Several structures for Adaptive Iterative Detection (AID) for fading channels have been described in the literature. One approach to AID, iterative detection with a decoupled estimator, has been proposed with hard decision feedback. Recently, it was noted that a soft decoder (e.g., turbo decoder) makes it possible to feed back soft information on data to the decoupled channel estimator. In this paper we present adaptive iterative detection with a decoupled channel estimator (decoupled-AID) based on hard or soft decision feedback from a turbo decoder. The performance of the decoupled-AID on two modulation methods (e.g, Punctured-QPSK,8PSK) is compared. As a decoupled channel estimator, the Wiener filter and Kalman filter are considered based on probabilistic channel models. A new feedback method, which uses partial soft information with or without amplitude normalization, is proposed.