Coverage analysis over terrain profiles using an adaptation of the spectral accelerated forward-backward method

The Forward-Backward (FB) method and its accelerated version (SA-FB, Spectral Accelerated Forward-Backward) were developed to compute the electromagnetic scattering from ocean-like rough surfaces. The FB algorithm provides very accurate scattering results and a very fast convergence, but its computational cost is still O(N2) per iteration, being N the number of unknowns used to discretize the surface. The Spectral Acceleration Algorithm proposed later reduces this cost to O(N). Nevertheless, the SA-FB can only be applied to quasi-planar structures or slightly rough surfaces (such as the sea surface), but it cannot be used to solve problems involving very undulating surfaces such as terrain profiles. In this paper the SA-FB method is modified to enhance its scope of application to considerable undulating surfaces. It will be seen that significant changes with respect to the original formulation as well as modifications of the integration path are necessary to get accurate results when dealing with terrain profiles. The proposed method is presented for vertical and horizontal polarizations and for PEC and non-PEC surfaces.

A robust and accurate iterative algorithm is proposed for the solution of electromagnetic wave scattering from 1-D layered rough surfaces. The forward–backward method (FBM) has been applied extensively for solving electromagnetic scattering from single-layer rough surfaces due to its rapid convergence rate. Nevertheless, the performance of the FBM deteriorates, as it is applied to layered random rough surface problems. The proposed method greatly improves the convergence rate of the FBM by applying a residual minimization step. The computational cost of the minimization step and the forward–backward sweeps is expedited by using the spectral acceleration. In this communication, the proposed algorithm is applied as a solution to the problem of electromagnetic wave scattering from layered rough surfaces. Numerical results are presented to demonstrate the better convergence properties of the proposed method as compared with the standard FBM. In addition, the proposed method is shown to be more robust than the FBM, especially as the distance between interfaces decreases. The computational complexity of the proposed algorithm is also presented and discussed.

The iterative forward backward (FB) method has been proposed to solve the magnetic field integral equation for smooth one-dimensional rough surfaces. This method has proved to be very efficient, converging in a very small number of iterations. Nevertheless, this solution becomes unstable when some obstacle, like a ship or a large breaking wave, is included in the original problem. In this paper we propose a new extension of the FB method: the generalized forward backward (GFB) method, to solve such kinds of composite problems.

In this paper we propose an efficient and accurate iterative numerical approach to analyze EM scattering from 1-D dielectric rough surfaces. It is based on a new splitting of the impedance matrix Z to improve the asymptotic convergence rate of the resultant iterative system. The structure of split matrix is then fully explored, in combination with the application of an identity for inverse of block matrix, to further reduce the computational and storage complexity. The embedded matrix-vector product is computed using the spectral acceleration technique. Extensive numerical simulations demonstrate a couple of appealing features of this proposed method for Gaussian surface with Gaussian spectrum: (1) It converges faster than both forward-backward method (FBM) and FBM with spectral acceleration (FBM-SA); (2) For HH polarization, the proposed method is about twice as fast as FBM-SA. For VV polarization, the proposed method is better when the rms slope is not larger than 16° or interestingly when rms height is beyond 2.0 wavelengths. Moreover, it converges for cases where FBM-SA fails for both polarizations. These features indicate that the proposed method can be effectively used to analyze EM scattering from 1-D dielectric Gaussian surface with Gaussian spectrum.

To analyze EM scattering of a dielectric Target above the dielectric Gauss rough surface, a fast Cross Coupling iterative Approach is present in this paper. This algorithm combines the merit of both the bi-conjugate gradient method (Bi-CG) and forward backward method (FBM). At first, the electric field integral equations (EFIE) of the induced currents on the rough surface and the target are derived. An iterative approach was developed to solve the two EFIEs and scattering from both the target and underlying surface. The EFIE of the rough surface and the target are solved by using FBM and bi-conjugate gradient method (Bi-CG), respectively. The mutual effect between the rough surface and the target are implemented by iterative Calculation. The results of EM scattering form a dielectric cylinder above the dielectric Gauss rough surface showed that CCIA was well agreement with MOM. The accuracy, efficiency, and convergence of the method are then studied for rough surfaces with various parameters. The effect of these parameters for the scattering pattern was also discussed.

Acceleration of the capacitance extraction of planar structures on a single‐layered medium is reported in this article, using the forward‐backward (FB) method with a spectral acceleration (SA) algorithm. The conventional spectral‐layered medium Green's function is modified appropriately so that it can be effectively incorporated into this method. The SA algorithm substantially speeds up the computational time involving in performing matrix‐vector multiplications in the iterative method of moments (MM). However, the memory requirement for the SA algorithm is comparable to that of the FB method. The computational complexity and the memory requirement are shown to be O(N) for large capacitance extraction problems, where N is the total number of unknowns in the MM for increasing one of the surface dimensions of planar structures and fixed neighborhood distance. © 2014 Wiley Periodicals, Inc. Microwave Opt Technol Lett 56:694–700, 2014

It is shown for both rough and undulating surfaces that the mean radio power reflected by the ionosphere averaged over a sufficiently long time is exactly the same as for a smooth flat surface at the same height provided the sounder is equally sensitive for echoes from all directions. When making radio wave absorption measurements under spread conditions the total integrated power over the whole time the direct echoes are being received must be used but the distance attenuation factor must be calculated from the time of arrival of the first echo.

A discrete‐Fourier‐transform (DFT) based forward‐backward (FB) algorithm has been developed for the fast and accurate analysis of electrically large freestanding dipole arrays [1]. In this paper, an extension of the FB method (FBM) with a DFT‐based acceleration approach is presented to provide a relatively efficient analysis of EM radiation/scattering from an electrically large, planar, periodic, finite dipole array printed on a grounded dielectric substrate. Computational complexity of this new approach is O(Ntot), where Ntot is the number of unknowns. Numerical results are presented to validate the efficiency and accuracy of the method. © 2003 Wiley Periodicals, Inc. Microwave Opt Technol Lett 37: 20–26, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.10813

In this paper, a fast Cross Coupling iterative Approach (CCIA) is proposed for studying the composite scattering of the layered rough surfaces with buried target, which uses forward backward method (FBM) to solve the electric field integral equations (EFIE) of the layered rough surface and bi-conjugate gradient method (BI-CG) to solve the EFIE of the target, and the interaction between the rough surface and the target is achieved by updating the excitation term. The algorithm is applied to calculate the composite scattering coefficients of the rough surface with a buried target, the results match with those of the traditional numerical algorithm MOM while the error can be reduced to 10−3 by 6 iterations, and the convergence speed and calculation accuracy meet the requirements. The composite scattering coefficients and Angular Correlation Function (ACF) amplitudes of layered rough surface and dielectric targets with different conditions are calculated, and the effects of various factors such as target size and burial depth on the composite scattering characteristics are discussed. It is found that the buried targets will have a great influence on the scattering characteristics, weakening or neglecting the coupling between them will lead to larger errors. Moreover, the results show that ACF can suppress scattering from rough surfaces well, making the scattering characteristics of the target more obvious, which is important for detecting underground targets.

The rigorous evaluation of the NRCS (Normalized Radar Cross Section) of an object above a one-dimensional sea surface (2D case) needs to numerically solve a set of discretized integral equations involving a large number of unknowns. Thus, the direct solution of the impedance matrix equation via LU decomposition becomes the most expensive step in the MoM (Method of Moments) procedure. So, in order to minimize the computation cost, the iterative domain decomposition method called EPILE (Extended Propagation-Inside-Layer Expansion) was used and then was combined with the FBSA (Forward-Backward with Spectral Acceleration) to calculate the local interactions on the rough sea surface. The resulting fast method is called EPILE+FBSA. In this paper, we take advantage of the rank-deflcient nature of the coupling matrices, corresponding to the object-surface interactions, to further reduce the complexity of the method by using the ACA (Adaptive Cross Approximation). Thus, the coupling matrices are strongly compressed without a loss of accuracy and the memory requirement is then strongly reduced. For a cylinder above a rough sea surface, the results show the e-ciency of the accelerated EPILE+FBSA+ACA method.

The subject of research in this article is the process of building a mobile communication system that operates under electronic countermeasures. The aim is to develop recommendations for building a wireless mobile communication system that operates effectively in a complex interfering electromagnetic environment. The strategy for building a mobile wireless communication system is based on the use of a grouping of low-altitude UAVs with ultra-wideband signal technology circulating in control and communication channels, with the integration of artificial intelligence elements into its structure. The objective of this study is to ensure the stable and secure operation of a wireless mobile communication system despite electronic countermeasures. The methods of analytical, temporal positional pulse coding, and fuzzy logical inference were used to make decisions on the transfer of service in the network. The following results were obtained. A strategy for building a wireless mobile communication system despite electronic countermeasures has been developed. It is shown that in order to obtain high noise immunity of control and communication channels and to protect information from interception, wireless ultra-wideband communication technology should be used. This will provide large volumes and speeds of information transmission. A technical solution for the design of an ultra-wideband transceiver antenna system is proposed. Moreover, it is recommended to use the results of data processing in a fuzzy decision-making system for the transfer of service between mobile network nodes in conditions of interference. Conclusions. The scientific novelty of the obtained results is as follows. The use of ultra-wideband channels makes it possible to increase the number of control and communication channels in a wireless mobile system almost unlimitedly. The preliminary distribution of orthogonal codes between the channels realizes the process of control and communication without the interception of information and mutual interference. The use of the time-position-pulse coding method prevents the occurrence of intercharacter distortions of the encoding ultrashort pulses. This also reduces the level of distortion of information signals caused by multipath propagation, which guarantees the security of information in the system. The use of a fuzzy decision-making system for the transfer of services between mobile network nodes allows dynamically changing the network topology in real time and maintaining high quality of service under electronic countermeasures.

The accuracy of most widely used empirical models are investigated using the spectrally accelerated forward-backward (FBSA) method as a benchmark solution. First, FBSA results are obtained for propagation over large scale terrain profiles and compared with measurements to assess the accuracy of FBSA. Then, accuracy of some International Telecommunication Union (ITU) and Federal Communications Commission (FCC) propagation models are investigated. It has been observed that, for rural areas, the prediction of the most recent ITU recommended propagation model (Rec. 1546) deviates much more than older models do.

To numerically calculate bistatic scattering from a fractal rough surface with high permittivity, a comprehensive approach of the forward-backward method (FBM) with spectral acceleration algorithm (SAA) combined with the physics-based two-grid (PBTG) method is developed. Bistatic scattering from and transmitting through one-dimensional (1-D) fractal rough surface with high permittivity, under TE and TM tapered wave incidence, are numerically simulated. Angular reflectivity and transmittivity demonstrate the energy conservation and the functional dependences upon the surface parameters.

Basing on the exact spectral formalism, using the composite method that combines the numerical and approximate algorithms, the reconstruction problem for the rough surface is investigated. For the direct problem, the scattering data is obtained by the numerical algorithm-the method of moments (MOM), the Banded-Matrix-Iterative-Approach/Canonical Grid method (BMIA/CAG), and the forward-backward iterative method (FBM); For the inverse problem, the profile of rough surface with different roughness is reconstructed by two approximate algorithms - the small perturbation approximation (SPA) and the Kirchhoff approximation (KA) combined with the method of moments, the Banded-Matrix-Iterative-Approach/ Canonical Grid method, and forward-backward iterative method (FBM). The numerical results of reconstructed rough surface with different roughness are presented with the composite method, and the data are compared and analyzed.

Predictive demand and collapse fragility functions are two essential components of the probabilistic seismic demand analysis that are commonly developed based on statistics with enormous, costly and time consuming data gathering. Although this approach might be justified for research purposes, it is not appealing for practical applications because of its computational cost. Thus, in this paper, Bayesian regression-based demand and collapse models are proposed to eliminate the need of timeconsuming analyses. The demand model developed in the form of linear equation predicts overall maximum inter-story drift of the lowto mid-rise regular steel moment resisting frames (SMRFs), while the collapse model mathematically expressed by lognormal cumulative distribution function provides collapse occurrence probability for a given spectral acceleration at the fundamental period of the structure. Next, as an application, the proposed demand and collapse functions are implemented in a seismic fragility analysis to develop fragility and consequently seismic demand curves of three example buildings. The accuracy provided by utilization of the proposed models, with considering computation reduction, are compared with those directly obtained from Incremental Dynamic analysis, which is a computer-intensive procedure.