Search Results (84)

A multiplexing method for orbital angular momentum (OAM) beams was proposed. The aperture size as a new information carrier was provided, and it could be modulated by the external variable aperture. The field of the beams propagating through turbulence was derived and discretized with Gauss–Legendre quadrature formulas. Based on this, the demultiplexing method was improved, and the beam OAM states, amplitude, Gaussian spot radius and aperture radius were decoded. Moreover, the influence of turbulence on the multiplexing parameters was also analyzed, and the decoding precision of the aperture radius was higher than that of other parameters. The aperture radius was recommended as an extra carrier for multiplexing communication. This study provides a simple method to modulate the information carried by OAM beams, and it has promising applications in large capacity laser communication. Full article

In this paper, the remainder term of anti-Gaussian quadrature rules for analytic integrands with respect to Jacobi weight functions ${\omega }_{a,b}\left(x\right)={(1-x)}^a{(1+x)}^b$, where $a,b>-1$, is analyzed, and sharp estimates of the error are provided. These kinds of quadrature formulas were introduced by D.P. Laurie and have been recently studied by M.M. Spalević for the case of Jacobi-type weight functions $\omega$. Full article

This article presents an alternative variant of motion planning techniques for autonomous vehicles (AVs) centered on an inverse approach that concurrently optimizes both trajectory and speed. This method emphasizes searching for a trajectory and distributing its speed within a single road segment, regarded as a final element. The references for the road lanes are represented by splines that interpolate the path length, derivative, and curvature using Cartesian coordinates. This approach enables the determination of parameters at the final node of the road segment while varying the reference length. Instead of directly modeling the trajectory and velocity, the second derivatives of curvature and speed are modeled to ensure the continuity of all kinematic parameters, including jerk, at the nodes. A specialized inverse numerical integration procedure based on Gaussian quadrature has been adapted to reproduce the trajectory, speed, and other key parameters, which can be referenced during the motion tracking phase. The method emphasizes incorporating kinematic, dynamic, and physical restrictions into a set of nonlinear constraints that are part of the optimization procedure based on sequential quadratic optimization. The objective function allows for variation in multiple parameters, such as speed, longitudinal and lateral jerks, final time, final angular position, final lateral offset, and distances to obstacles. Additionally, several motion planning variants are calculated simultaneously based on the current vehicle position and the number of lanes available. Graphs depicting trajectories, speeds, accelerations, jerks, and other relevant parameters are presented based on the simulation results. Finally, this article evaluates the efficiency, speed, and quality of the predictions generated by the proposed method. The main quantitative assessment of the results may be associated with computing performance, which corresponds to time costs of 0.5–2.4 s for an average power notebook, depending on optimization settings, desired accuracy, and initial conditions. Full article

In this paper, we investigate efficient numerical methods for highly oscillatory integrals with Bessel function kernels over finite and infinite domains. Initially, we decompose the two types of integrals into the sum of two integrals. For one of these integrals, we reformulate the Bessel function $J_{\nu }(z)$ as a linear combination of the modified Bessel function of the second kind $K_{\nu }(z)$, subsequently transforming it into a line integral over an infinite interval on the complex plane. This transformation allows for efficient approximation using the Cauchy residue theorem and appropriate Gaussian quadrature rules. For the other integral, we achieve efficient computation by integrating special functions with Gaussian quadrature rules. Furthermore, we conduct an error analysis of the proposed methods and validate their effectiveness through numerical experiments. The proposed methods are applicable for any real number $\nu$ and require only the first $\lfloor \nu \rfloor$ derivatives of f at 0, rendering them more efficient than existing methods that typically necessitate higher-order derivatives. Full article

Free space optics (FSOs) is an emerging technology offering solutions for secure and high data rate transmission in dense urban areas, back haul link in telecommunication networks, and last mile access applications. It is important to investigate the performance of the FSO link as a result of aggregate attenuation caused by different weather conditions in a region. In the present work, empirical models have been derived in terms of visibility, considering fog, haze, and cloud conditions of diverse geographical regions of Delhi, Washington, London, and Cape Town. Mean square error (MSE) and goodness of fit (R squared) have been employed as measures for estimating model performance. The dual polarization-quadrature phase shift keying (DP-QPSK) modulation technique has been employed with hybrid mode and the wave division multiplexing (MDM-WDM) scheme for analyzing the performance of the FSO link with two Laguerre Gaussian modes (LG00 and LG 01) at 5 different wavelengths from 1550 nm to 1554 nm. The performance of the system has been analyzed in terms of received power and signal to noise ratio with respect to the transmission range of the link. Minimum received power and SNR values of −52 dBm and −33 dB have been obtained over the observed transmission range as a result of multiple impairments. Random forest (RF), k-nearest neighbors (KNN), multi-layer perceptron (MLP), gradient boosting (GB), and machine learning (ML) techniques have also been employed for estimating the SNR of the received signal. The maximum R squared (0.99) and minimum MSE (0.11), MAE (0.25), and RMSE (0.33) values have been reported in the case of the GB model, compared to other ML techniques, resulting in the best fit model. Full article

This paper considers a numerical method for solving the stochastic semilinear subdiffusion equation which is driven by integrated fractional Gaussian noise and the Hurst parameter $H\in (1/2,1)$. The finite element method is employed for spatial discretization, while the L1 scheme and Lubich’s first-order convolution quadrature formula are used to approximate the Caputo time-fractional derivative of order $\alpha \in (0,1)$ and the Riemann–Liouville time-fractional integral of order $\gamma \in (0,1)$, respectively. Using the semigroup approach, we establish the temporal and spatial regularity of the mild solution to the problem. The fully discrete solution is expressed as a convolution of a piecewise constant function with the inverse Laplace transform of a resolvent-related function. Based on the Laplace transform method and resolvent estimates, we prove that the proposed numerical scheme has the optimal convergence order $O({\tau }^{min\{H+\alpha +\gamma -1-\epsilon ,\alpha \}}),\epsilon >0$. Numerical experiments are presented to validate these theoretical convergence orders and demonstrate the effectiveness of this method. Full article

We investigate the underwater propagation of multi-Gaussian correlated asymmetric Bessel beam with partial coherence in the condition of quadrature amplitude modulation. The oceanic turbulence optical power spectrum is used to characterize turbulence effects under variable temperature and salinity. Based on the derivation of orbital angular momentum mode distribution, the theoretical model of bit error rate (BER) is constructed. Numerical analyses show that the low-temperature oceanic channel is more beneficial to BER reduction than the low-salinity channel. Due to the better resistance to turbulence, low-order modulation is superior in BER performance. As for beam optimization, the increments in wavelength and source coherence width, or the decrements of topological charge and asymmetry factor, help to obtain a lower BER. The research is instructive for the construction of underwater transmission links based on vortex beams. Full article

Gaussian quadrature rules are commonly used to approximate integrals with respect to a non-negative measure $d\widehat{\sigma }$. It is important to be able to estimate the quadrature error in the Gaussian rule used. A common approach to estimating this error is to evaluate another quadrature rule that has more nodes and higher algebraic degree of precision than the Gaussian rule, and use the difference between this rule and the Gaussian rule as an estimate for the error in the latter. This paper considers the situation when $d\widehat{\sigma }$ is a Chebyshev measure that is modified by a linear factor and a linear divisor, and investigates whether the rules in a recently proposed new class of quadrature rules for estimating the error in Gaussian rules are internal, i.e., if all nodes of the new quadrature rules are in the interval $(-1,1)$. These new rules are defined by two measures, one of which is a modified Chebyshev measure $d\widehat{\sigma }$. The other measure is auxiliary. Full article

Digital terrestrial television is now implemented in many countries worldwide and is now mature. Digital Video Broadcasting-Terrestrial, second generation (DVB-T2) is the European standard adopted or deployed by European and African countries which uses Orthogonal Frequency-Division Multiplexing (OFDM) modulation to achieve good throughput performance. However, its main particularity is the number of subcarriers operated for OFDM modulation which varies from 1024 to 32,768 subcarriers. Also, mobile reception is planned in DVB-T2 in addition to rooftop antenna and portable receptions planned in DVB-T. However, the main challenge of DVB-T2 for mobile reception is the presence of a carrier frequency offset (CFO) which degrades the system performance by inducing an Intercarrier Interference (ICI) on the DVB-T2 signal. This paper evaluates the system performance in the presence of the CFO when Gaussian noise and a TU6 channel are applied. Universal Filtered Multicarrier (UFMC) and non-uniform constellations (NUCs) have previously demonstrated good performance in comparison with OFDM and Quadrature Amplitude Modulation (QAM) in DVB-T2. The impact of CFO on the UFMC- and NUC-based DVB-T2 system is additionally investigated in this work. The results demonstrate that the penalties induced by CFO insertion in UFMC- and NUC-based DVB-T2 are highly reduced in comparison to those for the native DVB-T2. At a bit error rate (BER) of ${10}^{-3}$, the CFO penalties induced by the native DVB-T2 are $0.96$$\mathrm{d}$$\mathrm{B}$ and 4 $\mathrm{d}$$\mathrm{B}$, respectively, when only Additive White Gaussian Noise (AWGN) is used and when TU6 is additionally considered. The penalties are equal to $0.84$$\mathrm{d}$$\mathrm{B}$ and $0.2$$\mathrm{d}$$\mathrm{B}$ for UFMC/NUC-based DVB-T2. Full article

Counterparty risk, which combines market and credit risks, gained prominence after the 2008 financial crisis due to its complexity and systemic implications. Traditional management methods, such as netting and collateralization, have become computationally demanding under frameworks like the Fundamental Review of the Trading Book (FRTB). This paper explores the combined application of Gaussian process regression (GPR) and Bayesian quadrature (BQ) to enhance the efficiency and accuracy of counterparty risk metrics, particularly credit valuation adjustment (CVA). This approach balances excellent precision with significant computational performance gains. Focusing on fixed-income derivatives portfolios, such as interest rate swaps and swaptions, within the One-Factor Linear Gaussian Markov (LGM-1F) model framework, we highlight three key contributions. First, we approximate swaption prices using Bachelier’s formula, showing that forward-starting swap rates can be modeled as Gaussian dynamics, enabling efficient CVA computations. Second, we demonstrate the practical relevance of an analytical approximation for the CVA of an interest rate swap portfolio. Finally, the combined use of Gaussian processes and Bayesian quadrature underscores a powerful synergy between precision and computational efficiency, making it a valuable tool for credit risk management. Full article

We analyze the error estimates of a fully discrete scheme for solving a semilinear stochastic subdiffusion problem driven by integrated fractional Gaussian noise with a Hurst parameter $H\in (0,1)$. The covariance operator Q of the stochastic fractional Wiener process satisfies $\parallel A^{-\rho }{Q}^{1/2}{\parallel }_{HS}<\infty$ for some $\rho \in [0,1)$, where ${\parallel ·\parallel }_{HS}$ denotes the Hilbert–Schmidt norm. The Caputo fractional derivative and Riemann–Liouville fractional integral are approximated using Lubich’s convolution quadrature formulas, while the noise is discretized via the Euler method. For the spatial derivative, we use the spectral Galerkin method. The approximate solution of the fully discrete scheme is represented as a convolution between a piecewise constant function and the inverse Laplace transform of a resolvent-related function. By using this convolution-based representation and applying the Burkholder–Davis–Gundy inequality for fractional Gaussian noise, we derive the optimal convergence rates for the proposed fully discrete scheme. Numerical experiments confirm that the computed results are consistent with the theoretical findings. Full article

In this study, we introduce a novel local fractional integral identity related to the Gaussian two-point left Radau rule. Based on this identity, we establish some new fractal inequalities for functions whose first-order local fractional derivatives are generalized convex and concave. The obtained results not only represent an extension of certain previously established findings to fractal sets but also a refinement of these when the fractal dimension $\mu$ is equal to one. Finally, to support our findings, we present a practical application to demonstrate the effectiveness of our results. Full article

Gravity forward modeling as a basic tool has been widely used for topography correction and 3D density inversion. The source region is usually discretized into tesseroids (i.e., spherical prisms) to consider the influence of the curvature of planets in global or large-scale problems. Traditional gravity forward modeling methods in spherical coordinates, including the Taylor expansion and Gaussian–Legendre quadrature, are all based on spatial domains, which mostly have low computational efficiency. This study proposes a high-efficiency forward modeling method of gravitational fields in the spherical harmonic domain, in which the gravity anomalies and gradient tensors can be expressed as spherical harmonic synthesis forms of spherical harmonic coefficients of 3D density distribution. A homogeneous spherical shell model is used to test its effectiveness compared with traditional spatial domain methods. It demonstrates that the computational efficiency of the proposed spherical harmonic domain method is improved by four orders of magnitude with a similar level of computational accuracy compared with the optimized 3D GLQ method. The test also shows that the computational time of the proposed method is not affected by the observation height. Finally, the proposed forward method is applied to the topography correction of the Moon. The results show that the gravity response of the topography obtained with our method is close to that of the optimized 3D GLQ method and is also consistent with previous results. Full article

The Multi-Scale Multi-Group Wide-Band (MSMGWB) model was used to calculate radiative transfer in strongly non-isothermal and inhomogeneous media such as the remote infrared sensing of aircraft exhaust system and jet plume scenario. In this work, the reference temperature was introduced into the model as an independent variable for each spectral subinterval group. Then, to deal with the exceedingly vast parameter sample space (i.e., the combination of spectral subinterval grouping results, reference temperatures and Gaussian quadrature schemes), an MSMGWB model’s parameter optimization process superior to the exhaustive approach employed in previous studies was established, which was consisted of the Non-dominated Sorting Genetic Algorithm II method (NSGA2) and an iterative scan method. Through a series of 0-D test cases and two real 3-D remote infrared imaging results of an aircraft exhaust system, it was observed that the MSMGWB model established and optimiazed in current work demonstrated notable improvements in both accuracy and computational efficiency. Full article

As the era of sixth-generation (6G) communications approaches, there will be an unprecedented increase in the number of wireless internet-connected devices and a sharp rise in mobile data traffic. Faced with the scarcity of spectrum resources in traditional communication networks and challenges such as rapidly establishing communications after disasters, this study leverages unmanned aerial vehicles (UAVs) to promote an integrated multi-hop communication system combining free-space optical (FSO) communication, terahertz (THz) technology, and intelligent reflecting surface (IRS). This innovative amalgamation capitalizes on the flexibility of UAVs, the deployability of IRS, and the complementary strengths of FSO and THz communications. We have developed a comprehensive channel model that includes the effects of atmospheric turbulence, attenuation, pointing errors, and angle-of-arrival (AOA) fluctuations. Furthermore, we have derived probability density functions (PDFs) and cumulative distribution functions (CDFs) for various switching techniques. Employing advanced methods such as Gaussian–Laguerre quadrature and the central limit theorem (CLT), we have calculated key performance indicators including the average outage probability, bit error rate (BER), and channel capacity. The numerical results demonstrate that IRS significantly enhances the performance of the UAV-based hybrid FSO/THz system. The research indicates that optimizing the number of IRS elements can substantially increase throughput and reliability while minimizing switching costs. Additionally, the multi-hop approach specifically addresses the line-of-sight (LoS) dependency limitations inherent in FSO and THz systems by utilizing UAVs as dynamic relay points. This strategy effectively bridges longer distances, overcoming physical and atmospheric obstacles, and ensures stable communication links even under adverse conditions. This study underscores that the enhanced multi-hop FSO/THz link is highly effective for emergency communications after disasters, addressing the challenge of scarce spectrum resources. By strategically deploying UAVs as relay points in a multi-hop configuration, the system achieves greater flexibility and resilience, making it highly suitable for critical communication scenarios where traditional networks might fail. Full article