Application of the Spectral Acceleration Forward-Backward Method To Coverage Analysis Over Terrain Profiles

In this paper the forward-backward (FB) method is used to solve the problem of scattering on a very rough surface for practical application to radio planning and site optimization for mobile radio systems. Novel spectral acceleration was developed for this method to reduce its computational cost to O(N), but the original implementation cannot be applied to solve the scattering on very rough surfaces. In this paper the spectral acceleration for the FB method is adapted to apply it on the calculation of scattering on considerable undulating surfaces.

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.

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

Acoustic scattering modulation caused by an undulating sea surface on the space–time dimension seriously affects underwater detection and target recognition. Herein, underwater acoustic scattering modulation from a moving rough sea surface is studied based on integral equation and parabolic equation. And with the principles of grating and constructive interference, the mechanism of this acoustic scattering modulation is explained. The periodicity of the interference of moving rough sea surface will lead to the interference of the scattering field at a series of discrete angles, which will form comb-like and frequency-shift characteristics on the intensity and the frequency spectrum of the acoustic scattering field, respectively, which is a high-order Bragg scattering phenomenon. Unlike the conventional Doppler effect, the frequency shifts of the Bragg scattering phenomenon are multiples of the undulating sea surface frequency and are independent of the incident sound wave frequency. Therefore, even if a low-frequency underwater acoustic field is incident, it will produce obvious frequency shifts. Moreover, under the action of ideal sinusoidal waves, swells, fully grown wind waves, unsteady wind waves, or mixed waves, different moving rough sea surfaces create different acoustic scattering processes and possess different frequency shift characteristics. For the swell wave, which tends to be a single harmonic wave, the moving rough sea surface produces more obvious high-order scattering and frequency shifts. The same phenomena are observed on the sea surface under fully grown wind waves, however, the frequency shift slightly offsets the multiple peak frequencies of the wind wave spectrum. Comparing with the swell and fully-grown wind waves, the acoustic scattering and frequency shift are not obvious for the sea surface under unsteady wind waves.

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.

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.

We apply two approximate solutions of the quantum-classical Liouville equation (QCLE) in the mapping representation to the simulation of the laser-induced response of a quantum subsystem coupled to a classical environment. These solutions, known as the Poisson Bracket Mapping Equation (PBME) and the Forward-Backward (FB) trajectory solutions, involve simple algorithms in which the dynamics of both the quantum and classical degrees of freedom are described in terms of continuous variables, as opposed to standard surface-hopping solutions in which the classical degrees of freedom hop between potential energy surfaces dictated by the discrete adiabatic state of the quantum subsystem. The validity of these QCLE-based solutions is tested on a non-trivial electron transfer model involving more than two quantum states, a time-dependent Hamiltonian, strong subsystem-bath coupling, and an initial energy shift between the donor and acceptor states that depends on the strength of the subsystem-bath coupling. In particular, we calculate the time-dependent population of the photoexcited donor state in response to an ultrafast, on-resonance pump pulse in a three-state model of an electron transfer complex that is coupled asymmetrically to a bath of harmonic oscillators through the optically dark acceptor state. Within this approach, the three-state electron transfer complex is treated quantum mechanically, while the bath oscillators are treated classically. When compared to the more accurate QCLE-based surface-hopping solution and to the numerically exact quantum results, we find that the PBME solution is not capable of qualitatively capturing the population dynamics, whereas the FB solution is. However, when the subsystem-bath coupling is decreased (which also decreases the initial energy shift between the donor and acceptor states) or the initial shift is removed altogether, both the PBME and FB results agree better with the QCLE-based surface-hopping results. These findings highlight the challenges posed by various conditions such as a time-dependent external field, the strength of the subsystem-bath coupling, and the degree of asymmetry on the accuracy of the PBME and FB algorithms.

A novel forward method to establish the three-dimensional parametric scattering center models is developed to extract scattering centers from the combined target/rough surface models. Both scattering centers from the ship, including single-order and higher order scattering contributions, and from the multiple interactions between the ship and random rough sea surface would be described concisely with physically relevant parameters by this proposed method. Due to the statistical nature of the random rough surface for the Monte Carlo simulation, we acquire a large number of realizations for estimations of the amplitude and position parameters to overcome the problem that single realization cannot extract scattering centers effectively. This method is validated through parametric models of the ship in free space and on the sea surface, and a good agreement has been demonstrated between the constructed and simulated radar characteristics. Furthermore, we analyze the composite target/surface model's physics and feature stability in a visually spatial range and direct connections between scattering centers and scattering sources, which would be valuable to future target recognitions and classifications. Finally, we quantitatively calculate and analyze the coupling scattering centers from interactions between the ship and the ocean-like surface that provide more abundant contour information of the inverse synthetic aperture radar (ISAR) image to facilitate contour detections.

The problem of very high frequency (VHF) radiowave propagation over the sea surface at low grazing angles is of a great interest for a lot of applications including radar backscattering at different polarizations. Existing theoretical approaches predict much bigger backscattering cross section for vertical polarized (TM) waves as compared to horizontal polarized (TE) waves, and are unable to give satisfactory explanation of experimental results showing that these two values occasionally can be of the same order. In this paper two main features are taken into account in a theoretical investigation of the processes of VHF radiowave backscattering by the rough sea surface at low grazing angles: a) distortion of the incident plane wave by diffraction effects at the sea wave crests prior to scattering by smallscale roughness; b) the concave form of the most part of the visible undulating sea surface. The incident wave diffraction caused by sea wave crests is considered using the simplest model of the crest shape, i.e. a perfectly conducting wedge. It is shown that the diffraction in forward direction at low grazing angles increases the strength of the horizontal polarized field as compared to the vertical polarized one just near the boundary between shadowed and illuminated parts of the surface. Back scattering of electromagnetic waves from cylindrical impedance concave statistically rough surface is studied analytically by the small perturbation method.

In this paper, we present a novel class of simple soft-input soft-output (SISO) detection algorithms for transmission over phase-uncertain channels. In order to limit the complexity, the set of possible phase values (i.e., the interval [0,2pi)) is properly quantized. We then use a forward-backward (FB) algorithm in correspondence to each quantized phase value. The forward and backward metrics computed by the different FB algorithms are properly combined to make the receiver robust against the time-varying phase. We apply the proposed SISO algorithms to perform joint detection and decoding of serially concatenated low-density parity-check (LDPC) codes and differentially encoded (DE) quaternary phase shift keying (QPSK), transmitted over a phase-uncertain channel. As a validation of the effectiveness of the proposed algorithms, we show that the performance loss with respect to that of the corresponding ideal (i.e., perfectly coherent) system is limited. Besides having a limited complexity, the proposed SISO algorithms are blind, i.e., no knowledge of the channel phase statistics is required, and highly parallelizable, as desirable in high-throughput future wireless communication systems

ABSTRACTIn this paper, we present two penalty-splitting inspired iteration schemes (PFFSA) and (PFFSA) for hierarchical equilibrium problems in Hilbert space. Based on the Opial-Passty lemma, we propose weak ergodic convergence and weak convergence of the iterative sequences generated by the Forward–Forward algorithm (PFFSA) and the Forward–Backward algorithm (PFFSA), which are proved under quite mild conditions: the bifunction of the two level equilibrium problems are supposed pseudomonotone. For strong convergence, we first add a strong monotonicity condition on the objective bifunction. We present after, a strong convergence result of algorithm (PFFSA) by adding a topological assumption, i.e. the objective bifunction is of class . Some examples are given to illustrate our results. The first example deals with pseudomonotone variational inequalities and convex minimization problem in the upper level problem. In the second one, we propose a convex minimization in the lower-level problem, where strong convergence of (PFFSA) to a minimum point is insured under infcompactness condition for objective function. These convergence results are new and generalize some recent results in this field.

This paper is concerned with the Gaussian relay channel (GRC) under the one-code constraint, where the source and the relay utilize the same code to send message. An advantage of such one-code constraint is that the error propagation resulting from re-encoding can be mitigated as the relay can forward directly the decoded “codeword” to the destination. The maximal achievable rate of the considered GRC is derived using the technique of superposition block Markov encoding based on the single code. Moreover, the forward-backward (FB) decoding strategies over the sliding window are developed both at the destination and at the relay. When LDPC codes are applied to the GRC system, a practical FB message passing decoding algorithm is presented. Simulation results show that the decoding performance can be improved as the window length increases and a small length (no greater than 4) is good enough for the FB decoding, and that re-encoding at relay may degrade the decoding performance at the destination.

A fast hybrid method based on physical optics (PO) and the reciprocity theorem is proposed to analyse the Doppler spectrum of a two-dimensional, moving plasma-coated object above a one-dimensional time-evolving lossy dielectric rough sea surface. This hybrid method eliminates the need for numerical solution of the polarization currents on the object and the time-evolving sea surface, thereby greatly improving the computing speed. The method is verified by conventional numerical methods. The characteristics of the Doppler spectrum of a plasma-coated object above a time-evolving sea surface are analysed in detail, including the effects of several parameters such as the incident angle and the velocity of the moving object. The effects of some key parameters on the stealth performance are also examined.

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

This paper presents the characteristics of radio wave scattering from rough sea surfaces in Ka-band. The physical optics method, which is one of the high frequency approximation algorithm, is employed to calculate radar cross section of electromagnetic simulation models of rough sea surfaces with Ship-EDF software. Rough sea surfaces are divided into six levels according to the wind speed over them. The simulation results show the effection that wind speed, the grazinng angle and frequency of radio wave have on the monostatic radar cross section of rough sea surfaces under the conditions of both horizontal and vertical polarization. With the increase of the roughness of sea surfaces and grazing angle of radio wave, the radar cross section value of rough sea surfaces increase. The frequencies of Ka-band have little contribution to the radar cross section value.