A novel framework of sub-Nyquist sampling and reconstruction for linear frequency modulation (LFM) radar signals based on the theory of blind compressed sensing (BCS) is proposed. This structure takes LFM signals as a sparse linear combination under an unknown transform order \(p\) in fractional Fourier transform (FRFT) domain. First, making good use of energy concentration of LFM signal in the proper FRFT domain, we determine the optimal order \(p\) which meets the convergence conditions under subsampling condition. Second, discrete fractional Fourier transform (DFRFT) sparse basis is constructed according to the specific sparse FRFT domain dominated by \(p\). Third, based on the DFRFT basis dictionary, using the random demodulator and block reconstruction algorithm, a LFM signal subsampling and reconstruction system is designed in the framework of BCS theory. With this system, the unknown LFM signal in radar system can be sampled at about 1/8 of Nyquist rate without the knowledge of priori sparse basis, but still can be reconstructed with overwhelming probability. Finally, simulations are taken on verifying the feasibility and efficiency of the proposed method, the novel framework can bring a new way to subsample and reconstruct LFM signals under the environment of non-collaboration.
Blind compressed sensing (BCS) Linear frequency modulated (LFM) Fractional Fourier transform (FRFT) Sub-Nyquist sampling Random demodulator
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