LFM signal sampling and reconstruction based on compressed sensing and swept-frequency theory

Linear frequency modulated (LFM) signal is widely used in radar, sonar and communication system. In some application scenarios, the LFM signal should have ultra-wide band (UWB), with the result that the general hardware sampling system cannot satisfy the requirement of Nyquist sampling rate. Theory of compressed sensing (CS) enables the successful reconstruction of sparse signal by sampling at a sub-Nyquist sampling rate. However, LFM are not sparse enough in the traditional Fourier transformation domain. In this paper, we propose a method based on the theory of Factional Fourier Transformation (FRFT) domain to improve the performance of LFM signal reconstruction. First, we present an orthogonal discrete FRFT matrix as the sparse dictionary which will reduce the sparsity level. Second, a swept-frequency modulator based on FRFT domain, has been implemented to estimate parameters of LFM signal. Besides, it also improves the signal reconstruction result and reduces sampling rate. Finally, simulations are taken on testing the proposed framework on LFM signals, and evaluation results demonstrate high feasibility and efficiency of this method.