In this paper, we propose a two-time slot cooperative spectrum sharing protocol employing transform domain processing technology, in which primary users and secondary users adopt sinusoidal signals and chirp signals, respectively. Moreover, an adaptive relaying mechanism is used in our protocol to improve the flexibility of cooperation. Then, a Newton iteration method based sub-optimal power allocation algorithm is presented to reduce the complexity of exhaustive method while guaranteeing the outage probability constraint of the primary system. After that, a secondary user selection algorithm which focuses on the statistical channel conditions is proposed to further improve the performance of spectrum sharing. Simulation results show that compared with the existing protocol, outage probability, achievable data rate and average energy efficiency are significantly improved for the secondary system in our proposed protocol. Moreover, lower outage probability, higher achievable data rate and average energy efficiency of the secondary system can be realized with an increase in the number of secondary users.