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An efficient dual-scale method, which integrates parabolic equation (PE) with electric field integral equation (EFIE) formulated via the Rao-Wilton-Glisson moment method (RWG-MOM), is proposed to analyze the electromagnetic interference (EMI) problems resulted from radiation sources. This method is implemented by decomposing the original intractable multi-scale problem domain into two sub-regions: (1) modeling of the complicated ambient electromagnetic fields by PE and (2) solution of the fields coupling to the exposed electronic devices by RWG-MOM. Frequency-sweep and Fourier synthesis techniques are applied to calculate the transient currents and voltages. The proposed method is able to fully model the disturbances of the electromagnetic fields by multi-path effects. Besides, it reduces the memory footprint and the CPU computing time effectively compared to the traditional full-wave electromagnetic methods. Numerical examples are presented, and the simulation results indicate that this method is well suitable for the EMI analysis of external radiation sources. [ABSTRACT FROM AUTHOR]

The prediction of radar target echo signal in a large-scale complex environment is of great significance in target detection, radar design and other applications. In this paper, a novel PE/FDTD hybrid model is proposed to predict monostatic radar target echo signals in large-scale complex environments. The target echo signal can be regarded as the output response of the transmitted signal which passes through a linear time invariant system composed of complex environment and target. The transport function of the complex environment is computed by the parabolic equation (PE) method and the scattering characteristics of the target are calculated by finite difference time domain method (FDTD). The combination of PE and FDTD is realized through the system response function. In combination with the “stop-go” method, the prediction of moving target echo signal is realized. In addition, the error of combining PE with FDTD is analyzed, and the result shows that the error is less than 0.1% when the target distance is more than 10km. Additional numerical examples are given to demonstrate the correctness of the method in semi-space, rain, fog and atmospheric duct environments. The calculated results are compared with those of theoretical method, time-domain shooting and bouncing ray (TDSBR), multi-level fast multi-pole method (MLFMM) and waveguide mode theory, and good agreement among them is observed. Finally, the simulation analysis of the missile echo signal in the mixed sea-land environment with surface duct is carried out. The simulation results show that this model can be used to predict the echo signal of airborne targets in a large-scale complex environment. It is a promising option for multi-scale computing involving radar target and large-scale environment.

Wireless channel analysis is essential in the design, performance evaluation, and error correction of radar system. In this paper, an efficient parabolic equation (PE) method, which employs the split-step Fourier transform (SSFT) solution and Fourier synthesis technique, is developed for the propagation and parameter estimation of pulse-compression signals in the troposphere considering anomalous propagation conditions. A sliding window method is applied to reduce computational loads for long-distance propagation in time-domain PE. The signal delay is obtained via searching the peak of the correlation function of the received signal and a known reference signal according to the autocorrelation of the signals. The numerical examples indicate that the presented method is well suited for pulse-compression signals. Beyond that, a multiple signal classification (MUSIC) algorithm with spatial smoothing technique is introduced to obtain the signal direction of arrival (DOA) in PE model, where the covariance matrix is constructed via the array fields obtained from PE and the curvature of wavefronts due to the atmospheric refraction is considered in the array steering vector. The numerical examples verify the accuracy of the presented method. The simulation experiments in a typical sea-to-land scenario are presented to analyze the sensitivity of pulse-compression signals to evaporation ducts, including pulse waveform, time delay, and DOA, utilizing the presented methods.

To efficiently solve the coupling problems of two-wire line in complex large-scale environments excited by electromagnetic pulses, a novel hybrid PE-TL method consisting of transmission line (TL) equations and parabolic equations (PEs) is presented in this article. In this hybrid method, the PE model is applied to calculate the spatial fields in the presence of irregular terrains and buildings based on an efficient split-step Fourier transform technique and two-way propagation processing first. Then, the TL equations are employed to build the coupling model of a long two-wire line, and the excitation fields calculated by the PE method are introduced into the TL equations as distribution sources. Finally, transient current responses on termination loads of the two-wire line are calculated by inverse fast Fourier transform. Numerical examples are given to demonstrate the accuracy and high efficiency of the hybrid method, and the application of this presented method for the coupling of long two-wire line in realistic terrain constructed by the digital map technique is presented. It shows that the PE-TL method can tremendously decrease the memory requirement and computation time compare with the MoM method, and have the ability to simulate the coupling problem of long two-wire line in complex large-scale environments excited by electromagnetic pulses rapidly. [ABSTRACT FROM AUTHOR]

This article presents a two-way parabolic equation (2WPE) method based on the Pade(2,2) approximation form, which can model bidirectional electromagnetic wave (EW) propagation in a sea environment. Compared with other common approximation forms, the Pade(2,2) approximation has better convergence and accuracy. To accurately simulate the reflection and refraction effects of EW propagation near the sea surface, an improved fractal sea surface model is used to construct the geometric rough sea surface. The results of the Pade(2,2) approximation PE model are compared with those of the Miller–Brown model, and good agreement is observed. Numerous experiments prove that the 2WPE model is more accurate than the one-way parabolic equation model for predicting large-scale radio wave propagation in marine environments. Furthermore, we investigate the relationship between the backward-scattered EWs and the wind speed. The polynomial fitting method is adopted to process a large amount of sampled data for backward-scattered EWs with different wind speeds and frequencies. Through accurate judgment of the points of the polynomial fitting curve in a certain frequency range, the wind speed over the sea surface can be precisely determined. Thus, this article provides a novel theoretical method for marine remote sensing. [ABSTRACT FROM AUTHOR]

A theoretical foundation of wave propagation modeling for tunnels in complex meteorological environments is presented by using the parabolic equation (PE) method. The finite differential scheme is applied to solve the PE; thus, the calculation can be taken in each 2-D transverse plane. As a result, the computational efficiency can be enhanced greatly. Moreover, the effective permittivity of the meteorological environment is given and then the propagation attenuation in the meteorological environment can be estimated. In this way, the wave propagation of tunnels in the complex meteorological environment can be modeled by updating the refractive index for PE. Finally, the vehicles in the tunnels for diverse meteorological environments are also considered in the numerical results. [ABSTRACT FROM AUTHOR]

This research is concerned with the numerical methods for the electromagnetic wave propagation over the Earth's surface. Discrete nonlocal boundary conditions for the Padé parabolic equation are derived. A linear dependence of the modified refractive index on the height outside the computational domain can be taken into account. Thus, the earth-flattening transformation can be used. The proposed approach gives an opportunity to truncate the integration domain without introducing an artificial absorbing layer in the vicinity of the upper boundary. Padé approximations of the exponential propagation operator allow one to carry out the calculations with a rather large step along the longitudinal coordinate. The elaborated method can utilize the two-way parabolic equation approach for scattering problems. Comparison with the results obtained by the split-step Fourier method is given. [ABSTRACT FROM AUTHOR]

We previously introduced an efficient parabolic equation (PE) method to solve the Loran-C additional secondary factors (ASFs) in the presence of irregular terrain. However, traditional PE analysis, based on the approximation of a narrowband Loran-C source to a 100 kHz sinusoidal source, is not sufficient for realistic Loran-C ASF prediction. In this letter, a pulse PE method is employed to further improve the accuracy of the Loran-C ASF prediction over irregular terrain. The main idea of this approach is that it converts the time-domain wave propagation problems to the frequency-domain wave propagation ones, which can be solved by the traditional PE solution. Numerical examples illustrate the accuracy and effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

This paper presents the Greene second-order parabolic equation (PE) solution to model radio propagation over irregular terrain. This solution is implemented by finite-difference and shift-map technique. The second-order finite-difference approach performs well for slopes up to about 15°, and discontinuous slope changes up to about 30°, which is better than can be achieved using the split-step/Fourier approach. The results prove that the Greene PE solution has greater propagation angles than does the Claerbout PE solution. Thus, the Greene second-order solution can certainly give better results for large angle propagation over complicated terrain boundaries. Besides, we treat the important problem of accuracy of the different approximations of the PE-based propagation models, and derive the general PE solutions with respect to the terrain slope for the different approximations. It is useful to have collected in one paper, the most important PE approximations for radio propagation. [ABSTRACT FROM AUTHOR]

Alternate direction implicit (ADI) method has been widely used to analyze the tunnel propagation or electromagnetic scattering problem for the finite difference method. In this paper, a novel alternate direction decomposition (ADD) scheme is proposed to simplify the split-step Fourier transform (SSFT) algorithm in parabolic equation (PE) model. The spatial matrix of electric field is decoupled into two subarrays by ADD-SSFT algorithm, which is used to decrease the computational burden for 3-D PE problems in a large scale environment after the integration order exchanged. Also, the phase error of this approximation is analyzed to show the algorithm performance, along with several numerical results, including the tunnel cases with traditional modal theory, and they are provided to validate and calibrate the PE model, and demonstrate the efficiency and accuracy of the proposed algorithm. Moreover, the scattering computation is investigated and compared with multilevel fast multipole method to show that ADD-SSFT is appropriate for solving the scattering problems for the electrical large target. [ABSTRACT FROM PUBLISHER]

Constructing digital war-field electromagnetic environment needs to model and simulate the transmitting course of electric waves combining various environment factors. The Parabolic Equation (PE) described model is suitable for computing the waveguide propagation characteristics from an area in the horizon to that over the horizon, and there is Split-Step Fourier Transform (SSFT) algorithm to resolve the model. But it is an iterative method based on step length and is difficult to be realized in parallels, thus it is difficult to meet the requirement time wise and bring the obstacles to constructing war-field electromagnetic environment fastly. This paper puts forward a parallel computing method based on matrix transposing, and realizes parallel computing of the algorithm by constructing two-dimensional matrixes and distributing them to different process in line or in row. The method makes full use of the operating ability of calculation clusters, decreasing computing time. The result of computer simulating shows that parallel algorithm can have a speedup as four times large as that of sequential algorithm, thus verifies the effectiveness of the method.

The parabolic equation (PE) method is employed to solve the Loran-C additional secondary factors (ASFs) over irregular terrain. Based on the split-step Fourier transform (SSFT) algorithm, the method has been proven to be numerically efficient. The ASF results are compared to those of the integral equation (IE) method and the finite-difference time-domain (FDTD) method. Very good agreements are observed. The computational time of the PE method is several orders less than that of the other two. The memory requirement is similar to the IE, and less than the FDTD method. [ABSTRACT FROM PUBLISHER]

In this paper, a two-way parabolic equation (PE) method is developed for modeling rough interface reverberation. The model is employed to estimate the reverberation envelope probability density function from bottom roughness with Gaussian and exponential height distributions. For Gaussian-distributed roughness, the PE gives envelope statistics that closely conform to the expected Rayleigh distribution. However, for non-Gaussian-distributed roughness heights, heavy-tailed reverberation envelope statistics are observed. The PE simulation results are compared to the analytical model of K-distributed reverberation by Abraham and Lyons [IEEE J. Ocean. Eng., vol. 29, pp. 800-813, 2002] for discrete scatterers and to numerical predictions of the first and second moments of the reverberation intensity estimated with a coupled mode reverberation model for the multipath insonification of rough surfaces. [ABSTRACT FROM AUTHOR]

A wide-angle parabolic wave equation solution is presented using shift-map and finite-difference techniques. The corresponding split-step Fourier solution is well known. The solution using finite-difference technique, where the standard parabolic wave equation is modified into the so-called Claerbout equation allowing propagation angles up to 450 from the paraxial direction, is also well known. Here, we present an extension to that solution in which the shift-map technique is incorporated into the finite-difference scheme allowing a varying terrain to be considered. The result is a solution that corresponds to the well known split-step solution, which is believed to perform well for terrain slopes up to 10°–15° and discontinuous slope changes on the order of 15°–20°. This solution is a first-order one with respect to the terrain slope. However, when using the finite-difference technique, it is also possible to find a second-order solution with respect to the terrain slope. This new solution performs well for slopes up to about 15° and discontinuous slope changes up to about 30°, which is an improvement. [ABSTRACT FROM AUTHOR]