Detection and Reconstruction for LFM Echo Signal Based on Blind Compressed Sensing

A novel framework of sub-Nyquist sampling and reconstruction for linear frequency modulation (LFM) radar echo signal based on the theory of blind compressive sensing is proposed. This mechanism takes LFM echo signals as a sparse linear combination under an unknown order p of fractional Fourier transform (FRFT) domain. Firstly, make use of good energy concentration of LFM signal in proper FRFT domain to determine the optimal order, which meets the convergence conditions. Secondly, construct DFRFT basis dictionary according to the specific sparse FRFT domain dominated by p. To reconstruct the sources, the simple orthogonal matching pursuit (OMP) is chosen with less data storage and lower computational complexity. Finally, simulations are taken on testing the proposed framework, realizing the undersampling and reconstruction without the knowledge of priori sparse basis for LFM radar echo signals, and the results are provided to verify the feasibility and efficiency of the novel method.