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An adaptive resource allocation scheme is proposed for regenerative relay-based orthogonal frequency division multiplexing access systems. This scheme allocates subchannels to guarantee fairness between users, and also saves energy by minimising the transmission power. The subchannel allocation for data rate fairness is considered between direct link users and relay stations in the first time subslot and among relay link users in the second time subslot by introducing a proportional fair scheduling algorithm. However, the data rate between the two hop links of each RS will still be mismatched under equal power allocation, so the transmission power of the base station and the relay stations will adjust adaptively in terms of the data rate difference between the two hop links. In this way, the data rate on the two hop links of one relay station will be matched and the total transmission power will be reduced. Simulation results comparing this approach with standard scheduling methods show that this approach achieves an overwhelming performance improvement on the long-term fairness of the user data rate and the total transmission power of base station and relay stations can be reduced greatly.