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In this paper, we consider the lifetime maximization problem in a wireless cognitive radio sensor network, where the joint design of cognitive radio and multi-carrier modulation is proposed to achieve high power efficiency. Sensor nodes first sense the entire spectrum and locate the available subcarriers based on a pilot tone detection scheme. After each node locates the available subcarrier set, information is transmitted over the favorite channel that has the largest channel gain. Under this setting, an adaptive modulation strategy is proposed to maximize the network lifetime by selecting the optimal constellation size. Simulation results demonstrate the effectiveness of our approach. In addition, the impact of conflicting transmissions upon the network lifetime is also investigated.