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This paper presents an architectural solution for a MMSE equalizer of iterative receiver for linearly precoded MIMO systems. Two transmit antennas, two receive antennas, and a preceding size of two were chosen for the linearly precoded MIMO system. Thanks to the orthogonality property of Hadamard matrix that is used for the linear preceding and the block-fading nature of the MIMO channel, the inversion of the 4times4 covariance matrix can be done by inverting a single 2times2 matrix only once per data block. A survey of matrix inversion, which is the critical part of the MMSE equalizer is presented and different architectures are compared. We show that the direct analytical method gives the more efficient architectures to invert small matrices, typically 2times2 or 4times4. Furthermore, an architectural design and a time analysis for the MMSE equalizer are detailed. Each block of the architecture was designed to achieve a throughput of two complex estimated symbols per time cycle at the output of the MMSE equalizer.