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The maximum-likelihood (ML) detection is the optimal detection for vertical Bell Laboratories layered space-time (V-BLAST) systems if the channel is perfectly known at the receiver. Unfortunately, the perfect channel knowledge is always unavailable in practical systems. In this paper, we investigate the joint design of channel estimation and data detection for V- BLAST systems in spatially correlated channels, and develop an optimal joint channel estimation and data detection scheme under the ML criterion. To reduce its complexity, we also propose a simplified scheme based on list sphere decoding (LSD). Moreover, we analyze its relationship with the conventional optimal channel estimation and the conventional optimal detection, and evaluate its performance by computer simulation.