Energy detectors for sparse signals

In this paper, compressive sampling (CS) based energy detectors are developed for sparse communication signals, namely, pulse-position modulation (PPM) and frequency shift-keying (FSK) signals so as to reduce the complexity and sampling rate at the receiver. We focus on noncoherent detection, thereby avoiding the channel estimation step. Exact bit error probability (BEP) expressions for receivers sampling at the Nyquist rate are derived to ascertain the performance of CS-based energy detectors. Simulation results provide insight into the choice of measurement matrices for a practical implementation of CS.