Compressive Sampling and Reconstruction for LFM Signals with Unknown Modulating Rate Based on Gabor Space

In order to solve the problems existing in the current compressive sampling systems， such as the inapplicability of sampling system and the dependence for modulation information， a compressive sampling and reconstruction method based on Gabor space is proposed to realize the compressive sampling and effective reconstruction for LFM signals under the condition of unknown modulation rate. Firstly， combined with compressive sensing theory and translation invariant space theory， the compressive sampling system based on Gabor space is designed. The components and working principle of the compressive sampling system are analyzed. Then， utilizing the sparsity of signals in Gabor space， the compressive and reconstruction models of Gabor coefficients are established. The upper bound of the reconstruction error is also analyzed with full considerations of noises and mismatch. Finally， the effectiveness of the proposed method is verified by numerical simulation. The results show that the compressive sampling system based on Gabor space has the advantages of low sampling rate， low sample number and high working robustness.