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In this paper, we present a novel hybrid framework combining compressive spectrum sensing with geo-location database to find spectrum holes in a decentralized cognitive radio. In the hybrid framework, a geo-location database algorithm is proposed to be stored locally at secondary users (SUs) to remove the extra transmission link to a centralized remote geo-location database. Specifically, by utilizing the output of the locally stored geo-location database algorithm, a data-assisted noniteratively reweighted least squares (DNRLS)-based compressive spectrum sensing algorithm is proposed to improve detection performance under sub-Nyquist sampling rates for wideband spectrum sensing, and to reduce the computational complexity of signal recovery. In addition, an efficient method for the calculation of maximum allowable equivalent isotropic radiated power in TV white space (TVWS) is also designed to further …