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In this study, we present a new reduced-complexity scheme for maximum-likelihood (ML) estimate of both carrier-frequency offset (CFO) and channel coefficients in multi antenna OFDM transmission, assuming that a training sequence is available. Our scheme is also capable to accommodate any space-time coded (STC) transmission. Moreover, to benchmark the performance of the proposed scheme, the Cramer-Rao bounds (CRBs) are derived for both CFO and channel estimators. Simulation results show that the proposed scheme achieves almost ideal performance compared with the CRBs in all ranges of signal-to-noise ratios (SNR) for both channel and frequency offset estimates.