Electromagnetic Scattering From a Rough Layer: Propagation-Inside-Layer Expansion Method Combined to the Forward-Backward Novel Spectral Acceleration

In this paper, an efficient method is developed to calculate the bistatic cross section (BSC) from a stack of two one-dimensional rough interfaces separating homogeneous media. The PILE (propagation-inside-layer expansion) method recently developed by Dechamps was efficient with a complexity ( being the number of samples per interface). To reduce this complexity, a fast method valid for a single rough surface, the forward-backward with novel spectral acceleration (FBNSA) is combined to the PILE method. Furthermore, the calculation of the coupling interactions between both interfaces are also accelerated using the NSA. The PILE-FBNSA method reaches then a complexity of only . A study of the convergence of the PILE is done and compared to the FBNSA of Moss     

Monte-Carlo simulations of large-scale problems of random roughsurface scattering and applications to grazing incidence with theBMIA/canonical grid method

Scattering of a TE incident wave from a perfectly conducting one-dimensional random rough surface is studied with the banded matrix iterative approach/canonical grid (BMIA/CAG) method. The BMIA/CAG is an improvement over the previous BMIA. The key idea of BMIA/CAG is that outside the near-field interaction, the rest of the interactions can be translated to a canonical grid by Taylor series expansion. The use of a flat surface as a canonical grid for a rough surface facilitates the use of the fast Fourier transform for nonnear field interaction. The method can be used for Monte-Carlo simulations of random rough surface problems with a large surface length including all the coherent wave interactions within the entire surface. We illustrate results up to a surface length of 2500 wavelengths with 25000 surface unknowns. The method is also applied to study scattering from random rough surfaces at near-grazing incidence. The numerical examples illustrate the importance of using a large surface length for some backscattering problems     

Application of stochastic second-degree method to electromagnetic scattering from randomly rough surfaces

Application of a stochastic second-degree method in combination with the banded matrix canonical grid (BMIA/CAG) method for two- dimensional electromagnetic scattering from PEC randomly rough surfaces is presented. This method can improve convergence while preserving the computational attractiveness of the BMIA/CAG method. Numerical examples illustrate the effectiveness of the proposed method.     

Monte Carlo simulations of wave scattering from lossy dielectricrandom rough surfaces using the physics-based two-grid method and thecanonical-grid method

In using the method of moments to solve scattering by lossy dielectric surfaces, usually a single dense grid (SDG) with 30 points per wavelength is required for accurate results. A single coarse grid (SCG) of ten points per wavelength does not give accurate results. However, the central processing unit (CPU) and memory requirements of SDG are much larger than that of SCG. In a physics-based two-grid method (PBTG) two grids are used: a dense grid and a coarse grid. The method is based on the two observations: (1) Green's function of the lossy dielectric is attenuative and (2) the free-space Green's function is slowly varying on the dense grid. In this paper, the PBTG method is combined with the banded-matrix iterative approach/canonical grid method to solve rough surface scattering problem for both TE and TM cases and also for near grazing incidence. We studied cases of dielectric permittivities as high as (25+i)ϵ₀ and incidence angle up to 85°. Salient features of the numerical results are: (1) an SCG has poorer accuracy for TM case than TE case; (2) PBTG-banded-matrix iterative approach/canonical grid BMIA/CAG method speeds up CPU and preserves the accuracy; it has an accuracy comparable to single dense grid and yet has CPU comparable to single coarse grid; (3) PBTG-BMIA/CAG gives accurate results for emissivity calculations and also for low grazing backscattering problems (LGBA); and (4) the computational complexity and the memory requirements of the present algorithm are O(N log(N)) and O(N), respectively, where N is the number of surface unknowns on the coarse grid     

On the canonical grid method for two-dimensional scatteringproblems

The banded matrix iterative approach with a canonical grid expansion (BMIA/CAG) has been shown by Tsang et al. (see ibid., vol.43, p.851-9, 1995) to be an efficient method for the calculation of scattering for near planar two-dimensional (2-D) geometries such as one-dimensional rough surfaces. However, in the article of Tsang et. al, only the first three terms in the canonical grid series for TE polarization above a perfectly conducting surface were discussed and methods for implementing only a portion of these terms were presented. In this paper, a general form for all terms in the canonical grid series is provided for both TE and TM polarizations above an impedance surface and an efficient algorithm for calculating their contributions is described. The relationship between the canonical grid and operator expansion methods is also discussed. A sample surface scattering problem is shown to illustrate the utility of higher order terms in the canonical grid method     

Application of iterative moment-method solutions to ocean surfaceradar scattering

Numerical methods such as the banded matrix iterative approach (BMIA) represent a major advance in the direct numerical simulation of rough surface-wave scattering. This paper considers the application of iterative methods such as the BMIA to ocean-radar scattering. It is shown that for typical microwave radar frequencies and sea-surface roughness, the BMIA is actually of limited use. A more general iterative solution based on a multigrid decomposition and the generalized conjugate residual (GCR) method, is thus developed. The multigrid approach is ideally suited to the broad-band ocean surface, as it solves the scattering problem on a sequence of grids, each corresponding to a different range of spatial frequencies or length scales. This approach is applied here to several sea scattering problems, including very low grazing angles and both horizontal and vertical polarization. Good agreement is obtained with perturbation theory in the appropriate limits and several qualitative characteristics of radar backscatter data are reproduced     

Monte Carlo simulations of large-scale one-dimensional randomrough-surface scattering at near-grazing incidence: Penetrable case

Scattering from dielectric one-dimensional (1-D) random rough surfaces at near grazing incidence is studied for both TE and TM cases. To obtain accurate results at incidence angles of 80°-85°, we use long surface lengths of up to 1000 wavelengths. Numerical results are illustrated for dielectric surfaces corresponding to soil surfaces with various moisture contents. Results indicate that TM backscattering is much larger than that of TE backscattering. The ratio of TM to TE backscattering increases as a function of soil moisture and can be used as an indicator of soil moisture in remote sensing applications. However, the ratio of TM to TE backscattering is much lower than that predicted by the small perturbation method. To facilitate computation of scattering by such long surfaces, the previously developed banded-matrix iteration approach/canonical grid method (BMIA/CG) has been extended to dielectric surfaces. The numerical algorithm consists of translating the nonnear-field interaction to a flat surface and the interaction subsequently calculated by fast Fourier transform (FFT)     

Quasi-ray Gaussian beam algorithm for short-pulse two-dimensional scattering by moderately rough dielectric interfaces

We consider short-pulse (SP) time-domain (TD) two-dimensional (2-D) scattering by moderately rough interfaces, which separate free space from a slightly lossy dielectric half-space, and are excited by one-dimensional (1-D) SP-TD aperture field distributions. This study extends to the SP-TD in our previous investigation of time-harmonic high frequency 2-D scattering of Gabor-based quasi-ray Gaussian beam fields excited by 1-D aperture field distributions in the presence of moderately rough dielectric interfaces (Galdi et al.). The proposed approach is based on the Kirchhoff physical optics (PO) approximation in conjunction with the Gabor-based quasi-ray narrow-waisted Gaussian pulsed-beam (PB) discretization (Galdi et al.), which is applied to the SP-induced equivalent magnetic surface currents on the interface that establish the TD reflected/transmitted fields. We show that, for well-collimated truncated SP incident fields, the PO-PB synthesis of the reflected/transmitted fields yields an approximate explicit physically appealing, numerically efficient asymptotic algorithm, with well-defined domains of validity based on the problem parameters. An extensive series of numerical experiments verifies the accuracy of our method by comparison with a rigorously-based numerical reference solution, and assesses its computational utility. The algorithm is intended for use as a rapid forward solver in SP-TD inverse scattering and imaging scenarios in the presence of moderately rough dielectric interfaces.     

基于粗糙集的多类CVM

 标准的SVM对于训练集具有O(l³)的时间复杂度和O(l²)的空间复杂度,2005年提出的CVM具有线性的时间复杂度和与训练集大小无关的空间复杂度.本文结合粗糙集和CVM,提出了一种新的多类分类RSCVM方法,该方法对二类CVM定义上近似和下近似,然后扩展到多类情形.本文最后给出在真实世界数据集上的实验结果及其分析,显示RSCVM方法具有快速和产生较少支持向量的优点.     

Monte Carlo simulation of electromagnetic scattering fromtwo-dimensional random rough surfaces

The fast multipole method fast Fourier transform (FMM-FFT) method is developed to compute the scattering of an electromagnetic wave from a two-dimensional (2-D) rough surface. The resulting algorithm computes a matrix-vector multiply in O(N log N) operations. This algorithm is shown to be more efficient than another O(N log N) algorithm, the multilevel fast multipole algorithm (MLFMA), for surfaces of small height. For surfaces with larger roughness, the MLFMA is found to be more efficient. Using the MLFMA, Monte Carlo simulations are carried out to compute the statistical properties of the electromagnetic scattering from 2-D random rough surfaces using a workstation. For the rougher surface, backscattering enhancement is clearly observable as a pronounced peak in the backscattering direction of the computed bistatic scattering coefficient. For the smoother surface, the Monte Carlo results compare well with the results of the approximate Kirchhoff theory     

Sparse matrix/canonical grid method applied to 3-D dense medium simulations

The sparse matrix/canonical grid (SMCG) method, which has been shown to be an efficient method for calculating the scattering from one-dimensional and two-dimensional random rough surfaces, is extended to three-dimensional (3-D) dense media scattering. In particular, we study the scattering properties of media containing randomly positioned and oriented dielectric spheroids. Mutual interactions between scatterers are formulated using a method of moments solution of the volume integral equation. Iterative solvers for the resulting system matrix normally require O(N/sup 2/) operations for each matrix-vector multiply. The SMCG method reduces this complexity to O(NlogN) by defining a neighborhood distance, r/sub d/, by which particle interactions are decomposed into "strong" and "weak." Strong interaction terms are calculated directly requiring O(N) operations for each iteration. Weak interaction terms are approximated by a multivariate Taylor series expansion of the 3-D background dyadic Green's function between any given pair of particles. Greater accuracy may be achieved by increasing r/sub d/, using a higher order Taylor expansion, and/or increasing mesh density at the cost of more interaction terms, more fast Fourier transforms (FFTs), and longer FFTs, respectively. Scattering results, computation times, and accuracy for large-scale problems with r/sub d/ up to 2 gridpoints, 14/spl times/14/spl times/14 canonical grid size, fifth-order Taylor expansion, and 15 000 discrete scatterers are presented and compared against full solutions.     

A low power scheduling scheme with resources operating at multiplevoltages

This paper presents resource and latency constrained scheduling algorithms to minimize power/energy consumption when the resources operate at multiple voltages (5 V, 3.3 V, 2.4 V, and 1.5 V). The proposed algorithms are based on efficient distribution of slack among the nodes in the data-flow graph. The distribution procedure tries to implement the minimum energy relation derived using the Lagrange multiplier method in an iterative fashion. Two algorithms are proposed, 1) a low complexity O(n²) algorithm and 2) a high complexity O(n² log(L)) algorithm, where n is the number of nodes and L is the latency. Experiments with some HLS benchmark examples show that the proposed algorithms achieve significant power/energy reduction. For instance, when the latency constraint is 1.5 times the critical path delay, the average reduction is 39%     

Electromagnetic scattering from a buried cylinder in layered media with rough interfaces

A solution to scattering from a cylinder buried arbitrarily in layered media with rough interfaces based on extended boundary condition method (EBCM) and scattering matrix technique is developed. The reflection and transmission matrices of arbitrary rough interfaces as well as an isolated single cylinder are constructed using EBCM and recursive T-matrix algorithm, respectively. The cylinder/rough surface interactions are taken into account by applying the generalized scattering matrix technique. The scattering matrix technique is used to cascade reflection and transmission matrices from individual systems (i.e., rough surfaces or cylinders) in order to obtain the scattering pattern from the overall system. Bistatic scattering coefficients are then obtained by incoherently averaging the power computed from the resulting Floquet modes of the overall system. In numerical simulations, the bistatic scattering coefficients are first validated by comparing the simulation results with the existing solutions which are the limiting cases including scattering from two-interface rough surfaces without any buried object and from a buried cylinder beneath a single rough surface. Subsequently, the numerical simulations of scattering from a buried cylinder in layered rough surfaces are performed to investigate the relative importance and sensitivity of various physical parameters of layered rough surfaces to incoherent scattering coefficients. Results show layered rough interfaces can significantly alter the scattering behaviors of a buried cylinder.     

A low-complexity zero-forcing CFO compensation scheme for OFDMA uplink systems

Similar to the conventional orthogonal frequencydivision multiplexing (OFDM) system, an OFDM multiple access (OFDMA) system will have a carrier frequency offset (CFO) problem. Since CFOs of all users are different, CFO compensation in the OFDMA uplink system is much more involved. A simple, yet efficient, method is the zero-forcing (ZF) compensation method. However, it involves an inverse of an N × N CFO-induced ICI matrix, where N is the number of subcarriers. Thus, the complexity can become very high when N is large, a case commonly seen in OFDMA systems. In this work, we propose a low-complexity ZF method to overcome the problem. The main idea is to use Newton's method to solve matrix inversion iteratively. We explore the structure of the CFOinduced ICI matrix and develop a method that can implement Newton's method with fast Fourier transforms (FFTs). As a result, the required computational complexity is significantly reduced from O(N³) to O(2N log₂N). Simulations show that, with only three iterations, the proposed method can have similar performance to the direct ZF method.     

基于前缀区间集合的IPv6路由查找算法

对IPv6相关的通用型与特定型路由算法进行了分析,重点研究了以BSR为基础的IPv6路由算法在查找和更新时的不平衡问题,提出了基于前缀区间集合的IPv6路由算法。通过对路由前缀（N）进行范围（K）、集合（M）划分以及更新节点自修复提高查询速度、降低不平衡性的影响,具有O(log2N/K)和O(log2N/K+2M)的查询与更新时间复杂度,空间复杂度为O(K+2N)。实验表明,该算法具有良好的查询性能,降低了更新不平衡性的影响。     

Fast generalized minimum-distance decoding of algebraic-geometryand Reed-Solomon codes

Generalized minimum-distance (GMD) decoding is a standard soft-decoding method for block codes. We derive an efficient general GMD decoding scheme for linear block codes in the framework of error-correcting pairs. Special attention is paid to Reed-Solomon (RS) codes and one-point algebraic-geometry (AG) codes. For RS codes of length n and minimum Hamming distance d the GMD decoding complexity turns out to be in the order O(nd), where the complexity is counted as the number of multiplications in the field of concern. For AG codes the GMD decoding complexity is highly dependent on the curve in consideration. It is shown that we can find all relevant error-erasure-locating functions with complexity O(o₁nd), where o₁ is the size of the first nongap in the function space associated with the code. A full GMD decoding procedure for a one-point AG code can be performed with complexity O(dn²)     

A fast multipole-method-based calculation of the capacitance matrixfor multiple conductors above stratified dielectric media

An efficient static fast-multipole-method (FMM)-based algorithm is presented in this paper for the evaluation of the parasitic capacitance of three-dimensional microstrip signal lines above stratified dielectric media. The effect of dielectric interfaces on the capacitance matrix is included in the stage of FMM when outgoing multipole expansions are used to form local multipole expansions by the use of interpolated image outgoing-to-local multipole translation functions. The increase in computation time and memory usage, compared to the free-space case, is, therefore, small. The algorithm retains O(N) computational and memory complexity of the free-space FMM, where N is the number of conductor patches     

MEI系数的快速算法

不变性测试方程法已被证明是解决电磁问题的一种有效方法。目前电大尺寸问题中ＭＥＩ系数的计算已成为一个瓶颈。提出了一个快速算法用于加速ＭＥＩ系数的计算,它使用快速多极子方法计算测试子的散射场,使得ＭＥＩ系数的计算速度从Ｏ（Ｎ＾２）变为Ｏ（Ｎ＾１．５Ｌｏｇ２Ｎ）。     

在线multicast数据传输网络中的一个优化问题

首先建立了数据传输网络选择的最小成本模型，给出了有效支撑树代表集的概念，并给出了一个时间复杂性为D(mlogen)的算法产生代表集。然后对静态数据传输问题和在线数据传输问题，分别给出了一个时间复杂性为D(mlogen)和O(m^2 mlogen)的多项式时间的算法。     

Low complexity detection algorithm based on optimized Neumann series for massive MIMO system

An optimized Neumann series ( NS ) approximation isdescribed based on Frobenius matrix decomposition, this method aims to reduce the high complexity, which caused by the large matrix inversion of detection algorithm in the massive multiple input multiple output (MIMO) system. The large matrix in the inversion is decomposed into the sum of the hollow matrix and a Frobenius matrix, and the Frobenius matrix has the diagonal elements and the first column of the large matrix. In order to ensure the detection performance approach to minimum mean square error (MMSE) algorithm, the first three terms of the series approximation are needed, which results in high complexity as O(K³), where K is the number of users. This paper further optimize the third term of the series approximation to reduce the computational complexity from O(K³) to O(K²). The computational complexity analysis and simulation results show that the performance of proposed algorithm can approach to MMSE algorithm with low complexity O(K²).