Showing papers on "Closed-form expression published in 2022"
TL;DR: In this article, the authors presented exact closed-form solutions for free vibration of discretely supported Euler-Bernoulli (DEB) and Timoshenko beams (DTB) in the presence of an arbitrary number of intermediate elastic constraints.
10 citations
TL;DR: Based on non-sequential ray tracing simulations, this article proposed a closed-form path loss expression as a function of transceiver and infrastructure parameters and statistically analyzed the path loss and derived an approximate closedform bit error rate (BER) expression.
Abstract: Visible light communication (VLC) has emerged as a potential wireless connectivity solution for infrastructure-to-vehicle (I2V) communications. In this paper, we investigate the performance of I2V VLC systems with access points in the form of streetlights. Particularly, we consider a typical two-lane highway road where the light poles are located at both roadsides and uniformly separated from each other. Based on non-sequential ray tracing simulations, we first propose a closed-form path loss expression as a function of transceiver and infrastructure parameters. Then, we statistically analyze the path loss and derive a closed-form expression for its probability distribution function (PDF). Utilizing the derived PDF, we derive an approximate closed-form bit error rate (BER) expression. We confirm the accuracy of derived BER expression through comparison with Monte Carlo simulation results and demonstrate the effect of transceiver and infrastructure parameters such as receiver aperture, pole height, car height, lateral shift, and spacing between light poles on the BER performance.
9 citations
TL;DR: In this paper, a flexible nonparametric representation of a concave or an S-shaped production function is derived using expressions with focus on the distinction between hinge location and the bending along each hinge.
9 citations
TL;DR: In this article , the performance analysis and relaying strategies for two-relays buffer-aided (BA) parallel relaying cooperative free space optical (FSO) networks are tackled.
Abstract: This paper tackles the performance analysis and relaying strategies for two-relays buffer-aided (BA) parallel relaying cooperative free space optical (FSO) networks. We first provide an asymptotic analysis of the existing selective relaying scheme that simultaneously activates the strongest source-relay (S-R) and relay-destination (R-D) optical links. We then propose an improvement of this scheme and highlight on its advantages by deriving closed-form accurate expressions for the asymptotic values of the outage probability (OP) and average packet delay (APD). The theoretical evaluation and numerical analysis demonstrate the capability of the improved scheme in enhancing the diversity order with finite buffer sizes unlike the selective relaying scheme that achieves diversity gains only with infinite-size buffers entailing infinite delays. The OP performance is significantly enhanced for all network topologies whether the relays are closer to S, closer to D or placed at the same distance from S and D. On the other hand, the reaped APD gains depend on the positions of the relays.
2 citations
TL;DR: In this article , a closed-form analytical function is proposed to approximate the relations in a van der Pauw configuration using only basic operators, which can be easily implemented in a given software.
Abstract: Measurements in a van der Pauw configuration often require the use of complicated mathematical expressions or implicit relations, which may be computer-time-consuming or tedious to implement in a given software. Thus, a closed-form expression is often desirable. We propose to approximate these relations by closed-form analytical functions using only basic operators that can be easily implemented. We present explicitly the functions and the numerical values of their parameters for the cases of standard van der Pauw measurement, anisotropic resistivities, and the probe position correction factor. The discrepancy with the exact values is smaller than 10-5, which is sufficient for practical purposes.
1 citations
TL;DR: In this article , the magnetic shielding effectiveness of a single planar screen of infinite extent against a parallel current loop source is evaluated through an analytic closed-form expression which is valid for arbitrarily thick screens and for any source-observation distance.
Abstract: The magnetic shielding effectiveness of a single planar screen of infinite extent against a parallel current loop source is evaluated through an analytic closed-form expression which is valid for arbitrarily thick screens and for any source-observation distance. The only assumption in the formulation consists in considering small loops having a constant current. The resulting formula can be expressed in terms of only elementary functions and is believed to represent the most general closed-form expression for the magnetic shielding effectiveness of a planar screen in the presence of a parallel loop. Numerical results are provided to show the generality and the validity of the proposed formula.
1 citations
1 citations
TL;DR: In this paper , an analytical method for fast spectral fatigue-life prediction under Broad-Band random loading is proposed, based on the power spectral density of stress in the structure and the Rice peak stress distribution of a stationary Gaussian random process.
13 Oct 2022
TL;DR: In this paper , a simple closed-form solution to the discrete Lyapunov equation (DLE) is established for certain families of matrices, expressed in terms of the eigen decomposition (ED) for which closed form solutions are known for all 2 × 2, 3 × 3 and certain familiesof matrices.
Abstract: Abstract A simple closed-form solution to the discrete Lyapunov equation(DLE) is established for certain families of matrices. This solution isexpressed in terms of the eigen decomposition (ED) for which closed-form solutions are known for all 2 × 2, 3 × 3 and certain familiesof matrices. For general matrices, the proposed ED based closed-formsolution can be used as an efficient numerical solution when the EDcan be computed. The result is then extended to give closed-formsolutions for a generalization of the DLE, called the Stein equation.The proposed explicit solution’s complexity is of the same order asiterative solutions and significantly smaller than known closed-formsolutions. These solutions may prove convenient for analysis and syn-thesis problems related to these equations due to their compact form.
02 Nov 2022
TL;DR: In this paper , the authors proposed a general framework for a comprehensive performance analysis of cooperative spectrum sensing (CSS) in cognitive radio (CR) networks, and investigated the detection accuracy of a relay-based CR network over independent non-identical Nakagami-m fading channels.
Abstract: <p>We propose a general framework for a comprehensive performance analysis of cooperative spectrum sensing (CSS) in cognitive radio (CR) networks. Specifically, we investigate the detection accuracy of a relay-based CR network over independent nonidentical Nakagami-m fading channels. Based on the probability density function (pdf) approach, we derive new exact and approximated closed-form expressions for the average detection probability and the average false alarm probability employing two diversity combining techniques, namely, the maximal ratio combining (MRC) scheme and the selection combining (SC) scheme. We also investigate the convergence rate of infinite series that appears in the derived exact closed-form expressions and propose to use a powerful acceleration algorithm that allows for the series termination with a finite number of terms. The results obtained reveal the importance of including the relaying link statistics and the combination techniques in the performance analysis of CR networks. The derived closed-form expression can be used to determine the energy threshold and the relaying power constraint that meet a given detection accuracy value over nonidentically distributed Nakagami-mfading.</p>
11 Aug 2022
TL;DR: In this paper , the spectrum sensing performance of a distributed satellite clusters (DSC), where the sensing signals received by each cooperative satellite can be fused at the signal-level to enhance the sensing ability of weak signals, is investigated.
Abstract: This paper investigates the spectrum sensing performance of a distributed satellite clusters (DSC), where the sensing signals received by each cooperative satellite can be fused at the signal-level to enhance the sensing ability of weak signals. In particular, by assuming that the satellite-relay link undergoes shadowed-Rician (SR) fading, we first derive a closed-form expression for correct detection probability $(P_{d})$ of the considered system with maximum ratio combining (MRC). However, when the channel state information can not meet the requirements, equal gain combining (EGC) provides an alternative to slightly reduce the complexity. Therefore, we provide another closed-form expression of $P_{d}$ based on EGC, using the specially derived probability density function of the sum of SR random variables with independently identical distribution. Simulation results are provided to validate our theoretical analysis and to show that the proposed scheme can achieve the best spectrum-sensing performance, comparing with the traditional energy detection, eigenvalue ratio test and the generalized likelihood ratio test.
09 Oct 2022
TL;DR: In this article , a closed-form expression for quasi-static 2D Green's function of fully-shielded layered medium is proposed, which allows to analytically add up contributions from infinite number of source images with respect to the vertical side walls of the rectangular enclosure.
Abstract: New closed-form expression for quasi-static 2-D Green's function of fully-shielded layered medium is proposed. Along the vertical direction of the medium stratification the spectrum of the Green's function can be obtained through the 1-D ordinary differential equation and expressed as pole-residual form. This rational function representation of the spectrum allows to evaluate space domain Green's function in layered medium shielded from top and bottom with horizontal ground planes in a closed-form. This closed-form expression allows to analytically add up contributions from infinite number of source images with respect to the vertical side walls of the rectangular enclosure, hence, producing the new closed-form expression for the 2-D Green's function of rectangular enclosure vertically filled with multilayered medium. Availability of such Green's functions enable construction of integral equation based magneto-quasi-static and electro-quasi-static 2-D extractors. Such 2-D magneto-quasi-static extractor based on solution of Surface-Volume-Surface Electric Field Integral Equation (SVS-EFIE) for multi-conductor transmission lines (MTLs) situated in shielded layered media is demonstrated.
03 Oct 2022
TL;DR: Closed-form algebraic expressions for the pH of ideal weak acid and weak acid buffer solutions were obtained and analyzed with the aid of computer algebra systems as discussed by the authors , and the pH expressions for all the systems under study can be obtained from an unique closed-form expression in terms of an effective weak acid constant and an effective acid concentration.
Abstract: Closed-form algebraic expressions for the pH of ideal weak acid and weak acid buffer solutions (and their titration with a strong base) were obtained and analyzed with the aid of computer algebra systems. These expressions are used to evaluate, without the use of numerical approximations, the precision and accuracy of different approximations commonly employed to calculate the pH. The closed-form expression for the pH of a buffer solution is used to obtain an analytical expression for the pH stability when a strong base is added. Finally, it is shown that the pH expressions for all the systems under study can be obtained from an unique closed-form expression in terms of an effective weak acid constant and an effective acid concentration.
02 Nov 2022
TL;DR: In this paper , the authors proposed a general framework for a comprehensive performance analysis of cooperative spectrum sensing (CSS) in cognitive radio (CR) networks, and investigated the detection accuracy of a relay-based CR network over independent non-identical Nakagami-m fading channels.
Abstract: <p>We propose a general framework for a comprehensive performance analysis of cooperative spectrum sensing (CSS) in cognitive radio (CR) networks. Specifically, we investigate the detection accuracy of a relay-based CR network over independent nonidentical Nakagami-m fading channels. Based on the probability density function (pdf) approach, we derive new exact and approximated closed-form expressions for the average detection probability and the average false alarm probability employing two diversity combining techniques, namely, the maximal ratio combining (MRC) scheme and the selection combining (SC) scheme. We also investigate the convergence rate of infinite series that appears in the derived exact closed-form expressions and propose to use a powerful acceleration algorithm that allows for the series termination with a finite number of terms. The results obtained reveal the importance of including the relaying link statistics and the combination techniques in the performance analysis of CR networks. The derived closed-form expression can be used to determine the energy threshold and the relaying power constraint that meet a given detection accuracy value over nonidentically distributed Nakagami-mfading.</p>
12 Mar 2022
TL;DR: This paper derives closed expression of range-direction of arrival (R-DOA) information in phased-array radar by employing the a posteriori probability density function of the range and direction of arrival to extract R- DOA information from echoes.
Abstract: In this paper, we derive closed expression of range-direction of arrival (R-DOA) information in phased-array radar. In our previous works, the theoretical expression of R-DOA information is proposed. Firstly, a uniform linear array system model is given, where R-DOA information is formulated as the mutual information between range, direction of arrival and the received signals with with complex additive white Gaussian noise. Then employing the a posteriori probability density function (PDF) of the range and direction of arrival to extract R-DOA information from echoes. Moreover, by dividing the integral region of the a posteriori PDF into the signal part and noise part, a closed approximate expression of R-DOA information is derived. Finally, numerical results are presented to verify the effectiveness of the proposed approximate closed expression.
11 Oct 2022
TL;DR: In this article , a closed-form solution to the directivity of a planar array with arbitrary topology is presented. But the analytical method is validated by numerical integration using Simpson's 1/3 method.
Abstract: This work presents a new analytical (i.e., closed-form) solution to the directivity of a planar array with arbitrary topology. The derived method also makes use of a novel element pattern model which can take into account radial asymmetries in both θ and ϕ: a generic pattern suitable for a wide range of applications. The analytical method is validated by numerical integration using Simpson's 1/3 rd method. The analytical method enables fast topology optimization of phased array designs by avoiding time-consuming numerical integration.
11 Oct 2022
TL;DR: In this paper , closed-form algebraic expressions for the pH of ideal weak acid and weak acid buffer solutions were obtained and analyzed with the aid of computer algebra systems and used to evaluate the precision and accuracy of different approximations commonly employed to calculate the pH.
Abstract: Abstract Closed-form algebraic expressions for the pH of ideal weak acid and weak acid buffer solutions (and their titration with a strong base) were obtained and analyzed with the aid of computer algebra systems. These expressions are used to evaluate, without the use of numerical approximations, the precision and accuracy of different approximations commonly employed to calculate the pH. The closed-form expression for the pH of a buffer solution is used to obtain an analytical expression for the pH stability when a strong base is added. Finally, it is shown that the pH expressions for all the systems under study can be obtained from an unique closed-form expression in terms of an effective weak acid constant and an effective acid concentration.
TL;DR: In this article , the exact solution for the concentration breakthrough curves resulting from a solute injection in radially converging flow in an aquifer obtained using Laplace transforms has a complex form and cannot be given in closed-form expression.
Abstract: The exact solution for the concentration breakthrough curves resulting from a solute injection in radially converging flow in an aquifer obtained using Laplace transforms has a complex form difficult to compute, and cannot be given in closed-form expression. This makes it difficult to use for tracer tests analysis in radial flow. To overcome this difficulty new simple approximate but accurate closed-form expressions are derived in the present paper for slug and continuous injections. The improvement of accuracy of these new closed-form expressions is demonstrated. The paper establishes also that the breakthrough curves resulting from slug injections into a radially diverging or radially converging flow are exactly identical at the sampling well in domains having the same spatial extension. Solutions were also derived for tracers or solutes subject to degradation. The new closed-form expressions were used for the analysis of 12 field tracer tests to highlight the difference in transport parameters determination compared to previous approximate expressions.
23 Sep 2022
TL;DR: In this article , a simple closed-form solution to the discrete Lyapunov equation (DLE) is established for certain families of matrices, expressed in terms of the eigen decomposition (ED) for which closed form solutions are known for all 2 × 2, 3 × 3 and certain familiesof matrices.
Abstract: Abstract A simple closed-form solution to the discrete Lyapunov equation(DLE) is established for certain families of matrices. This solution isexpressed in terms of the eigen decomposition (ED) for which closed-form solutions are known for all 2 × 2, 3 × 3 and certain familiesof matrices. For general matrices, the proposed ED based closed-formsolution can be used as an efficient numerical solution when the EDcan be computed. The result is then extended to give closed-formsolutions for a generalization of the DLE, called the Stein equation. The proposed explicit solution’s complexity is of the same order asiterative solutions and significantly smaller than known closed-formsolutions. These solutions may prove convenient for analysis and syn-thesis problems related to these equations due to their compact form.
12 May 2022
TL;DR: In this paper , a closed-form solution for the two-dimensional unit normal loss integral (UNLI) is proposed, which can be applied to the scalar incremental net benefit.
Abstract: In Value of Information (VoI) analysis, the unit normal loss integral (UNLI) frequently emerges as a solution for the computation of various VoI metrics. However, one limitation of the UNLI has been that its closed-form solution is available for only one dimension, and thus can be used for comparisons involving only two strategies (where it is applied to the scalar incremental net benefit). We derived a closed-form solution for the two-dimensional UNLI, enabling closed-form VoI calculations for three strategies. We verified the accuracy of this method via simulation studies. A case study based on a three-arm clinical trial was used as an example. VoI methods based on the closed-form solutions for the UNLI can now be extended to three-decision comparisons, taking a fraction of a second to compute and not being subject to Monte Carlo error. An R implementation of this method is provided as part of the predtools package (https://github.com/resplab/predtools/).
16 Nov 2022
TL;DR: In this article , the authors considered beamforming for a reconfigurable intelligent surface (RIS)-aided multiple input single output (MISO) communication system in the presence of Rician multipath fading.
Abstract: This paper considers beamforming for a reconfigurable intelligent surface (RIS)-aided multiple input single output (MISO) communication system in the presence of Rician multipath fading. Our aim is to jointly optimize the transmit beamformer and RIS phase shift matrix for maximizing the mean signal-to-noise (SNR) of the combined signal received over direct and indirect links. While numerical solutions are known for such optimization problems, this is the first paper to derive closed-form expressions for the optimal beamformer and the phase shifter for a closely related problem. In particular, we maximize a carefully constructed lower bound of the mean SNR, which is more conducive to analytical treatment. Further, we show that effective channel gain under optimal beamforming follows Rice distribution. Next, we use these results to characterize a closed-form expression for the outage probability under the proposed beamforming scheme, which is subsequently employed to derive an analytical expression for the ergodic capacity. Finally, we numerically demonstrate the efficacy of the proposed beamformer solution in comparison with the existing algorithmically obtained optimal solution for the exact mean SNR maximization.