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In this paper, a wireless cognitive radio sensor network is considered, where each sensor node is equipped with cognitive radio and the network is a multi-carrier system operating on time slots. In each slot, the users with new traffic demand will sense the entire spectrum and locate the available subcarrier set. Given the required data rate and power bound, a fully distributed subcarrier selection and power allocation algorithm is proposed for each individual user to minimize the energy consumption per bit over all subcarriers, while avoid introducing harmful interference to the existing users. The multi-dimensional and non-quasi-convex/concave nature of the energy efficiency optimization problem in multi-carrier systems makes it more challenging than throughput/power optimization problems or the energy efficiency problem in the single carrier system. The optimal solution is derived by using a two-stage algorithm where the original problem is decoupled into an unconstrained problem and branch and bound method is applied thereafter to reduce the search space. In addition, a distributed power control is performed to manage the co-channel interference among new users when needed. Simulation results demonstrate that the proposed approach performs close to the centralized optimal solution, and it provides prolonged network lifetime.