Compressive detection of unknown-parameters signals without signal reconstruction

•We propose to detect unknown-parameters signal by using compressed sensing method under low SNR without signal reconstruction.•We model the distribution of each element in the sparse vector, and design the detector via comparing the maximum element with the threshold.•The performance of the proposed detector is formulated and receiver operating characteristic (ROC) is drawn in this paper.

A novel algorithm for detecting compressed signals in low Signal-Noise-Ratio (SNR) without signal reconstruction is proposed in this letter. When signals are projected in a sparse domain, the sparse vector with fixed position of non-zero elements is obtained and the non-zero elements obey Rician distribution. However, additive white Gaussian noise (AWGN) is not sparse in this transformed domain, and the weight vector element amplitudes follow Rayleigh distribution while the AWGN is projected in the field. Thus, the distribution of sparse vector element amplitudes (SVEA) is considered to design a detector for an unknown-parameters signal. In addition, the accumulation of sparse vector in a sparse domain solves the problem of low-SNR signal detection. Later, the performance of the proposed detector is studied, and computer simulations show that it can detect the signals with a probability of 95% under the conditions that SNR=−28dB and compressive ratio M/N=0.15. Furthermore, the receiver operating characteristic (ROC) theoretical and simulation curves are drawn.