SGER: Physics-Based Propagation Models for Wireless Communications

99010804Parker用镜像法给出了无限大理想导体地平面上或部分埋在无限大理想导体地平面上的介质球散射体的电磁散射问题的解析解。这是为开发新的无线通信传播模型而引入的一系列规范问题之一。基本假设是，地球可以用一个球体来模拟，其表面最初被认为是局部光滑和平坦的，而它上面的所有物体都可以用球体/椭球体来模拟，其中一些可能部分埋在地下。模型中使用的所有球体/椭球体的范围从一个极端的完全导电到另一个极端的复介电常数不完全导电。这一正则问题的解对于分析塑料地雷、冰山、粗糙表面等复杂三维体的散射特别相关，其中假设的局部平坦背景可以用地平面来模拟，而复杂物体可以用自由空间中的球体/椭球或球体/球体系统来模拟，或者部分地埋在地平面中。假定入射波为任意入射角的均匀平面电磁波。用镜像的方法，用两个大小相等的重叠球体代替地平面中的部分埋藏的球体，或者如果球体位于地平面上，则用两个大小相等的相互接触的球体和一个辅助的入射平面电磁波来代替，使得在原问题中地平面所在的所有点上总电场是满足的。入射场、补充场和散射场用适当的球面波函数表示。为了在球体表面施加边界条件，利用球面波函数的平移加法定理，将一个球体散射场的坐标系表示为另一个球体的坐标系，从而得到一个矩阵方程，该矩阵方程可以数值求逆，从而恢复散射场系数。问题的表述使得每个球面上的边界条件也可以通过迭代方法来满足。这种迭代过程一直持续到解收敛，而且由于每次迭代得到散射场系数并在下一次迭代中使用，因此它具有不需要矩阵求逆的明显优点。通过精确方法和迭代方法得到散射场系数，由此可以计算任何地方的散射场。为了解决逆散射问题，我们采用了一种径向基函数网络，该网络由四个输入层、一个高斯非线性函数的隐层和一个三个输出层组成。输入层的4个输入是TE和TM极化情况下计算的散射场复系数的实值和虚值，输出是训练球的电半径、埋距和相对介电常数。然后使用具有指定范围的电半径和指定数量的学习数据样本(每个输出50个)的正交最小二乘算法来训练该网络，以便为与学习数据不同的新数据(通常是实验数据)检索测试球的半径、埋藏距离和相对介电常数。

99010804ParkerAn analytic solution of the problem of electromagnetic scattering by a dielectric spherical scatterer resting on, or partially buried in, an infinite perfectly conducting ground plane is formulated using the method of images. This is one of a series of canonical problems introduced to develop new propagation models for wireless communications. The basic assumption is that the earth can be modeled by a sphere whose surface is initially considered to be locally smooth and flat, while all objects above it can be simulated by spheres/spheroids, some of which may be partially buried in the ground. All the spheres/spheroids used in the model range from perfectly conducting on the one extreme to imperfectly conducting- with complex permittivity on the other extreme. The solution of this canonical problem is particularly relevant to analyzing the scattering by complex three-dimensional bodies, such as plastic mines, icebergs, rough surfaces, etc., in which the assumed locally-flat background can be modeled by the ground plane and the complex body can be simulated by a sphere/spheroid or a system of spheres/spheroids in free space or partially buried in the ground plane. The incident wave is assumed to be a uniform plane electromagnetic wave of arbitrary angle of incidence. The method of images is applied to replace the partially buried sphere in a ground plane by two overlapping spheres of equal size, or by two touching spheres of equal size if the sphere is resting on the ground plane, and a supplementary incident plane electromagnetic wave such that the total electric field is satisfied at all points where the ground plane is located in the original problem. The incident, supplementary and scattered fields are expressed in terms of appropriate spherical wave functions. To impose the boundary conditions on the surfaces of the spheres, the translation addition theorem for the spherical wave functions are used to express the coordinate system of the scattered field from one sphere in terms of the coordinate system of the other sphere leading to a matrix equation which can be inverted numerically to recover the scattered field coefficients. The problem is formulated such that the boundary condition on the surface of each sphere can also be satisfied by an iterative approach. This iterative procedure continues until the solution converges, and has the obvious advantage that it does not require matrix inversion since the scattered field coefficients in each iteration are obtained and used in the next iteration. The scattered field coefficients generated by the exact and iterative methods are obtained, from which the scattered field can be evaluated everywhere. In particular, the scattering cross section can be calculated as a function of the sphere radius and permittivity as well as the burial distance for any specified angle of incidence.In order to solve the inverse scattering problem, we employ a radial basis function network which consists of an input layer with four inputs, a hidden layer using Gaussian nonlinearity functions, and an output layer with three outputs. The four inputs in the input layer are the real and imaginary values of the computed scattered field complex coefficients for the TE and TM polarization cases, while the outputs are the electrical radius and burial distance of the training sphere as well as its relative permittivity. This network is then trained using the orthogonal least-squares algorithm with a specified range of the electrical radius and a specified number of learning data samples (50 for each output) to train the network in order to retrieve the radius, burial distance and relative permittivity of the test sphere for new data (usually experimental) which is different from the learning data.***