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This paper proposes a subcarrier power allocation scheme for broadband OFDM cooperative communications, in the typical single-relay scenario with the amplify-and-forward protocol. The design criterion is to minimize the mean square error (MSE) of the received signal at the destination. Relying on the Lagrange multiplier techniques we derive a closed-form solution of the optimal power loading factors. Numerical simulation result shows that the proposed scheme significantly improves the bit-error-rate performance when compared with the systems without power loading.