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In this paper, we present a complexity-reduced iterative algorithm for joint maximum a posteriori (MAP) detection and channel estimation in spatial multiplexing systems. To reduce the complexity associated with the MAP detection, which increases exponentially as the number of transmit antennas and the modulation order increase, we propose a modified sphere decoder (SD) algorithm for the MAP detection. It enumerates the symbol sequences with the high extrinsic probabilities, which fall inside a sphere centered at the received signal point at the same time. Extensive simulations demonstrate that the proposed scheme dramatically reduces the complexity as compared to that of the original SD algorithm with moderate performance degradation. Since a degree of the complexity reduction depends on the sphere radius, we also discuss a suitable distance to warrant the good performance/complexity tradeoffs.