On the Amplitude Distributions of Bistatic Scattered Fields From Rough Surfaces

Non-Rayleigh distributed radar clutter is widely reported in studies of radar scattering from sea and land surfaces. Existing models of scattered field amplitude distributions have been developed primarily through empirical fits to the statistics of radar backscatter measurements. In contrast, this paper investigates a physics-based approach to determine the amplitude distributions of fields scattered from rough surfaces using Monte Carlo simulations and analytical methods, for both backscattering and bistatic configurations. The rough surface is represented using a “two-scale” model. An individual surface facet contains “small-scale” roughness, for which scattered fields are evaluated using the second-order small slope approximation. Individual surface facets are tilted by the slopes of the “large-scale” roughness in a given observation. The results show that non-Rayleigh amplitude distributions are obtained when tilting is performed, and that the departure from the Rayleigh distribution becomes more significant as the variance of the tilting slope increases. Further analysis shows that this departure results from variations in the mean scattering amplitude from a facet (the texture) as tilting occurs. The distribution of the texture is studied and compared with existing models. Finally, the distribution of the scattered field amplitude is modeled through the compound Gaussian model, first using the distribution of the texture, and then in terms of the probability density function of tilting slopes (which avoids the requirement of the knowledge of the texture distribution). The results from the above two methods are in good agreement and both agree well with the Monte Carlo simulation.