Sparse Fractional Energy Distribution and its Application to Radar Detection of Marine Targets with Micro-Motion

The fractional Fourier transform (FRFT), a time-frequency analysis tool, is an effective tool for non-stationary signal processing. Some non-stationary signals, especially chirp signals, appear sparse in fractional Fourier domain (FRFD). To leverage this inherent sparsity, by combining adaptive atomic decomposition in FRFD with sparse representation technique, a novel energy density function, called sparse fractional energy distribution, is proposed for signals that are sparsely represented in FRFD. The relationships between the proposed distribution and other time-frequency distributions are depicted. The performance of the proposed distribution in chirp signal processing is analyzed. Both the theoretical analysis and simulations demonstrate that the proposed distribution achieves multicomponent resolution and robustness against noise. Furthermore, the application to detection and extraction for marine target with micro-motion of the proposed distribution is presented. Experiments are conducted to validate that the proposed distribution can yield promising detection results.