scholarly journals Joint Resource Allocation for SWIPT-Based Two-Way Relay Networks

Energies ◽  
2020 ◽  
Vol 13 (22) ◽  
pp. 6024
Author(s):  
Chunling Peng ◽  
Guozhong Wang ◽  
Fangwei Li ◽  
Huaping Liu
Keyword(s):  
Resource Allocation ◽  
Outage Probability ◽  
Closed Form ◽  
Time Allocation ◽  
Closed Form Solution ◽  
Form Solution ◽  
Closed Form Expression ◽  
Power Splitting ◽  
Decode And Forward ◽  
Joint Resource Allocation

This paper considers simultaneous wireless information and power transfer (SWIPT) in a decode-and-forward two-way relay (DF-TWR) network, where a power splitting protocol is employed at the relay for energy harvesting. The goal is to jointly optimize power allocation (PA) at the source nodes, power splitting (PS) at the relay node, and time allocation (TA) of each duration to minimize the system outage probability. In particular, we propose a static joint resource allocation (JRA) scheme and a dynamic JRA scheme with statistical channel properties and instantaneous channel characteristics, respectively. With the derived closed-form expression of the outage probability, a successive alternating optimization algorithm is proposed to tackle the static JRA problem. For the dynamic JRA scheme, a suboptimal closed-form solution is derived based on a multistep optimization and relaxation method. We present a comprehensive set of simulation results to evaluate the proposed schemes and compare their performances with those of existing resource allocation schemes.

scholarly journals Outage-Based Resource Allocation for DF Two-Way Relay Networks with Energy Harvesting

Sensors ◽  
2018 ◽  
Vol 18 (11) ◽  
pp. 3946 ◽  
Author(s):  
Chunling Peng ◽  
Fangwei Li ◽  
Huaping Liu ◽  
Guozhong Wang
Keyword(s):  
Resource Allocation ◽  
Energy Harvesting ◽  
Outage Probability ◽  
Relay Network ◽  
Total Power ◽  
Power Splitting ◽  
Decode And Forward ◽  
Resource Allocation Algorithm ◽  
Joint Resource Allocation ◽  
System Outage Probability

A joint resource allocation algorithm to minimize the system outage probability is proposed for a decode-and-forward (DF) two-way relay network with simultaneous wireless information and power transfer (SWIPT) under a total power constraint. In this network, the two sources nodes exchange information with the help of a passive relay, which is assumed to help the two source nodes’ communication without consuming its own energy by exploiting an energy-harvesting protocol, the power splitting (PS) protocol. An optimization framework to jointly optimize power allocation (PA) at the source nodes and PS at the relay is developed. Since the formulated joint optimization problem is non-convex, the solution is developed in two steps. First, the conditionally optimal PS ratio at the relay node for a given PA ratio is explored; then, the closed-form of the optimal PA in the sense of minimizing the system outage probability with instantaneous channel state information (CSI) is derived. Analysis shows that the optimal design depends on the channel condition and the rate threshold. Simulation results are obtained to validate the analytical results. Comparison with three existing schemes shows that the proposed optimized scheme has the minimum system outage probability.

A Closed-Form Solution for the Global Quadratic Hedging of Options under Geometric Gaussian Random Walks

2019 ◽  
Keyword(s):  
Closed Form ◽  
Recursive Algorithm ◽  
Closed Form Solution ◽  
Form Solution ◽  
Closed Form Expression ◽  
Problem Solution ◽  
Underlying Asset ◽  
Quadratic Hedging ◽  
Hedging Problem ◽  
The Impact

This study obtains a closed-form solution for the discrete-time global quadratic hedging problem of Schweizer (1995) applied to vanilla European options under the geometric Gaussian random walk model for the underlying asset. This extends the work of Rémillard and Rubenthaler (2013), who obtained closed-form formulas for some components of the hedging problem solution. Coefficients embedded in the closed-form expression can be computed either directly or through a recursive algorithm. The author also presents a brief sensitivity analysis to determine the impact of the underlying asset drift and the hedging portfolio rebalancing frequency on the optimal hedging capital and the initial hedge ratio.

EXACT PRICING WITH STOCHASTIC VOLATILITY AND JUMPS

2010 ◽  
Vol 13 (06) ◽  
pp. 901-929 ◽  
Author(s):  
FERNANDA D'IPPOLITI ◽  
ENRICO MORETTO ◽  
SARA PASQUALI ◽  
BARBARA TRIVELLATO
Keyword(s):  
Closed Form ◽  
Stochastic Volatility ◽  
Closed Form Solution ◽  
Exact Algorithm ◽  
Form Solution ◽  
Closed Form Expression ◽  
Barrier Options ◽  
Form Expression ◽  
Variance Swaps ◽  
Jump Diffusion Model

A stochastic volatility jump-diffusion model for pricing derivatives with jumps in both spot return and volatility underlying dynamics is presented. This model admits, in the spirit of Heston, a closed-form solution for European-style options. The structure of the model is also suitable to explicitly obtain the fair delivery price for variance swaps. To evaluate derivatives whose value does not admit a closed-form expression, a methodology based on an "exact algorithm", in the sense that no discretization of equations is required, is developed and applied to barrier options. Goodness of pricing algorithm is tested using DJ Euro Stoxx 50 market data for European options. Finally, the algorithm is applied to compute prices and Greeks for barrier options and to determine the fair delivery prices for variance swaps.

A Closed-Form Solution for the Eshelby Tensor and the Elastic Field Outside an Elliptic Cylindrical Inclusion

2011 ◽  
Vol 78 (3) ◽  
Author(s):  
Xiaoqing Jin ◽  
Leon M. Keer ◽  
Qian Wang
Keyword(s):  
Closed Form ◽  
Closed Form Solution ◽  
Elastic Field ◽  
Form Solution ◽  
Eshelby Tensor ◽  
Cylindrical Inclusion ◽  
Closed Form Expression ◽  
Equivalent Inclusion Method ◽  
Explicit Analytical Solution ◽  
Present Solution

From the analytical formulation developed by Ju and Sun [1999, “A Novel Formulation for the Exterior-Point Eshelby’s Tensor of an Ellipsoidal Inclusion,” ASME Trans. J. Appl. Mech., 66, pp. 570–574], it is seen that the exterior point Eshelby tensor for an ellipsoid inclusion possesses a minor symmetry. The solution to an elliptic cylindrical inclusion may be obtained as a special case of Ju and Sun’s solution. It is noted that the closed-form expression for the exterior-point Eshelby tensor by Kim and Lee [2010, “Closed Form Solution of the Exterior-Point Eshelby Tensor for an Elliptic Cylindrical Inclusion,” ASME Trans. J. Appl. Mech., 77, p. 024503] violates the minor symmetry. Due to the importance of the solution in micromechanics-based analysis and plane-elasticity-related problems, in this work, the explicit analytical solution is rederived. Furthermore, the exterior-point Eshelby tensor is used to derive the explicit closed-form solution for the elastic field outside the inclusion, as well as to quantify the elastic field discontinuity across the interface. A benchmark problem is used to demonstrate a valuable application of the present solution in implementing the equivalent inclusion method.

scholarly journals Enhancing the electrical and thermal conductivities of polymer composites via curvilinear fibers: An analytical study

2019 ◽  
Vol 24 (10) ◽  
pp. 3231-3253 ◽  
Author(s):  
Marco Salviato ◽  
Sean E Phenisee
Keyword(s):  
Closed Form ◽  
Electric Conductivity ◽  
Electrostatic Potential ◽  
Mechanical Performance ◽  
Transverse Isotropy ◽  
Closed Form Solution ◽  
Transversely Isotropic ◽  
Form Solution ◽  
Closed Form Expression ◽  
Element Analysis

The new generation of manufacturing technologies such as additive manufacturing and automated fiber placement has enabled the development of material systems with desired functional and mechanical properties via particular designs of inhomogeneities and their mesostructural arrangement. Among these systems, particularly interesting are materials exhibiting curvilinear transverse isotropy (CTI), in which the inhomogeneities take the form of continuous fibers following curvilinear paths designed to, for example, optimize the electric and thermal conductivity, and the mechanical performance of the system. In this context, the present work proposes a general framework for the exact, closed-form solution of electrostatic problems in materials featuring CTI. First, the general equations for the fiber paths that optimize the electric conductivity are derived, leveraging a proper conformal coordinate system. Then, the continuity equation for the curvilinear transversely isotropic system is derived in terms of electrostatic potential. A general exact, closed-form expression for the electrostatic potential and electric field is derived and validated by finite element analysis. Finally, potential avenues for the development of materials with superior electric conductivity and damage sensing capabilities are discussed.

scholarly journals Scattering from Spheres: A New Look into an Old Problem

Electronics ◽  
2021 ◽  
Vol 10 (2) ◽  
pp. 216
Author(s):  
Giuseppe Ruello ◽  
Riccardo Lattanzi
Keyword(s):  
Closed Form ◽  
Transmission Lines ◽  
Electromagnetic Scattering ◽  
Impedance Matching ◽  
Closed Form Solution ◽  
Mie Scattering ◽  
Form Solution ◽  
Closed Form Expression ◽  
Spherical Waves ◽  
Scattered Fields

In this work, we introduce a theoretical framework to describe the scattering from spheres. In our proposed framework, the total field in the outer medium is decomposed in terms of inward and outward electromagnetic fields, rather than in terms of incident and scattered fields, as in the classical Lorenz–Mie formulation. The fields are expressed as series of spherical harmonics, whose combination weights can be interpreted as reflection and transmission coefficients, which provides an intuitive understanding of the propagation and scattering phenomena. Our formulation extends the previously proposed theory of non-uniform transmission lines by introducing an expression for impedance transfer, which yields a closed-form solution for the fields inside and outside the sphere. The power transmitted in and scattered by the sphere can be also evaluated with a simple closed-form expression and related with the modulus of the reflection coefficient. We showed that our method is fully consistent with the classical Mie scattering theory. We also showed that our method can provide an intuitive physical interpretation of electromagnetic scattering in terms of impedance matching and resonances, and that it is especially useful for the case of inward traveling spherical waves generated by sources surrounding the scatterer.

scholarly journals A Closed Form Solution for Nonlinear Oscillators Frequencies Using Amplitude-Frequency Formulation

2012 ◽  
Vol 19 (6) ◽  
pp. 1415-1426 ◽  
Author(s):  
A. Barari ◽  
A. Kimiaeifar ◽  
M.G. Nejad ◽  
M. Motevalli ◽  
M.G. Sfahani
Keyword(s):  
Closed Form ◽  
Numerical Solutions ◽  
Closed Form Solution ◽  
Analytical Techniques ◽  
Nonlinear Oscillators ◽  
Form Solution ◽  
Closed Form Expression ◽  
System Response ◽  
Classical Dynamics ◽  
Analytical Technique

Many nonlinear systems in industry including oscillators can be simulated as a mass-spring system. In reality, all kinds of oscillators are nonlinear due to the nonlinear nature of springs. Due to this nonlinearity, most of the studies on oscillation systems are numerically carried out while an analytical approach with a closed form expression for system response would be very useful in different applications. Some analytical techniques have been presented in the literature for the solution of strong nonlinear oscillators as well as approximate and numerical solutions. In this paper, Amplitude-Frequency Formulation (AFF) approach is applied to analyze some periodic problems arising in classical dynamics. Results are compared with another approximate analytical technique called Energy Balance Method developed by the authors (EBM) and also numerical solutions. Close agreement of the obtained results reveal the accuracy of the employed method for several practical problems in engineering.

Pointing Error Effects on Mixed RF-FSO Link

2019 ◽  
Vol 0 (0) ◽  
Author(s):  
Rashi Jain ◽  
Sakshi Dhiman ◽  
Rahul Kaushik
Keyword(s):  
Radio Frequency ◽  
Outage Probability ◽  
Closed Form ◽  
Atmospheric Turbulence ◽  
Closed Form Expression ◽  
Communication Link ◽  
Form Expression ◽  
Decode And Forward ◽  
Pointing Error ◽  
Outage Performance

AbstractIn this paper, the performance of a mixed dual hop asymmetric radio frequency andfree space optical (RF-FSO) communication link is investigated. A closed form analytical expression for evaluating outage probability of mixed RF-FSO link is obtained. The source to relay link is RF link modelled using Nakagami-m fading. The relay to destination link is an FSO link subjected to atmospheric turbulence, modelled using K-distribution. Decode-and-Forward (DF) relaying protocol is used. Further, the effect of pointing error on the performance of the link is analysed using obtained closed form expression. It has been observed that increase in the pointing error leads to reduction in outage performance of the link.

scholarly journals On the Derivation of a Closed-Form Expression for the Solutions of a Subclass of Generalized Abel Differential Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-9
Author(s):  
Panayotis E. Nastou ◽  
Paul Spirakis ◽  
Yannis C. Stamatiou ◽  
Apostolos Tsiakalos
Keyword(s):  
Differential Equation ◽  
General Solution ◽  
Differential Equations ◽  
Closed Form ◽  
Closed Form Solution ◽  
Form Solution ◽  
Closed Form Expression ◽  
Form Expression ◽  
Abel Differential Equations ◽  
Solution Methodology

We investigate the properties of a general class of differential equations described bydy(t)/dt=fk+1(t)y(t)k+1+fk(t)y(t)k+⋯+f2(t)y(t)2+f1(t)y(t)+f0(t),withk>1a positive integer andfi(t), 0≤i≤k+1, withfi(t), real functions oft. Fork=2, these equations reduce to the class ofAbel differential equations of the first kind,for which a standard solution procedure is available. However, fork>2no general solution methodology exists, to the best of our knowledge, that can lead to their solution. We develop a general solution methodology that for odd values ofkconnects the closed form solution of the differential equations with the existence of closed-form expressions for the roots of the polynomial that appears on the right-hand side of the differential equation. Moreover, the closed-form expression (when it exists) for the polynomial roots enables the expression of the solution of the differential equation in closed form, based on the class of Hyper-Lambert functions. However, for certain even values ofk, we prove that such closed form does not exist in general, and consequently there is no closed-form expression for the solution of the differential equation through this methodology.

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