Signal Detection for Cognitive Radios with Smashed Filtering

Compressed sensing and the related recently introduced smashed filter are novel signal processing methods, which allow for low-complexity parameter estimation by projecting the signal under analysis on a random subspace. In this paper the smashed filter of Davenport et al. is applied to a principal problem of digital communications: pilot-based time offset and frequency offset estimation. An application, motivated by current cognitive radio research, is wide-band detection of a narrowband signal, e.g. to synchronize terminals without prior channel or frequency allocation. Smashed filter estimation and maximum likelihood-based, uncompressed estimation for a signal corrupted by additive white Gaussian noise (matched filter estimation) are compared. Smashed Filtering adds a degree of freedom to signal detection and estimation problems, which effectively allows to trade signal-to-noise ratio against processing bandwidth for arbitrary signals.