Spectrum sensing is one of the key technologies to realize spectrum reuse and increase the spectrum efficiency in cognitive radio networks (CRNs). In this paper, we study energy-efficient cooperative multi-channel spectrum sensing in CRNs. We first propose a cooperative spectrum sensing and accessing (CSSA) scheme for all the secondary users (SUs). The SUs cooperatively sense the licensed channels of the primary users (PUs) in the sensing slot. If a channel is determined to be idle, the SUs which have sensed that channel will have a chance to transmit packets in the data transmission slot. We then formulate this multi- channel spectrum sensing problem as a coalition formation game, where a coalition corresponds to the SUs that have chosen to sense and access a particular channel. The utility function of each coalition takes into account both the sensing accuracy and energy efficiency. We propose distributed algorithms to find the optimal partition that maximizes the aggregate utility of all the coalitions in the system. We prove analytically that the proposed algorithms terminate at a stable partition that achieves the optimal aggregate utility. Simulation results show that the proposed algorithms result in the self-organization of the SUs that achieves a higher aggregate utility after each iteration. Also, the convergence and optimality of the proposed algorithms are proved by simulation results.
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