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In this letter, we consider the problem of joint channel estimation and data detection for single-input multi-output (SIMO) systems under fast-fading environment with unknown spatially correlated noise. We present a computationally efficient iterative receiver based on the expectation conditional maximization (ECM) algorithm. Bit error rate (BER) performance of the proposed iterative receiver is simulated and compared with that of the maximum likelihood (ML) receiver with perfect channel state information (CSI). Simulation results show that the proposed iterative receiver achieves nearly the performance of ML receiver with perfect CSI and requires only a few iterations.