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The paper describes a novel approach to overcome the need for matrix inversion required by minimum mean square error (MMSE) turbo equalization in MIMO systems. In particular, turbo MMSE equalization based on an efficient series expansion from a truncated Taylor series expansion to approximate the matrix inversion is addressed. By adjusting a scaling factor, the proposed series expansion is directly optimized according to a fixed order with respect to a system performance criterion for each source to be estimated. The proposed approach enables low complexity receiver without the need for a complicated eigenvalue calculation procedure. From the first order, the proposed series expansion ensures the best bit error rate performance with a simple non iterative receiver in comparison with previous approaches. Taking advantage of the iterative process, the resulting MMSE turbo equalizer reaches the matched filter bound.