Simulation of a Radio Signal Scattered from a Rough Surface by the Method of Stationary Points

Abstract

Introduction. Many radar and radio navigation problems require adequate (i.e., corresponding to the physics of radio wave scattering under a certain set of conditions) simulation of a radio signal scattered from a rough surface. At present, four categories of mathematical models are used for these purposes, with each corresponding to a particular group of methods for solving the scattering problem. These methods include those based on a rigorous solution of the electrodynamic equations (methods of moments, finite elements, finite differences); approximate methods for solving electrodynamic problems (methods of small perturbations, tangent plane (Kirchhoff method), two-scale model); those of statistical equivalents; and phenomenological models. In the former two categories, the electromagnetic field is computed on a surface grid, whose step must be much smaller than the signal wavelength. This makes the simulation of a scattered radio signal effectively unrealizable for two-dimensional rough surfaces. The method of statistical equivalents is based on the calculation of the probabilistic characteristics of a scattered signal. Difficulties arising in this case narrow the possibilities of simulation, largely due to the impossibility of obtaining closed expressions for the required characteristics without significant simplifications. In addition, carrying out analytical calculations, the solution is restricted to the class of surfaces with the Gaussian distribution of roughness heights. Phenomenological models, although providing for a qualitative analysis of signal scattering from a rough surface, fail to take the physics of the scattering process into account.Aim. To create a simple and adequate model of a signal scattered from a two-dimensional rough surface using the tangent plane approximation of the boundary conditions (the Kirchhoff method), which can be realized on modern computers.Materials and methods. The proposed model of the scattered signal is based on its representation as a sum of signals reflected from stationary points on the surface, i.e., those points where the law of specular reflection of the incident electromagnetic wave is locally fulfilled.Results. The implementation of the model is reduced to determination of the positions of stationary points on a twodimensional rough surface. This problem is solved on modern computers quite simply without computations with complex numbers. It turns out that the number of stationary points, even with a large surface roughness, rarely exceeds two. This fact, along with the simplicity of finding the coordinates of stationary points, makes this model suitable for long series of statistical runs.Conclusion. The proposed model is easy to implement and can be used to study the accuracy of low-altitude target estimation, altimeters, Doppler and correlation speed and drift angle estimators.