Abstract: A novel multichannel framework of sub-Nyquist sampling and reconstruction for linear frequency modulation (LFM) radar echo signal is proposed based on the theory of blind compressive sensing (BCS). Making use of good energy concentration of LFM signal in proper fractional Fourier transform (FRFT) domain to determine the optimal order meeting the convergence condition, this mechanism takes LFM echo signals as a sparse linear combination of an unknown order p of fractional Fourier transform (FRFT) domains. Based on subsampling, time delay correlation and direct dechirp operation, the sparse FRFT domains corresponding to the chirp rates are estimated unambiguously one by one. Then it constructs discrete FRFT (DFRFT) basis dictionary according to the specific sparse FRFT domain dominated. To reconstruct the sources, the fast group reconstruction algorithms are chosen for less data storage and lower computational complexity. Finally, simulations are taken to show that the proposed framework can realize undersampling and reconstruction without priori knowledge of sparse basis for LFM radar echo signals under the theory of blind compressive sensing, and to verify the feasibility and efficiency of the novel method.