A Weak Signal Detection Algorithm based on Accumulation of Sparse Domain Element Location Information

In this paper, a new algorithm is proposed to detect weak signal based on Compressive Sensing(CS) and the sparse feature of the signal. When the sparse signal is projected in a special dictionary, we can obtain the sparse vector whose positions of non-zero elements are fixed. When the Gaussian white noise is projected in a dictionary, the weight vector whose positions of non-zero elements presents the characteristics of uniform distribution. In our study, the proposed method can accomplish the accumulation of weak signal in the sparse domain with the characteristics of the sparse representation mentioned above. The threshold is obtained by calculating the correlation of the positions non-zero elements of the Gauss white noise and the positions of non-zero elements of the signal to finish detecting the target signal. Finally, the simulations verify the proposed algorithm can achieve detecting the signal precisely with a low signal-to-noise ratio(SNR) of -15dB.