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This paper proposes a low-complexity signal detection algorithm for spatially correlated multiple-input multiple-output (MIMO) channels. The proposed algorithm sets a minimum mean-square error (MMSE) detection result to a starting point, and searches for signal candidates in multi-dimensions of the noise enhancement from which the MMSE detection suffers. The multi-dimensional search is needed because the number of dominant directions of the noise enhancement is likely to be more than one over the correlated MIMO channels. To reduce computational complexity of the multi-dimensional search, the proposed algorithm limits the number of signal candidates to O(NT) where NT is the number of transmit antennas. Specifically, the signal candidates, which are unquantized, are obtained as the solution of a minimization problem under a constraint that a stream of the candidates should be equal to a constellation point. Finally, the detected signal is selected from hard decisions of both the MMSE detection result and unquantized signal candidates on the basis of the log likelihood function. For reducing the complexity of this process, the proposed algorithm decreases the number of calculations of the log likelihood functions for the quantized signal candidates. Computer simulations under a correlated MIMO channel condition demonstrate that the proposed scheme provides an excellent trade-off between BER performance and complexity, and that it is superior to conventional one-dimensional search algorithms in BER performance while requiring less complexity than that of the conventional algorithms.