Fractal characteristic in frequency domain for target detection within sea clutter

This study mainly describes the fractal property of the frequency spectrum of the sea clutter and the application of the obtained fractal characteristic in frequency domain to the constant-false-alarm-rate (CFAR) target detection within sea clutter. First, this study takes fractional Brownian motion (FBM) for example, and the spectrum of the FBM is proved to be fractal theoretically on condition that the time series of the FBM is fractal. This argument lays the foundation for the application of fractal theory to the frequency spectrum. Next, X- and S-band real radar data are used for the verification of the fractal property of the real sea clutter frequency spectrum. Finally, the effects of the length of the time series and fast Fourier transform (FFT) are analysed in detail. The results show that the frequency spectrum of the real sea clutter is fractal in the statistical sense and the frequency Hurst exponents of clutter range bins and target range bins are distinguishable. Therefore the frequency Hurst exponent is used for the CFAR target detection within sea clutter.