Supervised Dictionary Learning for Block Threshold Feature in Compressive Spectrum Sensing

With the development of communication systems towards the high-frequency band, the demand for spectrum resources is ever-increasing, where the research interest has changed from narrowband spectrum sensing to wideband spectrum sensing. The Nyquist-rate-based wideband spectrum sensing with high-rate sampling is being questioned whether it is suitable for real-time applications. On the contrary, the well-known compressive spectrum sensing (CSS) is more appealing due to the compressive sensing (CS) technology, resulting in lower signal acquisition costs. However, the CS algorithms for recovering sparse spectrum generally require multiple iterations, which presents a challenge to the low complexity implementation of spectrum sensing. To address this issue, this paper proposes a novel method for solving the block CSS (BCSS) problem, where the spectrum of primary users is modeled as a block structure signal. Specifically, the block threshold feature (BTF) is utilized to reconstruct the spectrum while bypassing any iterative operations. Furthermore, to improve the performance of the BTF-based BCSS, we develop a novel supervised dictionary learning (SDL) model, based on the theoretical analysis of mutual incoherence and restricted isometry properties. Simulation results not only verify the compatibility of BTF and the SDL model, but also demonstrate the effectiveness and robustness of SDL-BTF-based BCSS for practical implementation.