New algorithms for wideband spectrum sensing via compressive sensing

We consider the problem of spectrum sensing in a Cognitive Radio (CR) system when the primaries can be occupying a few subbands in a wideband spectrum. Since the primary signal dimension is large, Nyquist rate can be very high. Compressive sensing (CS) can be useful in this setup. However a CR system needs to operate at a very low SNR(~ -20dB) where the compressive sensing techniques are usually not successful. Combining them with statistical techniques can be useful. But this has been difficult because the statistics of the parameters obtained from the recovery algorithms (e.g., OMP) are not available. We develop a suboptimal recovery algorithm COR for which the statistics can be easily approximated. This allows us to use Neyman Pearson technique as well as sequential detection techniques with CS. The resulting algorithms provide satisfactory performance at -20 dB SNR. In fact COR´s recovery performance is better than OMP itself at low SNR. We also modify the algorithm for the scenario when the channel gains and the noise variance may also not be available^.