In this correspondence, we propose a cooperative-generalized-sensing-based spectrum sharing approach in centralized cognitive radio networks. Differently from the conventional cooperative approaches, where the secondary base station (SBS) takes a decision on the busy/idle status of the primary user and transmits with constant/binary power, the proposed approach allows the SBS to transmit with power as a continuous function of the detection information vector. We treat the cases of lossless-compression and hard-decision information separately. Optimal sensing time, detection threshold, and power allocation are derived to maximize the achievable rate at the SBS. In this paper, we only consider the case where secondary users (SUs) are merely receivers, and the SBS uses the allocated power to communicate with the SUs; however, the conclusions can also be expanded to the case where SUs use the allocated power under the assumption of a common control channel to exchange the information between the SBS and SUs. Simulation results demonstrate that the proposed approach can improve the performance of the SBS compared with the conventional approaches.