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In a sensor-aided cognitive radio network, collaborating battery-powered sensors are deployed to aid the network in cooperative spectrum sensing. These sensors consume energy for spectrum sensing and therefore deplete their life-time, thus we study the key issue in minimizing the sensing energy consumed by such group of collaborating sensors. The IEEE P802.22 standard specifies spectrum sensing accuracy by the detection and false alarm probabilities, hence we address the energy minimization problem under this detection accuracy constraint. Firstly, we derive the bounds for the number of sensors to simultaneously guarantee the thresholds for high detection probability and low false alarm probability. With these bounds, we then formulate the optimization problem to find the optimal sensing interval and the optimal number of sensor that minimize the energy consumption. Thirdly, the approximated analytical solutions are derived to solve the optimization accurately and efficiently in polynomial time. Finally, numerical results show that the minimized energy is significantly lower than the energy consumed by a group of randomly selected sensors. The mean absolute error of the approximated optimal sensing interval compared with the exact value is less than 4% and 8% under good and bad SNR conditions, respectively. The approximated optimal number of sensors is shown to be very close to the exact number.

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