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We present a maximum likelihood (ML) method for semi-blind estimation of single-input multi-output (SIMO) flat-fading channels in spatially correlated noise having unknown covariance. An expectation-maximization (EM) algorithm is utilized to compute the ML estimates of the channel and spatial noise covariance. We derive the Crame´r-Rao bound (CRB) matrix for the unknown parameters and present a symbol detector that utilizes the EM channel estimates. Numerical simulations demonstrate the performance of the proposed method.