Closed-form Formulation Research Articles

Optimal Scheduling of Multicluster Tools With Constant Robot Moving Times, Part II: Tree-Like Topology Configurations

In this paper, we analyze optimal scheduling of a tree-like multicluster tool with single-blade robots and constant robot moving times. We present a recursive minimal cycle time algorithm to reveal a multi-unit resource cycle for multicluster tools under a given robot schedule. For a serial-cluster tool, we provide a closed-form formulation for the minimal cycle time. The formulation explicitly provides the interaction relationship among clusters. We further present decomposition conditions under which the optimal scheduling of multicluster becomes much easier and straightforward. Optimality conditions for the widely used robot pull schedule are also provided. An example from industry production is used to illustrate the analytical results. The decomposition and optimality conditions for the robot pull schedule are also illustrated by Monte Carlo simulation for the industrial example.

Bit Error Rate Performance of MIMO MMSE Receivers in Correlated Rayleigh Flat-Fading Channels

This paper analyzes the average bit error rate (BER) of multiple-input–multiple-output (MIMO) systems in transmit-correlated Rayleigh flat-fading channels. The receiver scheme is based on the minimum mean square error (MMSE) criterion, and the input may be precoded to optimize the communication. Accurate closed-form formulations for the average BER are derived.

Optimal resource allocation for relay-assisted wireless communication systems

The design, analysis and optimization of cooperative/relaying communication systems have recently become a very active research area within both the information theory as well as communications engineering societies. It is now well understood that relaying strategies can improve the coverage of wireless networks by providing higher data rates or better transmission reliability to user terminals at the edge of a wireless cell, or terminals having faded connectivity with the base station. Relaying technologies are also becoming part of the telecommunication standards. Although we can find studies, in the academic literature, on advanced relaying schemes, which are based on user terminals cooperating to help each other while applying decentralized resource allocation strategies, the first actual deployment step which will take place within the 3GPP long-term evolution (LTE)-advanced standard is based on fixed access points to do the relaying and within a centralized scheme in which the e-nodeB (base station with backhaul connection) takes the scheduling and resource allocation decisions. One major objective in 3GPP evolution is to utilize the scarce wireless system resources efficiently because achieving the high quality of service (QoS) targets through over-provisioning is uneconomical due to the relatively high cost for transmission capacity in cellular access networks. Our objective here is to obtain the optimal (from an information theory perspective) resource allocation schemes taking into considerations the system constraints that are relevant to the LTE-advanced standard. We have been able to derive optimal resource allocation polices that are provably based on closed-form formulations which are practical for implementation. They include the policies for (i) transmission mode selection (i.e. deciding whether the user needs the assistance of a relay or not), (ii) power allocation for the base station and the relays, and (iii) criterion for user scheduling over the available air-link resource units. Simulation results demonstrate that our proposed resource allocation scheme provides considerable throughput gains especially for users receiving low power through the direct link with the base station.

Analysis of Soil-Structure Interaction (SSI) Effects on Seismic Response of Base-Isolated Structures

A new modified model for assessing the effects of SSI on base-isolated structures is presented from the case of conventional structures. The equations of motion of the equivalent fixed-base 2-DOF system are formulated in frequency domain. Based on this, rigorous and closed-form formulations for fundamental period and composite damping are derived. Finally, analysis of parameters based on frequency independent coefficients in detail is conducted. The analytical model and method presented can serve to assess the effects of SSI in the design of base-isolated structures including high-rise structures. Significant differences between the system with and without radiation damping and the flexibility of supporting soil have been observed in this study. For the results of the analysis, overall SSI effects have been identified as elongation of fundamental period of the system and decreased composite damping, especially for the high-rise and slender isolated structures.

ASYMPTOTICALLY OPTIMAL LOAD DISTRIBUTION FOR MULTIPATH STREAMING UNDER FEC

Multipath streaming protocols have recently attracted much attention because they provide an effective means to provide high-quality streaming over the Internet. Most existing multipath streaming schemes also apply forward error correction (FEC) encoding in the stream so as to provide high-quality streaming of prestored or live media content. However, the problem of how to intelligently split the FEC-encoded stream among multiple available paths has not been fully addressed. Most previous work focused on protocol design or heuristic-based engineering approaches. Exact analysis turns out to be hard, as it involves heavy combinatorics computation. In this article, we develop an analytical model and use asymptotic analysis to address the problem of optimal load distribution. Using asymptotic approximations, we propose a closed-form formulation for the optimal load distribution problem. We then develop interesting properties of the optimal solution based on majorization, interchanging argument, and optimization techniques. These results are surprisingly simple yet insightful. We further demonstrate through simulation that our asymptotic solution works quite well in practice.

First-best marginal cost toll for a traffic network with stochastic demand

First-best marginal cost pricing (MCP) in traffic networks has been extensively studied with the assumption of deterministic travel demand. However, this assumption may not be realistic as a transportation network is exposed to various uncertainties. This paper investigates MCP in a traffic network under stochastic travel demand. Cases of both fixed and elastic demand are considered. In the fixed demand case, travel demand is represented as a random variable, whereas in the elastic demand case, a pre-specified random variable is introduced into the demand function. The paper also considers a set of assumptions of traveler behavior. In the first case, it is assumed that the traveler considers only the mean travel time in the route choice decision (risk-neutral behavior), and in the second, both the mean and the variance of travel time are introduced into the route choice model (risk-averse behavior). A closed-form formulation of the true marginal cost toll for the stochastic network (SN-MCP) is derived from the variational inequality conditions of the system optimum and user equilibrium assignments. The key finding is that the calculation of the SN-MCP model cannot be made by simply substituting related terms in the original MCP model by their expected values. The paper provides a general function of SN-MCP and derives the closed-form SN-MCP formulation for specific cases with lognormal and normal stochastic travel demand. Four numerical examples are explored to compare network performance under the SN-MCP and other toll regimes.

Cooperative wireless multicast: performance analysis and power/location optimization

The popularity of multimedia multicast/broadcast applications over wireless networks makes it critical to address the error-prone, heterogeneous and dynamically changing nature of wireless channels. A promising solution to combat channel fading is to explore the cooperative diversity in which users may help each other forward packets. This paper investigates cooperative multicast schemes that use a maximal ratio combiner to enhance the received signal-to-noise ratio (SNR), and provides a thorough performance analysis. Two relay selection schemes are considered: the distributed and the genie-aided cooperation schemes. We derive the closed-form formulation and the approximations of their average outage probabilities.We also analyze the optimal power allocation and relay location strategies, and show that allocating half of the total transmission power to the source minimizes the average outage probability. Our analysis and simulation results show that cooperative multicast gives better performance when more relays help forward signals. Cooperative multicast helps achieve diversity order 2, and user cooperation can significantly reduce the outage probability, especially in the high SNR region. Finally, we compare the two cooperation strategies, and show that distributed cooperative multicast is preferred since it achieves a lower outage probability without introducing extra overhead for control messages.

Modeling and simulation of closed loop multibody systems with bodies-joints composite modules

Modular approaches are effective in improving the modeling efficiency in multibody system dynamics. A modular method, called bodies-joints composite simulation (BJCS) is presented in this paper. Two types of bodies-joints composite modules, i.e., f modules and 0 modules, are defined according to topology design rules of closed loop mechanisms. By this module partitioning, the differential-algebraic equations of motion of the system can be separated into purely algebraic and differential equations by structure decomposition. The stability criterion for the simulation is derived and a closed-form formulation to solve the algebraic loop problem is proposed. Simulation results of the forward dynamics of a 5R mechanism and a 6-UPS platform are presented to show the feasibility of the method. The CPU times of these two case studies are provided and compared with the generalized coordinate partitioning of Wehage and Haug and the modular simulation method of Kubler and Schiehlen, which indicate that the closed-form algebraic loop solver is more efficient than the numerical ones.

Efficient PAPR reduction for OFDM system based on optimized power allocation

To solve the problem of high Peak-to-Average Power Ratio(PAPR) in Orthogonal Frequency Division Multiplexing(OFDM) systems,an efficient PAPR reduction scheme called OPAR was proposed based on optimized power allocation.This paper also analyzed the relationship between power efficiency of power amplifier and PAPR,and deduced the closed form formulation of power allocation between superimposing pilot signal and data signal.OPAR could allocate optimized power quickly with the given sub-carrier number and probability threshold of PAPR.Simulation results and comparison with the existing schemes demonstrate that the proposed OPAR scheme can obtain better performance in PAPR reduction.

Smith-Purcell radiation from a charge moving above a grating of finite length and width

Smith-Purcell radiation (SPR), emitted when a charge passes above a periodic grating, is important for applications such as terahertz production and nondestructive bunch-length diagnostics. The grating width is shown to become an important parameter for accurately predicting the radiation, and especially in the highly relativistic regime where the charge wakefield considerably stretches in the transverse direction. The SPR radiation is rigorously calculated by the electric-field integral equation (EFIE) method for a grating of finite width and length. The integral equation is arranged as a multilevel block-Toeplitz matrix by using symmetry under translation with respect to the grating period and width directions. Following Barrowes et al. [Microw. Opt. Technol. Lett. 31, 28 (2001)] enhanced computational efficiency can be achieved by matrix to vector projection of the essential matrix elements. A numerical example is calculated for a relativistic ($\ensuremath{\gamma}=36$), 1-mm long, bunch traveling 0.6-mm above a ten-period grating with a period of 2.0 mm and width of 10 mm. The SPR resonance relationship and its broadening due to the finite number of grooves are consistent with the closed-form formulations. The surface current was shown to be concentrated along the center of the grating and decreasing towards its edges. The surface current, power spectrum, and radiated energy were compared to the EFIE formulation in which an infinitely wide grating was assumed. The above parameters resulted in considerable difference of up to a factor of 2.5 between the finite width and the infinitely wide grating assumption, which means that for accurate calculations the grating width should be taken into consideration. A general rule for the required grating width to achieve an accurate SPR radiation result relative to the infinite width result, and the expected accuracy by the infinite width assumption for most radiation angles, is provided.

Singularity-free dynamic equations of vehicle–manipulator systems

In this paper we derive the singularity-free dynamic equations of vehicle–manipulator systems using a minimal representation. These systems are normally modeled using Euler angles, which leads to singularities, or Euler parameters, which is not a minimal representation and thus not suited for Lagrange’s equations. We circumvent these issues by introducing quasi-coordinates which allows us to derive the dynamics using minimal and globally valid non-Euclidean configuration coordinates. This is a great advantage as the configuration space of the vehicle in general is non-Euclidean. We thus obtain a computationally efficient and singularity-free formulation of the dynamic equations with the same complexity as the conventional Lagrangian approach. The closed form formulation makes the proposed approach well suited for system analysis and model-based control. This paper focuses on the dynamic properties of vehicle–manipulator systems and we present the explicit matrices needed for implementation together with several mathematical relations that can be used to speed up the algorithms. We also show how to calculate the inertia and Coriolis matrices and present these for several different vehicle–manipulator systems in such a way that this can be implemented for simulation and control purposes without extensive knowledge of the mathematical background. By presenting the explicit equations needed for implementation, the approach presented becomes more accessible and should reach a wider audience, including engineers and programmers.

Output Formulation for Symmetrically Excited One-to-$N$ Multimode Interference Coupler

In this paper, we present a closed form formulation for the output signals of one-to-N multimode interference coupler under symmetric excitation. We derive the output ports phases and show that the output phase has a quadratic dependence on the output port number. Using beam propagation simulations, we compare the analytical phase profile with the simulation results for different waveguiding structures. In the case of Si/SiO2 structures, our formulation predicts the output phase profile with errors not more than about 1°. Finally, we show that nonideal effects, such as limited number of guided modes, modal phase errors, and extension of the field profile into the cladding layers have minimal effects on the phase profile in comparison with the output amplitudes. These results can be used in variety of optoelectronic applications, where the knowledge of the phase profile is crucial, such as optical phased arrays.

Singularity-Free Dynamic Equations of AUV-Manipulator Systems

In this paper we derive the singularity-free dynamic equations of AUV-manipulator systems using a minimal representation. Autonomous underwater vehicles (AUVs) are normally modeled using the singularity-prone Euler angles, but introducing quasi-coordinates allows us to derive the dynamics using minimal and globally valid non-Euclidean configuration coordinates. This is a great advantage as the configuration space of an AUV is non-Euclidean. We thus obtain a computationally efficient and singularity-free formulation of the dynamic equations with the same complexity as the conventional Lagrangian approach. The closed form formulation makes the proposed approach well suited for system analysis and model-based control. This paper focuses on the kinematic and dynamic properties of AUV-manipulator systems and we present the explicit matrices needed for implementation together with several mathematical relations that can be used to speed up the algorithms. The hydrodynamic and damping forces are also included in the equations. By presenting the explicit equations needed for implementation, the approach presented becomes more accessible and engineers and programmers can implement the results without extensive knowledge of the mathematical background.

A NOVEL PHASE RETRIEVAL APPROACH FOR ELECTROMAGNETIC INVERSE SCATTERING PROBLEM WITH INTENSITY-ONLY DATA

To measure the phase of signal with very high working frequency such as THz, and optics band is still a challenging problem. In this paper, based on the relationship between radiating current and measured intensity of electrical fleld a novel phase retrieval algorithm has been developed. As opposed to the existing approaches of phase retrieval where usually the Fourier coe-cients of measured data will be flrstly reconstructed, the proposed approach is to reconstruct the so-called radiating currents, with more physical meaning than the former. It has a much smaller number of freedoms of radiating current than that of measurements, which means that the obtained equations are over-determined. Thus one can e-ciently model the intensity of measured electric fleld via the radiating part, and reconstruct it quickly and stably. The novelty is that this physical consideration 1) leads to e-ciently avoiding false solutions due to the ill-posedness of phase retrieval problem, and 2) ofiers a good initial guess for inverse scattering based imaging algorithm. Importantly, a closed-form formulation of phase retrieve also has been derived when the intensity of incident wave is much stronger than one of the scattered wave, for example, for the weak scattering objects. Finally, several numerical experiments are provided to show the high performance of proposed algorithm.

A Closed-Form Refined Model of the Cables' Nonlinear Response in Cable-Stayed Structures

In this paper a refined second-order model for the analysis of the elastic response of cables in cable-stayed structures is proposed. Starting from the exact catenary theory, the Dischinger-Ernst formulation is rationally deduced and, performing a second order approximation both with respect to the stress variation and the apparent chord-strain one, a refined explicit equivalent constitutive relationship for elastic stays is obtained. Moreover, the geometrical non-linearities induced on the cable by the deformation of the stay-supported structure are taken into account through a second order displacement approach. Accordingly, a closed-form formulation describing nonlinear cable-structure interaction effects is obtained which, unlike the classical secant model, does not need iterative procedures, opening the possibility to develop refined analytical solutions for cable structures. Several numerical examples and benchmarks on different stay configurations are presented, showing the effectiveness and the accuracy of the proposed model.

Theory and Experimental Results of a Class F AB-C Doherty Power Amplifier

The aim of this paper is to present a closed-form formulation suitable for a direct computer-aided design synthesis of a Doherty amplifier employing a Class F design strategy for the Main (or Carrier) device. For this purpose, starting from a simplified model for the adopted active devices, the behavioral analysis of the Class F Doherty amplifier is carried out as a function of the input signal. A particular emphasis is dedicated to put into evidence the differences existing when a simple tuned load harmonic termination is considered. The theoretical aspects are deeply discussed and an experimental validation is also provided.

Fracture Prediction of Adhesively Bonded Structures Using Energy Release Rates

This paper investigates fracture prediction of adhesively bonded structures using energy release rates. Novel closed-form formulations for calculating energy release rates of adhesive joints and interlaminar delamination are presented and then used to discuss fracture predictions. In the present formulation, the Timoshenko beam is used to model substrates, and an interface between the substrates is described using the adhesive model with two-parameter elastic medium. The energy release rates are initially given for adhesive joints and thereafter are derived for interface fracture by letting the adhesive thickness approach zero. The numerical results are presented for cohesive fracture of an adhesive joint, delamination or interface fracture.

Non-rotationally invariant invisibility cloaks and concentrators of EM Waves

We present electromagnetic invisible cloaks and concentrators which are composed of inhomogeneous and anisotropic metamaterials with a square-shaped outer boundary and a circular-shaped inner boundary. Using the technique of coordinate transformation, closed-form formulations of the permittivity and permeability tensors have been derived for the metamaterials to realize the invisible cloaking and to concentrate electromagnetic waves. Full-wave simulation results are given to validate the non-rotationally invariant cloaks and concentrators.

Expression of Concern: On the Optimal Design, Performance, and Reliability of Future Carbon Nanotube-Based Interconnect Solutions

In this paper, we develop comprehensive modeling and design techniques for carbon nanotube (CNT)-based interconnects, which we utilize to examine the performance, reliability, and fabrication requirements for future nanotube-based interconnect solutions. We create a generalized model for CNT-based interconnect systems that achieves a high degree of accuracy compared to experimental CNT measurements. Leveraging the model, we develop the first closed-form formulation for the optimal nanotube diameter and bundle height for multi-walled CNT (MWCNT) and single-walled CNT (SWCNT) bundle interconnects for a general set of geometric and process parameters. The results indicate that the proposed design method decreases delay by 21% and 29% on average compared to nonoptimized MWCNT and SWCNT bundles. We also find that future CNT bundle fabrication processes must achieve a nanotube area coverage of at least 30% for optimized CNT bundles and 40% for nonoptimized CNT bundles to obtain competitive performance results compared to copper interconnects. In terms of reliability, we find that large diameter MWCNT bundles are significantly more susceptible to process variations than SWCNT bundles, which will have important implications for their utilization in future nanoscale integrated circuits.

Minimax Design of Variable Fractional-Delay FIR Digital Filters by Iterative Weighted Least-Squares Approach

In this letter, an iterative weighted least-squares (LS) approach is proposed for the design of variable fractional-delay (VFD) finite impulse response (FIR) digital filters in minimax sense. For deriving the elements of relevant matrices, there is no need for numerical integration or closed-form formulation and they obey given specifications. Comparing with the existing method, the proposed method does not lead to a misleading problem, and the performance of convergence is also better. Especially, it is found that the used LS weighting function is only dependent on the frequency, not on the tunable parameter, which makes it easier for the minimax design of VFD FIR digital filters.