Range dependence of volume scattering from a fractal medium: Simulation results

Range variation of scattered signal power in atmospheric radar experiments seems to be well understood for a point target and for volume scattering from a homogeneous random medium. In these cases the signal power decays, respectively, as inverse fourth power and inverse square of range. Intermediate cases of scattering from patchy random media with partial space‐filling characteristics are numerically examined for a simple fractal model. Planar targets, oriented along the beam, are successively divided into cells of smaller size, eventually reduced to isotropic “point” targets. At each stage of division the cells are activated with a probability p. This probability controls the degree to which the medium fills the scattering region, and it is related to its fractal dimension D. For each realization of the medium the signal power is obtained by coherently adding the complex received voltage due to each point target. It is found that volume scattering is a good approximation even for targets that only fill up a plane, i.e., have fractal dimension D∼2.