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This paper addresses the problem of joint carrier frequency offset (CFO) and channel estimation in multiuser multiple-input-multiple-output (MIMO) orthogonal frequency-division multiplexing (OFDM) systems. To choose the optimal training sequences with the goal of providing the smallest estimation mean square error (MSE), the asymptotic Cramer-Rao bounds (asCRBs) are derived. The optimal training sequences are designed that minimize the asCRBs for both CFO and channel estimation under the constraint that the asCRBs being channel independent. A joint CFO and channel estimator is derived based on the maximum likelihood (ML) criterion. A computationally efficient method using importance sampling technique is proposed to solve the highly demanding multidimensional exhaustive search required by the ML multi-CFO estimation. Simulation results illustrate the merits of the proposed training …