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This paper develops the optimal power-allocation algorithm to maximize the sum-rate in Orthogonal Frequency-Division Multiple-Access (OFDMA) regenerative relaying downlink systems with separate power constraints. The optimal algorithm is based on the Lagrange dual-decomposition method when subchannels are pre-assigned to users and Relay Stations (RS). This paper also proposes a heuristic algorithm, which performance is exactly the same as that of the optimal algorithm in almost all cases. The simulation results show that OFDMA relaying systems with proposed algorithms outperform the systems without the algorithms by more than 250 % and outperform OFDMA systems without RSs by more than 45% when the power of a base station and the power of RSs are optimally adjusted.

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