Fast matching pursuit for wideband spectrum sensing in cognitive radio networks

Wideband spectrum sensing is one of the most challenging components of cognitive radio networks. It should be performed as fast and accurately as possible. Traditional wideband spectrum sensing techniques suffer from the requirement of analog-to-digital converters with very high sampling rates. Compressed sensing has been recently considered as a technique that may enable wideband spectrum sensing at a much lower sampling rate than that dictated by the Nyquist theorem. However, the complexity and speed of existing compressed sensing reconstruction techniques remained a barrier for such an application. In this paper, we introduce fast matching pursuit (FMP), a fast and accurate greedy recovery algorithm for compressed sensing. We show that the spectral data are sparse in the Haar wavelet and wavelet packet domains. We apply FMP to wideband spectrum sensing for cognitive radio networks. Our proposed algorithm is capable of reconstructing spectrum signals from samples at a rate of about 25% of the Nyquist rate, significantly faster than other related algorithms, at more than 99% probability of detection and less than 1% probability of false alarm.