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This paper proposes a transmit power allocation scheme for distributed transmit antenna Alamouti space-time block coded (STBC) orthogonal frequency division multiplexing (OFDM) systems using Cholesky decision-feedback detection in the presence of multiple residual frequency offsets (RFOs). Multipath Rayleigh fading is considered, and separate power constraint on each transmit antenna is assumed. The lower bound on the average bit error ratio (BER) performance is derived, and the optimal power allocation scheme based on minimizing that bound is then proposed. Simulation results show that the proposed power allocation scheme in certain cases only consumes as little as 50-65% of the transmit power used by the full power allocation scheme while enhancing the BER performance.