systems.acceptedVersionPeer reviewe
On the derivative of the associated Legendre function of the first kind of integer order with respect to its degree
In our recent works [R. Szmytkowski, J. Phys. A 39 (2006) 15147; corrigendum:
40 (2007) 7819; addendum: 40 (2007) 14887], we have investigated the derivative
of the Legendre function of the first kind, , with respect to its
degree . In the present work, we extend these studies and construct
several representations of the derivative of the associated Legendre function
of the first kind, , with respect to the degree , for
. At first, we establish several contour-integral
representations of . They are then
used to derive Rodrigues-type formulas for with . Next, some closed-form
expressions for are
obtained. These results are applied to find several representations, both
explicit and of the Rodrigues type, for the associated Legendre function of the
second kind of integer degree and order, ; the explicit
representations are suitable for use for numerical purposes in various regions
of the complex -plane. Finally, the derivatives
, and , all with , are evaluated in terms
of .Comment: LateX, 40 pages, 1 figure, extensive referencin
Gravitational Atom in Compactified Extra Dimensions
We consider quantum mechanical effects of the modified Newtonian potential in
the presence of extra compactified dimensions. We develop a method to solve the
resulting Schroedinger equation and determine the energy shifts caused by the
Yukawa-type corrections of the potential. We comment on the possibility of
detecting the modified gravitational bound state Energy spectrum by present day
and future experiments.Comment: 12 pages, 2 figure
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