Method Of Ordered Multiple Interactions Research Articles

Numerical study on the phase and amplitude statistics of backscattered signals from time-evolving sea surfaces

A statistical analysis based on modulated compound Gaussian (CG) fields is performed on the phase and amplitude of backscattered signals, numerically generated using the method of ordered multiple interactions (MOMIs) for time-evolving one-dimensional (1D) Creamer surfaces. According to CG fields, theoretical models are revisited to investigate the statistics of phase difference and amplitude ratio as a function of time lag to reveal the modulation mechanisms of the backscattered signals. Numerical results demonstrate good agreements between the numerically generated statistics and the theoretical counterparts, providing with clear evidence that the numerically generated backscattered fields are jointly Gaussian distributed on short time-scales but, are modulated in amplitude by the long surface waves, which make the clutter returns departing from joint Gaussian model gradually. Such modulation mechanisms are coincident with the findings from the analysis of radar measurements published in references, further validating the applicability of the MOMI-based electromagnetic modelling process for sea clutter.

Scattering From Very Large Randomly Rough Surfaces Using a Markov Random Field Equivalent Current

A Markov random field (MRF) model is employed to learn the statistical properties of an equivalent current situated above a rough surface, where this equivalent current represents near-field electromagnetic scattered fields. The MRF parameters are learned by considering numerical scattering from a relatively small rough surface, which can be solved efficiently via existing numerical methods. The MRF parameters may then be used to synthesize multiple realizations of the equivalent current associated with scattering from a much larger rough surface. These equivalent currents may be used to efficiently calculate the far-field scattered-field statistics for large surfaces. The advantages of this approach are manifested in the fact that once the MRF parameters are learned, a forward model is no longer needed to generate random realizations of the equivalent currents, and the MRF model can be employed to generate equivalent surfaces of size beyond the capability of existing numerical models. To improve the accuracy of the MRF model, a narrowband filter is used to preprocess the computed current distributions prior to MRF model training. One-dimensional rough surfaces are considered here to demonstrate the idea, and the method of ordered multiple interactions (MOMI) is employed to perform the numerical forward modeling. Promising MRF-generated results are demonstrated, with comparison to direct MOMI solutions.

The method of ordered multiple interactions for closed bodies

Boundary integral methods for calculating bistatic scatter start with a specified sample grid over the surface that defines the scatterer. Whereas standard method of moments (MOM) implementations can be applied independent of the mesh structure, the method of ordered multiple interactions (MOMI) effectively defines a surface trajectory over the sample grid. This paper introduces source-directed slice sampling whereby a variant of the MOMI method applied to three-dimensional (3D) objects becomes a strict forward-backward recursion. Applications of MOMI to 1D rough surfaces first demonstrated the rapid convergence that can be obtained when the surface sampling follows the projected direction of the incident radiation. With a 3D object source-directed sampling can be implemented with no projection, although the surface must be resampled for each new source direction. The first iteration of the MOMI recursion makes a partial backward correction. With strict forward-backward sampling, the initial forward sweep, which we call the forward-approximation, often provides a good approximation to the source currents. The results are demonstrated for the scalar problem, but the extension to the vector problem is straightforward.

An accelerated boundary integral equation scheme for propagation over the ocean surface

In two recent papers, C. L. Rino, H. Ngo and V. Kruger (RNK) proposed a novel scheme for tropospheric propagation over one‐dimensional (1D) terrain or ocean surfaces. This scheme is based on a boundary integral equation (BIE) formalism, the iterative solution of which is carried out efficiently via the method of ordered multiple interactions (MOMI). An important merit of the RNK scheme is the fact that, being a BIE‐based model, it rigorously accounts for the effect of the multiple‐scale ocean surface roughness on the propagated field. In their most recent paper, C. L. Rino and V. Kruger suggested that the accelerated version of MOMI proposed by H.‐T. Chou and J. T. Johnson (MOMI/CJ) could substantially enhance the efficiency of their scheme. Motivated by this suggestion, this paper proposes a combined RNK/CJ algorithm for propagation over finitely conducting (FC) ocean surfaces. While maintaining its accuracy, the proposed scheme enhances the computational efficiency of the rigorous RNK model by reducing the number of mathematical operations needed in the iterative solution of the governing BIE.

Numerical simulations of scattering from time-varying, randomly rough surfaces

The literature has seen the development of robust and efficient numerical techniques for exact calculations of rough surface scattering. We discuss how such methods, typically formulated for time-independent surfaces, can be extended to calculate scattering from time-evolving ocean-like surfaces. Estimates are provided for the choice of parameters in such time-varying simulations. The method of ordered multiple interactions (MOMI) is used to calculate time-varying scattering from surfaces generated according to linear and nonlinear (Creamer) models for incidence angles ranging from normal to low grazing. We discuss the runtime considerations and demonstrate that combining the MOMI with a fast multipole method (FMM)-type acceleration technique makes large-scale time-varying Monte Carlo simulations possible. The average Doppler spectra of backscattered signals obtained from such simulations are compared for different incident angles, polarizations, and surface models. In particular, the simulations show a broadening of the Doppler spectra for nonlinear surfaces, especially at low grazing angles (LGA) and a separation of the vertical and horizontal polarization spectra at LGA for nonlinear surfaces. This spectral separation at LGA is not observed when the linear surfaces are used.

Low-grazing angle scattering from rough surfaces in a duct formed by a linear-square refractive index profile

The problem of rough surface scattering and propagation over rough terrain in a ducting environment has been receiving considerable attention in the literature. One popular method of modeling this problem is the parabolic wave equation (PWE) method. An alternative method is the boundary integral equation (BIE) method. The implementation of the BIE in inhomogeneous media (ducting environments) is not straightforward, however, since the Green's function for such a medium is not usually known. In this paper, a closed-form approximation of the Green's function for a two-dimensional (2-D) ducting environment formed by a linear-square refractive index profile is derived using asymptotic techniques. This Green's function greatly facilitates the use of the BIE approach to study low-grazing angle (LGA) rough surface scattering and propagation over rough surfaces in the aforementioned ducting environment. This paper demonstrates how the BIE method can model the combined effects of surface roughness and medium inhomogeneity in a very rigorous fashion. Furthermore, it illustrates its capability of accurately predicting scattering in all directions including backscattering. The boundary integral equation of interest is solved via the method of ordered multiple interactions (MOMI), which eliminates the requirements of matrix storage and inversion and, hence, allows the application of the BIE method to very long rough surfaces.

A rapidly convergent iterative method for two‐dimensional closed‐body scattering problems

The method of ordered multiple interactions (MOMI) provides a robust iterative series solution to the problem of wave scattering from rough surfaces. In this letter, a rapidly convergent MOMI series is obtained for closed-body scattering problems using a dual-surface magnetic field integral equation. The MOMI series is shown to provide a significant reduction of the iteration count relative to another technique. ©1999 John Wiley & Sons, Inc. Microwave Opt Technol Lett 20: 179–183, 1999.

A rapidly convergent iterative method for two-dimensional closed-body scattering problems

The method of ordered multiple interactions (MOMI) provides a robust iterative series solution to the problem of wave scattering from rough surfaces. In this letter, a rapidly convergent MOMI series is obtained for closed-body scattering problems using a dual-surface magnetic field integral equation. The MOMI series is shown to provide a significant reduction of the iteration count relative to another technique. ©1999 John Wiley & Sons, Inc. Microwave Opt Technol Lett 20: 179–183, 1999.

A combined field approach to scattering from infinite elliptical cylinders using the method of ordered multiple interactions

The method of ordered multiple interactions (MOMI) is an iterative procedure which has been demonstrated to provide a rapidly convergent series for the problem of wave scattering from perfectly conducting surfaces rough in a single dimension. In this paper, we consider the extension of this technique to the problem of scattering from infinite elliptical cylinders. For an incident plane wave having its electric field polarized along the axis of the cylinder a combined field formulation of the scattering problem is found to provide a rapidly convergent MOMI series. The determination of an optimal combined field representation for the scattering problem in this case is also discussed. An extension of the MOMI method is necessary to properly treat the remaining polarization.

Use of fast multipole method with method of ordered multiple interactions

The method of ordered multiple interactions (MOMI) provides a rapidly convergent iterative solution to a large number of scattering problems in two dimensions. The authors demonstrate that the MOMI can be combined with the fast multipole method (FMM) to obtain a numerically efficient algorithm.

On the discretization of the integral equation describing scattering by rough conducting surfaces

Numerical simulations of scattering from one-dimensional (1-D) randomly rough surfaces with Pierson-Moskowitz (P-M) spectra show that if the kernel (or propagator) matrix with zeros on its diagonal is used in the discretized magnetic field integral equation (MFIE), the results exhibit an excessive sensitivity to the current sampling interval, especially for backscattering at low-grazing angles (LGAs). Though the numerical results reported in this paper were obtained using the method of ordered multiple interactions (MOMI), a similar sampling interval sensitivity has been observed when a standard method of moments (MoM) technique is used to solve the MFIE. A subsequent analysis shows that the root of the problem lies in the correct discretization of the MFIE kernel. We found that the inclusion of terms proportional to the surface curvature (regarded by some authors as an additional correction) in the diagonal of the kernel matrix virtually eliminates this sampling sensitivity effect. By reviewing the discretization procedure for MFIE we show that these curvature terms indeed must be included in the diagonal in order for the propagator matrix to be represented properly. The recommended current sampling interval for scattering calculations with P-M surfaces is also given.