On the applicability of numerical tools for simulating wave-ports close to the cutoff frequency

This paper focuses on a common drawback in electromagnetic numerical computer aided design computer aided design (CAD) tools: high frequency structure simulator (HFSS), computer simulation technology (CST) and FEKO, where the excitation by using a wave-port below and close to the cutoff frequency has unreliable values for the reflection coefficient. An example for such problem is presented in the design of a dual horn antenna fed by two different waveguide sections. To overcome this numerical error in the results of these CAD tools, a tapered waveguide section is used in the simulation as an excitation mechanism to the feeding waveguide. The cross section of the input port at this tapered waveguide section is designed to have a cutoff frequency smaller than the lowest frequency under investigation for the original problem. Then, by extracting the effect of the tapered section from the obtained reflection coefficient, it would be possible to obtain the reflection coefficient of the original problem.

Orthonormal piecewise Bernoulli functions: Application for optimal control problems generated using fractional integro-differential equations

In this study, the orthonormal piecewise Bernoulli functions are generated as a new kind of basis functions. An explicit matrix related to fractional integration of these functions is obtained. An efficient direct method is developed to solve a novel set of optimal control problems defined using a fractional integro-differential equation. The presented technique is based on the expressed basis functions and their fractional integral matrix together with the Gauss–Legendre integration method and the Lagrange multipliers algorithm. This approach converts the original problem into a mathematical programming one. Three examples are investigated numerically to verify the capability and reliability of the approach.

Data Rate Maximization in RIS-Assisted D2D Communication with Transceiver Hardware Impairments

We maximize the transmit rate of device-to-device (D2D) in a reconfigurable intelligent surface (RIS) assisted D2D communication system by satisfying the unit-modulus constraints of reflectin elements, the transmit power limit of base station (BS) and the transmitter in a D2D pair. Since it is a non-convex optimization problem, the block coordinate descent (BCD) technique is adopted to decouple this problem into three subproblems. Then, the non-convex subproblems are approximated into convex problems by using successive convex approximation (SCA) and penalty convex-concave procedure (CCP) techniques. Finally, the optimal solution of original problem is obtained by iteratively optimizing the subproblems. Simulation results reveal the validity of the algorithm that we proposed to solve the optimization problem and illustrate the effectiveness of RIS to improve the transmit rate of the D2D pair even with hardware impairments.

Robust Security Beamforming for SWIPT-Assisted Relay System with Channel Uncertainty

This paper considers the physical layer security (PLS) of a simultaneous wireless information and power transfer (SWIPT) relay communication system composed of a legitimate source–destination pair and some eavesdroppers. Supposing a disturbance of channel status information (CSI) between relay and eavesdroppers in a bounded ellipse, we intend to design a robust beamformer to maximum security rate in the worst case on the constraints of relay energy consumption. To handle this non-convex optimization problem, we introduce a slack variable to transform the original problem into two sub-problems firstly, then an algorithm employing a semidefinite relaxation (SDR) technique and S-procedure is proposed to tackle above two sub-problems. Although our study was conducted in the scene of a direct link among source, destination, and eavesdroppers that is non-existing, we demonstrate that our conclusions can be easily extended to the scene for which a direct link among source, destination and eavesdroppers exist. Numerical simulation results compared with the benchmark scheme are provided to prove the effectiveness and superior performance of our algorithm.

Investigation of dynamics of elastic element of vibration device

ва подхода к решению аэрогидродинамической части задачи, основанные на методах теории функций комплексного переменного и методе Фурье. В результате применения каждого подхода решение исходной задачи сведено к исследованию дифференциального уравнения с частными производными для деформации элемента, позволяющего изучать его динамику. На основе метода Галеркина произведены численные эксперименты для конкретных примеров механической системы, подтверждающие идентичность решений, найденных для каждого дифференциального уравнения с частными производными. The dynamics of an elastic element of a vibration device, simulated by a channel, inside which a stream of a liquid flows, is investigated. Two approaches to solving the aerohydrodynamic part of the problem, based on the methods of the theory of functions of a complex variable and the Fourier method, are given. As a result of applying each approach, the solution to the original problem is reduced to the study of a partial differential equation for the deformation of an element, which makes it possible to study its dynamics. Based on the Galerkin method, the numerical experiments were carried out for specific examples of mechanical system, confirming the identity of the solutions found for each partial differential equation.

Stashing And Parallelization Pentagons

Parallelization is an algebraic operation that lifts problems to sequences in a natural way. Given a sequence as an instance of the parallelized problem, another sequence is a solution of this problem if every component is instance-wise a solution of the original problem. In the Weihrauch lattice parallelization is a closure operator. Here we introduce a dual operation that we call stashing and that also lifts problems to sequences, but such that only some component has to be an instance-wise solution. In this case the solution is stashed away in the sequence. This operation, if properly defined, induces an interior operator in the Weihrauch lattice. We also study the action of the monoid induced by stashing and parallelization on the Weihrauch lattice, and we prove that it leads to at most five distinct degrees, which (in the maximal case) are always organized in pentagons. We also introduce another closely related interior operator in the Weihrauch lattice that replaces solutions of problems by upper Turing cones that are strong enough to compute solutions. It turns out that on parallelizable degrees this interior operator corresponds to stashing. This implies that, somewhat surprisingly, all problems which are simultaneously parallelizable and stashable have computability-theoretic characterizations. Finally, we apply all these results in order to study the recently introduced discontinuity problem, which appears as the bottom of a number of natural stashing-parallelization pentagons. The discontinuity problem is not only the stashing of several variants of the lesser limited principle of omniscience, but it also parallelizes to the non-computability problem. This supports the slogan that "non-computability is the parallelization of discontinuity".

Inverse problem of determining the coefficient and kernel in an integro - differential equation of parabolic type

This article is concerned with the study of the unique solvability of inverse boundary value problem for integro-differential heat equation. To study the solvability of the inverse problem, we first reduce the considered problem to an auxiliary system with trivial data and prove its equivalence (in a certain sense) to the original problem. Then using the Banach fixed point principle, the existence and uniqueness of a solution to this system is shown.

Ambient BackCom in Beyond 5G NOMA Networks: A Multi-Cell Resource Allocation Framework

This article proposes a new resource allocation framework that uses the dual theory approach. Specifically, the sum-rate of the multi-cell network having backscatter tags and NOMA user equipments is maximized by formulating a joint optimization problem. To find the efficient base station transmit power and backscatter reflection coefficient in each cell, the original problem is first divided into two subproblems and then derived the closed-form solutions. A comparison with the orthogonal multiple access (OMA) ambient BackCom and pure NOMA transmission has been provided.

Ambient BackCom in Beyond 5G NOMA Networks: A Multi-Cell Resource Allocation Framework

This article proposes a new resource allocation framework that uses the dual theory approach. Specifically, the sum-rate of the multi-cell network having backscatter tags and NOMA user equipments is maximized by formulating a joint optimization problem. To find the efficient base station transmit power and backscatter reflection coefficient in each cell, the original problem is first divided into two subproblems and then derived the closed-form solutions. A comparison with the orthogonal multiple access (OMA) ambient BackCom and pure NOMA transmission has been provided.

Parameter Estimation for Interrupted Sampling Repeater Jamming Based on ADMM

By repeatedly sampling, storing, and retransmitting parts of the radar signal, interrupted sampling repeater jamming (ISRJ) based on digital radio frequency memory (DRFM) can produce a train of secondary false targets symmetrical to the main false target, threatening to mislead or deceive the victim radar system. This paper proposes a computationally-effective method to estimating the parameters for ISRJ by resorting to the framework of alternating direction method of multipliers (ADMM). Firstly, the analytical form of pulse compression is derived. Then, for the purpose of estimating the parameters of ISRJ, the original problem is transformed into a nonlinear integer optimization model with respect to a window vector. On this basis, the ADMM is introduced to decompose the nonlinear integer optimization model into a series of sub-problems to estimate the width and number of ISRJ’s sample slices. Finally, the numerical simulation results show that, compared with the traditional time-frequency (TF) method, the proposed method exhibits much better performance in accuracy and stability.