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Conditional minimum mean square error (CMMSE) estimation problems commonly appear in iterative (turbo) signal detectors that utilize soft feedback from soft-input soft-output (SISO) channel decoders. To solve CMMSE problems, covariance matrix inverse has to be calculated for the output vector of soft-cancellation of interfering components, which requires a cubic order of computational complexity of the row size of the equivalent space-time channel matrix. This paper first proposes a computationally efficient method to calculate strictly the matrix inversion for CMMSE. It is shown that the proposed technique can be implemented in a highly pipelined manner. This paper also presents an approximated version of the algorithm that further reduces the computational complexity to a square order of the channel matrix's row size without causing any significant loss in performance. Results of model-based and field measurement data-based simulations for the approximated version of the algorithm are presented.