Source number estimation algorithm for wideband LFM signal based on compressed sensing

Because of the samples which gained through compressive measurement effectively preserve the features information of the original signal, Compressed Sensing (CS) has been successfully applied to the detection and parameter estimation of Linear Frequency Modulation (LFM) signal. However, the source number of multi-component signal often be used as a prior knowledge which is out of accord with the practice. In this paper, we proposed a source number estimation algorithm based on compressed sensing. In particular, we analyzed the algorithm's shortcoming under low Signal to Noise Ratio (SNR) condition in theory and proposed an improved algorithm to solve the problem. The theoretical analysis and simulation results both proved that the proposed improved algorithm has a better anti-noise performance than the original algorithm under the condition SNR ≤ 3dB. Furthermore, compared with the conventional algorithm, the improved algorithm in this paper could obtain a higher correct rate of source number estimation with few samples under low SNR.