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This paper considers multicell multiuser MIMO systems with very large antenna arrays at the base station. We propose an eigenvalue-decomposition-based approach to channel estimation, that estimates the channel blindly from the received data. The approach exploits the asymptotic orthogonality of the channel vectors in very large MIMO systems. We show that the channel to each user can be estimated from the covariance matrix of the received signals, up to a remaining scalar multiplicative ambiguity. A short training sequence is required to resolve this ambiguity. Furthermore, to improve the performance of our approach, we combine it with the iterative least-square with projection (ILSP) algorithm. Numerical results verify the effectiveness of our channel estimation approach.