Statistical characteristics of microwave signals scattered from a randomly rough surface

Scattering of microwave signals from rough surfaces has been extensively studied. However, a vast majority of such studies is on the characteristics of the normalized scattering cross section. This paper is an investigation of the statistical characteristics of scattered signals. When the area of illumination is large it is seen that the scattering from a rough surface may be considered to be contributions from a large number of individual cells. One may hence appeal to the central limit theorem and show that the amplitude of the scattered signal satisfies the Rayleigh distribution. This observation was first made by Rayleigh a hundred years ago for the general case of randomly scattered signals. Beckmann demonstrated that similar arguments and deductions may be employed for the case of scattering from rough surfaces. It is apparent that certain conditions are necessary to deduce that the amplitude statistics are Rayleigh distributed. When such conditions do not exist the amplitude statistics are not Rayleigh and in such situations we would like to know which statistical distribution is most representative. It has been found that the K-distribution is a good model for randomly scattered signals. We consider this and some other appropriate non-Rayleigh statistical distributions. For our study we used numerically simulated signals scattered from a randomly rough surface. We employ the moment method to estimate the parameters of the various distributions. We next use Kolmogorov-Smirnov statistic to determine which of the distributions most closely fit the simulated data.