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In this paper, we introduce an iterative joint channel estimation and data detection technique based on the expectation-maximization (EM) algorithm for multiple-input multiple-output (MIMO) code-division multiple-access (CDMA) systems over correlated fading channels. Based on the Kronecker model, we study the effect of channel correlation on the space-time (ST) EM-based joint detection and estimation (JDE) receiver assuming that there is no prior knowledge of channel correlation at the receiver. Then, we derive a new ST EM-based JDE receiver, which adapts the correlation between different MIMO channel coefficients. Different from the uncorrelated MIMO channel, the optimized weight coefficient are derived jointly based on the minimum mean-square error (MMSE) criterion. Considering fixed correlation channel matrix, our results show that our proposed receiver attains the diversity gain of uncorrelated MIMO channels. In addition, the effect of channel correlation is only interpreted as signal-to-noise-ratio (SNR) loss, especially in high receive correlation scenarios.