Compressive detection with sparse random projections

Abstract

This paper addresses the problem of sparse signal detection based on compressive sensing (CS) framework. In order to reduce the computational complexity of detection, we propose a sparse compressive detection approach by substituting sparse random projection matrix for conventional dense matrix, and develop a theoretical model that exactly characterizes the relationship of the detection probability with the number of measurements, the signal-to-noise ratio (SNR), as well as the degree of sparsity. Simulation results show that the performance of the proposed detector is comparable to the conventional CS detector in which Gaussian dense projections are employed.