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The multiple-input multiple-output (MIMO) detection in the iterative receiver is investigated for a modulation of square constellation. For computationally efficient MIMO detection, we employ the hard-decision bit-level cancellation (BLC) to reduce the dimension of the MIMO detection as it has advantages over the symbol-level cancellation: 1) it can provide better performance and 2) the extrinsic bit information can be directly used for the BLC. A set of reliably decoded bits from the channel decoder in iterations is used for hard-decision BLC to approximate the maximum a posteriori probability (MAP) detection under the partial MAP detection principle. For the bits that are not canceled, the ing using projection is employed to approximate the MAP detection. This approach is applicable for a lower order modulation. For a higher order modulation, the minimum mean square error (MMSE) filtering with soft-decision cancellation (SC) is applied to further mitigate the bits that are not canceled.