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We consider the issues of frequency offset and channel estimation in downlink coordinated multiple-input multiple-output orthogonal frequency-division multiplexing systems. Multiple carrier frequency offsets exist in this coordinated system. Without implementing an appropriate compensation for these offsets, both inter-carrier and inter-cell interference will degrade system performance. In response, we adopt parallel interference cancelation to iteratively mitigate inter-cell interference, and propose a frequency offset estimator, approximated by Hadamard product and Taylor expansion, to eliminate the inter-carrier interference. Our scheme is significantly less computational complex than the existing methods. Furthermore, the proposed channel estimator is robust to frequency offsets and performs comparably to conventional approaches.