Two-frequency mutual coherence function for electromagnetic pulse propagation over rough surfaces

The propagation of a transient electromagnetic pulse over irregular terrain is considered. We model the wave propagation using the parabolic wave equation, which is valid for near-horizontal propagation. We model the effect of scattering from the rough terrain by introducing a surface-flattening coordinate transform. This coordinate transform simplifies the boundary condition of our problem, and introduces an effective refractive index into our wave equation. As a result, the problem of propagation over an irregular surface becomes equivalent to the problem of propagation through random media. The parabolic equation is solved analytically using the path integral method. Both vertically polarized and horizontally polarized signals are treated. Cumulant expansion is introduced to obtain an approximate expression for the two-frequency mutual coherence function. From the mutual coherence function, spatial and temporal dependence of the propagating signal can be determined. It can be shown that scattering from the irregular surface can cause broadening of the transient signal. This can have a significant impact on the performance of radio communication systems.     

Investigation on global positioning system signal scattering and propagation over the rough sea surface

This paper is devoted to the study of polarization properties, scattering properties and propagation properties of global positioning system (GPS) scattering signal over the rough sea surface. To investigate the polarization and the scattering properties, the scattering field and the bistatic scattering coefficient of modified Kirchhoff approximation with using the tapered incident wave is derived in detail. In modeling the propagation properties of the GPS scattering signal in the evaporation duct, the initial field of parabolic equation traditionally computed by the antenna pattern with using fast Fourier transform (FFT) is replaced by the GPS scattering field. And the propagation properties of GPS scattering signal in the evaporation duct with different evaporation duct heights and elevation angles of GPS are discussed by the improved discrete mixed Fourier transform with taking into account the sea surface roughness.     

Correlation characteristics of waves in lossy media with smooth fluctuations of the refractive index with oblique incidence on boundary

Abstract

The features of coherence function (and angular spectrum) and also the fluctuation of amplitude and phase of wavefield in a random strongly absorptive medium are investigated in the case of arbitrary angle of incidence at the surface.

In this paper it is elucidated that with oblique incidence a dissipation in the random medium can accelerate the accumulation of wave fluctuations and its incoherence. This effect strongly depends on the rate of decrease of the ‘wings’ of the scattering indicatrix. An analytical theory (Rytov's approximation and modified method of parabolic equation) has been modelled by Monte Carlo simulation of wave propagation, and also by numerical solution of the model transfer equation. It is revealed that the width of an angle spectrum can nonmonotonically change with the immersion to the absorptive medium.     

Estimation of co-channel interference between cities caused by ducting and turbulence

With the rapid development of the fifth-generation(5 G)mobile communication technology,the application of each frequency band has reached the extreme,causing mutual interference between different modules.Hence,there is a requirement for detecting filtering and preventing interference.In the troposphere,over-the-horizon propagation occurs in atmospheric ducts and turbulent media.The effects of both ducting and turbulence can increase the probability of occurrence of long-distance co-channel interference(CCI),in turn,severely affecting the key performance indicators such as system access,handover and drop.In the 5 G era,to ensure communication channels and information security,CCI must be reduced.This paper introduces a scattering parabolic equation algorithm for calculating signal propagation in atmospheric ducts on irregular terrain boundaries.It combines Hitney’s radio physical optical model and Wagner’s nonuniform turbulent scattering model for calculating the tropospheric scattering in an evaporation duct or a surface-based duct.The new model proposes a tropospheric scattering parabolic equation algorithm for various tropospheric duct environments.Finally,as a specific case,the topographical boundaries between several cities in the East China Plain were considered,and the over-the-horizon propagation loss was simulated for various ducting and turbulent environments.The simulation results were used to evaluate whether CCI would occur between cities in a specific environment.     

复杂地理环境的图像分割及电波传播特性

复杂地理环境是电波传播不可避免的传播环境,不仅不规则地形会对电波传播产生影响,不同的地表媒质对电波传播也会产生不同的影响。为了使得电波传播特性的预测结果更加地准确有效,通过图像分割算法实现地表环境的简单分类,同时对不同的媒质赋予不同的电磁参数,并结合数字高程模型(DEM)数据,实现了既具有地形起伏信息又具有地表电磁环境参数的复杂地理环境建模。在此基础上,对地表电磁环境信息做了网格剖分处理,利用抛物方程(PE)模型对复杂地理环境下的电波传播特性进行了预测。     

Target detection beneath foliage using polarimetric synthetic aperture radar interferometry

Abstract

In this paper, we demonstrate how the new technology of polarimetric synthetic aperture radar (SAR) interferometry can be used to enhance the detection of targets hidden beneath foliage. The key idea is to note that for random volume scattering, the interferometric coherence is invariant to changes in wave polarization. On the other hand, in the presence of a target the coherence changes with polarization. We show that under general symmetry constraints this change is linear in the complex coherence plane. These observations can be used to devise a filter to suppress the returns from foliage clutter while maintaining the signal from hidden targets. We illustrate the algorithm by applying it to coherent L-band SAR simulations of corner reflectors hidden in a forest. The simulations are performed using a voxel-based vector wave propagation and scattering code coupled to detailed structural models of tree architecture. In this way, the spatial statistics and radar signal fluctuations closely match those observed for natural terrain. We demonstrate significant improvements in the detection of hidden targets, which suggests that this technology has great potential for future foliage penetration (FOPEN) applications.     

Application of the Beilis-Tappert parabolic equation method to sound propagation over irregular terrain

The Beilis-Tappert (1979) parabolic equation method is attractive for irregular terrain because it treats surface variations in terms of a simple multiplicative factor ("phase screen"). However, implementing the exact sloping-surface impedance condition is problematic if one wants the computational efficiency of a Fourier parabolic equation algorithm. This article investigates an approximate flat-ground impedance condition that allows the Beilis-Tappert phase screen method to be used with a Fourier algorithm without any added complications. The exact sloping-surface impedance condition is derived and applied to propagation predictions over hills with maximum slopes from 5° to 22°. The predictions with the exact impedance condition are compared to predictions using the approximate flat-ground impedance condition. It is found that for slopes less than 15°-20°, the flat-ground impedance condition is sufficiently accurate. For slopes greater than approximately 20°, the limiting factor on numerical accuracy is not the flat-ground impedance approximation, but rather the narrow-angle approximation required by the Beilis-Tappert method. Thus, within the 20° limitation and using the flat-ground impedance condition with a Fourier parabolic equation, sound propagation over irregular terrain can be computed simply, efficiently, and accurately.     

存在障碍物时电波传播抛物线方程分析及其验证

双向抛物线方法主要用于起伏地形下电波传播问题的计算,该算法本身无法处理地面存在障碍物,尤其是真实环境下障碍物与地面为不同媒质的情况.因此本文提出一种用于存在障碍物时电波传播计算的抛物线方程新算法.该方法采用区域分解,对不同障碍物区域的场值进行分区计算,并对计算结果进行相位修正,从而实现该情况下空间中场值的计算.在此基础上,使用矩量法来精确验证抛物线方法的计算精度.通过实例分析,证明了存在障碍物时新算法的精确性,为之后求解真实环境下的电波传播问题提供了参考.     

Acoustic scattering from a rough sea surface: the mean field by the integral equation method

Abstract

The scattering of an acoustic signal incident from below at low angles on a rough sea surface is treated by the integral equation method in the parabolic approximation. Equations are obtained allowing the mean scattered field to be calculated even when the surface causes a large phase modulation in the incident wave. Solutions are found using the method of Laplace transforms and some results are presented for a specific type of rough surface.     

Time-reversal imaging of objects near rough surfaces based on surface flattening transform

This paper considers the imaging of objects located close to rough surfaces such as ocean or terrain. If transmitters and receivers are also located close to rough surfaces, incident wave is no longer a plane wave nor a spherical wave in free space and it is necessary to consider Green’s functions with the point source located close to the surface, similar to the Sommerfeld dipole problem. This paper considers the near-surface imaging by making use of time-reversal imaging and surface flattening transform. Surface flattening transform converts the rough surface problem into flat surface with inhomogeneous random medium. Mutual coherence function is obtained and used to obtain imaging of point target near rough surface, making use of the multi-static data matrix, time-reversal matrix, the eigenvectors, and the steering matrix. Numerical examples are given. An important point is that integration of stochastic wave propagation and signal processing is necessary to obtain imaging through complex clutter environment. Surface flattening transform is related to the transformation electromagnetics which attracted much interest because of cloaking possibilities. This paper includes some discussions on the relations between surface flattening and transformation electromagnetics.     

Pulse broadening and two-frequency mutual coherence function of the scattered wave from rough surfaces

Abstract

Analytical expressions for the two-frequency mutual coherence function and angular correlation function of the scattered wave from rough surfaces based on the Kirchhoff approximation are presented. The coherence bandwidth depends on the illumination area as well as on the incident and scattered angles and the surface characteristics. Scattered pulse shapes are calculated as the Fourier transform of the two-frequency mutual coherence function. Calculations based on analytical solutions are compared with millimetre wave experimental data and Monte Carlo simulations showing good agreement.     

基于数字地图的二维电波传播问题仿真

为快速预测二维地理环境下的电磁环境特性,应用二维抛物方程模型对电磁环境进行仿真。为了得到真实有效的地形数据,研究了从GeoTiff中抽取网格点上地理信息的方法,并利用双线性插值法计算了任意位置处的高程值。同时研究了地球表面两点之间计算距离的方法,将该方法的计算结果与GIS软件结果进行对比,验证了该方法的可靠性。在标准大气环境下,利用二维抛物方程模型仿真分析了不同距离处不同高度的电波传播传播因子的变化情况,为预测真实地理环境中的电波传播特性提供了一种有效的方法。     

Singular perturbation method for short waves in random media

Abstract

The problem of wave propagation in a randomly inhomogeneous medium is considered on the basis of the parabolic equation approximation. The method of asymptotic expansions construction in powers of the radius of correlation of the random media for the moments of the wave field are proposed.     

Correlation characteristics of waves in lossy media with smooth fluctuations of the refractive index with oblique incidence on boundary

The features of coherence function (and angular spectrum) and also the fluctuation of amplitude and phase of wavefield in a random strongly absorptive medium are investigated in the case of arbitrary angle of incidence at the surface.

In this paper it is elucidated that with oblique incidence a dissipation in the random medium can accelerate the accumulation of wave fluctuations and its incoherence. This effect strongly depends on the rate of decrease of the 'wings' of the scattering indicatrix. An analytical theory (Rytov's approximation and modified method of parabolic equation) has been modelled by Monte Carlo simulation of wave propagation, and also by numerical solution of the model transfer equation. It is revealed that the width of an angle spectrum can nonmonotonically change with the immersion to the absorptive medium.     

An extended parabolic equation and its application to the calculation of transverse and longitudinal mutual coherence functions in atmospheric turbulence

An extended, wide forward angle scattering version of the parabolic equation is considered and an operator expression for the solution of the generalized nmth moment of the electromagnetic wave field is obtained. Here, 'generalized' connotes the consideration of both the transverse as well as the longitudinal spatial moments of the wave field. A unified solution for the generalized second-order moment, i.e. the mutual coherence function (MCF), is found. The solution is applied to the case of Kolmogorov turbulent fluctuations within the atmosphere. In addition to demonstrating an interesting decaying oscillatory behaviour of the longitudinal MCF in atmospheric turbulence, it is found that the use of the extended parabolic equation yields negligible corrections to the transverse MCF, as calculated from the parabolic equation in the paraxial approximation.     

Transverse spectra of waves in random media

Abstract

We consider the statistics of the transverse spectra of forward-propagating waves in a stationary random medium. A short-range perturbation solution is used to derive the difference equations that govern the long-range evolution of the ensemble-averaged transverse wave spectrum and coherence. The conditions under which these equations may be approximated by differential and integro-differential equations are given, and it is shown that the approximation is valid for the treatment of beam propagation provided that the transverse dimension of the beam is sufficiently large, and at ranges where the transverse coherence length of the beam remains larger than a wavelength. The equations that are derived are not limited by the parabolic approximation, and are amenable to numerical solution by marching techniques. We use the equation that governs the spectral density of the total energy flux, and also the propagation of waves which are statistically homogeneous in transverse planes, to show the conditions under which previously studied approximations derive from the present formulation, and to illustrate the numerical solution of the problem.     

抛物方程的多重非均匀网格模型及其应用

提出了抛物方程的多重非均匀网格模型,以准确求解三维空间存在多辐射源的电波传播问题。通过对不同辐射源建立不同的坐标系,并对其仿真空间采用不同的非均匀网格划分,构建了抛物方程的多重非均匀网格模型。在此基础上,实现了三维多辐射源问题的并行计算。实例仿真了空间存在四个辐射源的电波传播特性。结果表明,抛物方程的多重非均匀网格模型能够准确求解多源的空间电磁场分布特性,且在该算例中,并行技术使得抛物方程的计算速度提升了2.41倍,极大地提高了抛物方程对三维多源问题的求解效率。     

Propagation of circularly polarized light in media with large-scale inhomogeneities

Small-angle multiple scattering of circularly polarized waves in disordered systems composed of large (larger than the light wavelength) spherical particles is discussed. The equation for Stokes’s fourth parameter V — the difference between the intensities of the left-and right-hand polarized light — is shown to have the form similar to that of the scalar transport equation for intensity I, the only difference being the presence of an additional “non-small-angle” term responsible for depolarization. In the case of small-angle scattering, depolarizing collisions are relatively rare and, in contrast to the scalar case, the problem contains an additional spatial scale, namely the depolarization depth. The polarization degree and helicity of the scattered light are calculated for the case of purely elastic scattering and in the presence of absorption in the medium. For strong absorption, depolarization is shown to follow the transition to the asymptotic regime of wave propagation. The features appearing in strong (non-Born) single scattering are also discussed. Zh. éksp. Teor. Fiz. 115, 769–790 (March 1999)     

基于柱坐标系抛物方程和矩量法的电波传播混合算法

针对包含近源障碍物条件下的电波传播问题,提出了一种新颖的电波传播预测混合建模方法:矩量法(MOM)和圆柱坐标系抛物方程法(PEM)混合建模方法(MOM-PEM);MOM用于包含辐射源和近源障碍物的小圆柱区域内的电波传播建模,PEM用于MOM计算空间外的大区域范围内电波传播建模。MOM和PEM的计算过渡区域进行精细化网格剖分处理以避免场强数值传递的不兼容。仿真模拟了三类近源障碍物存在场景下的电波传播问题:有限开窗屏障碍物、立方体障碍物以及包含辐射源的半封闭空间障碍物,并将混合算法计算得到的结果和相同环境下采用全矩量法计算得到的结果进行了数值对比,结果表明混合算法和矩量法在精度上吻合较好。     

Resonant Processes of Scattering with Allowance for Different Populations of Magnetic Sublevels

The effect of different populations of the magnetic sublevels of the ground state on the propagation of polarized radiation through resonant media is studied theoretically. The nonlinear refractive indices for circularly and linearly polarized waves in media with arbitrary angular momenta j ₁ and j ₂ are found. The influence of the coherence between the magnetic sublevels on multiphoton effects is analyzed. It is shown that, as a result of elastic Rayleigh scattering, energy transfer from one component of the wave polarization to the other takes place. The picture of induced four-photon parametric scattering of a weak wave in the presence of a strong wave also changes.