Extended fractal analysis of sea clutter frequency spectrum

Extended self-similar (ESS) process, as a generalized fractional Brownian motion (fBm) process, characterizes rough surfaces by a series of extended Hurst exponents instead of one single Hurst parameter that is used in the fBm process. So the ESS process is able to provide more clues about the local roughness of the surface at different scales. In this paper, the ESS process is applied to modelling the sea clutter frequency spectrum, for the reason that (a) for coherent radar, the signal-to-clutter ratio (SCR) can be promoted effectively by Fourier transform (namely in frequency domain); (b) through Fourier transform, the self-similarity in time domain can be held in frequency domain in statistical sense. Then based on X-band real sea clutter data, the extended self-similarity and the local roughness of the sea clutter frequency spectrum at different scales are analyzed. The results show that at some specific scales the extended Hurst exponents are sensitive to the existence of a target. And this sensitivity is propitious to promoting the performance of detecting weak moving target within sea clutter.