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An alternative simple derivation for the well-known soft-in soft-out LMMSE (linear minimum mean square error) detector in a turbo system is presented. The derivation leads to a concise representation for the LMMSE detector in terms of the extrinsic means and extrinsic variances of the data symbols, and provides new perspectives for its implementation.
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Guo et al. (2011) studied this question.
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