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In parallel with the amazing increase of mobile data traffic, the fast-growing requirement and development of the green communication technology have led to many energy-saving designs in mobile networks. Meanwhile, as advanced cellular technologies progress, more than one component carrier (CCs) can now be jointly utilized in a base station (BS). As a result, the energy consumption of the BS has become an important concern. In this paper, we thus propose a novel green rate-and-power control transmission scheme for the BS transmission to address the problem of the energy minimization at BS transceivers subject to certain quality-of-service and fairness requirements for users. Communication activities in downlink transmissions of the BS with multiple OFDMA-based CCs are considered. Simulation results demonstrate that the energy consumption of our proposed scheme is much better than that of the case in which all CCs are always active, when both schemes satisfy the same constraints.