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This paper presents a large sample analysis of the covariance of the beamformers computed by the analytical constant modulus algorithm (ACMA) method for blindly separating constant modulus sources. This can be used to predict the signal-to-interference plus noise ratio (SINR) performance of these beamformers, as well as their deviation from the (nonblind) Wiener receivers to which they asymptotically converge. The analysis is based on viewing ACMA as a subspace fitting optimization, where the subspace is spanned by the eigenvectors of a fourth-order covariance matrix. The theoretical performance is illustrated by numerical simulations and shows a good match.