Study on the fractional power spectrum of the scattered echoes from 1-D time-varying sea surface

The classical two-scale model based on linear hydrodynamics may account for the “slow signals” which include Bragg scattering from both free and bound capillary waves but it is insufficient to describe the non-Bragg scattering from “fast scatterers” associated with breaking wave crests. Here, a realistic model of the time-varying sea surface with a quadratic phase is proposed and the characteristic of fractional power spectrum (FPS) of scattered echoes is investigated. The FPS of the proposed scattered field is found to be distributed as sum of sinc functions, whose locations in the fractional Fourier domain are relative to the chirp rate and central frequency of the 1-D sea surface model. Numerical results using X-band real sea clutter data prove that the proposed model provides a good description of the time-varying sea surface especially for the analysis of non-Bragg scattering.