Dynamic spectrum access policy is crucial in improving the performance of overlay cognitive radio networks.Most of the previous works on spectrum sensing and dynamic spectrum access consider the sensing effectiveness and spectrum utilization as the design criteria,while ignoring the energy related issues and QoS constraints.In this article,we propose a QoS provisioning energy saving dynamic access policy using stochastic control theory considering the time-varying characteristics of wireless channels because of fading and mobility.The proposed scheme determines the sensing action and selects the optimal spectrum using the corresponding power setting in each decision epoch according to the channel state with the objective being to minimise both the frame error rate and energy consumption.We use the Hidden Markov Model(HMM) to model a wireless channel,since the channel state is not directly observable at the receiver,but is instead embedded in the received signal.The procedure of dynamic spectrum access is formulated as a Markov decision process which can be solved using linear programming and the primaldual index heuristic algorithm,and the obtained policy has an index-ability property that can be easily implemented in real systems.Simulation results are presented to show the performance improvement caused by the proposed approach. Dynamic spectrum access policy is crucial in improving the performance of overlay cognitive radio networks. Host of the previous works on spectrum sensing and dynamic spectrum access consider the sensing effectiveness and spectrum utilization as the design criteria, while ignoring the energy related issues and QoS constraints. In this article, we propose a QoS provisioning energy saving dynamic access policy using stochastic control theory considering the time-varying characteristics of wireless channels because of fading and mobility. Proposed scheme determines that the sensing action and selects the optimal spectrum using the corresponding power setting in each decision epoch according to the channel state with the objective being to minimize both the frame error rate and energy consumption. We use the Hidden Markov Model (HMM) to model a wireless channel, since the channel state is not directly observable at the receiver , but is instead embedded embedded in the received signal. The procedure of dynamic spectrum access is formulated as a Markov decision process which can be solved using linear programming and the primaldual index heuristic algorithm, and the resulting policy has an index-ability property that can be readily implemented in real systems. Simulation results are presented to show the performance improvement caused by the proposed approach.