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In cognitive radio networks, multiple discontinuous spectrum opportunities are detected by spectrum sensing and utilized together to satisfy the service requirement by spectrum aggregation. In this paper, we develop an analytical framework for joint spectrum sensing and access scheme based on Partially Observable Markov Decision Process (POMDP). Considering the hardware limitations, the spectrum aggregation range is restricted and only a part of channels can be sensed. For obtaining the reward function of POMDP, the channel switch probability is estimated by theoretic deduction. Under this POMDP framework, an optimal spectrum sensing and access scheme is proposed to minimize the channel switch times. Simulation results show that our proposed optimal scheme reduces the times of channel switches significantly.