Direct Spectrum Sensing from Compressed Measurements

Because current Cognitive Radios are limited in their operational bandwidth by existing hardware devices, much of the extensive theoretical work on spectrum sensing is impossible to realize in practice over a wide frequency band. To solve this problem, many have used Compressive Sensing (CS) in sequence with CRs: first acquiring compressed samples, then reconstructing the Nyquist Rate signal, and lastly performing spectrum sensing on the reconstructed signal. While CS alleviates the bandwidth constraints imposed by front-end ADCs, the resulting increase in computation/complexity is non-trivial, especially in a power-constrained mobile CR. This motivates us to look at different ways to reduce computational complexity while achieving the same goals. In this paper, we will demonstrate how directly performing spectrum sensing from the compressed measurements can achieve the sampling reduction advantage of Compressive Sensing with significantly less computational complexity. Our key observation is that the CR does not have to reconstruct the entire signal because it is only interested in detecting the presence of Primary Users. Our algorithm takes advantage of this observation by estimating signal parameters directly from the compressed signal, thereby eliminating the reconstruction stage and reducing the computational complexity. In addition, our framework provides a measure of the quality of estimation allowing the system to optimize its data acquisition process to always acquire the minimum number of compressed measurements, even in a dynamic spectral environment.