Comparison of scattering from fractional Brownian motion and asymptotic fractional Brownian motion rough surfaces

An asymptotic fractional Brownian motion (afBm) model is introduced by extending the self-similarity condition in fBm. then the incremental Fourier synthesis algorithm is applied to generate fBm and afBm rough surfaces, and an estimation algorithm is presented to extract the generalized multiscale Hurst parameter. Finally, the bistatic- and back-scattering coefficient from fBm and afBm rough surfaces is calculated with method of moments (MOM). By comparison it can be concluded that a single Hurst parameter in fBm model is insufficient for the complete description of rough surfaces, and other parameters should be considered just as in the afBm model.