LFM宽带雷达信号的多通道盲压缩感知模型研究

在传统压缩感知(Compressed sensing, CS)基础上,提出了一种基于盲压缩感知(Blind compressed sensing, BCS)理论的线性调频(Linear frequency modulated, LFM)雷达信号欠采样与重构的多通道模型.这一机制在稀疏基未知的条件下,利用LFM信号在分数阶傅里叶变换(Fractional Fourier transform, FRFT)域上良好的能量聚集特性,将多个LFM信号看作是在多个未知阶次下FRFT域的稀疏表达,通过时延相关解线调和逐次消去相结合的的欠采样方法逐一估计出每个通道的LFM信号满足聚集性条件的特定分数阶傅里叶域,以此构造出该通道LFM信号对应的DFRFT正交稀疏基字典,以各DFRFT 正交基为对角块构建混合信号正交稀疏基字典,最后利用块重构算法从测量值中估计出稀疏信号,同时验证了LF M信号多通道BCS问题解的唯一性,从而实现了稀疏基未知情况下针对多路LFM宽带雷达信号的多通道盲压缩感知.

A Multichannel Blind Compressed Sensing Framework for Linear Frequency Modulated Wideband Radar Signals

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.