A Modified Regularized Adaptive Matching Pursuit Algorithm for Linear Frequency Modulated Signal Detection Based on Compressive Sensing

Compressive Sensing (CS) is a novel signal sampling theory under the condition that the signal is sparse or compressible. It has the ability of compressing a signal during the process of sampling. Reconstruction algorithm is one of the key parts in compressive sensing. We propose a novel iterative greedy algorithm for reconstructing sparse signals, called Modified Regularized Adaptive Matching Pursuit (MRAMP). Compared with other state-of-the-art greedy algorithms, MRAMP has the characteristics of several approaches: the speed and transparency of Orthogonal Matching Pursuit (OMP), the strong uniform guarantees of l1-minimization and the most innovative feature is its capability of signal reconstruction without prior information of the sparsity as Sparsity Adaptive Matching Pursuit (SAMP). Recently, the idea of CS has been used in radar system, and the concept of Compressive Sensing Radar (CSR) has been proposed in which the target scene can be sparsely represented in the range domain. CS plays an important role in the detection of Linear Frequency Modulated (LFM) signal. A sparse dictionary which could match LFM signal is constructed, and with the dictionary we can get access to a more effective sparse signal, then LFM signal can be calculated according to classical least square solution. Simulation results show that by using the method this paper proposed, it outperforms many existing iterative algorithms, especially for compressible signals.