Closed-form Analytical Expressions Research Articles

Graph learning from band-limited data by graph Fourier transform analysis

A graph provides an effective means to represent the statistical dependence or similarity among signals observed at different vertices. A critical challenge is to excavate graphs underlying observed signals, because of non-convex problem structure and associated high computational requirements. This paper presents a new graph learning technique that is able to efficiently infer the graph structure underlying observed graph signals. The key idea is that we reveal the intrinsic relation between the frequency-domain representation of general band-limited graph signals, and the graph Fourier transform (GFT) basis. Accordingly, we derive a new closed-form analytic expression for the GFT basis, which depends deterministically on the observed signals (as opposed to being solved numerically and approximately in the literature). Given the GFT basis, the estimation of the graph Laplacian, more explicitly, its eigenvalues, is convex and efficiently solved using the alternating direction method of multipliers (ADMM). Simulations based on synthetic data and experiments based on public weather and brain signal datasets show that the new technique outperforms the state of the art in accuracy and efficiency.

Performance Analysis of ACO/DCO-OFDM Hybrid PLC-VLC Receivers With Blanking Non-Linearity

Blanking non-linearity is broadly used in impulsive noise communication environments due to its efficiency and ease of deployment to mitigate such noise. During the blanking procedure, data samples with impulsive noise are identified and clipped to zero, which removes impulsive noise from the system thereby, improving the system performance. In this regard, this paper investigates the performance of hybrid power line communication-visible light communication (PLC-VLC) systems with blanking nonlinearity. The signal-to-noise (SNR) ratio at the output of the blanking device is deduced using a closed-form analytical expression. The results show that there is good agreement between simulation results and theory if there is a sufficiently large number of orthogonal frequency division multiplexing (OFDM) sub-carriers. In addition, the study also indicates that the blanking method is more effective in curbing impulsive noise in comparison to the clipping technique. According to the threshold optimisation investigations, there exists a worst-case SINR value that minimizes the output SNR at the OFDM receiver after blanking. Furthermore, the findings also revealed that proper blanking threshold selection is essential for obtaining the best performance.

A Unified Framework for Full-Duplex Massive MIMO Cellular Networks With Low Resolution Data Converters

In this work, we provide a unified framework for full-duplex (FD) massive multiple-input multiple-output (MIMO) cellular networks with low-resolution analog-to-digital and digital-to-analog converters (ADCs and DACs). An objective of this work is to derive an accurate model to account for a wide variety of network irregularities and imperfections, including loopback self-interference (SI) that arises in full-duplex systems and quantization error from low-resolution data converters. Our contributions for forward and reverse links include (1) deriving signal-to-quantization-plus-interference-plus-noise ratio (SQINR) under pilot contamination, linear minimum mean square error (LMMSE) channel estimation and channel hardening; (2) deriving closed-form and approximate analytical expressions of spectral efficiency; (3) deriving asymptotic results and power scaling laws with respect to the number of quantization bits, base station antennas, and users, as well as base station and user equipment power budgets; and (4) analyzing outage probability and spectral efficiency vs. cell shape, shadowing, noise, cellular interference, pilot contamination, pilot overhead, and frequency reuse. Cell shapes include hexagonal, square, and Poisson Point Process (PPP) tessellations. In simulation, we quantify spectral and energy efficiency as well as the impact of SI power, inter-user interference, and cell shape on outage probability. We carry out the analysis for sub-7 GHz long term evolution (LTE) bands and then extend the framework to support millimeter wave (mmWave) bands.

Performance analysis of MPPM FSO transmission over Gamma–Chi-square strong atmospheric turbulence

In this paper, performance analysis of free space optical (FSO) system operating in conditions of strong atmospheric turbulence over Gamma–Chi-square turbulence model, has been carried out. We have observed reception over multi-pulse pulse-position (MPPM) modulation format for the case of strong atmospheric turbulence conditions modeled with Gamma–Chi-square turbulence model and have compared it with turbulence modeling distributions such are: Gamma–Gamma distribution, K-distribution, negative exponential distribution, log–normal distribution. First, we have provided closed-form analytical expressions for average bit error rate (ABER) at the reception for each observed case and then based on them, we have obtained numerical and Monte Carlo simulation results in order to observe turbulence level impact on system performance.

A Novel Cooperative NOMA Coding for Uplink MTC Networks

In this paper we consider machine-type communications (MTC) in 5G cellular networks for internet-of-thing (IoT) applications, where a large number of MTC devices simultaneously communicate with a base station (BS) over an uplink channel. To overcome the resource-constrained nature of the MTC nodes, we introduce a novel cooperative non-orthogonal multiple access (NOMA) coding scheme for supporting multi-user uplink transmissions with low complexity and signaling overhead, where the assumption of no feedback link hence no channel state information (CSI) available at the transmitting MTC nodes is taken. To gain deep understanding of its performance, we derive close-form analytical expressions on outage probability and diversity-multiplexing tradeoff (DMT) curve in the asymptotic regime of high signal-to-noise ratio (SNR), and optimize the end-to-end performance in terms of the exponential decay rate of expected distortion (ED). The asymptotic analytical result can be translated into a significant SNR gains of practical implementations with general SNR values, which is further confirmed via extensive simulation.

Performance analysis of a fluid flow system modulated by a single server queue prone to catastrophic failures and repairs

<p style='text-indent:20px;'>This article deals with a new class of fluid flow queue regulated by an <inline-formula><tex-math id="M1">\begin{document}$ M/M/1 $\end{document}</tex-math></inline-formula> queueing system in the presence of active catastrophic failures and subsequent repairs of the server. The distribution of the stationary buffer-content is determined in terms of modified Bessel function of first kind. Besides, an explicit closed-form analytical expression for the probability density function of the fluid level in the stationary regime is derived in an elegant manner. Some important and essential performance measures are obtained. Finally, numerical results are provided to illustrate the behaviour of the buffer content distribution and the performance measures for the proposed fluid flow queueing model.</p>

Inclined Large-angle Pendulum May Produce Endless Linear Motion of a Cart When Friction is Negligible

We present the mechanics for the oscillation of an inclined large-angle pendulum-drive attached to a cart which is allowed to perform translation in one direction only. Neglecting the overall friction, the application of Newton’s second law shows that the oscillation of the pendulum is continuously converted into oscillating linear motion thus achieving a travel of infinite length. It is also shown that the frequency depends on the usual data of any pendulum plus the mass of the cart on which it is attached. After the determination of a novel effective pendulum length, a closed-form accurate analytical expression is presented for the amplitude of the pendulum, whereas semi-analytical formulas are provided for the period as well as the time-variation of the large azimuthal-like angle. Moreover, a simple expression was found for the position of the cart in terms of the azimuthal angle of the pendulum and the elapsed time. The extraction of the analytical formulas was facilitated by a computer model programmed in MATLAB®.

Performance analysis of the functionally graded flexoelectric-piezoelectric energy harvesting

In the present paper, the output performances of the functionally graded flexoelectric-piezoelectric (FGFP) energy harvesting subjected to an external harmonic excitation, considering the effect of piezoelectric polarization direction, are addressed. Based on the Euler-Bernoulli beam model and generalized Hamiltonian principle, the dynamic governing equations and the corresponding boundary conditions of the functionally graded flexoelectric-piezoelectric energy harvesting are obtained. The natural frequency equation and the closed-form analytical expressions of electromechanical responses are further deduced. The numerical results show that the output performance of the functionally graded flexoelectric-piezoelectric energy harvesting is dependent on the piezoelectric polarization direction, gradient index and structure size. At the nanoscale, the flexoelectric effect dominates the output performances; however, at the microscale, the gradient piezoelectric effect dominates the output performances. At transition scales, from nano to micro, the output performances are very small sometimes, where, in some case, the gradient piezoelectric effect and flexoelectric effect cancel each other. The present study reveals the importance of the piezoelectric polarization direction and gradient index on the output performance of the functionally graded flexoelectric-piezoelectric energy harvesting from nano to micro scales.

Secure MIMO systems with nonlinear energy harvesting using optimal transmit antenna selection over [formula omitted] fading channels

This paper investigates the secrecy performance of multiple-input multiple-output systems with a nonlinear energy harvesting (EH) scheme used at the transmitter to improve energy efficiency and extend the lifetime of energy-constrained systems. Most of the current literature investigates cognitive radio networks with linear EH model. However, in order to realize more realistic scenarios due to hardware constraints, such as the saturation and sensitivity characteristics of the EH components, a nonlinear EH model is examined here and compared with a simpler linear EH scheme. In particular, a practical nonlinear energy harvester model with a source, a destination, an active eavesdropper, and a power beacon is considered under generalized α−μ fading conditions. Here, the eavesdropper can overhear the data transmission messages when the source communicates with the destination using wiretap channels. Furthermore, the source employs all its antennas to combine the radio frequency signals emitted by the power beacon via the maximal ratio combining (MRC) scheme. Moreover, the MRC scheme is used at the destination and eavesdropper to improve the signal’s quality (i.e., at the receiver side). Closed-form expressions for the lower bound and asymptotic security performance are investigated. Next, optimal antenna selection (OAS) scheme and traditional space–time transmission (STT) scheme are compared based on whether the channel state information (CSI) of the wiretap link is available. In addition to deriving the secrecy diversity order and secrecy array gain, asymptotic closed-form analytical expressions for security performance and closed-form analytical expressions for the probability of strictly positive secrecy capacity are also derived for various selection schemes. Finally, numerical results indicate that, compared to the linear EH scheme with just minimal trade-offs, the nonlinear EH scheme represents more realistic and dependable outcomes.

How, Why and When Tsallis Statistical Mechanics Provides Precise Descriptions of Natural Phenomena.

The limit of validity of ordinary statistical mechanics and the pertinence of Tsallis statistics beyond it is explained considering the most probable evolution of complex systems processes. To this purpose we employ a dissipative Landau-Ginzburg kinetic equation that becomes a generic one-dimensional nonlinear iteration map for discrete time. We focus on the Renormalization Group (RG) fixed-point maps for the three routes to chaos. We show that all fixed-point maps and their trajectories have analytic closed-form expressions, not only (as known) for the intermittency route to chaos but also for the period-doubling and the quasiperiodic routes. These expressions have the form of q-exponentials, while the kinetic equation's Lyapunov function becomes the Tsallis entropy. That is, all processes described by the evolution of the fixed-point trajectories are accompanied by the monotonic progress of the Tsallis entropy. In all cases the action of the fixed-point map attractor imposes a severe impediment to access the system's built-in configurations, leaving only a subset of vanishing measure available. Only those attractors that remain chaotic have ineffective configuration set reduction and display ordinary statistical mechanics. Finally, we provide a brief description of complex system research subjects that illustrates the applicability of our approach.

An Efficient Power Allocation Algorithm for Green Reconfigurable Intelligent Surface Assisted Vehicular Network

It is an irreversible trend to build a green and sustainable vehicular network facing with the dramatic increase in urban traffic. Reducing energy consumption has been an important aspect for green transportation. Reconfigurable intelligent surface (RIS) is considered as a promising technology to enhance the communication quality with higher energy efficiency. In this paper, we focus on the RIS-assisted vehicular networks. We obtain the closed-form analytical expressions for outage probability, ergodic achievable rate and average energy efficiency. A series of insights are further explored. Based on these, we discuss the performance under high SNR case, as well as, weak interference case. And then, the approximations in simpler form expressions are provided for each case, respectively. Outage diversity order and high SNR rate slope are also investigated. In addition, we propose a power allocation algorithm to maximize the ergodic achievable sum rate guaranteeing the outage probability and average energy efficiency. Numerical results show that our analytical results agree well with the Monte Carlo simulations in various network configurations. Besides, our proposed power allocation scheme significantly enhances the ergodic achievable sum rate compared with the equal power strategy.

On Secure Uplink Transmission in Hybrid RF-FSO Cooperative Satellite-Aerial-Terrestrial Networks

This work investigates the secrecy outage performance of the uplink transmission of a radio-frequency (RF)-free-space optical (FSO) hybrid cooperative satellite-aerial-terrestrial network (SATN). Specifically, in the considered cooperative SATN, a terrestrial source (S) transmits its information to a satellite receiver (D) via the help of a cache-enabled aerial relay (R) terminal with the most popular content caching scheme, while a group of eavesdropping aerial terminals (Eves) trying to overhear the transmitted confidential information. Moreover, RF and FSO transmissions are employed over S-R and R-D links, respectively. Considering the randomness of R, D, and Eves, and employing a stochastic geometry framework, the secrecy outage performance of the cooperative uplink transmission in the considered SATN is investigated and a closed-form analytical expression for the end-to-end secrecy outage probability is derived. Finally, Monte-Carlo simulations are shown to verify the accuracy of our analysis.

GMM-Based Symbol Error Rate Analysis for Multicarrier Systems With Impulsive Noise Suppression

Theoretical analysis of orthogonal frequency division multiplexing (OFDM) systems, equipped at the receiver by a non-linear impulsive noise suppressor, is very challenging. Indeed, although an exact closed-form expression for the output signal-to-noise ratio (SNR) of such OFDM systems is available for widely used impulsive noise models, theoretical analysis of the associated symbol error rate (SER) is still open. The analytical SER available in the literature, exploit a Gaussian approximation of the non-linear distortion noise, which however holds true only under specific conditions. Conversely, this work develops an accurate analytical closed-form expression of the distortion noise distribution at the nonlinearity output, as well as its approximation by a Gaussian mixture model (GMM). By using GMMs we unify the SER analysis for communication systems equipped by non-linear impulsive noise suppressors, typically also used in vehicular communications. Closed form expressions for the SER are derived both for non-fading and frequency-selective Rayleigh/Rician fading channels affected by impulsive noise, which is also modeled by a GMM, including Bernoulli-Gaussian (BG), Middleton Class-A, and alpha-stable noises. Theoretical SER performance are compared with simulations, showing very good agreement for all the impulsive noise scenarios and the non-linear suppressors.

Nonorthogonal Multiple Access Enabled Two-Way Relay System Using Signal Alignment

In the conventional two-way relay nonorthogonal multiple access (TWR-NOMA) system, its diversity order is equal to zero even under the perfect successive interference cancellation (pSIC). In this article, we leverage multiple-input–multiple-output (MIMO) technique in the TWR-NOMA system to extract spatial diversity gain for the performance enhancement. Communications between two user pairs are assisted by a relay. Precoding vectors at users as well as the matrix at the relay are specially designed to perform the signal alignment (SA). We derive analytical closed-form expressions for the outage probability and diversity order with both pSIC and imperfect successive interference cancellation (ipSIC). In addition, the ergodic rate and ergodic sum rate are analyzed. Optimal power allocations for the system outage probability and ergodic sum rate are analyzed based on the quality of service. Simulation results are provided to confirm the derived analytical results. The results show that the combination of SA and TWR-NOMA can decrease the outage probability and improve the diversity order effectively. The ergodic rates finally arise ceilings with both pSIC and ipSIC, and the ergodic sum rate can keep increasing as the power allocated to the distant user increases. However, the conventional TWR-NOMA is complete opposite. In summary, compared to TWR-NOMA, TWR-NOMA-SA has higher diversity order and enables distant users to contribute more to system performance.

Analysis of thermoelastic damping and modeling of piezothermoelastic plate resonators with voids

A comprehensive micro-electro mechanical systems (MEMS) model for analysis of a smart composite piezothermoelastic thin plate with voids, in context of Lord-Shulman theory of thermoelasticity has been developed. The work culminates in the derivation of the closed form analytic expressions for thermoelastic damping, frequency shift, electric potential change, volume fraction change, and displacements. Some numerical illustrations and graphical interpretations of analytical developments in case of PZT-5A material piezothermoelastic plate under clamped-simply supported (CS) and simply supported-simply supported (SS) boundary conditions have been presented with the help of MATLAB programming software.

Zernike-like Laguerre-Gaussian orthonormal polynomials for optical field reconstruction.

Analytic closed form expressions for orthonormal polynomials exhibiting both rotational and Gaussian symmetries are derived for both circular and elliptical geometries. They exhibit a close correspondence to the Zernike polynomials but are of Gaussian shape and orthogonal over the (x,y) plane. Consequently, they may be expressed in terms of Laguerre polynomials. Formulas for calculating the centroid of a real function are also presented and, along with the analytic expressions for the polynomials, may prove to be of especial use in reconstruction of the intensity distribution incident on a Shack-Hartmann wavefront sensor.

Graphene multilayers for coherent perfect absorption: effects of interlayer separation.

We present a model study to estimate the sensitivity of the optical absorption of multilayered graphene structure to the subnanometer interlayer separation. Starting from a transfer-matrix formalism we derive semi-analytical expressions for the far-field observables. Neglecting the interlayer separation, results in upper bounds to the absorption of 50% for real-valued sheet conductivities, exactly the value needed for coherent perfect absorption (CPA), while for complex-valued conductivities we identify upper bounds that are always lower. For pristine graphene the number of layers required to attain this maximum is found to be fixed by the fine structure constant. For finite interlayer separations we find that this upper bound of absorption only exists until a particular value of interlayer separation (Dlim) which is less than the realistic interlayer separation in graphene multilayers. Beyond this value, we find a strong dependence of absorption with the interlayer separation. For an infinite number of graphene layers a closed-form analytical expression for the absorption is derived, based on a continued-fraction analysis that also leads to a simple expression for Dlim. Our comparison with experiments illustrates that multilayer Van der Waals crystals suitable for CPA can be more accurately modelled as electronically independent layers and more reliable predictions of their optical properties can be obtained if their subnanometer interlayer separations are carefully accounted for.

Capacity analysis of the fluctuating double-Rayleigh with line-of-sight fading channel

The proposed research performs the capacity analysis of the wireless channel described by the fluctuating double-Rayleigh with the line-of-sight model. The closed-form analytical expressions for the conditional capacity (in the case of arbitrary noninteger fading parameter) and the ergodic capacity (in the case of the integer fading parameter) are derived in terms of the extended generalized bivariate Meijer G-function. The exact solutions are succeeded by the approximating expressions deduced for the cases of small and large ratios between the Rician K-factor and the fading parameter. The performed numeric simulation verifies the correctness of the derived results and analyzes the proposed capacity approximation quality performance.

Covariance based moment equations for improved variance component estimation

ABSTRACT ANOVA-based estimators of variance components for nested-error regression models are always constructed based on moment equations through residual variance. We consider moment equations associated with residual covariance and construct improved ANOVA-based estimators. The proposed estimators have closed-form analytic expressions, which enables easy computation. Moreover, they are shown to be consistent, asymptotically unbiased, and robust to the choice of distribution of the random effects. These estimators have comparable and often better performances than many traditional estimators of variance components like the Prasad-Rao, maximum likelihood, and the restricted maximum likelihood estimators for almost all kinds of sample allocations. Their improved performances are demonstrated analytically as well as through detailed simulation studies and applications to real data sets.

Experimental tests and numerical modeling of full-scale unbonded fiber reinforced elastomeric isolators (UFREIs) under bidirectional excitation

Unbonded fiber reinforced elastomeric isolators (UFREIs) can be used for the seismic protection of structures as a lower-cost alternative to conventional laminated rubber bearings, by replacing internal steel shims with fiber reinforcement and exploiting the frictional mechanism at the rubber-concrete interface to avoid anchorage bolts. In this paper, the hysteretic behavior of full-scale (diameter 620 mm) UFREIs is investigated in both an experimental and a numerical framework when subjected to triaxial loading (i.e., simultaneous imposed displacement along two horizontal directions with concurrently applied vertical load), to account for the inherent multi-directional nature of a real earthquake scenario. Experimental results of UFREIs tested under two bidirectional orbits involving different velocities and amplitudes up to 100% shear strain are presented, and peculiar effects ascribed to the lateral coupling of the devices are identified by comparison with monodirectional test results. Then, an efficient nonlinear phenomenological model is proposed to simulate the isotropically coupled biaxial hysteretic behavior of UFREIs detected from the experiments. This model consists of a set of nonlinear springs arranged in a circular configuration and governed by just three parameters with clear mechanical significance. Novel analytical (closed-form) expressions for the model calibration are ad-hoc developed in this paper. This modeling approach is used to quantify the impact of biaxial coupling of UFREIs on the structural performance of base-isolated structures under bidirectional seismic excitation. To this aim, the seismic response of a three-dimensional reinforced concrete building isolated with UFREIs is numerically simulated. Numerical results show that isolator displacements and superstructure accelerations tend to be higher by using an uncoupled model, calibrated upon monodirectional tests and that neglects bidirectional interaction, as usually performed in practice.