Fractal property of sea clutter FRFT spectrum for small target detection

Because the detection of small target in the background of sea clutter is strongly influenced by the sea condition, this paper studies the fractal property of sea clutter in fractional Fourier transform (FRFT) domain and proposes the fractal detection method in single and high dimensions. The FRFT deduced from mathematical definition is not consistent with the self-similar properties in orders and scales. Multifractal detrended fluctuation analysis (MF-DFA) method is used to determine the fractal parameter H(q) and analyze the fractal property of the sea clutter in different situations, distances, and polarizations. In single dimension, the small target detection method is proposed based on an adaptive order. By comparing different factors of the multifractal parameters, the results show that the transform order method in sea clutter FRFT domain can detect small signals under complicated sea conditions. The detection threshold mostly increases above 200%, which is 26.3% higher than the method of time domain signal. H (q) has an obvious multifractal difference on high negative scale, the H(q)-q curve satisfies the arctangent distribution. The fitting amplitude ratios of pure sea clutter and target data are greater than 1.8 (HH) and 1.4 (VV), which provide the basis for the small target detection in sea clutter background.