关键词: 压缩感知, 线性调频信号, 分数阶傅里叶变换, 欠采样, 盲压缩感知

Abstract:

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 mechanism takes LFM signals as a sparse linear combination under an unknown order p of fractional Fourier transform (FRFT) domain. Firstly, we make use of the scheme of delays correction dechirp and good energy concentration of LFM signal in proper FRFT domain to determine the optimal order, which meets the convergence conditions. Secondly, we construct discrete FRFT (DFRFT) basis dictionary according to the specific sparse FRFT domain dominated by p. To reconstruct the sources, group sparse reconstruction algorithms are chosen with less data storage and lower computational complexity. Finally, the results are provided to verify the uniqueness of the proposed framework, realizing the undersampling and reconstruction without the knowledge of priori sparse basis for LFM radar signals under the theory of BCS. The novel framework can bring a new solution concerned about the under-sampling and detection for LFM signals under the environment of non-collaboration.

Key words: compressed sensing, linear frequency modulated, fractional Fourier transform, under-sampling, blind compressed sensing