In this paper, we propose a new method to simultaneously estimate the channel state information (CSI) of several transmitters that use orthogonal space-time block codes to communicate with a receiver. Our approach is based on a generalization of the well-known Capon technique to the problem of multiuser CSI estimation. Such a generalization allows us to estimate blindly the subspace spanned by the user channels. To extract the CSI from this subspace, only a few training blocks have to be used. The so-obtained CSI can then be used in any coherent multiuser MIMO receiver.