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We consider the joint estimation of channel impulse response (CIR) and frequency offset (FO) for a multiple-input multiple-output (MIMO) frequency selective fading channel. We average the joint likelihood function of the CIR and the FO over the distribution of CIR and maximize the resulting marginal likelihood function to estimate the FO. We also derive the design criteria for the training sequences (TS) which maximize the performance of our proposed estimator. Simulation results show that the optimal TS can improve the performance of the joint ML estimator.