Compressive Sampling for Signal Detection

Compressive sampling (CS) refers to a generalized sampling paradigm in which observations are inner products between an unknown signal vector and user-specified test vectors. Among the attractive features of CS is the ability to reconstruct any sparse (or nearly sparse) signal from a relatively small number of samples, even when the observations are corrupted by additive noise. However, the potential of CS in other signal processing applications is still not fully known. This paper examines the performance of CS for the problem of signal detection. A generalized restricted isometry property (GRIP) is introduced, which guarantees that angles are preserved, in addition to the usual norm preservation, by CS. The GRIP is leveraged to derive error bounds for a CS matched filtering scheme, and to show that the scheme is robust to signal mismatch.