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In this contribution we consider the carrier frequency offset estimation in the case of linear digital modulation, transmitted over a flat-fading multiple-input multiple-output (MIMO) Channel. For this problem, maximum-likelihood (ML) estimation gives rise to a carrier frequency offset algorithm that involves the maximization of the magnitude of a Fourier transform. Since no closed-form solution can be derived and numerical calculation of the estimate is computationally hard, we propose a suboptimal solution. Our simulation results show that the proposed estimator yields a performance that is comparable with the Cramer-Rao bound.