Performance analysis of stochastic signal detection with compressive measurements

Compressed sensing (CS) enables the recovery of sparse or compressible signals from relatively a small number of randomized measurements compared to Nyquist-rate samples. Although most of the CS literature has focused on sparse signal recovery, exact recovery is not actually necessary in many signal processing applications. Solving inference problems with compressive measurements has been addressed by recent CS literature. This paper takes some further steps to investigate the potential of CS in signal detection problems. We provide theoretical performance limits verified by simulations for detection performance in arbitrary random signal detection with compressive measurements.