Wideband spectrum energy detection without reconstruction based on compressed samples

Spectrum energy detection should have a rapid detection speed and an acceptable anti-noise performance in practical application. In the conventional wideband spectrum energy detection based on compressed sensing, there are terrible time consuming problem and extremely bad anti-noise performance. To solve these problems, this paper makes full use of the feature that compressed samples are the linear combination of original signal in compressed sensing, then constructs a specific measurement matrix to measure the energy spectrum of original signal for the sake of obtaining the total energy message. The measurement matrix what we constructed not only satisfies the restricted isometry property (RIP), but also has some specific feature what we pursue. Finally, paper proposes a wideband energy detection method that using compressed samples to compare with energy threshold directly without reconstruction. Theoretical analysis and simulation results show that, our algorithm can greatly improve the detection speed and have a better anti-noise performance relative to the conventional energy detection method.