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Cognitive radio allows unlicensed (cognitive) users to use licensed frequency bands by exploiting spectrum sensing techniques to detect whether or not the licensed (primary) users are present. In this paper, we present a compressed sensing applied to spectrumoccupancy detection in wideband applications. The collected analog signals from each cognitive radio (CR) receiver at a fusion center are transformed to discretetime signals by using analogtoinformation converter (AIC) and then employed to calculate the autocorrelation. For signal reconstruction, we exploit a novel approach to solve the optimization problem consisting of minimizing both a quadratic (l2) error term and an l1regularization term. In specific, we propose the Basic gradient projection (GP) and projected BarzilaiBorwein (PBB) algorithm to offer a better performance in terms of the mean squared error of the power spectrum density estimate and the detection probability of licensed signal occupancy.
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