ABSTRACT
The distributions are said to be
infinitely divisible
. This is a useful property in the statistical analysis of system performance. For example, the coherent addition of independent vectors is often used to model the effect of illuminating independently contributing elements of a scattering target. Since one might anticipate that the number of independent scatterers will be proportional to the total area illuminated for the case of an extended target, a plot of normalized second moment against (1/illuminated area) should be a straight line from the ordinate two at abscissa zero, which corresponds to the large illuminated area limit. This behavior has indeed been observed in light scattering experiments [6]. However, it does not appear to hold for microwave sea echo near grazing incidence, where it is found experimentally that the
K
-distribution shape parameter scales like resolution length to the power of 5/8 [7]. This is probably a consequence of shadowing and the multiscale nature of the sea surface, which requires a more sophisticated definition of “independent” contributing areas than used in the previous argument. It has recently been shown how the required range correlation of
K
-distributed microwave sea echo can be simulated numerically through memory-less nonlinear transformation of a fractal [8].
