Equivalent Number of Scatterers for SAR Speckle Modeling

In this paper, the equivalent number of scatterers of a rough scattering surface is defined, physically justified, and evaluated. New-generation spaceborne synthetic aperture radar (SAR) sensors are acquiring images at such a high ground resolution that, quite often, the statistics of these images do not match with those predicted by the classical Rayleigh speckle model. Non-Rayleigh speckle is frequently mathematically modeled via K-distribution in terms of a parameter that presently can be estimated (i.e., a posteriori) on the SAR images and is linked to the number of scatterers per resolution cell. However, to model and predict (i.e., a priori) the statistical behavior of the SAR images, a full characterization of the scatterers is required. To this aim, the concept of equivalent number of scatterers of a rough scattering surface is here defined and physically justified. This parameter is then analytically evaluated in closed form as a function of the roughness of the illuminated surface and of SAR sensor parameters. The presented analytical evaluation applies to both classical and fractal descriptions of the surface roughness. Finally, the dependence of the equivalent number of scatterers on the roughness of the illuminated surface and on SAR sensor parameters is analyzed for a range of values of roughness parameters actually encountered in natural surfaces and by considering typical system parameters of modern high-resolution spaceborne SAR systems. It is shown that, actually, for some combinations of realistic surface and system parameters, the equivalent number of scatterers can be on the order of unity.