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提出一种新的基于压缩感知CS(Compressed Sensing)理论的LFM信号检测算法。利用LFM信号在分数阶Fourier变换(Fractional Fourier Transform,Fr FT)域稀疏的特点,构造Fr FT矩阵作为LFM信号的稀疏变换基,通过少量待检测LFM信号的随机投影,求解信号在Fr FT域的系数向量,然后对该系数向量进行检测判决,进而达到对感兴趣信号检测的目的。理论分析和仿真实验表明,随机投影点数低至奈奎斯特采样点数的1/10、信噪比低至-8 d B时,该算法对感兴趣的LFM信号检测的成功率可达到95%以上,并且对强窄带干扰不敏感;与波形一致算法相比,该算法在相同信噪比条件下,可以获得更高的信号检测概率。
A new LFM signal detection algorithm based on Compressed Sensing (CS) theory is proposed. The Fr FT matrix is constructed as a sparse transform base of LFM signal by using the feature of LFM signal sparse in Fractional Fourier Transform (Fr FT) domain. By stochastic projection of a small amount of LFM signal to be detected, the Fr FT matrix Coefficient vector, and then the coefficient vector detection decision, and then to achieve the purpose of detecting the signal of interest. Theoretical analysis and simulation results show that the success rate of LFM signal detection can reach 95% when the number of random projection points is as low as 1/10 of the Nyquist sampling points and the SNR is as low as -8 d B, , And is not sensitive to strong and narrowband interference. Compared with the waveform consistent algorithm, this algorithm can obtain a higher signal detection probability under the same signal-to-noise ratio.